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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.
