Abstract
Abstract. Various post-processing techniques are compared for both deterministic and ensemble forecasts, all based on linear regression between forecast data and observations. In order to evaluate the quality of the regression methods, three criteria are proposed, related to the effective correction of forecast error, the optimal variability of the corrected forecast and multicollinearity. The regression schemes under consideration include the ordinary least-square (OLS) method, a new time-dependent Tikhonov regularization (TDTR) method, the total least-square method, a new geometric-mean regression (GM), a recently introduced error-in-variables (EVMOS) method and, finally, a "best member" OLS method. The advantages and drawbacks of each method are clarified. These techniques are applied in the context of the 63 Lorenz system, whose model version is affected by both initial condition and model errors. For short forecast lead times, the number and choice of predictors plays an important role. Contrarily to the other techniques, GM degrades when the number of predictors increases. At intermediate lead times, linear regression is unable to provide corrections to the forecast and can sometimes degrade the performance (GM and the best member OLS with noise). At long lead times the regression schemes (EVMOS, TDTR) which yield the correct variability and the largest correlation between ensemble error and spread, should be preferred.
Highlights
Meteorological ensemble prediction systems provide a forecast, and an estimate of its uncertainty
The classical linear regression approach of ensemble regression is based on ordinary least-square (OLS) fitting
One of the well-known problems with the classical linear regression approach is the fact that the corrected forecast converges to the climatological mean for long lead times (Wilks, 2006)
Summary
Meteorological ensemble prediction systems provide a forecast, and an estimate of its uncertainty. Unger et al (2009), in an effort to prolong the correlation time, take a “best member” approach and average over the ensemble of forecasts to obtain the OLS regression parameters They compensate the lack of climatological variability by a kernel method which consists in adding Gaussian noise, an approach used by Glahn et al (2009). In Vannitsem (2009), a new regression scheme was proposed which accounts for the presence of both the observational errors and the forecast errors This approach which gives the correct variability at all lead times was tested against the nonhomogeneous Gaussian regression using re-forecast data of ECMWF (Vannitsem and Hagedorn, 2011) and found to have good skill.
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