Nonhomogeneous Gaussian regression

Non-homogeneous Gaussian regression (NGR) is a type of statistical regression analysis used in the atmospheric sciences as a way to convert ensemble forecasts into probabilistic forecasts. Relative to simple linear regression, NGR uses the ensemble spread as an additional predictor, which is used to improve the prediction of uncertainty and allows the predicted uncertainty to vary from case to case. The prediction of uncertainty in NGR is derived from both past forecast errors statistics and the ensemble spread. NGR was originally developed for site-specific medium range temperature forecasting, but has since also been applied to site-specific medium-range wind forecasting and to seasonal forecasts, and has been adapted for precipitation forecasting. The introduction of NGR was the first demonstration that probabilistic forecasts that take account of the varying ensemble spread could achieve better skill scores than forecasts based on standard Model output statistics approaches applied to the ensemble mean. Weather forecasts generated by computer simulations of the atmosphere and ocean typically consist of an ensemble of individual forecasts. Ensembles are used as a way to attempt to capture and quantify the uncertainties in the weather forecasting process, such as uncertainty in the initial conditions and uncertainty in the parameterisations in the model. For point forecasts of normally distributed variables, one can summarize an ensemble forecast with the mean and the standard deviation of the ensemble. The ensemble mean is often a better forecast than any of the individual forecasts, and the ensemble standard deviation may give an indication of the uncertainty in the forecast. However, direct output from computer simulations of the atmosphere needs calibration before it can be meaningfully compared with observations of weather variables. This calibration process is often known as model output statistics (MOS). The simplest form of such calibration is to correct biases, using a bias correction calculated from past forecast errors.