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Localization of optimal perturbations using a projection operator
Author(s) -
Buizza Roberto
Publication year - 1994
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.49712052010
Subject(s) - northern hemisphere , perturbation (astronomy) , numerical weather prediction , nonlinear system , meteorology , data assimilation , truncation (statistics) , environmental science , climatology , southern hemisphere , mathematics , projection (relational algebra) , statistics , physics , geology , algorithm , quantum mechanics
Ensemble prediction is an attempt to estimate the probability distribution of forecast states through a finite sample of nonlinear deterministic integrations of a numerical weather‐prediction model. At the European Centre for Medium‐range Weather Forecasts (ECMWF) it is based on 32+1 (control) model integrations at horizontal spectral triangular truncation T63, with 19 vertical levels. The initial conditions of the perturbed forecasts are generated from optimal perturbations, which identify the directions in the phase space of the system that guarantee the maximum growth of the total energy of the perturbation over a fixed time interval. Since the ECMWF is mainly interested in predicting the atmospheric flow over the northern hemisphere, in particular over the European region, optimal perturbations are chosen to give different forecasts in this region. One of the problems faced during the first months of ensemble prediction was that, on some occasions, the spread between the perturbed and the control forecasts appeared to be small. One case, for 14 February 1993, which represents an extreme among these cases, is analysed in detail. For that period, for three consecutive days, the two unperturbed forecasts (the control T63L19 and the high‐resolution operational forecast) and all the perturbed forecasts of the ensemble system were very similar over the European region. A second problem, closely related to the first, that had to be prevented, was the inability of the system to identify optimal perturbations which amplify over the northern hemisphere during the warm seasons, when the relative instability of the northern hemisphere is smaller than the instability of the southern hemisphere. It is shown how the introduction of a local projection operator, which confines the region over which the optimal perturbation growth is maximized, can improve the spread among the ensemble members. Moreover, it is proven that its application avoids the occurrence of the second problem.