Articles | Volume 6, issue 3
https://doi.org/10.5194/gmd-6-735-2013
© Author(s) 2013. 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-6-735-2013
© Author(s) 2013. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
The ICON-1.2 hydrostatic atmospheric dynamical core on triangular grids – Part 1: Formulation and performance of the baseline version
Max Planck Institute for Meteorology, Hamburg, Germany
International Max Planck Research School on Earth System Modelling, Hamburg, Germany
now at: Pacific Northwest National Laboratory, Richland, WA, USA
M. A. Giorgetta
Max Planck Institute for Meteorology, Hamburg, Germany
G. Zängl
German Weather Service, Offenbach am Main, Germany
M. Restelli
MOX – Department of Mathematics F. Brioschi, Politecnico di Milano, Milan, Italy
D. Majewski
German Weather Service, Offenbach am Main, Germany
L. Bonaventura
MOX – Department of Mathematics F. Brioschi, Politecnico di Milano, Milan, Italy
K. Fröhlich
Max Planck Institute for Meteorology, Hamburg, Germany
German Weather Service, Offenbach am Main, Germany
D. Reinert
German Weather Service, Offenbach am Main, Germany
P. Rípodas
German Weather Service, Offenbach am Main, Germany
L. Kornblueh
Max Planck Institute for Meteorology, Hamburg, Germany
J. Förstner
German Weather Service, Offenbach am Main, Germany
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Marco A. Giorgetta, William Sawyer, Xavier Lapillonne, Panagiotis Adamidis, Dmitry Alexeev, Valentin Clément, Remo Dietlicher, Jan Frederik Engels, Monika Esch, Henning Franke, Claudia Frauen, Walter M. Hannah, Benjamin R. Hillman, Luis Kornblueh, Philippe Marti, Matthew R. Norman, Robert Pincus, Sebastian Rast, Daniel Reinert, Reiner Schnur, Uwe Schulzweida, and Bjorn Stevens
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Hui Wan, Kai Zhang, Philip J. Rasch, Vincent E. Larson, Xubin Zeng, Shixuan Zhang, and Ross Dixon
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Hui Wan, Shixuan Zhang, Philip J. Rasch, Vincent E. Larson, Xubin Zeng, and Huiping Yan
Geosci. Model Dev., 14, 1921–1948, https://doi.org/10.5194/gmd-14-1921-2021, https://doi.org/10.5194/gmd-14-1921-2021, 2021
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Trang Van Pham, Christian Steger, Burkhardt Rockel, Klaus Keuler, Ingo Kirchner, Mariano Mertens, Daniel Rieger, Günther Zängl, and Barbara Früh
Geosci. Model Dev., 14, 985–1005, https://doi.org/10.5194/gmd-14-985-2021, https://doi.org/10.5194/gmd-14-985-2021, 2021
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A new regional climate model was prepared based on a weather forecast model. Slow processes of the climate system such as ocean state development and greenhouse gas emissions were implemented. A model infrastructure and evaluation tools were also prepared to facilitate long-term simulations and model evalution. The first ICON-CLM results were close to observations and comparable to those from COSMO-CLM, the recommended model being used at the Deutscher Wetterdienst and CLM Community.
Sebastian Borchert, Guidi Zhou, Michael Baldauf, Hauke Schmidt, Günther Zängl, and Daniel Reinert
Geosci. Model Dev., 12, 3541–3569, https://doi.org/10.5194/gmd-12-3541-2019, https://doi.org/10.5194/gmd-12-3541-2019, 2019
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We present an upper-atmosphere extension of the ICOsahedral Non-hydrostatic (ICON) model.
This includes an extension of the model dynamics from a shallow to a deep atmosphere
and the implementation of upper-atmosphere physics parameterizations.
Idealized test cases and climate simulations are performed in order to evaluate this new configuration, named UA-ICON.
Chandan Sarangi, Yun Qian, Karl Rittger, Kathryn J. Bormann, Ying Liu, Hailong Wang, Hui Wan, Guangxing Lin, and Thomas H. Painter
Atmos. Chem. Phys., 19, 7105–7128, https://doi.org/10.5194/acp-19-7105-2019, https://doi.org/10.5194/acp-19-7105-2019, 2019
Short summary
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Colin M. Zarzycki, Christiane Jablonowski, James Kent, Peter H. Lauritzen, Ramachandran Nair, Kevin A. Reed, Paul A. Ullrich, David M. Hall, Mark A. Taylor, Don Dazlich, Ross Heikes, Celal Konor, David Randall, Xi Chen, Lucas Harris, Marco Giorgetta, Daniel Reinert, Christian Kühnlein, Robert Walko, Vivian Lee, Abdessamad Qaddouri, Monique Tanguay, Hiroaki Miura, Tomoki Ohno, Ryuji Yoshida, Sang-Hun Park, Joseph B. Klemp, and William C. Skamarock
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Johannes Eckstein, Roland Ruhnke, Stephan Pfahl, Emanuel Christner, Christopher Diekmann, Christoph Dyroff, Daniel Reinert, Daniel Rieger, Matthias Schneider, Jennifer Schröter, Andreas Zahn, and Peter Braesicke
Geosci. Model Dev., 11, 5113–5133, https://doi.org/10.5194/gmd-11-5113-2018, https://doi.org/10.5194/gmd-11-5113-2018, 2018
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We present ICON-ART-Iso, an extension to the global circulation model ICON, which allows for the simulation of the stable isotopologues of water. The main advantage over other isotope-enabled models is its flexible design with respect to the number of tracers simulated. We compare the results of several simulations to measurements of different scale. ICON-ART-Iso is able to reasonably reproduce the measurements. It is a promising tool to aid in the investigation of the atmospheric water cycle.
Jennifer Schröter, Daniel Rieger, Christian Stassen, Heike Vogel, Michael Weimer, Sven Werchner, Jochen Förstner, Florian Prill, Daniel Reinert, Günther Zängl, Marco Giorgetta, Roland Ruhnke, Bernhard Vogel, and Peter Braesicke
Geosci. Model Dev., 11, 4043–4068, https://doi.org/10.5194/gmd-11-4043-2018, https://doi.org/10.5194/gmd-11-4043-2018, 2018
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In this paper, we introduce the most up-to-date version of the flexible tracer framework for the ICOsahedral Nonhydrostatic model with
Aerosols and Reactive Trace gases (ICON-ART).
We performed multiple simulations using different ICON physics configurations for weather and climate with ART.
The flexible tracer framework within ICON-ART 2.1 suits the demands of a large variety of different applications ranging from numerical weather prediction to climate integrations.
Kai Zhang, Philip J. Rasch, Mark A. Taylor, Hui Wan, Ruby Leung, Po-Lun Ma, Jean-Christophe Golaz, Jon Wolfe, Wuyin Lin, Balwinder Singh, Susannah Burrows, Jin-Ho Yoon, Hailong Wang, Yun Qian, Qi Tang, Peter Caldwell, and Shaocheng Xie
Geosci. Model Dev., 11, 1971–1988, https://doi.org/10.5194/gmd-11-1971-2018, https://doi.org/10.5194/gmd-11-1971-2018, 2018
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The conservation of total water is an important numerical feature for global Earth system models. Even small conservation problems in the water budget can lead to systematic errors in century-long simulations for sea level rise projection. This study quantifies and reduces various sources of water conservation error in the atmosphere component of the Energy Exascale Earth System Model.
Yawen Liu, Kai Zhang, Yun Qian, Yuhang Wang, Yufei Zou, Yongjia Song, Hui Wan, Xiaohong Liu, and Xiu-Qun Yang
Atmos. Chem. Phys., 18, 31–47, https://doi.org/10.5194/acp-18-31-2018, https://doi.org/10.5194/acp-18-31-2018, 2018
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Fire aerosols have large impact on weather and climate through their effect on clouds and radiation, but it is difficult to quantify. Here we investigated the short-term effective radiative forcing of fire aerosols using the nudged hindcast ensemble simulations from global aerosol-climate model. Results show large effects of fire aerosols on both liquid and ice cloud and large ensemble spread of regional mean shortwave cloud radiative forcing over southern Mexico and the central US.
Paul A. Ullrich, Christiane Jablonowski, James Kent, Peter H. Lauritzen, Ramachandran Nair, Kevin A. Reed, Colin M. Zarzycki, David M. Hall, Don Dazlich, Ross Heikes, Celal Konor, David Randall, Thomas Dubos, Yann Meurdesoif, Xi Chen, Lucas Harris, Christian Kühnlein, Vivian Lee, Abdessamad Qaddouri, Claude Girard, Marco Giorgetta, Daniel Reinert, Joseph Klemp, Sang-Hun Park, William Skamarock, Hiroaki Miura, Tomoki Ohno, Ryuji Yoshida, Robert Walko, Alex Reinecke, and Kevin Viner
Geosci. Model Dev., 10, 4477–4509, https://doi.org/10.5194/gmd-10-4477-2017, https://doi.org/10.5194/gmd-10-4477-2017, 2017
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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.
Hui Wan, Kai Zhang, Philip J. Rasch, Balwinder Singh, Xingyuan Chen, and Jim Edwards
Geosci. Model Dev., 10, 537–552, https://doi.org/10.5194/gmd-10-537-2017, https://doi.org/10.5194/gmd-10-537-2017, 2017
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Solution reproductibility testing is an important task for assuring the software quality of a climate model. A new method is developed using the concept of numerical convergence with respect to temporal resolution. The method is objective, easy to implement, and computationally efficient. This paper describes the new test and demonstrates its utility in the Community Atmosphere Model version 5 (CAM5).
Kai Zhang, Chun Zhao, Hui Wan, Yun Qian, Richard C. Easter, Steven J. Ghan, Koichi Sakaguchi, and Xiaohong Liu
Geosci. Model Dev., 9, 607–632, https://doi.org/10.5194/gmd-9-607-2016, https://doi.org/10.5194/gmd-9-607-2016, 2016
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A sub-grid treatment based on Weibull distribution is introduced to CAM5 to take into account the impact of unresolved variability of surface wind speed on sea salt and dust emissions. Simulations show that sub-grid wind variability has relatively small impacts on the global mean sea salt emissions, but considerable influence on dust emissions. Dry convective eddies and mesoscale flows associated with complex topography are the major causes of dust emission enhancement.
D. Rieger, M. Bangert, I. Bischoff-Gauss, J. Förstner, K. Lundgren, D. Reinert, J. Schröter, H. Vogel, G. Zängl, R. Ruhnke, and B. Vogel
Geosci. Model Dev., 8, 1659–1676, https://doi.org/10.5194/gmd-8-1659-2015, https://doi.org/10.5194/gmd-8-1659-2015, 2015
R. Hommel, C. Timmreck, M. A. Giorgetta, and H. F. Graf
Atmos. Chem. Phys., 15, 5557–5584, https://doi.org/10.5194/acp-15-5557-2015, https://doi.org/10.5194/acp-15-5557-2015, 2015
H. Wan, P. J. Rasch, K. Zhang, Y. Qian, H. Yan, and C. Zhao
Geosci. Model Dev., 7, 1961–1977, https://doi.org/10.5194/gmd-7-1961-2014, https://doi.org/10.5194/gmd-7-1961-2014, 2014
K. Zhang, H. Wan, X. Liu, S. J. Ghan, G. J. Kooperman, P.-L. Ma, P. J. Rasch, D. Neubauer, and U. Lohmann
Atmos. Chem. Phys., 14, 8631–8645, https://doi.org/10.5194/acp-14-8631-2014, https://doi.org/10.5194/acp-14-8631-2014, 2014
P. H. Lauritzen, P. A. Ullrich, C. Jablonowski, P. A. Bosler, D. Calhoun, A. J. Conley, T. Enomoto, L. Dong, S. Dubey, O. Guba, A. B. Hansen, E. Kaas, J. Kent, J.-F. Lamarque, M. J. Prather, D. Reinert, V. V. Shashkin, W. C. Skamarock, B. Sørensen, M. A. Taylor, and M. A. Tolstykh
Geosci. Model Dev., 7, 105–145, https://doi.org/10.5194/gmd-7-105-2014, https://doi.org/10.5194/gmd-7-105-2014, 2014
S. Carcano, L. Bonaventura, T. Esposti Ongaro, and A. Neri
Geosci. Model Dev., 6, 1905–1924, https://doi.org/10.5194/gmd-6-1905-2013, https://doi.org/10.5194/gmd-6-1905-2013, 2013
H. Wan, P. J. Rasch, K. Zhang, J. Kazil, and L. R. Leung
Geosci. Model Dev., 6, 861–874, https://doi.org/10.5194/gmd-6-861-2013, https://doi.org/10.5194/gmd-6-861-2013, 2013
Related subject area
Numerical methods
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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
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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
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)
Development and preliminary validation of a land surface image assimilation system based on the common land model
A comparison of Eulerian and Lagrangian methods for vertical particle transport in the water column
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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
Decision-making strategies implemented in SolFinder 1.0 to identify eco-efficient aircraft trajectories: application study in AirTraf 3.0
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
A model instability issue in the National Centers for Environmental Prediction Global Forecast System version 16 and potential solutions
A comparison of 3-D spherical shell thermal convection results at low to moderate Rayleigh number using ASPECT (version 2.2.0) and CitcomS (version 3.3.1)
Developing meshing workflows for Geologic Uncertainty Assessment in High-Temperature Aquifer Thermal Energy Storage
LISFLOOD-FP 8.1: new GPU-accelerated solvers for faster fluvial/pluvial flood simulations
Fast approximate Barnes interpolation: illustrated by Python-Numba implementation fast-barnes-py v1.0
Strategies for conservative and non-conservative monotone remapping on the sphere
Modeling large‐scale landform evolution with a stream power law for glacial erosion (OpenLEM v37): benchmarking experiments against a more process-based description of ice flow (iSOSIA v3.4.3)
A mixed finite-element discretisation of the shallow-water equations
Multifidelity Monte Carlo estimation for efficient uncertainty quantification in climate-related modeling
Massively parallel modeling and inversion of electrical resistivity tomography data using PFLOTRAN
Parallelized domain decomposition for multi-dimensional Lagrangian random walk mass-transfer particle tracking schemes
The Intelligent Prospector v1.0: geoscientific model development and prediction by sequential data acquisition planning with application to mineral exploration
Assessing Effects of Climate and Technology Uncertainties in Large Natural Resource Allocation Problems
Predicting peak daily maximum 8 h ozone and linkages to emissions and meteorology in Southern California using machine learning methods (SoCAB-8HR V1.0)
Transfer learning for landslide susceptibility modeling using domain adaptation and case-based reasoning
ISMIP-HOM benchmark experiments using Underworld
spyro: a Firedrake-based wave propagation and full-waveform-inversion finite-element solver
Spatial filtering in a 6D hybrid-Vlasov scheme to alleviate adaptive mesh refinement artifacts: a case study with Vlasiator (versions 5.0, 5.1, and 5.2.1)
A Bayesian data assimilation framework for lake 3D hydrodynamic models with a physics-preserving particle filtering method using SPUX-MITgcm v1
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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.
Gianandrea Mannarini, Mario Leonardo Salinas, Lorenzo Carelli, Nicola Petacco, and Josip Orović
EGUsphere, https://doi.org/10.5194/egusphere-2023-2060, https://doi.org/10.5194/egusphere-2023-2060, 2023
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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 now quasi-linear. VISIR-2 yields, for more than ten days in a year, two-digit savings for a ferry sailing in the Mediterranean Sea. Sailboat routes with wind and currents can be optimised as well.
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.
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