Climate index weighting of ensemble streamflow forecasts using a simple Bayesian approach

Abstract

Climate state can be an important predictor of future hydrologic conditions. 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 climate state. Using a climate index, each forecast variable member of the ensemble is selectively weighted to reflect the climate state at the time of the forecast. A new approach to climate index weighting of ensemble forecasts is presented. The method is based on a sampling-resampling approach for Bayesian updating. The original hydrologic ensemble members define a sample drawn from 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 weights define the probability of each ensemble member outcome given the observed climate index. The weighted ensemble forecast is then used to estimate the posterior distribution of the forecast variable conditioned on the climate index. The Bayesian climate index weighting approach is easy to apply to hydrologic ensemble forecasts; its parameters do not require calibration with hindcasts, and it adapts to the strength of the relation between climate and the forecast variable, defaulting to equal weighting of ensemble members when no relationship exists. A hydrologic forecasting application illustrates the approach and contrasts it with traditional climate index weighting approaches.

Weighting of NMME temperature and precipitation forecasts across Europe

“…In hydrologic forecasting, Bayesian merging has been used to develop a multimodel seasonal hydrologic ensemble prediction system (Luo and Wood, 2008), to obtain probabilistic streamflow forecasts (Wang et al, 2013), or to weight the forecasts using a climate index such as the El Niño-Southern Oscillation or Pacific Decadal Oscillation (Bradley et al, 2015). However,…”

“…Assuming that the single-model forecasts are independent (Luo et al 2007), the multi-model weight * i w is the product of the eight model weights for each observation y i in the historical sample, normalized to produce a set of multi-model weights that sum to 1 (Bradley et al 2015) ( ) …”

“…For example, Madadgar et al (2016) developed a multivariate Bayesian model based on copula functions to predict drought as a function of atmosphere-ocean teleconnections and showed that the multi-model Bayesian forecasts performed considerably better than the initial NMME forecasts. In BU, each individual forecast adjusts the prior probability of the forecast variable, defined by the sample climatology of historical observations (Bradley et al, 2015). By expressing the observed values of the historic record in terms of their likelihood, given the forecasts made by each model, Bayesian approaches take full advantage of the historical record length.…”

An intercomparison of approaches for improving operational seasonal streamflow forecasts

“…Our ability to leverage the second source (climate predictability) depends both on how well we can characterize and predict the state of the climate and on how effectively we can incorporate this information into streamflow forecasting methods. This idea has been explored in different frameworks using standard indices, e.g., Niño3.4, the Pacific Decadal Oscillation (PDO), and/or custom (i.e., watershed-specific) climate indices derived from climate reanalyses (e.g., Grantz et al, 2005;Bradley et al, 2015), or using seasonal climate forecasts to run hydrologic model simulations (e.g., Wood et al, 2005;Yuan et al, 2013).…”

“…One line of research has examined the potential benefits of using simulated watershed state variables -either from hydrologic or land surface modelsas predictors for statistical models (e.g., Rosenberg et al, 2011;Robertson et al, 2013). Another popular technique consists of incorporating climate information within ESP frameworks, either deriving input sequences of mean areal precipitation and temperature from current climate or climate forecast considerations (e.g., Werner et al, 2004;Wood and Lettenmaier, 2006;Luo and Wood, 2008;Gobena and Gan, 2010;Yuan et al, 2013) -referred to as pre-ESP -or ESP weighting (also referred to as post-ESP) based on climate information (e.g., Smith et al, 1992;Werner et al, 2004;Najafi et al, 2012;Bradley et al, 2015). Werner et al (2004) found that the post-ESP method (termed "trace weighting") was more effective than pre-ESP for improving forecast skill.…”