+ Post-processing of multimodel hydrological forecasts for the Baskatong catchment Fabian Tito Arandia Martinez Marie-Amélie Boucher Jocelyn Gaudet Maria-Helena Ramos
+ Context n Master degree subject: «Conception of an operational multimodel hydrologic ensemble forecasts system» n Partnership : IREQ (Hydro-Quebec Research Institute) n Goal: Compare the performance of ensemble hydrological forecasts produced with 3 state-of-the-art atmospheric models (EU, CAN, USA) to Hydro-Quebec analog type hydrological forecasts.
Atmospheric Model(s) Downscalling Streamflow Observations (if available) Meteorological Observations Spatial interpolation Under-captation correction Pre-processing Initial conditions Parameters Hydrological Model(s) HSAMI Ensemble forecasts (members) Decision making Management constraints Risk aversion Forecasts value Assimilation Post-processing Communication forecaster-user
+ Introduction n Raw forecasts are undispersive. n Sources of uncertainty: Meteorological model structure, initial conditions. n Does the multi-model approach performs well in an operational context? n Kernel-based post-processing and BMA n Sample: 2011 to 2013
+ Baskatong
+ Baskatong
+ Multi-model meteorological forecasts Country Institution Location Members Lead time Canada U.S.A Meteorological Service of Canada NOAA Climate Center Montreal 20 10 days 1 x1 Washington 20 10 days 1 x1 Resolution Europe ECMWF Reading 50 15 days 0.33 x0.33 As available in the TIGGE Database
+ Bias correction 2011-2012
+ Bias correction
+ Bias correction 2013
+ Best-member (Roulston and Smith, 2003) n «The basic idea is to dress each raw ensemble member with a probability distribution function (the kernel) defined by it s bandwitdth (spread) and next forming a mixture distribution by summing all the members» (Boucher et al., 2014) n Non-parametric methods n Do not require major calculation ressources
+ Best member method n Kernel based approach n Best member error: n Post-processed ensemble: n Compute the bandwidth based on the best member errors.
+ Weighted kernel dressing method (Fortin et al.) n Based on rank statistics n Store errors by rank statistics into a vector (2011-2012). n Weight each rank according to its frequency using a Beta distribution. n Weight and dress each member according to its rank (2013).
+ Regression method n Applied to bias-corrected forecasts n Simplified version of Gneiting et al. (2005) n Post processed members are drawn from a gaussian distribution n The parameters a, b, c and d are obtained by minimizing the CRPS
+ Bayesian Model Averaging (Raftery et al., 2003) n Competition among models (CMC, NOAA, ECMWF) n Atmospheric model uncertainty n Previously used with temperature and wind forecasts n Sliding window: 60 days n E-M Algorithm: weights and parameters of gamma distribution (Tolerance) Training dataset n Exchangeable members (Same weight for all members of a given model)
+ Bayesian Model Averaging p(y f 1, f 3 ) Model 1 σ 1 p(y f 1 ) f 1 w 1 f 1 + Σw k f k Model 2 σ 2 f 2 w 2 f 2 = Model 3 p(y f 2 ) + Multimodel Average σ 3 f 3 w 3 f 3 p(y f 3 ) Adapted from Woods, EGU 2006
+ Results Kernel Post-Processing (CAN)
+ Results Kernel Post-Processing (USA)
+ Results Kernel Post-Processing (EU)
+ Results BMA BSKG CRPS CRPS (m^3/s) 0 20 40 60 80 LEGEND ECMF CWAO KWBC GE BMA 2 4 6 8 Lead Time
+
+ Weights
+ Weights
+ Weights
+ Conclusion n Post-processing clearly improves the forecasts performance n BMA Weights: Why this variation on the weights? n Spread of the BMA: Problem with high flows n Find a common ground performance assessment metric for both analog based HQ forecasts and multi-model ensemble forecasts.
+ Questions
+ Modèle Hydrologique HSAMI n Modèle conceptuel et global à base de réservoirs linéaires. n Apport en eau au bassin versant: Ruissellement de surface, vidange de la réserve intermédiaire, vidange de la zone saturée. n Intrants du modèle : Température minimale, température maximale, pluie, neige, neige au sol (optionnel) (V. Fortin, 2000)
+ HSAMI: Modèles des apports améliorés Les paramètres calés seront fournis (23 paramètres à calibrer) Algorithme de simulation: Évaporation potentielle Précipitation directe au réservoir Interception pluie et neige Séparation eau en surface: infiltration et ruissellement de surface Écoulement eau vertical Écoulement horizontal Calcul de l apport naturel au réservoir Chauffe: variables d état stables (Historique depuis 1950) Source: Fortin, 2000
+ Performance d une prévision Source: Notes de cours 6MDI868 Sujets spéciaux en hydrologie 14/ 26
+ CRPS (Continous Ranked Probability Score) F i f (x) F i o (x) CRPS( forecast ) = 1 ncases ncases i=1 x= x= F f i (x) F o 2 ( i (x)) dx Probabilité de la Fonction de densité cumulative de la prévision D ensemble Probabilité de la Fonction de densité cumulative de la prévision De l observation. Source: Hamill Source: T. Gneiting, et A. E. Raftery, 2007 19/ 26