Laplace transform integration of a baroclinic model

Abstract

A time integration scheme based on the Laplace transform (LT) has been implemented in a baroclinic primitive equation model. The LT scheme provides an attractive alternative to the popular semi-implicit (SI) scheme. Analysis shows that it is more accurate than SI for both linear and nonlinear terms of the equations. Numerical experiments confirm the superior performance of the LT scheme. The algorithmic complexity of the LT scheme is comparable with SI, with just an additional transformation to vertical eigenmodes each time step, and it provides the possibility of improving weather forecasts at comparable computational cost. KEYWORDS filtering, forecast accuracy, Laplace transform, numerical weather prediction, time integration 1 Q J R Meteorol Soc. 2019;145:347-355.wileyonlinelibrary.com/journal/qj

A Lagrange-Laplace Integration Scheme for Weather Prediction and Climate Modelling

“…Before considering the details of the PEAK model, we describe the general approach to integration using the LaSI and LaLT schemes. The original EuSI scheme is comprehensively documented by Ehrendorfer [10] and the EuLT scheme by Harney and Lynch [12].…”

“…An accuracy analysis of the Laplace transform (LT) and semi-implicit (SI) schemes was presented in [12]. The main conclusions are reviewed here.…”

“…This is due to the fact that the LT scheme does not involve time-averaging of the linear terms. Harney & Lynch [12] described a Laplace transform integration scheme in an Eulerian baroclinic model and showed that it yields more accurate forecasts than SI.…”

“…EuSI is the original Eulerian semi-implicit scheme described in [10]. EuLT is the Eulerian Laplace transform scheme described in Harney and Lynch, 2019 [12]. The two Lagrangian schemes are denoted LaSI and LaLT.…”

“…The two Lagrangian schemes are denoted LaSI and LaLT. [10,12]. The Lagrangian schemes, LaSI and LaLT, are described in this paper.…”