Articles | Volume 13, issue 2
Geosci. Model Dev., 13, 735–761, 2020
https://doi.org/10.5194/gmd-13-735-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Special issue: The Firedrake automatic code generation system
Geosci. Model Dev., 13, 735–761, 2020
https://doi.org/10.5194/gmd-13-735-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Development and technical paper 25 Feb 2020
Development and technical paper | 25 Feb 2020
Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond
Thomas H. Gibson et al.
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Tuomas Kärnä, Stephan C. Kramer, Lawrence Mitchell, David A. Ham, Matthew D. Piggott, and António M. Baptista
Geosci. Model Dev., 11, 4359–4382, https://doi.org/10.5194/gmd-11-4359-2018, https://doi.org/10.5194/gmd-11-4359-2018, 2018
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Unstructured meshes are attractive for coastal ocean modeling, as they allow more accurate representation of complex coastal topography. Unstructured mesh models are, however, often perceived as slow and inaccurate. We present a novel discontinuous Galerkin ocean model: Thetis. We demonstrate that the model is able to simulate baroclinic ocean flows with high accuracy on a triangular prismatic mesh. This work paves the way for highly accurate and efficient three-dimensional coastal ocean models.
Gheorghe-Teodor Bercea, Andrew T. T. McRae, David A. Ham, Lawrence Mitchell, Florian Rathgeber, Luigi Nardi, Fabio Luporini, and Paul H. J. Kelly
Geosci. Model Dev., 9, 3803–3815, https://doi.org/10.5194/gmd-9-3803-2016, https://doi.org/10.5194/gmd-9-3803-2016, 2016
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Unstructured meshes offer flexibility but are perceived as slow. Some applications, including atmosphere or ocean simulations, admit an extruded mesh: the horizontal mesh may be unstructured, but the vertical dimension can be traversed in a structured way. By extending the Firedrake automated simulation framework to this case, we show that an extruded mesh can be traversed as fast as a structured mesh. This paves the way for highly efficient unstructured mesh models of the ocean and atmosphere.
J. Thuburn, C. J. Cotter, and T. Dubos
Geosci. Model Dev., 7, 909–929, https://doi.org/10.5194/gmd-7-909-2014, https://doi.org/10.5194/gmd-7-909-2014, 2014
J. Hill, E. E. Popova, D. A. Ham, M. D. Piggott, and M. Srokosz
Ocean Sci., 10, 323–343, https://doi.org/10.5194/os-10-323-2014, https://doi.org/10.5194/os-10-323-2014, 2014
M. E. Rognes, D. A. Ham, C. J. Cotter, and A. T. T. McRae
Geosci. Model Dev., 6, 2099–2119, https://doi.org/10.5194/gmd-6-2099-2013, https://doi.org/10.5194/gmd-6-2099-2013, 2013
Related subject area
Numerical methods
A nested multi-scale system implemented in the large-eddy simulation model PALM model system 6.0
Extending legacy climate models by adaptive mesh refinement for single-component tracer transport: a case study with ECHAM6-HAMMOZ (ECHAM6.3-HAM2.3-MOZ1.0)
Using the Després and Lagoutière (1999) antidiffusive transport scheme: a promising and novel method against excessive vertical diffusion in chemistry-transport models
Porosity and permeability prediction through forward stratigraphic simulations using GPM™ and Petrel™: application in shallow marine depositional settings
Effects of transient processes for thermal simulations of the Central European Basin
A note on precision-preserving compression of scientific data
Ocean Plastic Assimilator v0.1: Assimilation of Plastics Concentration Data Into Lagrangian Dispersion Models
An N-dimensional Fortran interpolation programme (NterGeo.v2020a) for geophysics sciences – application to a back-trajectory programme (Backplumes.v2020r1) using CHIMERE or WRF outputs
A framework to evaluate IMEX schemes for atmospheric models
Inequality-constrained free-surface evolution in a full Stokes ice flow model (evolve_glacier v1.1)
A fast and efficient MATLAB-based MPM solver: fMPMM-solver v1.1
An iterative process for efficient optimisation of parameters in geoscientific models: a demonstration using the Parallel Ice Sheet Model (PISM) version 0.7.3
Necessary conditions for algorithmic tuning of weather prediction models using OpenIFS as an example
Development of a submerged aquatic vegetation growth model in the Coupled Ocean–Atmosphere–Wave–Sediment Transport (COAWST v3.4) model
Retrieving monthly and interannual total-scale pH (pHT) on the East China Sea shelf using an artificial neural network: ANN-pHT-v1
Efficient Bayesian inference for large chaotic dynamical systems
Retrieval of process rate parameters in the general dynamic equation for aerosols using Bayesian state estimation
A discontinuous Galerkin finite element model for fast channelized lava flows v1.0
Development of a semi-Lagrangian advection scheme for the NEMO ocean model (3.1)
Constraining stochastic 3-D structural geological models with topology information using Approximate Bayesian Computation using GemPy 2.1
Efficient multi-scale Gaussian process regression for massive remote sensing data with satGP v0.1.2
PDE-NetGen 1.0: from symbolic partial differential equation (PDE) representations of physical processes to trainable neural network representations
Simple algorithms to compute meridional overturning and barotropic streamfunctions on unstructured meshes
Development of a two-way-coupled ocean–wave model: assessment on a global NEMO(v3.6)–WW3(v6.02) coupled configuration
Surrogate-assisted Bayesian inversion for landscape and basin evolution models
Towards an objective assessment of climate multi-model ensembles – a case study: the Senegalo-Mauritanian upwelling region
QuickSampling v1.0: a robust and simplified pixel-based multiple-point simulation approach
A full Stokes subgrid scheme in two dimensions for simulation of grounding line migration in ice sheets using Elmer/ICE (v8.3)
On the numerical integration of the Lorenz-96 model, with scalar additive noise, for benchmark twin experiments
Data assimilation of in situ and satellite remote sensing data to 3D hydrodynamic lake models: a case study using Delft3D-FLOW v4.03 and OpenDA v2.4
A one-dimensional model of turbulent flow through “urban” canopies (MLUCM v2.0): updates based on large-eddy simulation
A model of Black Sea circulation with strait exchange (2008–2018)
The Land Variational Ensemble Data Assimilation Framework: LAVENDAR v1.0.0
Evaluation of lossless and lossy algorithms for the compression of scientific datasets in netCDF-4 or HDF5 files
Efficiency and robustness in Monte Carlo sampling for 3-D geophysical inversions with Obsidian v0.1.2: setting up for success
LSCE-FFNN-v1: a two-step neural network model for the reconstruction of surface ocean pCO2 over the global ocean
FESOM-C v.2: coastal dynamics on hybrid unstructured meshes
A new method (M3Fusion v1) for combining observations and multiple model output for an improved estimate of the global surface ozone distribution
DCMIP2016: the splitting supercell test case
FVM 1.0: a nonhydrostatic finite-volume dynamical core for the IFS
Particle swarm optimization for the estimation of surface complexation constants with the geochemical model PHREEQC-3.1.2
GemPy 1.0: open-source stochastic geological modeling and inversion
Weak-constraint inverse modeling using HYSPLIT-4 Lagrangian dispersion model and Cross-Appalachian Tracer Experiment (CAPTEX) observations – effect of including model uncertainties on source term estimation
Global sensitivity analysis of parameter uncertainty in landscape evolution models
Symmetric equations on the surface of a sphere as used by model GISS:IB
The VOLNA-OP2 tsunami code (version 1.5)
Bayesian earthquake dating and seismic hazard assessment using chlorine-36 measurements (BED v1)
Challenges and design choices for global weather and climate models based on machine learning
The multi-assumption architecture and testbed (MAAT v1.0): R code for generating ensembles with dynamic model structure and analysis of epistemic uncertainty from multiple sources
faSavageHutterFOAM 1.0: depth-integrated simulation of dense snow avalanches on natural terrain with OpenFOAM
Antti Hellsten, Klaus Ketelsen, Matthias Sühring, Mikko Auvinen, Björn Maronga, Christoph Knigge, Fotios Barmpas, Georgios Tsegas, Nicolas Moussiopoulos, and Siegfried Raasch
Geosci. Model Dev., 14, 3185–3214, https://doi.org/10.5194/gmd-14-3185-2021, https://doi.org/10.5194/gmd-14-3185-2021, 2021
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Large-eddy simulation (LES) of the urban atmospheric boundary layer involves a large separation of turbulent scales, leading to prohibitive computational costs. An online LES–LES nesting scheme is implemented into the PALM model system 6.0 to overcome this problem. Test results show that the accuracy within the high-resolution nest domains approach the non-nested high-resolution reference results. The nesting can reduce the CPU by time up to 80 % compared to the fine-resolution reference runs.
Yumeng Chen, Konrad Simon, and Jörn Behrens
Geosci. Model Dev., 14, 2289–2316, https://doi.org/10.5194/gmd-14-2289-2021, https://doi.org/10.5194/gmd-14-2289-2021, 2021
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Mesh adaptivity can reduce overall model error by only refining meshes in specific areas where it us necessary in the runtime. Here we suggest a way to integrate mesh adaptivity into an existing Earth system model, ECHAM6, without having to redesign the implementation from scratch. We show that while the additional computational effort is manageable, the error can be reduced compared to a low-resolution standard model using an idealized test and relatively realistic dust transport tests.
Sylvain Mailler, Romain Pennel, Laurent Menut, and Mathieu Lachâtre
Geosci. Model Dev., 14, 2221–2233, https://doi.org/10.5194/gmd-14-2221-2021, https://doi.org/10.5194/gmd-14-2221-2021, 2021
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Representing the advection of thin polluted plumes in numerical models is a challenging task since these models usually tend to excessively diffuse these plumes in the vertical direction. This numerical diffusion process is the cause of major difficulties in representing such dense and thin polluted plumes in numerical models. We propose here, and test in an academic framework, a novel method to solve this problem through the use of an antidiffusive advection scheme in the vertical direction.
Daniel Otoo and David Hodgetts
Geosci. Model Dev., 14, 2075–2095, https://doi.org/10.5194/gmd-14-2075-2021, https://doi.org/10.5194/gmd-14-2075-2021, 2021
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The forward stratigraphic simulation method is used to predict lithofacies, porosity, and permeability in a reservoir model. The objective of using this approach is to enhance subsurface property modelling through geologic realistic 3-D stratigraphic patterns.
Results show realistic stratigraphic sequences. Given this, we can derive spatial and geometric data as secondary data to constrain property simulation in a reservoir model. The approach can reduce the uncertainty of property modelling.
Denise Degen and Mauro Cacace
Geosci. Model Dev., 14, 1699–1719, https://doi.org/10.5194/gmd-14-1699-2021, https://doi.org/10.5194/gmd-14-1699-2021, 2021
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In this work, we focus on improving the understanding of subsurface processes with respect to interactions with climate dynamics. We present advanced, open-source mathematical methods that enable us to investigate the influence of various model properties on the final outcomes. By relying on our approach, we have been able to showcase their importance in improving our understanding of the subsurface and highlighting the current shortcomings of currently adopted models.
Rostislav Kouznetsov
Geosci. Model Dev., 14, 377–389, https://doi.org/10.5194/gmd-14-377-2021, https://doi.org/10.5194/gmd-14-377-2021, 2021
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Resetting of non-significant figures (precision trimming) enables efficient data compression and helps to avoid excessive use of storage space and network bandwidth while having well-constrained distortion to the data. The paper analyses accuracy losses and artifacts caused by trimming methods and by the widely used linear packing method. The paper presents several methods with implementation, evaluation, and illustrations and includes subroutines directly usable in geoscientific models.
Axel Peytavin, Bruno Sainte-Rose, Gael Forget, and Jean-Michel Campin
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2020-385, https://doi.org/10.5194/gmd-2020-385, 2021
Revised manuscript accepted for GMD
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We present a new algorithm developed at The Ocean Cleanup to update ocean plastic models based on measurements collected in the field to improve future cleaning operations. Prepared in collaboration with MIT researchers, this initial study presents its use in several test cases in which two observers in a simulated flow field record regular observations to update a plastic forecast. We demonstrate this improves the prediction, even with inaccurate knowledge of the water flows driving plastic.
Bertrand Bessagnet, Laurent Menut, and Maxime Beauchamp
Geosci. Model Dev., 14, 91–106, https://doi.org/10.5194/gmd-14-91-2021, https://doi.org/10.5194/gmd-14-91-2021, 2021
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This paper presents a new interpolator useful for geophysics applications. It can explore N-dimensional meshes, grids or look-up tables. The code accepts irregular but structured grids. Written in Fortran, it is easy to implement in existing codes and very fast and portable. We have compared it with a Python library. Python is convenient but suffers from portability and is sometimes not optimized enough. As an application case, this method is applied to atmospheric sciences.
Oksana Guba, Mark A. Taylor, Andrew M. Bradley, Peter A. Bosler, and Andrew Steyer
Geosci. Model Dev., 13, 6467–6480, https://doi.org/10.5194/gmd-13-6467-2020, https://doi.org/10.5194/gmd-13-6467-2020, 2020
Anna Wirbel and Alexander Helmut Jarosch
Geosci. Model Dev., 13, 6425–6445, https://doi.org/10.5194/gmd-13-6425-2020, https://doi.org/10.5194/gmd-13-6425-2020, 2020
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We present an open-source numerical tool to simulate the free-surface evolution of gravity-driven flows (e.g. glaciers) constrained by bed topography. No ad hoc post-processing is required to enforce positive ice thickness and mass conservation. We utilise finite elements, define benchmark tests, and showcase glaciological examples. In addition, we provide a thorough analysis of the applicability and robustness of different spatial stabilisation and time discretisation methods.
Emmanuel Wyser, Yury Alkhimenkov, Michel Jaboyedoff, and Yury Y. Podladchikov
Geosci. Model Dev., 13, 6265–6284, https://doi.org/10.5194/gmd-13-6265-2020, https://doi.org/10.5194/gmd-13-6265-2020, 2020
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In this work, we present an efficient and fast material point method (MPM) implementation in MATLAB. We first discuss the vectorization strategies to adapt this numerical method to a MATLAB implementation. We report excellent agreement of the solver compared with classical analysis among the MPM community, such as the cantilever beam problem. The solver achieves a performance gain of 28 compared with a classical iterative implementation.
Steven J. Phipps, Jason L. Roberts, and Matt A. King
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2020-382, https://doi.org/10.5194/gmd-2020-382, 2020
Revised manuscript accepted for GMD
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Simplified schemes, known as parameterisations, are sometimes used to describe physical processes within numerical models. However, the values of the parameters are uncertain. This introduces uncertainty into the model outputs. We develop a simple approach to identify plausible ranges for model parameters. Using a model of the Antarctic Ice Sheet, we find that the value of one parameter can depend on the values of others. We conclude that a single optimal set of parameter values does not exist.
Lauri Tuppi, Pirkka Ollinaho, Madeleine Ekblom, Vladimir Shemyakin, and Heikki Järvinen
Geosci. Model Dev., 13, 5799–5812, https://doi.org/10.5194/gmd-13-5799-2020, https://doi.org/10.5194/gmd-13-5799-2020, 2020
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This paper presents general guidelines on how to utilise computer algorithms efficiently in order to tune weather models so that they would produce better forecasts. The main conclusions are that the computer algorithms work most efficiently with a suitable cost function, certain forecast length and ensemble size. We expect that our results will facilitate the use of algorithmic methods in the tuning of weather models.
Tarandeep S. Kalra, Neil K. Ganju, and Jeremy M. Testa
Geosci. Model Dev., 13, 5211–5228, https://doi.org/10.5194/gmd-13-5211-2020, https://doi.org/10.5194/gmd-13-5211-2020, 2020
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The paper covers the description of a 3-D open-source model that dynamically couples the biophysical interactions between submerged aquatic vegetation (SAV), hydrodynamics (currents, waves), sediment dynamics, and nutrient loading. Based on SAV growth model, SAV can use growth or dieback while contributing and sequestering nutrients from the water column (modifying the biological environment) and subsequently affect the hydrodynamics and sediment transport (modifying the physical environment).
Xiaoshuang Li, Richard Garth James Bellerby, Jianzhong Ge, Philip Wallhead, Jing Liu, and Anqiang Yang
Geosci. Model Dev., 13, 5103–5117, https://doi.org/10.5194/gmd-13-5103-2020, https://doi.org/10.5194/gmd-13-5103-2020, 2020
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We have developed an ANN model to predict pH using 11 cruise datasets from 2013 to 2017,
demonstrated its reliability using three cruise datasets during 2018 and applied it to
retrieve monthly pH for the period 2000 to 2016 on the East China Sea shelf using the
ANN model in combination with input variables from the Changjiang biology Finite-Volume
Coastal Ocean Model. This approach may be a valuable tool for understanding the seasonal
variation of pH in poorly observed regions.
Sebastian Springer, Heikki Haario, Jouni Susiluoto, Aleksandr Bibov, Andrew Davis, and Youssef Marzouk
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2020-350, https://doi.org/10.5194/gmd-2020-350, 2020
Revised manuscript accepted for GMD
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The model predictions always contain uncertainty. But in some cases, such as weather forecasting or climate modelling, chaotic unpredictability increases the difficulty to say exactly how much uncertainty there is. We combine two recently proposed mathematical methods to show how the uncertainty can be analyzed in models that are simplifications of true weather models. The results can be extended in the future to show how forecasts from the large-scale models can be improved.
Matthew Ozon, Aku Seppänen, Jari P. Kaipio, and Kari E. J. Lehtinen
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2020-236, https://doi.org/10.5194/gmd-2020-236, 2020
Revised manuscript accepted for GMD
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Experimental research has provided large amounts of high quality data on aerosol in the last two decades. However, the inference of the process rates, e.g. the rate at which particles are generated, is still typically done by simple curve-fitting methods, and does not assess the credibility of the estimation. The devised method takes advantage of the Baysesian framework to, not only retrieves the state of the observed aerosol system, but also estimates the process rates, e.g. growth rate.
Colton J. Conroy and Einat Lev
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2020-184, https://doi.org/10.5194/gmd-2020-184, 2020
Revised manuscript accepted for GMD
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Lava flows present a natural hazard to communities around volcanoes and are usually slow moving (< 1–5 cm/s). Lava flows during the 2018 eruption of Kilauea Volcano, Hawai’i, however, reached speeds as high as 11 m/s. To investigate these dynamics we develop a new lava flow computer model that incorporates a nonlinear expression for the fluid viscosity. Model results indicate that the lava flows at Site 8 of the eruption displayed shear thickening behavior due to the flows high bubble content.
Christopher Subich, Pierre Pellerin, Gregory Smith, and Frederic Dupont
Geosci. Model Dev., 13, 4379–4398, https://doi.org/10.5194/gmd-13-4379-2020, https://doi.org/10.5194/gmd-13-4379-2020, 2020
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This work presents a semi-Lagrangian advection module for the NEMO (OPA) ocean model. Semi-Lagrangian advection transports fluid properties (temperature, salinity, velocity) between time steps by following fluid motion and interpolating from upstream locations of fluid parcels.
This method is commonly used in atmospheric models to extend time step size, but it has not previously been applied to operational ocean models. Overcoming this required a new approach for solid boundaries (coastlines).
Alexander Schaaf, Miguel de la Varga, Florian Wellmann, and Clare E. Bond
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2020-136, https://doi.org/10.5194/gmd-2020-136, 2020
Revised manuscript accepted for GMD
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Uncertainty is an inherent property of any model of the subsurface. We show how geological topology information – how different regions of rocks in the subsurface are connected – can be used to learn uncertain geological models to reduce uncertainty. More widely, the method demonstrates the use of probabilistic machine learning (Bayesian inference) to learn structural geological models on auxiliary geological knowledge that can be encoded in graph structures.
Jouni Susiluoto, Alessio Spantini, Heikki Haario, Teemu Härkönen, and Youssef Marzouk
Geosci. Model Dev., 13, 3439–3463, https://doi.org/10.5194/gmd-13-3439-2020, https://doi.org/10.5194/gmd-13-3439-2020, 2020
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We describe a new computer program that is able produce maps of carbon dioxide or other quantities based on data collected by satellites that orbit the Earth. When working with such data there is often too much data in one area and none in another. The program is able to describe the fields even when data is not available. To be able to do so, new computational methods were developed. The program is also able to describe how uncertain the estimated carbon dioxide or other fields are.
Olivier Pannekoucke and Ronan Fablet
Geosci. Model Dev., 13, 3373–3382, https://doi.org/10.5194/gmd-13-3373-2020, https://doi.org/10.5194/gmd-13-3373-2020, 2020
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Learning physics from data using a deep neural network is a challenge that requires an appropriate but unknown network architecture. The package introduced here helps to design an architecture by translating known physical equations into a network, which the experimenter completes to capture unknown physical processes. A test bed is introduced to illustrate how this learning allows us to focus on truly unknown physical processes in the hope of making better use of data and digital resources.
Dmitry Sidorenko, Sergey Danilov, Nikolay Koldunov, Patrick Scholz, and Qiang Wang
Geosci. Model Dev., 13, 3337–3345, https://doi.org/10.5194/gmd-13-3337-2020, https://doi.org/10.5194/gmd-13-3337-2020, 2020
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Computation of barotropic and meridional overturning streamfunctions for models formulated on unstructured meshes is commonly preceded by interpolation to a regular mesh. This operation destroys the original conservation, which can be then be artificially imposed to make the computation possible. An elementary method is proposed that avoids interpolation and preserves conservation in a strict model sense.
Xavier Couvelard, Florian Lemarié, Guillaume Samson, Jean-Luc Redelsperger, Fabrice Ardhuin, Rachid Benshila, and Gurvan Madec
Geosci. Model Dev., 13, 3067–3090, https://doi.org/10.5194/gmd-13-3067-2020, https://doi.org/10.5194/gmd-13-3067-2020, 2020
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Within the framework of the Copernicus Marine Environment Monitoring Service (CMEMS), an objective is to demonstrate the contribution of coupling the high-resolution analysis and forecasting system with a wave model. This study describes the necessary steps and discusses the various choices made for coupling a wave model and an oceanic model for global-scale applications.
Rohitash Chandra, Danial Azam, Arpit Kapoor, and R. Dietmar Müller
Geosci. Model Dev., 13, 2959–2979, https://doi.org/10.5194/gmd-13-2959-2020, https://doi.org/10.5194/gmd-13-2959-2020, 2020
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Forward landscape and sedimentary basin evolution models pose a major challenge in the development of efficient inference and optimization methods. Bayesian inference provides a methodology for estimation and uncertainty quantification of free model parameters. In this paper, we present an application of a surrogate-assisted Bayesian parallel tempering method where that surrogate mimics a landscape evolution model. We use the method for parameter estimation and uncertainty quantification.
Juliette Mignot, Carlos Mejia, Charles Sorror, Adama Sylla, Michel Crépon, and Sylvie Thiria
Geosci. Model Dev., 13, 2723–2742, https://doi.org/10.5194/gmd-13-2723-2020, https://doi.org/10.5194/gmd-13-2723-2020, 2020
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The most robust representation of climate is usually obtained by averaging a large number of simulations, thereby cancelling individual model errors. Here, we work towards an objective way of selecting the least biased models over a certain region, based on physical parameters. This statistical method based on a neural classifier and multi-correspondence analysis is illustrated here for the Senegalo-Mauritanian region, but it could potentially be developed for any other region or process.
Mathieu Gravey and Grégoire Mariethoz
Geosci. Model Dev., 13, 2611–2630, https://doi.org/10.5194/gmd-13-2611-2020, https://doi.org/10.5194/gmd-13-2611-2020, 2020
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Stochastic simulations are key tools to generate complex spatial structures uses as input in geoscientific models. In this paper, we present a new open-source tool that enables to simulate complex structures in a straightforward and efficient manner, based on analogues. The method is tested on a variety of use cases to demonstrate the generality of the framework.
Gong Cheng, Per Lötstedt, and Lina von Sydow
Geosci. Model Dev., 13, 2245–2258, https://doi.org/10.5194/gmd-13-2245-2020, https://doi.org/10.5194/gmd-13-2245-2020, 2020
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A full Stokes subgrid scheme in two dimensions for the grounding line migration problem is presented in the open-source finite-element framework Elmer/ICE. This method can achieve comparable results to previous research using a more than 20 times larger mesh size, which can be used to improve the efficiency in marine ice sheet simulations.
Colin Grudzien, Marc Bocquet, and Alberto Carrassi
Geosci. Model Dev., 13, 1903–1924, https://doi.org/10.5194/gmd-13-1903-2020, https://doi.org/10.5194/gmd-13-1903-2020, 2020
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All scales of a dynamical physical process cannot be resolved accurately in a multiscale, geophysical model. The behavior of unresolved scales of motion are often parametrized by a random process to emulate their effects on the dynamically resolved variables, and this results in a random–dynamical model. We study how the choice of a numerical discretization of such a system affects the model forecast and estimation statistics, when the random–dynamical model is unbiased in its parametrization.
Theo Baracchini, Philip Y. Chu, Jonas Šukys, Gian Lieberherr, Stefan Wunderle, Alfred Wüest, and Damien Bouffard
Geosci. Model Dev., 13, 1267–1284, https://doi.org/10.5194/gmd-13-1267-2020, https://doi.org/10.5194/gmd-13-1267-2020, 2020
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Lake physical processes occur at a wide range of spatiotemporal scales. 3D hydrodynamic lake models are the only information source capable of solving those scales; however, they still need observations to be calibrated and to constrain their uncertainties. The optimal combination of a 3D hydrodynamic model, in situ measurements, and remote sensing observations is achieved through data assimilation. Here we present a complete data assimilation experiment for lakes using open-source tools.
Negin Nazarian, E. Scott Krayenhoff, and Alberto Martilli
Geosci. Model Dev., 13, 937–953, https://doi.org/10.5194/gmd-13-937-2020, https://doi.org/10.5194/gmd-13-937-2020, 2020
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We present an update to the Multi-Layer Urban Canopy Model by revisiting the parameterization of length scales based on high-resolution and validated large-eddy simulations. Additionally, the inclusion of dispersive fluxes in the parameterization schemes are also discussed. The results demonstrate that updated parameterizations improve the accuracy of the vertical exchange of momentum in the street canyon.
Murat Gunduz, Emin Özsoy, and Robinson Hordoir
Geosci. Model Dev., 13, 121–138, https://doi.org/10.5194/gmd-13-121-2020, https://doi.org/10.5194/gmd-13-121-2020, 2020
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The Bosphorus exchange is of critical importance for hydrodynamics and hydroclimatology of the Black Sea. In this study, we report on the development of a medium-resolution circulation model of the Black Sea, making use of surface atmospheric forcing with high space and time resolution, climatic river fluxes and strait exchange, enabled by adding elementary details of strait and coastal topography and seasonal hydrology specified in an artificial box on the Marmara Sea side.
Ewan Pinnington, Tristan Quaife, Amos Lawless, Karina Williams, Tim Arkebauer, and Dave Scoby
Geosci. Model Dev., 13, 55–69, https://doi.org/10.5194/gmd-13-55-2020, https://doi.org/10.5194/gmd-13-55-2020, 2020
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We present LAVENDAR, a mathematical method for combining observations with models of the terrestrial environment. Here we use it to improve estimates of crop growth in the UK Met Office land surface model. However, the method is model agnostic, requires no modification to the underlying code and can be applied to any part of the model. In the example application we improve estimates of maize yield by 74 % by assimilating observations of leaf area, crop height and photosynthesis.
Xavier Delaunay, Aurélie Courtois, and Flavien Gouillon
Geosci. Model Dev., 12, 4099–4113, https://doi.org/10.5194/gmd-12-4099-2019, https://doi.org/10.5194/gmd-12-4099-2019, 2019
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This research aimed at finding a compression method suitable for the ground processing of CFOSAT and SWOT satellite datasets. Lossless algorithms did not allow enough compression. That is why we began studying lossy alternatives. This work introduces the digit rounding algorithm which reduces the volume of scientific datasets keeping only the significant digits in each sample value. The number of digits kept is relative to each sample so that both small and high values are similarly preserved.
Richard Scalzo, David Kohn, Hugo Olierook, Gregory Houseman, Rohitash Chandra, Mark Girolami, and Sally Cripps
Geosci. Model Dev., 12, 2941–2960, https://doi.org/10.5194/gmd-12-2941-2019, https://doi.org/10.5194/gmd-12-2941-2019, 2019
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Producing 3-D models of structures under the Earth's surface based on sensor data is a key problem in geophysics (for example, in mining exploration). There may be multiple models that explain the data well. We use the open-source Obsidian software to look at the efficiency of different methods for exploring the model space and attaching probabilities to models, leading to less biased results and a better idea of how sensor data interact with geological assumptions.
Anna Denvil-Sommer, Marion Gehlen, Mathieu Vrac, and Carlos Mejia
Geosci. Model Dev., 12, 2091–2105, https://doi.org/10.5194/gmd-12-2091-2019, https://doi.org/10.5194/gmd-12-2091-2019, 2019
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This work is dedicated to a new model that reconstructs the surface ocean partial pressure of carbon dioxide (pCO2) over the global ocean on a monthly 1°×1° grid. The model is based on a feed-forward neural network and represents the nonlinear relationships between pCO2 and the ocean drivers. Reconstructed pCO2 has a satisfying accuracy compared to independent observational data and shows a good agreement in seasonal and interannual variability with three existing mapping methods.
Alexey Androsov, Vera Fofonova, Ivan Kuznetsov, Sergey Danilov, Natalja Rakowsky, Sven Harig, Holger Brix, and Karen Helen Wiltshire
Geosci. Model Dev., 12, 1009–1028, https://doi.org/10.5194/gmd-12-1009-2019, https://doi.org/10.5194/gmd-12-1009-2019, 2019
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We present a description of a coastal ocean circulation model designed to work on variable-resolution meshes made of triangular and quadrilateral cells. This hybrid mesh functionality allows for higher numerical performance and less dissipative solutions.
Kai-Lan Chang, Owen R. Cooper, J. Jason West, Marc L. Serre, Martin G. Schultz, Meiyun Lin, Virginie Marécal, Béatrice Josse, Makoto Deushi, Kengo Sudo, Junhua Liu, and Christoph A. Keller
Geosci. Model Dev., 12, 955–978, https://doi.org/10.5194/gmd-12-955-2019, https://doi.org/10.5194/gmd-12-955-2019, 2019
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We developed a new method for combining surface ozone observations from thousands of monitoring sites worldwide with the output from multiple atmospheric chemistry models. The result is a global surface ozone distribution with greater accuracy than any single model can achieve. We focused on an ozone metric relevant to human mortality caused by long-term ozone exposure. Our method can be applied to studies that quantify the impacts of ozone on human health and mortality.
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
Geosci. Model Dev., 12, 879–892, https://doi.org/10.5194/gmd-12-879-2019, https://doi.org/10.5194/gmd-12-879-2019, 2019
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We summarize the results of the Dynamical Core Model Intercomparison Project's idealized supercell test case. Supercells are storm-scale weather phenomena that are a key target for next-generation, non-hydrostatic weather prediction models. We show that the dynamical cores of most global numerical models converge between approximately 1 and 0.5 km grid spacing for this test, although differences in final solution exist, particularly due to differing grid discretizations and numerical diffusion.
Christian Kühnlein, Willem Deconinck, Rupert Klein, Sylvie Malardel, Zbigniew P. Piotrowski, Piotr K. Smolarkiewicz, Joanna Szmelter, and Nils P. Wedi
Geosci. Model Dev., 12, 651–676, https://doi.org/10.5194/gmd-12-651-2019, https://doi.org/10.5194/gmd-12-651-2019, 2019
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We present a novel finite-volume dynamical core formulation considered for future numerical weather prediction at ECMWF. We demonstrate that this formulation can be competitive in terms of solution quality and computational efficiency to the proven spectral-transform dynamical core formulation currently operational at ECMWF, while providing a local, more scalable discretization, conservative and monotone advective transport, and flexible meshes.
Ramadan Abdelaziz, Broder J. Merkel, Mauricio Zambrano-Bigiarini, and Sreejesh Nair
Geosci. Model Dev., 12, 167–177, https://doi.org/10.5194/gmd-12-167-2019, https://doi.org/10.5194/gmd-12-167-2019, 2019
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The paper presents a robust tool to estimate the thermodynamic surface complexation parameter for the sorption of uranium(VI) onto quartz surfaces. The optimization package hydroPSO R is coupled with the geochemical speciation code PHREEQC. hydroPSO used the m parameter estimation tool for geochemical modeling with PHREEQC. Coupled hydroPSO with PHREEQC proved to be a robust tool to estimate surface complexation constants for uranium(VI) species on quartz.
Miguel de la Varga, Alexander Schaaf, and Florian Wellmann
Geosci. Model Dev., 12, 1–32, https://doi.org/10.5194/gmd-12-1-2019, https://doi.org/10.5194/gmd-12-1-2019, 2019
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GemPy is an open-source Python-based 3-D structural geological modeling software, which allows the implicit (i.e. automatic) creation of complex geological models from interface and orientation data. GemPy is implemented in the programming language Python, making use of a highly efficient underlying library, Theano, for efficient code generation that performs automatic differentiation. This enables the link to probabilistic machine-learning and Bayesian inference frameworks.
Tianfeng Chai, Ariel Stein, and Fong Ngan
Geosci. Model Dev., 11, 5135–5148, https://doi.org/10.5194/gmd-11-5135-2018, https://doi.org/10.5194/gmd-11-5135-2018, 2018
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While model predictions depend on release parameters, model uncertainties in inverse modeling should also vary with the source terms. In this paper, model uncertainties that will change with the source terms are introduced in a weak-constraint inverse modeling system. Tests using HYSPLIT model and CAPTEX observations show that adding such model uncertainty terms improves release rate estimates. A cost function normalization scheme introduced to avoid spurious solutions proves to be effective.
Christopher J. Skinner, Tom J. Coulthard, Wolfgang Schwanghart, Marco J. Van De Wiel, and Greg Hancock
Geosci. Model Dev., 11, 4873–4888, https://doi.org/10.5194/gmd-11-4873-2018, https://doi.org/10.5194/gmd-11-4873-2018, 2018
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Landscape evolution models are computer models used to understand how the Earth’s surface changes over time. Although designed to look at broad changes over very long time periods, they could potentially be used to predict smaller changes over shorter periods. However, to do this we need to better understand how the models respond to changes in their set-up – i.e. their behaviour. This work presents a method which can be applied to these models in order to better understand their behaviour.
Gary L. Russell, David H. Rind, and Jeffrey Jonas
Geosci. Model Dev., 11, 4637–4656, https://doi.org/10.5194/gmd-11-4637-2018, https://doi.org/10.5194/gmd-11-4637-2018, 2018
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This paper presents the Fortran 90 source code for one-layer model GISS:IB on an icosahedral grid. The model solves the shallow water equations on the sphere using three symmetric horizontal components of angular momentum instead of velocity. One-layer shallow water models are a basic building block used in complex global weather and climate models.
Istvan Z. Reguly, Daniel Giles, Devaraj Gopinathan, Laure Quivy, Joakim H. Beck, Michael B. Giles, Serge Guillas, and Frederic Dias
Geosci. Model Dev., 11, 4621–4635, https://doi.org/10.5194/gmd-11-4621-2018, https://doi.org/10.5194/gmd-11-4621-2018, 2018
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We present the VOLNA-OP2 tsunami simulation code, built on the OP2 library. It is unique among such solvers in its support for several high-performance computing platforms: CPUs, the Intel Xeon Phi, and GPUs. This is achieved in a way that the scientific code is kept separate from various parallel implementations, enabling easy maintainability. Scalability and efficiency are demonstrated on three supercomputers built with CPUs, Xeon Phi's, and GPUs.
Joakim Beck, Sören Wolfers, and Gerald P. Roberts
Geosci. Model Dev., 11, 4383–4397, https://doi.org/10.5194/gmd-11-4383-2018, https://doi.org/10.5194/gmd-11-4383-2018, 2018
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Seismic hazard assessment requires records of earthquake recurrence with many slip events. Current data from paleoseismology on individual faults are sparse and do not provide stable estimates of earthquake recurrence. We propose a statistical model-based method to study timings of earthquakes over the past few millennia. The results agree with historical earthquakes for faults in the Italian Apennines, and can aid future studies of fault interactions over multiple earthquake cycles.
Peter D. Dueben and Peter Bauer
Geosci. Model Dev., 11, 3999–4009, https://doi.org/10.5194/gmd-11-3999-2018, https://doi.org/10.5194/gmd-11-3999-2018, 2018
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We discuss the question of whether weather forecast models that are based on deep learning and trained on atmospheric data can compete with conventional weather and climate models that are based on physical principles and the basic equations of motion. We discuss the question in the context of global weather forecasts. A toy model for global weather predictions will be presented and used to identify challenges and fundamental design choices for a forecast system based on neural networks.
Anthony P. Walker, Ming Ye, Dan Lu, Martin G. De Kauwe, Lianhong Gu, Belinda E. Medlyn, Alistair Rogers, and Shawn P. Serbin
Geosci. Model Dev., 11, 3159–3185, https://doi.org/10.5194/gmd-11-3159-2018, https://doi.org/10.5194/gmd-11-3159-2018, 2018
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Large uncertainty is inherent in model predictions due to imperfect knowledge of how to describe the processes that a model is intended to represent. Yet methods to quantify and evaluate this model hypothesis uncertainty are limited. To address this, the multi-assumption architecture and testbed (MAAT) automates the generation of all possible models by combining multiple representations of multiple processes. MAAT provides a formal framework for quantification of model hypothesis uncertainty.
Matthias Rauter, Andreas Kofler, Andreas Huber, and Wolfgang Fellin
Geosci. Model Dev., 11, 2923–2939, https://doi.org/10.5194/gmd-11-2923-2018, https://doi.org/10.5194/gmd-11-2923-2018, 2018
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We present a physical model for the simulation of dense snow avalanches and other gravitational mass flows. The model is solved with OpenFOAM, a popular open-source toolkit for the numerical solution of partial differential equations. The solver has a modular design and is easy to extend. Therefore, it represents an ideal platform for implementing and testing new model approaches.
Cited articles
Arnold, D. N., Falk, R. S., and Winther, R.: Multigrid in H(div) and
H(curl), Num. Mathe., 85, 197–217,
https://doi.org/10.1007/s002110000137, 2000. a
Balay, S., Gropp, W. D., McInnes, L. C., and Smith, B. F.: Efficient management
of parallelism in object-oriented numerical software libraries, in: Modern
software tools for scientific computing, 163–202, Springer, 1997. a
Balay, S., Abhyankar, S., Adams, M. F., Brown, J., Brune, P., Buschelman, K.,
Dalcin, L., Eijkhout, V., Gropp, W. D., Karpeyev, D., Kaushik, D., Knepley,
M. G., May, D. A., McInnes, L. C., Mills, R. T., Munson, T., Rupp, K., Sanan,
P., Smith, B. F., Zampini, S., Zhang, H., and Zhang, H.: PETSc Users
Manual, Tech. Rep. ANL-95/11 – Revision 3.11, Argonne National Laboratory,
2019. a, b
Bauer, W. and Cotter, C.: Energy-enstrophy conserving compatible finite element
schemes for the rotating shallow water equations with slip boundary
conditions, J. Comput. Phys., 373, 171–187,
https://doi.org/10.1016/j.jcp.2018.06.071, 2018. a
Bramble, J. H., Pasciak, J. E., and Xu, J.: The analysis of multigrid
algorithms for nonsymmetric and indefinite elliptic problems, Math.
Comput., 51, 389–414, 1988. a
Bramble, J. H., Kwak, D. Y., and Pasciak, J. E.: Uniform convergence of
multigrid V-cycle iterations for indefinite and nonsymmetric problems, SIAM
J. Num. Anal., 31, 1746–1763, 1994. a
Brezzi, F., Douglas, J., Durán, R., and Fortin, M.: Mixed finite elements
for second order elliptic problems in three variables, Num. Mathe.,
51, 237–250, 1987. a
Brown, J., Knepley, M. G., May, D. A., McInnes, L. C., and Smith, B.:
Composable linear solvers for multiphysics, in: Parallel and Distributed
Computing (ISPDC), 2012 11th International Symposium on, 55–62, IEEE,
2012. a
Cockburn, B.: Static condensation, hybridization, and the devising of the HDG
methods, in: Building Bridges: Connections and Challenges in Modern
Approaches to Numerical Partial Differential Equations, 129–177,
Springer, 2016. a
Cockburn, B., Dubois, O., Gopalakrishnan, J., and Tan, S.: Multigrid for an HDG
method, IMA J. Num. Anal., 34, 1386–1425, 2014. a
Cullen, M.: Alternative implementations of the semi-Lagrangian semi-implicit
schemes in the ECMWF model, Q. J. Roy. Meteorol.
Soc., 127, 2787–2802, 2001. a
Devloo, P., Faria, C., Farias, A., Gomes, S., Loula, A., and Malta, S.: On
continuous, discontinuous, mixed, and primal hybrid finite element methods
for second-order elliptic problems, Int. J. Num.
Method. Eng., 115, 1083–1107, https://doi.org/10.1002/nme.5836, 2018. a
Elman, H. C., Ernst, O. G., and O'leary, D. P.: A multigrid method enhanced by
Krylov subspace iteration for discrete Helmholtz equations, SIAM J.
Sci. Comput., 23, 1291–1315, 2001. a
Falgout, R. D., Jones, J. E., and Yang, U. M.: The design and implementation of hypre, a library of parallel high performance preconditioners, in: Numerical solution of partial differential equations on parallel computers,
267–294, Springer, 2006. a
Fraeijs de Veubeke, B.: Displacement and equilibrium models in the finite
element method, in: Stress Analysis, edited by: Zienkiewicz, O. and Holister,
G. S., John Wiley & Sons, reprinted in Internat, J. Numer. Methods Engrg.,
52, 287–342, 1965. a
Gopalakrishnan, J.: A Schwarz preconditioner for a hybridized mixed method,
Comput. Methods Appl. Math., 3, 116–134, 2003. a
Guennebaud, G., Jacob, B., Avery, P., Bachrach, A., and Barthelemy, S.: Eigen v3, 2010, available at: http://eigen.tuxfamily.org (last access: 7 February 2020), 2015. a
Hecht, F.: New development in FreeFem++, J. Num. Mathe., 20, 251–266, 2012. a
Hiptmair, R. and Xu, J.: Nodal auxiliary space preconditioning in
H(curl) and H(div) spaces, SIAM J. Num.
Anal., 45, 2483–2509, https://doi.org/10.1137/060660588, 2007. a
Homolya, M., Mitchell, L., Luporini, F., and Ham, D. A.: TSFC: a
structure-preserving form compiler, SIAM J. Sci. Comput.,
40, C401–C428, https://doi.org/10.1137/17M1130642, 2018. a, b
Kang, S., Giraldo, F. X., and Bui-Thanh, T.: IMEX HDG-DG: A coupled implicit
hybridized discontinuous Galerkin and explicit discontinuous Galerkin
approach for shallow water systems, J. Comput. Phys., 401, 109010, 2020. a
Kirby, R. C.: Algorithm 839: FIAT, a new paradigm for computing finite element
basis functions, ACM Trans. Mathe. Softw. (TOMS), 30,
502–516, 2004. a
Kirby, R. C. and Logg, A.: A compiler for variational forms, ACM Trans.
Mathe. Softw. (TOMS), 32, 417–444, 2006. a
Kirby, R. C. and Mitchell, L.: Solver composition across the PDE/linear
algebra barrier, SIAM J. Sci. Comput., 40, C76–C98,
https://doi.org/10.1137/17M1133208, 2018. a
Kirby, R. M., Sherwin, S. J., and Cockburn, B.: To CG or to HDG: a comparative
study, J. Sci. Comput., 51, 183–212, 2012. a
Logg, A. and Wells, G. N.: DOLFIN: Automated finite element computing, ACM
Trans. Mathe. Softw. (TOMS), 37, 20, 2010. a
Logg, A., Ølgaard, K. B., Rognes, M. E., and Wells, G. N.: FFC: the FEniCS
form compiler, Automated Solution of Differential Equations by the Finite
Element Method, 227–238, 2012b. a
Long, K., Kirby, R., and van Bloemen Waanders, B.: Unified embedded parallel
finite element computations via software-based Fréchet differentiation,
SIAM J. Sci. Comput., 32, 3323–3351, 2010. a
Mandel, J.: Multigrid convergence for nonsymmetric, indefinite variational
problems and one smoothing step, Appl. Mathe. Comput., 19,
201–216, 1986. a
Melvin, T., Benacchio, T., Shipway, B., Wood, N., Thuburn, J., and Cotter, C.:
A mixed finite-element, finite-volume, semi-implicit discretization for
atmospheric dynamics: Cartesian geometry, Q. J. Roy.
Meteorol. Soc., 145, 2835–2853, https://doi.org/10.1002/qj.3501, 2019. a, b
Nair, R. D., Thomas, S. J., and Loft, R. D.: A discontinuous Galerkin global
shallow water model, Mon. Weather Rev., 133, 876–888, 2005. a
Natale, A. and Cotter, C. J.: A variational H (div) finite-element
discretization approach for perfect incompressible fluids, IMA J. Num.
Anal, 38, p. drx033, https://doi.org/10.1093/imanum/drx033, 2017. a
Natale, A., Shipton, J., and Cotter, C. J.: Compatible finite element spaces
for geophysical fluid dynamics, Dynam. Stat. Clim.
Syst., 1, dzw005, https://doi.org/10.1093/climsys/dzw005, 2016. a, b, c, d
Nechaev, D. and Yaremchuk, M.: On the approximation of the Coriolis terms in
C-grid models, Mon. Weather Rev., 132, 2283–2289, 2004. a
Nédélec, J.-C.: Mixed finite elements in ℝ3, Num.
Mathe., 35, 315–341, 1980. a
Prud'Homme, C., Chabannes, V., Doyeux, V., Ismail, M., Samake, A., and Pena,
G.: Feel++: A computational framework for galerkin methods and advanced
numerical methods, in: ESAIM: Proceedings, 38, 429–455, EDP
Sciences, 2012. a
Rathgeber, F., Markall, G. R., Mitchell, L., Loriant, N., Ham, D. A., Bertolli, C., and Kelly, P. H. J.: PyOP2: A high-level framework for
performance-portable simulations on unstructured meshes, in: High Performance Computing, Networking, Storage and Analysis (SCC), 2012 SC Companion:, 1116–1123, IEEE, 2012. a, b
Rathgeber, F., Ham, D. A., Mitchell, L., Lange, M., Luporini, F., McRae, A.
T. T., Bercea, G.-T., Markall, G. R., and Kelly, P. H. J.: Firedrake:
automating the finite element method by composing abstractions, ACM
Trans. Mathe. Softw. (TOMS), 43, 1–27, 2016. a
Raviart, P.-A. and Thomas, J.-M.: A mixed finite element method for 2-nd order elliptic problems, in: Mathematical aspects of finite element methods, 292–315, Springer, 1977. a
Temperton, C.: Treatment of the Coriolis terms in semi-Lagrangian spectral
models, Atmos.-Ocean, 35, 293–302, 1997. a
Thomas, S. J., Hacker, J. P., Smolarkiewicz, P. K., and Stull, R. B.: Spectral
preconditioners for nonhydrostatic atmospheric models, Mon. Weather
Rev., 131, 2464–2478, 2003. a
Ullrich, P. A., Jablonowski, C., and Van Leer, B.: High-order finite-volume
methods for the shallow-water equations on the sphere, J.
Comput. Phys., 229, 6104–6134, 2010. a
Wood, N., Staniforth, A., White, A., Allen, T., Diamantakis, M., Gross, M.,
Melvin, T., Smith, C., Vosper, S., Zerroukat, M., et al.: An inherently
mass-conserving semi-implicit semi-Lagrangian discretization of the
deep-atmosphere global non-hydrostatic equations, Q. J.
Roy. Meteorol. Soc., 140, 1505–1520, 2014. a
Zenodo/Firedrake: Software used in 'Slate: extending Firedrake's
domain-specific abstraction to hybridized solvers for geoscience and
beyond', Zenodo, https://doi.org/10.5281/zenodo.2587072, 2019. a
Zenodo/Tabula-Rasa: Tabula Rasa: experimentation framework for hybridization
and static condensation, Zenodo, https://doi.org/10.5281/zenodo.2616031, 2019. a, b, c, d
Special issue
Short summary
Galerkin finite element discretizations for atmospheric modeling often require the solution of ill-conditioned, saddle point equations which can be efficiently solved using a hybridized method. By extending Firedrake's domain-specific abstraction, we provide a mechanism for the rapid implementation of hybridization methods for a wide class of methods. In this paper, we show that hybridization is an effective alternative to traditional block solvers for simulating geophysical flows.
Galerkin finite element discretizations for atmospheric modeling often require the solution of...
