Normal Mode Initialization Procedure Applied to Forecasts with the Global Shallow Water Equations

Abstract

Conventional procedures designed to balance global initial data for primitive equation forecast models often result in unrealistic large-amplitude, high-frequency oscillations during the initial stages of the forecasts. In an attempt to reduce these oscillations, Dickinson and Williamson (1972) proposed a method to initialize data by expanding the data into the normal modes or free oscillations of the linearized version of the forecast model. Once the data are expanded into the normal modes, the modal amplitudes thought to be erroneously large can be reduced or set to zero. This procedure is tested here with the shallow water equations. In the first set of one-day forecasts performed, the method eliminates the large-amplitude, high-frequency waves which occur when using analyzed heights and winds for initial data by removing the gravity waves and computational Rossby waves from the initial data. The standard deviation of the error and the S1 skill score show substantial improvement in the filtered case. This improvement is a result of the smoothing due to the initial filtering rather than an improvement in the forecast of the waves retained. When included, the gravity waves do not interact significantly with the Rossby waves during the one-day forecast. Additional experiments are performed to examine the effect on the one-day forecast of removing the small-scale Rossby waves from the initial data. In general, except for the smallest longitudinal-scale Rossby waves, removal of these modes degrades the forecasts. A third set of forecasts examines the effect of the large-scale gravity waves on the forecast. The largest latitudinal-scale gravity waves have little effect on the forecast skill scores; they neither improve nor degrade the forecast with the shallow water equations. Inclusion of the medium-and smaller-scale gravity waves in the initial data degrades the forecasts. Several forecasts are repeated with the mean depth decreased. The conclusions with respect to the modal filtering are unchanged although the impact of the filtering is less dramatic in these cases. The results are also insensitive to the particular longitudinal filtering used near the poles to allow longer time steps.