Articles | Volume 15, issue 6
Geosci. Model Dev., 15, 2561–2597, 2022
https://doi.org/10.5194/gmd-15-2561-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Geosci. Model Dev., 15, 2561–2597, 2022
https://doi.org/10.5194/gmd-15-2561-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Development and technical paper
28 Mar 2022
Development and technical paper
| 28 Mar 2022
Improved double Fourier series on a sphere and its application to a semi-implicit semi-Lagrangian shallow-water model
Hiromasa Yoshimura
Related authors
Hideaki Kawai, Seiji Yukimoto, Tsuyoshi Koshiro, Naga Oshima, Taichu Tanaka, Hiromasa Yoshimura, and Ryoji Nagasawa
Geosci. Model Dev., 12, 2875–2897, https://doi.org/10.5194/gmd-12-2875-2019, https://doi.org/10.5194/gmd-12-2875-2019, 2019
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The representation of clouds was significantly improved in the climate model MRI-ESM2. The model is planned for use in the sixth phase of the Coupled Model Intercomparison Project (CMIP6) simulations. In particular, a notorious lack of reflection of solar radiation over the Southern Ocean was drastically improved in the model. The score of the spatial pattern of radiative fluxes for MRI-ESM2 is better than for any CMIP5 model. We present modifications implemented in the various physics schemes.
Masuo Nakano, Akiyoshi Wada, Masahiro Sawada, Hiromasa Yoshimura, Ryo Onishi, Shintaro Kawahara, Wataru Sasaki, Tomoe Nasuno, Munehiko Yamaguchi, Takeshi Iriguchi, Masato Sugi, and Yoshiaki Takeuchi
Geosci. Model Dev., 10, 1363–1381, https://doi.org/10.5194/gmd-10-1363-2017, https://doi.org/10.5194/gmd-10-1363-2017, 2017
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Three 7 km mesh next-generation global models and a 20 km mesh conventional global model were run to improve tropical cyclone (TC) prediction. The 7 km mesh models reduce systematic errors in the TC track, intensity and wind radii predictions. However, the simulated TC structures and their intensities in each case are very different for each model. These results suggest that the development of more sophisticated initialization techniques and model physics is needed to further improvement.
Hideaki Kawai, Seiji Yukimoto, Tsuyoshi Koshiro, Naga Oshima, Taichu Tanaka, Hiromasa Yoshimura, and Ryoji Nagasawa
Geosci. Model Dev., 12, 2875–2897, https://doi.org/10.5194/gmd-12-2875-2019, https://doi.org/10.5194/gmd-12-2875-2019, 2019
Short summary
Short summary
The representation of clouds was significantly improved in the climate model MRI-ESM2. The model is planned for use in the sixth phase of the Coupled Model Intercomparison Project (CMIP6) simulations. In particular, a notorious lack of reflection of solar radiation over the Southern Ocean was drastically improved in the model. The score of the spatial pattern of radiative fluxes for MRI-ESM2 is better than for any CMIP5 model. We present modifications implemented in the various physics schemes.
Masuo Nakano, Akiyoshi Wada, Masahiro Sawada, Hiromasa Yoshimura, Ryo Onishi, Shintaro Kawahara, Wataru Sasaki, Tomoe Nasuno, Munehiko Yamaguchi, Takeshi Iriguchi, Masato Sugi, and Yoshiaki Takeuchi
Geosci. Model Dev., 10, 1363–1381, https://doi.org/10.5194/gmd-10-1363-2017, https://doi.org/10.5194/gmd-10-1363-2017, 2017
Short summary
Short summary
Three 7 km mesh next-generation global models and a 20 km mesh conventional global model were run to improve tropical cyclone (TC) prediction. The 7 km mesh models reduce systematic errors in the TC track, intensity and wind radii predictions. However, the simulated TC structures and their intensities in each case are very different for each model. These results suggest that the development of more sophisticated initialization techniques and model physics is needed to further improvement.
Related subject area
Numerical methods
SciKit-GStat 1.0: a SciPy-flavored geostatistical variogram estimation toolbox written in Python
Flow-Py v1.0: a customizable, open-source simulation tool to estimate runout and intensity of gravitational mass flows
Emulation of high-resolution land surface models using sparse Gaussian processes with application to JULES
A three-dimensional variational data assimilation system for aerosol optical properties based on WRF-Chem v4.0: design, development, and application of assimilating Himawari-8 aerosol observations
Implementation of a Gaussian Markov random field sampler for forward uncertainty quantification in the Ice-sheet and Sea-level System Model v4.19
A method for assessment of the general circulation model quality using the K-means clustering algorithm: a case study with GETM v2.5
AIEADA 1.0: Efficient high-dimensional variational data assimilation with machine-learned reduced-order models
An explicit GPU-based material point method solver for elastoplastic problems (ep2-3De v1.0)
MagIC v5.10: a two-dimensional message-passing interface (MPI) distribution for pseudo-spectral magnetohydrodynamics simulations in spherical geometry
Machine-learning models to replicate large-eddy simulations of air pollutant concentrations along boulevard-type streets
Recalculation of error growth models' parameters for the ECMWF forecast system
How biased are our models? – a case study of the alpine region
B-flood 1.0: an open-source Saint-Venant model for flash-flood simulation using adaptive refinement
A micro-genetic algorithm (GA v1.7.1a) for combinatorial optimization of physics parameterizations in the Weather Research and Forecasting model (v4.0.3) for quantitative precipitation forecast in Korea
SymPKF (v1.0): a symbolic and computational toolbox for the design of parametric Kalman filter dynamics
NDCmitiQ v1.0.0: a tool to quantify and analyse greenhouse gas mitigation targets
Combining ensemble Kalman filter and reservoir computing to predict spatiotemporal chaotic systems from imperfect observations and models
The Coastline Evolution Model 2D (CEM2D) 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
Ocean Plastic Assimilator v0.2: assimilation of plastic concentration data into Lagrangian dispersion models
Development of a moving point source model for shipping emission dispersion modeling in EPISODE–CityChem v1.3
Efficient Bayesian inference for large chaotic dynamical systems
Constraining stochastic 3-D structural geological models with topology information using approximate Bayesian computation in GemPy 2.1
Retrieval of process rate parameters in the general dynamic equation for aerosols using Bayesian state estimation: BAYROSOL1.0
A discontinuous Galerkin finite-element model for fast channelized lava flows v1.0
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
On numerical broadening of particle size spectra: a condensational growth study using PyMPDATA 1.0
A note on precision-preserving compression of scientific data
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
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
Development of a semi-Lagrangian advection scheme for the NEMO ocean model (3.1)
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
Mirko Mälicke
Geosci. Model Dev., 15, 2505–2532, https://doi.org/10.5194/gmd-15-2505-2022, https://doi.org/10.5194/gmd-15-2505-2022, 2022
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I preset SciKit-GStat, a well-documented and tested Python package for variogram estimation. The variogram is the core means of geostatistics, which almost all other methods rely on. Geostatistical interpolation and field generation are widely spread in geoscience, i.e., for data assimilation or modeling.
While SciKit-GStat focuses on effective and intuitive variogram estimation, it can interface with other prominent packages and make its variograms available for a multitude of methods.
Christopher J. L. D'Amboise, Michael Neuhauser, Michaela Teich, Andreas Huber, Andreas Kofler, Frank Perzl, Reinhard Fromm, Karl Kleemayr, and Jan-Thomas Fischer
Geosci. Model Dev., 15, 2423–2439, https://doi.org/10.5194/gmd-15-2423-2022, https://doi.org/10.5194/gmd-15-2423-2022, 2022
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The term gravitational mass flow (GMF) covers various natural hazard processes such as snow avalanches, rockfall, landslides, and debris flows. Here we present the open-source GMF simulation tool Flow-Py. The model equations are based on simple geometrical relations in three-dimensional terrain. We show that Flow-Py is an educational, innovative GMF simulation tool with three computational experiments: 1. validation of implementation, 2. performance, and 3. expandability.
Evan Baker, Anna B. Harper, Daniel Williamson, and Peter Challenor
Geosci. Model Dev., 15, 1913–1929, https://doi.org/10.5194/gmd-15-1913-2022, https://doi.org/10.5194/gmd-15-1913-2022, 2022
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We have adapted machine learning techniques to build a model of the land surface in Great Britain. The model was trained using data from a very complex land surface model called JULES. Our model is faster at producing simulations and predictions and can investigate many different scenarios, which can be used to improve our understanding of the climate and could also be used to help make local decisions.
Daichun Wang, Wei You, Zengliang Zang, Xiaobin Pan, Yiwen Hu, and Yanfei Liang
Geosci. Model Dev., 15, 1821–1840, https://doi.org/10.5194/gmd-15-1821-2022, https://doi.org/10.5194/gmd-15-1821-2022, 2022
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This paper presents a 3D variational data assimilation system for aerosol optical properties, including aerosol optical thickness (AOT) retrievals and lidar-based aerosol profiles, which was developed for a size-resolved sectional model in WRF-Chem. To directly assimilate aerosol optical properties, an observation operator based on the Mie scattering theory was designed. The results show that Himawari-8 AOT assimilation can significantly improve model aerosol analyses and forecasts.
Kevin Bulthuis and Eric Larour
Geosci. Model Dev., 15, 1195–1217, https://doi.org/10.5194/gmd-15-1195-2022, https://doi.org/10.5194/gmd-15-1195-2022, 2022
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We present and implement a stochastic solver to sample spatially and temporal varying uncertain input parameters in the Ice-sheet and Sea-level System Model, such as ice thickness or surface mass balance. We represent these sources of uncertainty using Gaussian random fields with Matérn covariance function. We generate random samples of this random field using an efficient computational approach based on solving a stochastic partial differential equation.
Urmas Raudsepp and Ilja Maljutenko
Geosci. Model Dev., 15, 535–551, https://doi.org/10.5194/gmd-15-535-2022, https://doi.org/10.5194/gmd-15-535-2022, 2022
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A model's ability to reproduce the state of a simulated object is always a subject of discussion. A new method for the multivariate assessment of numerical model skills uses the K-means algorithm for clustering model errors. All available data that fall into the model domain and simulation period are incorporated into the skill assessment. The clustered errors are used for spatial and temporal analysis of the model accuracy. The method can be applied to different types of geoscientific models.
Romit Maulik, Vishwas Rao, Jiali Wang, Gianmarco Mengaldo, Emil Constantinescu, Bethany Lusch, Prasanna Balaprakash, Ian Foster, and Rao Kotamarthi
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2021-415, https://doi.org/10.5194/gmd-2021-415, 2022
Revised manuscript accepted for GMD
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In numerical weather prediction, data assimilation is frequently utilized to enhance the accuracy of forecasts from equation-based models. In this work – we use a machine learning framework that approximates a complex dynamical system given by the geopotential height. Instead of using an equation-based model, we utilize this machine-learned alternative to dramatically accelerate both the forecast and the assimilation of data thereby reducing need for large computational resources.
Emmanuel Wyser, Yury Alkhimenkov, Michel Jaboyedoff, and Yury Y. Podladchikov
Geosci. Model Dev., 14, 7749–7774, https://doi.org/10.5194/gmd-14-7749-2021, https://doi.org/10.5194/gmd-14-7749-2021, 2021
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We propose an implementation of the material point method using graphical processing units (GPUs) to solve elastoplastic problems in three-dimensional configurations, such as the granular collapse or the slumping mechanics, i.e., landslide. The computational power of GPUs promotes fast code executions, compared to a traditional implementation using central processing units (CPUs). This allows us to study complex three-dimensional problems tackling high spatial resolution.
Rafael Lago, Thomas Gastine, Tilman Dannert, Markus Rampp, and Johannes Wicht
Geosci. Model Dev., 14, 7477–7495, https://doi.org/10.5194/gmd-14-7477-2021, https://doi.org/10.5194/gmd-14-7477-2021, 2021
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In this work we discuss a two-dimensional distributed parallelization of MagIC, an open-source code for the numerical solution of the magnetohydrodynamics equations. Such a parallelization involves several challenges concerning the distribution of work and data. We detail our algorithm and compare it with the established, optimized, one-dimensional distribution in the context of the dynamo benchmark and discuss the merits of both implementations.
Moritz Lange, Henri Suominen, Mona Kurppa, Leena Järvi, Emilia Oikarinen, Rafael Savvides, and Kai Puolamäki
Geosci. Model Dev., 14, 7411–7424, https://doi.org/10.5194/gmd-14-7411-2021, https://doi.org/10.5194/gmd-14-7411-2021, 2021
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This study aims to replicate computationally expensive high-resolution large-eddy simulations (LESs) with regression models to simulate urban air quality and pollutant dispersion. The model development, including feature selection, model training and cross-validation, and detection of concept drift, has been described in detail. Of the models applied, log-linear regression shows the best performance. A regression model can replace LES unless high accuracy is needed.
Hynek Bednář, Aleš Raidl, and Jiří Mikšovský
Geosci. Model Dev., 14, 7377–7389, https://doi.org/10.5194/gmd-14-7377-2021, https://doi.org/10.5194/gmd-14-7377-2021, 2021
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Forecast errors in numerical weather prediction systems grow in time. To quantify the impacts of this growth, parametric error growth models may be employed. This study recalculates and newly defines parameters for several statistic models approximating error growth in the ECMWF forecasting system. Accurate values of parameters are important because they are used to evaluate improvements of the forecasting systems or to estimate predictability.
Denise Degen, Cameron Spooner, Magdalena Scheck-Wenderoth, and Mauro Cacace
Geosci. Model Dev., 14, 7133–7153, https://doi.org/10.5194/gmd-14-7133-2021, https://doi.org/10.5194/gmd-14-7133-2021, 2021
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In times of worldwide energy transitions, an understanding of the subsurface is increasingly important to provide renewable energy sources such as geothermal energy. To validate our understanding of the subsurface we require data. However, the data are usually not distributed equally and introduce a potential misinterpretation of the subsurface. Therefore, in this study we investigate the influence of measurements on temperature distribution in the European Alps.
Geoffroy Kirstetter, Olivier Delestre, Pierre-Yves Lagrée, Stéphane Popinet, and Christophe Josserand
Geosci. Model Dev., 14, 7117–7132, https://doi.org/10.5194/gmd-14-7117-2021, https://doi.org/10.5194/gmd-14-7117-2021, 2021
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The development of forecasting tools may help to limit the impacts of flash floods. Our purpose here is to demonstrate the possibility of using b-flood, which is a 2D tool based on shallow-water equations and adaptive mesh refinement.
Sojung Park and Seon K. Park
Geosci. Model Dev., 14, 6241–6255, https://doi.org/10.5194/gmd-14-6241-2021, https://doi.org/10.5194/gmd-14-6241-2021, 2021
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One of the biggest uncertainties in numerical weather predictions (NWPs) comes from treating subgrid-scale physical processes. Physical processes, such as cumulus, microphysics, and planetary boundary layer processes, are parameterized in NWP models by empirical and theoretical backgrounds. We developed an interface between a micro-genetic algorithm and the WRF model for a combinatorial optimization of physics for heavy rainfall events in Korea. The system improved precipitation forecasts.
Olivier Pannekoucke and Philippe Arbogast
Geosci. Model Dev., 14, 5957–5976, https://doi.org/10.5194/gmd-14-5957-2021, https://doi.org/10.5194/gmd-14-5957-2021, 2021
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This contributes to research on uncertainty prediction, which is important either for determining the weather today or estimating the risk in prediction. The problem is that uncertainty prediction is numerically very expensive. An alternative has been proposed wherein uncertainty is presented in a simplified form with only the dynamics of certain parameters required. This tool allows for the determination of the symbolic equations of these parameter dynamics and their numerical computation.
Annika Günther, Johannes Gütschow, and Mairi Louise Jeffery
Geosci. Model Dev., 14, 5695–5730, https://doi.org/10.5194/gmd-14-5695-2021, https://doi.org/10.5194/gmd-14-5695-2021, 2021
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The mitigation components of the nationally determined contributions (NDCs) under the Paris Agreement are essential in our fight against climate change. Regular updates with increased ambition are requested to limit global warming to 1.5–2 °C. The new and easy-to-update open-source tool NDCmitiQ can be used to quantify the NDCs' mitigation targets and construct resulting emissions pathways. In use cases, we show target uncertainties from missing clarity, data, and methodological challenges.
Futo Tomizawa and Yohei Sawada
Geosci. Model Dev., 14, 5623–5635, https://doi.org/10.5194/gmd-14-5623-2021, https://doi.org/10.5194/gmd-14-5623-2021, 2021
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A new method to predict chaotic systems from observation and process-based models is proposed by combining machine learning with data assimilation. Our method is robust to the sparsity of observation networks and can predict more accurately than a process-based model when it is biased. Our method effectively works when both observations and models are imperfect, which is often the case in geoscience. Therefore, our method is useful to solve a wide variety of prediction problems in this field.
Chloe Leach, Tom Coulthard, Andrew Barkwith, Daniel R. Parsons, and Susan Manson
Geosci. Model Dev., 14, 5507–5523, https://doi.org/10.5194/gmd-14-5507-2021, https://doi.org/10.5194/gmd-14-5507-2021, 2021
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Numerical models can be used to understand how coastal systems evolve over time, including likely responses to climate change. However, many existing models are aimed at simulating 10- to 100-year time periods do not represent a vertical dimension and are thus unable to include the effect of sea-level rise. The Coastline Evolution Model 2D (CEM2D) presented in this paper is an advance in this field, with the inclusion of the vertical coastal profile against which the water level can be altered.
Steven J. Phipps, Jason L. Roberts, and Matt A. King
Geosci. Model Dev., 14, 5107–5124, https://doi.org/10.5194/gmd-14-5107-2021, https://doi.org/10.5194/gmd-14-5107-2021, 2021
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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.
Axel Peytavin, Bruno Sainte-Rose, Gael Forget, and Jean-Michel Campin
Geosci. Model Dev., 14, 4769–4780, https://doi.org/10.5194/gmd-14-4769-2021, https://doi.org/10.5194/gmd-14-4769-2021, 2021
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We present a new algorithm developed at The Ocean Cleanup to update ocean plastic models based on measurements from the field to improve future cleaning operations. Prepared in collaboration with MIT researchers, this initial study presents its use in several analytical and real test cases in which two observers in a 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.
Kang Pan, Mei Qi Lim, Markus Kraft, and Epaminondas Mastorakos
Geosci. Model Dev., 14, 4509–4534, https://doi.org/10.5194/gmd-14-4509-2021, https://doi.org/10.5194/gmd-14-4509-2021, 2021
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A new moving point source (MPS) model was developed to simulate the dispersion of emissions generated by the moving ships. Compared to the commonly used line source (LS) or fixed point source (FPS) model, the MPS model provides more emission distribution details generated by the moving ships and matches reasonably with the measurements. Therefore, the MPS model should be a valuable alternative for the environmental society to evaluate the pollutant dispersion contributed from the moving ships.
Sebastian Springer, Heikki Haario, Jouni Susiluoto, Aleksandr Bibov, Andrew Davis, and Youssef Marzouk
Geosci. Model Dev., 14, 4319–4333, https://doi.org/10.5194/gmd-14-4319-2021, https://doi.org/10.5194/gmd-14-4319-2021, 2021
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Model predictions always contain uncertainty. But in some cases, such as weather forecasting or climate modeling, 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 large-scale models can be improved.
Alexander Schaaf, Miguel de la Varga, Florian Wellmann, and Clare E. Bond
Geosci. Model Dev., 14, 3899–3913, https://doi.org/10.5194/gmd-14-3899-2021, https://doi.org/10.5194/gmd-14-3899-2021, 2021
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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 train uncertain geological models to reduce uncertainty. More widely, the method demonstrates the use of probabilistic machine learning (Bayesian inference) to train structural geological models on auxiliary geological knowledge that can be encoded in graph structures.
Matthew Ozon, Aku Seppänen, Jari P. Kaipio, and Kari E. J. Lehtinen
Geosci. Model Dev., 14, 3715–3739, https://doi.org/10.5194/gmd-14-3715-2021, https://doi.org/10.5194/gmd-14-3715-2021, 2021
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Experimental research has provided large amounts of high-quality data on aerosol over the last 2 decades. However, inference of the process rates (e.g., the rates 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 Bayesian framework to not only retrieve the state of the observed aerosol system but also to estimate the process rates (e.g., growth rate).
Colton J. Conroy and Einat Lev
Geosci. Model Dev., 14, 3553–3575, https://doi.org/10.5194/gmd-14-3553-2021, https://doi.org/10.5194/gmd-14-3553-2021, 2021
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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 flow's high bubble content.
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.
Michael Olesik, Sylwester Arabas, Jakub Banaśkiewicz, Piotr Bartman, Manuel Baumgartner, and Simon Unterstrasser
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2020-404, https://doi.org/10.5194/gmd-2020-404, 2021
Revised manuscript accepted for GMD
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.
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.
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.
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).
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.
Cited articles
Akahori, K., Ishiguro, T., Hattori, K., Suda, R., and Sugihara, M.: A global
model based on a double Fourier series, Extended abstract of the 3rd
International Workshop on Next Generation Climate Models for Advanced High
Performance Computing Facilities, Japan, March 2001.
Asselin, R. A.: Frequency filter for time integrations, Mon. Weather Rev., 100,
487–490, https://doi.org/10.1175/1520-0493(1972)100<0487:FFFTI>2.3.CO;2, 1972.
Bihar: Netlib BIHAR library, Netlib Repository [code], https://www.netlib.org/bihar/, last access: 20 March 2022.
Boer, G. J. and Steinberg, L.: Fourier series on spheres, Atmosphere, 13,
180–191, https://doi.org/10.1080/00046973.1975.9648396, 1975.
Boyd, J. P.: The choice of spectral functions on a sphere for boundary and
eigenvalue problems: A comparison of Chebyshev, Fourier and associated
Legendre expansions, Mon. Weather Rev., 106, 1184–1191,
https://doi.org/10.1175/1520-0493(1978)106<1184:TCOSFO>2.0.CO;2, 1978.
Browning, G. L., Hack, J. J., and Swarztrauber, P. N.: A comparison of three
numerical methods for solving differential equations on the sphere, Mon.
Weather Rev., 117, 1058–1075,
https://doi.org/10.1175/1520-0493(1989)117<1058:ACOTNM>2.0.CO;2, 1989.
Cheong, H.-B.: Double Fourier series on a sphere: applications to elliptic
and vorticity equations, J. Comput. Phys., 157, 327–349,
https://doi.org/10.1006/jcph.1999.6385, 2000a.
Cheong, H.-B.: Application of double Fourier series to shallow water
equations on a sphere, J. Comput. Phys., 165, 261–287,
https://doi.org/10.1006/jcph.2000.6615, 2000b.
Cheong, H.-B.: A dynamical core with double Fourier series: Comparison with
the spherical harmonics method, Mon. Weather Rev., 134, 1299–1315,
https://doi.org/10.1175/MWR3121.1, 2006.
Cheong, H.-B., Kwon, I.-H., and Goo, T.-Y.: Further study on the high-order
double-Fourier-series spectral filtering on a sphere, J. Comput. Phys., 193,
180–197, https://doi.org/10.1016/j.jcp.2003.07.029, 2004.
Cheong, H.-B., Kwon, I.-H., Goo, T.-Y., and M.-J. Lee: High-order harmonic
spectral filter with the double Fourier series on a sphere, J. Comput. Phys.,
177, 313–335, https://doi.org/10.1006/jcph.2002.6997, 2002.
Cooley, J. W. and Tukey, J. W.: An algorithm for the machine calculation of
complex Fourier series, Math. Comput., 19, 297–301,
https://doi.org/10.2307/2003354, 1965.
Dueben, P. D., Wedi, N., Saarinen, S., and Zeman, C.: Global simulations of
the atmosphere at 1.45 km grid-spacing with the Integrated Forecasting
System, J. Meteorol. Soc. Jpn., 98, 551–572,
https://doi.org/10.2151/jmsj.2020-016, 2020.
Galewsky, J., Scott, R. K., and Polvani, L. M.: An initial-value problem for
testing numerical models of the global shallow-water equations, Tellus A,
56, 429–440, https://doi.org/10.3402/tellusa.v56i5.14436, 2004.
Gander, W. and Golub, G. H.: Cyclic reduction – History and applications,
Proceedings of the Workshop on Scientific Computing, Hong Kong, 10–12 March, 1997.
Gospodinov, I. G., Spiridonov, V. G., and Geleyn, J.-F.: Second-order
accuracy of two-time-level semi-Lagrangian schemes, Q. J. Roy. Meteor. Soc.,
127, 1017–1033, https://doi.org/10.1002/qj.49712757317, 2001.
Hortal, M.: The development and testing of a new two-time-level
semi-Lagrangian scheme (SETTLS) in the ECMWF forecast model, Q. J. Roy.
Meteor. Soc., 128, 1671–1687, https://doi.org/10.1002/qj.200212858314, 2002.
Hortal, M. and Simmons, A. J.: Use of reduced Gaussian grids in spectral
models, Mon. Weather Rev., 119, 1057–1074,
https://doi.org/10.1175/1520-0493(1991)119<1057:UORGGI>2.0.CO;2, 1991.
Hotta, D. and Ujiie, M.: A nestable, multigrid-friendly grid on a sphere for
global spectral models based on Clenshaw–Curtis quadrature, Q. J. Roy.
Meteor. Soc., 144, 1382–1397, https://doi.org/10.1002/qj.3282, 2018.
Ishioka, K.: A New Recurrence Formula for Efficient Computation, J.
Meteorol. Soc. Jpn., 96, 241–249, https://doi.org/10.2151/jmsj.2018-019,
2018.
Ishioka, K.: ISPACK library, GFD-DENNOU Club [code], https://www.gfd-dennou.org/arch/ispack/, last access: 20 March 2022.
Japan Meteorological Agency (JMA): Outline of the operational numerical
weather prediction at the Japan Meteorological Agency, Appendix to WMO
technical progress report on the global data-processing and forecasting
system and numerical weather prediction, 229 pp.,
http://www.jma.go.jp/jma/jma-eng/jma-center/nwp/outline2019-nwp/index.htm (last access: 20 March 2022),
2019.
Juang, H.-M. H.: A reduced spectral transform for the NCEP seasonal forecast
global spectral atmospheric model, Mon. Weather Rev., 132, 1019–1035,
https://doi.org/10.1175/1520-0493(2004)132<1019:ARSTFT>2.0.CO;2, 2004.
Koo, M.-S. and Hong, S.-Y.: Double Fourier series dynamical core with hybrid
sigma-pressure vertical coordinate, Tellus A, 65, 19851,
https://doi.org/10.3402/tellusa.v65i0.19851, 2013.
Kwon, I.-H., Cheong, H.-B., Joh, M., Chung, I.-U., Cho, C.-H., and Lee,
W.-J.: Application of double-Fourier-series spectral method to a large size
problem: Two dimensional simulations of the shear instability on the sphere,
J. Meteorol. Soc. Jpn., 82, 1301–1314,
https://doi.org/10.2151/jmsj.2004.1301, 2004.
Lambert, S. J.: A global available potential energy-kinetic energy budget in
terms of the two-dimensional wavenumber for the FGGE year, Atmos. Ocean,
22, 265–282, https://doi.org/10.1080/07055900.1984.9649199, 1984.
Layton, A. T. and Spotz, W. F.: A semi-Lagrangian double Fourier method for
the shallow water equations on the sphere, J. Comput. Phys., 189, 180–196,
https://doi.org/10.1016/S0021-9991(03)00207-9, 2003.
Malardel, S., Wedi, N., Deconinck, W., Diamantakis, M., Kühnlein, C.,
Mozdzynski, G., Hamrud, M., and Smolarkiewicz, P.: A new grid for the IFS,
ECMWF Newsletter, 146, 23–28, https://doi.org/10.21957/zwdu9u5i, 2016.
Merilees, P. E.: An alternative scheme for the simulation of a series of
spherical harmonics, J. Appl. Meteorol. Clim., 12, 224–227,
https://doi.org/10.1175/1520-0450(1973)012<0224:AASFTS>2.0.CO;2, 1973a.
Merilees, P. E.: The pseudospectral approximation applied to the shallow
water equations on a sphere, Atmosphere, 11, 13–20,
https://doi.org/10.1080/00046973.1973.9648342, 1973b.
Merilees, P. E.: Numerical experiments with the pseudospectral method in
spherical coordinates, Atmosphere, 12, 77–96,
https://doi.org/10.1080/00046973.1974.9648374, 1974.
Miyamoto, K.: Introduction of the Reduced Gaussian Grid into the Operational
Global NWP model at JMA, CAS/JSC WGNE Research Activities in Atmospheric and
Ocean Modelling, 36, 6.9–6.10, 2006.
Nakano, M., Wada, A., Sawada, M., Yoshimura, H., Onishi, R., Kawahara, S., Sasaki, W., Nasuno, T., Yamaguchi, M., Iriguchi, T., Sugi, M., and Takeuchi, Y.: Global 7 km mesh nonhydrostatic Model Intercomparison Project for improving TYphoon forecast (TYMIP-G7): experimental design and preliminary results, Geosci. Model Dev., 10, 1363–1381, https://doi.org/10.5194/gmd-10-1363-2017, 2017.
Orszag, S. A.: On the elimination of aliasing in finite-difference schemes
by filtering high-wavenumber components, J. Atmos. Sci., 28, 1074–1074,
https://doi.org/10.1175/1520-0469(1971)028<1074:OTEOAI>2.0.CO;2, 1971.
Orszag, S. A.: Fourier series on spheres, Mon. Weather Rev., 102, 56–75,
https://doi.org/10.1175/1520-0493(1974)102<0056:FSOS>2.0.CO;2, 1974.
Park, H., Hong, S.-Y., Cheong, H.-B., and Koo, M.-S.: A Double Fourier
Series (DFS) Dynamical Core in a Global Atmospheric Model with Full Physics.
Mon. Weather Rev., 141, 3052–3061,
https://doi.org/10.1175/MWR-D-12-00270.1, 2013.
Ritchie, H.: Application of the semi-Lagrangian method to a spectral model
of the shallow water equations, Mon. Weather Rev., 116, 1587–1598,
https://doi.org/10.1175/1520-0493(1988)116<1587:AOTSLM>2.0.CO;2, 1988.
Ritchie, H. and Tanguay, M.: A comparison of spatially averaged Eulerian and
semi-Lagrangian treatments of mountains, Mon. Weather Rev., 124,
167–181, https://doi.org/10.1175/1520-0493(1996)124<0167:ACOSAE>2.0.CO;2, 1996.
Ritchie, H., Temperton, C., and Simmons, A.: Implementation of the
semi-Lagrangian method in a high-resolution version of the ECMWF forecast
model, Mon. Weather Rev., 123, 489–514,
https://doi.org/10.1175/1520-0493(1995)123<0489:IOTSLM>2.0.CO;2, 1995.
Robert, A. J.: The integration of a low order spectal form of the primitive
meteorological equations, J. Meteorol. Soc. Jpn., 44, 237–245,
https://doi.org/10.2151/jmsj1965.44.5_237, 1966.
Schaeffer, N.: Efficient spherical harmonic transforms aimed at
pseudospectral numerical simulations, Geochem. Geophys. Geosy., 14,
751–758, https://doi.org/10.1002/ggge.20071, 2013.
Sneeuw, N. and Bun, R.: Global spherical harmonic computation by
two-dimensional Fourier methods, J. Geodesy, 70, 224–232,
https://doi.org/10.1007/BF00873703, 1996.
Spotz, W. F., Taylor, M. A., and Swarztrauber, P. N.: Fast shallow-water
equations solvers in latitude-longitude coordinates, J. Comput. Phys., 145,
432–444, https://doi.org/10.1006/jcph.1998.6026, 1998.
Suda, R.: Fast spherical harmonic transform routine FLTSS applied to the
shallow water test set, Mon. Weather Rev., 133, 634–648,
https://doi.org/10.1175/MWR-2871.1, 2005.
Swarztrauber, P. N.: Vectorizing the FFTs, edited by: Rodrigue, G., Parallel Comput., Academic Press, 51–83,
https://doi.org/10.1016/B978-0-12-592101-5.50007-5, 1982.
Swarztrauber, P. N.: The vector harmonic transform method for solving
partial differential equations in spherical geometry, Mon. Weather Rev., 121,
3415–3437, https://doi.org/10.1175/1520-0493(1993)121<3415:TVHTMF>2.0.CO;2, 1993.
Swarztrauber, P. N.: Shallow water flow on the sphere, Mon. Weather Rev.,
132, 3010–3018, https://doi.org/10.1175/MWR2829.1, 2004.
Swarztrauber, P. N. and Spotz, W. F.: Generalized discrete spherical
harmonic transforms, J. Comput. Phys., 159, 213–230,
https://doi.org/10.1006/jcph.2000.6431, 2000.
Temperton, C.: On scalar and vector transform methods for global spectral
models, Mon. Weather Rev., 119, 1303–1307,
https://doi.org/10.1175/1520-0493-119-5-1303.1, 1991.
Temperton, C.: Treatment of the Coriolis terms in semi-Lagrangian spectral
models, Atmos. Ocean, 35, 293–302,
https://doi.org/10.1080/07055900.1997.9687353, 1997.
Temperton, C., Hortal, M., and Simmons, A.: A two-time-level semi-Lagrangian
global spectral model, Q. J. Roy. Meteor. Soc., 127, 111–127,
https://doi.org/10.1002/qj.49712757107, 2001.
Tygert, M.: Fast algorithms for spherical harmonic expansions, II, J.
Comput. Phys., 227, 4260–4279, https://doi.org/10.1016/j.jcp.2007.12.019,
2008.
Wedi, N. P., Hamrud, M., and Mozdzynski, G.: A fast spherical harmonics
transform for global NWP and climate models, Mon. Weather Rev., 141,
3450–3461, https://doi.org/10.1175/MWR-D-13-00016.1, 2013.
Wedi, N. P.: Increasing horizontal resolution in numerical weather
prediction and climate simulations: illusion or panacea?, Philos. T. R. Soc.
A, 372, 20130289, https://doi.org/10.1098/rsta.2013.0289, 2014.
Williamson, D. L., Drake, J. B., Hack, J. J., Jacob, R., and Swarztrauber,
P. N.: A standard test set for numerical approximations to the shallow water
equations in spherical geometry, J. Comput. Phys., 102, 211–224,
https://doi.org/10.1016/S0021-9991(05)80016-6, 1992.
Yee, S. Y. K.: Solution of Poisson's equation on a sphere by truncated
double Fourier series, Mon. Weather Rev., 109, 501–505,
https://doi.org/10.1175/1520-0493(1981)109<0501:SOPEOA>2.0.CO;2, 1981.
Yoshimura, H.: Development of a nonhydrostatic global spectral atmospheric
model using double Fourier series, CAS/JSC WGNE Research Activities in
Atmospheric and Ocean Modelling, 42, 3.05–3.06, 2012.
Yoshimura, H.: DFS shallow-water test cases, Meteorological Research Institute [data set], https://climate.mri-jma.go.jp/pub/archives/Yoshimura_DFS_SW_Testcase/, last access: 20 March 2022.
Yoshimura, H. and Matsumura, T.: A two-time-level vertically conservative
semi-Lagrangian semi-implicit double Fourier series AGCM, CAS/JSC WGNE
Research Activities in Atmospheric and Ocean Modelling, 35, 3.25–3.26,
2005.
Yukimoto, S., Yoshimura, H., Hosaka, M., Sakami, T., Tsujino, H., Hirabara, M., Tanaka, T. Y., Deushi, M., Obata, A., Nakano, H., Adachi, Y., Shindo, E., Yabu, S., Ose, T., and Kitoh, A.: Meteorological Research Institute-Earth System
Model Version 1 (MRI-ESM1) – Model Description –, Technical Reports of
the Meteorological Research Institute, No. 64,
https://doi.org/10.11483/mritechrepo.64, 2011.
Yukimoto, S., Kawai, H., Koshiro, T., Oshima, N., Yoshida, K., Urakawa, S., Tsujino, H., Deushi, M., Tanaka, T., Hosaka, M., Yabu, S., Yoshimura, H., Shindo, E., Mizuta, R., Obata, A., Adachi, Y., and Ishii, M.: The Meteorological Research Institute Earth
System Model Version 2.0, MRI-ESM2.0: Description and Basic Evaluation of
the Physical Component, J. Meteorol. Soc. Jpn., 97, 931–965,
https://doi.org/10.2151/jmsj.2019-051, 2019.
Short summary
This paper proposes a new double Fourier series (DFS) method on a sphere that improves the numerical stability of a model compared with conventional DFS methods. The shallow-water model and the advection model using the new DFS method give stable results without the appearance of high-wavenumber noise near the poles. The model using the new DFS method is faster than the model using spherical harmonics (especially at high resolutions) and gives almost the same results.
This paper proposes a new double Fourier series (DFS) method on a sphere that improves the...
