Reforecasts might also be profitably extended by using them with multi-model ensembles. However, the forecast predictors then reside in a high-dimensional space, and such spaces are ``terribly empty" (Tarantola 2005) with each point tending to be far separated from other points. Again, we are faced with the problem of interpolating and extrapolating near-analogs, because a perfect analog does not exist.
We can interpolate near-analogs by computing a conditional probability density function (PDF). That is, we can compute a corrected probabilistic weather forecast, conditional on the current forecasts from our models. We propose to approximate such conditional probabilities using the assumed PDF method, which fits an assumed PDF functional form to reforecasts and observations. This a nonlinear method of weighting various forecasts, in contrast to the linear regression method that is often used.