Articles | Volume 27, issue 2
https://doi.org/10.5194/npg-27-209-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-27-209-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
16 Apr 2020
Research article |
| 16 Apr 2020
| 16 Apr 2020
Data-driven versus self-similar parameterizations for stochastic advection by Lie transport and location uncertainty
Valentin Resseguier
CORRESPONDING AUTHOR
Lab, SCALIAN DS, Espace Nobel, 2 Allée de Becquerel, 35700 Rennes, France
Wei Pan
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
Baylor Fox-Kemper
Department of Earth, Environmental and Planetary Sciences (DEEPS), Brown University, Providence, RI 02912, USA
Institute at Brown for Environment and Society (IBES), Brown University, Providence, RI 02912, USA
Related authors
Yicun Zhen, Valentin Resseguier, and Bertrand Chapron
Nonlin. Processes Geophys., 30, 237–251, https://doi.org/10.5194/npg-30-237-2023, https://doi.org/10.5194/npg-30-237-2023, 2023
Short summary
Short summary
This paper provides perspective that the displacement vector field of physical state fields should be determined by the tensor fields associated with the physical fields. The advantage of this perspective is that certain physical quantities can be conserved while applying a displacement vector field to transfer the original physical field. A direct application of this perspective is the physically constrained covariance inflation scheme proposed in this paper.
Qiang Wang, Qi Shu, Alexandra Bozec, Eric P. Chassignet, Pier Giuseppe Fogli, Baylor Fox-Kemper, Andy McC. Hogg, Doroteaciro Iovino, Andrew E. Kiss, Nikolay Koldunov, Julien Le Sommer, Yiwen Li, Pengfei Lin, Hailong Liu, Igor Polyakov, Patrick Scholz, Dmitry Sidorenko, Shizhu Wang, and Xiaobiao Xu
Geosci. Model Dev., 17, 347–379, https://doi.org/10.5194/gmd-17-347-2024, https://doi.org/10.5194/gmd-17-347-2024, 2024
Short summary
Short summary
Increasing resolution improves model skills in simulating the Arctic Ocean, but other factors such as parameterizations and numerics are at least of the same importance for obtaining reliable simulations.
Xiaoyu Fan, Baylor Fox-Kemper, Nobuhiro Suzuki, Qing Li, Patrick Marchesiello, Francis Auclair, Peter P. Sullivan, and Paul S. Hall
EGUsphere, https://doi.org/10.5194/egusphere-2023-1657, https://doi.org/10.5194/egusphere-2023-1657, 2023
Short summary
Short summary
Simulations of the oceanic turbulent boundary layer using the nonhydrostatic CROCO ROMS and NCAR-LES models are compared. CROCO and the NCAR-LES are similarly accurate, but CROCO’s additional features (e.g., nesting and realism) and its compressible turbulence formulation carry additional costs.
Anne Marie Treguier, Clement de Boyer Montégut, Alexandra Bozec, Eric P. Chassignet, Baylor Fox-Kemper, Andy McC. Hogg, Doroteaciro Iovino, Andrew E. Kiss, Julien Le Sommer, Yiwen Li, Pengfei Lin, Camille Lique, Hailong Liu, Guillaume Serazin, Dmitry Sidorenko, Qiang Wang, Xiaobio Xu, and Steve Yeager
Geosci. Model Dev., 16, 3849–3872, https://doi.org/10.5194/gmd-16-3849-2023, https://doi.org/10.5194/gmd-16-3849-2023, 2023
Short summary
Short summary
The ocean mixed layer is the interface between the ocean interior and the atmosphere and plays a key role in climate variability. We evaluate the performance of the new generation of ocean models for climate studies, designed to resolve
ocean eddies, which are the largest source of ocean variability and modulate the mixed-layer properties. We find that the mixed-layer depth is better represented in eddy-rich models but, unfortunately, not uniformly across the globe and not in all models.
Yicun Zhen, Valentin Resseguier, and Bertrand Chapron
Nonlin. Processes Geophys., 30, 237–251, https://doi.org/10.5194/npg-30-237-2023, https://doi.org/10.5194/npg-30-237-2023, 2023
Short summary
Short summary
This paper provides perspective that the displacement vector field of physical state fields should be determined by the tensor fields associated with the physical fields. The advantage of this perspective is that certain physical quantities can be conserved while applying a displacement vector field to transfer the original physical field. A direct application of this perspective is the physically constrained covariance inflation scheme proposed in this paper.
Gustavo M. Marques, Nora Loose, Elizabeth Yankovsky, Jacob M. Steinberg, Chiung-Yin Chang, Neeraja Bhamidipati, Alistair Adcroft, Baylor Fox-Kemper, Stephen M. Griffies, Robert W. Hallberg, Malte F. Jansen, Hemant Khatri, and Laure Zanna
Geosci. Model Dev., 15, 6567–6579, https://doi.org/10.5194/gmd-15-6567-2022, https://doi.org/10.5194/gmd-15-6567-2022, 2022
Short summary
Short summary
We present an idealized ocean model configuration and a set of simulations performed using varying horizontal grid spacing. While the model domain is idealized, it resembles important geometric features of the Atlantic and Southern oceans. The simulations described here serve as a framework to effectively study mesoscale eddy dynamics, to investigate the effect of mesoscale eddies on the large-scale dynamics, and to test and evaluate eddy parameterizations.
Takaya Uchida, Julien Le Sommer, Charles Stern, Ryan P. Abernathey, Chris Holdgraf, Aurélie Albert, Laurent Brodeau, Eric P. Chassignet, Xiaobiao Xu, Jonathan Gula, Guillaume Roullet, Nikolay Koldunov, Sergey Danilov, Qiang Wang, Dimitris Menemenlis, Clément Bricaud, Brian K. Arbic, Jay F. Shriver, Fangli Qiao, Bin Xiao, Arne Biastoch, René Schubert, Baylor Fox-Kemper, William K. Dewar, and Alan Wallcraft
Geosci. Model Dev., 15, 5829–5856, https://doi.org/10.5194/gmd-15-5829-2022, https://doi.org/10.5194/gmd-15-5829-2022, 2022
Short summary
Short summary
Ocean and climate scientists have used numerical simulations as a tool to examine the ocean and climate system since the 1970s. Since then, owing to the continuous increase in computational power and advances in numerical methods, we have been able to simulate increasing complex phenomena. However, the fidelity of the simulations in representing the phenomena remains a core issue in the ocean science community. Here we propose a cloud-based framework to inter-compare and assess such simulations.
Eric P. Chassignet, Stephen G. Yeager, Baylor Fox-Kemper, Alexandra Bozec, Frederic Castruccio, Gokhan Danabasoglu, Christopher Horvat, Who M. Kim, Nikolay Koldunov, Yiwen Li, Pengfei Lin, Hailong Liu, Dmitry V. Sein, Dmitry Sidorenko, Qiang Wang, and Xiaobiao Xu
Geosci. Model Dev., 13, 4595–4637, https://doi.org/10.5194/gmd-13-4595-2020, https://doi.org/10.5194/gmd-13-4595-2020, 2020
Short summary
Short summary
This paper presents global comparisons of fundamental global climate variables from a suite of four pairs of matched low- and high-resolution ocean and sea ice simulations to assess the robustness of climate-relevant improvements in ocean simulations associated with moving from coarse (∼1°) to eddy-resolving (∼0.1°) horizontal resolutions. Despite significant improvements, greatly enhanced horizontal resolution does not deliver unambiguous bias reduction in all regions for all models.
Hiroyuki Tsujino, L. Shogo Urakawa, Stephen M. Griffies, Gokhan Danabasoglu, Alistair J. Adcroft, Arthur E. Amaral, Thomas Arsouze, Mats Bentsen, Raffaele Bernardello, Claus W. Böning, Alexandra Bozec, Eric P. Chassignet, Sergey Danilov, Raphael Dussin, Eleftheria Exarchou, Pier Giuseppe Fogli, Baylor Fox-Kemper, Chuncheng Guo, Mehmet Ilicak, Doroteaciro Iovino, Who M. Kim, Nikolay Koldunov, Vladimir Lapin, Yiwen Li, Pengfei Lin, Keith Lindsay, Hailong Liu, Matthew C. Long, Yoshiki Komuro, Simon J. Marsland, Simona Masina, Aleksi Nummelin, Jan Klaus Rieck, Yohan Ruprich-Robert, Markus Scheinert, Valentina Sicardi, Dmitry Sidorenko, Tatsuo Suzuki, Hiroaki Tatebe, Qiang Wang, Stephen G. Yeager, and Zipeng Yu
Geosci. Model Dev., 13, 3643–3708, https://doi.org/10.5194/gmd-13-3643-2020, https://doi.org/10.5194/gmd-13-3643-2020, 2020
Short summary
Short summary
The OMIP-2 framework for global ocean–sea-ice model simulations is assessed by comparing multi-model means from 11 CMIP6-class global ocean–sea-ice models calculated separately for the OMIP-1 and OMIP-2 simulations. Many features are very similar between OMIP-1 and OMIP-2 simulations, and yet key improvements in transitioning from OMIP-1 to OMIP-2 are also identified. Thus, the present assessment justifies that future ocean–sea-ice model development and analysis studies use the OMIP-2 framework.
Anson Cheung, Baylor Fox-Kemper, and Timothy Herbert
Clim. Past, 15, 1985–1998, https://doi.org/10.5194/cp-15-1985-2019, https://doi.org/10.5194/cp-15-1985-2019, 2019
Short summary
Short summary
We test two assumptions that are often made in paleoclimate studies by using observations and ask whether temperature and productivity proxy records in the Southern California Current can be used to reconstruct Ekman upwelling. By examining the covariation between alongshore wind stress, temperature, and productivity, we found that the dominant covarying pattern does not reflect Ekman upwelling. Other upwelling patterns found are timescale dependent. Multiple proxies can improve reconstruction.
Christopher Horvat, Lettie A. Roach, Rachel Tilling, Cecilia M. Bitz, Baylor Fox-Kemper, Colin Guider, Kaitlin Hill, Andy Ridout, and Andrew Shepherd
The Cryosphere, 13, 2869–2885, https://doi.org/10.5194/tc-13-2869-2019, https://doi.org/10.5194/tc-13-2869-2019, 2019
Short summary
Short summary
Changes in the floe size distribution (FSD) are important for sea ice evolution but to date largely unobserved and unknown. Climate models, forecast centres, ship captains, and logistic specialists cannot currently obtain statistical information about sea ice floe size on demand. We develop a new method to observe the FSD at global scales and high temporal and spatial resolution. With refinement, this method can provide crucial information for polar ship routing and real-time forecasting.
Seonmin Ahn, Baylor Fox-Kemper, Timothy Herbert, and Charles Lawrence
Clim. Past Discuss., https://doi.org/10.5194/cp-2018-1, https://doi.org/10.5194/cp-2018-1, 2018
Revised manuscript not accepted
Arin D. Nelson, Jeffrey B. Weiss, Baylor Fox-Kemper, Royce K. P. Zia, and Fabienne Gaillard
Ocean Sci. Discuss., https://doi.org/10.5194/os-2016-105, https://doi.org/10.5194/os-2016-105, 2017
Revised manuscript has not been submitted
Short summary
Short summary
We quantify the skill in observing the variability of global upper ocean heat content (OHC) by applying the ISAS13 observing strategy to a CCSM simulation. We find that variability is unreliably observed before 2005, while observed annual running means for 2005–2013 correlate well with model "truth" to a median of 95 %. When scaled to the real ocean, we find signal-to-noise ratios of 1.9 for pre-Argo times (1990–2005) and 14.7 after Argo is introduced (2005–2013). The global warming is robust.
Stephen M. Griffies, Gokhan Danabasoglu, Paul J. Durack, Alistair J. Adcroft, V. Balaji, Claus W. Böning, Eric P. Chassignet, Enrique Curchitser, Julie Deshayes, Helge Drange, Baylor Fox-Kemper, Peter J. Gleckler, Jonathan M. Gregory, Helmuth Haak, Robert W. Hallberg, Patrick Heimbach, Helene T. Hewitt, David M. Holland, Tatiana Ilyina, Johann H. Jungclaus, Yoshiki Komuro, John P. Krasting, William G. Large, Simon J. Marsland, Simona Masina, Trevor J. McDougall, A. J. George Nurser, James C. Orr, Anna Pirani, Fangli Qiao, Ronald J. Stouffer, Karl E. Taylor, Anne Marie Treguier, Hiroyuki Tsujino, Petteri Uotila, Maria Valdivieso, Qiang Wang, Michael Winton, and Stephen G. Yeager
Geosci. Model Dev., 9, 3231–3296, https://doi.org/10.5194/gmd-9-3231-2016, https://doi.org/10.5194/gmd-9-3231-2016, 2016
Short summary
Short summary
The Ocean Model Intercomparison Project (OMIP) aims to provide a framework for evaluating, understanding, and improving the ocean and sea-ice components of global climate and earth system models contributing to the Coupled Model Intercomparison Project Phase 6 (CMIP6). This document defines OMIP and details a protocol both for simulating global ocean/sea-ice models and for analysing their output.
Related subject area
Subject: Predictability, probabilistic forecasts, data assimilation, inverse problems | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Simulation
Comparative study of strongly and weakly coupled data assimilation with a global land–atmosphere coupled model
Reducing manipulations in a control simulation experiment based on instability vectors with the Lorenz-63 model
Control simulation experiments of extreme events with the Lorenz-96 model
A range of outcomes: the combined effects of internal variability and anthropogenic forcing on regional climate trends over Europe
Using a hybrid optimal interpolation–ensemble Kalman filter for the Canadian Precipitation Analysis
Control simulation experiment with Lorenz's butterfly attractor
Reduced non-Gaussianity by 30 s rapid update in convective-scale numerical weather prediction
A study of capturing Atlantic meridional overturning circulation (AMOC) regime transition through observation-constrained model parameters
Fast hybrid tempered ensemble transform filter formulation for Bayesian elliptical problems via Sinkhorn approximation
Simulating model uncertainty of subgrid-scale processes by sampling model errors at convective scales
Generalization properties of feed-forward neural networks trained on Lorenz systems
Kenta Kurosawa, Shunji Kotsuki, and Takemasa Miyoshi
Nonlin. Processes Geophys., 30, 457–479, https://doi.org/10.5194/npg-30-457-2023, https://doi.org/10.5194/npg-30-457-2023, 2023
Short summary
Short summary
This study aimed to enhance weather and hydrological forecasts by integrating soil moisture data into a global weather model. By assimilating atmospheric observations and soil moisture data, the accuracy of forecasts was improved, and certain biases were reduced. The method was found to be particularly beneficial in areas like the Sahel and equatorial Africa, where precipitation patterns vary seasonally. This new approach has the potential to improve the precision of weather predictions.
Mao Ouyang, Keita Tokuda, and Shunji Kotsuki
Nonlin. Processes Geophys., 30, 183–193, https://doi.org/10.5194/npg-30-183-2023, https://doi.org/10.5194/npg-30-183-2023, 2023
Short summary
Short summary
This research found that weather control would change the chaotic behavior of an atmospheric model. We proposed to introduce chaos theory in the weather control. Experimental results demonstrated that the proposed approach reduced the manipulations, including the control times and magnitudes, which throw light on the weather control in a real atmospheric model.
Qiwen Sun, Takemasa Miyoshi, and Serge Richard
Nonlin. Processes Geophys., 30, 117–128, https://doi.org/10.5194/npg-30-117-2023, https://doi.org/10.5194/npg-30-117-2023, 2023
Short summary
Short summary
This paper is a follow-up of a work by Miyoshi and Sun which was published in NPG Letters in 2022. The control simulation experiment is applied to the Lorenz-96 model for avoiding extreme events. The results show that extreme events of this partially and imperfectly observed chaotic system can be avoided by applying pre-designed small perturbations. These investigations may be extended to more realistic numerical weather prediction models.
Clara Deser and Adam S. Phillips
Nonlin. Processes Geophys., 30, 63–84, https://doi.org/10.5194/npg-30-63-2023, https://doi.org/10.5194/npg-30-63-2023, 2023
Short summary
Short summary
Past and future climate change at regional scales is a result of both human influences and natural (internal) variability. Here, we provide an overview of recent advances in climate modeling and physical understanding that has led to new insights into their respective roles, illustrated with original results for the European climate. Our findings highlight the confounding role of internal variability in attribution, climate model evaluation, and accuracy of future projections.
Dikraa Khedhaouiria, Stéphane Bélair, Vincent Fortin, Guy Roy, and Franck Lespinas
Nonlin. Processes Geophys., 29, 329–344, https://doi.org/10.5194/npg-29-329-2022, https://doi.org/10.5194/npg-29-329-2022, 2022
Short summary
Short summary
This study introduces a well-known use of hybrid methods in data assimilation (DA) algorithms that has not yet been explored for precipitation analyses. Our approach combined an ensemble-based DA approach with an existing deterministically based DA. Both DA scheme families have desirable aspects that can be leveraged if combined. The DA hybrid method showed better precipitation analyses in regions with a low rate of assimilated surface observations, which is typically the case in winter.
Takemasa Miyoshi and Qiwen Sun
Nonlin. Processes Geophys., 29, 133–139, https://doi.org/10.5194/npg-29-133-2022, https://doi.org/10.5194/npg-29-133-2022, 2022
Short summary
Short summary
The weather is chaotic and hard to predict, but the chaos implies an effective control where a small control signal grows rapidly to make a big difference. This study proposes a control simulation experiment where we apply a small signal to control
naturein a computational simulation. Idealized experiments with a low-order chaotic system show successful results by small control signals of only 3 % of the observation error. This is the first step toward realistic weather simulations.
Juan Ruiz, Guo-Yuan Lien, Keiichi Kondo, Shigenori Otsuka, and Takemasa Miyoshi
Nonlin. Processes Geophys., 28, 615–626, https://doi.org/10.5194/npg-28-615-2021, https://doi.org/10.5194/npg-28-615-2021, 2021
Short summary
Short summary
Effective use of observations with numerical weather prediction models, also known as data assimilation, is a key part of weather forecasting systems. For precise prediction at the scales of thunderstorms, fast nonlinear processes pose a grand challenge because most data assimilation systems are based on linear processes and normal distribution errors. We investigate how, every 30 s, weather radar observations can help reduce the effect of nonlinear processes and nonnormal distributions.
Zhao Liu, Shaoqing Zhang, Yang Shen, Yuping Guan, and Xiong Deng
Nonlin. Processes Geophys., 28, 481–500, https://doi.org/10.5194/npg-28-481-2021, https://doi.org/10.5194/npg-28-481-2021, 2021
Short summary
Short summary
A general methodology is introduced to capture regime transitions of the Atlantic meridional overturning circulation (AMOC). The assimilation models with different parameters simulate different paths for the AMOC to switch between equilibrium states. Constraining model parameters with observations can significantly mitigate the model deviations, thus capturing AMOC regime transitions. This simple model study serves as a guideline for improving coupled general circulation models.
Sangeetika Ruchi, Svetlana Dubinkina, and Jana de Wiljes
Nonlin. Processes Geophys., 28, 23–41, https://doi.org/10.5194/npg-28-23-2021, https://doi.org/10.5194/npg-28-23-2021, 2021
Short summary
Short summary
To infer information of an unknown quantity that helps to understand an associated system better and to predict future outcomes, observations and a physical model that connects the data points to the unknown parameter are typically used as information sources. Yet this problem is often very challenging due to the fact that the unknown is generally high dimensional, the data are sparse and the model can be non-linear. We propose a novel approach to address these challenges.
Michiel Van Ginderachter, Daan Degrauwe, Stéphane Vannitsem, and Piet Termonia
Nonlin. Processes Geophys., 27, 187–207, https://doi.org/10.5194/npg-27-187-2020, https://doi.org/10.5194/npg-27-187-2020, 2020
Short summary
Short summary
A generic methodology is developed to estimate the model error and simulate the model uncertainty related to a specific physical process. The method estimates the model error by comparing two different representations of the physical process in otherwise identical models. The found model error can then be used to perturb the model and simulate the model uncertainty. When applying this methodology to deep convection an improvement in the probabilistic skill of the ensemble forecast is found.
Sebastian Scher and Gabriele Messori
Nonlin. Processes Geophys., 26, 381–399, https://doi.org/10.5194/npg-26-381-2019, https://doi.org/10.5194/npg-26-381-2019, 2019
Short summary
Short summary
Neural networks are a technique that is widely used to predict the time evolution of physical systems. For this the past evolution of the system is shown to the neural network – it is
trained– and then can be used to predict the evolution in the future. We show some limitations in this approach for certain systems that are important to consider when using neural networks for climate- and weather-related applications.
Cited articles
Berner, J., Achatz, U., Batte, L., Camara, A. D. L., Crommelin, D., Christensen, H., Colangeli, M., Dolaptchiev, S., Franzke, C., Friederichs, P., Imkeller, P., Jarvinen, H., Juricke, S., Kitsios, V., Lott, F., Lucarini, V., Mahajan, S., Palmer, T. N., Penland, C., Storch, J.-S. V., Sakradzija, M., Weniger, M., Weisheimer, A., Williams, P. D., and Yano, J.-I.: Stochastic Parameterization: Towards a new view of Weather and Climate Models, B.
Am. Meteorol. Soc., 98, 565–588, 2017. a
Blumen, W.: Uniform potential vorticity flow: part I. theory of wave interactions and two-dimensional turbulence, J. Atmos. Sci., 35, 774–783, 1978. a
Blumen, W.: Wave-Interactions in Quasi-Geostrophic Uniform Potential Vorticity Flow, J. Atmos. Sci., 39, 2388–2396, 1982. a
Cai, S., Mémin, E., Dérian, P., and Xu, C.: Motion estimation under location uncertainty for turbulent fluid flows, Exp. Fluids, 59, 8, https://doi.org/10.1007/s00348-017-2458-z, 2018. a
Callies, J., Flierl, G., Ferrari, R., and Fox-Kemper, B.: The role of mixed-layer instabilities in submesoscale turbulence, J. Fluid Mech., 788, 5–41, 2016. a
Chapron, B., Dérian, P., Mémin, E., and Resseguier, V.: Large-scale flows under location uncertainty: a consistent stochastic framework, Q. J. Roy. Meteor. Soc., 144, 251–260, 2018. a
Charney, J. G.: Geostrophic Turbulence, J. Atmos. Sci., 28, 1087–1095, 1971. a
Chekroun, M. D., Kondrashov, D., and Ghil, M.: Predicting stochastic systems by noise sampling, and application to the El Niño-Southern Oscillation,
P. Natl. Acad. Sci. USA, 108, 11766–11771, 2011. a
Constantin, P., Nie, Q., and Schörghofer, N.: Front formation in an active scalar equation, Phys. Rev. E, 60, 2858, https://doi.org/10.1103/PhysRevE.60.2858, 1999. a, b, c, d
Cotter, C. J., Gottwald, G. A., and Holm, D. D.: Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics, P. Roy. Soc. A-Math. Phy., 473, 20170388, https://doi.org/10.1098/rspa.2017.0388, 2017. a, b, c, d
Crisan, D. and Lang, O.: Well-posedness for 2D Euler equations with stochastic Lie transport noise, arXiv 1907.00451, 2018. a
Crisan, D., Flandoli, F., and Holm, D. D.: Solution properties of a 3D stochastic Euler fluid equation, J. Nonlinear Sci., 29, 813–870, 2019. a
Da Prato, G. and Zabczyk, J.: Stochastic equations in infinite dimensions, Cambridge University Press, https://doi.org/10.1017/CBO9781107295513, 1992. a
Falkovich, G., Gawedzki, K., and Vergassola, M.: Particles and fields in fluid turbulence, Rev. Mod. Phys., 73, 913, https://doi.org/10.1103/RevModPhys.73.913, 2001. a, b, c
Ferrari, R. and Nikurashin, M.: Suppression of Eddy Diffusivity across Jets in the Southern Ocean, J. Phys. Oceanogr., 40, 1501–1519, 2010. a
Flandoli, F.: The interaction between noise and transport mechanisms in PDEs, Milan J. Math., 79, 543–560, 2011. a
Fox-Kemper, B.: New Frontiers in Operational Oceanography, chap.: Notions for the Motions of the Oceans, GODAE OceanView, 27–73, https://doi.org/10.17125/gov2018, 2018. a
Frank, J. and Gottwald, G.: Stochastic homogenization for an energy conserving multi-scale toy model of the atmosphere, Physica D, 254, 46–56, 2013. a
Frisch, U.: Turbulence: the legacy of AN Kolmogorov, Cambridge university press, https://doi.org/10.1017/CBO978113917066670666, 1995. a, b, c
Gawedzky, K. and Kupiainen, A.: Anomalous scaling of the passive scalar, Phys. Rev. Lett., 75, 3834–3837, 1995. a
Gay-Balmaz, F. and Holm, D. D.: Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows, J. Nonlinear Sci., 28, 873–904, https://doi.org/10.1007/s00332-017-9431-0, 2018. a
GitHub repository: https://github.com/vressegu/LU_SALT_SelfSim, last access: 27 March 2020. a
Gordon, A. L.: Indian-Atlantic transfer of thermocline water at the Agulhas retroflection, Science, 227, 1030–1033, 1985. a
Gottwald, G. and Melbourne, I.: Homogenization for deterministic maps and multiplicative noise, P. Roy. Soc. A-Math. Phy., 469, 20130201, https://doi.org/10.1098/rspa.2013.0201, 2013. a
Hallberg, R. and Gnanadesikan, A.: The role of eddies in determining the structure and response of the wind-driven Southern Hemisphere overturning: Results from the Modeling Eddies in the Southern Ocean (MESO) project, J. Phys. Oceanogr., 36, 2232–2252, 2006. a
Held, I., Pierrehumbert, R., Garner, S., and Swanson, K.: Surface quasi-geostrophic dynamics, J. Fluid Mech., 282, 1–20, 1995. a
Holm, D. D.: Variational principles for stochastic fluid dynamics, P. Roy. Soc. A-Math. Phy., 471, 20140963, https://doi.org/10.1098/rspa.2014.0963, 2015. a, b, c, d
Isern-Fontanet, J., Chapron, B., Lapeyre, G., and Klein, P.: Potential use of microwave sea surface temperatures for the estimation of ocean currents, Geophys. Res. Lett., 33, L24608, https://doi.org/10.1029/2006GL027801, 2006. a
Isern-Fontanet, J., Lapeyre, G., Klein, P., Chapron, B., and Hecht, M. W.: Three-dimensional reconstruction of oceanic mesoscale currents from surface information, J. Geophys. Res., 113, C09005, https://doi.org/10.1029/2007JC004692, 2008. a
Janjić, T., McLaughlin, D., Cohn, S. E., and Verlaan, M.: Conservation of mass and preservation of positivity with ensemble-type Kalman filter algorithms, Mon. Weather Rev., 142, 755–773, 2014. a
Klein, P., Isern-Fontanet, J., Lapeyre, G., Roullet, G., Danioux, E., Chapron, B., Le Gentil, S., and Sasaki, H.: Diagnosis of vertical velocities in the upper ocean from high resolution sea surface height, Geophys. Res. Lett., 36, L12603, https://doi.org/10.1029/2009GL038359, 2009. a
Kolmogorov, A. N.: The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Cr Acad. Sci. URSS, 30, 301–305, 1941. a
Kraichnan, R.: Small-scale structure of a scalar field convected by turbulence, Phys. Fluids, 11, 945–963, 1968. a
Kraichnan, R.: Anomalous scaling of a randomly advected passive scalar, Phys. Rev. Lett., 72, 1016, https://doi.org/10.1103/PhysRevLett.72.1016, 1994. a
Kraichnan, R. H.: Inertial Ranges in Two-Dimensional Turbulence, Phys.
Fluids, 16, 1417–1423, 1967. a
LaCasce, J. and Mahadevan, A.: Estimating subsurface horizontal and vertical velocities from sea-surface temperature, J. Mar. Res., 64, 695–721, 2006. a
Lapeyre, G.: Surface quasi-geostrophy, Fluids, 2, 7, https://doi.org/10.3390/fluids2010007, 2017. a
Lapeyre, G. and Klein, P.: Dynamics of the upper oceanic layers in terms of surface quasigeostrophy theory, J. Phys. Oceanogr., 36, 165–176, 2006a. a
Lapeyre, G. and Klein, P.: Dynamics of the upper oceanic layers in terms of surface quasigeostrophy theory, J. Phys. Oceanogr., 36, 165–176, 2006b. a
Leith, C.: Atmospheric predictability and two-dimensional turbulence, J. Atmos. Sci, 28, 145–161, 1971. a
Lilly, J. M., Sykulski, A. M., Early, J. J., and Olhede, S. C.: Fractional Brownian motion, the Matérn process, and stochastic modeling of turbulent dispersion, Nonlin. Processes Geophys., 24, 481–514, https://doi.org/10.5194/npg-24-481-2017, 2017. a
Lim, S. and Teo, L.: Generalized Whittle–Matérn random field as a model of correlated fluctuations, J. Phys. A-Math. Theor., 42, 105202, https://doi.org/10.1088/1751-8113/42/10/105202, 2009. a
Lu, F., Lin, K. K., and Chorin, A. J.: Data-based stochastic model reduction for the Kuramoto–Sivashinsky equation, Physica D, 340, 46–57, 2017. a
Majda, A. and Kramer, P.: Simplified models for turbulent diffusion: Theory, numerical modelling, and physical phenomena, Phys. Rep., 314, 237–574, 1999. a
Majda, A., Timofeyev, I., and Vanden-Eijnden, E.: Models for stochastic climate prediction, P. Natl. Acad. Sci. USA, 96, 14687–14691, 1999. a
Majda, A. J.: Statistical energy conservation principle for inhomogeneous turbulent dynamical systems, P. Natl. Acad. Sci. USA, 112, 8937–8941, 2015. a
Margolin, L. G., Rider, W. J., and Grinstein, F. F.: Modeling turbulent flow with implicit LES, J. Turbul., 7, N15, https://doi.org/10.1080/14685240500331595, 2006. a
Mémin, E.: Fluid flow dynamics under location uncertainty, Geophys. Astro. Fluid, 108, 119–146, https://doi.org/10.1080/03091929.2013.836190, 2014. a, b
Mikulevicius, R. and Rozovskii, B.: Stochastic Navier–Stokes equations for turbulent flows, SIAM J. Math. Anal., 35, 1250–1310, 2004a. a
Mikulevicius, R. and Rozovskii, B.: Stochastic Navier–Stokes equations for turbulent flows, SIAM J. Math. Anal., 35, 1250–1310, 2004b. a
Mitchell, L. and Gottwald, G.: Data assimilation in slow fast systems using homogenized climate models, J. Atmos. Sci., 69, 1359–1377, 2012. a
Orszag, S.: Analytical theories of turbulence, J. Fluid Mech., 41, 363–386, 1970. a
Pearson, B. and Fox-Kemper, B.: Log-Normal Turbulence Dissipation in Global Ocean Models, Phys. Rev. Lett., 120, 094501, https://doi.org/10.1103/PhysRevLett.120.094501, 2018. a
Pearson, B., Fox-Kemper, B., Bachman, S. D., and Bryan, F. O.: Evaluation of scale-aware subgrid mesoscale eddy models in a global eddy-rich model, Ocean Model., 115, 42–58, 2017. a
Prévôt, C. and Röckner, M.: A concise course on stochastic partial differential equations, in: Lecture Notes in Mathematics, 1905, 148 pp., Springer-Verlag, Berlin Heidelberg, 2007. a
Resseguier, V., Mémin, E., and Chapron, B.: Geophysical flows under location uncertainty, Part I: Random transport and general models, Geophys. Astro. Fluid, 111, 149–176, https://doi.org/10.1080/03091929.2017.1310210, 2017a. a, b, c, d
Resseguier, V., Mémin, E., and Chapron, B.: Geophysical flows under location uncertainty, Part III: SQG and frontal dynamics under strong turbulence, Geophys. Astro. Fluid, 11, 209–227, https://doi.org/10.1080/03091929.2017.1312102, 2017c. a
San, O., Staples, A. E., and Iliescu, T.: Approximate deconvolution large eddy simulation of a stratified two-layer quasigeostrophic ocean model, Ocean Model., 63, 1–20, 2013. a
Sapsis, T. and Majda, A.: A statistically accurate modified quasilinear Gaussian closure for uncertainty quantification in turbulent dynamical systems, Physica D, 252, 34–45, 2013. a
Sardeshmukh, P. D. and Sura, P.: Reconciling non-Gaussian climate statistics with linear dynamics, J. Climate, 22, 1193–1207, 2009. a
Sardeshmukh, P. D., Compo, G. P., and Penland, C.: Need for caution in interpreting extreme weather statistics, J. Climate, 28, 9166–9187, 2015. a
Scott, R. B. and Straub, D. N.: Small Viscosity Behavior of a Homogeneous, Quasigeostrophic, Ocean Circulation Model, J. Mar. Res., 56, 1225–1258, 1998. a
Tandeo, P., Autret, E., Chapron, B., Fablet, R., and Garello, R.: SST spatial anisotropic covariances from METOP-AVHRR data, Remote Sens. Environ., 141, 144–148, 2014. a
Vallis, G.: Atmospheric and oceanic fluid dynamics: fundamentals and large-scale circulation, Cambridge University Press, https://doi.org/10.1017/9781107588417, 2006. a, b, c
Voosen, P.: The Earth Machine, Science, 361, 344–347, 2018. a
Wang, J., Flierl, G. R., LaCasce, J. H., McClean, J. L., and Mahadevan, A.: Reconstructing the ocean's interior from surface data, J. Phys. Oceanogr., 43, 1611–1626, 2013. a
Williams, C. K. and Rasmussen, C. E.: Gaussian processes for machine learning, in: Adaptive Computation and Machine Learning series, The MIT Press, 272 pp., 2006. a
Short summary
Geophysical flows span a broader range of temporal and spatial scales than can be resolved numerically. One way to alleviate the ensuing numerical errors is to combine simulations with measurements, taking account of the accuracies of these two sources of information. Here we quantify the distribution of numerical simulation errors without relying on high-resolution numerical simulations. Specifically, small-scale random vortices are added to simulations while conserving energy or circulation.
Geophysical flows span a broader range of temporal and spatial scales than can be resolved...
