A split explicit integration scheme for numerical weather prediction

Abstract

An economical explicit integration scheme for numerical weather prediction models is described. A splitting technique is used, in which the horizontal advection terms in the governing equations are integrated with a timestep limited by the wind speed, whilst the terms which describe gravity‐inertia oscillations are integrated in a succession of shorter steps. A two‐level numerical scheme with small phase speed errors is used for the advection stage and a forward‐backward method for the gravity‐inertia terms. The split explicit scheme has been applied to the Meteorological Office operational 10‐level model, and to a similar sigma coordinate model, to compute forecasts for periods up to six days ahead. The quality of the numerical forecasts obtained is not reduced when the timesteps used are close to the limits set by linear computational stability criteria. The use of such timesteps leads to a substantial computational economy relative to previously available integration schemes. For the northern hemisphere version of the 10‐level model the computing time required is one‐third of that for a split semi‐implicit scheme and one‐sixth of that for the original explicit Lax‐Wendroff scheme. Verification statistics for split explicit forecasts indicate improved accuracy when compared with those for earlier operational models.

Future climate extreme events in the Mediterranean simulated by a regional climate model: a first approach

“…Large-scale values are updated every 6 h. The vertical interpolation of the driving fields to model levels follows the procedure described in Gaertner and Castro (1996). PROMES model uses a split-explicit integration scheme, based on Gadd (1978). The different terms of the equations are integrated with time steps depending on their typical time-scale.…”

Analysis of the Turkel-Zwas scheme for the shallow-water equations

“…The rate of decay decreases as (L1x) 2 /A. 2 increases. If the initial imbalance has a scale that is small in comparison with the scale of the region, the geostrophic adjustment process operates very efficiently.…”

“…2 • When the scale of the initial field L is small compared to the Rossby radius of deformation, LR the final state is determined by the rotational part of the initial wind field, wheras when L >LR the final state is determined by the initial pressure (mass field) (see also Appendix B).…”

Numerical study of 1998 late summer flood in East Asia

“…Sun's advection scheme (1993c) and a local reference to calculate the pressure gradient, which reduces the error over steep topography (Sun, 1995), are used. A time-splitting scheme is utilized, which allows the application of different numerical methods and time intervals to different terms or groups of terms in the governing equations (Gadd, 1978). The forward-backward scheme with a small time interval is applied to the terms involving inertia-gravity waves (Sun, 1980(Sun, , 1984.…”