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  • Author or Editor: Kenta Kurosawa x
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Kenta Kurosawa
and
Jonathan Poterjoy

Abstract

The ensemble Kalman filter (EnKF) and the 4D variational method (4DVar) are the most commonly used filters and smoothers in atmospheric science. These methods typically approximate prior densities using a Gaussian and solve a linear system of equations for the posterior mean and covariance. Therefore, strongly nonlinear model dynamics and measurement operators can lead to bias in posterior estimates. To improve the performance in nonlinear regimes, minimization of the 4DVar cost function typically follows multiple sets of iterations, known as an “outer loop,” which helps reduce bias caused by linear assumptions. Alternatively, “iterative ensemble methods” follow a similar strategy of periodically relinearizing model and measurement operators. These methods come with different, possibly more appropriate, assumptions for drawing samples from the posterior density, but have seen little attention in numerical weather prediction (NWP) communities. Last, particle filters (PFs) present a purely Bayesian filtering approach for state estimation, which avoids many of the assumptions made by the above methods. Several strategies for applying localized PFs for NWP have been proposed very recently. The current study investigates intrinsic limitations of current data assimilation methodology for applications that require nonlinear measurement operators. In doing so, it targets a specific problem that is relevant to the assimilation of remotely sensed measurements, such as radar reflectivity and all-sky radiances, which pose challenges for Gaussian-based data assimilation systems. This comparison includes multiple data assimilation approaches designed recently for nonlinear/non-Gaussian applications, as well as those currently used for NWP.

Free access
Kenta Kurosawa
and
Jonathan Poterjoy

Abstract

Particle filters avoid parametric estimates for Bayesian posterior densities, which alleviates Gaussian assumptions in nonlinear regimes. These methods, however, are more sensitive to sampling errors than Gaussian-based techniques such as ensemble Kalman filters. A recent study by the authors introduced an iterative strategy for particle filters that match posterior moments—where iterations improve the filter’s ability to draw samples from non-Gaussian posterior densities. The iterations follow from a factorization of particle weights, providing a natural framework for combining particle filters with alternative filters to mitigate the impact of sampling errors. The current study introduces a novel approach to forming an adaptive hybrid data assimilation methodology, exploiting the theoretical strengths of nonparametric and parametric filters. At each data assimilation cycle, the iterative particle filter performs a sequence of updates while the prior sample distribution is non-Gaussian, then an ensemble Kalman filter provides the final adjustment when Gaussian distributions for marginal quantities are detected. The method employs the Shapiro–Wilk test to determine when to make the transition between filter algorithms, which has outstanding power for detecting departures from normality. Experiments using low-dimensional models demonstrate that the approach has a significant value, especially for nonhomogeneous observation networks and unknown model process errors. Moreover, hybrid factors are extended to consider marginals of more than one collocated variables using a test for multivariate normality. Findings from this study motivate the use of the proposed method for geophysical problems characterized by diverse observation networks and various dynamic instabilities, such as numerical weather prediction models.

Significance Statement

Data assimilation statistically processes observation errors and model forecast errors to provide optimal initial conditions for the forecast, playing a critical role in numerical weather forecasting. The ensemble Kalman filter, which has been widely adopted and developed in many operational centers, assumes Gaussianity of the prior distribution and solves a linear system of equations, leading to bias in strong nonlinear regimes. On the other hand, particle filters avoid many of those assumptions but are sensitive to sampling errors and are computationally expensive. We propose an adaptive hybrid strategy that combines their advantages and minimizes the disadvantages of the two methods. The hybrid particle filter–ensemble Kalman filter is achieved with the Shapiro–Wilk test to detect the Gaussianity of the ensemble members and determine the timing of the transition between these filter updates. Demonstrations in this study show that the proposed method is advantageous when observations are heterogeneous and when the model has an unknown bias. Furthermore, by extending the statistical hypothesis test to the test for multivariate normality, we consider marginals of more than one collocated variable. These results encourage further testing for real geophysical problems characterized by various dynamic instabilities, such as real numerical weather prediction models.

Restricted access
Shunji Kotsuki
,
Kenta Kurosawa
,
Shigenori Otsuka
,
Koji Terasaki
, and
Takemasa Miyoshi

Abstract

Over the past few decades, precipitation forecasts by numerical weather prediction (NWP) models have been remarkably improved. Yet, precipitation nowcasting based on spatiotemporal extrapolation tends to provide a better precipitation forecast at shorter lead times with much less computation. Therefore, merging the precipitation forecasts from the NWP and extrapolation systems would be a viable approach to quantitative precipitation forecast (QPF). Although the optimal weights between the NWP and extrapolation systems are usually defined as a global constant, the weights would vary in space, particularly for global QPF. This study proposes a method to find the optimal weights at each location using the local threat score (LTS), a spatially localized version of the threat score. We test the locally optimal weighting with a global NWP system composed of the local ensemble transform Kalman filter and the Nonhydrostatic Icosahedral Atmospheric Model (NICAM-LETKF). For the extrapolation system, the RIKEN’s global precipitation nowcasting system called GSMaP_RNC is used. GSMaP_RNC extrapolates precipitation patterns from the Japan Aerospace Exploration Agency (JAXA)’s Global Satellite Mapping of Precipitation (GSMaP). The benefit of merging in global precipitation forecast lasts longer compared to regional precipitation forecast. The results show that the locally optimal weighting is beneficial.

Open access