The proposed hybrid approach benefits from the predictability of an analog-year model based on teleconnection indices. We propose a Bayesian modelbased on copula functions to represent the joint distribution of teleconnectionindices and seasonal precipitation:

AHybridStatistical-DynamicalDroughtPredictionFrameworkAmirAghaKouchak1,S.Madadgar1,S.Shukla2,L.Cheng1,K.Hsu1,A.W.Wood3,MSvoboda4

(1) UniversityofCalifornia,Irvine,(2) UCSantaBarbara,(3) NationalCenterforAtmosphericResearch,(4) 5NationalDroughtMitigationCenter

ABSTRACTNumerous statistical and dynamical model simulations have been developed for predicting precipitation. However,both types of models offer limited seasonal predictability. This study outlines a hybrid statistical-dynamical modelingframework for predicting seasonal precipitation. The dynamical component relies on the physically based NorthAmerican Multi-Model Ensemble (NMME) model simulations (99 ensemble members). The statistical component relieson a multivariate Bayesian-based model that relates precipitation to atmosphere-ocean teleconnections (also known asan analog-year statistical model). Here, the Pacific Decadal Oscillation (PDO), Multivariate ENSO Index (MEI), andAtlantic Multi-decadal Oscillation (AMO) are used in the statistical component. The dynamical and statisticalpredictions are linked using the so-called Expert Advice algorithm, which offers an ensemble response (as analternative to the ensemble mean). The latter part leads to the best precipitation prediction based on contributingstatistical and dynamical ensembles. It combines the strength of physically based dynamical simulations and thecapability of an analog-year model. An application of the framework in the southwestern United States, which hassuffered from major droughts over the past decade, improves seasonal precipitation predictions (3- to 5-month leadtime) by 5-60 percent relative to the NMME simulations. Overall, the hybrid framework performs better in predictingnegative precipitation anomalies (10-60% improvement over NMME) than positive precipitation anomalies (5-25%improvement over NMME). The results indicate that the framework would likely improve our ability to predict droughtssuch as the 2012-2014 event in the western United States that resulted in significant socio-economic impacts.

CONCLUSIONS

Figure 1: Comparison between a) theobserved precipitation and b) the NMMEsimulation for the anomalies of theprecipitation rate from Dec, 2014 to Feb,2015. The forecast initial condition is set toOct, 2014.

Figure 4a: Precipitationanomaly (mm/day) duringthe rainy season of 2006-2007 with different leadtimes (NDJ, NDJF, NDJFM,DJF, DJFM, and JFM).Forecasts are initiated fromOctober of each year, i.e. IC =Oct. The observations (1stcol.), NMME forecasts (2ndcol.), statistical modelpredictions (3rd col.), andhybrid model predictions (4thcol.) are shown for the targetperiods of each year.

Results

Figure 6: The area [mi2] withthe observed negativeprecipitation anomaly (lightgray bars) correctly capturedby the NMME (dark graybars), statistical model(yellow bars), and hybridmodel (blue bars)simulations. The targetprediction periods start atNov, Dec, or Jan andcontinues up to the followingMarch.

The proposed hybrid method aims to improve drought prediction by combining these two fundamentally different seasonalprecipitation prediction methods. The hybrid model combines dynamical model forecasts from the NMME with Bayesian statisticalforecasts using teleconnections indices (PDO, MEI, and AMO). The hybrid model utilizes the EA algorithm to merge the dynamicalmodel forecasts and statistical model predictions. The results indicate that although the dynamical model simulations capture some ofthe recent droughts, they do not offer high predictability. The integration of the statistical and dynamical methods appears to improvethe prediction of seasonal precipitation in this case study. The predictability of seasonal precipitation increases by 5-60% after theapplication of hybrid model. Overall, the hybrid framework performs better in predicting below-normal precipitation than above-normal precipitation. We acknowledge that several issues such as the relatively short record, uncertainty in the observeddependencies, and model parameterization may have affected predictions of wet and drought anomalies. More efforts and evaluationsof the proposedmodel are required before this model can be used in water resourcesmanagement.Reference: Madadgar S., AghaKouchak A., Shukla S., Wood A.W., Cheng L., Hsu K., Svoboda M., 2016, A Hybrid Statistical-Dynamical Framework forMeteorological Drought Prediction: Application to the Southwestern United States, Water Resources Research, in press.

Methodology

Figure 4b: Similar to Figure4a but for the rainy season of2006-2007.

Figure 2: Flowchart of the proposedhybrid statistical-dynamical precipitationforecasting algorithm.

Figure 3: The flowchart (a) andschematic view (b) of the ExpertAdvice (EA) algorithm.

(a)2006-2007– DryYear (b)2014-2015– DryYear

mm/day

Figure 5: Comparing theperformance of the hybridmodel and the dynamicaland statistical models incapturing positive anomaliesduring the rainy season of2010-2011.

𝑃 𝑥#,… , 𝑥&,… , 𝑥' = 𝐶 𝑃 𝑥# ,… ,𝑃 𝑥& ,… , 𝑃 𝑥' = 𝐶 𝑢#,… , 𝑢&, … , 𝑢'

where, 𝐶 is the Cumulative Distribution Function(CDF) of the copula, and 𝑃 𝑥& is the marginaldistribution of 𝑥& being uniform on the interval0, 1 , which is also denoted by 𝑢&. We use theconditional probability distribution function basedon copulas to estimate the predictive distributionof precipitation given the joint status of theteleconnection indices𝑝 𝑥#|𝑥0… , 𝑥' =

𝑐 𝑢#,… , 𝑢' ∏ 𝑝 𝑥&'&3#

𝑐 𝑢0,… , 𝑢' ∏ 𝑝 𝑥&'&30

where, 𝑝 𝑥#|𝑥0 … , 𝑥' is the conditionaldistribution of the random variable 𝑥# given theset (𝑥0 … , 𝑥') of random variables; 𝑐 𝑢#, … , 𝑢'is the PDF of the continuous copula function; and𝑝 𝑥& is the PDF of 𝑖78 random variable. Theconditional probability of bivariate and trivariatecases are expressed as follows:𝑝 𝑥#|𝑥0 = 𝑐 𝑢#,𝑢0 .𝑝 𝑥#

𝑝 𝑥#|𝑥0,𝑥: = 𝑐 𝑢#,𝑢0,𝑢: .𝑝 𝑥#

𝑐 𝑢0,𝑢:

We estimate the conditional probability ofprecipitation at each grid cell in the study area(denoted by 𝑥#) given multiple teleconnectionindices such as PDO, MEI, and AMO (denoted by𝑥0 and 𝑥: ) that have been observed in theprecedingmonths/seasons.