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- Author or Editor: P. A. Ullrich x
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Abstract
In this study, an alternative local Galerkin method (LGM), the o3o3 scheme, is proposed. o3o3 is a variant or generalization of the third-order spectral element method (SEM3). It uses third-order piecewise polynomials for the representation of a field and piecewise third-degree polynomials for fluxes. For the discretization, SEM3 uses the irregular Legendre–Gauss–Lobatto grid while o3o3 uses a regular collocation grid. o3o3 can be regarded as an inhomogeneous finite-difference scheme on a uniform grid, which means that the finite-difference equations are different for each group with three points. A particular version of o3o3 is set as an example of many possibilities to construct LGM schemes on piecewise polynomial spaces in which the basis functions used are continuous at corner points and function spaces having continuous derivatives are shortly discussed. We propose a standard o3o3 scheme and a spectral o3o3 scheme as alternatives to the standard method of using the quadrature approximation. These two particular schemes selected were chosen for ease of implementation rather than optimal performance. In one dimension, compared to standard SEM3, o3o3 has a larger CFL condition benefiting from the use of a regular collocation grid. While SEM3 uses the irregular Legendre–Gauss–Lobatto collocation grid, o3o3 uses a regular grid. This is considered an advantage for physical parameterizations. The shortest resolved wave is marginally smaller than that with SEM3. In two dimensions, o3o3 is implemented on a sparse grid where only a part of the points on the underlying regular grid are used for forecasting.
Abstract
In this study, an alternative local Galerkin method (LGM), the o3o3 scheme, is proposed. o3o3 is a variant or generalization of the third-order spectral element method (SEM3). It uses third-order piecewise polynomials for the representation of a field and piecewise third-degree polynomials for fluxes. For the discretization, SEM3 uses the irregular Legendre–Gauss–Lobatto grid while o3o3 uses a regular collocation grid. o3o3 can be regarded as an inhomogeneous finite-difference scheme on a uniform grid, which means that the finite-difference equations are different for each group with three points. A particular version of o3o3 is set as an example of many possibilities to construct LGM schemes on piecewise polynomial spaces in which the basis functions used are continuous at corner points and function spaces having continuous derivatives are shortly discussed. We propose a standard o3o3 scheme and a spectral o3o3 scheme as alternatives to the standard method of using the quadrature approximation. These two particular schemes selected were chosen for ease of implementation rather than optimal performance. In one dimension, compared to standard SEM3, o3o3 has a larger CFL condition benefiting from the use of a regular collocation grid. While SEM3 uses the irregular Legendre–Gauss–Lobatto collocation grid, o3o3 uses a regular grid. This is considered an advantage for physical parameterizations. The shortest resolved wave is marginally smaller than that with SEM3. In two dimensions, o3o3 is implemented on a sparse grid where only a part of the points on the underlying regular grid are used for forecasting.
ABSTRACT
Regional climate modeling addresses our need to understand and simulate climatic processes and phenomena unresolved in global models. This paper highlights examples of current approaches to and innovative uses of regional climate modeling that deepen understanding of the climate system. High-resolution models are generally more skillful in simulating extremes, such as heavy precipitation, strong winds, and severe storms. In addition, research has shown that fine-scale features such as mountains, coastlines, lakes, irrigation, land use, and urban heat islands can substantially influence a region’s climate and its response to changing forcings. Regional climate simulations explicitly simulating convection are now being performed, providing an opportunity to illuminate new physical behavior that previously was represented by parameterizations with large uncertainties. Regional and global models are both advancing toward higher resolution, as computational capacity increases. However, the resolution and ensemble size necessary to produce a sufficient statistical sample of these processes in global models has proven too costly for contemporary supercomputing systems. Regional climate models are thus indispensable tools that complement global models for understanding physical processes governing regional climate variability and change. The deeper understanding of regional climate processes also benefits stakeholders and policymakers who need physically robust, high-resolution climate information to guide societal responses to changing climate. Key scientific questions that will continue to require regional climate models, and opportunities are emerging for addressing those questions.
ABSTRACT
Regional climate modeling addresses our need to understand and simulate climatic processes and phenomena unresolved in global models. This paper highlights examples of current approaches to and innovative uses of regional climate modeling that deepen understanding of the climate system. High-resolution models are generally more skillful in simulating extremes, such as heavy precipitation, strong winds, and severe storms. In addition, research has shown that fine-scale features such as mountains, coastlines, lakes, irrigation, land use, and urban heat islands can substantially influence a region’s climate and its response to changing forcings. Regional climate simulations explicitly simulating convection are now being performed, providing an opportunity to illuminate new physical behavior that previously was represented by parameterizations with large uncertainties. Regional and global models are both advancing toward higher resolution, as computational capacity increases. However, the resolution and ensemble size necessary to produce a sufficient statistical sample of these processes in global models has proven too costly for contemporary supercomputing systems. Regional climate models are thus indispensable tools that complement global models for understanding physical processes governing regional climate variability and change. The deeper understanding of regional climate processes also benefits stakeholders and policymakers who need physically robust, high-resolution climate information to guide societal responses to changing climate. Key scientific questions that will continue to require regional climate models, and opportunities are emerging for addressing those questions.
Abstract
Process-oriented diagnostics (PODs) aim to provide feedback for model developers through model analysis based on physical hypotheses. However, the step from a diagnostic based on relationships among variables, even when hypothesis driven, to specific guidance for revising model formulation or parameterizations can be substantial. The POD may provide more information than a purely performance-based metric, but a gap between POD principles and providing actionable information for specific model revisions can remain. Furthermore, in coordinating diagnostics development, there is a trade-off between freedom for the developer, aiming to capture innovation, and near-term utility to the modeling center. Best practices that allow for the former, while conforming to specifications that aid the latter, are important for community diagnostics development that leads to tangible model improvements. Promising directions to close the gap between principles and practice include the interaction of PODs with perturbed physics experiments and with more quantitative process models as well as the inclusion of personnel from modeling centers in diagnostics development groups for immediate feedback during climate model revisions. Examples are provided, along with best-practice recommendations, based on practical experience from the NOAA Model Diagnostics Task Force (MDTF). Common standards for metrics and diagnostics that have arisen from a collaboration between the MDTF and the Department of Energy’s Coordinated Model Evaluation Capability are advocated as a means of uniting community diagnostics efforts.
Abstract
Process-oriented diagnostics (PODs) aim to provide feedback for model developers through model analysis based on physical hypotheses. However, the step from a diagnostic based on relationships among variables, even when hypothesis driven, to specific guidance for revising model formulation or parameterizations can be substantial. The POD may provide more information than a purely performance-based metric, but a gap between POD principles and providing actionable information for specific model revisions can remain. Furthermore, in coordinating diagnostics development, there is a trade-off between freedom for the developer, aiming to capture innovation, and near-term utility to the modeling center. Best practices that allow for the former, while conforming to specifications that aid the latter, are important for community diagnostics development that leads to tangible model improvements. Promising directions to close the gap between principles and practice include the interaction of PODs with perturbed physics experiments and with more quantitative process models as well as the inclusion of personnel from modeling centers in diagnostics development groups for immediate feedback during climate model revisions. Examples are provided, along with best-practice recommendations, based on practical experience from the NOAA Model Diagnostics Task Force (MDTF). Common standards for metrics and diagnostics that have arisen from a collaboration between the MDTF and the Department of Energy’s Coordinated Model Evaluation Capability are advocated as a means of uniting community diagnostics efforts.
