Articles | Volume 13, issue 4
https://doi.org/10.5194/gmd-13-1903-2020
© 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/gmd-13-1903-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Development and technical paper
| 
16 Apr 2020
Development and technical paper |
| 16 Apr 2020
| 16 Apr 2020
On the numerical integration of the Lorenz-96 model, with scalar additive noise, for benchmark twin experiments
Department of Mathematics and Statistics, University of Nevada, Reno, Reno, Nevada, USA
Nansen Environmental and Remote Sensing Center, Bergen, Norway
Marc Bocquet
CEREA, joint laboratory École des Ponts ParisTech and EDF R&D, Université Paris-Est, Champs-sur-Marne, France
Alberto Carrassi
Department of Meteorology and National Centre for Earth Observations, University of Reading, Reading, UK
Mathematical Institute, Utrecht University, Utrecht, Netherlands
Nansen Environmental and Remote Sensing Center, Bergen, Norway
Related authors
Colin Grudzien and Marc Bocquet
Geosci. Model Dev., 15, 7641–7681, https://doi.org/10.5194/gmd-15-7641-2022, https://doi.org/10.5194/gmd-15-7641-2022, 2022
Short summary
Short summary
Iterative optimization techniques, the state of the art in data assimilation, have largely focused on extending forecast accuracy to moderate- to long-range forecast systems. However, current methodology may not be cost-effective in reducing forecast errors in online, short-range forecast systems. We propose a novel optimization of these techniques for online, short-range forecast cycles, simultaneously providing an improvement in forecast accuracy and a reduction in the computational cost.
Colin Grudzien, Alberto Carrassi, and Marc Bocquet
Nonlin. Processes Geophys., 25, 633–648, https://doi.org/10.5194/npg-25-633-2018, https://doi.org/10.5194/npg-25-633-2018, 2018
Short summary
Short summary
Using the framework Lyapunov vectors, we analyze the asymptotic properties of ensemble based Kalman filters and how these are influenced by dynamical chaos, especially in the context of random model errors and small ensemble sizes. Particularly, we show a novel derivation of the evolution of forecast uncertainty for ensemble-based Kalman filters with weakly-nonlinear error growth, and discuss its impact for filter design in geophysical models.
Charlotte Durand, Tobias Sebastian Finn, Alban Farchi, Marc Bocquet, Julien Brajard, and Laurent Bertino
EGUsphere, https://doi.org/10.5194/egusphere-2024-4028, https://doi.org/10.5194/egusphere-2024-4028, 2025
This preprint is open for discussion and under review for The Cryosphere (TC).
Short summary
Short summary
This paper presents a four-dimensional variational data assimilation system based on a neural network emulator for sea-ice thickness, learned from neXtSIM simulation outputs. Testing with simulated and real observation retrievals, the system improves forecasts and bias error, performing comparably to operational methods, demonstrating the promise of sea-ice data-driven data assimilation systems.
Simon Driscoll, Alberto Carrassi, Julien Brajard, Laurent Bertino, Einar Ólason, Marc Bocquet, and Amos Lawless
EGUsphere, https://doi.org/10.5194/egusphere-2024-2476, https://doi.org/10.5194/egusphere-2024-2476, 2024
Short summary
Short summary
The formation and evolution of sea ice melt ponds (ponds of melted water) are complex, insufficiently understood and represented in models with considerable uncertainty. These uncertain representations are not traditionally included in climate models potentially causing the known underestimation of sea ice loss in climate models. Our work creates the first observationally based machine learning model of melt ponds that is also a ready and viable candidate to be included in climate models.
Joffrey Dumont Le Brazidec, Pierre Vanderbecken, Alban Farchi, Grégoire Broquet, Gerrit Kuhlmann, and Marc Bocquet
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2024-156, https://doi.org/10.5194/gmd-2024-156, 2024
Revised manuscript accepted for GMD
Short summary
Short summary
We developed a deep learning method to estimate CO2 emissions from power plants using satellite images. Trained and validated on simulated data, our model accurately predicts emissions despite challenges like cloud cover. When applied to real OCO3 satellite image, the results closely match reported emissions. This study shows that neural networks trained on simulations can effectively analyse real satellite data, offering a new way to monitor CO2 emissions from space.
Tobias Sebastian Finn, Lucas Disson, Alban Farchi, Marc Bocquet, and Charlotte Durand
Nonlin. Processes Geophys., 31, 409–431, https://doi.org/10.5194/npg-31-409-2024, https://doi.org/10.5194/npg-31-409-2024, 2024
Short summary
Short summary
We train neural networks as denoising diffusion models for state generation in the Lorenz 1963 system and demonstrate that they learn an internal representation of the system. We make use of this learned representation and the pre-trained model in two downstream tasks: surrogate modelling and ensemble generation. For both tasks, the diffusion model can outperform other more common approaches. Thus, we see a potential of representation learning with diffusion models for dynamical systems.
Marc Bocquet, Pierre J. Vanderbecken, Alban Farchi, Joffrey Dumont Le Brazidec, and Yelva Roustan
Nonlin. Processes Geophys., 31, 335–357, https://doi.org/10.5194/npg-31-335-2024, https://doi.org/10.5194/npg-31-335-2024, 2024
Short summary
Short summary
A novel approach, optimal transport data assimilation (OTDA), is introduced to merge DA and OT concepts. By leveraging OT's displacement interpolation in space, it minimises mislocation errors within DA applied to physical fields, such as water vapour, hydrometeors, and chemical species. Its richness and flexibility are showcased through one- and two-dimensional illustrations.
Lilian Garcia-Oliva, Alberto Carrassi, and François Counillon
EGUsphere, https://doi.org/10.5194/egusphere-2024-1843, https://doi.org/10.5194/egusphere-2024-1843, 2024
Short summary
Short summary
We used a simple coupled model and a data assimilation method to find the correct initialisation for climate predictions. We aim to clarify when weakly or strongly coupled data assimilation (WCDA or SCDA) is best, depending on the system's dynamical characteristics (spatio-temporal) and data coverage.
We found that WCDA is better in full data coverage. When we have a partially observed system, SCDA is better. This result depends on the temporal and spatial scale of the observed quantity.
We found that WCDA is better in full data coverage. When we have a partially observed system, SCDA is better. This result depends on the temporal and spatial scale of the observed quantity.
Yumeng Chen, Polly Smith, Alberto Carrassi, Ivo Pasmans, Laurent Bertino, Marc Bocquet, Tobias Sebastian Finn, Pierre Rampal, and Véronique Dansereau
The Cryosphere, 18, 2381–2406, https://doi.org/10.5194/tc-18-2381-2024, https://doi.org/10.5194/tc-18-2381-2024, 2024
Short summary
Short summary
We explore multivariate state and parameter estimation using a data assimilation approach through idealised simulations in a dynamics-only sea-ice model based on novel rheology. We identify various potential issues that can arise in complex operational sea-ice models when model parameters are estimated. Even though further investigation will be needed for such complex sea-ice models, we show possibilities of improving the observed and the unobserved model state forecast and parameter accuracy.
Charlotte Durand, Tobias Sebastian Finn, Alban Farchi, Marc Bocquet, Guillaume Boutin, and Einar Ólason
The Cryosphere, 18, 1791–1815, https://doi.org/10.5194/tc-18-1791-2024, https://doi.org/10.5194/tc-18-1791-2024, 2024
Short summary
Short summary
This paper focuses on predicting Arctic-wide sea-ice thickness using surrogate modeling with deep learning. The model has a predictive power of 12 h up to 6 months. For this forecast horizon, persistence and daily climatology are systematically outperformed, a result of learned thermodynamics and advection. Consequently, surrogate modeling with deep learning proves to be effective at capturing the complex behavior of sea ice.
Joffrey Dumont Le Brazidec, Pierre Vanderbecken, Alban Farchi, Grégoire Broquet, Gerrit Kuhlmann, and Marc Bocquet
Geosci. Model Dev., 17, 1995–2014, https://doi.org/10.5194/gmd-17-1995-2024, https://doi.org/10.5194/gmd-17-1995-2024, 2024
Short summary
Short summary
Our research presents an innovative approach to estimating power plant CO2 emissions from satellite images of the corresponding plumes such as those from the forthcoming CO2M satellite constellation. The exploitation of these images is challenging due to noise and meteorological uncertainties. To overcome these obstacles, we use a deep learning neural network trained on simulated CO2 images. Our method outperforms alternatives, providing a positive perspective for the analysis of CO2M images.
Ieuan Higgs, Jozef Skákala, Ross Bannister, Alberto Carrassi, and Stefano Ciavatta
Biogeosciences, 21, 731–746, https://doi.org/10.5194/bg-21-731-2024, https://doi.org/10.5194/bg-21-731-2024, 2024
Short summary
Short summary
A complex network is a way of representing which parts of a system are connected to other parts. We have constructed a complex network based on an ecosystem–ocean model. From this, we can identify patterns in the structure and areas of similar behaviour. This can help to understand how natural, or human-made, changes will affect the shelf sea ecosystem, and it can be used in multiple future applications such as improving modelling, data assimilation, or machine learning.
Tobias Sebastian Finn, Charlotte Durand, Alban Farchi, Marc Bocquet, Yumeng Chen, Alberto Carrassi, and Véronique Dansereau
The Cryosphere, 17, 2965–2991, https://doi.org/10.5194/tc-17-2965-2023, https://doi.org/10.5194/tc-17-2965-2023, 2023
Short summary
Short summary
We combine deep learning with a regional sea-ice model to correct model errors in the sea-ice dynamics of low-resolution forecasts towards high-resolution simulations. The combined model improves the forecast by up to 75 % and thereby surpasses the performance of persistence. As the error connection can additionally be used to analyse the shortcomings of the forecasts, this study highlights the potential of combined modelling for short-term sea-ice forecasting.
Joffrey Dumont Le Brazidec, Pierre Vanderbecken, Alban Farchi, Marc Bocquet, Jinghui Lian, Grégoire Broquet, Gerrit Kuhlmann, Alexandre Danjou, and Thomas Lauvaux
Geosci. Model Dev., 16, 3997–4016, https://doi.org/10.5194/gmd-16-3997-2023, https://doi.org/10.5194/gmd-16-3997-2023, 2023
Short summary
Short summary
Monitoring of CO2 emissions is key to the development of reduction policies. Local emissions, from cities or power plants, may be estimated from CO2 plumes detected in satellite images. CO2 plumes generally have a weak signal and are partially concealed by highly variable background concentrations and instrument errors, which hampers their detection. To address this problem, we propose and apply deep learning methods to detect the contour of a plume in simulated CO2 satellite images.
Sukun Cheng, Yumeng Chen, Ali Aydoğdu, Laurent Bertino, Alberto Carrassi, Pierre Rampal, and Christopher K. R. T. Jones
The Cryosphere, 17, 1735–1754, https://doi.org/10.5194/tc-17-1735-2023, https://doi.org/10.5194/tc-17-1735-2023, 2023
Short summary
Short summary
This work studies a novel application of combining a Lagrangian sea ice model, neXtSIM, and data assimilation. It uses a deterministic ensemble Kalman filter to incorporate satellite-observed ice concentration and thickness in simulations. The neXtSIM Lagrangian nature is handled using a remapping strategy on a common homogeneous mesh. The ensemble is formed by perturbing air–ocean boundary conditions and ice cohesion. Thanks to data assimilation, winter Arctic sea ice forecasting is enhanced.
Pierre J. Vanderbecken, Joffrey Dumont Le Brazidec, Alban Farchi, Marc Bocquet, Yelva Roustan, Élise Potier, and Grégoire Broquet
Atmos. Meas. Tech., 16, 1745–1766, https://doi.org/10.5194/amt-16-1745-2023, https://doi.org/10.5194/amt-16-1745-2023, 2023
Short summary
Short summary
Instruments dedicated to monitoring atmospheric gaseous compounds from space will provide images of urban-scale plumes. We discuss here the use of new metrics to compare observed plumes with model predictions that will be less sensitive to meteorology uncertainties. We have evaluated our metrics on diverse plumes and shown that by eliminating some aspects of the discrepancies, they are indeed less sensitive to meteorological variations.
Joffrey Dumont Le Brazidec, Marc Bocquet, Olivier Saunier, and Yelva Roustan
Geosci. Model Dev., 16, 1039–1052, https://doi.org/10.5194/gmd-16-1039-2023, https://doi.org/10.5194/gmd-16-1039-2023, 2023
Short summary
Short summary
When radionuclides are released into the atmosphere, the assessment of the consequences depends on the evaluation of the magnitude and temporal evolution of the release, which can be highly variable as in the case of Fukushima Daiichi.
Here, we propose Bayesian inverse modelling methods and the reversible-jump Markov chain Monte Carlo technique, which allows one to evaluate the temporal variability of the release and to integrate different types of information in the source reconstruction.
Colin Grudzien and Marc Bocquet
Geosci. Model Dev., 15, 7641–7681, https://doi.org/10.5194/gmd-15-7641-2022, https://doi.org/10.5194/gmd-15-7641-2022, 2022
Short summary
Short summary
Iterative optimization techniques, the state of the art in data assimilation, have largely focused on extending forecast accuracy to moderate- to long-range forecast systems. However, current methodology may not be cost-effective in reducing forecast errors in online, short-range forecast systems. We propose a novel optimization of these techniques for online, short-range forecast cycles, simultaneously providing an improvement in forecast accuracy and a reduction in the computational cost.
Francine Schevenhoven and Alberto Carrassi
Geosci. Model Dev., 15, 3831–3844, https://doi.org/10.5194/gmd-15-3831-2022, https://doi.org/10.5194/gmd-15-3831-2022, 2022
Short summary
Short summary
In this study, we present a novel formulation to build a dynamical combination of models, the so-called supermodel, which needs to be trained based on data. Previously, we assumed complete and noise-free observations. Here, we move towards a realistic scenario and develop adaptations to the training methods in order to cope with sparse and noisy observations. The results are very promising and shed light on how to apply the method with state of the art general circulation models.
Yumeng Chen, Alberto Carrassi, and Valerio Lucarini
Nonlin. Processes Geophys., 28, 633–649, https://doi.org/10.5194/npg-28-633-2021, https://doi.org/10.5194/npg-28-633-2021, 2021
Short summary
Short summary
Chaotic dynamical systems are sensitive to the initial conditions, which are crucial for climate forecast. These properties are often used to inform the design of data assimilation (DA), a method used to estimate the exact initial conditions. However, obtaining the instability properties is burdensome for complex problems, both numerically and analytically. Here, we suggest a different viewpoint. We show that the skill of DA can be used to infer the instability properties of a dynamical system.
Joffrey Dumont Le Brazidec, Marc Bocquet, Olivier Saunier, and Yelva Roustan
Atmos. Chem. Phys., 21, 13247–13267, https://doi.org/10.5194/acp-21-13247-2021, https://doi.org/10.5194/acp-21-13247-2021, 2021
Short summary
Short summary
The assessment of the environmental consequences of a radionuclide release depends on the estimation of its source. This paper aims to develop inverse Bayesian methods which combine transport models with measurements, in order to reconstruct the ensemble of possible sources.
Three methods to quantify uncertainties based on the definition of probability distributions and the physical models are proposed and evaluated for the case of 106Ru releases over Europe in 2017.
Francine Schevenhoven, Frank Selten, Alberto Carrassi, and Noel Keenlyside
Earth Syst. Dynam., 10, 789–807, https://doi.org/10.5194/esd-10-789-2019, https://doi.org/10.5194/esd-10-789-2019, 2019
Short summary
Short summary
Weather and climate predictions potentially improve by dynamically combining different models into a
supermodel. A crucial step is to train the supermodel on the basis of observations. Here, we apply two different training methods to the global atmosphere–ocean–land model SPEEDO. We demonstrate that both training methods yield climate and weather predictions of superior quality compared to the individual models. Supermodel predictions can also outperform the commonly used multi-model mean.
Thomas Lauvaux, Liza I. Díaz-Isaac, Marc Bocquet, and Nicolas Bousserez
Atmos. Chem. Phys., 19, 12007–12024, https://doi.org/10.5194/acp-19-12007-2019, https://doi.org/10.5194/acp-19-12007-2019, 2019
Short summary
Short summary
A small-size ensemble of mesoscale simulations has been filtered to characterize the spatial structures of transport errors in atmospheric CO2 mixing ratios. The extracted error structures in in situ and column CO2 show similar length scales compared to other meteorological variables, including seasonality, which could be used as proxies in regional inversion systems.
Ali Aydoğdu, Alberto Carrassi, Colin T. Guider, Chris K. R. T Jones, and Pierre Rampal
Nonlin. Processes Geophys., 26, 175–193, https://doi.org/10.5194/npg-26-175-2019, https://doi.org/10.5194/npg-26-175-2019, 2019
Short summary
Short summary
Computational models involving adaptive meshes can both evolve dynamically and be remeshed. Remeshing means that the state vector dimension changes in time and across ensemble members, making the ensemble Kalman filter (EnKF) unsuitable for assimilation of observational data. We develop a modification in which analysis is performed on a fixed uniform grid onto which the ensemble is mapped, with resolution relating to the remeshing criteria. The approach is successfully tested on two 1-D models.
Marc Bocquet, Julien Brajard, Alberto Carrassi, and Laurent Bertino
Nonlin. Processes Geophys., 26, 143–162, https://doi.org/10.5194/npg-26-143-2019, https://doi.org/10.5194/npg-26-143-2019, 2019
Short summary
Short summary
This paper describes an innovative way to use data assimilation to infer the dynamics of a physical system from its observation only. The method can operate with noisy and partial observation of the physical system. It acts as a deep learning technique specialised to dynamical models without the need for machine learning tools. The method is successfully tested on chaotic dynamical systems: the Lorenz-63, Lorenz-96, and Kuramoto–Sivashinski models and a two-scale Lorenz model.
Julien Brajard, Alberto Carrassi, Marc Bocquet, and Laurent Bertino
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2019-136, https://doi.org/10.5194/gmd-2019-136, 2019
Revised manuscript not accepted
Short summary
Short summary
We explore the possibility of combining data assimilation with machine learning. We introduce a new hybrid method for a two-fold scope: (i) emulating hidden, possibly chaotic, dynamics and (ii) predicting its future states. Numerical experiments have been carried out using the chaotic Lorenz 96 model, proving both the convergence of the hybrid method and its statistical skills including short-term forecasting and emulation of the long-term dynamics.
Liza I. Díaz-Isaac, Thomas Lauvaux, Marc Bocquet, and Kenneth J. Davis
Atmos. Chem. Phys., 19, 5695–5718, https://doi.org/10.5194/acp-19-5695-2019, https://doi.org/10.5194/acp-19-5695-2019, 2019
Short summary
Short summary
We demonstrate that transport model errors, one of the main contributors to the uncertainty in regional CO2 inversions, can be represented by a small-size ensemble carefully calibrated with meteorological data. Our results also confirm transport model errors represent a significant fraction of the model–data mismatch in CO2 mole fractions and hence in regional inverse CO2 fluxes.
Alban Farchi and Marc Bocquet
Nonlin. Processes Geophys., 25, 765–807, https://doi.org/10.5194/npg-25-765-2018, https://doi.org/10.5194/npg-25-765-2018, 2018
Short summary
Short summary
Data assimilation looks for an optimal way to learn from observations of a dynamical system to improve the quality of its predictions. The goal is to filter out the noise (both observation and model noise) to retrieve the true signal. Among all possible methods, particle filters are promising; the method is fast and elegant, and it allows for a Bayesian analysis. In this review paper, we discuss implementation techniques for (local) particle filters in high-dimensional systems.
Colin Grudzien, Alberto Carrassi, and Marc Bocquet
Nonlin. Processes Geophys., 25, 633–648, https://doi.org/10.5194/npg-25-633-2018, https://doi.org/10.5194/npg-25-633-2018, 2018
Short summary
Short summary
Using the framework Lyapunov vectors, we analyze the asymptotic properties of ensemble based Kalman filters and how these are influenced by dynamical chaos, especially in the context of random model errors and small ensemble sizes. Particularly, we show a novel derivation of the evolution of forecast uncertainty for ensemble-based Kalman filters with weakly-nonlinear error growth, and discuss its impact for filter design in geophysical models.
Olivier Pannekoucke, Marc Bocquet, and Richard Ménard
Nonlin. Processes Geophys., 25, 481–495, https://doi.org/10.5194/npg-25-481-2018, https://doi.org/10.5194/npg-25-481-2018, 2018
Short summary
Short summary
The forecast of weather prediction uncertainty is a real challenge and is crucial for risk management. However, uncertainty prediction is beyond the capacity of supercomputers, and improvements of the technology may not solve this issue. A new uncertainty prediction method is introduced which takes advantage of fluid equations to predict simple quantities which approximate real uncertainty but at a low numerical cost. A proof of concept is shown by an academic model derived from fluid dynamics.
Anthony Fillion, Marc Bocquet, and Serge Gratton
Nonlin. Processes Geophys., 25, 315–334, https://doi.org/10.5194/npg-25-315-2018, https://doi.org/10.5194/npg-25-315-2018, 2018
Short summary
Short summary
This study generalizes a paper by Pires et al. (1996) to state-of-the-art data assimilation techniques, such as the iterative ensemble Kalman smoother (IEnKS). We show that the longer the time window over which observations are assimilated, the better the accuracy of the IEnKS. Beyond a critical time length that we estimate, we show that this accuracy finally degrades. We show that the use of the quasi-static minimizations but generalized to the IEnKS yields a significantly improved accuracy.
Matthias Rabatel, Pierre Rampal, Alberto Carrassi, Laurent Bertino, and Christopher K. R. T. Jones
The Cryosphere, 12, 935–953, https://doi.org/10.5194/tc-12-935-2018, https://doi.org/10.5194/tc-12-935-2018, 2018
Short summary
Short summary
Large deviations still exist between sea ice forecasts and observations because of both missing physics in models and uncertainties on model inputs. We investigate how the new sea ice model neXtSIM is sensitive to uncertainties in the winds. We highlight and quantify the role of the internal forces in the ice on this sensitivity and show that neXtSIM is better at predicting sea ice drift than a free-drift (without internal forces) ice model and is a skilful tool for search and rescue operations.
J.-M. Haussaire and M. Bocquet
Geosci. Model Dev., 9, 393–412, https://doi.org/10.5194/gmd-9-393-2016, https://doi.org/10.5194/gmd-9-393-2016, 2016
Short summary
Short summary
The focus is on the development of low-order models of atmospheric transport and chemistry and their use for data assimilation purposes. A new low-order coupled chemistry meteorology model is developed. It consists of the Lorenz40-variable model used as a wind field coupled with a simple ozone photochemistry module. Advanced ensemble variational methods are applied to this model to obtain insights on the use of data assimilation with coupled models, in an offline mode or in an online mode.
M. Bocquet, P. N. Raanes, and A. Hannart
Nonlin. Processes Geophys., 22, 645–662, https://doi.org/10.5194/npg-22-645-2015, https://doi.org/10.5194/npg-22-645-2015, 2015
Short summary
Short summary
The popular data assimilation technique known as the ensemble Kalman filter (EnKF) suffers from sampling errors due to the limited size of the ensemble. This deficiency is usually cured by inflating the sampled error covariances and by using localization. This paper further develops and discusses the finite-size EnKF, or EnKF-N, a variant of the EnKF that does not require inflation. It expands the use of the EnKF-N to a wider range of dynamical regimes.
M. Bocquet, H. Elbern, H. Eskes, M. Hirtl, R. Žabkar, G. R. Carmichael, J. Flemming, A. Inness, M. Pagowski, J. L. Pérez Camaño, P. E. Saide, R. San Jose, M. Sofiev, J. Vira, A. Baklanov, C. Carnevale, G. Grell, and C. Seigneur
Atmos. Chem. Phys., 15, 5325–5358, https://doi.org/10.5194/acp-15-5325-2015, https://doi.org/10.5194/acp-15-5325-2015, 2015
Short summary
Short summary
Data assimilation is used in atmospheric chemistry models to improve air quality forecasts, construct re-analyses of concentrations, and perform inverse modeling. Coupled chemistry meteorology models (CCMM) are atmospheric chemistry models that simulate meteorological processes and chemical transformations jointly. We review here the current status of data assimilation in atmospheric chemistry models, with a particular focus on future prospects for data assimilation in CCMM.
Y. Wang, K. N. Sartelet, M. Bocquet, P. Chazette, M. Sicard, G. D'Amico, J. F. Léon, L. Alados-Arboledas, A. Amodeo, P. Augustin, J. Bach, L. Belegante, I. Binietoglou, X. Bush, A. Comerón, H. Delbarre, D. García-Vízcaino, J. L. Guerrero-Rascado, M. Hervo, M. Iarlori, P. Kokkalis, D. Lange, F. Molero, N. Montoux, A. Muñoz, C. Muñoz, D. Nicolae, A. Papayannis, G. Pappalardo, J. Preissler, V. Rizi, F. Rocadenbosch, K. Sellegri, F. Wagner, and F. Dulac
Atmos. Chem. Phys., 14, 12031–12053, https://doi.org/10.5194/acp-14-12031-2014, https://doi.org/10.5194/acp-14-12031-2014, 2014
Y. Wang, K. N. Sartelet, M. Bocquet, and P. Chazette
Atmos. Chem. Phys., 14, 3511–3532, https://doi.org/10.5194/acp-14-3511-2014, https://doi.org/10.5194/acp-14-3511-2014, 2014
O. Saunier, A. Mathieu, D. Didier, M. Tombette, D. Quélo, V. Winiarek, and M. Bocquet
Atmos. Chem. Phys., 13, 11403–11421, https://doi.org/10.5194/acp-13-11403-2013, https://doi.org/10.5194/acp-13-11403-2013, 2013
M. Bocquet and P. Sakov
Nonlin. Processes Geophys., 20, 803–818, https://doi.org/10.5194/npg-20-803-2013, https://doi.org/10.5194/npg-20-803-2013, 2013
M. R. Koohkan, M. Bocquet, Y. Roustan, Y. Kim, and C. Seigneur
Atmos. Chem. Phys., 13, 5887–5905, https://doi.org/10.5194/acp-13-5887-2013, https://doi.org/10.5194/acp-13-5887-2013, 2013
Y. Wang, K. N. Sartelet, M. Bocquet, and P. Chazette
Atmos. Chem. Phys., 13, 269–283, https://doi.org/10.5194/acp-13-269-2013, https://doi.org/10.5194/acp-13-269-2013, 2013
Related subject area
Numerical methods
Hydro-geomorphological modelling of leaky wooden dam efficacy from reach to catchment scale with CAESAR-Lisflood 1.9j
Enhancing single precision with quasi-double precision: achieving double-precision accuracy in the Model for Prediction Across Scales – Atmosphere (MPAS-A) version 8.2.1
Advances in land surface forecasting: a comparison of LSTM, gradient boosting, and feed-forward neural networks as prognostic state emulators in a case study with ecLand
Subgrid corrections for the linear inertial equations of a compound flood model – a case study using SFINCS 2.1.1 Dollerup release
Introducing Iterative Model Calibration (IMC) v1.0: a generalizable framework for numerical model calibration with a CAESAR-Lisflood case study
Development of a high-order global dynamical core using the discontinuous Galerkin method for an atmospheric large-eddy simulation (LES) and proposal of test cases: SCALE-DG v0.8.0
A joint reconstruction and model selection approach for large-scale linear inverse modeling (msHyBR v2)
Assimilation of snow water equivalent from AMSR2 and IMS satellite data utilizing the local ensemble transform Kalman filter
The Paleochrono-1.1 probabilistic model to derive a common age model for several paleoclimatic sites using absolute and relative dating constraints
Explicit stochastic advection algorithms for the regional-scale particle-resolved atmospheric aerosol model WRF-PartMC (v1.0)
Potential based Thermodynamics with Consistent Conservative Cascade Transport for Implicit Large Eddy Simulation: PTerodaC3TILES version 1.0
The Measurement Error Proxy System Model: MEPSM v0.2
Numerical stabilization methods for level-set-based ice front migration
Modelling chemical advection during magma ascent
Consistent point data assimilation in Firedrake and Icepack
A computationally efficient parameterization of aerosol, cloud and precipitation pH for application at global and regional scale (EQSAM4Clim-v12)
Assessing the benefits of approximately exact step sizes for Picard and Newton solver in simulating ice flow (FEniCS-full-Stokes v.1.3.2)
Assessing effects of climate and technology uncertainties in large natural resource allocation problems
VISIR-2: ship weather routing in Python
Incremental analysis update (IAU) in the Model for Prediction Across Scales coupled with the Joint Effort for Data assimilation Integration (MPAS–JEDI 2.0.0)
Decision-making strategies implemented in SolFinder 1.0 to identify eco-efficient aircraft trajectories: application study in AirTraf 3.0
CLAQC v1.0 – Country Level Air Quality Calculator. An Empirical Modeling Approach
Developing meshing workflows in Gmsh v4.11 for the geologic uncertainty assessment of high-temperature aquifer thermal energy storage
Development and preliminary validation of a land surface image assimilation system based on the Common Land Model
NorSand4AI: a comprehensive triaxial test simulation database for NorSand constitutive model materials
ParticleDA.jl v.1.0: a distributed particle-filtering data assimilation package
HETerogeneous vectorized or Parallel (HETPv1.0): an updated inorganic heterogeneous chemistry solver for the metastable-state NH4+–Na+–Ca2+–K+–Mg2+–SO42−–NO3−–Cl−–H2O system based on ISORROPIA II
Three-dimensional geological modelling of igneous intrusions in LoopStructural v1.5.10
Estimating volcanic ash emissions using retrieved satellite ash columns and inverse ash transport modeling using VolcanicAshInversion v1.2.1, within the operational eEMEP (emergency European Monitoring and Evaluation Programme) volcanic plume forecasting system (version rv4_17)
Accounting for uncertainties in forecasting tropical-cyclone-induced compound flooding
An automatic mesh generator for coupled 1D–2D hydrodynamic models
Numerical coupling of aerosol emissions, dry removal, and turbulent mixing in the E3SM Atmosphere Model version 1 (EAMv1) – Part 1: Dust budget analyses and the impacts of a revised coupling scheme
Numerical coupling of aerosol emissions, dry removal, and turbulent mixing in the E3SM Atmosphere Model version 1 (EAMv1) – Part 2: A semi-discrete error analysis framework for assessing coupling schemes
jsmetrics v0.2.0: a Python package for metrics and algorithms used to identify or characterise atmospheric jet streams
P3D-BRNS v1.0.0: a three-dimensional, multiphase, multicomponent, pore-scale reactive transport modelling package for simulating biogeochemical processes in subsurface environments
MinVoellmy v1: a lightweight model for simulating rapid mass movements based on a modified Voellmy rheology
Scalable Feature Extraction and Tracking (SCAFET): a general framework for feature extraction from large climate data sets
Sweep interpolation: a cost-effective semi-Lagrangian scheme in the Global Environmental Multiscale model
CHONK 1.0: landscape evolution framework: cellular automata meets graph theory
Perspectives of physics-based machine learning strategies for geoscientific applications governed by partial differential equations
Calibration of absorbing boundary layers for geoacoustic wave modeling in pseudo-spectral time-domain methods
GeoINR 1.0: an implicit neural network approach to three-dimensional geological modelling
Parameterization and tuning of the Bay of Biscay Atlantis model v1
A comparison of Eulerian and Lagrangian methods for vertical particle transport in the water column
AutoQS v1: automatic parametrization of QuickSampling based on training images analysis
Implementation and application of ensemble optimal interpolation on an operational chemistry weather model for improving PM2.5 and visibility predictions
A dynamical core based on a discontinuous Galerkin method for higher-order finite-element sea ice modeling
GStatSim V1.0: a Python package for geostatistical interpolation and conditional simulation
Leveraging Google's Tensor Processing Units for tsunami-risk mitigation planning in the Pacific Northwest and beyond
An improved subgrid channel model with upwind-form artificial diffusion for river hydrodynamics and floodplain inundation simulation
Joshua M. Wolstenholme, Christopher J. Skinner, David Milan, Robert E. Thomas, and Daniel R. Parsons
Geosci. Model Dev., 18, 1395–1411, https://doi.org/10.5194/gmd-18-1395-2025, https://doi.org/10.5194/gmd-18-1395-2025, 2025
Short summary
Short summary
Leaky wooden dams are a type of natural flood management intervention that aims to reduce flood risk downstream by temporarily holding back water during a storm event and releasing it afterwards. These structures alter the river hydrology, and therefore the geomorphology, yet often this is excluded from numerical models. Here we show that by not simulating geomorphology, we are currently underestimating the efficacy of these structures to reduce the flood peak and store water.
Jiayi Lai, Lanning Wang, Qizhong Wu, Yizhou Yang, and Fang Wang
Geosci. Model Dev., 18, 1089–1102, https://doi.org/10.5194/gmd-18-1089-2025, https://doi.org/10.5194/gmd-18-1089-2025, 2025
Short summary
Short summary
High-performance computing limitations often hinder numerical model development. Traditional models use double precision for accuracy, which is computationally expensive. Lower precision reduces costs but can introduce errors. The quasi-double-precision (QDP) algorithm helps mitigate these errors. This study applies the QDP algorithm to the Model for Prediction Across Scales – Atmosphere, showing reduced errors and computational time, making it an efficient solution for large-scale simulations.
Marieke Wesselkamp, Matthew Chantry, Ewan Pinnington, Margarita Choulga, Souhail Boussetta, Maria Kalweit, Joschka Bödecker, Carsten F. Dormann, Florian Pappenberger, and Gianpaolo Balsamo
Geosci. Model Dev., 18, 921–937, https://doi.org/10.5194/gmd-18-921-2025, https://doi.org/10.5194/gmd-18-921-2025, 2025
Short summary
Short summary
We compared spatiotemporal forecasts of three machine learning models that learned water and energy
states on the land surface from a physical model scheme. The forecasting models were developed with reanalysis data and simulations on a European scale and transferred to the globe. We found that all approaches deliver highly accurate approximations of the physical dynamic at long time horizons, implying their usefulness to advance land surface forecasting with synthetic data.
states on the land surface from a physical model scheme. The forecasting models were developed with reanalysis data and simulations on a European scale and transferred to the globe. We found that all approaches deliver highly accurate approximations of the physical dynamic at long time horizons, implying their usefulness to advance land surface forecasting with synthetic data.
Maarten van Ormondt, Tim Leijnse, Roel de Goede, Kees Nederhoff, and Ap van Dongeren
Geosci. Model Dev., 18, 843–861, https://doi.org/10.5194/gmd-18-843-2025, https://doi.org/10.5194/gmd-18-843-2025, 2025
Short summary
Short summary
Accurate flood risk assessments are crucial for storm protection. To achieve efficiency, computational costs must be minimized. This paper introduces a novel subgrid approach for linear inertial equations (LIEs) with bed level and friction variations, implemented in the Super-Fast INundation of CoastS (SFINCS) model. Pre-processed lookup tables enhance simulation precision with lower costs. Validations show significant accuracy improvement even at coarser resolutions.
Chayan Banerjee, Kien Nguyen, Clinton Fookes, Gregory Hancock, and Thomas Coulthard
Geosci. Model Dev., 18, 803–818, https://doi.org/10.5194/gmd-18-803-2025, https://doi.org/10.5194/gmd-18-803-2025, 2025
Short summary
Short summary
In geosciences, the reliance on numerical models necessitates the precise calibration of their parameters to effectively translate information from observed to unobserved settings. We introduce a generalizable framework for calibrating numerical models, with a case study of the geomorphological model CAESAR-Lisflood. This approach efficiently identifies the optimal set of parameters for a given numerical model, enabling retrospective and prospective analyses at various temporal resolutions.
Yuta Kawai and Hirofumi Tomita
Geosci. Model Dev., 18, 725–762, https://doi.org/10.5194/gmd-18-725-2025, https://doi.org/10.5194/gmd-18-725-2025, 2025
Short summary
Short summary
When considering future high-resolution atmospheric simulations with O(10–100 m) grid spacing, such as global large-eddy simulations, numerical errors with the conventional low-order dynamical cores can contaminate the effects of turbulent parameterization. To achieve high-order discretization, we developed a global atmospheric dynamical core using the discontinuous Galerkin method (DGM). By conducting several validation tests, we discussed the impact of a high-order DGM on atmospheric flows.
Malena Sabaté Landman, Julianne Chung, Jiahua Jiang, Scot M. Miller, and Arvind K. Saibaba
Geosci. Model Dev., 17, 8853–8872, https://doi.org/10.5194/gmd-17-8853-2024, https://doi.org/10.5194/gmd-17-8853-2024, 2024
Short summary
Short summary
Making an informed decision about what prior information to incorporate or discard in an inverse model is important yet very challenging, as it is often not straightforward to distinguish between informative and non-informative variables. In this study, we develop a new approach for incorporating prior information in an inverse model using predictor variables, while simultaneously selecting the relevant predictor variables for the estimation of the unknown quantity of interest.
Joonlee Lee, Myong-In Lee, Sunlae Tak, Eunkyo Seo, and Yong-Keun Lee
Geosci. Model Dev., 17, 8799–8816, https://doi.org/10.5194/gmd-17-8799-2024, https://doi.org/10.5194/gmd-17-8799-2024, 2024
Short summary
Short summary
We developed an advanced snow water equivalent (SWE) data assimilation framework using satellite data based on a land surface model. The results of this study highlight the beneficial impact of data assimilation by effectively combining land surface model and satellite-derived data according to their relative uncertainty, thereby controlling not only transitional regions but also the regions with heavy snow accumulation that are difficult to detect by satellite.
Frédéric Parrenin, Marie Bouchet, Christo Buizert, Emilie Capron, Ellen Corrick, Russell Drysdale, Kenji Kawamura, Amaëlle Landais, Robert Mulvaney, Ikumi Oyabu, and Sune Olander Rasmussen
Geosci. Model Dev., 17, 8735–8750, https://doi.org/10.5194/gmd-17-8735-2024, https://doi.org/10.5194/gmd-17-8735-2024, 2024
Short summary
Short summary
The Paleochrono-1.1 probabilistic dating model allows users to derive a common and optimized chronology for several paleoclimatic sites from various archives (ice cores, speleothems, marine cores, lake cores, etc.). It combines prior sedimentation scenarios with chronological information such as dated horizons, dated intervals, stratigraphic links and (for ice cores) Δdepth observations. Paleochrono-1.1 is available under an open-source license.
Jeffrey H. Curtis, Nicole Riemer, and Matthew West
Geosci. Model Dev., 17, 8399–8420, https://doi.org/10.5194/gmd-17-8399-2024, https://doi.org/10.5194/gmd-17-8399-2024, 2024
Short summary
Short summary
This paper introduces a numerical method for simulating particle-based aerosol transport in atmospheric models. We detail the various numerical properties of the advection order method and demonstrate its implementation in a 3D weather prediction model (WRF) for the first time. Particle-based techniques improve the accuracy of aerosol size and composition predictions, which are key for aerosol–cloud and aerosol–radiation interactions.
John Thuburn
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2024-153, https://doi.org/10.5194/gmd-2024-153, 2024
Revised manuscript accepted for GMD
Short summary
Short summary
A new computational fluid dynamics code for simulating the atmospheric boundary layer and convection is presented. Moist thermodynamics is formulated via thermodynamic potentials, avoiding inconsistencies that can be introduced with conventional approaches. Numerical methods typical of weather and climate models are used, with no explicit subgrid scheme. Results highlight some advantages (e.g., large time steps) and disadvantages (e.g., weak vertical fluxes near the surface) of this approach.
Matt J. Fischer
Geosci. Model Dev., 17, 6745–6760, https://doi.org/10.5194/gmd-17-6745-2024, https://doi.org/10.5194/gmd-17-6745-2024, 2024
Short summary
Short summary
In paleoclimate research, proxy system models (PSMs) model chemical or biological systems which receive environmental input and output (e.g., geochemical signals). The environmental inputs are rarely noiseless, which causes problems when calibrating multi-input PSMs. Here a PSM is developed which includes generalized noise in both model inputs and outputs and prior information. A quasi-Bayesian method enhances the stability of the solution of the Measurement Error Proxy System Model.
Gong Cheng, Mathieu Morlighem, and G. Hilmar Gudmundsson
Geosci. Model Dev., 17, 6227–6247, https://doi.org/10.5194/gmd-17-6227-2024, https://doi.org/10.5194/gmd-17-6227-2024, 2024
Short summary
Short summary
We conducted a comprehensive analysis of the stabilization and reinitialization techniques currently employed in ISSM and Úa for solving level-set equations, specifically those related to the dynamic representation of moving ice fronts within numerical ice sheet models. Our results demonstrate that the streamline upwind Petrov–Galerkin (SUPG) method outperforms the other approaches. We found that excessively frequent reinitialization can lead to exceptionally high errors in simulations.
Hugo Dominguez, Nicolas Riel, and Pierre Lanari
Geosci. Model Dev., 17, 6105–6122, https://doi.org/10.5194/gmd-17-6105-2024, https://doi.org/10.5194/gmd-17-6105-2024, 2024
Short summary
Short summary
Predicting the behaviour of magmatic systems is important for understanding Earth's matter and heat transport. Numerical modelling is a technique that can predict complex systems at different scales of space and time by solving equations using various techniques. This study tests four algorithms to find the best way to transport the melt composition. The "weighted essentially non-oscillatory" algorithm emerges as the best choice, minimising errors and preserving system mass well.
Reuben W. Nixon-Hill, Daniel Shapero, Colin J. Cotter, and David A. Ham
Geosci. Model Dev., 17, 5369–5386, https://doi.org/10.5194/gmd-17-5369-2024, https://doi.org/10.5194/gmd-17-5369-2024, 2024
Short summary
Short summary
Scientists often use models to study complex processes, like the movement of ice sheets, and compare them to measurements for estimating quantities that are hard to measure. We highlight an approach that ensures accurate results from point data sources (e.g. height measurements) by evaluating the numerical solution at true point locations. This method improves accuracy, aids communication between scientists, and is well-suited for integration with specialised software that automates processes.
Swen Metzger, Samuel Rémy, Jason E. Williams, Vincent Huijnen, and Johannes Flemming
Geosci. Model Dev., 17, 5009–5021, https://doi.org/10.5194/gmd-17-5009-2024, https://doi.org/10.5194/gmd-17-5009-2024, 2024
Short summary
Short summary
EQSAM4Clim has recently been revised to provide an accurate and efficient method for calculating the acidity of atmospheric particles. It is based on an analytical concept that is sufficiently fast and free of numerical noise, which makes it attractive for air quality forecasting. Version 12 allows the calculation of aerosol composition based on the gas–liquid–solid and the reduced gas–liquid partitioning with the associated water uptake for both cases, including the acidity of the aerosols.
Niko Schmidt, Angelika Humbert, and Thomas Slawig
Geosci. Model Dev., 17, 4943–4959, https://doi.org/10.5194/gmd-17-4943-2024, https://doi.org/10.5194/gmd-17-4943-2024, 2024
Short summary
Short summary
Future sea-level rise is of big significance for coastal regions. The melting and acceleration of glaciers plays a major role in sea-level change. Computer simulation of glaciers costs a lot of computational resources. In this publication, we test a new way of simulating glaciers. This approach produces the same results but has the advantage that it needs much less computation time. As simulations can be obtained with fewer computation resources, higher resolution and physics become affordable.
Jevgenijs Steinbuks, Yongyang Cai, Jonas Jaegermeyr, and Thomas W. Hertel
Geosci. Model Dev., 17, 4791–4819, https://doi.org/10.5194/gmd-17-4791-2024, https://doi.org/10.5194/gmd-17-4791-2024, 2024
Short summary
Short summary
This paper applies a cutting-edge numerical method, SCEQ, to show how uncertain climate change and technological progress affect the future utilization of the world's scarce land resources. The paper's key insight is to illustrate how much global cropland will expand when future crop yields are unknown. The study finds the range of outcomes for land use change to be smaller when using this novel method compared to existing deterministic models.
Gianandrea Mannarini, Mario Leonardo Salinas, Lorenzo Carelli, Nicola Petacco, and Josip Orović
Geosci. Model Dev., 17, 4355–4382, https://doi.org/10.5194/gmd-17-4355-2024, https://doi.org/10.5194/gmd-17-4355-2024, 2024
Short summary
Short summary
Ship weather routing has the potential to reduce CO2 emissions, but it currently lacks open and verifiable research. The Python-refactored VISIR-2 model considers currents, waves, and wind to optimise routes. The model was validated, and its computational performance is quasi-linear. For a ferry sailing in the Mediterranean Sea, VISIR-2 yields the largest percentage emission savings for upwind navigation. Given the vessel performance curve, the model is generalisable across various vessel types.
Soyoung Ha, Jonathan J. Guerrette, Ivette Hernández Baños, William C. Skamarock, and Michael G. Duda
Geosci. Model Dev., 17, 4199–4211, https://doi.org/10.5194/gmd-17-4199-2024, https://doi.org/10.5194/gmd-17-4199-2024, 2024
Short summary
Short summary
To mitigate the imbalances in the initial conditions, this study introduces our recent implementation of the incremental analysis update (IAU) in the Model for Prediction Across Scales – Atmospheric (MPAS-A) component coupled with the Joint Effort for Data assimilation Integration (JEDI) through the cycling system. A month-long cycling run demonstrates the successful implementation of the IAU capability in the MPAS–JEDI cycling system.
Federica Castino, Feijia Yin, Volker Grewe, Hiroshi Yamashita, Sigrun Matthes, Simone Dietmüller, Sabine Baumann, Manuel Soler, Abolfazl Simorgh, Maximilian Mendiguchia Meuser, Florian Linke, and Benjamin Lührs
Geosci. Model Dev., 17, 4031–4052, https://doi.org/10.5194/gmd-17-4031-2024, https://doi.org/10.5194/gmd-17-4031-2024, 2024
Short summary
Short summary
We introduce SolFinder 1.0, a decision-making tool to select trade-offs between different objective functions for optimal aircraft trajectories, including fuel use, flight time, NOx emissions, contrail distance, and climate impact. The module is included in the AirTraf 3.0 submodel and uses weather conditions simulated by the EMAC atmospheric model. This paper focuses on the ability of SolFinder to identify eco-efficient trajectories, reducing a flight's climate impact at limited cost penalties.
Stefania Renna, Francesco Granella, Lara Aleluia Reis, and Paulina Estela Schulz-Antipa
EGUsphere, https://doi.org/10.2139/ssrn.4591252, https://doi.org/10.2139/ssrn.4591252, 2024
Short summary
Short summary
The Country Level Air Quality Calculator (CLAQC) is a new fast modeling tool that predicts globally country-level monthly and annual concentrations of two major air pollutants, fine particulate matter (PM2.5) and tropospheric ozone (O3). It was designed to inform national and regional climate and pollution mitigation policies. It is easy to use and computationally efficient, allowing the simulation of a large number of policy scenarios for policy assessments and optimization frameworks.
Ali Dashti, Jens C. Grimmer, Christophe Geuzaine, Florian Bauer, and Thomas Kohl
Geosci. Model Dev., 17, 3467–3485, https://doi.org/10.5194/gmd-17-3467-2024, https://doi.org/10.5194/gmd-17-3467-2024, 2024
Short summary
Short summary
This study developed new meshing workflows to enable the automatic generation of meshes that follow geological models. The workflow allows for importing several geological models as input for Gmsh and later exporting the same number of high-quality meshes. This way, geological uncertainty is directly included in the numerical simulations. This study evaluates the impact of the geological uncertainty on thermohydraulic performance of two reservoirs for high-temperature heat storage applications.
Wangbin Shen, Zhaohui Lin, Zhengkun Qin, and Juan Li
Geosci. Model Dev., 17, 3447–3465, https://doi.org/10.5194/gmd-17-3447-2024, https://doi.org/10.5194/gmd-17-3447-2024, 2024
Short summary
Short summary
In this study, a land surface image assimilation system capable of optimizing the spatial structure of the background field is constructed by introducing the curvelet analysis method and taking the similarity of image structure as a weak constraint. The findings demonstrate that the assimilation of surface soil moisture observation images effectively and reasonably enhances the spatial structure of soil moisture analysis field.
Luan Carlos de Sena Monteiro Ozelim, Michéle Dal Toé Casagrande, and André Luís Brasil Cavalcante
Geosci. Model Dev., 17, 3175–3197, https://doi.org/10.5194/gmd-17-3175-2024, https://doi.org/10.5194/gmd-17-3175-2024, 2024
Short summary
Short summary
The paper addresses synthetic dataset challenges in nonlinear constitutive modeling of soils, providing two datasets: one with 2000 soil types, 40 test conditions each (160 000 triaxial tests), and a second with 2048 soil types, 42 test conditions each (172 032 triaxial tests). Each dataset is a 4000×10 matrix applicable for multivariate forecasting and geotechnical simulations. In addition, a new Python code is introduced, empowering researchers to leverage Python packages for NorSand analyses.
Daniel Giles, Matthew M. Graham, Mosè Giordano, Tuomas Koskela, Alexandros Beskos, and Serge Guillas
Geosci. Model Dev., 17, 2427–2445, https://doi.org/10.5194/gmd-17-2427-2024, https://doi.org/10.5194/gmd-17-2427-2024, 2024
Short summary
Short summary
Digital twins of physical and human systems informed by real-time data are becoming ubiquitous across a wide range of settings. Progress for researchers is currently limited by a lack of tools to run these models effectively and efficiently. A key challenge is the optimal use of high-performance computing environments. The work presented here focuses on a developed open-source software platform which aims to improve this usage, with an emphasis placed on flexibility, efficiency, and scalability.
Stefan J. Miller, Paul A. Makar, and Colin J. Lee
Geosci. Model Dev., 17, 2197–2219, https://doi.org/10.5194/gmd-17-2197-2024, https://doi.org/10.5194/gmd-17-2197-2024, 2024
Short summary
Short summary
This work outlines a new solver written in Fortran to calculate the partitioning of metastable aerosols at thermodynamic equilibrium based on the forward algorithms of ISORROPIA II. The new code includes numerical improvements that decrease the computational speed (compared to ISORROPIA II) while improving the accuracy of the partitioning solution.
Fernanda Alvarado-Neves, Laurent Ailleres, Lachlan Grose, Alexander R. Cruden, and Robin Armit
Geosci. Model Dev., 17, 1975–1993, https://doi.org/10.5194/gmd-17-1975-2024, https://doi.org/10.5194/gmd-17-1975-2024, 2024
Short summary
Short summary
Previous work has demonstrated that adding geological knowledge to modelling methods creates more accurate and reliable models. Following this reasoning, we added constraints from magma emplacement mechanisms into existing modelling frameworks to improve the 3D characterisation of igneous intrusions. We tested the method on synthetic and real-world case studies, and the results show that our method can reproduce intrusion morphologies with no manual processing and using realistic datasets.
André R. Brodtkorb, Anna Benedictow, Heiko Klein, Arve Kylling, Agnes Nyiri, Alvaro Valdebenito, Espen Sollum, and Nina Kristiansen
Geosci. Model Dev., 17, 1957–1974, https://doi.org/10.5194/gmd-17-1957-2024, https://doi.org/10.5194/gmd-17-1957-2024, 2024
Short summary
Short summary
It is vital to know the extent and concentration of volcanic ash in the atmosphere during a volcanic eruption. Whilst satellite imagery may give an estimate of the ash right now (assuming no cloud coverage), we also need to know where it will be in the coming hours. This paper presents a method for estimating parameters for a volcanic eruption based on satellite observations of ash in the atmosphere. The software package is open source and applicable to similar inversion scenarios.
Kees Nederhoff, Maarten van Ormondt, Jay Veeramony, Ap van Dongeren, José Antonio Álvarez Antolínez, Tim Leijnse, and Dano Roelvink
Geosci. Model Dev., 17, 1789–1811, https://doi.org/10.5194/gmd-17-1789-2024, https://doi.org/10.5194/gmd-17-1789-2024, 2024
Short summary
Short summary
Forecasting tropical cyclones and their flooding impact is challenging. Our research introduces the Tropical Cyclone Forecasting Framework (TC-FF), enhancing cyclone predictions despite uncertainties. TC-FF generates global wind and flood scenarios, valuable even in data-limited regions. Applied to cases like Cyclone Idai, it showcases potential in bettering disaster preparation, marking progress in handling cyclone threats.
Younghun Kang and Ethan J. Kubatko
Geosci. Model Dev., 17, 1603–1625, https://doi.org/10.5194/gmd-17-1603-2024, https://doi.org/10.5194/gmd-17-1603-2024, 2024
Short summary
Short summary
Models used to simulate the flow of coastal and riverine waters, including flooding, require a geometric representation (or mesh) of geographic features that exhibit a range of disparate spatial scales from large, open waters to small, narrow channels. Representing these features in an accurate way without excessive computational overhead presents a challenge. Here, we develop an automatic mesh generation tool to help address this challenge. Our results demonstrate the efficacy of our approach.
Hui Wan, Kai Zhang, Christopher J. Vogl, Carol S. Woodward, Richard C. Easter, Philip J. Rasch, Yan Feng, and Hailong Wang
Geosci. Model Dev., 17, 1387–1407, https://doi.org/10.5194/gmd-17-1387-2024, https://doi.org/10.5194/gmd-17-1387-2024, 2024
Short summary
Short summary
Sophisticated numerical models of the Earth's atmosphere include representations of many physical and chemical processes. In numerical simulations, these processes need to be calculated in a certain sequence. This study reveals the weaknesses of the sequence of calculations used for aerosol processes in a global atmosphere model. A revision of the sequence is proposed and its impacts on the simulated global aerosol climatology are evaluated.
Christopher J. Vogl, Hui Wan, Carol S. Woodward, and Quan M. Bui
Geosci. Model Dev., 17, 1409–1428, https://doi.org/10.5194/gmd-17-1409-2024, https://doi.org/10.5194/gmd-17-1409-2024, 2024
Short summary
Short summary
Generally speaking, accurate climate simulation requires an accurate evolution of the underlying mathematical equations on large computers. The equations are typically formulated and evolved in process groups. Process coupling refers to how the evolution of each group is combined with that of other groups to evolve the full set of equations for the whole atmosphere. This work presents a mathematical framework to evaluate methods without the need to first implement the methods.
Tom Keel, Chris Brierley, and Tamsin Edwards
Geosci. Model Dev., 17, 1229–1247, https://doi.org/10.5194/gmd-17-1229-2024, https://doi.org/10.5194/gmd-17-1229-2024, 2024
Short summary
Short summary
Jet streams are an important control on surface weather as their speed and shape can modify the properties of weather systems. Establishing trends in the operation of jet streams may provide some indication of the future of weather in a warming world. Despite this, it has not been easy to establish trends, as many methods have been used to characterise them in data. We introduce a tool containing various implementations of jet stream statistics and algorithms that works in a standardised manner.
Amir Golparvar, Matthias Kästner, and Martin Thullner
Geosci. Model Dev., 17, 881–898, https://doi.org/10.5194/gmd-17-881-2024, https://doi.org/10.5194/gmd-17-881-2024, 2024
Short summary
Short summary
Coupled reaction transport modelling is an established and beneficial method for studying natural and synthetic porous material, with applications ranging from industrial processes to natural decompositions in terrestrial environments. Up to now, a framework that explicitly considers the porous structure (e.g. from µ-CT images) for modelling the transport of reactive species is missing. We presented a model that overcomes this limitation and represents a novel numerical simulation toolbox.
Stefan Hergarten
Geosci. Model Dev., 17, 781–794, https://doi.org/10.5194/gmd-17-781-2024, https://doi.org/10.5194/gmd-17-781-2024, 2024
Short summary
Short summary
The Voellmy rheology has been widely used for simulating snow and rock avalanches. Recently, a modified version of this rheology was proposed, which turned out to be able to predict the observed long runout of large rock avalanches theoretically. The software MinVoellmy presented here is the first numerical implementation of the modified rheology. It consists of MATLAB and Python classes, where simplicity and parsimony were the design goals.
Arjun Babu Nellikkattil, Danielle Lemmon, Travis Allen O'Brien, June-Yi Lee, and Jung-Eun Chu
Geosci. Model Dev., 17, 301–320, https://doi.org/10.5194/gmd-17-301-2024, https://doi.org/10.5194/gmd-17-301-2024, 2024
Short summary
Short summary
This study introduces a new computational framework called Scalable Feature Extraction and Tracking (SCAFET), designed to extract and track features in climate data. SCAFET stands out by using innovative shape-based metrics to identify features without relying on preconceived assumptions about the climate model or mean state. This approach allows more accurate comparisons between different models and scenarios.
Mohammad Mortezazadeh, Jean-François Cossette, Ashu Dastoor, Jean de Grandpré, Irena Ivanova, and Abdessamad Qaddouri
Geosci. Model Dev., 17, 335–346, https://doi.org/10.5194/gmd-17-335-2024, https://doi.org/10.5194/gmd-17-335-2024, 2024
Short summary
Short summary
The interpolation process is the most computationally expensive step of the semi-Lagrangian (SL) approach. In this paper we implement a new interpolation scheme into the semi-Lagrangian approach which has the same computational cost as a third-order polynomial scheme but with the accuracy of a fourth-order interpolation scheme. This improvement is achieved by using two third-order backward and forward polynomial interpolation schemes in two consecutive time steps.
Boris Gailleton, Luca C. Malatesta, Guillaume Cordonnier, and Jean Braun
Geosci. Model Dev., 17, 71–90, https://doi.org/10.5194/gmd-17-71-2024, https://doi.org/10.5194/gmd-17-71-2024, 2024
Short summary
Short summary
This contribution presents a new method to numerically explore the evolution of mountain ranges and surrounding areas. The method helps in monitoring with details on the timing and travel path of material eroded from the mountain ranges. It is particularly well suited to studies juxtaposing different domains – lakes or multiple rock types, for example – and enables the combination of different processes.
Denise Degen, Daniel Caviedes Voullième, Susanne Buiter, Harrie-Jan Hendricks Franssen, Harry Vereecken, Ana González-Nicolás, and Florian Wellmann
Geosci. Model Dev., 16, 7375–7409, https://doi.org/10.5194/gmd-16-7375-2023, https://doi.org/10.5194/gmd-16-7375-2023, 2023
Short summary
Short summary
In geosciences, we often use simulations based on physical laws. These simulations can be computationally expensive, which is a problem if simulations must be performed many times (e.g., to add error bounds). We show how a novel machine learning method helps to reduce simulation time. In comparison to other approaches, which typically only look at the output of a simulation, the method considers physical laws in the simulation itself. The method provides reliable results faster than standard.
Carlos Spa, Otilio Rojas, and Josep de la Puente
Geosci. Model Dev., 16, 7237–7252, https://doi.org/10.5194/gmd-16-7237-2023, https://doi.org/10.5194/gmd-16-7237-2023, 2023
Short summary
Short summary
This paper develops a calibration methodology of all absorbing techniques typically used by Fourier pseudo-spectral time-domain (PSTD) methods for geoacoustic wave simulations. The main contributions of the paper are (a) an implementation and quantitative comparison of all absorbing techniques available for PSTD methods through a simple and robust numerical experiment, and (b) a validation of these absorbing techniques in several 3-D seismic scenarios with gradual heterogeneity complexities.
Michael Hillier, Florian Wellmann, Eric A. de Kemp, Boyan Brodaric, Ernst Schetselaar, and Karine Bédard
Geosci. Model Dev., 16, 6987–7012, https://doi.org/10.5194/gmd-16-6987-2023, https://doi.org/10.5194/gmd-16-6987-2023, 2023
Short summary
Short summary
Neural networks can be used effectively to model three-dimensional geological structures from point data, sampling geological interfaces, units, and structural orientations. Existing neural network approaches for this type of modelling are advanced by the efficient incorporation of unconformities, new knowledge inputs, and improved data fitting techniques. These advances permit the modelling of more complex geology in diverse geological settings, different-sized areas, and various data regimes.
Ane Lopez de Gamiz-Zearra, Cecilie Hansen, Xavier Corrales, Iñaki Quincoces, Izaskun Preciado, and Eider Andonegi
EGUsphere, https://doi.org/10.5194/egusphere-2023-1368, https://doi.org/10.5194/egusphere-2023-1368, 2023
Short summary
Short summary
This paper describes the development of the first calibrated end-to-end Atlantis model for the Bay of Biscay that will help us improve the comprehension of the spatial functioning of the Bay of Biscay ecosystem and help establishing management measures of human activities. Our results highlighted the importance of lower trophic levels to the pelagic system and demonstrate the importance of having accurate and precise data for biological processes.
Tor Nordam, Ruben Kristiansen, Raymond Nepstad, Erik van Sebille, and Andy M. Booth
Geosci. Model Dev., 16, 5339–5363, https://doi.org/10.5194/gmd-16-5339-2023, https://doi.org/10.5194/gmd-16-5339-2023, 2023
Short summary
Short summary
We describe and compare two common methods, Eulerian and Lagrangian models, used to simulate the vertical transport of material in the ocean. They both solve the same transport problems but use different approaches for representing the underlying equations on the computer. The main focus of our study is on the numerical accuracy of the two approaches. Our results should be useful for other researchers creating or using these types of transport models.
Mathieu Gravey and Grégoire Mariethoz
Geosci. Model Dev., 16, 5265–5279, https://doi.org/10.5194/gmd-16-5265-2023, https://doi.org/10.5194/gmd-16-5265-2023, 2023
Short summary
Short summary
Multiple‐point geostatistics are widely used to simulate complex spatial structures based on a training image. The use of these methods relies on the possibility of finding optimal training images and parametrization of the simulation algorithms. Here, we propose finding an optimal set of parameters using only the training image as input. The main advantage of our approach is to remove the risk of overfitting an objective function.
Siting Li, Ping Wang, Hong Wang, Yue Peng, Zhaodong Liu, Wenjie Zhang, Hongli Liu, Yaqiang Wang, Huizheng Che, and Xiaoye Zhang
Geosci. Model Dev., 16, 4171–4191, https://doi.org/10.5194/gmd-16-4171-2023, https://doi.org/10.5194/gmd-16-4171-2023, 2023
Short summary
Short summary
Optimizing the initial state of atmospheric chemistry model input is one of the most essential methods to improve forecast accuracy. Considering the large computational load of the model, we introduce an ensemble optimal interpolation scheme (EnOI) for operational use and efficient updating of the initial fields of chemical components. The results suggest that EnOI provides a practical and cost-effective technique for improving the accuracy of chemical weather numerical forecasts.
Thomas Richter, Véronique Dansereau, Christian Lessig, and Piotr Minakowski
Geosci. Model Dev., 16, 3907–3926, https://doi.org/10.5194/gmd-16-3907-2023, https://doi.org/10.5194/gmd-16-3907-2023, 2023
Short summary
Short summary
Sea ice covers not only the pole regions but affects the weather and climate globally. For example, its white surface reflects more sunlight than land. The oceans around the poles are therefore kept cool, which affects the circulation in the oceans worldwide. Simulating the behavior and changes in sea ice on a computer is, however, very difficult. We propose a new computer simulation that better models how cracks in the ice change over time and show this by comparing to other simulations.
Emma J. MacKie, Michael Field, Lijing Wang, Zhen Yin, Nathan Schoedl, Matthew Hibbs, and Allan Zhang
Geosci. Model Dev., 16, 3765–3783, https://doi.org/10.5194/gmd-16-3765-2023, https://doi.org/10.5194/gmd-16-3765-2023, 2023
Short summary
Short summary
Earth scientists often have to fill in spatial gaps in measurements. This gap-filling or interpolation can be accomplished with geostatistical methods, where the statistical relationships between measurements are used to inform how these gaps should be filled. Despite the broad utility of these methods, there are few freely available geostatistical software applications. We present GStatSim, a Python package for performing different geostatistical interpolation methods.
Ian Madden, Simone Marras, and Jenny Suckale
Geosci. Model Dev., 16, 3479–3500, https://doi.org/10.5194/gmd-16-3479-2023, https://doi.org/10.5194/gmd-16-3479-2023, 2023
Short summary
Short summary
To aid risk managers who may wish to rapidly assess tsunami risk but may lack high-performance computing infrastructure, we provide an accessible software package able to rapidly model tsunami inundation over real topography by leveraging Google's Tensor Processing Unit, a high-performance hardware. Minimally trained users can take advantage of the rapid modeling abilities provided by this package via a web browser thanks to the ease of use of Google Cloud Platform.
Youtong Rong, Paul Bates, and Jeffrey Neal
Geosci. Model Dev., 16, 3291–3311, https://doi.org/10.5194/gmd-16-3291-2023, https://doi.org/10.5194/gmd-16-3291-2023, 2023
Short summary
Short summary
A novel subgrid channel (SGC) model is developed for river–floodplain modelling, allowing utilization of subgrid-scale bathymetric information while performing computations on relatively coarse grids. By including adaptive artificial diffusion, potential numerical instability, which the original SGC solver had, in low-friction regions such as urban areas is addressed. Evaluation of the new SGC model through structured tests confirmed that the accuracy and stability have improved.
Cited articles
Arnold, H. M., Moroz, I. M., and Palmer, T. N.: Stochastic parametrizations and model uncertainty in the Lorenz'96 system, Phil. Trans. R. Soc. A, 371, 20110479, https://doi.org/10.1098/rsta.2011.0479, 2013. a
Berry, T. and Harlim, J.: Linear theory for filtering nonlinear multiscale
systems with model error, Proc. R. Soc. A, 470, 20140168, https://doi.org/10.1098/rspa.2014.0168, 2014. a
Bocquet, M. and Carrassi, A.: Four-dimensional ensemble variational data
assimilation and the unstable subspace, Tellus A, 69, 1304504, https://doi.org/10.1080/16000870.2017.1304504, 2017. a
Bocquet, M., Gurumoorthy, K. S., Apte, A., Carrassi, A., Grudzien, C., and
Jones, C. K. R. T.: Degenerate Kalman Filter Error Covariances and Their
Convergence onto the Unstable Subspace, SIAM/ASA J. Uncertainty
Quantification, 5, 304–333, 2017. a
Boers, N., Chekroun, M. D., Liu, H., Kondrashov, D., Rousseau, D.-D., Svensson, A., Bigler, M., and Ghil, M.: Inverse stochastic–dynamic models for high-resolution Greenland ice core records, Earth Syst. Dynam., 8, 1171–1190, https://doi.org/10.5194/esd-8-1171-2017, 2017. a
Burrage, K. and Burrage, P. M.: High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations, Appl. Numer.
Math., 22, 81–101, 1996. a
Burrage, K. and Burrage, P. M.: General order conditions for stochastic
Runge-Kutta methods for both commuting and non-commuting stochastic ordinary
differential equation systems, Appl. Numer.
Math., 28, 161–177, 1998. a
Carrassi, A. and Vannitsem, S.: Deterministic treatment of model error in
geophysical data assimilation, in: Mathematical paradigms of climate science, Springer, 175–213, 2016. a
Carrassi, A., Bocquet, M., Bertino, L., and Evensen, G.: Data Assimilation in
the Geosciences-An overview on methods, issues and perspectives, WIREs Clim.
Change, 9, e535, https://doi.org/10.1002/wcc.535, 2018. a, b, c, d
Chekroun, M. D., Simonnet, E., and Ghil, M.: Stochastic climate dynamics:
Random attractors and time-dependent invariant measures, Physica D, 240, 1685–1700, 2011. a
Cotter, C., Crisan, D., Holm, D. D., Pan, W., and Shevchenko, I.: Numerically
Modeling Stochastic Lie Transport in Fluid Dynamics, Multiscale Model.
Sim., 17, 192–232, 2019. a
Crommelin, D. and Vanden-Eijnden, E.: Subgrid-scale parameterization with
conditional Markov chains, J. Atmos. Sci., 65,
2661–2675, 2008. a
Demaeyer, J. and Vannitsem, S.: Stochastic Parameterization of Subgrid-Scale
Processes: A Review of Recent Physically Based Approaches, in: Advances in
Nonlinear Geosciences, Springer, 55–85, 2018. a
Dijkstra, H. A.: Nonlinear climate dynamics, Cambridge University Press, 2013. a
Evensen, G.: The ensemble Kalman filter: Theoretical formulation and
practical implementation, Ocean Dynam., 53, 343–367, 2003. a
Frank, J. and Zhuk, S.: A detectability criterion and data assimilation for
nonlinear differential equations, Nonlinearity, 31, 5235, https://doi.org/10.1088/1361-6544/aaddcb, 2018. a
Franzke, C., O'Kane, T., Berner, J., Williams, P., and Lucarini, V.: Stochastic
climate theory and modeling, WIRES Clim. Change,
6, 63–78, 2015. a
Ghil, M.: The wind-driven ocean circulation: Applying dynamical systems theory to a climate problem, Discrete Cont. Dyn.-A, 37,
189–228, 2017. a
Ghil, M.: A century of nonlinearity in the geosciences, Earth and Space Science, 6, 1007–1042, https://doi.org/10.1029/2019EA000599, 2018. a
Ghil, M., Chekroun, M. D., and Simonnet, E.: Climate dynamics and fluid
mechanics: Natural variability and related uncertainties, Physica D, 237, 2111–2126, 2008. a
Gottwald, G. A. and Harlim, J.: The role of additive and multiplicative noise
in filtering complex dynamical systems, Proc. R. Soc. A, 469, 20130096, https://doi.org/10.1098/rspa.2013.0096, 2013. a
Gottwald, G. A., Crommelin, D., and Franzke, C.: Stochastic climate theory,
Nonlinear and Stochastic Climate Dynamics, 209–240, https://doi.org/10.1017/9781316339251, 2015. a
Gottwald, G. A., Peters, K., and Davies, L.: A data-driven method for the
stochastic parametrisation of subgrid-scale tropical convective area
fraction, Q. J. Roy. Meteor. Soc., 142,
349–359, 2016. a
Grudzien, C.: cgrudz/lorenz_96_sde: Revision Release,
https://doi.org/10.5281/zenodo.3701601, 2020. a, b
Grudzien, C., Carrassi, A., and Bocquet, M.: Asymptotic forecast uncertainty
and the unstable subspace in the presence of additive model error, SIAM/ASA
J. Uncertainty Quantification, 6, 1335–1363, 2018a. a
Grudzien, C., Carrassi, A., and Bocquet, M.: Chaotic dynamics and the role of covariance inflation for reduced rank Kalman filters with model error, Nonlin. Processes Geophys., 25, 633–648, https://doi.org/10.5194/npg-25-633-2018, 2018b. a
Gurumoorthy, K. S., Grudzien, C., Apte, A., Carrassi, A., and Jones, C. K.
R. T.: Rank deficiency of Kalman error covariance matrices in linear
time-varying system with deterministic evolution, SIAM J. Control Optim., 55, 741–759, 2017. a
Herrera, S., Pazó, D., Fernández, J., and Rodríguez, M. A.: The
role of large-scale spatial patterns in the chaotic amplification of
perturbations in a Lorenz'96 model, Tellus A, 63, 978–990, 2011. a
Iacus, S. M.: Simulation and inference for stochastic differential equations:
with R examples, Springer Science & Business Media, 2009. a
Jazwinski, A. H.: Stochastic Processes and Filtering Theory, Academic Press,
New-York, 1970. a
Kang, E. L. and Harlim, J.: Filtering Partially Observed Multiscale Systems
with Heterogeneous Multiscale Methods–Based Reduced Climate Models, Mon.
Weather Rev., 140, 860–873, 2012. a
Leutbecher, M. and Palmer, T. N.: Ensemble forecasting, J.
Comput. Phys., 227, 3515–3539, 2008. a
Lewis, J. M.: Roots of ensemble forecasting, Mon. Weather Rev., 133,
1865–1885, 2005. a
Lorenz, E. N.: Deterministic nonperiodic flow, J. Atmos.
Sci., 20, 130–141, 1963. a
Lorenz, E. N.: Designing chaotic models, J. Atmos. Sci.,
62, 1574–1587, 2005. a
Lorenz, E. N. and Emanuel, K. A.: Optimal sites for supplementary weather
observations: Simulation with a small model, J. Atmos.
Sci., 55, 399–414, 1998. a
Lu, F., Tu, X., and Chorin, A. J.: Accounting for Model Error from Unresolved
Scales in Ensemble Kalman Filters by Stochastic Parameterization, Mon.
Weather Rev., 145, 3709–3723, 2017. a
Maclean, J. and Van Vleck, E. S.: Projected Data Assimilation, arXiv preprint,
arXiv:1902.04212, 2019. a
Mitchell, L. and Gottwald, G. A.: Data assimilation in slow–fast systems using homogenized climate models, J. Atmos. Sci., 69,
1359–1377, 2012. a
Palmer, T. N., Shutts, G. J., Hagedorn, R., Doblas-Reyes, F. J., Jung, T., and Leutbecher, M.: Representing model uncertainty in weather and climate
prediction, Annu. Rev. Earth Planet. Sci., 33, 163–193, 2005. a
Pichler, L., Masud, A., and Bergman, L. A.: Numerical solution of the
Fokker–Planck equation by finite difference and finite element
methods–a comparative study, in: Computational Methods in Stochastic
Dynamics, Springer, 69–85, 2013. a
Pulido, M., Tandeo, P., Bocquet, M., Carrassi, A., and Lucini, M.: Stochastic
parameterization identification using ensemble Kalman filtering combined
with maximum likelihood methods, Tellus A, 70, 1442099, https://doi.org/10.1080/16000870.2018.1442099, 2018. a
Raanes, P. N., Carrassi, A., and Bertino, L.: Extending the square root method
to account for additive forecast noise in ensemble methods, Mon. Weather
Rev., 143, 3857–3873, 2015. a
Raanes, P. N., Bocquet, M., and Carrassi, A.: Adaptive covariance inflation in the ensemble Kalman filter by Gaussian scale mixtures, Q. J. Roy. Meteor. Soc., 145, 53–75, 2018. a
Rößler, A.: Runge–Kutta methods for the strong approximation of
solutions of stochastic differential equations, SIAM J. Num.
Anal., 48, 922–952, 2010. a
Rüemelin, W.: Numerical treatment of stochastic differential equations,
SIAM J. Num.
Anal., 19, 604–613, 1982. a
Shapiro, S. and Wilk, M.: An analysis of variance test for normality (complete samples), Biometrika, 52, 591–611, 1965. a
Tranninger, M., Seeber, R., Zhuk, S., Steinberger, M., and Horn, M.:
Detectability Analysis and Observer Design for Linear Time Varying Systems,
IEEE Contr. Syst. Lett., 4, 331–336, 2019. a
Short summary
All scales of a dynamical physical process cannot be resolved accurately in a multiscale, geophysical model. The behavior of unresolved scales of motion are often parametrized by a random process to emulate their effects on the dynamically resolved variables, and this results in a random–dynamical model. We study how the choice of a numerical discretization of such a system affects the model forecast and estimation statistics, when the random–dynamical model is unbiased in its parametrization.
All scales of a dynamical physical process cannot be resolved accurately in a multiscale,...
