Articles | Volume 8, issue 4
https://doi.org/10.5194/gmd-8-1005-2015
© Author(s) 2015. 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-8-1005-2015
© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Model description paper
| 
08 Apr 2015
Model description paper |
| 08 Apr 2015
libmpdata++ 1.0: a library of parallel MPDATA solvers for systems of generalised transport equations
Institute of Geophysics, Faculty of Physics, University of Warsaw, Warsaw, Poland
S. Arabas
Institute of Geophysics, Faculty of Physics, University of Warsaw, Warsaw, Poland
D. Jarecka
National Center for Atmospheric Research, Boulder, CO, USA
Institute of Geophysics, Faculty of Physics, University of Warsaw, Warsaw, Poland
H. Pawlowska
CORRESPONDING AUTHOR
Institute of Geophysics, Faculty of Physics, University of Warsaw, Warsaw, Poland
P. K. Smolarkiewicz
European Centre for Medium-Range Weather Forecasts, Reading, UK
M. Waruszewski
Institute of Geophysics, Faculty of Physics, University of Warsaw, Warsaw, Poland
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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.
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Xiaqiong Zhou and Hann-Ming Henry Juang
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EGUsphere, https://doi.org/10.5194/egusphere-2023-661, https://doi.org/10.5194/egusphere-2023-661, 2023
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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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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.
André R. Brodtkorb, Anna Benedictow, Heiko Klein, Arve Kylling, Agnes Nyiri, Alvaro Valdebenito, Espen Sollum, and Nina Kristiansen
EGUsphere, https://doi.org/10.5194/egusphere-2023-51, https://doi.org/10.5194/egusphere-2023-51, 2023
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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.
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.
Ziqi Gao, Yifeng Wang, Petros Vasilakos, Cesunica E. Ivey, Khanh Do, and Armistead G. Russell
Geosci. Model Dev., 15, 9015–9029, https://doi.org/10.5194/gmd-15-9015-2022, https://doi.org/10.5194/gmd-15-9015-2022, 2022
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While the national ambient air quality standard of ozone is based on the 3-year average of the fourth highest 8 h maximum (MDA8) ozone concentrations, these predicted extreme values using numerical methods are always biased low. We built four computational models (GAM, MARS, random forest and SVR) to predict the fourth highest MDA8 ozone in Southern California using precursor emissions, meteorology and climatological patterns. All models presented acceptable performance, with GAM being the best.
Zhihao Wang, Jason Goetz, and Alexander Brenning
Geosci. Model Dev., 15, 8765–8784, https://doi.org/10.5194/gmd-15-8765-2022, https://doi.org/10.5194/gmd-15-8765-2022, 2022
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A lack of inventory data can be a limiting factor in developing landslide predictive models, which are crucial for supporting hazard policy and decision-making. We show how case-based reasoning and domain adaptation (transfer-learning techniques) can effectively retrieve similar landslide modeling situations for prediction in new data-scarce areas. Using cases in Italy, Austria, and Ecuador, our findings support the application of transfer learning for areas that require rapid model development.
Till Sachau, Haibin Yang, Justin Lang, Paul D. Bons, and Louis Moresi
Geosci. Model Dev., 15, 8749–8764, https://doi.org/10.5194/gmd-15-8749-2022, https://doi.org/10.5194/gmd-15-8749-2022, 2022
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Knowledge of the internal structures of the major continental ice sheets is improving, thanks to new investigative techniques. These structures are an essential indication of the flow behavior and dynamics of ice transport, which in turn is important for understanding the actual impact of the vast amounts of water trapped in continental ice sheets on global sea-level rise. The software studied here is specifically designed to simulate such structures and their evolution.
Keith J. Roberts, Alexandre Olender, Lucas Franceschini, Robert C. Kirby, Rafael S. Gioria, and Bruno S. Carmo
Geosci. Model Dev., 15, 8639–8667, https://doi.org/10.5194/gmd-15-8639-2022, https://doi.org/10.5194/gmd-15-8639-2022, 2022
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Finite-element methods (FEMs) permit the use of more flexible unstructured meshes but are rarely used in full waveform inversions (FWIs), an iterative process that reconstructs velocity models of earth’s subsurface, due to computational and memory storage costs. To reduce those costs, novel software is presented allowing the use of high-order mass-lumped FEMs on triangular meshes, together with a material-property mesh-adaptation performance-enhancing strategy, enabling its use in FWIs.
Konstantinos Papadakis, Yann Pfau-Kempf, Urs Ganse, Markus Battarbee, Markku Alho, Maxime Grandin, Maxime Dubart, Lucile Turc, Hongyang Zhou, Konstantinos Horaites, Ivan Zaitsev, Giulia Cozzani, Maarja Bussov, Evgeny Gordeev, Fasil Tesema, Harriet George, Jonas Suni, Vertti Tarvus, and Minna Palmroth
Geosci. Model Dev., 15, 7903–7912, https://doi.org/10.5194/gmd-15-7903-2022, https://doi.org/10.5194/gmd-15-7903-2022, 2022
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Vlasiator is a plasma simulation code that simulates the entire near-Earth space at a global scale. As 6D simulations require enormous amounts of computational resources, Vlasiator uses adaptive mesh refinement (AMR) to lighten the computational burden. However, due to Vlasiator’s grid topology, AMR simulations suffer from grid aliasing artifacts that affect the global results. In this work, we present and evaluate the performance of a mechanism for alleviating those artifacts.
Artur Safin, Damien Bouffard, Firat Ozdemir, Cintia L. Ramón, James Runnalls, Fotis Georgatos, Camille Minaudo, and Jonas Šukys
Geosci. Model Dev., 15, 7715–7730, https://doi.org/10.5194/gmd-15-7715-2022, https://doi.org/10.5194/gmd-15-7715-2022, 2022
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Reconciling the differences between numerical model predictions and observational data is always a challenge. In this paper, we investigate the viability of a novel approach to the calibration of a three-dimensional hydrodynamic model of Lake Geneva, where the target parameters are inferred in terms of distributions. We employ a filtering technique that generates physically consistent model trajectories and implement a neural network to enable bulk-to-skin temperature conversion.
Colin Grudzien and Marc Bocquet
Geosci. Model Dev., 15, 7641–7681, https://doi.org/10.5194/gmd-15-7641-2022, https://doi.org/10.5194/gmd-15-7641-2022, 2022
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Iterative optimization techniques, the state of the art in data assimilation, have largely focused on extending forecast accuracy to moderate- to long-range forecast systems. However, current methodology may not be cost-effective in reducing forecast errors in online, short-range forecast systems. We propose a novel optimization of these techniques for online, short-range forecast cycles, simultaneously providing an improvement in forecast accuracy and a reduction in the computational cost.
Yangyang Yu, Shaoqing Zhang, Haohuan Fu, Lixin Wu, Dexun Chen, Yang Gao, Zhiqiang Wei, Dongning Jia, and Xiaopei Lin
Geosci. Model Dev., 15, 6695–6708, https://doi.org/10.5194/gmd-15-6695-2022, https://doi.org/10.5194/gmd-15-6695-2022, 2022
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To understand the scientific consequence of perturbations caused by slave cores in heterogeneous computing environments, we examine the influence of perturbation amplitudes on the determination of the cloud bottom and cloud top and compute the probability density function (PDF) of generated clouds. A series of comparisons of the PDFs between homogeneous and heterogeneous systems show consistently acceptable error tolerances when using slave cores in heterogeneous computing environments.
Vijay S. Mahadevan, Jorge E. Guerra, Xiangmin Jiao, Paul Kuberry, Yipeng Li, Paul Ullrich, David Marsico, Robert Jacob, Pavel Bochev, and Philip Jones
Geosci. Model Dev., 15, 6601–6635, https://doi.org/10.5194/gmd-15-6601-2022, https://doi.org/10.5194/gmd-15-6601-2022, 2022
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Coupled Earth system models require transfer of field data between multiple components with varying spatial resolutions to determine the correct climate behavior. We present the Metrics for Intercomparison of Remapping Algorithms (MIRA) protocol to evaluate the accuracy, conservation properties, monotonicity, and local feature preservation of four different remapper algorithms for various unstructured mesh problems of interest. Future extensions to more practical use cases are also discussed.
Yilin Fang, L. Ruby Leung, Ryan Knox, Charlie Koven, and Ben Bond-Lamberty
Geosci. Model Dev., 15, 6385–6398, https://doi.org/10.5194/gmd-15-6385-2022, https://doi.org/10.5194/gmd-15-6385-2022, 2022
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Accounting for water movement in the soil and water transport within the plant is important for plant growth in Earth system modeling. We implemented different numerical approaches for a plant hydrodynamic model and compared their impacts on the simulated aboveground biomass (AGB) at single points and globally. We found care should be taken when discretizing the number of soil layers for numerical simulations as it can significantly affect AGB if accuracy and computational costs are of concern.
Andrew M. Bradley, Peter A. Bosler, and Oksana Guba
Geosci. Model Dev., 15, 6285–6310, https://doi.org/10.5194/gmd-15-6285-2022, https://doi.org/10.5194/gmd-15-6285-2022, 2022
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Tracer transport in atmosphere models can be computationally expensive. We describe a flexible and efficient interpolation semi-Lagrangian method, the Islet method. It permits using up to three grids that share an element grid: a dynamics grid for computing quantities such as the wind velocity; a physics parameterizations grid; and a tracer grid. The Islet method performs well on a number of verification problems and achieves high performance in the E3SM Atmosphere Model version 2.
Léo Pujol, Pierre-André Garambois, and Jérôme Monnier
Geosci. Model Dev., 15, 6085–6113, https://doi.org/10.5194/gmd-15-6085-2022, https://doi.org/10.5194/gmd-15-6085-2022, 2022
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This contribution presents a new numerical model for representing hydraulic–hydrological quantities at the basin scale. It allows modeling large areas at a low computational cost, with fine zooms where needed. It allows the integration of local and satellite measurements, via data assimilation methods, to improve the model's match to observations. Using this capability, good matches to in situ observations are obtained on a model of the complex Adour river network with fine zooms on floodplains.
Ludovic Räss, Ivan Utkin, Thibault Duretz, Samuel Omlin, and Yuri Y. Podladchikov
Geosci. Model Dev., 15, 5757–5786, https://doi.org/10.5194/gmd-15-5757-2022, https://doi.org/10.5194/gmd-15-5757-2022, 2022
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Continuum mechanics-based modelling of physical processes at large scale requires huge computational resources provided by massively parallel hardware such as graphical processing units. We present a suite of numerical algorithms, implemented using the Julia language, that efficiently leverages the parallelism. We demonstrate that our implementation is efficient, scalable and robust and showcase applications to various geophysical problems.
Meriem Krouma, Pascal Yiou, Céline Déandreis, and Soulivanh Thao
Geosci. Model Dev., 15, 4941–4958, https://doi.org/10.5194/gmd-15-4941-2022, https://doi.org/10.5194/gmd-15-4941-2022, 2022
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We evaluated the skill of a stochastic weather generator (SWG) to forecast precipitation at different time scales and in different areas of western Europe from analogs of Z500 hPa. The SWG has the skill to simulate precipitation for 5 and 10 d. We found that forecast weaknesses can be associated with specific weather patterns. The comparison with ECMWF forecasts confirms the skill of our model. This work is important because it provides information about weather forecasts over specific areas.
Piotr Dziekan and Piotr Zmijewski
Geosci. Model Dev., 15, 4489–4501, https://doi.org/10.5194/gmd-15-4489-2022, https://doi.org/10.5194/gmd-15-4489-2022, 2022
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Detailed computer simulations of clouds are important for understanding Earth's atmosphere and climate. The paper describes how the UWLCM has been adapted to work on supercomputers. A distinctive feature of UWLCM is that air flow is calculated by processors at the same time as cloud droplets are modeled by graphics cards. Thanks to this, use of computing resources is maximized and the time to complete simulations of large domains is not affected by communications between supercomputer nodes.
Amir Golparvar, Matthias Kästner, and Martin Thullner
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2022-86, https://doi.org/10.5194/gmd-2022-86, 2022
Revised manuscript accepted for GMD
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Coupled reaction-transport modeling is an established and highly 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 modeling the transport of reactive species is missing. We presented a model that overcomes this limitation and represents a novel numerical simulation toolbox.
Hynek Bednář and Holger Kantz
Geosci. Model Dev., 15, 4147–4161, https://doi.org/10.5194/gmd-15-4147-2022, https://doi.org/10.5194/gmd-15-4147-2022, 2022
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A scale-dependent error growth described by a power law or by a quadratic hypothesis is studied in Lorenz’s system with three spatiotemporal levels. The validity of power law is extended by including a saturation effect. The quadratic hypothesis can only serve as a first guess. In addition, we study the initial error growth for the ECMWF forecast system. Fitting the parameters, we conclude that there is an intrinsic limit of predictability after 22 days.
Michael A. Olesik, Jakub Banaśkiewicz, Piotr Bartman, Manuel Baumgartner, Simon Unterstrasser, and Sylwester Arabas
Geosci. Model Dev., 15, 3879–3899, https://doi.org/10.5194/gmd-15-3879-2022, https://doi.org/10.5194/gmd-15-3879-2022, 2022
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In systems such as atmospheric clouds, droplets undergo growth through condensation of vapor. The broadness of the resultant size spectrum of droplets influences precipitation likelihood and the radiative properties of clouds. One of the inherent limitations of simulations of the problem is the so-called numerical diffusion causing overestimation of the spectrum width, hence the term numerical broadening. In the paper, we take a closer look at one of the algorithms used in this context: MPDATA.
Cited articles
Arabas, S., Jarecka, D., Jaruga, A., and Fijałkowski, M.: Formula translation in Blitz++, NumPy and modern Fortran: a case study of the language choice tradeoffs, Sci. Prog., 22, 201–222, https://doi.org/10.3233/SPR-140379, 2014.
Arakawa, A. and Lamb, V. R.: Computational design of the basic dynamical process of the UCLA general circulation model, in: General Circulation Models of the Atmosphere, vol. 17 of Methods in Computational Physics: Advances in Research and Applications, Elsevier, 173–265, https://doi.org/10.1016/B978-0-12-460817-7.50009-4, 1977.
Bangerth, W. and Heister, T.: What makes computational open source software libraries successful?, Comp. Sci. & Discuss., 6, 015010, https://doi.org/10.1088/1749-4699/6/1/015010, 2013.
Charbonneau, P. and Smolarkiewicz, P.: Modeling the solar dynamo, Science, 340, 42–43, https://doi.org/10.1126/science.1235954, 2013.
Cotter, C. S., Smolarkiewicz, P. K., and Szczyrba, I. N.: A viscoelastic fluid model for brain injuries, Int. J. Numer. Meth. Fl., 40, 303–311, https://doi.org/10.1002/fld.287, 2002.
Frei, C.: Dynamics of a two-dimensional ribbon of shallow water on an f-plane, Tellus A, 45, 44–53, https://doi.org/10.1034/j.1600-0870.1993.00004.x, 1993.
Grabowski, W. and Smolarkiewicz, P.: A multiscale anelastic model for meteorological research, Mon. Weather Rev., 130, 939–955, https://doi.org/10.1175/1520-0493(2002)130<0939:AMAMFM>2.0.CO;2, 2002.
Hyman, J., Smolarkiewicz, P., and Winter, C.: Heterogeneities of flow in stochastically generated porous media, Phys. Rev. E, 86, 056701, https://doi.org/10.1103/PhysRevE.86.056701, 2012.
Jarecka, D., Jaruga, A., and Smolarkiewicz, P.: A spreading drop of shallow water, J. Comput. Phys., 289, 53–61, https://doi.org/10.1016/j.jcp.2015.02.003, 2015.
Kahan, W.: Pracniques: further remarks on reducing truncation errors, Comm. ACM, 8, p. 40, https://doi.org/10.1145/363707.363723, 1965.
Kühnlein, C., Smolarkiewicz, P., and Dörnbrack, A.: Modelling atmospheric flows with adaptive moving meshes, J. Comput. Phys., 231, 2741–2763, https://doi.org/10.1016/j.jcp.2011.12.012, 2012.
Margolin, L. and Smolarkiewicz, P.: Antidiffusive velocities for multipass donor cell advection, J. Sci. Comput., 20, 907–929, https://doi.org/10.1137/S106482759324700X, 1998.
Maurin, K.: Analysis Part II: Integration, Distributions, Holomorphic Functions, Tensor and Harmonic Analysis, Reidel, 1980.
Molenkamp, C.: Accuracy of finite-difference methods applied to the advection equation., J. Appl. Meteorol., 7, 160–167, https://doi.org/10.1175/1520-0450(1968)007<0160:AOFDMA>2.0.CO;2, 1968.
Ortiz, P. and Smolarkiewicz, P. K.: Coupling the dynamics of boundary layers and evolutionary dunes, Phys. Rev., 79, 041307, https://doi.org/10.1103/PhysRevE.79.041307, 2009.
Press, W., Teukolsky, S., Vetterling, W., and Flannery, B.: Numerical recipes. The art of scientific computing, 3rd edn., Cambridge University Press, 2007.
Prusa, J., Smolarkiewicz, P., and Wyszogrodzki, A.: EULAG, a computational model for multiscale flows, Comput. Fluids, 37, 1193–1207, https://doi.org/10.1016/j.compfluid.2007.12.001, 2008.
Randall, D.: Lectures on numerical modelling of the atmosphere, available at: http://kiwi.atmos.colostate.edu/group/dave/at604pdf/Chapter_11.pdf (last access: October 2014), 2013.
Schär, C. and Smith, R. B.: Shallow-water flow past isolated topography. I – Vorticity production and wake formation, J. Atmos. Sci., 50, 1373–1412, https://doi.org/10.1175/1520-0469(1993)050<1373:SWFPIT>2.0.CO;2, 1993.
Schär, C. and Smolarkiewicz, P.: A synchronous and iterative flux-correction formalism for coupled transport equations, J. Comput. Phys., 128, 101–120, https://doi.org/10.1006/jcph.1996.0198, 1996.
Smolarkiewicz, P.: A simple positive definite advection scheme with small implicit diffusion, Mon. Weather Rev., 111, 479–486, https://doi.org/10.1175/1520-0493(1983)111<0479:ASPDAS>2.0.CO;2, 1983.
Smolarkiewicz, P.: A fully multidimensional positive definite advection transport algorithm with small implicit diffusion, J. Comput. Phys., 54, 325–362, https://doi.org/10.1016/0021-9991(84)90121-9, 1984.
Smolarkiewicz, P.: Multidimensional positive definite advection transport algorithm: an overview, Int. J. Numer. Meth. Fl., 50, 1123–1144, https://doi.org/10.1002/fld.1071, 2006.
Smolarkiewicz, P. and Clark, T.: The multidimensional positive definite advection transport algorithm – further development and applications, J. Computat. Phys., 67, 396–438, https://doi.org/10.1016/0021-9991(86)90270-6, 1986.
Smolarkiewicz, P. and Grabowski, W.: The multidimensional positive definite advection transport algorithm: Nonoscillatory option, J. Comput. Phys., 86, 355–375, https://doi.org/10.1016/0021-9991(90)90105-A, 1990.
Smolarkiewicz, P. and Margolin, L.: Variational elliptic solver for atmospheric applications, Tech. Rep. LA-12712-MS, Los Alamos National Lab., https://doi.org/10.2172/10130964, 1994.
Smolarkiewicz, P. and Margolin, L.: MPDATA: a finite-difference solver for geophysical flows, J. Comput. Phys., 140, 459–480, https://doi.org/10.1006/jcph.1998.5901, 1998.
Smolarkiewicz, P. and Pudykiewicz, J.: A class of semi-Lagrangian approximations for fluids, J. Atmos. Sci., 49, 2082–2096, https://doi.org/10.1175/1520-0469(1992)049<2082:ACOSLA>2.0.CO;2, 1992.
Smolarkiewicz, P. and Rasch, P.: Monotone advection on the sphere: an Eulerian versus semi-Lagrangian approach, J. Atmos. Sci., 48, 793–810, https://doi.org/10.1175/1520-0469(1991)048<0793:MAOTSA>2.0.CO;2, 1991.
Smolarkiewicz, P. and Szmelter, J.: MPDATA: an edge-based unstructured-grid formulation, J. Comp. Phys., 206, 624–649, https://doi.org/10.1016/j.jcp.2004.12.021, 2005.
Smolarkiewicz, P. and Szmelter, J.: Iterated upwind schemes for gas dynamics, J. Comput. Phys., 228, 33–54, https://doi.org/10.1016/j.jcp.2008.08.008, 2009.
Smolarkiewicz, P. and Szmelter, J.: A nonhydrostatic unstructured-mesh soundproof model for simulation of internal gravity waves, Acta Geophys., 59, 1109–1134, https://doi.org/10.2478/s11600-011-0043-z, 2011.
Smolarkiewicz, P. K., Grubišić, V., and Margolin, L. G.: On forward-in-time differencing for fluids: stopping criteria for iterative solutions of anelastic pressure equations, Mon. Weather Rev., 125, 647–654, https://doi.org/10.1175/1520-0493(1997)125<0647:OFITDF>2.0.CO;2, 1997.
Smolarkiewicz, P., Kühnlein, C., and Wedi, N.: A consistent framework for discrete integrations of soundproof and compressible PDEs of atmospheric dynamics, J. Comput. Phys., 263, 185–205, https://doi.org/10.1016/j.jcp.2014.01.031, 2014.
Szmelter, J. and Smolarkiewicz, P.: An edge-based unstructured mesh discretisation in geospherical framework, J. Comput. Phys., 229, 4980–4995, https://doi.org/10.1016/j.jcp.2010.03.017, 2010.
Veldhuizen, T.: Blitz++ user's guide. A C++ class library for scientific computing, Tech. rep., available at: http://blitz.sf.net/resources/blitz-0.9.pdf (last access: October 2014), 2006.
Williamson, D. and Rasch, P.: Two-dimensional semi-Lagrangian transport with shape-preserving interpolation, Mon. Weather Rev., 117, 102–129, https://doi.org/10.1175/1520-0493(1989)117<0102:TDSLTW>2.0.CO;2, 1989.
Wilson, G., Aruliah, D. A., Brown, C. T., Chue Hong, N. P., Davis, M., Guy, R. T., Haddock, S. H. D., Huff, K., Mitchell, I. M., Plumbley, M., Waugh, B., White, E. P., and Wilson, P.: Best practices for scientific computing, PLoS Biol., 12, e1001745, https://doi.org/10.1371/journal.pbio.1001745, 2014.
Short summary
This paper accompanies the first release of libmpdata++, a C++ library implementing the multidimensional positive-definite advection transport algorithm (MPDATA) on a regular structured grid. The library offers basic numerical solvers for systems of generalised transport equations. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide.
This paper accompanies the first release of libmpdata++, a C++ library implementing the...
