Generation of Precipitation Ensemble Forecasts from Single-Value

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					Generation of Precipitation Ensemble Forecasts from Single-Value SingleQPF via Mixed-Type Meta-Gaussian Model MixedMetaUCAR
2

L. Wu1,3, D.-J. Seo1,2, J. Demargne1,2, and J.D. Brown1,2
Weather Service, Office of Hydrologic Development, University Corporation for Atmospheric Research, 3 Wyle Information Systems Contact: limin.wu@noaa.gov
1 NOAA/National

Motivation
Reliable and skillful precipitation ensemble forecasts are necessary for hydrologic ensemble forecasting. Precipitation ensemble forecasts produced by the Numerical Weather Prediction forecast models tend to be biased in the mean and, more so, in the spread (Hamill et al. 2007). Short-range single-value Quantitative Precipitation Forecasts (QPF) issued by forecasters at the NOAA/National Weather Service River Forecast Centers (RFCs) tend to be more skillful in the mean sense. A technique has been developed (Schaake et al. 2007) to capture the skill in the single-value QPF and prescribe reliable uncertainty spread based on historical data. The work presented here attempts to improve the quality of such single-value QPF-based precipitation ensemble forecasts by: 1) explicit modeling of precipitation intermittency, 2) nonparametric modeling of marginal distribution of precipitation, and 3) reducing conditional bias through an optimization scheme.

Approach
•Model the bivariate probability distribution between the single-value QPF and the verifying observation from historical data using the mixed-type meta-Gaussian distribution (Herr and Krzysztofowicz 2005). Sample ensemble members from the probability distribution of observed precipitation conditional on the single-value forecast. Meta-Gaussian model Ensemble Generation

Mix-type meta-Gaussian model
•Precipitation accumulation over short duration is a discretecontinuous variable. Therefore, normal quantile transformation (NQT), used in modeling of bivariate distribution of precipitation in Schaake et al. (2007), is not directly applicable. •Decompose the conditional distribution: P(Y ≤ y | X = x) = a + (1 - a)•P(Y ≤ y | X = x, Y > 0) where a=P(Y=0|X=x) •Recognize that P(Y ≤ y | X = x, Y > 0) can be expressed in terms of P(X ≤ x, Y ≤ y | X > 0, Y > 0), which can be modeled by meta-Gaussian distribution (Kelly and Krzysztofowicz, 1997) via NQT.
Y

Joint distribution
Sample Space
NQT

Joint distribution
Y

Conditional distribution given xfcst
1

Model Space

Observed

Observed

Correlation(X,Y) X 0

Joint distribution
Y

Model Space

Forecast Observed

xfcst

X

Forecast

PDF of Forecast

PDF of STD Normal

Probability

x1 … xn

Ensemble members

0

x1 xi

xn

Ensemble forecast
NQT X

Forecast

Obtain conditional distribution given a single-value forecast

xfcst

Applying “Schaake Shuffle” (Clark et al. 2004) to the ensembles replicates (in the rank correlation sense) space-time variability and co-variability that historical ensembles exhibit.

Nonparametric modeling of marginal distribution
•Probability distribution of precipitation (observed mean areal, singlevalue QPF) varies depending on season, region, time scale of aggregation, etc. •Difficult to model well, particularly the all important upper tail, with a limited choice of parametric models alone (Weibull, etc.) •Use kernel-based nonparametric models with bandwidth selection based on sensitivity analysis •We find that this improves the overall quality of precipitation ensembles.

Parameter optimization
•Once transformed by applying NQT, single-value QPF and verifying observation are assumed to be bivariate normal: E[Y|X=x]=ρ•x Var[Y|X=x]=1-ρ2 •However, this assumption may not always hold in applications, resulting in biases in the ensembles. •In this work: Model Y=b•X+ε Optimize b using performance criteria in the original space In general, we observe b > ρ •We find that this improves resolution, but not necessarily reliability.

Validation results
Below are the results of a selected test basin (TIFM7) from the Arkansas-Red Basin River Forecast Center. Results are for 6-hourly precipitation ensembles, aggregated over 24 hours for forecast lead day 1. The validation period is 07/01/2003-06/30/2008.

Validation procedures
•Dependent validation: 1) Estimate model parameters using all the available N-yr data. 2) Generate N-yr hindcasts and verify them •Independent validation: 1) Split the N-yr data into (N-1) years for model parameter estimation and 1 year for hindcasting and verification. 2) Repeat until all such combinations are exhausted. 3) Verify the union of all 1-year ensemble hindcasts against the corresponding observations. Independent validation provides approximate performance envelope that may be expected in the mean sense for the next year or so if one uses all the available data for parameter estimation today.
Test basin TIFM7

Reliability Diagram

Relative Operating Characteristic

Dependent validation

Independent validation

Dependent validation

Independent validation

Conclusions and future work
•The dependent validation results indicate that the technique is capable of generating reliable precipitation ensembles that capture the skill in the singlevalue QPF. •The independent validation results indicate that performance close to that in dependent validation is attained for smaller event thresholds, though difficult to be confident due to limited sample size. Reduction in both reliability and resolution is noticeable for large precipitation amount (event threshold > 1.0 (in)). •Carry out large-sample independent verification using the GFS reforecast data set to assess sensitivity of performance to the size of historical data. •Carry out comparative evaluation with post-processed operational GEFS forecast (with Middle Atlantic River forecast Center and NCEP).

•Complete implementation of the techniques presented here into the Hydrologic Ensemble Forecast System developed by the NOAA/NWS Office of Hydrologic Development. The HEFS is developed within the Community Hydrologic Prediction System, which is based on service-oriented architecture.
REFERENCES Hamill, T.M., Hagedorn, R., Whitaker, J.S., 2007. Probability forcast calibration using ECMWF and GFS ensemble reforecasts. Part II: Precipitation. Monthly Weather Review 136, 2620-2632. Herr, H.D., Krzysztofowicz, R., 2005. Generic probability distribution of rainfall in space: the bivariate model. Journal of Hydrology 306, 234–263. Kelly, K.S., Krzysztofowicz, R., 1997. A bivariate meta-Gaussian density for use in hydrology. Statistic Hydrology and hydraulics 11, 17–31. Schaake J.C., J. Demargne, M. Mullusky, E. Welles, L. Wu, H. Herr, X. Fan, and D.J. Seo, 2006: Precipitation and temperature short-term ensemble forecasts from existing operational single-value forecasts, HESSD, Special Issue “Hydrological Prediction Uncertainty”.