Communication-Efficient Property Preservation in Tracer Transport

Abstract

Atmospheric tracer transport is a computationally demanding component of the atmospheric dynamical core of weather and climate simulations. Simulations typically have tens to hundreds of tracers. A tracer field is required to preserve several properties, including mass, shape, and tracer consistency. To improve computational efficiency, it is common to apply different spatial and temporal discretizations to the tracer transport equations than to the dynamical equations. Using different discretizations increases the difficulty of preserving properties. This paper provides a unified framework to analyze the property preservation problem and classes of algorithms to solve it. We examine the primary problem and a safety problem; describe three classes of algorithms to solve these; introduce new algorithms in two of these classes; make connections among the algorithms; analyze each algorithm in terms of correctness, bound on its solution magnitude, and its communication efficiency; and study numerical results. A new algorithm, QLT, has the smallest communication volume, and in an important case it redistributes mass approximately locally. These algorithms are only very loosely coupled to the underlying discretizations of the dynamical and tracer transport equations and thus are broadly and efficiently applicable. In addition, they may be applied to remap problems in applications other than tracer transport.

Separating Physics and Dynamics Grids for Improved Computational Efficiency in Spectral Element Earth System Models

“…It can be applied to a field in an element in either basis. There are a number of limiters that provide such outputs q′; we use ClipAndAssuredSum, Algorithm 3.1 in Bradley et al (2019).…”

“…There are a number of limiters that provide such outputs q′ ; we use ClipAndAssuredSum , Algorithm 3.1 in Bradley et al. (2019).…”

Comparison of Semi-Lagrangian Discontinuous Galerkin Schemes for Linear and Nonlinear Transport Simulations

“…More recently, an SLDG method based on the forward characteristics tracing mechanism has been developed [6], which can be considered as an extension of the SL continuous finite element method, see, e.g., [31]. In such a formulation, the DG solution is first evolved forward following the characteristics from t n to t n+1 , yielding an intermediate solution which in general does not belong to space V k h .…”

“…The forward SLDG formulation is inherently nonconservative for mass, as opposed to the backward formulation (2.5), while a mass fixer can be coupled to ensure global mass conservation. On the other hand, an extra cost is incurred, and the original high-order accuracy of the SLDG method may be destroyed, see [6].…”

Islet: Interpolation semi-Lagrangian element-based transport

“…There are a number of types of SL methods; see, e.g., Giraldo et al (2003); Natarajan and Jacobs (2020); Bradley et al (2019) for a review of these. This article focuses on remap-form interpolation methods.…”