Brazilian Journal of Probability and Statistics

Spatio-temporal dynamic model and parallelized ensemble Kalman filter for precipitation data

Luis Sánchez, Saba Infante, Victor Griffin, and Demetrio Rey

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Abstract

This paper presents a spatiotemporal dynamic model which allows Bayesian inference of precipitation states in some Venezuelan meteorological stations. One of the limitations that are reported in digital databases is the reliability of the records and the lack of information for certain days, weeks, or months. To complete the missing data, the Gibbs algorithm, a Markov Chain Monte Carlo (MCMC) procedure, was used. A feature of precipitation series is that their distribution contains discrete and continuous components implying complicated dynamics. A model is proposed based on a discrete representation of a stochastic integro-difference equation. Given the difficulty of obtaining explicit analytical expressions for the predictive posterior distribution, approximations were obtained using a sequential Monte Carlo algorithm called the parallelized ensemble Kalman filter. The proposed method permits the completion of the missing data in the series where required and secondly allows the splitting of a large database into smaller ones for separate evaluation and eventual combination of the individual results. The objective is to reduce the dimension and computational cost in order to obtain models that are able to describe the reality in real time. It was shown that the obtained models are able to predict spatially and temporally the states of rainfall for at least three to four days quickly, efficiently and accurately. Three methods of statistical validation were used to evaluate the performance of the model and showed no significant discrepancies. Speedup and efficiency factors were calculated to compare the speed of calculation using the parallelized ensemble Kalman filter algorithm with the speed of the sequential version. The improvement in speed for four pthread executions was greatest.

Article information

Source
Braz. J. Probab. Stat., Volume 30, Number 4 (2016), 653-675.

Dates
Received: February 2014
Accepted: July 2015
First available in Project Euclid: 13 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1481619620

Digital Object Identifier
doi:10.1214/15-BJPS297

Mathematical Reviews number (MathSciNet)
MR3582393

Zentralblatt MATH identifier
1381.86027

Keywords
Precipitation modeling missing data spatio temporal models stochastic integro-difference equation parallelized ensemble Kalman filter

Citation

Sánchez, Luis; Infante, Saba; Griffin, Victor; Rey, Demetrio. Spatio-temporal dynamic model and parallelized ensemble Kalman filter for precipitation data. Braz. J. Probab. Stat. 30 (2016), no. 4, 653--675. doi:10.1214/15-BJPS297. https://projecteuclid.org/euclid.bjps/1481619620


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