On the prediction of persistent processes using the output of deterministic models

A problem frequently met in engineering hydrology is the forecasting of hydrological variables conditional on their historical observations and the hindcasts and forecasts of a deterministic model. On the contrary, it is a common practice for climatologists to use the output of general circulation models (GCMs) for the prediction of climatic variables despite their inability to quantify the uncertainty of the predictions. Here we apply the well-established Bayesian processor of forecasts (BPF) for forecasting hydroclimatic variables using stochastic models through coupling them with GCMs. We extend the BPF to cases where long-term persistence appears, using the Hurst-Kolmogorov process (HKp, also known as fractional Gaussian noise) and we investigate its properties analytically. We apply the framework to calculate the distributions of the mean annual temperature and precipitation stochastic processes for the time period 2016–2100 in the United States of America conditional on historical observations and the respective output of GCMs.