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Chaotic variability and modeling uncertainties in the ocean

Theoretical and model studies show that the ocean is a chaotic system which spontaneously generates a strong, multi-scale intrinsic chaotic variability: uncertainties in ocean model initial states may grow and strongly affect the simulated variability up to multi-decadal and basin scales, with or without coupling to the atmosphere. In addition, ocean simulations require both the use of subgrid-scale parameterizations that crudely mimic unresolved processes, and the calibration of the parameters associated with these parameterizations. In this context of multiple uncertainties, oceanographers are increasingly adopting ensemble simulation strategies, probabilistic analysis methods, and developing stochastic parameterizations for modeling and understanding ocean variability.

Presentations are solicited about the conception and analysis of ocean ensemble simulations, the characterization of ocean model uncertainties, and the development of stochastic parameterizations for ocean models. The session will also cover the dynamics and structure of chaotic ocean variability, its relationship with atmospheric variability, and the use of dynamical system or information theories for the investigation of oceanic variability. We welcome as well studies about the propagation of chaotic ocean variability towards other components of the climate system, about its consequences regarding ocean predictability, operational forecasts, detection and attribution of climate signals, climate simulations and projections.

Co-organized by NP2
Convener: Thierry Penduff | Co-conveners: William K. Dewar, Sally Close, Guillaume SérazinECSECS
| Mon, 23 May, 08:30–09:52 (CEST)
Room 1.15/16

Mon, 23 May, 08:30–10:00

Chairpersons: Thierry Penduff, William K. Dewar

Ryo Furue et al.

It has been known for some time that the ocean basins are populated by what is known as ‘‘zonal jets’’, ‘‘deep zonal jets’’, or ‘‘striations’’. Since the oceanic flow is, at least weakly, chaotic, it is not known whether the positions of the jets are ‘‘deterministic’’, that is, entirely determined by external parameters. A number of theories have been proposed to explain them, some of them predicting zonal jets at fixed latitudes and others implying that the positions of the jets are random. To investigate how deterministic the zonal jets are in the eastern North Pacific, a ten-member ensemble of long-term integrations of a semi-global, eddy-resolving ocean general circulation model is analyzed.

The positions of the equatorial jets, even their variability, seem to obey deterministic dynamics and some of the jets in the tropics (5°–15°N) migrate poleward coherently (similarly between ensemble members). The jets in the subtropics (15°–45°N) systematically migrate equatorward but their positions are less coherent; the jets in the subpolar region (45°N–) are random and without systematic migration. Jets near the coast of North and South America tend to have shorter meridional wavelengths than interior ones and those in the northern hemisphere are fairly coherent whereas those in the southern hemisphere seem more random. There are a few quasi-barotropic jets which are anchored to steep bottom topographic features and which also appear to trap shallower counter-flows on their poleward and equatorward flanks.

How to cite: Furue, R., Nonaka, M., and Sasaki, H.: Zonal jets in the eastern North Pacific in an ensemble of eddy-resolving ocean general circulation model runs, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-6754, https://doi.org/10.5194/egusphere-egu22-6754, 2022.

Angelo Rubino et al.

Intrinsic chaotic variability in the oceans is an active field of research in modern oceanography, with important implications concerning the understanding and predictability of the ocean system. The focus is mainly on open ocean basins while very little attention is devoted to enclosed or semi-enclosed seas. The intrinsic variability of the Mediterranean Sea, in particular, has not yet been investigated. Here, results obtained with an eddy-resolving nonlinear multilayer ocean model are presented shedding light on relevant aspects of the intrinsic low-frequency variability of the Mediterranean Sea circulation.

An ensemble of multi-centennial ocean runs is performed to allow for a significant statistical analysis. The statistically stationary state obtained after long simulations shows a robust meridional structure consistent with the observed Mediterranean mean state. Among the various features emerging in the decadal and multidecadal temporal ranges are abrupt shifts in the water mass stratification structure. Differences and similarities with observed patterns are finally discussed. 

How to cite: Rubino, A., Pierini, S., Rubinetti, S., and Zanchettin, D.: Intrinsic low-frequency variability of the Mediterranean Sea circulation studied using a multilayer ocean model, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-2167, https://doi.org/10.5194/egusphere-egu22-2167, 2022.

Lin Lin et al.

Internal variability, unprovoked by external forcing, emerges in the hydrodynamics of the marginal seas. Ensemble ocean simulations are used to analyze the characteristics, scales, and intensities of such variability in the Bohai, Yellow Sea, and South China Sea. With the signal defined as the covariation in the ensemble, and the noises as the independent variations, a scale dependency of the Signal-to-Noise Ratio (S/N ratio) is found in the Bohai, Yellow Sea, and South China Sea. The external forcing and related signal are dominant for large scales, while most of the internal variability is generated for small scales. The intensities of internal variability of the Bohai and Yellow sea are about half of the intensities of South China Sea, likely because eddies are less energetic in the Bohai and Yellow Sea, which likely is the main source of noise in South China Sea.

In addition, we investigate the effect of tides on internal variability in the Bohai and Yellow Sea by three ensembles of numerical experiments with tidal forcing, with half tidal forcing, and without tidal forcing. When the tides are weakened or turned off, the S/N ratios are reduced in large and medium scales, more so in the Yellow Sea than in the Bohai. The increase in the S/N ratio is largest for large scales and for depth-averaged velocity. The reduction in tidal forcing results in an approximately 30% increase in S/N ratios in the Bohai at large scales. Thus, the absence of tidal forcing favours the emergence of unprovoked variability at large and medium scales but not at small scales. We suggest that the main mechanism for the increase of covarying variability when tides are active, is the additional mixing induced by the tides.

How to cite: Lin, L., von Storch, H., Chen, X., and Tang, S.: The Characteristics and Significance of Hydrodynamical Internal Variability in Modelling Dynamics in Marginal Seas, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-1973, https://doi.org/10.5194/egusphere-egu22-1973, 2022.

William K. Dewar et al.

An ensemble of North Atlantic simulations is analyzed, providing estimates of kinetic energy spectra.  A wavelet transform technique is used permitting comparisons to be made between spectra at different locations in this highly inhomogeneous environment.  We find a strong tendency towards anisotropy in the spectra, with meridional spectra typically stronger than zonal spectra.  This holds even in the gyre interior where conditions might be expected to be homogeneous.  The spectra show reasonable ranges consistent with a downscale enstrophy cascade, but also a persistent tendency to exhibit steeper slopes at smaller scales.  The only location where the presence of an upscale cascade is supported is the Gulf Stream extension.  This is amongst first attempts to quantify and compare spectra and their differences in the inhomogeneous setting of the North Atlantic.

How to cite: Dewar, W. K., Uchida, T., Jamet, Q., and Poje, A.: The Structure of North Atlantic Kinetic Energy Spectra, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-2849, https://doi.org/10.5194/egusphere-egu22-2849, 2022.

Takaya Uchida et al.

The analysis of eddy-mean flow interaction provides key insights into the structures and dynamics of inhomogeneous and anisotropic flows such as atmospheric and oceanic jets. As the divergence of Eliassen-Palm (E-P) flux formally encapsulates the interaction, the community has had a long-standing interest in accurately diagnosing this term. Here, we revisit the E-P flux divergence with an emphasis on the Gulf Stream, using a 48-member, eddy-rich (1/12°) ensemble of the North Atlantic ocean partially coupled to identical atmospheric states amongst all members via an atmospheric boundary layer model. This dataset allows for an unique decomposition where we define the mean flow as the ensemble mean, and interpret it as the oceanic response to the atmospheric state. The eddies are subsequently defined as fluctuations about the ensemble mean. Our results highlight two points: i) the implementation of the Thickness-Weighted Averaged (TWA) framework for a realistic ocean simulation in diagnosing the E-P flux divergence, and ii) validity of the ergodic assumption where one treats the temporal mean equivalent to the ensemble mean, which is questionable for a temporally varying system such as the ocean and climate.

How to cite: Uchida, T., Jamet, Q., Dewar, W., Le Sommer, J., Penduff, T., and Balwada, D.: Diagnosing the thickness-weighted averaged eddy-mean flow interaction from an eddying North Atlantic ensemble, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-770, https://doi.org/10.5194/egusphere-egu22-770, 2022.

Quentin Jamet et al.

Understanding processes associated with eddy-mean flow interactions helps our interpretation of the ocean energetic balance, and guides the development of parameterizations. Here, we focus on the non-local nature of Kinetic Energy (KE) transfers between mean (MKE) and turbulent (EKE) reservoirs. Following previous studies, we interpret these transfers as non-local when the energy extraction from the mean flow does not locally sustain energy production of the turbulent flow, or vice versa. The novelty of our approach is to use ensemble statistics, rather than time averaging or coarse-graining methods, to define the mean and the turbulent flow. Based on KE budget considerations, we first rationalize the eddy-mean separation in the ensemble framework, and discuss the interpretation of a mean flow (<u>) driven by the prescribed (surface and boundary) forcing and a turbulent flow (u') driven by non-linear dynamics sensitive to initial conditions. Our results, based on the analysis of 120-day long, 20-member ensemble simulations of the Western Mediterranean basin run at 1/60o, suggest that eddy-mean kinetic energy exchanges are largely non-local at small scales. Our main contribution is to recognize the prominent contribution of the cross energy term (<u>.u') to explain this non-locality, providing a strong constraint on the horizontal organization of eddy-mean flow KE exchanges since this term vanishes identically for perturbations (u') orthogonal to the mean flow ( Our results also highlight the prominent contribution of vertical turbulent fluxes for energy exchanges within the surface mixed layer. Analyzing the scale dependence of these non-local energy exchanges supports the local approximation usually made in the development of meso-scale, energy-aware parameterizations for non-eddying models, but points out to the necessity of accounting for these non-local effects in the meso-to-submeso scale range.

How to cite: Jamet, Q., Leroux, S., Dewar, W. K., Penduff, T., Le Sommer, J., Molines, J.-M., and Gula, J.: Non-local eddy-mean kinetic energy transfers in submesoscale-permitting ensemble simulations, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-1428, https://doi.org/10.5194/egusphere-egu22-1428, 2022.

Chris Wilson et al.

Mesoscale eddy-permitting ocean models will be needed as a component of climate ensemble projections most likely for the next decade or more.   However, the kinetic energy and other measures of variability are typically an order of magnitude too weak at this nominal 0.25 degree lon-lat resolution.    This is predominantly due to excessive gridscale damping of momentum, needed for computational stability, which is believed to kill a large fraction of the energy source of the kinetic energy inverse cascade.   The KE inverse cascade is associated with the generation of intrinsic chaotic variability and ensemble spread, hence the estimation of potential predictability, but also with slower, larger-scale variability associated with climate.  The familiar Gent and McWilliams (1990) eddy parameterisation is problematic when applied to eddy-permitting models, where eddies are partially resolved, and it also tends to damp variability rather than energise it.   In response to this problem, several recent studies have focussed on the KE backscatter problem, which each attempt to increase the upscale transfer of KE, either deterministically or stochastically.

Stochastic parameterisation of sub-gridscale eddies has recently become a popular approach in ocean modelling, having been used in atmospheric modelling for many years, but there is still a diverse range of approaches for constraining either the underlying physics (how the forcing is applied) or the statistics (the spatiotemporal signature of the forcing).   This study explores some basic recipes for constructing the stochastic model from statistics of either observations or higher-resolution models.  The stochastic forcing, representing the sub-gridscale effects of eddies in our eddy-permitting simulations, is also applied adiabatically – to mimic the predominant behaviour of mesoscale eddies in the ocean interior and to preserve large-scale watermasses.   A theoretical challenge, which we explore, is to connect the applied, weakly imbalanced forcing, to a response in kinetic energy and upscale transfer.  This must also be applied without generating numerical instability.  

How to cite: Wilson, C., Hughes, C. W., Williams, S. D. P., and Blaker, A. T.: Adiabatic, Constrained, Stochastic Eddy Parameterisation, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-750, https://doi.org/10.5194/egusphere-egu22-750, 2022.

Long Li et al.

In this work, we aim to describe atmosphere-ocean coupling through a physically-based stochastic formulation. We adopt the framework of modelling under Location Uncertainty (LU) [Bauer2020a], which is based on a temporal-scale separation and a stochastic transport principle. One important characteristic of such random model is that it conserves the total energy of the resolved flow. This representation has been successfully tested for ocean-only models, such as the barotropic quasi-geostrophic (QG) model [Bauer2020b], the multi-layered QG model [Li2021], as well as the rotating shallow-water model [Brecht2021]. Here, we consider the ocean-atmosphere coupled QG model [Hogg2003]. The LU scheme has been tested for coarse-grid simulations, in which the spatial structure of ocean uncertainty is calibrated from eddy-resolving simulation data while the atmosphere component is parameterized from the ongoing simulation. In other words, the ocean dynamics has a data-driven stochastic component whereas the large-scale atmosphere dynamics is fully parameterized. Two major benefits of the resulting random model are provided on the coarse mesh: it enables us to reproduce the ocean eastward jet and its adjacent recirculation zones; it improves the prediction of intrinsic variability for both ocean and atmosphere components. These capabilities of the proposed stochastic coupled QG model are demonstrated through several statistical criteria and an energy transfers analysis.


  • [Bauer2020a] W. Bauer, P. Chandramouli, B. Chapron, L. Li, and E. Mémin. Deciphering the role of small-scale inhomogeneity on geophysical flow structuration: a stochastic approach. Journal of Physical Oceanography, 50(4):983-1003, 2020.
  • [Bauer2020b] W. Bauer, P. Chandramouli, L. Li, and E. Mémin. Stochastic representation of mesoscale eddy effects in coarse-resolution barotropic models. Ocean Modelling, 151:101646, 2020.
  • [Li2021] Li, L., 2021. Stochastic modelling and numerical simulation of ocean dynamics. PhD Thesis. Université Rennes 1.
  • [Brecht2021] Rüdiger Brecht, Long Li, Werner Bauer and Etienne Mémin. Rotating Shallow Water Flow Under Location Uncertainty With a Structure-Preserving Discretization. Journal of Advances in Modeling Earth Systems, 13, 2021MS002492.
  • [Hogg2003] A.M. Hogg, W.K. Dewar, P.D. Killworth, J.R. Blundell. A quasi-geostrophic coupled model (Q-GCM). Monthly Weather Review, 131:2261-2278, 2003.


How to cite: Li, L., Mémin, E., Chapron, B., and Lahaye, N.: Quasi-geostrophic coupled model under location uncertainty, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-5287, https://doi.org/10.5194/egusphere-egu22-5287, 2022.

Francesco Tucciarone et al.

Planetary flows and large scale circulation systems are characterised by an interaction between scales that range over several orders of magnitude, with contributions given by mesoscale and submesoscale dynamics. Resolving numerically  such interactions for realistic configuration is, however, far beyond reach. Any large-scale simulation must then rely on parameterizations of the effects of the small scales on  the large scales. In this work, a stochastic parameterization is proposed based on a decomposition of the flow in terms of a smooth-in-time large-scale contribution and a random fast-evolving uncorrelated small-scale part  accounting for  mesoscales and submesoscales unresolved eddies. This  approach, termed modelling under location uncertainty (LU) [4], relies on a stochastic version of Reynolds Transport Theorem to cast physically meaningful conservation principles in this scale-separated framework. Such a scheme has been successfully applied to several large-scale models of the  ocean dynamics [1, 2, 3, 5]. Here a LU version of the  hydrostatic primitive equations is  implemented within the  NEMO community code (https://www.nemo-ocean.eu) with a data-driven approach to establish the spatial correlation of the fast evolving scales. In comparison to a corresponding deterministic counterpart, this stochastic large-scale representation  is shown to improve, in terms of the eastward jet resolution and variabilities, the  flow prediction of an idealized wind forced double gyre circulation. The results are assessed through several statistical criterion as well as an energy transfer analysis [2,5].
[1] W. Bauer, P. Chandramouli, B. Chapron, L. Li, and E. Mémin. Deciphering the
role of small-scale inhomogeneity on geophysical flow structuration: a stochastic approach.
Journal of Physical Oceanography, 50(4):983-1003, 2020.
[2] W. Bauer, P. Chandramouli, L. Li, and E. Mémin. Stochastic representation of
mesoscale eddy effects in coarse-resolution barotropic models. Ocean Modelling, 151:101646,
[3] Rüdiger Brecht, Long Li, Werner Bauer and Etienne Mémin. Rotating Shallow
Water Flow Under Location Uncertainty With a Structure-Preserving Discretization. Journal of
Advances in Modeling Earth Systems, 13, 2021MS002492.
[4], E. Mémin Fluid flow dynamics under location uncertainty,(2014), Geophysical & Astrophysical Fluid Dynamics, 108, 2, 119–146.
[5] V. Resseguier, L. Li, G. Jouan, P. Dérian, E. Mémin, B. Chapron, (2021), New trends in ensemble forecast strategy: uncertainty quantification for coarse-grid computational fluid dynamics, Archives of Computational Methods in Engineering.

How to cite: Tucciarone, F., Li, L., and Memin, E.: Stochastic data-driven model of mesoscale and submesoscale eddies in gyre circulation, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-7907, https://doi.org/10.5194/egusphere-egu22-7907, 2022.

Nabir Mamnun et al.

Marine biogeochemical (BGC) models are important tools in the hands of scientists and policymakers when assessing the impacts of climate change. Therefore, including an ocean BGC component in Earth System Modeling efforts is essential for climate simulation and predictions. However, current BGC models, used to simulate and thus better understand the marine ecosystem processes, are associated with large undefined uncertainties. Similar to other geoscientific models, complex biological and chemical processes are converted to simplified schemes in BGCs, a methodology known as parameterization. However, these parameter values can be poorly constrained and also involve unknown uncertainties. In turn, the uncertainty in the parameter values translates into uncertainty in the model outputs. Therefore, a systematic approach to properly quantify the uncertainties of the parameters is needed. In this study, we apply an ensemble data assimilation method to quantify the uncertainty arising from the parameterization within BGC models. We apply an ensemble Kalman filter provided by the parallel data assimilation framework (PDAF) into a one-dimensional vertical configuration of the biogeochemical model Regulated Ecosystem Model 2 (REcoM2) at two BGC time-series stations: the Bermuda Atlantic Time-series Study (BATS) and the Dynamique des Flux Atmosphériques en Méditerranée (DYFAMED). Satellite chlorophyll-a concentration data and in situ net primary production data are assimilated to estimate ten selected biogeochemical parameters and the model state. We present convergence and interdependence features of the estimated parameters in relation to the major biological processes and discuss their uncertainties. The major improvements on the parameters involved changes in phytoplankton photosynthesis rate, chlorophyll degradation, and grazing. In general, the change in the estimates of these parameters results in improvements in the model prediction and reduced prediction uncertainty. 

How to cite: Mamnun, N., Völker, C., Vrekoussis, M., and Nerger, L.: Uncertainty in ocean biogeochemical simulation: Application of ensemble data assimilation to a one-dimensional model, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-3668, https://doi.org/10.5194/egusphere-egu22-3668, 2022.

Ulrike Löptien and Heiner Dietze

Anthropogenic emissions of greenhouse gases, such as CO2 and N2O, warm the earth. This in turn modulates the atmospheric greenhouse gas concentrations. The underlying feedback mechanisms are complex and can be counterintuitive. Earth system models have recently matured to standard tools tailored to assess and understand these feedback mechanisms. Along comes the need to determine poorly-known model parameters. This is especially problematic for the ocean biogeochemical component where respective observational data, such as nutrient concentrations and phytoplankton growth, are rather sparse in time and space. In the present study, we illustrate common problems when attempting to estimate such parameters based on typical model evaluation metrics. We find very different parameter sets which are, on the one hand, equally consistent with (synthetic) historical observations while, on the other hand, they propose strikingly differing projections into a warming climate. By the example of simulated oxygen concentrations we propose a step forward by applying variance-based sensitivity analyses to map the respective parameter uncertainties onto their local manifestations - for both contemporary climate and climate projections. The mapping relates local uncertainties of projections to the uncertainty of specific model parameters. In a nutshell, we present a practical approach to the general question of where the present-day model fidelity may be indicative for reliable projections.


How to cite: Löptien, U. and Dietze, H.: Linking contemporary parametric model uncertainties to projections of biogeochemical cycles, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-3044, https://doi.org/10.5194/egusphere-egu22-3044, 2022.

Armineh Barkhordarian et al.

Over the last decade, the northeast Pacific experienced strong marine heatwaves (MHWs) that produced devastating marine ecological impacts and received major societal concerns. Here, we assess the link between the well-mixed greenhouse gas (GHG) forcing and the occurrence probabilities of the duration and intensity of the North Pacific MHWs. We investigate whether GHG forcing was necessary for the North Pacific MHWs to occur and whether it is a sufficient cause for such events to continue to repeatedly occur in the 21st Century. To begin with, we apply attribution technique on the long-term SST time series, and detect a region of systematically and externally-forced SST increase -- the long-term warming pool -- co-located with the past notably Blob-like SST anomalies. We further show that the anthropogenic signal has recently emerged from the natural variability of SST over the warming pool, which we attribute primarily to increased GHG concentrations, with anthropogenic aerosols playing a secondary role.

After we demonstrate that the GHG forcing has a dominant influence on the base climate state in the region, we pursue an event attribution analysis for MHWs on a more localized region. Extreme event attribution analysis reveals that GHG forcing is a necessary, but not sufficient, causation for the multi-year persistent MHW events in the current climate, such as that happened in 2014/2015 and 2019/2020. However, the occurrence of the 2019/2020 (2014/2015) MHW was extremely unlikely in the absence of GHG forcing. Thus, as GHG emissions continue to firmly rise, it is very likely that GHG forcings will become a sufficient cause for events of the magnitude of the 2019/2020 record event.



How to cite: Barkhordarian, A., Nielsen, D. M., and Baehr, J.: Greenhouse gas forcing a necessary, but not sufficient, causation for the northeast Pacific marine heatwaves , EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-6041, https://doi.org/10.5194/egusphere-egu22-6041, 2022.

Reyk Börner et al.

The multistability of the Atlantic Meridional Overturning Circulation (AMOC) challenges the predictability of long-term climate evolution. In light of an observed weakening in AMOC strength, it is crucial to study the probabilities of noise-induced transitions between the different competing flow regimes. From a dynamical systems perspective, the phase space of a multistable system can be characterised as a non-equilibrium potential landscape, with valleys corresponding to the different basins of attraction. Knowing the potential, one can infer the statistics and pathways of noise-induced transitions. Particularly, in the weak-noise limit, transition paths lead through special regions of the basin boundaries, called Melancholia states. Recent studies have applied these concepts to climate models of low and intermediate complexity. Here, we investigate the quasi-potential landscape of a three-box model of the AMOC, based on the popular model by Rooth. We analyse noise-induced transitions between the two stable circulation states and elucidate the role of the Melancholia state. Forcing the model with different noise laws, which represent fluctuations caused by different physical processes, we discuss how the properties of transitions change when considering non-Gaussian processes, specifically Lévy noise. Simulated transition rates are related to their theoretical values using the quasi-potential landscape. Our results yield a comprehensive picture of the dynamical properties of an inter-hemispheric three-box AMOC model under stochastic forcing. By relating the deterministic structure of this simple model to the statistics of critical transitions, we hope to build a basis for transferring this approach to more complex models of the AMOC.

How to cite: Börner, R., Lucarini, V., and Serdukova, L.: Dynamical Landscape and Noise-induced Transitions in a Box Model of the Atlantic Meridional Overturning Circulation, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-8332, https://doi.org/10.5194/egusphere-egu22-8332, 2022.