NP – Nonlinear Processes in Geosciences

NP1.1 – Mathematics of Planet Earth

The long-term average response of observables of chaotic systems to dynamical perturbations can often be predicted using linear response theory, but not all chaotic systems possess a linear response. Macroscopic observables of complex dissipative chaotic systems, however, are widely assumed to have a linear response even if the microscopic variables do not, but the mechanism for this is not well-understood.

We present a comprehensive picture for the linear response of macroscopic observables in high-dimensional coupled deterministic dynamical systems, where the coupling is via a mean field and the microscopic subsystems may or may not obey linear response theory. We derive stochastic reductions of the dynamics of these observables from statistics of the microscopic system, and provide conditions for linear response theory to hold in finite dimensional systems and in the thermodynamic limit. In particular, we show that for large systems of finite size, linear response is induced via self-generated noise.

We present examples in the thermodynamic limit where the macroscopic observable satisfies LRT, although the microscopic subsystems individually violate LRT, as well a converse example where the macroscopic observable does not satisfy LRT despite all microscopic subsystems satisfying LRT when uncoupled. This latter, maybe surprising, example is associated with emergent non-trivial dynamics of the macroscopic observable. We provide numerical evidence for our results on linear response as well as some analytical intuition.

How to cite: Gottwald, G. and Wormell, C.: Linear response theory for macroscopic observables in high-dimensional systems: when is it valid and when not?, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-1670,, 2020.

EGU2020-19177 | Displays | NP1.1

Studying heat waves and warm summers in numerical climate models with a rare event algorithm

Francesco Ragone and Freddy Bouchet

Extreme events are a major topic of interest in climate science. Studying rare extreme events with complex numerical climate models is computationally challenging, since in principle very long simulations are needed to sample a sufficient number of events to provide a reliable statistics. This problem can be tackled using rare event algorithms, numerical tools developed in the past decades in mathematics and statistical physics, dedicated to the reduction of the computational effort required to sample rare events in dynamical systems. Typically they are designed as genetic algorithms, in which a set of suppression and cloning rules are applied to an ensemble simulation in order to focus the computational effort on the trajectories leading to the events of interest. Recently we showed the great potential of rare event algorithms for climate modelling, applying a rare event algorithm to study extremes of European surface temperature in Plasim, an intermediate complexity model, in absence of external time dependent forcings (no seasonal and daily cycles). Here we go beyond these limitations, studying extreme heat waves and warm summers in the Northern extratropics in fully realistic conditions including daily and seasonal cycles, both in Plasim and in the state of the art Earth system model CESM. We show how the algorithm allows to sample extreme events characterised by persistency on different time scales, discussing links with large deviation theory. We show how one can characterise the statistics of heat waves and warm summers with extremely large return times, with computational costs orders of magnitude smaller than with direct sampling, and reach ultra rare events that would have been impossible to observe otherwise. We analyse the emergence of teleconnection patterns during the extreme events and their relation to the dynamics of planetary waves. Finally we discuss how these results open the way to the systematic application of these techniques to a vast range of applicative and theoretical studies.

How to cite: Ragone, F. and Bouchet, F.: Studying heat waves and warm summers in numerical climate models with a rare event algorithm, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-19177,, 2020.

Detecting causal relationships from observational time series datasets is a key problem in better understanding the complex dynamical system Earth. Recent methodological advances have addressed major challenges such as high-dimensionality and nonlinearity, e.g., PCMCI (Runge et al. Sci. Adv. 2019), but many more remain. In this talk I will give an overview of challenges and methods and present a novel algorithm to identify causal directions among contemporaneous (or instantaneous) relationships. Such contemporaneous relations frequently appear when time series are aggregated (e.g., at a monthly resolution). Then approaches such as Granger Causality and PCMCI fail because they currently only address time-lagged causal relations.
We present extensive numerical examples and results on the causal relations among major climate modes of variability. The work overcomes a major drawback of current causal discovery methods and opens up entirely new possibilities to discover causal relations from time series in climate research and other fields in geosciences.

Runge et al., Detecting and quantifying causal associations in large nonlinear time series datasets, Science Advances eeaau4996 (2019).

How to cite: Runge, J.: Recent progress and new methods for detecting causal relations in large nonlinear time series datasets, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-9554,, 2020.

Data assimilation is a term used to describe efforts to improve our knowledge
of a system by combining incomplete observations with imperfect models.
This is more generally known as filtering, which is ’optimal’ estimation of
the state of a system as it evolves over time, in the mean square sense. In
a Bayesian framework, the optimal filter is therefore naturally a sequence of
conditional probabilities of a signal given the observations and can be up-
dated recursively with new observations with Bayes’ formula. When, the
dynamics and observations errors are linear, this is equivalent to the Kalman
filter. In the nonlinear case, deriving an explicit form for the posterior dis-
tribution is in general not possible.
One of the important difficulties with applying the nonlinear filter in practice
is that the initial condition, the prior, is required to initialise the filtering.
However we are unlikely to know the correct initial distribution accurately
or at all. A filter is called stable if it is insensitive with respect to the
prior, that is, it converges to the same distribution, regardless of the initial
A body of work exists showing stability of the filter which rely on the stochas-
ticity of the underlying dynamics. In contrast, we show stability of the op-
timal filter for a class of nonlinear and deterministic dynamical systems and
our result relies on the intrinsic chaotic properties of the dynamics. We build
on the considerable knowledge that exists on the existence of SRB measures
in uniformly hyperbolic dynamical systems and we view the conditional prob-
abilities as SRB measures ‘conditional on the observation’ which are shown
to be absolutely continuous along the unstable manifold. This is in line with
the result of Bouquet, Carrassi et al [1] regarding data assimilation in the
“unstable subspace”, where they show stability of the filter if the unstable
and neutral subspaces are uniformly observed.

[1] M. Bocquet et al. “Degenerate Kalman Filter Error Covariances and
Their Convergence onto the Unstable Subspace”. In: SIAM/ASA Jour-
nal on Uncertainty Quantification 5.1 (2017), pp. 304–333. url: https:

How to cite: Oljaca, L., Broecker, J., and Kuna, T.: Insensitivety to initial condition/prior in data assimilation for the case of the optimal filter and deterministic model, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-19640,, 2020.

EGU2020-13794 | Displays | NP1.1 | Highlight

Data-driven parametrizations in numerical models using data assimilation and machine learning.

Julien Brajard, Alberto Carrassi, Marc Bocquet, and Laurent Bertino

Can we build a machine learning parametrization in a numerical model using sparse and noisy observations?

In recent years, machine learning (ML) has been proposed to devise data-driven parametrizations of unresolved processes in dynamical numerical models. In most of the cases, ML is trained by coarse-graining high-resolution simulations to provide a dense, unnoisy target state (or even the tendency of the model).

Our goal is to go beyond the use of high-resolution simulations and train ML-based parametrization using direct data. Furthermore, we intentionally place ourselves in the realistic scenario of noisy and sparse observations.

The algorithm proposed in this work derives from the algorithm presented by the same authors in principle is to first apply data assimilation (DA) techniques to estimate the full state of the system from a non-parametrized model, referred hereafter as the physical model. The parametrization term to be estimated is viewed as a model error in the DA system. In a second step, ML is used to define the parametrization, e.g., a predictor of the model error given the state of the system. Finally, the ML system is incorporated within the physical model to produce a hybrid model, combining a physical core with a ML-based parametrization.

The approach is applied to dynamical systems from low to intermediate complexity. The DA component of the proposed approach relies on an ensemble Kalman filter/smoother while the parametrization is represented by a convolutional neural network.  

We show that the hybrid model yields better performance than the physical model in terms of both short-term (forecast skill) and long-term (power spectrum, Lyapunov exponents) properties. Sensitivity to the noise and density of observation is also assessed.

How to cite: Brajard, J., Carrassi, A., Bocquet, M., and Bertino, L.: Data-driven parametrizations in numerical models using data assimilation and machine learning., EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-13794,, 2020.

EGU2020-17313 | Displays | NP1.1

Ergodicity of a stochastic Two Layer Quasi Geostrophic Model

Giulia Carigi, Jochen Bröcker, and Tobias Kuna

In the Climate Sciences, there is great interest in understanding the long term average behaviour of the climate system. In the context of climate models, this behaviour can be expressed intrinsically by concepts from the theory of dynamical systems such as attractors and invariant measures. In particular to ensure long term statistics of the model are well defined from a mathematical perspective, the model needs to admit a unique ergodic invariant probability measure.

In this work we consider a classic two layer quasi geostrophic model, with the upper layer perturbed by additive noise, white in time and coloured in space, in order to account for random forcing, for instance through wind shear. Existence and uniqueness of an ergodic invariant measure is established using a technique from stochastic analysis called asymptotic coupling as described in [1]. The main difficulty in the proof is to show that two copies of the system that are driven by the same noise realisation can be synchronised through a coupling. This coupling has to be finite dimensional and act only on the upper layer. 

Our results will be a key step to allow rigorous investigation of the response theory for the system under concern.


[1] Glatt-Holtz, N., Mattingly, J.C. & Richards, G. J Stat Phys (2017) 166: 618.  

How to cite: Carigi, G., Bröcker, J., and Kuna, T.: Ergodicity of a stochastic Two Layer Quasi Geostrophic Model, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-17313,, 2020.

EGU2020-10973 | Displays | NP1.1 | Highlight

The Lorenz convection model's random attractor (LORA) and its robust topology

Michael Ghil, Gisela D. Charó, Denisse Sciamarella, and Mickael D. Chekroun

Chekroun et al. (Physica D, 240, 2011) studied the global random attractor associated with the Lorenz (1963) model driven by multiplicative noise; they dubbed this time-evolving attractor LORA for short. The present talk examines the topological structure of the snapshots that approximate LORA’s evolution in time. 

Sciamarella & Mindlin (Phys. Rev. Lett., 82, 1999; Phys. Rev. E, 64, 2001) introduced the methodology of Branched Manifold Analysis through Homologies (BraMAH) to the study of chaotic flows. Here, the BraMAH methodology is extended for the first time, to the best of our knowledge, from deterministically chaotic flows to nonlinear noise-driven systems. 

The BraMAH algorithm starts from a cloud of points given by a large number of orbits and it builds a rough skeleton of the underlying branched manifold on which the points lie. This construction is achieved by local approximations of the manifold that use Euclidean closed sets; the nature of these sets depends on their topological dimension, e.g., segments or disks.  The skeleton is mathematically expressed as a complex of cells, whose algebraic topology is analyzed by computing its homology groups. 

The analysis is performed for a fixed realization of the driving noise at different time instants. We show that the topology of LORA changes in time and that it is quite distinct from the time-independent one of the classical Lorenz (1963) convection model, for the same values of the parameters. Topological tipping points are also studied by varying the parameter values from the classical ones.

How to cite: Ghil, M., Charó, G. D., Sciamarella, D., and Chekroun, M. D.: The Lorenz convection model's random attractor (LORA) and its robust topology, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-10973,, 2020.

Geophysical flows such as the atmosphere and the ocean are characterized by rotation and stratification, which together give rise to two dominant motions: the slow balanced and the fast unbalanced motions. The interaction between the balanced and unbalanced motions and the energy transfers between them impact the energy and momentum cycle of the flow, and is therefore crucial to understand the underlying energetics of the atmosphere and the ocean. Balanced motions, for instance mesoscale eddies, can transfer their energy to unbalanced motions, such as internal gravity waves, by spontaneous loss of balance amongst other processes. The exact mechanism of wave generation, however, remain less understood and is hindered to an extent by the challenge of separating the flow field into balanced and unbalanced motions.

This separation is achieved using two different balancing procedures in an identical model setup and assess the differences in the obtained balanced state and the resultant energy transfer to unbalanced motions. The first procedure we implement is a non-linear initialisation procedure based on Machenhauer (1977) but extended to higher orders in Rossby number. The second procedure implemented is the optimal potential vorticity balance to achieve the balanced state. The results show that the numerics of the model affect the obtained balanced state from the two procedures, and thus the residual signal which we interpret as the unbalanced motions, i.e. internal gravity waves.  A further complication is the presence of slaved modes, which appear along the unbalanced motions but are tied to the balanced motions, for which we need to extend the separation to higher orders in Rossby number. Further, we assess the energy transfers between balanced and unbalanced motions in experiments with different Rossby numbers and for different orders in Rossby number. We find that it is crucial to consider the effect of the numerics in models and make a suitable choice of the balancing procedure, as well as diagnose the unbalanced motions at higher orders to precisely detect the unbalanced wave signal.

How to cite: Chouksey, M.: Energy Transfers Between Balanced and Unbalanced Motions in Geophysical Flows, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-9994,, 2020.

EGU2020-18301 | Displays | NP1.1 | Highlight

Analysing Conceptual Climate Models with Monte Carlo Basin Bifurcation Analysis

Maximilian Gelbrecht, Jürgen Kurths, and Frank Hellmann

Many high-dimensional complex systems such as climate models exhibit an enormously complex landscape of possible asymptotic state. On most occasions these are challenging to analyse with traditional bifurcation analysis methods. Often, one is also more broadly interested in classes of asymptotic states. Here, we present a novel numerical approach prepared for analysing such high-dimensional multistable complex systems: Monte Carlo Basin Bifurcation Analysis (MCBB).  Based on random sampling and clustering methods, we identify the type of dynamic regimes with the largest basins of attraction and track how the volume of these basins change with the system parameters. In order to due this suitable, easy to compute, statistics of trajectories with randomly generated initial conditions and parameters are clustered by an algorithm such as DBSCAN. Due to the modular and flexible nature of the method, it has a wide range of possible applications. While initially oscillator networks were one of the main applications of this methods, here we present an analysis of a simple conceptual climate model setup up by coupling an energy balance model to the Lorenz96 system. The method is available to use as a package for the Julia language. 

How to cite: Gelbrecht, M., Kurths, J., and Hellmann, F.: Analysing Conceptual Climate Models with Monte Carlo Basin Bifurcation Analysis, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-18301,, 2020.

EGU2020-11557 | Displays | NP1.1

Correcting Budyko-Sellers boundary conditions: The Half-order Energy Balance Equation (HEBE)

Shaun Lovejoy, Lenin Del Rio Amador, and Roman Procyk

The conventional 1-D energy balance equation (EBE) has no vertical coordinate so that radiative imbalances between the earth and outer space are redirected in the horizontal in an ad hoc manner.  We retain the basic EBE but add a vertical coordinate so that the imbalances drive the system by imposing heat fluxes through the surface.   While this is theoretically correct, it leads to (apparently) difficult mixed boundary conditions.  However, using Babenko’s method, we directly obtain simple analytic equations for (2D) surface temperature anomalies Ts(x,t): the Half-order Energy Balance Equation (HEBE) and the Generalized HEBE, (GHEBE) [Lovejoy, 2019a].  The HEBE anomaly equation only depends on the local climate sensitivities and relaxation times.  We analytically solve the HEBE and GHEBE for Ts(x,t) and provide evidence that the HEBE applies at scales >≈10km.  We also calculate very long time diffusive transport dominated climate states as well as space-time statistics including the cross-correlation matrix needed for empirical orthogonal functions.

The HEBE is the special H = 1/2 case of the Fractional EBE (FEBE) [Lovejoy, 2019b], [Lovejoy, 2019c] and has a long (power law) memory up to its relaxation time t.  Several papers have empirically estimated H ≈ 0.5, as well as t ≈ 4 years, whereas the classical zero-dimensional EBE has H = 1 and t ≈ 4 years.   The former values permit accurate macroweather forecasts and low uncertainty climate projections; this suggests that the HEBE could apply to time scales as short as a month.  Future generalizations include albedo-temperature feedbacks and more realistic treatments of past and future climate states.



Lovejoy, S., The half-order energy balance equation, J. Geophys. Res. (Atmos.), (submitted, Nov. 2019), 2019a.

Lovejoy, S., Weather, Macroweather and Climate: our random yet predictable atmosphere, 334 pp., Oxford U. Press, 2019b.

Lovejoy, S., Fractional Relaxation noises, motions and the stochastic fractional relxation equation Nonlinear Proc. in Geophys. Disc.,, 2019c.

How to cite: Lovejoy, S., Del Rio Amador, L., and Procyk, R.: Correcting Budyko-Sellers boundary conditions: The Half-order Energy Balance Equation (HEBE), EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-11557,, 2020.

EGU2020-10021 | Displays | NP1.1

Network models for ponding on sea ice

Michael Coughlan, Ian Hewitt, Sam Howison, and Andrew Wells

Arctic sea ice forms a thin but significant layer at the ocean surface, mediating key climate feedbacks. During summer, surface melting produces considerable volumes of water, which collect on the ice surface in ponds. These ponds have long been suggested as a contributing factor to the discrepancy between observed and predicted sea ice extent. When viewed at large scales ponds have a complicated, approximately fractal geometry and vary in area from tens to thousands of square meters. Increases in pond depth and area lead to further increases in heat absorption and overall melting, contributing to the ice-albedo feedback.

Previous modelling work has focussed either on the physics of individual ponds or on the statistical behaviour of systems of ponds. We present a physically-based network model for systems of ponds which accounts for both the individual and collective behaviour of ponds. Each pond initially occupies a distinct catchment basin and evolves according to a mass-conserving differential equation representing the melting dynamics for bare and water-covered ice. Ponds can later connect together to form a network with fluxes of water between catchment areas, constrained by the ice topography and pond water levels.

We use the model to explore how the evolution of pond area and hence melting depends on the governing parameters, and to explore how the connections between ponds develop over the melt season. Comparisons with observations are made to demonstrate the ways in which the model qualitatively replicates properties of pond systems, including fractal dimension of pond areas and two distinct regimes of pond complexity that are observed during their development cycle. Different perimeter-area relationships exist for ponds in the two regimes. The model replicates these relationships and exhibits a percolation transition around the transition between these regimes, a facet of pond behaviour suggested by previous studies. Our results reinforce the findings of these studies on percolation thresholds in pond systems and further allow us to constrain pond coverage at this threshold - an important quantity in measuring the scale and effects of the ice-albedo feedback.

How to cite: Coughlan, M., Hewitt, I., Howison, S., and Wells, A.: Network models for ponding on sea ice, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-10021,, 2020.

EGU2020-8689 | Displays | NP1.1

Morphology of scallop patterns in erosion by dissolution

Michael Berhanu, Raphael Dubourg, Arthur Walbecq, Cyril Ozouf, Adrien Guerin, Julien Derr, and Sylvain Courrech du Pont

Erosion by dissolution is a decisive process shaping small-scale landscape morphology [1]. For fast dissolving minerals, the erosion rate is controlled by the solute transport [2] and characteristic erosion patterns can appear due to hydrodynamics mechanisms. Among the diversity of the dissolution patterns, the scallops are small depressions in a dissolving wall, appearing as cups with sharp edges. Their size varies from few millimeters to around ten centimeters. The scallops occur typically as the final steady form of ripple patterns created by the action of a turbulent flow on a dissolving surface [3,4]. Moreover, very similar shapes are also met, without imposed external flow, when the fluid motion results from the solutal convection induced by the dissolution [2,5,6]. Finally, scallop patterns resulting from similar mechanisms appear also on ice surfaces by melting in presence of a turbulent flow [7] or a convection flow [6].
Using three-dimensional surface reconstruction, we characterize quantitatively the scallop patterns mainly for experimental samples patterned by solutal convection. The temporal evolution of the scallop shape, of their spatial distribution and of the induced roughness are specifically investigated, in order to determine mechanisms explaining the generic aspects of dissolution patterns.

[1] P. Meakin and B. Jamtveit, Geological pattern formation by growth and dissolution in aqueous systems, Proc. R. Soc. A 466 659-694 (2010)

[2] J. Philippi, M. Berhanu, J. Derr and S. Courrech du Pont, Solutal convection induced by dissolution, Phys. Rev. Fluids, 4, 103801 (2019)

[3] P.N. Blumberg and R.L. Curl, Experimental and theoretical studies of dissolution roughness,  J. Fluid Mech. 65, 735 (1974)

[4] P. Claudin, O. Durán and B. Andreotti, Dissolution instability and roughening transition,  J. Fluid Mech. 832, R2  (1974)

[5] T.S. Sullivan, Y. Liu and R. E. Ecke, Turbulent solutal convection and surface patterning in solid dissolution, Phys. Rev. E 54, (1) 486, (1996)

[6] C. Cohen, M. Berhanu, J. Derr and S. Courrech du Pont, Erosion patterns on dissolving and melting bodies (2015 Gallery of Fluid motion), Phys. Rev. Fluids, 1, 050508 (2016)

[7] M. Bushuk, D. M. Holland, T. P. Stanton, A. Stern and C. Gray. Ice scallops: a laboratory investigation of the Ice-water interface, J. Fluid Mech. 873, 942 (2019)

How to cite: Berhanu, M., Dubourg, R., Walbecq, A., Ozouf, C., Guerin, A., Derr, J., and Courrech du Pont, S.: Morphology of scallop patterns in erosion by dissolution, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-8689,, 2020.

EGU2020-182 | Displays | NP1.1

Proto-dune formation under a bimodal wind regime

Pauline Delorme, Giles Wiggs, Matthew Baddock, Joanna Nield, James Best, Kenneth Christensen, Nathaniel Bristow, Andrew Valdez, and Philippe Claudin

Early-stage aeolian bedforms develop into sand dunes through complex interactions between flow, sediment transport and surface topography. Depending on the specific environmental and wind conditions the mechanisms of dune formation, and ultimately the shape of the nascent dunes, may differ. Here, we investigate the formation of a proto-dune-field, located in the Great Sand Dunes National Park ( Colorado, USA), using a three dimensional linear stability analysis.

We use in-situ measurements of wind and sediment transport, collected during a one-month field campaign, as part of a linear stability analysis to predict the orientation and wavelength of the proto-dunes.

We find that the output of the linear stability analysis compares well to high-resolution Digital Elevation Models measured using terrestrial laser scanning. Our findings suggest that the bed instability mechanism is a good predictor of proto-dune development on sandy surfaces with a bimodal wind regime.

How to cite: Delorme, P., Wiggs, G., Baddock, M., Nield, J., Best, J., Christensen, K., Bristow, N., Valdez, A., and Claudin, P.: Proto-dune formation under a bimodal wind regime, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-182,, 2020.

EGU2020-11309 | Displays | NP1.1

Optimality in landscape channelization and analogy with turbulence

Milad Hooshyar, Sara Bonetti, Arvind Singh, Efi Foufoula-Georgiou, and Amilcare Porporato

The channelization cascade observed in terrestrial landscapes describes the progressive formation of large channels from smaller ones starting from diffusion-dominated hillslopes. This behavior is reminiscent of other non-equilibrium complex systems, particularly fluids turbulence, where larger vortices break down into smaller ones until viscous dissipation dominates. Based on this analogy, we show that topographic surfaces emerging between parallel zero-elevation boundaries present a logarithmic scaling in the mean-elevation profile, which resembles the well-known logarithmic velocity profile in wall-bounded turbulence. Within this region of elevation fluctuation, the power spectrum exhibits a power-law decay resembling the Kolmogorov -5/3 scaling of turbulence. We also demonstrate that similar scaling behaviors emerge in surfaces from a laboratory experiment, natural basins, and constructed following optimality principles. In general, we show that the steady-state solutions of the governing equations of landscape evolution are the stationary surfaces of a functional defined as the average domain elevation. Depending on the exponent of the specific drainage area in the erosion term (m), the steady-state surfaces are local minimum (m<1) or maximum (m>1) of the average domain elevation.

How to cite: Hooshyar, M., Bonetti, S., Singh, A., Foufoula-Georgiou, E., and Porporato, A.: Optimality in landscape channelization and analogy with turbulence, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-11309,, 2020.

EGU2020-4854 | Displays | NP1.1

Response and Sensitivity Using Markov Chains

Manuel Santos Gutiérrez and Valerio Lucarini

Dynamical systems are often subject to forcing or changes in their governing parameters and it is of interest to study

how this affects their statistical properties. A prominent real-life example of this class of problems is the investigation

of climate response to perturbations. In this respect, it is crucial to determine what the linear response of a system is

as a quantification of sensitivity. Alongside previous work, here we use the transfer operator formalism to study the

response and sensitivity of a dynamical system undergoing perturbations. By projecting the transfer operator onto a

suitable finite dimensional vector space, one is able to obtain matrix representations which determine finite Markov

processes. Further, using perturbation theory for Markov matrices, it is possible to determine the linear and nonlinear

response of the system given a prescribed forcing. Here, we suggest a methodology which puts the scope on the

evolution law of densities (the Liouville/Fokker-Planck equation), allowing to effectively calculate the sensitivity and

response of two representative dynamical systems.

How to cite: Santos Gutiérrez, M. and Lucarini, V.: Response and Sensitivity Using Markov Chains, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-4854,, 2020.

EGU2020-9174 | Displays | NP1.1

Predicting Climate Change through Response Operators in a Coupled General Circulation Model

Valerio Lembo, Valerio Lucarini, and Francesco Ragone

Global Climate Models are key tools for predicting the future response of the climate system to a variety of natural and anthropogenic forcings. Typically, an ensemble of simulations is performed considering a scenario of forcing, in order to analyse the response of the climate system to the specific forcing signal. Given that the the climate response spans a very large range of timescales, such a strategy often requires a dramatic amount of computational resources. In this paper we show how to use statistical mechanics to construct operators able to flexibly predict climate change for a variety of climatic variables of interest, going beyond the limitation of having to consider specific time patterns of forcing. We perform our study on a fully coupled GCM - MPI-ESM v.1.2 - and for the first time we prove the effectiveness of response theory in predicting future climate response to CO2 increase on a vast range of temporal scales. We specifically treat atmospheric  (surface temperature) and oceanic variables (strength of the Atlantic Meridional Overturning Circulation and of the Antarctic Circumpolar Current), as well as the global ocean heat uptake.

How to cite: Lembo, V., Lucarini, V., and Ragone, F.: Predicting Climate Change through Response Operators in a Coupled General Circulation Model, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-9174,, 2020.

We investigate a new algorithm for estimating time-evolving global forcing in climate models. The method is an extension of a previous method by Forster et al. (2013), but here we also allow for a globally nonlinear feedback. We assume the nonlinearity of this global feedback can be explained as a time-scale dependence, associated with linear temperature responses to the forcing on different time scales, as in Proistosescu and Huybers (2017). With this method we obtain stronger forcing estimates than previously believed for the representative concentration pathway experiments in CMIP5 models. The reason for the higher future forcing is that the global feedback has a higher magnitude at the smaller time scales than at the longer time scales – this is closely related to provided arguments for the equilibrium climate sensitivity showing changes with time.

We find also that the linear temperature response to our new forcing predicts the modelled response quite well, although the response is a little overestimated for some CMIP5 models. Finally, we discuss the assumptions made in our study, and consistency of our assumptions with other leading hypotheses for why the global feedback is nonlinear.



Forster, P. M., T. Andrews, P. Good, J. M. Gregory, L. S. Jackson, and M. Zelinka (2013), Evaluating adjusted forcing and model spread for historical and future scenarios in the cmip5 generation of climate models, Journal of Geophysical Research, 118, 1139–1150, doi:10.1002/jgrd.50174.

Proistosescu, C., and P. J. Huybers (2017), Slow climate mode reconciles historical and model-based estimates of climate sensitivity, Sci. Adv., 3, e1602, 821, doi:10.1126/sciadv.1602821

How to cite: Fredriksen, H.-B.: Effective forcing in CMIP5 assuming nonconstant feedback parameter and linear response, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-17967,, 2020.

EGU2020-18823 | Displays | NP1.1

Unstable Periodic Orbits Sampling in Climate Models

Chiara Cecilia Maiocchi, Valerio Lucarini, Andrey Gritsun, and Grigorios Pavliotis

Unstable periodic orbits (UPOs) have been proved to be a relevant mathematical tool in the study of Climate Science. In a recent paper Lucarini and Gritsun [1] provided an alternative approach for understanding the properties of the atmosphere. Climate can be interpreted as a non-equilibrium steady state system and, as such, statistical mechanics can provide us with tools for its study.

UPOs decomposition plays a relevant role in the study of chaotic dynamical systems. In fact, UPOs densely populate the attractor of a chaotic system, and can therefore be thought as building blocks to construct the dynamic of the system itself. Since they are dense in the attractor, it is always possible to find a UPO arbitrarily near to a chaotic trajectory: the trajectory will remain close to the UPO, but it will never follow it indefinitely, because of its instability. Loosely speaking, a chaotic trajectory is repelled between neighbourhoods of different UPOs and can thus be approximated in terms of these periodic orbits. The characteristics of the system can then be reconstructed from the full set of periodic orbits in this fashion.

The sampling of UPOs is therefore a relevant problem for describing chaotic dynamical systems and can represent an interesting topic for the study of Climate Science. In this work we address this problem and present an algorithm to numerically extract UPOs from the attractor of a simple Climate Model such as Lorenz-63.

[1] V. Lucarini and A. Gritsun, “A new mathematical framework for atmospheric blocking events,” Climate Dynamics, vol. 54, pp. 575–598, Jan 2020.

How to cite: Maiocchi, C. C., Lucarini, V., Gritsun, A., and Pavliotis, G.: Unstable Periodic Orbits Sampling in Climate Models , EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-18823,, 2020.

EGU2020-11345 | Displays | NP1.1

Nonlinear Climate Dynamics: from Deterministic Behavior to Stochastic Excitability and Chaos

Michel Crucifix, Dmitri Alexandrov, irina Bashkirtseva, and Lev Ryashko

Glacial-interglacial cycles are global climatic changes which have characterised the last 3 million years. The eight latest
glacial-interglacial cycles represent changes in sea level over 100 m, and their average duration was around 100 000 years. There is a
long tradition of modelling glacial-interglacial cycles with low-order dynamical systems. In one view, the cyclic phenomenon is caused by
non-linear interactions between components of the climate system: The dynamical system model which represents Earth dynamics has a limit cycle. In an another view, the variations in ice volume and ice sheet extent are caused by changes in Earth's orbit, possibly amplified by feedbacks.
This response and internal feedbacks need to be non-linear to explain the asymmetric character of glacial-interglacial cycles and their duration. A third view sees glacial-interglacial cycles as a limit cycle synchronised on the orbital forcing.

The purpose of the present contribution is to pay specific attention to the effects of stochastic forcing. Indeed, the trajectories
obtained in presence of noise are not necessarily noised-up versions of the deterministic trajectories. They may follow pathways which
have no analogue in the deterministic version of the model.  Our purpose is to
demonstrate the mechanisms by which stochastic excitation may generate such large-scale oscillations and induce intermittency. To this end, we
consider a series of models previously introduced in the literature, starting by autonomous models with two variables, and then three
variables. The properties of stochastic trajectories are understood by reference to the bifurcation diagram, the vector field, and a
method called stochastic sensitivity analysis.  We then introduce models accounting for the orbital forcing, and distinguish forced and
synchronised ice-age scenarios, and show again how noise may generate trajectories which have no immediate analogue in the determinstic model. 

How to cite: Crucifix, M., Alexandrov, D., Bashkirtseva, I., and Ryashko, L.: Nonlinear Climate Dynamics: from Deterministic Behavior to Stochastic Excitability and Chaos, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-11345,, 2020.

The representation of cloud processes in weather and climate models is crucial for their feedback on atmospheric flows. Since there is no general macroscopic theory of clouds, the parameterization of clouds in corresponding simulation software depends fundamentally on the underlying modeling assumptions. We present a new model of intermediate complexity (a one-and-a-half moment scheme) for warm clouds, which is derived from physical principles. Our model consists of a system of differential-algebraic equations which allows for supersaturation and thus avoids the commonly used but somewhat outdated concept of so called 'saturation adjustment'. This is made possible by a non-Lipschitz right-hand side, which allows for nontrivial solutions. In a recent effort we have proved under mild assumptions on the external forcing that this system of equations has a unique physically consistent solution, i.e., a solution with a nonzero droplet population in the supersaturated regime. For the numerical solution of this system we have developed a semi-implicit integration scheme, with efficient solvers for the implicit parts. The model conserves air and water (if one accounts for the precipitation), and it comes with eight parameters that cannot be measured since they describe simplified processes, so they need to be fitted to the data. For further studies we implemented our cloud micro physics model into ICON, the weather forecast model operated by the German forecast center DWD.

How to cite: Porz, N.: Unique solvability of a system of ordinary differential equations modeling a warm cloud parcel and avoiding saturation adjustment, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-20030,, 2020.

EGU2020-22524 | Displays | NP1.1

Reduced stochastic aggregation of convection conditioned by large scale dynamics in the atmosphere

Robert Malte Polzin, Annette Müller, Peter Nevir, Henning Rust, and Peter Koltai

The presented work contains an investigation of the stochastic aggregation of convective structures on different scales in the atmosphere. A
computational framework is applied that provides highly scalable identification of reduced Bayesian models. The deterministic large scale
flow variables are reduced into latent states, whereas the stochastic small scale convective structures are affiliated to these. The analysis of
the latent states in number and maximization reduction improves the understanding for the large scale forcing of convective processes. The
convective structures are determined by vertical velocities. Different variables of the large-scale flow, such as the convective available
potential energy, available moisture, vertical windshear and the Dynamic State Index (DSI), a diabaticity indicator, are investigated. Our approach
does not require a distributional assumption but works instead with a discretised and categorised state vector.

How to cite: Polzin, R. M., Müller, A., Nevir, P., Rust, H., and Koltai, P.: Reduced stochastic aggregation of convection conditioned by large scale dynamics in the atmosphere, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-22524,, 2020.

EGU2020-7336 | Displays | NP1.1 | Highlight

On the connection between heat waves and large deviations of temperature

Jeroen Wouters, Vera Melinda Galfi, and Valerio Lucarini

We use large deviation theory to study persistent extreme events of temperature, like heat waves or cold spells. We consider the mid-latitudes of a simplified yet Earth-like general circulation model of the atmosphere and numerically estimate large deviation rate functions of near-surface temperature averages over different spatial scales. We find that, in order to represent persistent extreme events based on large deviation theory, one has to look at temporal averages of spatially averaged observables. The spatial averaging scale is crucial, and has to correspond with the scale of the event of interest. Accordingly, the computed rate functions indicate substantially different statistical properties of temperature averages over intermediate spatial scales (larger, but still of the order of the typical scale), as compared to the ones related to any other scale. Thus, heat waves (or cold spells) can be interpreted as large deviations of temperature averaged over intermediate spatial scales. Furthermore, we find universal characteristics of rate functions, based on the equivalence of temporal, spatial, and spatio-temporal rate functions if we perform a re-normalisation by the integrated auto-correlation.

How to cite: Wouters, J., Galfi, V. M., and Lucarini, V.: On the connection between heat waves and large deviations of temperature, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-7336,, 2020.

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Extremes for high dimensional chaotic systems

Tobias Kuna, Valerio Lucarini, Davide Faranda, Jerouen Wouters, and Viviane Baladi

Extremes are related to high impact and serious hazard events and hence their study and prediction have been and continue to be highly relevant for all kind of applications in geoscience and beyond. Extreme value theory is promising to be able to predict them reliably and robustly. In the last fifteen years the classical extreme value theory for stochastic processes has been extended to dynamical systems and has been related to properties of physical measure (statistical properties of the system), return and hitting times. We will review what one can say for highly dimensional perfectly chaotic systems.  We will concentrate on relations between the index of the extreme distribution and invariants of the underlying dynamical system which are stable, in the sense that they will continuously depend on changing parameters in the dynamics.  Furthermore, we explore whether there exists a response theory for extremes, that is, whether the change of extremes can be quantitatilvely expressed  in terms of changing parameters. 


How to cite: Kuna, T., Lucarini, V., Faranda, D., Wouters, J., and Baladi, V.: Extremes for high dimensional chaotic systems, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-16406,, 2020.

Approximations in the moist thermodynamics of atmospheric/weather models are often inconsistent. Different parts of numerical models may handle the thermodynamics in different ways, or the approximations may disagree with the laws of thermodynamics. In order to address these problems, we may derive all relevant thermodynamic quantities from a defined thermodynamic potential; approximations are then instead made to the potential itself — this guarantees self-consistency. This concept is viable for vapor and liquid water mixtures in a moist atmospheric system using the Gibbs function but on extension to include the ice phase an ambiguity presents itself at the triple-point. In order to resolve this the energy function must be utilised instead; constrained maximisation methods can then be used on the entropy in order to solve the system equilibrium state. Once this is done however, a further extension is necessary for atmospheric systems. In the Earth’s atmosphere many important non-equilibrium processes take place; for example, freezing of super-cooled water, evaporation, and precipitation. To fully capture these processes the equilibrium method must be reformulated to involve finite rates of approach towards equilibrium. This may be done using various principles of non-equilibrium thermodynamics, principally Onsager reciprocal relations. A numerical scheme may then be implemented which models competing finite processes in a moist thermodynamic system.

How to cite: Bowen, P.: Consistent Modelling of Non-Equilibrium Thermodynamic Processes in the Atmosphere, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-20739,, 2020.

EGU2020-9572 | Displays | NP1.1

Comparing water, energy and entropy budgets of aquaplanet climate attractors

Charline Ragon, Valerio Lembo, Valerio Lucarini, Jérôme Kasparian, and Maura Brunetti

The climate system can be seen as a thermal engine that generates entropy by irreversible processes and achieves a steady state by redistributing the input solar energy among its different components (ocean, atmosphere, etc) and by balancing the energy, water mass and entropy budgets over all the spatial scales. Biases in modern climate models are generally related to the fact that their statistical properties are not well represented, giving rise to imperfect closures of the energy cycle. Thus, a proper measurement of the efficiency of the thermal engine in each climate model is needed. Moreover, possible steady states (attractors) that can be approached at climate tipping-points are characterised by different feedbacks becoming dominant in the thermal engine.

We apply the Thermodynamic Diagnostic Tool (TheDiaTo) [1] to the attractors recently obtained using the MIT general circulation model (MITgcm) in a coupled aquaplanet [2], a planet where the ocean covers the entire globe. Such coupled aquaplanets, where nonlinear interactions between atmosphere, ocean and sea ice are fully taken into account, provide a relevant framework to understand the role of the main feedbacks at play in the climate system. Five attractors have been found, ranging from snowball (where ice covers the entire planet) to hot state conditions (where ice completely disappears) [2].

Using TheDiaTo, we analyse the five climate attractors by estimating: a) the energy budgets and meridional energy transports; b) the water mass and latent energy budgets and respective meridional transports; c) the Lorenz Energy Cycle; d) the material entropy production. We consider different coupled atmosphere-ocean-sea ice configurations and cloud parameterizations of MITgcm where the energy balance at the top of the atmosphere is progressively better closed in order to understand the occurrence of possible biases in the statistical properties of each attractor.

Our contribution will help clarify the thermodynamic differences in climate attractors and their stability to external perturbations that could shift the climate from a steady state to the other.

[1] Lembo V., Lunkeit F., Lucarini V., TheDiaTo (v1.0) – a new diagnostic tool for water, energy amd entropy budgets in climate models, Geosci. Model Dev. 12, 3805-3834 (2019)

[2] Brunetti M., Kasparian J., Vérard C., Co-existing climate attractors in a coupled aquaplanet, Climate Dynamics 53, 6293-6308 (2019)

How to cite: Ragon, C., Lembo, V., Lucarini, V., Kasparian, J., and Brunetti, M.: Comparing water, energy and entropy budgets of aquaplanet climate attractors, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-9572,, 2020.

Thermodynamic optimality principles, such as maximum entropy production or maximum power extraction, hold a great promise to help explain self-organisation of various compartments of planet Earth, including the climate system, catchments and ecosystems. There is a growing number of examples for more or less successful use of these principles in earth system science, but a common systematic approach to the formulation of the relevant system boundaries, state variables and exchange fluxes has not yet emerged. Here we present a blueprint for the thermodynamically consistent formulation of box models and rigorous testing of optimality principles, in particular the maximum entropy production (MEP) and the maximum power (MP) principle. We investigate under what conditions these principles can be used to predict energy transfer coefficients across internal system boundaries and demonstrate that, contrary to common perception, these principles do not lead to similar predictions if energy and entropy balances are explicitly considered for the whole system and the defined sub-systems. We further highlight various pitfalls that may result in thermodynamically inconsistent models and potentially wrong conclusions about the implications of thermodynamic optimality principles. 
The analysis is performed in an open source mathematical framework, using the notebook interface Jupyter, the programming language Python, Sympy and a newly developed package for Python, "Environmental Science using Symbolic Math" (ESSM, This ensures easy verifiability of the results and enables users to re-use and modify variable definitions, equations and mathematical solutions to suit their own thermodynamic problems. 

How to cite: Schymanski, S. and Westhoff, M.: A blueprint for thermodynamically consistent box models and a test bed for thermodynamic optimality principles, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-8084,, 2020.

EGU2020-7100 | Displays | NP1.1

Poroelastic aspects in geothermics

Bianca Kretz, Willi Freeden, and Volker Michel

The aspect of poroelasticity is anywhere interesting where a solid material and a fluid come into play and have an effect on each other. This is the case in many applications and we want to focus on geothermics. It is useful to consider this aspect since the replacement of the water in the reservoir below the Earth's surface has an effect on the sorrounding material and vice versa. The underlying physical processes can be described by partial differential equations, called the quasistatic equations of poroelasticity (QEP). From a mathematical point of view, we have a set of three (for two space and one time dimension) partial differential equations with the unknowns u (displacement) and p (pore pressure) depending on the space and the time.

Our aim is to do a decomposition of the data given for u and p in order that we can see underlying structures in the different decomposition scales that cannot be seen in the whole data.
For this process, we need the fundamental solution tensor of the QEP (cf. [1],[5]).
That means we assume that we have given data for u and p (they can be obtained for example by a method of fundamental solutions, cf. [1]) and want to investigate a post-processing method to these data. Here we follow the basic approaches for the Laplace-, Helmholtz- and d'Alembert equation (cf. [2],[4],[6]) and the  Cauchy-Navier equation as a tensor-valued ansatz (cf. [3]). That means we want to modify our elements of the fundamental solution tensor in such a way that we smooth the singularity concerning a parameter set τ=(τxt). 
With the help of these modified functions, we construct scaling functions which have to fulfil the properties of an approximate identity.
They are convolved with the given data to extract more details of u and p.


[1] M. Augustin: A method of fundamental solutions in poroelasticity to model the stress field in geothermal reservoirs, PhD Thesis, University of Kaiserslautern, 2015, Birkhäuser, New York, 2015.
[2] C. Blick, Multiscale potential methods in geothermal research: decorrelation reflected post-processing and locally based inversion, PhD Thesis, Geomathematics Group, Department of Mathematics, University of Kaiserslautern, 2015.
[3] C. Blick, S. Eberle, Multiscale density decorrelation by Cauchy-Navier wavelets, Int. J. Geomath. 10, 2019, article 24.
[4] C. Blick, W. Freeden, H. Nutz: Feature extraction of geological signatures by multiscale gravimetry. Int. J. Geomath. 8: 57-83, 2017.
[5] A.H.D. Cheng and E. Detournay: On singular integral equations and fundamental solutions of poroelasticity. Int. J. Solid. Struct. 35, 4521-4555, 1998.
[6] W. Freeden, C. Blick: Signal decorrelation by means of multiscale methods, World of Mining, 65(5):304-317, 2013.

How to cite: Kretz, B., Freeden, W., and Michel, V.: Poroelastic aspects in geothermics, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-7100,, 2020.

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A model for the longitudinal patterns shaped by water on erodible rocks

Matteo Bernard Bertagni and Carlo Camporeale

The interactions between water and rocks create an extensive variety of marvelous patterns, which span on several classes of time and space scales. In this work, we provide a mathematical model for the formation of longitudinal erosive patterns commonly found in karst and alpine environments. The model couples the hydrodynamics of a laminar flow of water (Orr-Somerfield equation) to the concentration field of the eroded-rock chemistry. Results show that an instability of the plane rock wetted by the water film leads to a longitudinal channelization responsible for the pattern formation. The spatial scales predicted by the model span over different orders of magnitude depending on the flow intensity and this may explain why similar patterns of different sizes are observed in nature (millimetric microrills, centimetric rillenkarren, decametric solution runnels).

How to cite: Bertagni, M. B. and Camporeale, C.: A model for the longitudinal patterns shaped by water on erodible rocks, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-7031,, 2020.

There exists a coupling mechanism between the troposphere and the stratosphere, which plays a fundamental role in weather and climate. The coupling is highly complex and rests upon radiative and chemical feedbacks, as well as dynamical coupling by Rossby waves. The troposphere acts as a source of Rossby waves which propagate upwards in to the stratosphere, affecting the zonal mean flow. Rossby waves are also likely to play a significant role in downward communication of information via reflection from the stratosphere in to the troposphere. A mechanism for this reflection could be from a so-called critical layer. A shear flow exhibits a critical layer where the phase speed equals the flow velocity, where viscous and nonlinear effects become important. A wave incident upon a critical layer may be absorbed, reflected or overreflected, whereby the amplitude of the reflected wave is larger than that of the incident wave. In the case of troposphere-stratosphere coupling, the concept of critical layer overreflection is key to understanding atmospheric instability.

Motivated by this, a mathematical framework for understanding the coupling will be presented together with an investigation in to the role of nonlinearity versus viscosity inside the critical layer.

How to cite: Dell, I.: Troposphere-Stratosphere Coupling and the Role of Critical Layer Nonlinearity, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-11841,, 2020.

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Variational Model Reduction for Rotating Geophysical Flows with Full Coriolis Force

Gözde Özden and Marcel Oliver

Consider the motion of a rotating fluid governed by the Boussinesq equations with full Coriolis parameter. This is contrary to the so-called ''traditional approximation'' in which the horizontal part of the Coriolis parameter is zero. The model is obtained using variational principle which depends on Lagrangian dynamics. The full Coriolis force is used since the horizontal component of the angular velocity has a crucial role in that it introduces a dependence on the direction of the geostrophic flow in the horizontal geostrophical plane. We aim that singularity near the equatorial region can be solved with this assumption. This gives a consistent balance relation for any latitude on the Earth. We follow the similar strategy to that Oliver and Vasylkevych (2016) for the system to derive the Euler-Poincaré equations. Firstly, the system is transformed into desired scale giving the differences with the other scales. We derive the balance model Lagrangian as called L1 model, R. Salmon, using Hamiltonian principles. Near identity transformation is applied to simplify the Hamiltonian. Whole calculations are done considering the smallness assumption of the Rossby number. Long term, we aim that results help to understand the global energy cycle with the goal of validity and improving climate models.

How to cite: Özden, G. and Oliver, M.: Variational Model Reduction for Rotating Geophysical Flows with Full Coriolis Force, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-11603,, 2020.

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The strange instability of the equatorial Kelvin wave

Stephen Griffiths

The Kelvin wave is perhaps the most important of the equatorially trapped waves in the terrestrial atmosphere and ocean, and plays a role in various phenomena such as tropical convection and El Nino. Theoretically, it can be understood from the linear dynamics of a stratified fluid on an equatorial β-plane, which, with simple assumptions about the disturbance structure, leads to wavelike solutions propagating along the equator, with exponential decay in latitude. However, when the simplest possible background flow is added (with uniform latitudinal shear), the Kelvin wave (but not the other equatorial waves) becomes unstable. This happens in an extremely unusual way: there is instability for arbitrarily small nondimensional shear λ, and the growth rate is proportional to exp(-1/λ^2) as λ → 0. This in contrast to most hydrodynamic instabilities, in which the growth rate typically scales as a positive power of λ-λc as the control parameter λ passes through a critical value λc.

This Kelvin wave instability has been established numerically by Natarov and Boyd, who also speculated as to the underlying mathematical cause by analysing a quantum harmonic oscillator perturbed by a potential with a remote pole. Here we show how the growth rate and full spatial structure of the Kelvin wave instability may be derived using matched asymptotic expansions applied to the (linear) equations of motion. This involves an adventure with confluent hypergeometric functions in the exponentially-decaying tails of the Kelvin waves, and a trick to reveal the exponentially small growth rate from a formulation that only uses regular perturbation expansions. Numerical verification of the analysis is also interesting and challenging, since special high-precision solutions of the governing ordinary differential equations are required even when the nondimensional shear is not that small (circa 0.5). 

How to cite: Griffiths, S.: The strange instability of the equatorial Kelvin wave , EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-9302,, 2020.

We consider recharge-discharge processes in a forced wave-mean flow interaction model and in a forced Rossby wave triad. Such processes are common in atmospheric dynamics and are typically modelled by nonlinear oscillators, for example for mid-latitude storms by Ambaum and Novak (2013) and for convective cycles by Yano and Plant (2012). A similar behaviour can be seen in the simulation of a forced wave number triad by Lynch (2009). Here we construct noncanonical Hamiltonian and Nambu representations in three-dimensional phase space for available and prescribed conservation laws during the recharge and discharge regimes. Divergence in phase space is modelled by a pre-factor. The approach allows the design of conservative and forced dynamical systems.

How to cite: Blender, R. and Fregin, J.: Wave-mean flow interaction, forced triads, and recharge-discharge Processes as noncanonical Hamiltonian Systems, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-13284,, 2020.

EGU2020-8740 | Displays | NP1.1

Inverting fluvial network topology to understand landscape dynamics

Stuart Grieve, Simon Mudd, Fiona Clubb, Michael Singer, Katerina Michaelides, and Shiuan-An Chen

The topology of fluvial networks has long been studied, with Horton's laws describing relationships between stream order, stream density, and stream length often cited as fundamental governing principles of drainage basin development. Building upon these principles, small scale studies have identified patterns of self-similarity in drainage networks in the continental USA, suggesting that to some extent, river networks self-organise in a scale invariant manner. More stringent measures of self-similarity have also been developed, which quantify the fractal nature of side branching structures in fluvial networks. Using such metrics, studies have identified similarities between leaf vein structures and fluvial networks, and have identified a potential climatic signature in North American river topology.

The appeal of such techniques over traditional methods of channel analysis using topographic data is that in self-similar networks, the precise location of channel heads is unimportant, allowing analysis to be performed at unprecedented scales, and in locations where data quality is limited. Here, we attempt to reconcile these two suites of techniques to understand the potential and limitations of network topology as an indicator of broader landscape dynamics. We achieve this through the analysis of fluvial networks extracted at a global scale from the Shuttle Radar Topography Mission dataset alongside other global earth observation data.

How to cite: Grieve, S., Mudd, S., Clubb, F., Singer, M., Michaelides, K., and Chen, S.-A.: Inverting fluvial network topology to understand landscape dynamics, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-8740,, 2020.

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The Origin of Aeolian Dunes – PIV measurements of flow structure over early stage protodunes in a refractive-index-matching flume

Nathaniel Bristow, James Best, Kenneth Christensen, Matthew Baddock, Giles Wiggs, Pauline Delorme, and Joanna Nield

Understanding the initiation of aeolian dunes poses significant challenges due to the strong couplings between turbulent fluid flow, sediment transport, and bedform morphology. While much is known concerning the dynamics of more mature bedforms, open questions remain as to how protodunes are formed, as well as the mechanisms by which they continue to evolve. The structure of the turbulent flow field drives the mobilization or deposition of sediment, thus controlling the initial formation of sand patches, yet is also strongly influenced itself by local conditions such as surface roughness and moisture. Furthermore, an additional feedback on the flow and transport is exerted by the sand patches themselves once they begin to form.

As protodunes begin to develop from this initial deposition, their morphologies possess unique characteristics involving a reverse asymmetry of the stoss and lee sides, wherein the crest begins upstream, close to the toe, and gradually shifts downstream toward the "regular" asymmetric profile exhibited by more mature dunes. However, these early stages of development also involve very gentle slopes and low profiles which make field measurements of the associated flow particularly challenging.

The current research effort involves a combination of field measurements, documenting the initiation and morphological development of sand patches and protodunes, in concert with detailed measurements of the flow-form interactions in a laboratory flume. The work presented herein focuses primarily on experiments conducted in a unique flow facility wherein high-resolution measurements of the turbulent flow field associated with the early stages of protodune development are obtained utilizing particle-image velocimetry (PIV) in a refractive-index-matched (RIM) environment. The RIM technique facilitates flow measurements extremely close to model surfaces as well as unimpeded optical access which are critical to understanding the flow-form coupling. A series idealized, fixed-bed models are fabricated to mimic the key morphological characteristics of early protodune development observed in the field, and the flow measurements associated with them are analyzed to reveal the mechanisms controlling the bedform dynamics.

How to cite: Bristow, N., Best, J., Christensen, K., Baddock, M., Wiggs, G., Delorme, P., and Nield, J.: The Origin of Aeolian Dunes – PIV measurements of flow structure over early stage protodunes in a refractive-index-matching flume, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-4259,, 2020.

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Data-driven reduced order modelling of tide-induced sand bars in confined channels

Tjebbe Hepkema, Huib de Swart, and Henk Schuttelaars
Tidal bars are bed forms in tidal channels that have a wave-like structure in both the along-channel and cross-channel direction. They are found in tidal channels all around the globe, for example, in the Western Scheldt in the Netherlands, the Exe Estuary in England, the Ord River Estuary in Australia and the Venice Lagoon in Italy. Typically, tidal bars are several meters high, have wavelengths of 1-15 km and migration speeds of meters per day. Understanding their dynamics is important as they are invaluable for many living organisms (e.g., migrating birds) but they hamper marine traffic.
It has been shown, by means of a linear stability analysis, that these bars emerge due to inherent feedbacks between the tidal currents and the erodible bed. When the bars mature, their dynamics becomes nonlinear. Schramkowski et al. (2004) applied a bifurcation analysis to analyse the bar dynamics, but their method was limited to small bottom friction. Here, we developed a numerical (time integration) model that simulates the nonlinear dynamics and the corresponding (stable) equilibrium patterns for realistic parameter values.
Using the output of the numerical model we derive a reduced order model with a method called SINDy (Brunton et al., 2016). Loiseau and Brunton (2018) showed that from output of complex numerical models simulating fully nonlinear fluid flows, SINDy can identify small systems of equations which govern the complex flows. Here we show that, for parameters regimes where the dynamics is weakly nonlinear, SINDy finds a Landau type equation that reproduces the tidal bar dynamics well. The Landau equation is a nonlinear ordinary differential equation in terms of the Fourier amplitude of the pattern that initially has the largest growth rate. The form of this equation corresponds with the one that is expected from the symmetry of the patterns. Also, the application of SINDy to the fully nonlinear dynamics of tidal bars will be discussed.
Brunton, S.L., Proctor, J.L., and Kutz, J.N. (2016). Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proceedings of the National Academy of Sciences, 113(15):3932-3937.
Loiseau, J.-C. and Brunton, S.L. (2018). Constrained sparse Galerkin regression. Journal of Fluid Mechanics, 838:42-67.
Schramkowski, G.P., Schuttelaars, H.M., and de Swart, H.E. (2004). Nonlinear channel-shoal dynamics in long tidal embayments. Ocean Dynamics, 54(3):399-407.

How to cite: Hepkema, T., de Swart, H., and Schuttelaars, H.: Data-driven reduced order modelling of tide-induced sand bars in confined channels, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-10258,, 2020.

Increasing Greenland discharge has contributed more than 5000 km3 of surplus fresh water to the Subpolar North Atlantic since the early 1990s. The volume of this freshwater anomaly is projected to cause freshening in the North Atlantic leading to changes in the intensity of deep convection and thermohaline circulation in the subpolar North Atlantic. This is roughly half of the freshwater volume of the Great Salinity Anomaly of the 1970s that caused notable freshening in the Subpolar North Atlantic. In analogy with the Great Salinity Anomaly, it has been proposed that, over the years, this additional Greenland freshwater discharge might have a great impact on convection driving thermohaline circulation in the North Atlantic with consequent impact on climate. Previous numerical studies demonstrate that roughly half of this Greenland freshwater anomaly accumulates in the Subpolar Gyre. However, time scales over which the Greenland freshwater anomaly can accumulate in the subpolar basins is not known. This study estimates the residence time of the Greenland freshwater anomaly in the Subpolar Gyre by approximating the process of the anomaly accumulation in the study domain with a first order autonomous dynamical system forced by the Greenland freshwater anomaly discharge. General solutions are obtained for two types of the forcing function. First, the Greenland freshwater anomaly discharge is a constant function imposed as a step function. Second, the surplus discharge is a linearly increasing function. The solutions are deduced by utilizing results from the numerical experiments that tracked spreading of the Greenland fresh water with a passive tracer. The residence time of the freshwater anomaly is estimated to be about 10–15 years. The main differences in the solutions is that under the linearly increasing discharge rate, the volume of the accumulated Greenland freshwater anomaly in the Subpolar Gyre does not reach a steady state. By contrast, solution for the constant discharge rate reaches a steady state quickly asymptoting the new steady state value for time exceeding the residence time. Estimated residence time is compared with the numerical experiments and observations.

How to cite: Dukhovskoy, D.: Using a first-order autonomous dynamical system to evaluate residence time of the Greenland freshwater anomaly in the Subpolar Gyre, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-1958,, 2020.

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Explicit inclusion of connectivity in geostatistical facies modelling.

Tom Manzocchi, Deirdre Walsh, Carneiro Marcus, Javier López-Cabrera, and Soni Kishan

Irrespective of the specific technique (variogram-based, object-based or training image-based) applied, geostatistical facies models usually use facies proportions as the constraining input parameter to be honoured in the output model. The three-dimensional interconnectivity of the facies bodies in these models increases as the facies proportion increases, and the universal percolation thresholds that define the onset of macroscopic connectivity in idealized statistical physics models define also the connectivity of these facies models. Put simply, the bodies are well connected when the model net:gross ratio exceeds about 30%, and because of the similar behaviour of different geostatistical approaches, some researchers have concluded that the same threshold applies to geological systems.

In this contribution we contend that connectivity in geological systems has more degrees of freedom than it does in conventional geostatistical facies models, and hence that geostatistical facies modelling should be constrained at input by a facies connectivity parameter as well as a facies proportion parameter. We have developed a method that decouples facies proportion from facies connectivity in the modelling process, and which allows systems to be generated in which both are defined independently at input. This so-called compression-based modelling approach applies the universal link between the connectivity and volume fraction in geostatistical modelling to first generate a model with the correct connectivity but incorrect volume fraction using a conventional geostatistical approach, and then applies a geometrical transform which scales the model to the correct facies proportions while maintaining the connectivity of the original model. The method is described and illustrated using examples representative of different geological systems. These include situations in which connectivity is both higher (e.g. fluid-driven injectite or karst networks) and lower (e.g. many depositional systems) than can be achieved in conventional geostatistical facies models.

How to cite: Manzocchi, T., Walsh, D., Marcus, C., López-Cabrera, J., and Kishan, S.: Explicit inclusion of connectivity in geostatistical facies modelling., EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-21710,, 2020.

The asymptotic shape of the marginal frequency distribution of geochemical variables has been proposed as indicator of multi-fractality. Transition into a certain statistical regime as inferred from the distribution function may be considered as criterion to delineate geochemical anomalies, including mineral resources or pollutants such as radioactive fallout or geogenic radon.

The argument is that asymptotic linearity in log-log scale, log(F(z)) = a - b log(z) as z→∞, b>0 a constant, indicates multi-fractality.

We discuss this with respect to two issues:

(1) What are the consequences of estimating the slope b for non-ergodic, in particular non-representative and preferential sampling schemes, as often the case in geochemical or pollution surveys?

(2) Frequently in geochemistry, multiplicative cascades are considered valid generators of multifractal fields, corroborated by observed f(α) functions and variograms (Matèrn or power, for low lags). This generator leads to marginally asymptotically (high cascade orders) log-normal distributions, which in log-log scale are asymptotically (high z) parabolic, not linear.

Theoretical aspects are addressed as well as examples given.

How to cite: Bossew, P.: Log-log linearity of the asymptotic distribution - a valid indicator of multi-fractality?, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-6447,, 2020.

EGU2020-268 | Displays | NP1.1

Multiscale measures of phase-space trajectories

Tommaso Alberti, Giuseppe Consolini, Peter D. Ditlevsen, Reik V. Donner, and Virgilio Quattrociocchi

Several attempts have been made in characterizing the multiscale nature of fluctuations from nonlinear and nonstationary time series. Particularly, the study of their fractal structure has made use of different approaches like the structure function analysis, the evaluation of the generalized dimensions, and so on. Here we report on a different approach for characterizing phase-space trajectories by using the empirical modes derived via the Empirical Mode Decomposition (EMD) method. We show how the derived Intrinsic Mode Functions (IMFs) can be used as source of local (in terms of scales) information allowing us in deriving multiscale measures when looking at the behavior of the generalized fractal dimensions at different scales. This formalism is applied to three pedagogical examples like the Lorenz system, the Henon map, and the standard map. We also show that this formalism is readily applicable to characterize both the behavior of the Earth’s climate during the past 5 Ma and the dynamical properties of the near-Earth electromagnetic environment as monitored by the SYM-H index.

How to cite: Alberti, T., Consolini, G., Ditlevsen, P. D., Donner, R. V., and Quattrociocchi, V.: Multiscale measures of phase-space trajectories, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-268,, 2020.

EGU2020-2299 | Displays | NP1.1

Fragmentation of steaming Surtseyan bombs

Mark McGuinness and Emma Greenbank

A Surtseyan volcanic eruption involves a bulk interaction between water and hot magma, mediated by the return of ejected ash. Surtsey Island, off the coast of Iceland, was born during such an eruption process in the 1940s. Mount Ruapehu in New Zealand also undergoes Surtseyan eruptions, due to its crater lake. 

One feature of such eruptions is ejected lava bombs, trailing steam, with evidence that watery slurry was trapped inside them during the ejection process. Simple calculations indicate that the pressures developed due to boiling inside such a bomb should shatter it. Yet intact bombs are routinely discovered in debris piles. In an attempt to crack this problem, and provide a criterion for fragmentation of Surtseyan bombs, a transient mathematical model of the flashing of water to steam inside one of these hot erupted lava balls is developed, with a particular focus on the maximum pressure attained, and how it depends on magma and fluid properties. Numerical and asymptotic solutions provide some answers for volcanologists.

How to cite: McGuinness, M. and Greenbank, E.: Fragmentation of steaming Surtseyan bombs, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-2299,, 2020.

EGU2020-20491 | Displays | NP1.1

Solving the erosion transport equation on three dimensional catchments

Michal Kuraz and Petr Mayer

Modeling the kinematic wave equation and sediment transport equation enables a deterministic approach for predicting surface runoff and resulting sediment transport. Both the kinematic wave equation and the sediment transport equation are first order differential equations. Moreover the kinematic wave equation is a quasilinear problem. In many engineering applications this set of equations is solved on one-dimensional representative cross-sections. However, a proper selection of representative cross-section(s) is  cumbersome. On the other hand integrating this set of equations on real catchment topography  yields difficulties for standard variational methods such as continous Galerkin method. These difficulties are two-fold (1) the nonlinearity of the kinematic wave, and (2) the absence of diffusion term, which acts as a stabilization term for convection-diffusion equation. In a theory, the Peclet number of numerical stability reaches infinity. 

In this contribution we will focus on a stable numerical approximation of this convection-only problem using least square method. With this method we are able to reliably solve both the kinematic wave equation and the sediment transport equation on computational  domains representing real catchment topography. Several examples representing real-world scenarios will be given.

How to cite: Kuraz, M. and Mayer, P.: Solving the erosion transport equation on three dimensional catchments, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-20491,, 2020.

EGU2020-2040 | Displays | NP1.1

Conditions for the emergence and growth of aeolian sand structures

Elena Malinovskaya and Otto Chkhetiani

One of the important characteristics of the wind process of dust removal is a critical or threshold wind velocity [1]. Saltating flow grows with increasing of the effective roughness [2] that affecting shear stress and friction velocity [3]. The drag coefficient increases depending on the density of the coating by particles of the surface [4]. The location of particles in the aeolian structure, their size and relative position determine their resistance to wind influence. Aeolian structures change the structure of flows and the balance of mass transfer of particles deposited and rising from the surface [5]. The surface microstructures and ripples significantly affect of sand removal.
The flow of particles with a size of 100 μm on the surface has been considered using the OPEN FOAM with LES model. The calculation area has sizes of 5x5x2 mm. For the velocity at the upper boundary, 2.8 m/s select in accordance with the experimental data [6]. It should be noted that with a relative increase in the distance between pairs of particles and a change in the level of the upper surface, the pressure difference between the base and top of the particle increases by 10-30 percents. Depending on the distance between the particles, the buoyant force acting from the side of the air flow, the critical velocity, and the departure velocity of the particle also change. When the distances between the surfaces of the particles are close to its size, the buoyant force is greater than the adhesion and gravity forces. As a result, areas with different probability for the sand removal by wind, due to which, in particular, the occurrence of aeolian ripples occurs.
The average critical velocity increases when moving up the windward slope of the dune [7, 8]. This phenomenon is possibly associated with the influence of ripples on the air flow. The flow around of the micro-ripples with a height of 0.1-1 mm was considered for air flow velocity of 2-4 m/s at a height of 1-2 cm. The addition of supplementary elements of heterogeneity at the apex near the rough surface of the streamlined aeolian structure leads to a displacement of the separation point of the ascending flows. Also we have a change in the length of the recirculation zone and the time intervals of the strengthening of the wind at the apex, which was observed in [6].
The study was supported by the RFBR project 19-05-50110 and partial support of the program of the Presidium of the Russian Academy of Sciences No. 12.
1. Shao Y. Physics and modeling of wind erosion. Springer.2008.p.452.
2. Martin R.L., Kok J.F. J.Geophys.Res.2018.123(7).1546-1565.
3. Turpin C et al. Earth Surf. Proc. and Land.2010.35(12). 1418-1429.
4. Yang X.I.A. et al. J. Fluid Mech.2019.880. 992-1019.
5. Luna M.C.M.M. et al. Geomorph.2011.129(3-4). 215-224.
6. Semenov O.E. Introduction to experimental meteorology and climatology of the sand storms. Almaty. 2011. p.580 (in Russian).
7. Neuman C.M.K et al. Sediment. 2000. 47(1). 211-226.
8. Malinovskaya E.A. Izv. Atmos. Oceanic Phys. 2019. 55(2). 86-92.

How to cite: Malinovskaya, E. and Chkhetiani, O.: Conditions for the emergence and growth of aeolian sand structures , EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-2040,, 2020.

NP2.1 – Nonlinear Multiscale and Stochastic Dynamics of the Earth System

Global coupled climate modeling requires the representation of multiple widely separated scales in each model component. In the ocean component, the separation of scales is especially dramatic as small scale turbulence exerts significant control on the global scale overturning circulation.  The importance of this control is demonstrated in the context of analyses of the Dansgaard-Oeschger oscillation of Marine Isotope Stage 3 (MIS 3; see Peltier and Vettoretti, 2014)). In the University of Toronto version of CCSM4 water column diapycnal diffusivity is represented using the KPP parameterization of Large et al (1994). This includes explicit contributions due to double diffusion processes which demonstrably play an important role in determining the period of the D-O oscillation itself.


We have developed a DNS-based methodology to test the accuracy of the doubly diffusive contributions to KPP. High-resolution turbulence data sets have been produced based upon two different models: the “unbounded gradient model” and the “interface model” with depth-dependent temperature and salinity gradients. By fitting the vertical fluxes in the unbounded gradient model (for equilibrium states) as a function of density ratio (the governing non-dimensional parameter) we derive a functional form on the basis of which KPP can be revised.  By applying the revised scheme to the interface model we demonstrate that the local fluxes predicted agree well with those from the numerical simulations. The difference between this new parametrization scheme and KPP demonstrates that KPP may significantly overestimate the diffusivities for both heat and salt at low-density ratio.

How to cite: Ma, Y. and Peltier, W.: A DNS-based Turbulence Parametrization for Global Climate Models: Doubly Diffusive Convection, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-2035,, 2020.

EGU2020-2398 | Displays | NP2.1

Effects of large scale advection and small scale turbulence on vertical phytoplankton dynamics

Vinicius Beltram Tergolina, Stefano Berti, and Gilmar Mompean

When studying the life cycle of phytoplankton frequently one is interested in the survival or death conditions of a population (bloom/no bloom). These dynamics have been studied extensively in the literature through a range of modelling scenarios but in summary the main factors affecting the vertical dynamics are: Water column mixing intensity, solar energy distribution, nutrients availability and predatory activity. The later two can be represented by different biological models whereas the vertical mixing is usually parameterized by a diffusive process. Even though turbulence has been recognized as a paramount factor in the survival dynamics of sinking phytoplankton species, dealing with the multi scale nature of turbulence is a formidable challenge from the modelling point of view. In addition, convective motions are being recognized to play a role in the survival of phytoplankton throughout winter stocking. With this in mind, in this work we revisit a theoretically appealing  model for phytoplankton vertical dynamics with turbulent diffusivity and numerically study how large-scale fluid motions affect its survival and extinction conditions. To achieve this and to work with realistic parameter values, we adopt a kinematic flow field to account for the different spatial and temporal scales of turbulent motions. The dynamics of the population density are described by a reaction-advection-diffusion model with a growth term proportional to sun light availability. Light depletion is modelled accounting for water turbidity and plankton self-shading; advection is represented by a sinking speed and a two-dimensional, multiscale, chaotic flow. Preliminary results show that under appropriate conditions for the flow, our model reproduces past results based on turbulent diffusivity. Furthermore, the presence of large scale vortices (such as those one might expect during winter convection) seems to hinder survival, an effect that is partially mitigated by turbulent  diffusion.

How to cite: Beltram Tergolina, V., Berti, S., and Mompean, G.: Effects of large scale advection and small scale turbulence on vertical phytoplankton dynamics, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-2398,, 2020.

EGU2020-4239 | Displays | NP2.1

Monitoring marine coastal areas

Ana M. Mancho, Guillermo Garcia-Sanchez, and José Antonio Jimenez-Madrid

The European Commission has invested in developing services such as the Copernicus Marine Environment Monitoring Services that offer opportunities to new downstream applications. This presentation describes the development of monitoring services in coastal areas at the submesoscale, by addressing synergies between different available marine technologies and products such as satellite images, autonomous surface and underwater vehicles, drone images, downscaled hydrodynamic models, etc, that get inspired in recent success cases [1, 2]. In particular ongoing efforts will be discussed that address the operational implementation of these tools for the management of marine pollution in harbors and coasts with a focus in the hydrodynamic modelling aspects.

Support is acknowledged  from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 821922 (IMPRESSIVE) and from Fundacion Biodiversidad and European Commission (BEWATS).


[1] A. G. Ramos, V. J. García-Garrido, A. M. Mancho, S. Wiggins, J. Coca, S. Glenn, O. Schofield, J. Kohut, D. Aragon, J. Kerfoot, T. Haskins, T. Miles, C. Haldeman, N. Strandskov, B. Allsup, C. Jones, J. Shapiro. Lagrangian coherent structure assisted path planning for transoceanic autonomous underwater vehicle missions.  Sci. Rep. 8, 4575 (2018).

[2] V. J. Garcia-Garrido, A. Ramos, A. M. Mancho, J. Coca, S. Wiggins. A dynamical systems perspective for a real-time response to a marine oil spill. Mar. Pollut. Bull. 112, 201-210, (2016).

How to cite: Mancho, A. M., Garcia-Sanchez, G., and Jimenez-Madrid, J. A.: Monitoring marine coastal areas, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-4239,, 2020.

EGU2020-17781 | Displays | NP2.1

Scaling Analysis of the China France Oceanography Satellite Along Track Wave and Wind Data

Yang Gao, Francois G Schmitt, Jianyu Hu, and Yongxiang Huang

Turbulence or turbulence-like phenomena are ubiquitous in nature, often showing a power-law behavior of the Fourier power spectrum in either spatial or temporal domains. This power-law behavior is due to interactions among different scales of motion, and to the absence of characteristic scale among several scale ranges. It can be further interpreted in the framework of turbulent cascade with movements on continuous range of scales. The power-law feature and the associate cascade picture are vitally important to our understanding of the ocean and atmosphere dynamics. In this work, we consider the China France Oceanography SATellite (CFOSAT) data in the general framework of ocean and atmosphere multi-scale dynamics. We apply both Fourier power spectrum analysis and second-order structure-function analysis, used in the fields of turbulence, to extract multiscale information from the wind speed (WS) and significant wave-height (Hs) data provided by CFOSAT project. The data analyzed here are along track data spatially collected from 29th July to 31th December 2019. The measured Fourier power spectrums for both WS and Hs illustrate a dual power-law behavior respectively from 5 to 25 km, and 30 to 500 km with measured scaling exponents β close to 2 and 5/3. The measured second-order structure-functions confirm the existence of the dual power-law behavior. The corresponding measured scaling exponents  ζ(2) close to 1 and 2/3 for the spatial scales mentioned above. Our preliminary results confirm the relevance of using multiscale statistical tools and turbulent theory to characterize the large-scale movements of both ocean and atmosphere.

How to cite: Gao, Y., Schmitt, F. G., Hu, J., and Huang, Y.: Scaling Analysis of the China France Oceanography Satellite Along Track Wave and Wind Data, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-17781,, 2020.

EGU2020-18620 | Displays | NP2.1

Submesoscales variability from surface drifter and HF radar measurements: scale and wind dependence of kinematic properties

Maristella Berta, Annalisa Griffa, Lorenzo Corgnati, Marcello Magaldi, Carlo Mantovani, Helga Huntley, Andrew Poje, and Tamay Ozgokmen

The dynamics of the near-surface ocean currents result from the nonlinear interaction of simultaneous mechanisms at different scales. Of these, the submesoscale range  (a few hundred meters to 10 km, hours to a few days) remains particularly challenging to observe directly, due to the high variability in both time and space.  In this study, the scale-dependence of kinematic properties (divergence, vorticity and strain) in the submesoscale range, as well as their response to atmospheric forcing, is investigated in two distinct geographic regions: the Ligurian (NW-Mediterranean) Sea and the Northern Gulf of Mexico. The two applications are characterized by different dynamics, and the estimates of kinematic properties are derived from distinctly different observational approaches: in situ GPS drifters observations and remote HF radar data.


The Ligurian Sea application is based on HF radar measurements obtained for the JERICO-NEXT (Joint European Research Infrastructure network for Coastal Observatory – Novel European eXpertise for coastal observaTories) and IMPACT (Port Impact on Protected Marine Areas: Cooperative Cross-Border Actions) projects. Surface current measurements span 40 km off the coast with 1.5 km resolution, available every hour. The velocity fields are used to estimate the kinematic properties with an Eulerian approach, which allows the identification of structures such as eddies and jets of the order of a few km. We focus in particular on the response of the submesoscales to an extreme wind event that was captured by the observations. The deformation of the spatial structures suggests nonlinear interactions with the wind forcing, and the kinematic properties' magnitudes are almost doubled (exceeding the Coriolis parameter, f).


In the Gulf of Mexico, velocity observations are available from a series of massive, nearly simultaneous drifter releases conducted by CARTHE (Consortium for Advanced Research of Transport of Hydrocarbons in the Environment). Drifter triplets are analysed to estimate the kinematic properties of the flow at scales between 100 m and 5 km over a time scale of a day. Results show that the mean kinematic properties increase in magnitude with decreasing scales, with winter values generally higher than summer ones. For winter flows, vorticity and divergence distributions have more substantial tails of values multiple times the Coriolis paramater f at scales up to 2 km, while in the summer such large values are restricted to smaller scales (100-500 m).


The Lagrangian estimates of kinematic properties obtained in the Gulf of Mexico were also compared to Eulerian estimates from concurrent X-band radar measurements, showing good correlation and validating the comparison across observational methods. Moreover, the scale-dependence of the kinematic properties from drifter triplets was found to be consistent with turbulence scaling laws evaluated as two-particle statistics. We conclude that the kinematic properties metric provides a robust complementary methodology to characterize submesoscales and can be used both with Lagrangian and Eulerian observations.

How to cite: Berta, M., Griffa, A., Corgnati, L., Magaldi, M., Mantovani, C., Huntley, H., Poje, A., and Ozgokmen, T.: Submesoscales variability from surface drifter and HF radar measurements: scale and wind dependence of kinematic properties, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-18620,, 2020.

EGU2020-3681 | Displays | NP2.1

Why can't models get the mesoscale atmospheric spectrum right?

Jih-Wang Aaron Wang and Prashant Sardeshmukh

Despite decades of development, global atmospheric models continue to have trouble in capturing the -5/3 slope of the atmospheric mesoscale kinetic energy (KE) spectrum suggested by conventional turbulence theory and upper tropospheric aircraft observations in the 1980s (e.g., Nastrom and Gage 1986). We have approached this issue in two ways: 1) How certain can we be that the “real” spectrum has a -5/3 slope? and 2) Are turbulent cascades the only determinants of the mesoscale spectrum? To address the first issue, especially in light of the vastly greater number of upper-air observations that have been analyzed since the 1980s, we have examined the 200-hPa KE spectra in several high-resolution global reanalysis datasets, including the NCEP GFS (resolution T1534 and T254), ERA-Interim (T255), ERA5 (T639), and JRA-55 (T319) datasets. We find that the mesoscale portions of the global spectra are highly mutually inconsistent. This is primarily because the global mesoscale KE has a large contribution from the KE in convective regions, which differs greatly among the various reanalyses. There is thus indeed some ambiguity concerning the slope of the “true” mesoscale spectrum.

To address the second issue, especially given the sensitivity of the reanalysis spectra to representations of convection and damping in the reanalysis models, we assessed the sensitivity of the model spectra in two ways: (a) by stochastically perturbing the physical tendencies and (b) by decreasing the hyper-viscosity coefficient, in large ensembles of 10-day forecasts made with the NCEP GFS (T254) model. Both changes increased the mesoscale KE and decreased the steep spectral slope. The impact of the stochastic physics varied with the specified length scale of the stochastic perturbations. 

Our conclusions about issues 1) and 2) raised above are that (1) we do not really know the “true” mesoscale KE spectrum, and (2) model KE spectra are sensitive to and can be manipulated by stochastically perturbing the parameterized physical tendencies and tuning the horizontal diffusion in a model.  It may therefore be misleading for modelers to pursue the -5/3 slope of the Nastrom-Gage spectrum.

How to cite: Wang, J.-W. A. and Sardeshmukh, P.: Why can't models get the mesoscale atmospheric spectrum right?, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-3681,, 2020.

An abrupt climatic transition  could be triggered by a single extreme event, and an alpha-stable non-Gaussian Levy noise  is regarded as a   type of noise to generate such extreme events. In contrast  with the classic Gaussian noise, a comprehensive approach of the most probable transition path  for systems under alpha-stable Levy noise is still lacking. We develop here a  probabilistic framework, based on  the nonlocal Fokker-Planck equation, to investigate  the maximum likelihood climate change for  an energy balance system under the influence of  greenhouse effect and  Levy fluctuations.  We find that a period of the  cold climate state can be interrupted by a sharp shift to the warmer one due to  larger noise jumps with low frequency. Additionally,  the climate change for warming 1.5 degree under an enhanced greenhouse effect generates a step-like growth process. These results provide  important insights into  the underlying mechanisms of abrupt climate transitions triggered by a Levy process.

How to cite: Zheng, Y.: The maximum likelihood climate change for global warming under the influence of greenhouse effect and Levy noise, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-6170,, 2020.

EGU2020-1667 | Displays | NP2.1

Detecting regime transitions in time series using dynamic mode decomposition

Georg Gottwald and Federica Gugole

We employ the framework of the Koopman operator and dynamic mode decomposition to devise a computationally cheap and easily implementable method to detect transient dynamics and regime changes in time series. We argue that typically transient dynamics experiences the full state space dimension with subsequent fast relaxation towards the attractor. In equilibrium, on the other hand, the dynamics evolves on a slower time scale on a lower dimensional attractor. The reconstruction error of a dynamic mode decomposition is used to monitor the inability of the time series to resolve the fast relaxation towards the attractor as well as the effective dimension of the dynamics. We illustrate our method by detecting transient dynamics in the Kuramoto-Sivashinsky equation. We further apply our method to atmospheric reanalysis data; our diagnostics detects the transition from a predominantly negative North Atlantic Oscillation (NAO) to a predominantly positive NAO around 1970, as well as the recently found regime change in the Southern Hemisphere atmospheric circulation around 1970.

How to cite: Gottwald, G. and Gugole, F.: Detecting regime transitions in time series using dynamic mode decomposition, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-1667,, 2020.

EGU2020-4849 | Displays | NP2.1

Screening the coupled atmosphere-ocean system based on Covariant Lyapunov Vectors

Vera Melinda Galfi, Lesley de Cruz, Valerio Lucarini, and Sebastian Schubert

We analyze linear perturbations of a coupled quasi-geostrophic atmosphere-ocean model based on Covariant Lyapunov Vectors (CLVs). CLVs reveal the local geometrical structure of the attractor, and point into the direction of linear perturbations applied to the trajectory. Thus they represent a link between the geometry of the attractor and basic dynamical properties of the system, and they are physically meaningful. We compute the CLVs based on the so-called Ginelli method using the tangent linear version of the quasi-geostrophic atmosphere-ocean model MAOOAM (Modular Arbitrary-Order Ocean-Atmosphere Model). Based on the CLVs, we can quantify the contribution of each model variable on each scale to the development of linear instabilities. We also study the changes in the structure of the attractor - and, consequently, in the basic dynamical properties of our system - as an effect of the ocean-atmopshere coupling strength and the model resolution.

How to cite: Galfi, V. M., de Cruz, L., Lucarini, V., and Schubert, S.: Screening the coupled atmosphere-ocean system based on Covariant Lyapunov Vectors, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-4849,, 2020.

Large scale motions in geophysical fluid models are often characterised by linear waves, which are obtained by linearising the equations. But there are also many explicit solutions of the fully nonlinear equations when posed the full space. The exact solutions we are investigating often characterise Rossby waves, since they are in geostrophic balance. They also can be compositions of waves, some are interacting with each other and some do not, showing wave interactions as explicit solutions in the fully nonlinear problem.

In this talk I will briefly introduce the idea behind these explicit nonlinear waves and show some of their properties, and their occurrence in different fluid models in extended domains.

As an application, we especially focus on a rotating shallow water model with simplified backscatter. In this case one finds not only geostrophic explicit solutions, but also ageostrophic ones. Moreover, here energy accumulates in selected scales due to the backscatter terms and causes exponentially and unboundedly growing ageostrophic nonlinear waves. This also relates to instability of coexisting stationary waves and is an instance of the role of nonlinear waves in energy transfer, and illustrates their role in preventing energy equidistribution for general data.

How to cite: Prugger, A. and Rademacher, J.: Explicit nonlinear waves of fluid models on extended domains and unbounded growth with backscatter, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-14052,, 2020.

EGU2020-5723 | Displays | NP2.1

What could we learn about climate sensitivity from variability in the surface temperature record?

James Annan, Julia Hargreaves, Thorsten Mauritsen, and Bjorn Stevens

We examine what can be learnt about climate sensitivity from variability in the surface air temperature record over the instrumental period, from around 1880 to the present. While many previous studies have used the trend in the time series to constrain equilibrium climate sensitivity, it has recently been argued that temporal variability may also be a powerful constraint. We explore this question in the context of a simple widely used energy balance model of the climate system. We consider two recently-proposed summary measures of variability and also show how the full information content can be optimally used in this idealised scenario. We find that the constraint provided by variability is inherently skewed and its power is inversely related to the sensitivity itself, discriminating most strongly between low sensitivity values and weakening substantially for higher values. As a result of this, is only when the sensitivity is very low that the variability can provide a tight constraint. Our results support the analysis of variability as a potentially useful tool in helping to constrain equilibrium climate sensitivity, but suggest caution in the interpretation of precise results.

How to cite: Annan, J., Hargreaves, J., Mauritsen, T., and Stevens, B.: What could we learn about climate sensitivity from variability in the surface temperature record?, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-5723,, 2020.

EGU2020-4671 | Displays | NP2.1

Extreme sensitivity and climate tipping points

Anna von der Heydt and Peter Ashwin

The equilibrium climate sensitivity (ECS) is widely used as a measure for possible future global warming. It has been determined from a wide range of climate models, observations and palaeoclimate records, however, it still remains relatively unconstrained. In particular, large values of warming as a consequence of atmospheric greenhouse gas increase cannot be excluded, with some of the most recent state-of-the-art climate models (CMIP6) supporting (much) more warming than previous generations of climate models. Moreover, a number of tipping elements have been identified within the climate system, some of which may affect the global mean temperature. Therefore, it is interesting to explore how the climate systems response (e.g. ECS) behaves when the system is close to a tipping point. 
A climate state close to a tipping point will have a degenerate linear response to perturbations, which can be associated with extreme values of the equilibrium climate sensitivity (ECS). In this talk we contrast linearized ('instantaneous') with fully nonlinear geometric ('two-point') notions of ECS, in both presence and absence of tipping points. For a stochastic energy balance model of the global mean surface temperature with two stable regimes, we confirm that tipping events cause the appearance of extremes in both notions of ECS. Moreover, multiple regimes with different mean sensitivities are visible in the two-point ECS. We confirm some of our findings in a physics-based multi-box model of the climate system.

P. Ashwin and A. S. von der Heydt (2019), Extreme Sensitivity and Climate Tipping Points, J. Stat. Phys.  370, 1166–24.

How to cite: von der Heydt, A. and Ashwin, P.: Extreme sensitivity and climate tipping points, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-4671,, 2020.

EGU2020-9262 | Displays | NP2.1

Wavenumber Decomposition and Extremes of Atmospheric Meridional Energy Transport in the Northern Hemisphere Midlatitudes

Valerio Lembo, Gabriele Messori, Rune Graversen, and Valerio Lucarini

The atmospheric meridional energy transport in the Northern Hemisphere midlatitudes is mainly accomplished by planetary and synoptic waves. A decomposition into wave components highlights the strong seasonal dependence of the transport, with both the total transport and the contributions from planetary and synoptic waves peaking in winter. In both winter and summer months, poleward transport extremes primarily result from a constructive interference between planetary and synoptic motions. The contribution of the mean meridional circulation is close to climatology. Equatorward transport extremes feature a mean meridional equatorward transport in winter, while the planetary and synoptic modes mostly transport energy poleward. In summer, a systematic destructive interference occurs, with planetary modes mostly transporting energy equatorward and synoptic modes again poleward. This underscores that baroclinic conversion dominates regardless of season in the synoptic wave modes, whereas the planetary waves can be either free or forced, depending on the season.

How to cite: Lembo, V., Messori, G., Graversen, R., and Lucarini, V.: Wavenumber Decomposition and Extremes of Atmospheric Meridional Energy Transport in the Northern Hemisphere Midlatitudes, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-9262,, 2020.

EGU2020-12286 | Displays | NP2.1

Stochastic modelling and prediction of monthly surface temperatures: StocSIPS

Lenin Del Rio Amador and Shaun Lovejoy

From hourly to decadal time scales, atmospheric fields are characterized by two scaling regimes: at high frequencies the weather, with fluctuations increasing with the time scale, and at low frequencies, macroweather with fluctuations decreasing with scale, the transition between the two at τw. This transition time is the lifetime of planetary structures and is therefore close to the deterministic predictability limit of conventional numerical weather prediction models. While it is thus the outer scale of deterministic weather models, conversely, it is the inner scale of stochastic macroweather models.

Here we explore the spatial dependence of this transition time. Starting at the surface (2m temperature) we found that the monthly average temperature falls in the macroweather regime for almost any location in the globe, except for parts of the tropical ocean where τw ∼ 1 - 2 years. As we increase in altitude, the dependence of τw with the location becomes more homogeneous and above 850mb τw < 1 month almost everywhere. The longer tropical ocean transition scales are presumably the deterministic outer scales of the “ocean weather” regime.

Knowledge of τw is fundamental for stochastic macroweather forecasting.   Such forecasting is based on symmetries, primarily the power-law behavior of the fluctuations that implies a huge memory that can be exploited for forecasts up to several years. In addition, there is another approximate symmetry called “statistical space-time factorization” relating spatial and temporal statistics. Finally, while weather regime temperature fluctuations are highly intermittent, in macroweather the intermittency is much lower, fluctuations are quasi Gaussian.

The Stochastic Seasonal and Interannual Prediction System (StocSIPS[1,2]) is a stochastic data-driven model that exploits these symmetries to perform macroweather (long-term) forecasts. Compared to traditional global circulation models (GCM), it has the advantage of forcing predictions to converge to the real-world climate (not the model climate). It extracts the internal variability (weather noise) directly from past data and does not suffer from model drift. Some other practical advantages include much lower computational cost, no need for downscaling and no ad hoc postprocessing.

We show that StocSIPS can predict monthly average surface temperature (nearly) to its stochastic predictability limits. Using monthly to annual lead time hindcasts, we compare StocSIPS predictions with those from the CanSIPS[3] GCM. Beyond a month, and especially over land, StocSIPS generally has higher skill. For regular StocSIPS forecasts, see


[1] Del Rio Amador, L. and Lovejoy, S. (2019) Clim Dyn, 53: 4373.

[2] Lovejoy, S., Del Rio Amador, L., Hébert, R. (2017) In Nonlinear Advances in Geosciences, A.A. Tsonis ed. Springer Nature, 305–355 DOI: 10.1007/978-3-319-58895-7

[3] Merryfield WJ, Denis B, Fontecilla JS, Lee WS, Kharin S, Hodgson J, Archambault B (2011) Rep., 51pp, Environment Canada.

How to cite: Del Rio Amador, L. and Lovejoy, S.: Stochastic modelling and prediction of monthly surface temperatures: StocSIPS, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-12286,, 2020.

EGU2020-6031 | Displays | NP2.1

Scaling and anisotropic heterogeneities of ocean SST images from satellite data

Francois Schmitt, Hussein Yahia, Joel Sudre, Véronique Garçon, and Guillaume Charria

Oceanic fields display a large variability over large temporal and spatial scales. One way to characterize such variability, borrowed from the field of turbulence, is to consider scaling regimes and multi-scaling properties.

He we use 2D power spectral analysis as well as 2D structure functions <X(M)-X(N)q>=F(q,d(M,N)), between tow points M and N belonging to the region of interest. By performing statistics with respect to the distance d(M,N), one may extract the scaling property of the 2D field, for a range of distances Lmin<d<Lmax, of the form F(q,d)=dζ(q). This approach can be used even for irregular images (having missing values due to cloud coverage) or for part of images in order to estimate the statistical heterogeneity of different zones of a given image.

In the framework of the French CNRS/IMECO project, we consider MODIS Aqua SST images, in France (English Channel versus Gascogne Golf) and in Chili (Eastern Boundary Upwelling System). We illustrate the use of the 2D structure function analysis for different part of these images and also different times. Scaling ranges and also scaling exponents are compared. To take into account the anisotropy of some of these zones, an anisotropic version of the 2D structure functions is also used.

How to cite: Schmitt, F., Yahia, H., Sudre, J., Garçon, V., and Charria, G.: Scaling and anisotropic heterogeneities of ocean SST images from satellite data, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-6031,, 2020.

EGU2020-8195 | Displays | NP2.1

Mesoscale eddy characteristics in the Labrador Sea from observations and a 1/60° numerical model

Arne Bendinger, Johannes Karstensen, Julien Le Sommer, Aurélie Albert, and Fehmi Dilmahamod

Mesoscale eddies play an important role in lateral property fluxes. Observational studies often use sea level anomaly maps from satellite altimetry to estimate eddy statistics (incl. eddy kinetic energy). Recent findings suggest that altimetry derived eddy characteristics may suffer from the low spatial resolution of past and current satellite-tracks in high-latitude oceans associated with small Rossby radii. Here we present results of an eddy reconstruction based on a nonlinear damping Gauss-Newton optimisation algorithm using ship based current profiler observations from two research expeditions in the Labrador Sea in 2014 and 2016. Overall we detect 14 eddies with radii ranging from 7 to 35 km.

In order to verify the skill of the reconstruction we used the submesoscale permitting NATL60 model (1/60°) as a reference data set. Spectral analysis of the horizontal velocity implies that the mesoscale regime is well represented in NATL60 compared with the observations. The submesoscale regime in the model spectra shows deviations to the observations at scales smaller than 10km near the ocean surface. The representation of the submesoscale flow further decreases in the model with increasing depth.

By subsampling the NATL60 model velocities along artificial ship tracks, applying our eddy reconstruction algorithm, and comparing the results with the full model field, a skill assessment of the reconstruction is done. We show that the reconstruction of the eddy characteristics can be affected by the location of the ship track through the velocity field.

In comparison with the observed eddies the NATL60 eddies have smaller radii and higher azimuthal velocities and thus are more nonlinear. The inner core velocity structure for observations and NATL60 suggests solid body rotation for 2/3 of the radius. The maximum azimuthal velocity may deviate by up to 50% from solid body rotation.

The seasonality of the submesoscale regime can be seen in the data as the power spectrum is reduced from spring to summer in both the ship-based measurements and model.

How to cite: Bendinger, A., Karstensen, J., Le Sommer, J., Albert, A., and Dilmahamod, F.: Mesoscale eddy characteristics in the Labrador Sea from observations and a 1/60° numerical model, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-8195,, 2020.

EGU2020-8222 | Displays | NP2.1

Multi-scale coastal surface temperature in the Bay of Biscay and the English Channel

Guillaume Charria, Sébastien Theetten, Adam Ayouche, Coline Poppeschi, Joël Sudre, Hussein Yahia, Véronique Garçon, and François Schmitt

The Bay of Biscay and the English Channel, in the North-eastern Atlantic, are considered as a natural laboratory to explore the coastal dynamics at different spatial and temporal scales. In those regions, the coastal circulation is constrained by a complex topography (e.g. varying width of the continental shelf, canyons), river runoffs, strong tides and a seasonally contrasted wind-driven circulation.


Based on different numerical model experiments (from 400m to 4km spatial resolution, from 40 to 100 sigma vertical layers using 3D primitive equation ocean models), different features of the Bay of Biscay and English Channel circulation are assessed and explored. Both spatial (submesoscale and mesoscale) and temporal (from hourly to monthly) scales are considered. Modelled spatial scales, with a specific focus on the variability of fine scale features (e.g. fronts, filaments, eddies), are compared with remotely sensed observations (i.e. Sea Surface Temperature). Different methodologies as singularity and Lyapunov exponents allow describing fine scales features and are applied on both modelled and observed datasets. For temporal scales, in situ high frequency surface temperature measurements from coastal moorings (from COAST-HF observing network) provide a reference for the temporal variability to be modelled. Exploring differences in the temporal scales (from an Empirical Mode Decomposition) advises on the efficiency of our coastal modelling approach.


This result overview in the Bay of Biscay and the English Channel aims illustrating the input of coastal modelling activities in understanding multi-scale interactions (spatial and temporal).

How to cite: Charria, G., Theetten, S., Ayouche, A., Poppeschi, C., Sudre, J., Yahia, H., Garçon, V., and Schmitt, F.: Multi-scale coastal surface temperature in the Bay of Biscay and the English Channel, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-8222,, 2020.

EGU2020-9821 | Displays | NP2.1

Detection and characterization of SCVs in the North Atlantic

Ashwita Chouksey, Xavier Carton, and Jonathan Gula

In recent years, the oceanographic community has devoted considerable interest to the study of SCVs (Submesoscale Coherent Vortices, i.e. vortices with radii between 2-30 km, below the first internal radius of deformation); indeed, both mesoscale and submesoscale eddies contribute to the transport and mixing of water masses and of tracers (active and passive), affecting the heat transport, the ventilation pathways and thus having an impact on the large scale circulation.

In different areas of the ocean, SCVs have been detected, via satellite or in-situ measurements, at the surface or at depth. From these data, SCVs were found to be of different shapes and sizes depending on their place of origin and on their location. Here, we will concentrate rather on the SCVs at depth.

In this study, we use a high resolution simulation of the North Atlantic ocean with the ROMS-CROCO model. In this simulation, we also identify the SCVs at different depths and densities; we analyse their site and mechanism of generation, their drift, the physical processes conducting to this drift and their interactions with the surrounding flows. We also quantify their physical characteristics (radius, thickness, intensity/vorticity, bias in polarity: cyclones versus anticyclones). We provide averages for these characteristics and standard deviations. 

We compare the model results with the observational data, in particular temperature and salinity profiles from Argo floats and velocity data from currentmeter recordings. 

This study is a first step in the understanding of the formation, occurrences and structure of SCVs in the North Atlantic Ocean, of help to improve their in-situ sampling.

How to cite: Chouksey, A., Carton, X., and Gula, J.: Detection and characterization of SCVs in the North Atlantic, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-9821,, 2020.

EGU2020-17939 | Displays | NP2.1

Scaling Analysis of the Algal Blooms

Yongxiang Huang, Yang Gao, Qianguo Xing, Francois Schmitt, and Jianyu Hu

Algal blooms, also known as ‘red tide’, are extremely harmful to the marine ecosystem since they infuse toxins into seawater and stifle oxygen in the water columns. Visually, they demonstrate rich patterns in spatial due to the interaction between the ocean current and the wind. Using the satelliate remote sensing data provided by the Chinese satellite Gaofeng 1, we first derive a normalized difference vegetation index (NDVI), which can be used to separate efficiently different types of cases, e.g., no algae bloom (NAB), macro algae bloom (MAB), and phytoplankton algae bloom (PAB), etc. The classical structure-function analysis is performed. Our preliminary results confirm the existence of the power-law behavior on the spatial scale range from 100 m to 400 m for the case of MAB. The corresponding scaling exponents are close to the ones of the classical passive scalar in three-dimension hydrodynamic turbulence. It suggests that the MAB could be treated as a passive scalar, which leads to not only a better understanding of the dynamics of algal blooms, but also a challenge of the modelling.

How to cite: Huang, Y., Gao, Y., Xing, Q., Schmitt, F., and Hu, J.: Scaling Analysis of the Algal Blooms, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-17939,, 2020.

The parameterization of surface exchange coefficients (Ch) representing land–atmosphere coupling strength plays a key role in land surface modeling. Previous studies have found that land–atmosphere coupling in land surface models (LSMs) is overestimated, which affects the predictability of weather and climate evolution. To improve the representation of land–atmosphere interactions in LSMs, this study investigated the dynamic canopy-height-dependent coupling strength in the offline Noah LSM with multiparameterization options (Noah-MP) when applied to China. Comparison with the default Noah-MP LSM showed the dynamic scheme significantly improved the Ch calculations and realistically reduced the biases of simulated surface energy and water components against observations. It is noteworthy that the improvements brought by the dynamic scheme differed across land cover types. The scheme was found superior in reproducing the observed Ch as well as surface energy and water variables for short vegetation (grass, crop, and shrub), while the improvement for tall canopy (forest) was found not significant, although the estimations were reasonable. The improved version benefits from the treatment of the roughness length for heat. Overall, the dynamic coupling scheme markedly affects the simulation of land–atmosphere interactions, and altering the dynamics of surface coupling has potential for improving the representation of land–atmosphere interactions and thus furthering LSM development.

How to cite: Zhang, X., Chen, L., Ma, Z., and Gao, Y.: Assessment of Surface Exchange Coefficients in the Noah-MP Land Surface Model for Different Land Cover Types over China, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-3570,, 2020.

EGU2020-5632 | Displays | NP2.1

Power-law behaviour of hourly precipitation intensity and dry spell duration over the United States

Christian Franzke, Lichao Yang, and Zuntao Fu

Precipitation is an important meteorological variable which is critical for weather risk assessment. For instance, intense but short precipitation events can lead to flash floods and landslides. Most statistical modelling studies assume that the occurrence of precipitation events is based on a Poisson process with exponentially distributed waiting times while precipitation intensities are typically described by a gamma distribution or a mixture of two exponential distributions. Here, we show by using hourly precipitation data over the United States that the waiting time between precipitation events is non-exponentially distributed and best described by a fractional Poisson process. A systematic model selection procedure reveals that the hourly precipitation intensities are best represented by a two-distribution model for about 90% of all stations. The two-distribution model consists of (a) a generalized Pareto distribution (GPD) model for bulk precipitation event sizes and (b) a power-law distribution for large and extreme events. Finally, we analyse regional climate model output to evaluate how the climate models represent the high-frequency temporal structure of U.S. precipitation. Our results reveal that these regional climate models fail to accurately reproduce the power-law behaviour of intensities and severely underestimate the long durations between events.

How to cite: Franzke, C., Yang, L., and Fu, Z.: Power-law behaviour of hourly precipitation intensity and dry spell duration over the United States, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-5632,, 2020.

EGU2020-13481 | Displays | NP2.1

Nonlinear time series models for the North Atlantic Oscillation

Abdel Hannachi, Thomas Önskog, and Christian Franzke

The North Atlantic Oscillation (NAO) is the dominant mode of climate variability over the North Atlantic basin and has a significant impact on seasonal climate and surface weather conditions. This is the result of complex and nonlinear interactions between many spatio-temporal scales. Here, the authors study a number of linear and nonlinear models for a station-based time series of the daily winter NAO index. It is found that nonlinear autoregressive models including both short and long lags perform excellently in reproducing the characteristic statistical properties of the NAO, such as skewness and fat tails of the distribution and the different time scales of the two phases. As a spinoff of the modelling procedure, we are able to deduce that the interannual dependence of the NAO mostly affects the positive phase and that timescales of one to three weeks are more dominant for the negative phase. The statistical properties of the model makes it useful for the generation of realistic climate noise.

How to cite: Hannachi, A., Önskog, T., and Franzke, C.: Nonlinear time series models for the North Atlantic Oscillation, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-13481,, 2020.

EGU2020-8544 | Displays | NP2.1

Understanding long-term persistence and multifractal behaviors in river runoff: A detailed study over China

Naiming Yuan, Wenlu Wu, Fenghua Xie, and Yanjun Qi

Long-term persistence (LTP) and multifractality in river runoff fluctuations have been well recognized over the recent decades, but the origins of these characteristics are still under debate. In this study, runoff and precipitation data from China are analyzed using detrended fluctuation analysis (DFA) and its generalized version, multifractal detrended fluctuation analysis (MF-DFA). By comparing the results between runoff and the nearby precipitation data, we find the multifractal behaviors in river runoff may be propagated from the nearby precipitation data, but the LTP is not inherited from precipitation. The LTP in river runoff may arise from the spatial aggregation effect, as it is closely related with the catchment area, especially for stations with large catchment areas. These findings are based on data from China, which was not analyzed systematically due to the poor data availability. Since the existence of LTP and multifractality makes the runoff change not completely random, one should further introduce these characteristics into hydrological models, for improved water managements and better estimations of hazard risks.

How to cite: Yuan, N., Wu, W., Xie, F., and Qi, Y.: Understanding long-term persistence and multifractal behaviors in river runoff: A detailed study over China, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-8544,, 2020.

The El-Niño index behaves as a nonlinear and non-Gaussian stochastic process. A well-known characteristic is its positive skewness coming from the occurrence of stronger episodes of El-Niño than of La Niña. Here, we use the period 1870-2018 of the standardized El-Niño index x(t), sampled in trimesters to analyze the spectral origin of the bicorrelation: sk(t1,t2)=E[x(t)x(t+t1)x(t+t2)] and skewness sk(0,0). For that, we estimate the two-dimensional Fourier transform of sk(t1,t2) or bispectrum B(f1,f2). Its sum over bi-frequencies (f1,f2) equals the skewness (0.45 in our case). Positive and negative bispectrum peaks are due to phase locking of frequency triplets: (f1,f2,f1+f2), contributing to extreme El-Niños and La Niñas respectively. Moreover, the most significant positive and/or negative bispectrum regions are rather well localized in the bispectrum domain. Here, we propose a partition of the El Niño signal into a set of band-pass spectrally separated components whose self and cross interactions can explain the broad structure of bispectrum. In the simplest case where the signal is decomposed into a fast and a slow component (with a cutoff frequency of (1/2.56) cycles/yr.), we verifty that slow-slow interactions (or phase locking) explain most of La-Niñas, particularly at the frequency triplet (1/4.9, 1/15 and 1/3.7 cycles/yr) whereas the fast-slow interactions explain most of El Niños, particularly at the frequency triplet (1/4.9, 1/4.9 and 1/2.5 cycles/yr). In order to simulate this stochastic behavior, we calibrate a set of nonlinearly coupled oscillators (Auto-regressive processes, forced by self and cross quadratic component terms), one for each component. In the case of weak cross-component interactions, and thus weak nonlinearity, the coupling coefficients between spectral-band components are proportional to the corresponding cross-skewnesses, which represent good first guesses in the calibration of the model parameters. The predictability of the model is then assessed, in particular for the anticipation of big El Niños and la Niñas. The authors would like to acknowledge the financial support FCT through project UIDB/50019/2020 – IDL.

How to cite: Pires, C. and Hannachi, A.: Stochastic modeling of extreme El-Niño and La Niña events by nonlinearly coupled oscillators, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-10741,, 2020.

Using observations and model simulations, the impact of the November Eurasian (EU) teleconnection on the following January Arctic Oscillation (Arctic Oscillation) and the possible mechanisms are investigated in this study.        We found that the positive (negative) phase of the November EU pattern favors the negative (positive) phase of AO during the subsequent January, and both the stratosphere-troposphere interactionsand the tropospheric Blocking High (BH) activity anomalies over the Euro-Atlantic sector play an important role in their connections. When the EU pattern is positive (negative) phase in November, the increased (decreased) vertical wave activity over Eurasia and North Atlantic gradually weakens (enhances) the Stratospheric polar vortex (SPV)from November to the following early January, which is then conducive to a downward propagation of positive height anomalies from the stratosphere to troposphere. On the other hand, due to the persistent stronger (weaker) and southward (northward) shifted storm tracks over the Euro-Atlantic sector from November to the following early January, the BH activities over this region are significantly decreased (increased) during the same period, whichthen contributesto positive (negative) height anomalies over the Arctic via the propagation of a zonal wave number 1-3. As both the SPVand BHanomalies over the Euro-Atlantic sector reach the maximum around the late December-early January, the resultant equivalent barotropic AO dipole patterndevelops and finally establishes during the following January.These results are useful for the predictability of the middle winter climate

How to cite: Qiao, S.: Impact of the November Eurasian teleconnection on the following January Arctic Oscillation, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-12542,, 2020.

Using hindcast and forecastdata from the National Centers for Environmental Prediction (NCEP) Climate Forecast System version 2 (CFSv2)for the period 1982-2017, we comprehensively assess the predictability of the climatology, interannual variability, and dominant modes of the wintertime 500 hPa geopotential height over Ural-Siberia (40-80°Nand 30-100°E). Although the climatic mean 500 hPa heightover Ural-Siberia simulated by NCEP CFSv2has a negative bias, especially over the eastern part of the region, NCEP CFSv2 well predicts the spatial distribution of the two major modes(EOF1 and EOF2) over this region 2 months in advance.The forecasting skill of the principal component (PC) of the two major modes,PC1 (PC2), is highest1 (0) month in advance, where the linear correlation coefficient between the predicted and observed time series reaches +0.36 (+0.67), exceeding the 95% confidence level. Conversely, the forecasting skill of PC1 (PC2) is very low 0 (1) month in advance. The main reason for the poorer(better) prediction of PC1 0 (1) month in advance is associated with a less (more) accurate response of the Eurasian teleconnection to SST anomalies over the southwestern Atlantic. For PC2, the better (poorer) prediction of PC2 0 (1) month in advance may be due to more (less) accurate responses of the stratospheric polar vortex and the Scandinavian teleconnection to the dipole SST anomalies over the North Pacific. These results are useful for evaluating the predictability of the East Asian winter climate.

How to cite: Zou, M.: Predictability of the Wintertime 500 hPa Geopotential Height over Ural-Siberia in the NCEP Climate Forecast System, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-13084,, 2020.

The estimations of various factors influence on weather regimes formation in Russian regions in transitional (spring, fall) seasons are presented. Changes in those regimes comparing to the middle of 20th century are analyzed, considering atmospheric circulation features under the changes in meridional heat transfer and Rossby waves stationary modes. Using long-term observations of surface air temperature from several locations across Russia, the multimodal features of the probability density functions (PDF) in several decades of 20th and 21st centuries are identified. Focusing on surface temperature anomalies in transitional seasons, we examine the connection between the multimodal features of their PDFs and the nonlinear dependence of surface albedo on temperature during the formation and melting of snow cover. We investigate the impacts of other mechanisms that can facilitate these features, including blocking of zonal atmospheric transport in middle latitudes and formation of blocking anticyclones (blockings) and stationary Rossby waves.

How to cite: Parfenova, M. and Mokhov, I. I.: Intraseasonal temperature variability features in Northern Eurasia regions under changing climate, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-20698,, 2020.

Sea surface temperature (SST) is the only oceanic parameter on which depend heat fluxes between ocean and atmosphere and, therefore, SST is one of the key factors that influence climate and its variability. Over the twentieth century, SSTs have significantly increased around the global ocean, warming that has been attributed to anthropogenic climate change, although it is not yet clear how much of it is related to natural causes and how much is due to human activities. A considerable part of available literature regarding climate change has been built based on the global or hemispheric analysis of surface temperature trends. There are, however, some key open questions that need to be answered and for this task estimates of long-term SST trend patterns represent a source of valuable information. Unfortunately, long-term SST trend patterns have large uncertainties and although SST constitutes one of the most-measured ocean variables of our historic records, their poor spatial and temporal sampling, as well as inhomogeneous measurements technics, hinder an accurate determination of long-term SST trends, which increases their uncertainty and, therefore, limit their physical interpretation as well as their use in the verification of climate simulations.
Most of the long-term SST trend patterns have been built using linear techniques, which are very usefull when they are used to extract information of measurements satisfying two key assumptions: linearity and stationarity. The global warming resulting of our economic activities, however, affect the state of the World Ocean and the atmosphere inducing changes in the climate that may result in oscillatory modes of variability of different frequencies, which may undergo non-stationary and non-linear evolutions. In this work, we construct long-term SST trend patterns by using non-linear techniques to extract non-linear, long-term trends in each grid-point of two available global SST datasets: the National Oceanic and Atmospheric Administration Extended Reconstructed SST (ERSST) and from the Hadley Centre sea ice and SST (HadISST). The used non-linear technique makes a good job even if the SST data are non-linear and non-stationary. Additionally, the nonlinearity of the extracted trends allows the use of the first and second derivative to get more information about the global, long-term evolution of the SST fields, favoring thus a deeper understanding and interpretation of the observed changes in SST. Particularly, our results clearly show, in both ERSST and HadISST datasets, the non-uniform warming observed in the tropical Pacific, which seems to be related to the enhanced vertical heat flux in the eastern equatorial Pacific and the strengthening of the warm pool in the western Pacific. By using the second derivative of the nonlinear SST trends, emerges an interesting pattern delimiting several zones in the Pacific Ocean which have been responded in a different way to the impose warming of the last century.

How to cite: Martinez-Lopez, B.: Non-linear, long-term evolution of sea surface temperature across the World Ocean, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-22546,, 2020.

NP2.3 – Extremes in Geophysical Sciences: Dynamics, Thermodynamics and Impacts

Cross-timescale interference involves linear and non-linear interactions between climate modes acting at multiple timescales (Muñoz et al., 2015, 2016, 2017; Robertson et al., 2015; Moron et al., 2015), and that are related to windows of opportunity for enhanced predictive skill (Mariotti et al., 2020), with relevant societal impacts (e.g., Doss-Gollin et al., 2018; Anderson et al., 2020). Using a simple mathematical model, reanalysis data and gridded observations, here we analyze plausible mechanisms for cross-timescale interference, describing conditions for coupling of oscillating modes and its impact on extreme rainfall occurrence and predictive skill. Concrete examples for Northeast North America and southern South America are discussed, as well as implications for climate model diagnostics.

How to cite: Muñoz, Á. G.: Cross-timescale interference and predictability of extremes: a chimera?, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-21105,, 2020.

EGU2020-3062 | Displays | NP2.3

Interannual-to-decadal variability of the Kuroshio extension: Analyzing an ensemble of global hindcasts from a Dynamical System viewpoint.

Giusy Fedele, Thierry Penduff, Stefano Pierini, M. Carmen Alvarez-Castro, Alessio Bellucci, and Simona Masina

The Kuroshio Extension (KE) is the inertial meandering jet formed by the convergence of the Kuroshio and Oyashio currents in the Northern Pacific. It is widely mentioned in the literature that the KE variability is bimodal on the decadal time scale. The nature of this low frequency variability (LFV) is still under debate; some authors suggest that internal oceanic mechanisms play a fundamental role in the phenomenon but there is also evidence from the observations that the KE LFV is connected with changes in broader patterns of variability such as the Pacific Decadal Oscillation.

We first inspect the interplay between the ocean and the atmosphere in the KE by taking advantage of the OCCIPUT 1/4° model dataset: it consists in an ensemble of 50 global ocean–sea-ice hindcasts performed over the period 1960–2015 (hereafter OCCITENS), and in a one-member 330-yr climatological simulation (hereafter OCCICLIM). In this context, OCCITENS simulates both the intrinsic and forced variability and allows for their separation via ensemble statistics, while OCCICLIM simulates the "pure" intrinsic variability of the jet. We then explore some features of the KE dynamical system attractor in the quasi-autonomous (OCCICLIM) and nonautonomous (OCCITENS) regimes: we thus assess the KE predictability in the OCCIPUT dataset in order to better understand the ocean-atmosphere interactions and the source of the associated predictability.

Our analyses show that both oceanic and atmospheric drivers control the KE LFV variability. In this framework, the results suggest that the jet oscillates between the two intrinsic oceanic modes with transitions triggered by the atmosphere.

How to cite: Fedele, G., Penduff, T., Pierini, S., Alvarez-Castro, M. C., Bellucci, A., and Masina, S.: Interannual-to-decadal variability of the Kuroshio extension: Analyzing an ensemble of global hindcasts from a Dynamical System viewpoint., EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-3062,, 2020.

EGU2020-17899 | Displays | NP2.3

Greatness from small beginnings: Impact of oceanic mesoscale on weather extremes and large-scale atmospheric circulation in midlatitudes

Joakim Kjellsson, Wonsun Park, Torge Martin, Eric Maisonnave, and Mojib Latif

We study how mesoscale air-sea interactions over the North Atlantic can influence weather extremes, e.g. heavy precipitation and wind storms, and the overall atmospheric circulation both locally and downstream in the midlatitudes. We use a global coupled climate model with a high-resolution North Atlantic grid (dx ~ 8 km) and an atmosphere model resolution of either 125 km or 25 km. The high-resolution North Atlantic grid allows the model to resolve the current systems and SST fronts associated with e.g. the Gulf Stream and North Atlantic Current. As air-sea fluxes of momentum, heat and freshwater are calculated on the atmosphere grid, spatial variations in fluxes associated with sharp SST fronts are much better represented when using the high-resolution atmosphere then when using the low-resolution model. 


Preliminary results show that coupling to the high-resolution (dx ~ 25 km) rather than low-resolution (dx ~ 125 km) atmosphere model increases the intensity and variance of surface heat and freshwater fluxes over eddy-rich regions such as the Gulf Stream. As a result, the high-resolution model simulates more intense heavy precipitation events over most of the North Atlantic Ocean. We also show that more frequent coupling between the atmosphere and ocean components increases the intensity of the air-sea fluxes, in particular wind stress, which has a large impact on the ocean. More intense air-sea fluxes can provide more energy for cyclogenesis and we will discuss how the oceanic mesoscale, in particular in the eddy-rich regions, can alter the storm tracks and jet stream to influence extreme weather and the climate over Europe.


The coupled model comprises NEMO 3.6/LIM2 ocean and OpenIFS 40r1 atmosphere, and works by allowing the global OpenIFS model to send and receive fields from both a global coarse-resolution ocean grid and a refined grid over the North Atlantic grid via the OASIS3-MCT4 coupler. The ability to run these simulations is a very recent development and we will give a brief overview of the coupled modelling system and benefits of using regional grid refinement in coupled models.


How to cite: Kjellsson, J., Park, W., Martin, T., Maisonnave, E., and Latif, M.: Greatness from small beginnings: Impact of oceanic mesoscale on weather extremes and large-scale atmospheric circulation in midlatitudes, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-17899,, 2020.

EGU2020-13802 | Displays | NP2.3

Storylines of the 2018 Northern Hemisphere heat wave at pre-industrial and higher global warming levels

Kathrin Wehrli, Mathias Hauser, and Sonia I. Seneviratne

The 2018 summer was unusually hot in large areas of the Northern Hemisphere and simultaneous heat waves on three continents led to major impacts to agriculture and society. The event was driven by the anomalous atmospheric circulation pattern during that summer and it was only possible in a climate with global warming. There are indications that in a future, warmer climate similar events might occur regularly, affecting major ‘breadbasket’ regions of the Northern Hemisphere.

This study aims to understand the role of climate change for driving the intensity of the 2018 summer and to explore the sensitivity to changing warming levels. Model simulations are performed using the Community Earth System Model to investigate storylines for the extreme 2018 summer given the observed atmospheric large-scale circulation but different levels of background global warming: no human imprint, the 2018 conditions, and different mean global warming levels (1.5°C, 2°C, 3°C, and 4°C). The storylines explore the consequences of the event in an alternative warmer or colder world and thus help to increase our understanding of the drivers involved. The results reveal a strong contribution by the present-day level of global warming and provide an outlook to similar events in a possible future climate.

How to cite: Wehrli, K., Hauser, M., and Seneviratne, S. I.: Storylines of the 2018 Northern Hemisphere heat wave at pre-industrial and higher global warming levels, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-13802,, 2020.

EGU2020-6687 | Displays | NP2.3

Characterizing large-scale circulation triggering heavy precipitation amounts over the northern French Alps

Antoine Blanc, Juliette Blanchet, and Jean-Dominique Creutin

Large-scale circulations (LSCs) explain a significant part of Alpine precipitations. Characterizing circulations triggering heavy precipitation is usually done using weather-type classifications. A different characterization is implemented here, based on analogy using the atmospheric descriptors proposed in Blanchet et al 2018, 2019. These descriptors are both related to the dynamics of LSC and to their relative position in the atmospheric space. This work is applied to the Isère river catchment for the 1950-2011 period, considering a 3-day time step. The 500 hPa and 1000 hPa geopotential heights covering part of the western Europe are used separately to represent LSC. Two analogy criteria are investigated for constructing the atmospheric descriptors, namely TWS and RMSE.

Our results reveal that LSCs triggering heavy precipitation amounts correspond to strong geostrophic wind with quasi constant direction during the three days, corresponding to blocking situations in altitude. Moreover, those patterns of circulation are among the least singulars, and they show the highest degree of clustering in the atmospheric space. We interpret the latest results by the fact that heavy precipitation LSCs feature twin circulation patterns. In addition, the 500 hPa geopotential height appears to discriminate better heavy precipitation situations than the 1000 hPa one. Finally, our work points out the benefit of a combined use of TWS and RMSE. TWS gives information about the direction of geostrophic wind, while RMSE -combined with TWS- informs about its strength.


Blanchet, J., Stalla, S., and Creutin, J.-D. (2018). Analogy of multi-day sequences of atmospheric circulation favoring large rainfall accumulation over the French Alps. Atmospheric Science Letters.

Blanchet, J., Creutin, J-D. (2019). Modelling rainfall accumulations over several days in the French Alps using low-dimensional atmospheric predictors based on analogy. Journal of Applied Meteorology and Climatology.

How to cite: Blanc, A., Blanchet, J., and Creutin, J.-D.: Characterizing large-scale circulation triggering heavy precipitation amounts over the northern French Alps, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-6687,, 2020.

EGU2020-8990 | Displays | NP2.3

More perceived but not faster evolution of heat stress than temperature extremes in the future

Audrey Brouillet and Sylvie Joussaume

Global warming is projected to intensify during the 21st century. This warming will be more readily perceived by human populations if it occurs rapidly and if it induces a thermal heat stress on the human body. Yet, only few studies investigate how climate change could be felt by future populations. Here we assess this possible perceived evolution between 1959 and 2100 only combining thermodynamic and statistical indicators. We analyse extremes of temperature (T99) and simplified Wet-Bulb Globe Temperature (WBGT99), a common heat stress index assessing the combined effect of elevated temperature and humidity on the human body. For each year of the period, we define the speed of change as a difference between two successive 20-year periods (i.e. with a moving baseline), and assess how these running changes emerge from each last 20-y inter-annual variability.

According to a subset of 12 CMIP5 Earth System Models and the RCP8.5 scenario, the change of T99 and WBGT99 will be twice as fast in the future compared to the current speed of change in the mid-latitudes, and by up to four times faster tropical regions such as Amazonia. Warming accelerations are thus similar for both T99 and WBGT99. However, in tropical regions by 2080, the speed is projected to be 2.3 times larger than the recent inter-annual variability for WBGT99, and only 1.5 to 1.8 times larger for T99. Currently, speeds of change are only 0.2 to 0.8 times as large as the recent year-to-year variability for both metrics. We also show that 36% of the total world population will experience an emergent WBGT99 intensification in 2080, but only 15% of the population for T99. According to future projections, the accelerated warming of future heat extremes will be more felt by populations than current changes, and this perceived change will be more severe for WBGT99 than for T99, particularly in the tropics.

How to cite: Brouillet, A. and Joussaume, S.: More perceived but not faster evolution of heat stress than temperature extremes in the future, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-8990,, 2020.

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The influence of greenhouse gases on the 1930s Dust Bowl heat waves across central United States

Sabine Undorf, Tim Cowan, Gabi Hegerl, Luke Harrington, and Friederike Otto

The central United States experienced the hottest summers of the twentieth century in 1934 and 1936, with over 40 heat wave days and maximum temperatures surpassing 44°C at some locations like Kansas and Oklahoma. In fact, as of 2019, the summer of 1936 is still the hottest on record. The heat waves coincided with the decade-long Dust Bowl drought, that caused wide-spread crop failures, dust storms that penetrated to New York and considerable out-migration. In a very-large ensemble regional modelling framework, we show that greenhouse gas increases slightly enhanced the frequency and duration of the Dust Bowl heat waves, and would strongly enhance similar heat waves in the present day under current, further elevated greenhouse gas levels. Specifically, present-day atmospheric greenhouse gas forcing would reduce the return period of a rare (less than once in a century) heat wave summer as observed in 1936 to about 1-in 40-years, with further contribution by sea surface warming. Here, we show that a key driver of this elevated heat wave risk is the reduction in evaporative cooling and increase in sensible heating during dry springs and summers.  Hence, we conclude that a warmer world is creating the potential for future extreme heat in moisture-limited regions, with potentially very damaging impacts.

How to cite: Undorf, S., Cowan, T., Hegerl, G., Harrington, L., and Otto, F.: The influence of greenhouse gases on the 1930s Dust Bowl heat waves across central United States, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-6177,, 2020.

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Storyline approach to extreme event characterization

Theodore Shepherd

Extreme climate events are invariably highly nonlinear, complex events, resulting from the confluence of multiple causal factors, and often quite singular. In any complex system there is a tension between analysis methods that respect the singularity of the extreme events at the price of statistical repeatability, and those that emphasize statistical repeatability at the price of nonlinearity and complexity; this dichotomy is found across all areas of science. In the climate context, the ‘storyline’ approach has emerged in recent years as a way of following the first of these two pathways. I will discuss how the storyline approach can be cast within the mathematical framework of causal networks, which provides a way to bridge between the storyline and probabilistic approaches. This also provides a way to interpret data in an appropriately conditional manner, thereby aiding model-measurement comparison.

How to cite: Shepherd, T.: Storyline approach to extreme event characterization, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-4896,, 2020.

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The substructure of extremely hot summers in the Northern Hemisphere

Matthias Röthlisberger, Michael Sprenger, Emmanouil Flaounas, Urs Beyerle, and Heini Wernli

In the last decades, extremely hot summers (hereafter extreme summers) have challenged societies worldwide through their adverse ecological, economic and public health effects. In this study, extreme summers are identified at all grid points in the Northern Hemisphere in the upper tail of the July–August (JJA) seasonal mean 2-meter temperature (T2m) distribution, separately in ERA-Interim reanalyses and in 700 simulated years with the Community Earth System Model (CESM) large ensemble for present-day climate conditions. A novel approach is introduced to characterize the substructure of extreme summers, i.e., to elucidate whether an extreme summer is mainly the result of the warmest days being anomalously hot, or of the coldest days being anomalously mild, or of a general shift towards warmer temperatures on all days of the season. Such a statistical characterization can be obtained from considering so-called rank day anomalies for each extreme summer, that is, by sorting the 92 daily mean T2m values of an extreme summer and by calculating, for every rank, the deviation from the climatological mean rank value of T2m.  

Applying this method in the entire Northern Hemisphere reveals spatially strongly varying extreme summer substructures, which agree remarkably well in the reanalysis and climate model data sets. For example, in eastern India the hottest 30 days of an extreme summer contribute more than 70% to the total extreme summer T2m anomaly, while the colder days are close to climatology. In the high Arctic, however, extreme summers occur when the coldest 30 days are substantially warmer than climatology. Furthermore, in roughly half of the Northern Hemisphere land area, the coldest third of summer days contribute more to extreme summers than the hottest third, which highlights that milder than normal coldest summer days are a key ingredient of many extreme summers. In certain regions, e.g., over western Europe and western Russia, the substructure of different extreme summers shows large variability and no common characteristic substructure emerges. Furthermore, we show that the typical extreme summer substructure in a certain region is directly related to the region’s overall T2m rank day variability pattern. This indicates that in regions where the warmest summer days vary particularly strongly from one year to the other, these warmest days are also particularly anomalous in extreme summers (and analogously for regions where variability is largest for the coldest days). Finally, for three selected regions, thermodynamic and dynamical causes of extreme summer substructures are briefly discussed, indicating that, for instance, the onset of monsoons, physical boundaries like the sea ice edge, or the frequency of occurrence of Rossby wave breaking, strongly determine the substructure of extreme summers in certain regions.

How to cite: Röthlisberger, M., Sprenger, M., Flaounas, E., Beyerle, U., and Wernli, H.: The substructure of extremely hot summers in the Northern Hemisphere, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-4441,, 2020.

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From severe droughts in South America to marine heatwaves in the South Atlantic

Regina Rodrigues, Andrea Taschetto, Alex Sen Gupta, and Gregory Foltz

In 2013/14 eastern South America experienced one of its worst droughts, leading to water shortages in São Paulo, the world’s fourth most populated city. This event was also responsible for a dengue fever outbreak that tripled the usual number of fatalities and reduced Brazilian coffee production leading to a global shortages and worldwide price increases. The drought was associated with an anomalous anticyclonic circulation off southeast South America that prevented synoptic systems reaching the region while inhibiting the development of the South Atlantic Convergence Zone and its associated rainfall. A concomitant and unprecedented marine heatwave also developed in the southwest Atlantic. Here we show from observations that such droughts and adjacent marine heatwaves have a common remote cause. Atmospheric blocking triggered by tropical convection in the Indian and Pacific oceans can cause persistent anticyclonic circulation that not only leads to severe drought but also generates marine heatwaves in the adjacent ocean. We show that increased shortwave radiation due to reduced cloud cover and reduced ocean heat loss from weaker winds are the main contributors to the establishment of marine heatwaves in the region. The proposed mechanism, which involves droughts, extreme air temperature over land and atmospheric blocking explains approximately 60% of the marine heatwave events in the western South Atlantic. We also identified an increase in frequency, duration, intensity and extension of marine heatwave events over the satellite period 1982–2016. Moreover, surface primary production was reduced during these events with implications for regional fisheries.

How to cite: Rodrigues, R., Taschetto, A., Sen Gupta, A., and Foltz, G.: From severe droughts in South America to marine heatwaves in the South Atlantic, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-5162,, 2020.

EGU2020-8636 | Displays | NP2.3

The role of spatial and temporal model resolution in a flood event storyline approach in Western Norway

Nathalie Schaller, Jana Sillmann, Malte Müller, Reindert Haarsma, Wilco Hazeleger, Trine Jahr Hegdahl, Timo Kelder, Gijs van den Oord, Albrecht Weerts, and Kirien Whan

A physical climate storyline approach is applied to an autumn flood event caused by an atmospheric river in the West Coast of Norway. The aim is to demonstrate the value and challenges of higher spatial and temporal resolution in simulating impacts. The modelling chain used is the same as the one used operationally, to issue flood warnings for example. Its output is therefore familiar to many users, which we expect will facilitate stakeholder engagement. Two different versions of a hydrological model are run to show that on the one hand, the higher spatial resolution between the global and regional model is necessary to realistically simulate the high spatial variability of precipitation in such a mountainous region. On the other hand we also show that the intensity of the peak streamflow is only captured realistically with hourly data. The higher resolution regional atmospheric model is able to simulate the fact that with the passage of an atmospheric river, some valleys receive high amounts of precipitation and others not. However, the coarser resolution global model shows uniform precipitation in the whole region. Translating the event into the future leads to similar results: while in some catchments, a future flood might be 50% larger than a present one, in others no event occurs because the atmospheric river does not hit that catchment.

How to cite: Schaller, N., Sillmann, J., Müller, M., Haarsma, R., Hazeleger, W., Jahr Hegdahl, T., Kelder, T., van den Oord, G., Weerts, A., and Whan, K.: The role of spatial and temporal model resolution in a flood event storyline approach in Western Norway, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-8636,, 2020.

EGU2020-12772 | Displays | NP2.3 | Highlight

Causality and information transfer in systems with extreme events

Milan Palus

The mathematical formulation of causality in measurable terms of predictability was given by the father of cybernetics N. Wiener [1] and formulated for time series by C.W.J. Granger [2]. The Granger causality is based on the evaluation of predictability in bivariate autoregressive models. This concept has been generalized for nonlinear systems using methods rooted in information theory [3,4]. The information-theoretic approach, defining causality as information transfer, has been successful in many applications and generalized to multivariate data and causal networks [e.g., 5]. This approach, rooted in the information theory of Shannon, usually ignores two important properties of complex systems, such as the Earth climate: the systems evolve on multiple time scales and their variables have heavy-tailed probability distributions. While the multiscale character of complex dynamics, such as air temperature variability, can be studied within the Shannonian framework [6, 7], the entropy concepts of Rényi and Tsallis have been proposed to cope with variables with heavy-tailed probability distributions. We will discuss how such non-Shannonian entropy concepts can be applied in inference of causality in systems with heavy-tailed probability distributions and extreme events, using examples from the climate system.

This study was supported by the Czech Science Foundation, project GA19-16066S.


 [1] N. Wiener, in: E. F. Beckenbach (Editor), Modern Mathematics for Engineers (McGraw-Hill, New York, 1956)

[2] C.W.J. Granger, Econometrica 37 (1969) 424

[3] K. Hlaváčková-Schindler et al., Phys. Rep. 441 (2007)  1

[4] M. Paluš, M. Vejmelka, Phys. Rev. E 75 (2007) 056211

[5] J. Runge et al., Nature Communications 6 (2015) 8502

[6] M. Paluš, Phys. Rev. Lett. 112 (2014) 078702

 [7] N. Jajcay, J. Hlinka, S. Kravtsov, A. A. Tsonis, M. Paluš, Geophys. Res. Lett. 43(2) (2016) 902–909

How to cite: Palus, M.: Causality and information transfer in systems with extreme events, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-12772,, 2020.

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Early warning of the Pacific Decadal Oscillation phase transition using complex network analysis

Zhenghui Lu, Naiming Yuan, Zhuguo Ma, Qing Yang, and Juergen Kurths

The different phases of the Pacific Decadal Oscillation (PDO) are a primary source of internal decadal climate variability which have distinct impacts on global climate and human society. However, obtaining a reliable prediction of the PDO phase transition is still challenging. Here, we employed the new technique of climate network analysis to uncover early warning signals prior to a PDO phase transition. An examination of cooperative behaviors in the PDO region revealed an enhanced signal that propagated from the western Pacific, passed through the Kuroshio extension (KE) and the subtropical oceanic frontal (STF) regions, and finally reached the northwest coast of the Americas. This signal captured all six of the PDO phase transitions from the 1890s to 2000s, with a warning time of 6.5±2.3 years in advance. It also underpinned the possible PDO phase transition at years around 2015, which may be triggered by the strong El Niño in 2014-2016.

How to cite: Lu, Z., Yuan, N., Ma, Z., Yang, Q., and Kurths, J.: Early warning of the Pacific Decadal Oscillation phase transition using complex network analysis, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-13047,, 2020.

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Robust extreme value analysis: the bulk matching method

Frank Kwasniok

Traditional extreme value analysis based on the generalised ex-
treme value (GEV) or generalised Pareto distribution (GPD) suffers
from two drawbacks: (i) Both methods are wasteful of data as only
block maxima or exceedances over a high threshold are taken into ac-
count and the bulk of the data is disregarded. (ii) Moreover, in the
GPD approach, there is no systematic way to determine the threshold
parameter. Here, all the data are fitted simultaneously using a gener-
alised exponential family model for the bulk and a GPD model for the
tail. At the threshold, the two distributions are linked together with
appropriate matching conditions. The model parameters are estimated
from the likelihood function of all the data. Also the threshold param-
eter can be determined via maximum likelihood in an outer loop. The
method is exemplified on wind speed data from an atmospheric model.

How to cite: Kwasniok, F.: Robust extreme value analysis: the bulk matching method , EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-22377,, 2020.

EGU2020-1723 | Displays | NP2.3

A Dynamical Systems Characterisation of Atmospheric Jet Regimes in a Simple Model and Reanalysis Data

Nili Harnik, Gabriele Messori, Erica Madonna, Orly Lachmy, and Davide Farranda

Atmospheric jet streams are typically separated into primarily "eddy-driven", or "polar-front" jets and primarily "thermally-driven", or "subtropical" jets. Some regions also display “merged” jets, resulting from the (quasi) co-location of the regions of eddy generation with the subtropical jet. The different location and driving mechanisms of the two jet structures, plus the intermediate “merged” jet, issue from very different underlying mechanisms, and result in very different jet characteristics. Here, we link our understanding of the dynamical jet maintenance mechanisms, mostly issuing from conceptual or idealised models, to the phenomena observed in reanalysis data. We specifically focus on developing a unitary analysis framework, grounded in dynamical systems theory, which may be applied to both the model and reanalysis data and allow for direct intercomparison. Our results provide a proof-of-concept for using dynamical systems indicators to diagnose jet regimes in a versatile, conceptually intuitive and computationally efficient fashion.

How to cite: Harnik, N., Messori, G., Madonna, E., Lachmy, O., and Farranda, D.: A Dynamical Systems Characterisation of Atmospheric Jet Regimes in a Simple Model and Reanalysis Data, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-1723,, 2020.

EGU2020-5626 | Displays | NP2.3

Increasing Strength of Compound Hot-Wet Dynamical Extremes Over the Mediterranean

Paolo De Luca, Gabriele Messori, Davide Faranda, and Dim Coumou

The Mediterranean (MED) basin is a hot-spot for climate change impacts. We present recently developed techniques derived from Dynamical System Theory to investigate long-term changes in compound hot-wet extremes over the MED. We use three reanalysis products, spanning a 40-year period from 1979 to 2018: ERA5, ERA-Interim and ERA5 10-member ensemble. From these datasets, we extract daily maximum temperature (degC) and total precipitation (mm), which we then use in the dynamical systems analysis.

Results show that the strength of the dynamical coupling between hot and wet extremes increased significantly at both annual and summer (June-August) timescales during the reanalysis period. This means that, regardless of changes in the occurrence of individual hot or wet extremes, joint occurrences may be becoming more frequent.

Compound hot-wet extremes mostly occur during July and August, and correspond to a low-pressure core over the Aegean Sea and the eastern MED. The increasing trends in compound extremes may be associated with surface MED warming. Such enhanced warming can therefore drive compound hot-wet extremes especially during the summer, when localised convection or mesoscale systems such as medicanes are responsible for extreme precipitation events.

How to cite: De Luca, P., Messori, G., Faranda, D., and Coumou, D.: Increasing Strength of Compound Hot-Wet Dynamical Extremes Over the Mediterranean, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-5626,, 2020.

EGU2020-7579 | Displays | NP2.3 | Highlight

Dynamical Systems Theory Sheds New Light on Compound Climate Extremes in Europe and Eastern North America

Flavio Pons, Paolo De Luca, Gabriele Messori, and Davide Faranda

We propose a novel approach to the study of compound extremes, grounded in dynamical systems theory. Specifically, we present the co-recurrence ratio (α), which elucidates the dependence structure between maps by quantifying their joint recurrences. This approach is applied to daily climate extremes, derived from the ERA-Interim reanalysis over the 1979-2018 period. The analysis focuses on concurrent (i.e. same-day) wet (total precipitation) and windy (10m wind gusts) extremes in Europe and concurrent cold (2m temperature) extremes in Eastern North America and wet extremes in Europe. Results for wet and windy extremes in Europe, which we use as a test-bed for our methodology, show that α peaks during boreal winter. High αvalues correspond to wet and windy extremes in north-western Europe, and to large-scale conditions resembling the positive phase of the North Atlantic Oscillation (NAO). This confirms earlier findings which link the positive NAO to a heightened frequency of extra-tropical cyclones impacting north-western Europe, resulting in frequent wet and windy extremes. For the Eastern North America-Europe case, α extremes once again reflect concurrent climate extremes -- in this case cold extremes over North America and wet extremes over Europe. Our analysis provides detailed spatial information on regional hotspots for these compound extreme occurrences, and encapsulates information on their spatial footprint which is typically not included in a conventional co-occurrence analysis. We conclude that α successfully characterises compound extremes by reflecting the evolution of the associated meteorological maps. This approach is entirely general, and may be applied to different types of compound extremes and geographical regions.

How to cite: Pons, F., De Luca, P., Messori, G., and Faranda, D.: Dynamical Systems Theory Sheds New Light on Compound Climate Extremes in Europe and Eastern North America, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-7579,, 2020.

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Evaluation of CMIP6 simulations of temperature extremes using proper evaluation methods, observations and reanalyses

Thordis Thorarinsdottir, Jana Sillmann, and Marion Haugen

Climate models aim to project future changes in important drivers of climate including atmosphere, oceans and ice, and their interactions. A comprehensive evaluation of climate models thus requires evaluation methods, or performance measures, that are flexible, specific and can address also extreme events. Climate models have traditionally been assessed by comparing summary statistics or point estimates that derive from the simulated model output to corresponding observed quantities using e.g. RMSE. However, it has been argued persuasively that probability distributions of model output need to be compared to the corresponding empirical distributions of observations or observation-based data products. Observation-based gridded datasets for climate extremes, despite having limitations, are particularly useful and necessary to assess model performance with respect to extremes.  We discuss proper performance measures for comparing distributions of model output against corresponding distributions from data products that are flexible and robust enough to handle the particular aspects of extremes such as limited data availability. The new measures are applied to evaluate CMIP5 and CMIP6 projections of extreme temperature indices over Europe and North-America against the HadEX2 data set as well as the ERA5 and ERA-Interim reanalyses. Several models perform well to the extent that when compared to the HadEX2 data product, these models' performance is competitive with the performance of the reanalysis. While the model rankings vary with region, season and index, the model evaluation is robust against changes in the grid resolution considered in the analysis. 

How to cite: Thorarinsdottir, T., Sillmann, J., and Haugen, M.: Evaluation of CMIP6 simulations of temperature extremes using proper evaluation methods, observations and reanalyses, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-5279,, 2020.

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Extreme Value Theory for Observations

Theophile caby, Davide Faranda, Sandro Vaienti, and Pascal Yiou

We study the properties of recurrence of a smooth observable computed along a trajectory of a chaotic system near a particular value of interest .  Using the framework of Extreme Value Theory, we are able to derive a limit law which is a Gumbel  distribution whose parameters relate to the dimensions of the image measure. We show that this approach allows to have access to the fine structure of the attractor, by using directly observational data. In particular, we are able to compute local dimensions associated to the underlying attractor whenever the dimensionality of the observable is larger than the dimension of the attractor. 

How to cite: caby, T., Faranda, D., Vaienti, S., and Yiou, P.: Extreme Value Theory for Observations, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-5795,, 2020.

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Evaluating CMIP6 Model Fidelity at Simulating Non-Gaussian Temperature Distribution Tails

Arielle Catalano, Paul Loikith, and J. David Neelin

Under global warming, changes in extreme temperatures will manifest in more complex ways in locations where temperature distribution tails deviate from Gaussian. For example, uniform warming applied to a temperature distribution with a shorter-than-Gaussian warm tail would lead to greater exceedances in warm-side temperature extremes compared with a Gaussian distribution. Confidence in projections of future temperature extremes and associated impacts under global warming therefore relies on the ability of global climate models (GCMs) to realistically simulate observed temperature distribution tail behavior. This presentation examines the ability of the latest state-of-the-art ensemble of GCMs from the Coupled Model Intercomparison Project phase six (CMIP6) to capture historical global surface temperature distribution tail shape in hemispheric winter and summer seasons. Comparisons between the multi-model ensemble mean and a reanalysis product reveal strong agreement on coherent spatial patterns of longer- and shorter-than-Gaussian tails for the cold and warm sides of the temperature distribution, suggesting that CMIP6 is broadly capturing tail behavior for plausible physical and dynamical reasons. Most individual GCMs are also reasonably skilled at capturing historical tail shape on a global scale, but a division of the domain into sub-regions reveals considerable model and spatial variability. To explore potential mechanisms driving these differences, a back trajectory analysis examining patterns in the origin of air masses on days experiencing extreme temperatures is also discussed.

How to cite: Catalano, A., Loikith, P., and Neelin, J. D.: Evaluating CMIP6 Model Fidelity at Simulating Non-Gaussian Temperature Distribution Tails, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-6113,, 2020.

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The thermal waters of the Portugal Star Geopark - methods for understanding its origin and sustainable exploitation.

Elsa Salzedas

EGU2020-7555 | Displays | NP2.3 | Highlight

Simulating compound weather extremes responsible for critical crop failure with stochastic weather generators

Pascal Yiou, Peter Pfleiderer, Aglaé Jézéquel, Juliette Legrand, Natacha Legrix, Jason Markantonis, and Edoardo Vignotto

In 2016, northern France experienced an unprecedented wheat crop loss. This extreme event was likely due to particular meteorological conditions, i.e.  too few cold days in late autumn and an abnormally high precipitation during the spring season. The cause of this event is not fully understood yet and none of the most used crop forecast models were able to predict the event (Ben-Ari et al, 2018).  

This work is motivated by two main questions: were the 2016 meteorological conditions the most extreme we could imagine under current climate? and what would be the worst case scenario we could expect that could lead to even worst crop loss? To answer these questions, instead of relying on computationally intensive climate model simulations, we use an analogue based importance sampling algorithm that was recently introduced into this field of research (Yiou and Jézéquel, 2019). This algorithm is a modification of a stochastic weather generator (SWG), which gives more weight to trajectories with more extreme meteorological conditions (here temperature and precipitation). This data driven technique constructs artificial weather events by combining daily observations in a dynamically realistic manner and in a relatively fast way.

This is the first application of SWGs to simulate warm winters and wet springs. We show that with some adjustments both (new) weather events can be adequately simulated with SWGs, highlighting the wide applicability of the method. 

While the number of cold days in late autumn 2015 was close to the plausible maximum, our simulations of extreme spring precipitation show that considerably wetter springs than what was observed in 2016 are possible. Although the crop loss of 2016 is not fully understood yet, these results indicate that similar events with higher impacts could be possible.

How to cite: Yiou, P., Pfleiderer, P., Jézéquel, A., Legrand, J., Legrix, N., Markantonis, J., and Vignotto, E.: Simulating compound weather extremes responsible for critical crop failure with stochastic weather generators, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-7555,, 2020.

Heatwaves are likely to occur more frequent, longer, and stronger due to the rise in CO2 concentrations. It is related to the change in the mean of a climate distribution, as well as through the change in variance. Mega-heatwaves, in particular, have a crucial impact on human health. Many studies are trying to understand the mechanisms of mega-heatwaves and also their characteristics included amplitude, duration, frequency. In spite of these efforts, researches are limited because of the small number of mega-heatwaves. In order to overcome these limitations, Earth system model should be needed. This study aims to figure out the comprehensive characteristics of mega-heatwaves using Community Earth System Model (CESM). First, the possibility of the occurrence of mega-heatwaves in preindustrial period in Europe was analyzed. Second, the relation between decadal climate variabilities and mega-heatwaves was investigated. In addition, changes in characteristics of mega-heatwaves were compared between preindustrial and present-day simulations.

How to cite: Shin, J. and An, S.-I.: Comparison of mega-heatwaves in preindustrial and present-day simulations over Europe, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-8006,, 2020.

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Influence of Pacific Decadal Oscillation on global precipitation extremes on decadal time scales

Wenguang Wei, Zhongwei Yan, and Zhen Li

On the decadal time scales, while the influence of Pacific Decadal Oscillation (PDO) on total or average precipitation had been extensively studied, works about its influence on precipitation extremes were limited, especially lack of a global picture.  Using two independent methods, nonstationary generalized extreme value (GEV) model which directly incorporates PDO index into its location parameter and moving GEV model which fits the annual extremes with a sliding window of 30 years and regresses the resulted changing location parameter onto the PDO index, we show that precipitation extremes over a large portion of stations are significantly affected by the PDO with stations in the Pacific Rim demonstrating distinct regional patterns. Over eastern China, the famous ‘southern flood and norther drought’ pattern corresponding to a positive PDO phase extends to extreme rainfalls; over Australia, a tri-polar pattern was revealed, in which the extremes over central Australia positively correlate with the PDO index and those over eastern and western Australia show a negative correlation; and the North America also demonstrates a dipole pattern, by which the northwest (southeast) experiences less (more) intense extreme rainfall in a PDO positive phase. Moreover, the western Europe and the large area between the Ural mountain and eastern Europe were discovered to hold a positive correlation with the PDO in their precipitation extremes. A comparative analysis to the local circulation controlling the precipitation extremes under different PDO phases further confirms the discovered relationships above. These findings have important implication for the future projection of extreme precipitation over related regions because the internal climate variability should be appropriately accounted for beyond the effects induced by global warming.

How to cite: Wei, W., Yan, Z., and Li, Z.: Influence of Pacific Decadal Oscillation on global precipitation extremes on decadal time scales, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-8138,, 2020.

EGU2020-12919 | Displays | NP2.3

Model evaluation for Heatwaves over South Korea in CMIP6 models

Ji-Seon Oh, Maeng-Ki Kim, Dae-Geun Yu, and Jeong Sang

In this study, we defined diagnostic indices to evaluate the CMIP6 models based on the heatwaves mechanisms of Korea presented in previous studies. Based on this, the simulation performance of the model was quantitatively evaluated using Relative Error (RE), Inter-annual Variability Skill-score (IVS), and Correlation Coefficient (CC). The REs in diagnostic indices are still large, especially in heat wave circulation index (HWCI) and Indian summer monsoon rainfall index (IMRI), which is mainly due to weak convective activity bias over the northwestern Pacific Ocean and the northwestern India. However, the IVSs in diagnostic indices have been improved overall in the CMIP6 compared to the CMIP5, especially in the IMRI. The CC between the daily maximum temperature (TMAX) and the diagnostic factors in the model is very higher in HWCI than other indices, indicating that the convective activity over the northwestern Pacific is very important in heat wave in Korea. As a result, the total ranking of the model performance for heatwaves in Korea suggested that EC-Earth3-Veg, EC-Earth3, and UKESM-1-0-LL ranked high in CMIP6.


This work was funded by the Korea Meteorological Administration Research and Development Program under Grant KMI(KMI2018-03410)

How to cite: Oh, J.-S., Kim, M.-K., Yu, D.-G., and Sang, J.: Model evaluation for Heatwaves over South Korea in CMIP6 models, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-12919,, 2020.

EGU2020-13717 | Displays | NP2.3

Predictability of large scale drivers leading intense Mediterranean cyclones

M. Carmen Alvarez-Castro, Silvio Gualdi, Pascal Yiou, Mathieu Vrac, Robert Vautard, Leone Cavicchia, David Gallego, Pedro Ribera, Cristina Pena-Ortiz, and Davide Faranda

Windstorms, extreme precipitations and instant floods seems to strike the Mediterranean area with increasing frequency. These events occur simultaneously during intense tropical-like Mediterranean cyclones. These intense Mediterranean cyclones are frequently associated with wind, heavy precipitation and changes in temperature, generating high risk situations such as flash floods and large-scale floods with significant impacts on human life and built environment. Although the dynamics of these phenomena is well understood, little is know about their climatology. It is therefore very difficult to make statements about the frequency of occurrence and its response to climate change. Thus, intense Mediterranean cyclones have many different physical aspects that can not be captured by a simple standard approach. 

The first challenge of this work is to provide an extended catalogue and climatology of these phenomena by reconstructing a database of intense Mediterranean cyclones dating back up to 1969 using the satellite, the literature and reanalyses. Applying a method based on dynamical systems theory we analyse and attribute their future changes under different anthropogenic forcings by using future simulations within CMIP framework. Preliminary results show a decrease of the large-scale circulation patterns favoring intense Mediterranean cyclones in all the seasons except summer.

How to cite: Alvarez-Castro, M. C., Gualdi, S., Yiou, P., Vrac, M., Vautard, R., Cavicchia, L., Gallego, D., Ribera, P., Pena-Ortiz, C., and Faranda, D.: Predictability of large scale drivers leading intense Mediterranean cyclones, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-13717,, 2020.

EGU2020-19940 | Displays | NP2.3

Application of an artificial neural network to generate wave projections at southern African coasts

Felix Soltau, Matthias Hirt, Jessica Kelln, Sara Santamaria-Aguilar, Sönke Dangendorf, and Jürgen Jensen

In the past decades, severe so called ‚compound events‘ led to critical high water levels at the coasts of southern Africa and as a consequence to property damage and loss of human life. The co-occurrence of storm surges, wind waves, heavy precipitation and resulting runoff increases the risk of coastal flooding and exacerbates the impacts along the vulnerable southern African coasts (e.g. Couasnon et al. 2019). To mitigate these high-impacts, it is essential to understand the underlying processes and driving factors (Wahl et al. 2015). As compound flooding events at southern African coasts are dominated by wind waves, it is of great importance to investigate the regional wave climate to understand the wave forcing as well as the origin of the wave energy.

Wind waves around southern African coasts are affected by the complex interactions between the Agulhas current and the atmosphere. In the research project CASISAC* we analyse the present evolution of the Agulhas Current system and quantify its impact on the future regional wave climate. Ocean waves contributing to high sea levels can be generated offshore resulting in swell or closer to the coasts by strong onshore winds. To identify responsible atmospheric pressure fields that force high wind wave events we apply a hybrid approach: (1) linking south hemispheric pressure fields with offshore wave data using an artificial neural network and (2) determine the prevailing nearshore wave conditions by regional numerical wave propagation models (SWAN). By validating the modelled nearshore wave data from hindcast runs with wave buoy records, this approach allows us to predict future extreme wind wave events and thus potential flooding. In a next step, extreme value analysis is used to determine future return periods of extreme wave events. These results can contribute to the development of more reliable adaptive protection strategies for southern African coast.

*CASISAC (Changes in the Agulhas System and its Impact on Southern African Coasts: Sea level and coastal extremes) is funded by the German Federal Ministry of Education and Research (BMBF) through the project management of Projektträger Jülich PTJ under the grant number 03F0796C


Couasnon, Eilander, Muis, Veldkamp, Haigh, Wahl, Winsemius, Ward (2019): Measuring compound flood potential from river discharge and storm surge extremes at the global scale and its implications for flood hazard. In: Natural Hazards and Earth System Sciences, Discussion Paper, S. 1–24. DOI: 10.5194/nhess-2019-205, in review.
Wahl, Jain, Bender, Meyers, Luther (2015): Increasing risk of compound flooding from storm surge and rainfall for major US cities. In: Nature Climate Change 5 (12), S. 1093–1097. DOI: 10.1038/nclimate2736.

How to cite: Soltau, F., Hirt, M., Kelln, J., Santamaria-Aguilar, S., Dangendorf, S., and Jensen, J.: Application of an artificial neural network to generate wave projections at southern African coasts, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-19940,, 2020.

NP4.1 – Complex geoscientific time series: linear, nonlinear, and computer science perspectives

The complex soil biome is a center piece in providing essential ecosystem services that humans rely on (carbon sequestration, food security, one-health interactions).  Agricultural engineers and soil scientists are developing wireless sensor networks (WSN) that collect large/big data on the soil key state variables (water content, temperature, chemistry) to better understand the soil biome primary environmental drivers. The profession extracts information from WSN records with methods including soil-process modeling and artificial-intelligence (AI) algorithms.  However, these approaches carry their own limitations.  A recent review article faulted current soil-process modeling for inadequately detecting and resolving model structural (abstraction) errors.  AI experts themselves caution against indiscriminant use of AI methods because of: a) problems including replication of past results due to inconsistent experimental methods; b) difficulty in explaining how a particular method arrives at its conclusions (the black box problem) and thus in correcting algorithms that learn ‘bad lessons’; and c) lack of rigorous criteria for selecting AI architectures.  An alternative approach to address these limitations is to investigate new strategies for reducing large/big data problems into smaller, more interpretable causal abstractions of the soil system.  

We develop an innovative data diagnostics framework—based on empirical nonlinear dynamics techniques from physics—that addresses the above concerns over soil-process modeling and AI algorithms.  We diagnose whether WSN and other similar environmental large/big data are likely generated by dimension-reducing (i.e., dissipative) nonlinear dynamics.  An n-dimensional nonlinear dynamic system is dissipative if long-term dynamics are bounded within m<<n dimensions, so that the problem of modeling long-term dynamics shrinks by the n-m inactive degrees of freedom.  If so, long-term system dynamics can be investigated with relatively few degrees of freedom that capture the complexity of the overall system generating observed data.  To make this diagnosis, we first apply signal processing to isolate structured variation (signal) from unstructured variation (noise) in large/big data time series records, and test signals for nonlinear stationarity.  We resolve the structure of isolated signals by distinguishing between stochastic-forcing and deterministic nonlinear dynamics; reconstruct phase space dynamics most likely generating signals, and test the statistical significance of reconstructed dynamics with surrogate data.  If the reconstructed phase space is dimension-reducing, we can formulate low-dimensional (phenomenological) ODE models to investigate nonlinear causal interactions between key soil environmental driving factors.  When we do not diagnose dimension-reducing nonlinear real-world dynamics, then underlying dynamics are most likely high dimensional and the information-extraction problem cannot be shrunk without losing essential dynamic information. In this case, other high-dimensional analysis techniques like AI offer a better modeling alternative for mapping out interactions.  Our framework supplies a decision-support tool for data practitioners toward the most informative and parsimonious information-extraction method—a win-win result.       

We will share preliminary results applying this empirical framework to three soil moisture sensor time series records analyzed with machine learning methods in Bean, Huffaker, and Migliaccio (2018).

How to cite: Huffaker, R. and Munoz-Carpena, R.: A nonlinear dynamics approach to data-enabled science: Reconstructing soil-moisture dynamics from big data collected by wireless sensor networks, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-1313,, 2020.

EGU2020-8763 | Displays | NP4.1 | Highlight

Probability estimation of a Carrington-like geomagnetic storm

Isabel Serra, David Moriña, Pere Puig, and Álvaro Corral

Intense geomagnetic storms can cause severe damage to electrical systems and communications. this work proposes a counting process with Weibull inter-occurrence times in order to estimate the probability of extreme geomagnetic events. It is found that the scale parameter of the inter-occurrence time distribution grows exponentially with the absolute value of the intensity threshold defining the storm, whereas the shape parameter keeps rather constant. The model is able to forecast the probability of occurrence of an event for a given intensity threshold; in particular, the probability of occurrence on the next decade of an extreme event of a magnitude comparable or larger than the well-known Carrington event of 1859 is explored, and estimated to be between 0.46% and 1.88% (with a 95% confidence), a much lower value than those reported in the existing literature.

How to cite: Serra, I., Moriña, D., Puig, P., and Corral, Á.: Probability estimation of a Carrington-like geomagnetic storm, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-8763,, 2020.