Post-processing through linear regression
Van Schaeybroeck, B.
Earth and related Environmental sciences
Tikhonov regression (TDTR)
Lorenz 1963 model
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We present a comparison of various post-processing schemes for ensemble forecasts, all based on linear regression between forecast data and observations. In order for the regression to be useful in practice, we put forward three criteria which are related to forecast errors, the correct climatological variability and multicollinearity. The regression schemes under consideration include the ordinary least squares (OLS) method, a new timedependent Tikhonov regression (TDTR), the total least squares (TLS) method, a new geometric mean regression (GM), a error-in-variables (EVMOS) method which was recently proposed by Vannitsem (2009), and finally, a “best member” OLS method (Unger et al.; 2009). We find that the EVMOS, the TDTR and GM schemes satisfy all three criteria. We clarify our theoretical findings using the Lorenz 1963 model. For short lead times, the amount and choice of predictors is more important than the regression method. At intermediate timescales linear regression is unable to provide corrections to the forecast. However, at long timescales the different regression schemes differ strongly and, in order to obtain physically relevant results, the use of OLS should be avoided.
CitationVan Schaeybroeck, B.; Vannitsem, S. (2011). Post-processing through linear regression. , Issue Nonldinear Processes in Geophysics, p. 147–160, IRM,