Forecast Calibration and Combination: A Simple Bayesian Approach for ENSO

Abstract

This study presents a new simple approach for combining empirical with raw (i.e., not bias corrected) coupled model ensemble forecasts in order to make more skillful interval forecasts of ENSO. A Bayesian normal model has been used to combine empirical and raw coupled model December SST Nifio-3.4 index forecasts started at the end of the preceding July (5-month lead time). The empirical forecasts were obtained by linear regression between December and the preceding July Nino-3.4 index values over the period 1950-2001. Coupled model ensemble forecasts for the period 1987-99 were provided by ECMWF, as part of the Development of a European Multimodel Ensemble System for Seasonal to Interannual Prediction (DEMETER) project. Empirical and raw coupled model ensemble forecasts alone have similar mean absolute error forecast skill score, compared to climatological forecasts, of around 50% over the period 1987-99. The combined forecast gives an increased skill score of 74% and provides a well-calibrated and reliable estimate of forecast uncertainty.

An analysis of the seasonal precipitation forecasts in South America using wavelets

“…It is apparent that the forecast skill improvements are more pronounced for areas where rainfall variations are more closely related to the ENSO teleconnections. This confirms previous findings on the rainfall simulations over SA obtained with the Bayesian approach (Coelho et al, 2004(Coelho et al, , 2006. We are aware that our super-ensemble model is not ideal, since only one model with three different physical parameterizations is used.…”

“…The Bayesian approach is another technique used to combine numerical forecasts with the historical observed data (Coelho et al, 2004(Coelho et al, , 2006. This method, based on statistical probability theory, combines dynamical forecast with historical observations and produces categorical and probabilistic forecasts.…”

“…Overall, the forecasts generated by the MMS technique (Krishnamurti et al, 2000a(Krishnamurti et al, ,b, 2001Chaves et al, 2005a,b) or Bayesian approach (Coelho et al, 2004(Coelho et al, , 2006 to combine and correct forecast have shown better skills than the forecast generated either by individual models or the arithmetic average of the ensembles (each with weight 1). This latter approach has been largely used to produce seasonal forecasts in many operational centres, including the Centro de Previsão de Tempo e Estudos Climáticos (CPTEC).…”

Weighting of NMME temperature and precipitation forecasts across Europe

“…Bayesian approaches were successfully introduced as part of the DEMETER project to enhance sea surface temperature and precipitation forecasts (Coelho 2004;Luo et al, 2007). 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).…”

“…Various approaches can be used to post-process ensemble forecasts based on their historical performance (e.g., Krishnamurti et al, 1999;Rajagopalan et al, 2002;Scheuerer and Büermann, 2014), but Bayesian schemes have gained increasing attention in recent years (e.g., Coelho et al 2004;Hodyss et al, 2016) as they generally improve the sharpness of the forecasts and can be updated as new information becomes available. 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.…”