Articles | Volume 15, issue 14
https://doi.org/10.5194/gmd-15-5757-2022
© Author(s) 2022. 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-15-5757-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Development and technical paper
| 
25 Jul 2022
Development and technical paper |
| 25 Jul 2022
| 25 Jul 2022
Assessing the robustness and scalability of the accelerated pseudo-transient method
Laboratory of Hydraulics, Hydrology and Glaciology (VAW), ETH Zurich, Zurich, Switzerland
Swiss Federal Institute for Forest, Snow and Landscape Research (WSL), Birmensdorf, Switzerland
Ivan Utkin
Laboratory of Hydraulics, Hydrology and Glaciology (VAW), ETH Zurich, Zurich, Switzerland
Swiss Federal Institute for Forest, Snow and Landscape Research (WSL), Birmensdorf, Switzerland
Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
Thibault Duretz
Institut für Geowissenschaften, Goethe‐Universität Frankfurt, Frankfurt, Germany
Univ. Rennes, CNRS, Géosciences Rennes UMR 6118, 35000 Rennes, France
Samuel Omlin
Swiss National Supercomputing Centre (CSCS), ETH Zurich, Lugano, Switzerland
Yuri Y. Podladchikov
Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
Institute of Earth Sciences, University of Lausanne, Lausanne, Switzerland
Swiss Geocomputing Centre, University of Lausanne, Lausanne, Switzerland
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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
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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
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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
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
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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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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
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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.
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
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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
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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.
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.
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.
Cited articles
Alamatian, J.: A new formulation for fictitious mass of the Dynamic Relaxation
method with kinetic damping, Comput. Struct., 90–91, 42–54,
https://doi.org/10.1016/j.compstruc.2011.10.010, 2012. a
Alkhimenkov, Y., Khakimova, L., and Podladchikov, Y.: Stability of discrete
schemes of Biot's poroelastic equations,
Geophys. J. Int.,
225, 354–377, https://doi.org/10.1093/gji/ggaa584, 2021a. a, b
Alkhimenkov, Y., Räss, L., Khakimova, L., Quintal, B., and Podladchikov,
Y.: Resolving Wave Propagation in Anisotropic Poroelastic Media
Using Graphical Processing Units (GPUs),
J. Geophys. Res.-Sol. Ea., 126, 7, https://doi.org/10.1029/2020JB021175, 2021b. a
Bakhvalov, N. S.: On the convergence of a relaxation method with natural
constraints on the elliptic operator,
USSR Comp. Math. Math.+, 6, 101–135, https://doi.org/10.1016/0041-5553(66)90118-2, 1966. a
Barnes, M. R.: Form Finding and Analysis of Tension Structures by Dynamic
Relaxation, International Journal of Space Structures, 14, 89–104,
https://doi.org/10.1260/0266351991494722, 1999. a
Baumgardner, J. R.: Three-dimensional treatment of convective flow in the
earth's mantle, J. Stat. Phys., 39, 501–511,
https://doi.org/10.1007/BF01008348, 1985. a
Besard, T., Foket, C., and De Sutter, B.: Effective Extensible Programming:
Unleashing Julia on GPUs,
IEEE T. Parall. Distr., 30, 827–841, https://doi.org/10.1109/TPDS.2018.2872064, 2018. a
Besard, T., Churavy, V., Edelman, A., and De Sutter, B.: Rapid software
prototyping for heterogeneous and distributed platforms,
Adv. Eng. Softw., 132, 29–46, 2019. a
Bezanson, J., Edelman, A., Karpinski, S., and Shah, V. B.: Julia: A fresh
approach to numerical computing, SIAM Rev., 59, 65–98,
https://doi.org/10.1137/141000671, 2017. a, b
Brandt, A.: Multi-level adaptive solutions to boundary-value problems,
Math. Comput., 31, 333–390,
https://doi.org/10.1090/S0025-5718-1977-0431719-X, 1977. a, b
Byrne, S., Wilcox, L. C., and Churavy, V.: MPI.jl: Julia bindings for the
Message Passing Interface, Proceedings of the JuliaCon Conferences, 1, 68,
https://doi.org/10.21105/jcon.00068, 2021. a
Cassell, A. C. and Hobbs, R. E.: Numerical stability of dynamic relaxation
analysis of non-linear structures,
Int. J. Numer. Meth. Eng., 10, 1407–1410, https://doi.org/10.1002/nme.1620100620, 1976. a
Chester, M.: Second sound in solids, Phys. Rev., 131, 2013–2015,
https://doi.org/10.1103/PhysRev.131.2013, 1963. a
Costa, A.: Permeability-porosity relationship: A reexamination of the
Kozeny-Carman equation based on a fractal pore-space geometry assumption,
Geophys. Res. Lett., 33, L02318, https://doi.org/10.1029/2005GL025134, 2006. a
Cox, S. and Zuazua, E.: The rate at which energy decays in a damped string,
Commun. Part. Diff. Eq., 19, 213–243,
https://doi.org/10.1080/03605309408821015, 1994. a
Cundall, A. P.: Explicit finite differnce method in geomechanics, Second Int.
Conf. Numerical Methods in Geomechanics, Blacksburg, 1976, 1, 132–150, 1976. a
Eager, D. L., Zahorjan, J., and Lazowska, E. D.: Speedup versus efficiency in
parallel systems, IEEE T. Comput., 38, 408–423,
https://doi.org/10.1109/12.21127, 1989. a
Fuhrer, O., Chadha, T., Hoefler, T., Kwasniewski, G., Lapillonne, X., Leutwyler, D., Lüthi, D., Osuna, C., Schär, C., Schulthess, T. C., and Vogt, H.: Near-global climate simulation at 1 km resolution: establishing a performance baseline on 4888 GPUs with COSMO 5.0, Geosci. Model Dev., 11, 1665–1681, https://doi.org/10.5194/gmd-11-1665-2018, 2018. a
Gaitonde, A. L.: A dual-time method for two-dimensional unsteady incompressible
flow calculations, Int. J. Numer. Meth. Eng., 41, 1153–1166,
https://doi.org/10.1002/(SICI)1097-0207(19980330)41:6<1153::AID-NME334>3.0.CO;2-9,
1998. a
Gustafson, J. L.: Reevaluating Amdahl's law, Commun. ACM, 31,
532–533, https://doi.org/10.1145/42411.42415, 1988. a
Hackbusch, W.: Multi-Grid Methods and Applications, vol. 4, Springer
Series in Computational Mathematics, Springer, Berlin,
Heidelberg, https://doi.org/10.1007/978-3-662-02427-0, 1985. a
Hoemmen, M. F.: Communication-avoiding Krylov subspace methods, PhD thesis,
EECS Department, University of California, Berkeley,
http://www2.eecs.berkeley.edu/Pubs/TechRpts/2010/EECS-2010-37.html (last access: 16 May 2022),
2010. a
Jordan, P. M. and Puri, A.: Digital signal propagation in dispersive media,
J. Appl. Phys., 85, 1273–1282, https://doi.org/10.1063/1.369258, 1999. a
Kaus, B. J. P., Popov, A. A., Baumann, T. S., Püsök, A. E., Bauville,
A., Fernandez, N., and Collignon, M.: Forward and Inverse Modelling of
Lithospheric Deformation on Geological Timescales, in: NIC Symposium 2016, Jülich, Germany, 11–12 February 2016,
edited by: Binder, K., Müller, M., Kremer, A., and Schnurpfeil, A.,
48, 299–307, Forschungszentrum Jülich, Jülich, 2016. a
Kilic, B. and Madenci, E.: Structural stability and failure analysis using
peridynamic theory, Int. J. NonLin. Mech., 44,
845–854, https://doi.org/10.1016/j.ijnonlinmec.2009.05.007, 2009. a
Kumar, V., Grama, A., Gupta, A., and Karypis, G.: Introduction to parallel
computing, Benjamin/Cummings Redwood City, CA, 110, ISBN 0805331700, 1994. a
Mandal, J., Sonawane, C., Iyer, A., and GosaviInamdar, S.: Incompressible flow
computations over moving boundary using a novel upwind method, Comput.
Fluid., 46, 348–352, 2011. a
Maxwell, J. C.: IV. On the dynamical theory of gases,
Philos. T. R. Soc. Lond., 157, 49–88,
https://doi.org/10.1098/rstl.1867.0004, 1867. a
May, D., Brown, J., and Le Pourhiet, L.: A scalable, matrix-free multigrid
preconditioner for finite element discretizations of heterogeneous Stokes
flow, Comput. Method Appl. M., 290,
496–523, https://doi.org/10.1016/j.cma.2015.03.014, 2015. a, b
McCalpin, J. D.: Memory bandwidth and machine balance in current high
performance computers, IEEE computer society technical committee on computer
architecture (TCCA) newsletter, 2, 19–25, 1995. a
McKee, S., Tomé, M., Ferreira, V., Cuminato, J., Castelo, A., Sousa, F.,
and Mangiavacchi, N.: The MAC method, Comput. Fluid., 37, 907–930,
https://doi.org/10.1016/j.compfluid.2007.10.006, 2008. a
Omlin, S.: Development of massively parallel near peak performance solvers for
three-dimensional geodynamic modelling, PhD thesis, University of Lausanne, https://doi.org/10.48550/ARXIV.2207.08716,
2017. a
Omlin, S. and Räss, L.: ImplicitGlobalGrid.jl,
https://github.com/eth-cscs/ImplicitGlobalGrid.jl (last access: 16 May 2022),
2021a. a
Omlin, S., Räss, L., and Podladchikov, Y.: HPC.m – the MATLAB HPC
Compiler and its Use for Solving 3D Poromechanics on Supercomputers, in:
Platform for Advanced Scientific Computing Conference (PASC15), 1–3 June 2015, Zurich, Switzerland, ETH Zurich,
Zurich, Switzerland, 2015a. a
Omlin, S., Räss, L., and Podladchikov, Y.: From MATLAB to
Supercomputing: the MATLAB HPC-Compiler, in: 2nd Frontiers in Computational
Physics: Energy Sciences Conference 2015, 3–5 June 2015, Zurich, Switzerland, ETH Zurich, Zurich, Switzerland,
2015b. a
Otter, J.: Computations for prestressed concrete reactor pressure vessels
using dynamic relaxation, Nuclear Structural Engineering, 1, 61–75,
https://doi.org/10.1016/0369-5816(65)90097-9, 1965. a
Otter, J. R. H., Cassell, A. C., and Hobbs, R. E.: Dynamic relaxation,
35,
633–656,
https://doi.org/10.1680/IICEP.1966.8604, 1966. a
Papadrakakis, M.: A method for the automatic evaluation of the dynamic
relaxation parameters, Comput. Method Appl. M., 25, 35–48, https://doi.org/10.1016/0045-7825(81)90066-9, 1981. a, b
Pascal, H.: Pressure wave propagation in a fluid flowing through a porous
medium and problems related to interpretation of Stoneley's wave attenuation
in acoustical well logging, Int. J. Eng. Sci., 24,
1553–1570, https://doi.org/10.1016/0020-7225(86)90163-1, 1986. a
Patankar, S.: Numerical heat transfer and fluid flow, CRC press, https://doi.org/10.1201/9781482234213, 1980. a
Podladtchikov, I. and Podladchikov, Y. Y.: Memory Bound Wave Propagation at
Hardware Limit,
http://on-demand.gputechconf.com/gtc/2013/video/S3176-Memory-Bound-Wave-Propagation-Hardware-Limit.flv (last access: 16 May 2022),
2013. a
Poliakov, A. N., Cundall, P. A., Podladchikov, Y. Y., and Lyakhovsky, V. A.:
An explicit inertial method for the simulation of viscoelastic flow: an
evaluation of elastic effects on diapiric flow in two- and three- layers
models, Flow and creep in the solar system: observations, modeling and
theory, NATO ASI Series, vol. 391, Springer, Dordrecht, 175–195, https://doi.org/10.1007/978-94-015-8206-3_12, 1993. a
Poliakov, A. N. B., Herrmann, H. J., Podladchikov, Y. Y., and Roux, S.:
Fractal plastic shear bands, Fractals, 2, 567–581,
https://doi.org/10.1142/s0218348x9400079x, 1994. a
Ramesh, G. and Krishnamoorthy, C. S.: Post‐buckling analysis of structures
by dynamic relaxation, Int. J. Numer. Meth. Eng., 36, 1339–1364, https://doi.org/10.1002/nme.1620360806, 1993. a
Räss, L. and Omlin, S.: ParallelRandomFields.jl,
https://github.com/luraess/ParallelRandomFields.jl (last access: 16 May 2022), 2021. a
Räss, L. and Utkin, I.: PTsolvers/PseudoTransientDiffusion.jl:
PseudoTransientDiffusion.jl 1.0.0, Zenodo [code], https://doi.org/10.5281/zenodo.6553699,
2022a. a, b
Räss, L. and Utkin, I.: PTsolvers/PseudoTransientStokes.jl:
PseudoTransientStokes.jl 1.0.0, Zenodo [code], https://doi.org/10.5281/zenodo.6553714,
2022b. a, b
Räss, L., Duretz, T., Podladchikov, Y. Y., and Schmalholz, S. M.: M2Di:
Concise and efficient MATLAB 2-D Stokes solvers using the Finite
Difference Method, Geochem. Geophy. Geosy., 18, 755–768,
https://doi.org/10.1002/2016GC006727, 2017. a, b
Räss, L., Kolyukhin, D., and Minakov, A.: Efficient parallel random field
generator for large 3-D geophysical problems, Comput. Geosci.,
131, 158–169, https://doi.org/10.1016/j.cageo.2019.06.007, 2019b. a
Räss, L., Omlin, S., and Podladchikov, Y. Y.: Resolving Spontaneous
Nonlinear Multi-Physics Flow Localization in 3-D: Tackling Hardware Limit,
https://developer.nvidia.com/gtc/2019/video/S9368 (last access: 16 May 2022), 2019c. a
Räss, L., Licul, A., Herman, F., Podladchikov, Y. Y., and Suckale, J.: Modelling thermomechanical ice deformation using an implicit pseudo-transient method (FastICE v1.0) based on graphical processing units (GPUs), Geosci. Model Dev., 13, 955–976, https://doi.org/10.5194/gmd-13-955-2020, 2020. a, b, c, d, e, f
Reuber, G. S., Holbach, L., and Räss, L.: Adjoint-based inversion for
porosity in shallow reservoirs using pseudo-transient solvers for non-linear
hydro-mechanical processes, J. Comput. Phys., 423, 109797,
https://doi.org/10.1016/j.jcp.2020.109797, 2020. a
Rezaiee-Pajand, M., Kadkhodayan, M., Alamatian, J., and Zhang, L. C.: A new
method of fictitious viscous damping determination for the dynamic relaxation
method, Comput. Struct., 89, 783–794,
https://doi.org/10.1016/J.COMPSTRUC.2011.02.002, 2011. a, b
Richardson, L. F.: IX. The approximate arithmetical solution by finite
differences of physical problems involving differential equations, with an
application to the stresses in a masonry dam, Philos. T.
R. Soc. A, 210, 307–357, https://doi.org/10.1098/rsta.1911.0009, 1911. a
Riley, J. D.: Iteration Procedures for the Dirichlet Difference
Problem, Mathematical Tables and Other Aids to Computation, 8, 125–131,
https://doi.org/10.2307/2001924, 1954. a, b
Saad, Y.: Iterative methods for linear systems of equations: A brief
historical journey, in: Contemporary Mathematics, edited by: Brenner, S.,
Shparlinski, I., Shu, C.-W., and Szyld, D., American
Mathematical Society, Providence, Rhode Island, 754, 197–215, https://doi.org/10.1090/conm/754/15141,
2020. a, b
Shin, D. and Strikwerda, J. C.: Inf-sup conditions for finite-difference
approximations of the Stokes equations, J. Aust.
Math. Soc. B, 39, 121–134, 1997. a
Swirydowicz, K., Langou, J., Ananthan, S., Yang, U., and Thomas, S.: Low
synchronization Gram-Schmidt and generalized minimal residual algorithms,
Numer. Linear Algebr., 28, e2343, https://doi.org/10.1002/nla.2343, 2020.
a
Tackley, P. J.: Effects of strongly variable viscosity on three-dimensional
compressible convection in planetary mantles, J. Geophys. Res.-Sol. Ea., 101, 3311–3332,
https://doi.org/10.1029/95JB03211, 1996. a
Trottenberg, U., Oosterlee, C. W. C. W., and Schüller, A.: Multigrid,
Academic Press, hardcover ISBN 9780127010700,
eBook ISBN 9780080479569, 2001. a
Virieux, J.: P-SV wave propagation in heterogeneous media: Velocity‐stress
finite‐difference method, Geophysics, 51, 889–901,
https://doi.org/10.1190/1.1442147, 1986. a
Wang, L. H., Yarushina, V., Alkhimenkov, Y., and Podladchikov, Y.:
Physics-inspired pseudo-transient method and its application in modelling
focused fluid flow with geological complexity, Geophys. J. Int., 229, 1–20, https://doi.org/10.1093/GJI/GGAB426, 2021. a, b, c
Wulf, W. A. and McKee, S. A.: Hitting the memory wall: implications of the
obvious, ACM Comp. Ar., 23, 20–24,
https://doi.org/10.1145/216585.216588, 1995. a
Young, D. M.: Second-degree iterative methods for the solution of large linear
systems, J. Approx. Theory, 5, 137–148,
https://doi.org/10.1016/0021-9045(72)90036-6, 1972. a
Zheng, L., Gerya, T., Knepley, M., Yuen, D. A., Zhang, H., and Shi, Y.: GPU
implementation of multigrid solver for stokes equation with strongly variable
viscosity, in: Lecture Notes in Earth System Sciences, 0, 321–333,
Springer, Berlin, Heidelberg, https://doi.org/10.1007/978-3-642-16405-7_21, 2013. a
Short summary
Continuum mechanics-based modelling of physical processes at large scale requires huge computational resources provided by massively parallel hardware such as graphical processing units. We present a suite of numerical algorithms, implemented using the Julia language, that efficiently leverages the parallelism. We demonstrate that our implementation is efficient, scalable and robust and showcase applications to various geophysical problems.
Continuum mechanics-based modelling of physical processes at large scale requires huge...
