HR: 0830h
AN: H11F-0908    [PDF]
TI: Expectation-Maximization Algorithm Based System Identification of Multiscale Stochastic Models for Scale Recursive Estimation of Precipitation: Application to Model Validation and Multisensor Data Fusion
AU: * Gupta, R
EM: gupt0087@umn.edu
AF: St. Anthony Falls Lab, University of Minnesota, Mississippi River at 3rd Ave SE, Minneapolis, MN 55414 United States
AU: Venugopal, V
EM: venu@macedonia.safl.umn.edu
AF: St. Anthony Falls Lab, University of Minnesota, Mississippi River at 3rd Ave SE, Minneapolis, MN 55414 United States
AU: Foufoula-Georgiou, E
EM: efi@umn.edu
AF: St. Anthony Falls Lab, University of Minnesota, Mississippi River at 3rd Ave SE, Minneapolis, MN 55414 United States
AB: Owing to the tremendous scale dependent variability of precipitation and discrepancies in scale or resolution among different types/sources of observations, comparing or merging observations at different scales, or validating Quantitative Precipitation Forecast (QPF) with observations is not trivial. Traditional methods of QPF (e.g., point to area) have been found deficient, and to alleviate some of the concerns, a new methodology called scale-recursive estimation (SRE) was introduced recently. This method, which has its root in Kalman filtering, can (i) handle disparate (in scale) measurement sources; (ii) account for observational uncertainty associated with each sensor; and (iii) incorporate a multiscale model (theoretical or empirical) which captures the observed scale-to-scale variability in precipitation. The result is an optimal (unbiased and minimum error variance) estimate at any desired scale along with its error statistics. Our preliminary studies have indicated that lognormal and bounded lognormal multiplicative cascades are the most successful candidates as state-propagation models for precipitation across a range of scales. However, the parameters of these models were found to be highly sensitive to the observed intermittency of precipitation fields. To address this problem, we have chosen to take a "system identification" approach instead of prescribing a priori the type of multiscale model. The first part of this work focuses on the use of Maximum Likelihood (ML) identification for estimating the parameters of a multiscale stochastic state space model directly from the given data. Expectation-Maximization (EM) algorithm is used to iteratively solve for ML estimates. The "expectation" step makes use of a Kalman smoother to estimate the state, while the "maximization" step re-estimates the parameters using these uncertain state estimates. Using high resolution forecast precipitation fields from ARPS (Advanced Regional Prediction System), concurrent rain gauge measurements and NEXRAD observations, the second part of this work presents the applicability and importance of the proposed approach towards QPF verification in an operational setting.
DE: 1854 Precipitation (3354)
DE: 3210 Modeling
DE: 3250 Fractals and multifractals
DE: 3260 Inverse theory
DE: 3337 Numerical modeling and data assimilation
SC: Hydrology [H]
MN: 2003 Fall Meeting