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Testing particle filters on simple convective‐scale models. Part 2: A modified shallow‐water model
Author(s) -
Haslehner Mylène,
Janjić Tijana,
Craig George C.
Publication year - 2016
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.2757
Subject(s) - data assimilation , particle filter , resampling , auxiliary particle filter , numerical weather prediction , ensemble kalman filter , mathematics , weighting , filter (signal processing) , meteorology , algorithm , computer science , statistics , kalman filter , extended kalman filter , physics , acoustics , computer vision
The nonlinearities and stochastic features of atmospheric dynamics pose severe challenges for data assimilation. The particle filter is a method that can potentially address these challenges and has attracted significant interest for convective‐scale applications. Unlike data assimilation techniques used in current numerical weather prediction (NWP), the particle filter does not presuppose Gaussian error statistics but estimates the full probability density function (PDF) with a small number of state vectors (particles). The nudging proposal particle filter operates as a hybrid combination of nudging and sequential importance resampling (SIR). In this article, we investigate a refined nudging proposal particle filter algorithm, the equivalent‐weight particle filter, that combines the nudging proposal particle filter with weight equalization and thus permits an improved representation of the PDF. An idealized, nonlinear, one‐dimensional shallow‐water model is used as a testbed to show that the equivalent‐weight particle filter outperforms both nudging and SIR filters under certain conditions. The selection mechanism of particles during resampling and the effect of nudging on the weights are analyzed. With the help of analytical and experimental results, we identify a numerical quantity that determines whether the equivalent‐weight particle filter can outperform nudging alone and we derive a theoretical criterion for the equivalent‐weight particle filter to outperform nudging. Further, we investigate the effect of equalizing weights on the resampling and the statistical behaviour of the ensemble.