A Simple Bayesian Climate Index Weighting Method for Seasonal Ensemble Forecasting

Climate information — in the form of a measure of climate state or a climate forecast — can be an important predictor of future hydrologic conditions. For instance, streamflow variability for many locations around the globe is related to large-scale atmospheric oscillations, like the El Nino Southern Oscillation (ENSO) or the Pacific/Decadal Oscillation (PDO). Furthermore, climate forecast models are growing more skillful in their predictions of future climate variables on seasonal time scales. Finding effective ways to translate this climate information into improved hydrometeorological predictions is an area of ongoing research. In ensemble streamflow forecasting, where historical weather inputs or streamflow observations are used to generate the ensemble, climate index weighting is one way to represent the influence of current climate information. Using a climate index, each forecast variable member of the ensemble is selectively weighted to reflect climate conditions at the time of the forecast.

A simple Bayesian climate index weighting of ensemble forecasts is presented. The original hydrologic ensemble members define a sample of the prior distribution; the relationship between the climate index and the ensemble member forecast variable is used to estimate a likelihood function. Given an observation of the climate index at the time of the forecast, the estimated likelihood function is then used to assign weights to each ensemble member. The weighted ensemble forecast is then used to estimate the posterior distribution of the forecast variable conditioned on the climate index. The proposed approach has several advantages over traditional climate index weighting methods. The weights assigned to the ensemble members accomplish the updating of the (prior) ensemble forecast distribution based on Bayes’ Theorem, so the method is theoretically sound. The method also automatically adapts to the strength of the relationship between the climate index and the forecast variable, defaulting to equal weighting of ensemble members when no relationship exists. Furthermore, unlike more traditional climate index weighting methods, it does not require hindcast calibration to assign optimal weights, so it can be applied to existing ensemble forecasting system.