Articles | Volume 7, issue 3
https://doi.org/10.5194/gmd-7-909-2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/gmd-7-909-2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Development and technical paper
| 
20 May 2014
Development and technical paper |
| 20 May 2014
A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal–icosahedral and cubed-sphere grids
J. Thuburn
University of Exeter, College of Engineering, Mathematics and Physical Sciences, Exeter, UK
C. J. Cotter
Imperial College, Department of Mathematics, London, UK
T. Dubos
IPSL/Laboratoire de Météorologie Dynamique, École Polytechnique, Palaiseau, France
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Accurate simulation of tropical cyclones (TCs) is essential to understanding their behavior in a changing climate. One way this is accomplished is through model intercomparison projects, where results from multiple climate models are analyzed to provide benchmark solutions for the wider climate modeling community. This study describes and analyzes the previously developed TC test case for nine climate models in an intercomparison project, providing solutions that aid in model development.
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Assessing uncertainty is computationally expensive because it requires multiple runs of expensive models. We take the novel approach of assessing uncertainty from coastal flooding using a multilevel multifidelity (MLMF) method which combines the efficiency of less accurate models with the accuracy of more expensive models at different resolutions. This significantly reduces the computational cost but maintains accuracy, making previously unfeasible real-world studies possible.
Thomas H. Gibson, Lawrence Mitchell, David A. Ham, and Colin J. Cotter
Geosci. Model Dev., 13, 735–761, https://doi.org/10.5194/gmd-13-735-2020, https://doi.org/10.5194/gmd-13-735-2020, 2020
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Galerkin finite element discretizations for atmospheric modeling often require the solution of ill-conditioned, saddle point equations which can be efficiently solved using a hybridized method. By extending Firedrake's domain-specific abstraction, we provide a mechanism for the rapid implementation of hybridization methods for a wide class of methods. In this paper, we show that hybridization is an effective alternative to traditional block solvers for simulating geophysical flows.
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Geosci. Model Dev., 12, 4901–4921, https://doi.org/10.5194/gmd-12-4901-2019, https://doi.org/10.5194/gmd-12-4901-2019, 2019
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WAVETRISK-1.0 is a new adaptive dynamical core for global climate modelling. It uses multiscale adaptive wavelet methods to adjust the grid resolution of the model at each time to guarantee error and make optimal use of computational resources. This technique has the potential to make climate simulations more accurate and allow much higher local resolutions. This "zoom" capability could also be used to focus on significant phenomena (such as hurricanes) or particular regions of the Earth.
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Atmospheric dynamical cores are a fundamental component of global atmospheric modeling systems and are responsible for capturing the dynamical behavior of the Earth's atmosphere. To better understand modern dynamical cores, this paper aims to provide a comprehensive review of 11 dynamical cores, drawn from modeling centers and groups that participated in the 2016 Dynamical Core Model Intercomparison Project (DCMIP) workshop and summer school.
N. K.-R. Kevlahan, T. Dubos, and M. Aechtner
Geosci. Model Dev., 8, 3891–3909, https://doi.org/10.5194/gmd-8-3891-2015, https://doi.org/10.5194/gmd-8-3891-2015, 2015
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In order to easily enforce solid-wall boundary conditions in the presence of complex coastlines, we propose a new mass and energy conserving Brinkman penalization for the rotating shallow water equations. This penalization does not lead to higher wave speeds in the solid region. The error estimates for the penalization are derived analytically and verified numerically for linearized one-dimensional equations. The penalization is implemented in a conservative dynamically adaptive wavelet method.
T. Dubos, S. Dubey, M. Tort, R. Mittal, Y. Meurdesoif, and F. Hourdin
Geosci. Model Dev., 8, 3131–3150, https://doi.org/10.5194/gmd-8-3131-2015, https://doi.org/10.5194/gmd-8-3131-2015, 2015
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The design of the icosahedral atmospheric dynamical core DYNAMICO is presented. The key contribution is to combine a strict separatation of kinematics from dynamics to a Hamiltonian formulation of the equations of motion in a non-Eulerian vertical coordinate to achieve energetic consistency. This approach allows for a unified treatment of various equations of motion: multi-layer shallow-water equations and hydrostatic primitive equations.
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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
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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.
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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
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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
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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
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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
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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
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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
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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.
Soyoung Ha, Jonathan J. Guerrette, Ivette Hernandez Banos, William C. Skamarock, and Michael G. Duda
EGUsphere, https://doi.org/10.5194/egusphere-2023-2299, https://doi.org/10.5194/egusphere-2023-2299, 2023
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To mitigate the imbalances in the initial conditions, this study introduces our recent implementation of the the incremental analysis update (IAU) in the Model for Prediction Across Scales for the Atmospheric component (MPAS-A), 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.
Wangbin Shen, Zhaohui Lin, Zhengkun Qin, and Juan Li
EGUsphere, https://doi.org/10.5194/egusphere-2023-2473, https://doi.org/10.5194/egusphere-2023-2473, 2023
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A land surface image assimilation system capable of optimizing the spatial structure of the background field from the common land model (CoLM) is constructed, by introducing the curvelet analysis method. The ideal experiment results show that the image assimilation system can remarkably improve the spatial structure similarity between the analysis field and the observed image, and improve the simulation accuracy of simulated soil moisture as well.
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
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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.
Luan Carlos de Sena Monteiro Ozelim, Michéle Dal Toé Casagrande, and André Luís Brasil Cavalcante
EGUsphere, https://doi.org/10.5194/egusphere-2023-1690, https://doi.org/10.5194/egusphere-2023-1690, 2023
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The paper addresses the quantity and complexity of synthetic datasets for nonlinear constitutive modelling of soils following the NorSand model by simulating both drained and undrained triaxial tests of 2000 soil types, with a total of 160000 triaxial test results made available. Each simulation dataset comprises a 4000 by 10 matrix that can be used for general multivariate forecasting benchmarks, apart from direct geotechnical and soil science applications.
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
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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
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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
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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.
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. Discuss., https://doi.org/10.5194/gmd-2023-88, https://doi.org/10.5194/gmd-2023-88, 2023
Revised manuscript accepted for GMD
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We introduce SolFinder 1.0, a decision-making tool to select trade-offs between different objective functions, including fuel use, flight time, NOx emissions, contrail distance, and climate impact. The module is included in the AirTraf 3.0 submodel, which optimizes trajectories under weather conditions simulated by an atmospheric model (EMAC). This paper focuses on the ability of the module to identify eco-efficient trajectories, which reduce the flights climate impact at limited cost penalties.
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
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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
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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
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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.
Xiaqiong Zhou and Hann-Ming Henry Juang
Geosci. Model Dev., 16, 3263–3274, https://doi.org/10.5194/gmd-16-3263-2023, https://doi.org/10.5194/gmd-16-3263-2023, 2023
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The National Centers for Environmental Prediction Global Forecast System version 16 experienced model instability failures in real-time runs resolved by increasing the minimum thickness depth parameter. Further investigation revealed that the issue was caused by the advection of geopotential heights at the model's layer interfaces. By replacing high-order boundary conditions with zero-gradient boundary conditions for interface-wind reconstruction, the instability was effectively addressed.
Grant T. Euen, Shangxin Liu, Rene Gassmöller, Timo Heister, and Scott D. King
Geosci. Model Dev., 16, 3221–3239, https://doi.org/10.5194/gmd-16-3221-2023, https://doi.org/10.5194/gmd-16-3221-2023, 2023
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Due to the increasing availability of high-performance computing over the past few decades, numerical models have become an important tool for research. Here we test two geodynamic codes that produce such models: ASPECT, a newer code, and CitcomS, an older one. We show that they produce solutions that are extremely close. As methods and codes become more complex over time, showing reproducibility allows us to seamlessly link previously known information to modern methodologies.
Ali Dashti, Jens Carsten Grimmer, Christophe Geuzaine, Florian Bauer, and Thomas Kohl
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2023-105, https://doi.org/10.5194/gmd-2023-105, 2023
Revised manuscript accepted for GMD
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This study developed a new meshing workflow to enable making meshes that follow geological models. This workflow also allows us to import several geological models as input for the mesh generator and later on export the same number of watertight meshes. This way, geological uncertainty can be directly included in the numerical simulations. This study evaluates the impact of the geological uncertainty on thermohydraulic performance of the reservoir for high temperature heat storage applications.
Mohammad Kazem Sharifian, Georges Kesserwani, Alovya Ahmed Chowdhury, Jeffrey Neal, and Paul Bates
Geosci. Model Dev., 16, 2391–2413, https://doi.org/10.5194/gmd-16-2391-2023, https://doi.org/10.5194/gmd-16-2391-2023, 2023
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This paper describes a new release of the LISFLOOD-FP model for fast and efficient flood simulations. It features a new non-uniform grid generator that uses multiwavelet analyses to sensibly coarsens the resolutions where the local topographic variations are smooth. Moreover, the model is parallelised on the graphical processing units (GPUs) to further boost computational efficiency. The performance of the model is assessed for five real-world case studies, noting its potential applications.
Bruno K. Zürcher
Geosci. Model Dev., 16, 1697–1711, https://doi.org/10.5194/gmd-16-1697-2023, https://doi.org/10.5194/gmd-16-1697-2023, 2023
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We present a novel algorithm to efficiently compute Barnes interpolation, which is a method for transforming data values recorded at irregularly spaced points into a corresponding regular grid. In contrast to naive implementations with an algorithmic complexity that depends on the product of the number of sample points and the number of grid points, our approach reduces this dependency to their sum.
David H. Marsico and Paul A. Ullrich
Geosci. Model Dev., 16, 1537–1551, https://doi.org/10.5194/gmd-16-1537-2023, https://doi.org/10.5194/gmd-16-1537-2023, 2023
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Climate models involve several different components, such as the atmosphere, ocean, and land models. Information needs to be exchanged, or remapped, between these models, and devising algorithms for performing this exchange is important for ensuring the accuracy of climate simulations. In this paper, we examine the efficacy of several traditional and novel approaches to remapping on the sphere and demonstrate where our approaches offer improvement.
Moritz Liebl, Jörg Robl, Stefan Hergarten, David Lundbek Egholm, and Kurt Stüwe
Geosci. Model Dev., 16, 1315–1343, https://doi.org/10.5194/gmd-16-1315-2023, https://doi.org/10.5194/gmd-16-1315-2023, 2023
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In this study, we benchmark a topography-based model for glacier erosion (OpenLEM) with a well-established process-based model (iSOSIA). Our experiments show that large-scale erosion patterns and particularly the transformation of valley length geometry from fluvial to glacial conditions are very similar in both models. This finding enables the application of OpenLEM to study the influence of climate and tectonics on glaciated mountains with reasonable computational effort on standard PCs.
James Kent, Thomas Melvin, and Golo Albert Wimmer
Geosci. Model Dev., 16, 1265–1276, https://doi.org/10.5194/gmd-16-1265-2023, https://doi.org/10.5194/gmd-16-1265-2023, 2023
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This paper introduces the Met Office's new shallow water model. The shallow water model is a building block towards the Met Office's new atmospheric dynamical core. The shallow water model is tested on a number of standard spherical shallow water test cases, including flow over mountains and unstable jets. Results show that the model produces similar results to other shallow water models in the literature.
Anthony Gruber, Max Gunzburger, Lili Ju, Rihui Lan, and Zhu Wang
Geosci. Model Dev., 16, 1213–1229, https://doi.org/10.5194/gmd-16-1213-2023, https://doi.org/10.5194/gmd-16-1213-2023, 2023
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This work applies a novel technical tool, multifidelity Monte Carlo (MFMC) estimation, to three climate-related benchmark experiments involving oceanic, atmospheric, and glacial modeling. By considering useful quantities such as maximum sea height and total (kinetic) energy, we show that MFMC leads to predictions which are more accurate and less costly than those obtained by standard methods. This suggests MFMC as a potential drop-in replacement for estimation in realistic climate models.
Piyoosh Jaysaval, Glenn E. Hammond, and Timothy C. Johnson
Geosci. Model Dev., 16, 961–976, https://doi.org/10.5194/gmd-16-961-2023, https://doi.org/10.5194/gmd-16-961-2023, 2023
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We present a robust and highly scalable implementation of numerical forward modeling and inversion algorithms for geophysical electrical resistivity tomography data. The implementation is publicly available and developed within the framework of PFLOTRAN (http://www.pflotran.org), an open-source, state-of-the-art massively parallel subsurface flow and transport simulation code. The paper details all the theoretical and implementation aspects of the new capabilities along with test examples.
Lucas Schauer, Michael J. Schmidt, Nicholas B. Engdahl, Stephen D. Pankavich, David A. Benson, and Diogo Bolster
Geosci. Model Dev., 16, 833–849, https://doi.org/10.5194/gmd-16-833-2023, https://doi.org/10.5194/gmd-16-833-2023, 2023
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We develop a multi-dimensional, parallelized domain decomposition strategy for mass-transfer particle tracking methods in two and three dimensions, investigate different procedures for decomposing the domain, and prescribe an optimal tiling based on physical problem parameters and the number of available CPU cores. For an optimally subdivided diffusion problem, the parallelized algorithm achieves nearly perfect linear speedup in comparison with the serial run-up to thousands of cores.
John Mern and Jef Caers
Geosci. Model Dev., 16, 289–313, https://doi.org/10.5194/gmd-16-289-2023, https://doi.org/10.5194/gmd-16-289-2023, 2023
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In this work, we formulate the sequential geoscientific data acquisition problem as a problem that is similar to playing chess against nature, except the pieces are not fully observed. Solutions to these problems are given in AI and rarely used in geoscientific data planning. We illustrate our approach to a simple 2D problem of mineral exploration.
Jevgenijs Steinbuks, Yongyang Cai, Jonas Jaegermeyr, and Thomas W. Hertel
EGUsphere, https://doi.org/10.5194/egusphere-2022-863, https://doi.org/10.5194/egusphere-2022-863, 2023
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This paper applies cutting-edge numerical methods to show how uncertain climate change and technological progress affect the future utilization of the scarce world's land resources. The paper's key insight is to illustrate how much global cropland will expand when future crop yields are unknown. The more uncertain the future crop yields are, the more forest conversion will be necessary to sustain human welfare. Some of that conversion takes place even when crop yields are not actually affected.
Ziqi Gao, Yifeng Wang, Petros Vasilakos, Cesunica E. Ivey, Khanh Do, and Armistead G. Russell
Geosci. Model Dev., 15, 9015–9029, https://doi.org/10.5194/gmd-15-9015-2022, https://doi.org/10.5194/gmd-15-9015-2022, 2022
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While the national ambient air quality standard of ozone is based on the 3-year average of the fourth highest 8 h maximum (MDA8) ozone concentrations, these predicted extreme values using numerical methods are always biased low. We built four computational models (GAM, MARS, random forest and SVR) to predict the fourth highest MDA8 ozone in Southern California using precursor emissions, meteorology and climatological patterns. All models presented acceptable performance, with GAM being the best.
Zhihao Wang, Jason Goetz, and Alexander Brenning
Geosci. Model Dev., 15, 8765–8784, https://doi.org/10.5194/gmd-15-8765-2022, https://doi.org/10.5194/gmd-15-8765-2022, 2022
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A lack of inventory data can be a limiting factor in developing landslide predictive models, which are crucial for supporting hazard policy and decision-making. We show how case-based reasoning and domain adaptation (transfer-learning techniques) can effectively retrieve similar landslide modeling situations for prediction in new data-scarce areas. Using cases in Italy, Austria, and Ecuador, our findings support the application of transfer learning for areas that require rapid model development.
Till Sachau, Haibin Yang, Justin Lang, Paul D. Bons, and Louis Moresi
Geosci. Model Dev., 15, 8749–8764, https://doi.org/10.5194/gmd-15-8749-2022, https://doi.org/10.5194/gmd-15-8749-2022, 2022
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Knowledge of the internal structures of the major continental ice sheets is improving, thanks to new investigative techniques. These structures are an essential indication of the flow behavior and dynamics of ice transport, which in turn is important for understanding the actual impact of the vast amounts of water trapped in continental ice sheets on global sea-level rise. The software studied here is specifically designed to simulate such structures and their evolution.
Keith J. Roberts, Alexandre Olender, Lucas Franceschini, Robert C. Kirby, Rafael S. Gioria, and Bruno S. Carmo
Geosci. Model Dev., 15, 8639–8667, https://doi.org/10.5194/gmd-15-8639-2022, https://doi.org/10.5194/gmd-15-8639-2022, 2022
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Finite-element methods (FEMs) permit the use of more flexible unstructured meshes but are rarely used in full waveform inversions (FWIs), an iterative process that reconstructs velocity models of earth’s subsurface, due to computational and memory storage costs. To reduce those costs, novel software is presented allowing the use of high-order mass-lumped FEMs on triangular meshes, together with a material-property mesh-adaptation performance-enhancing strategy, enabling its use in FWIs.
Konstantinos Papadakis, Yann Pfau-Kempf, Urs Ganse, Markus Battarbee, Markku Alho, Maxime Grandin, Maxime Dubart, Lucile Turc, Hongyang Zhou, Konstantinos Horaites, Ivan Zaitsev, Giulia Cozzani, Maarja Bussov, Evgeny Gordeev, Fasil Tesema, Harriet George, Jonas Suni, Vertti Tarvus, and Minna Palmroth
Geosci. Model Dev., 15, 7903–7912, https://doi.org/10.5194/gmd-15-7903-2022, https://doi.org/10.5194/gmd-15-7903-2022, 2022
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Vlasiator is a plasma simulation code that simulates the entire near-Earth space at a global scale. As 6D simulations require enormous amounts of computational resources, Vlasiator uses adaptive mesh refinement (AMR) to lighten the computational burden. However, due to Vlasiator’s grid topology, AMR simulations suffer from grid aliasing artifacts that affect the global results. In this work, we present and evaluate the performance of a mechanism for alleviating those artifacts.
Artur Safin, Damien Bouffard, Firat Ozdemir, Cintia L. Ramón, James Runnalls, Fotis Georgatos, Camille Minaudo, and Jonas Šukys
Geosci. Model Dev., 15, 7715–7730, https://doi.org/10.5194/gmd-15-7715-2022, https://doi.org/10.5194/gmd-15-7715-2022, 2022
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Reconciling the differences between numerical model predictions and observational data is always a challenge. In this paper, we investigate the viability of a novel approach to the calibration of a three-dimensional hydrodynamic model of Lake Geneva, where the target parameters are inferred in terms of distributions. We employ a filtering technique that generates physically consistent model trajectories and implement a neural network to enable bulk-to-skin temperature conversion.
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
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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.
Yangyang Yu, Shaoqing Zhang, Haohuan Fu, Lixin Wu, Dexun Chen, Yang Gao, Zhiqiang Wei, Dongning Jia, and Xiaopei Lin
Geosci. Model Dev., 15, 6695–6708, https://doi.org/10.5194/gmd-15-6695-2022, https://doi.org/10.5194/gmd-15-6695-2022, 2022
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To understand the scientific consequence of perturbations caused by slave cores in heterogeneous computing environments, we examine the influence of perturbation amplitudes on the determination of the cloud bottom and cloud top and compute the probability density function (PDF) of generated clouds. A series of comparisons of the PDFs between homogeneous and heterogeneous systems show consistently acceptable error tolerances when using slave cores in heterogeneous computing environments.
Vijay S. Mahadevan, Jorge E. Guerra, Xiangmin Jiao, Paul Kuberry, Yipeng Li, Paul Ullrich, David Marsico, Robert Jacob, Pavel Bochev, and Philip Jones
Geosci. Model Dev., 15, 6601–6635, https://doi.org/10.5194/gmd-15-6601-2022, https://doi.org/10.5194/gmd-15-6601-2022, 2022
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Coupled Earth system models require transfer of field data between multiple components with varying spatial resolutions to determine the correct climate behavior. We present the Metrics for Intercomparison of Remapping Algorithms (MIRA) protocol to evaluate the accuracy, conservation properties, monotonicity, and local feature preservation of four different remapper algorithms for various unstructured mesh problems of interest. Future extensions to more practical use cases are also discussed.
Cited articles
Arakawa, A. and Lamb, V. R.: Computational design of the basic dynamical processes of the UCLA general circulation model, in: "General Circulation Models of the Atmosphere", Methods in Computational Physics, Vol. 17, edited by: Chang, J., Academic Press, San Diego, 172–265, 1977.
Cotter, C. J. and Shipton, J.: Mixed finite elements for numerical weather prediction, J. Comput. Phys., 231, 7076–7091, 2012.
Crowley, W. P.: Numerical advection experiments, Mon. Weather Rev., 96, 1–11, 1968.
Cullen, M. J. P.: On the accuracy of the semi-geostrophic approximation, Q. J. Roy. Meteorol. Soc., 126, 1099–1115, 2000.
Cullen, M. J. P.: Modelling atmospheric flows, Acta Num., 16, 67–154, 2007.
Cullen, M. J. P.: A comparison of numerical solutions to the Eady frontogenesis problem, Q. J. Roy. Meteorol. Soc., 134, 2143–2155, 2008.
Du, Q., Faber, V., and Gunzburger, M.: Centroidal Voronoi tessellations: applications and algorithms, SIAM Rev., 41, 637–676, 1999.
Ford, R., McIntyre, M. E., and Norton, W. A.: Balance and the slow quasimanifold: some explicit results, J. Atmos. Sci., 57, 1236–1254, 2000.
Fulton, S. R., Ciesielski, P. E., and Schubert, W. H.: Multigrid methods for elliptic problems: a review, Mon. Weather Rev., 114, 943–959, 1986.
Galewsky, J., Scott, R. K., and Polvani, L. M.: An initial value problem for testing numerical models of the global shallow-water equations, Tellus A, 56, 429–440, 2004.
Heikes, R. and Randall, D.: Numerical integration of the shallow-water equations on a twisted icosahedral grid, Part I: Basic design and results of tests, Mon. Weather Rev., 123, 1862–1880, 1995a.
Heikes, R. and Randall, D.: Numerical integration of the shallow-water equations on a twisted icosahedral grid, Part II: A detailed description of the grid and analysis of numerical accuracy, Mon. Weather Rev., 123, 1881–1997, 1995b.
Heikes, R. P., Randall, D. A., and Konor, C. S.: Optimized Icosahedral Grids: Performance of Finite-Difference Operators and Multigrid Solver, Mon. Weather Rev., 141, 4450–4469, 2013.
Holdaway, D. R. E., Thuburn, J., and Wood, N.: On the relation between order of accuracy, convergence rate and spectral slope for linear numerical methods applied to multiscale problems, Int. J. Numer. Meth. Fl., 56, 1297–1303, 2008.
Kent, J., Thuburn, J., and Wood, N.: Assessing implicit large eddy simulation for two-dimensional flow, Q. J. Roy. Meteorol. Soc., 138, 365–376, 2012.
Lashley, R. K.: Automatic generation of accurate advection schemes on unstructured grids and their application to meteorological problems, Ph.D. Thesis, University of Reading, Reading, UK, 2002.
Leonard, B. P.: A stable and accurate convective modelling procedure based on quadratic upstream interpolation, Comp. Methods Appl. Mech. Eng., 19, 59–98, 1979.
Leonard, B. P., MacVean, M. K., and Lock, A. P.: Positivity-preserving numerical schemes for multi-dimensional advection, NASA Technical Memorandum TM-106055 ICOMP-93-05, 1993.
Leonard, B. P., MacVean, M. K., and Lock, A. P.: The flux integral method for multidimensional convection and diffusion, Appl. Math. Model., 19, 333–342, 1995.
Li, S. and Xiao, F.: A global shallow water model using high order multi-moment constrained finite volume method and icosahedral grid, J. Comput. Phys., 229, 1774–1796, 2010.
Lin, S.-J. and Rood, R. B.: An explicit flux-form semi-Lagrangian shallow-water model on the sphere, Q. J. Roy. Meteor. Soc., 123, 2477–2498, 1997.
Lipscomb, W. H. and Ringler, T.: An incremental remapping transport scheme on a spherical geodesic grid, Mon. Weather Rev., 133, 2235–2250, 2005.
Miura, H.: An upwind-biased conservative advection scheme for spherical hexagonal–pentagonal grids, Mon. Weather Rev., 135, 4038–4044, 2007.
Miura, H.: An upwind-biased conservative transport scheme for multistage temporal integrations on spherical icosahedral grids. Mon. Weather Rev., 141, 4049–4068, 2013.
Müller, E. H. and Scheichl, R.: Massively parallel solvers for elliptic PDEs in Numerical Weather- and Climate Prediction, Q. J. Roy. Meteorol. Soc., submitted, 2014.
Rancic, M., Purser, R. J., and Mesinger, F.: A global shallow-water model using an expanded spherical cube: gnomonic versus conformal coordinates, Q. J. Roy. Meteorol. Soc., 122, 959–982, 1996.
Ringler, T. D., Thuburn, J., Klemp, J. B., and Skamarock, W. C.: A unified approach to energy conservation and potential vorticity dynamics for arbitrarily structured C-grids, J. Comput. Phys., 229, 3065–3090, 2010.
Ronchi, C., Iacono, R., and Paolucci, P. S.: The "cubed sphere": a new method for the solution of partial differential equations in spherical geometry, J. Comput. Phys., 124, 93–114, 1996.
Salehipour, H., Stuhne, G. R., and Peltier, W. R.: A higher order discontinuous Galerkin, global shallow water model: global ocean tides and aquaplanet benchmarks, Ocean Model., 69, 93–107, 2013.
Skamarock, W. C. and Menchaca, M.: Conservative transport schemes for spherical geodesic grids: high-order reconstructions for forward-in-time schemes, Mon. Weather Rev., 138, 4497–4508, 2010.
Skamarock, W. C., Klemp, J. B., Duda, M. G., Fowler, L., Park, S.-H., and Ringler, T. D.: A multiscale nonhydrostatic atmospheric model using centroidal Voronoi tesselations and C-grid staggering, Mon. Weather Rev., 140, 3090–3105, 2012.
Staniforth, A. and Thuburn, J.: Horizontal grids for global weather and climate prediction models: a review, Q. J. Roy. Meteorol. Soc., 138, 1–26, 2012.
Thuburn, J.: Multidimensional flux-limited advection schemes, J. Comput. Phys., 123, 74–83, 1996.
Thuburn, J.: A PV-based shallow-water model on a hexagonal–icosahedral grid, Mon. Weather Rev., 125, 2328–2347, 1997.
Thuburn, J.: Numerical wave propagation on the hexagonal C-grid, J. Comput. Phys., 227, 5836–5858, 2008.
Thuburn, J. and Cotter, C. J.: A framework for mimetic discretization of the rotating shallow water equations on arbitrary polygonal grids, SIAM J. Sci. Comput., 34, 203–225, 2012.
Thuburn, J. and Li, Y.: Numerical simulations of Rossby-Haurwitz waves, Tellus, 52A, 181–189, 2000.
Thuburn, J., Ringler, T. D., Skamarock, W. C., and Klemp, J. B.: Numerical representation of geostrophic modes on arbitrarily structured C-grids, J. Comput. Phys., 228, 8321–8335, 2009.
Thuburn, J., Kent, J., and Wood, N.: Cascades, backscatter and conservation in numerical models of two-dimensional turbulence, Q. J. Roy. Meteorol. Soc., 140, 626–638, https://doi.org/10.1002/qj.2166, 2014.
Tremback, C. J., Powell, J., Cotton, W. R., and Pielke, R. A.: The forward-in-time upstream advection scheme: extension to higher orders, Mon. Weather Rev., 115, 540–555, 1987.
Ullrich, P. A., Lauritzen, P. H., and Jablonowksi, C.: Some considerations for high-order "incremental remap"-based transport schemes: edges, reconstructions, and area integration, Int. J. Numer. Meth. Fl., 71, 1131–1151, 2013.
Weller, H.: Controlling the computational modes of the arbitrarily structured C-grid, Mon. Weather Rev., 140, 3220–3234, 2012.
Williamson, D. L., Drake, J. B., Hack, J. J., Jakob, R., and Swarztrauber, P. N.: A standard test set for numerical approximations to the shallow water equations in spherical geometry, J. Comput. Phys., 102, 211–224, 1992.
Zerroukat, M., Wood., N., Staniforth, A., White, A. A., and Thuburn, J.: An inherently mass-conserving semi-implicit semi-Lagrangian discretisation of the shallow water equations on the sphere, Q. J. Roy. Meteor. Soc., 135, 1104–1116, 2009.
Zhang, K., Wan, H., Wang, B., and Zhang, M.: Consistency problem with tracer advection, Adv. Atmos. Sci., 25, 306–318, 2008.
