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Takemasa Miyoshi

Abstract

In ensemble Kalman filters, the underestimation of forecast error variance due to limited ensemble size and other sources of imperfection is commonly treated by empirical covariance inflation. To avoid manual optimization of multiplicative inflation parameters, previous studies proposed adaptive inflation approaches using observations. Anderson applied Bayesian estimation theory to the probability density function of inflation parameters. Alternatively, Li et al. used the innovation statistics of Desroziers et al. and applied a Kalman filter analysis update to the inflation parameters based on the Gaussian assumption. In this study, Li et al.’s Gaussian approach is advanced to include the variance of the estimated inflation as derived from the central limit theorem. It is shown that the Gaussian approach is an accurate approximation of Anderson’s general Bayesian approach. An advanced implementation of the Gaussian approach with the local ensemble transform Kalman filter is proposed, where the adaptive inflation parameters are computed simultaneously with the ensemble transform matrix at each grid point. The spatially and temporally varying adaptive inflation technique is implemented with the Lorenz 40-variable model and a low-resolution atmospheric general circulation model; numerical experiments show promising results both with and without model errors.

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Takemasa Miyoshi
and
Shozo Yamane

Abstract

A local ensemble transform Kalman filter (LETKF) is developed and assessed with the AGCM for the Earth Simulator at a T159 horizontal and 48-level vertical resolution (T159/L48), corresponding to a grid of 480 × 240 × 48. Following the description of the LETKF implementation, perfect model Observing Systems Simulation Experiments (OSSEs) with two kinds of observing networks and an experiment with real observations are performed. First, a regular observing network with approximately 1% observational coverage of the system dimension is applied to investigate computational efficiency and sensitivities with the ensemble size (up to 1000) and localization scale. A 10-member ensemble is large enough to prevent filter divergence. Using 20 or more members significantly stabilizes the filter, with the analysis errors less than half as large as the observation errors. There is nonnegligible dependence on the localization scale; tuning is suggested for a chosen ensemble size. The sensitivities of analysis accuracies and timing on the localization parameters are investigated systematically. A computational parallelizing ratio as large as 99.99% is achieved. Timing per analysis is less than 4 min on the Earth Simulator, peak performance of 64 GFlops per computational node, provided that the same number of nodes as the ensemble size is used, and the ensemble size is less than 80. In the other set of OSSEs, the ensemble size is fixed to 40, and the real observational errors and locations are adapted from the Japan Meteorological Agency’s (JMA’s) operational numerical weather prediction system. The analysis errors are as small as 0.5 hPa, 2.0 m s−1, and 1.0 K in major areas for sea level pressure, zonal and meridional winds, and temperature, respectively. Larger errors are observed in data-poor regions. The ensemble spreads capture the actual error structures, generally representing the observing network. However, the spreads are larger than the actual errors in the Southern Hemisphere; the opposite is true in the Tropics, which suggests the spatial dependence of the optimal covariance inflation. Finally, real observations are assimilated. The analysis fields look almost identical to the JMA operational analysis; 48-h forecast experiments initiated from the LETKF analysis, JMA operational analysis, and NCEP–NCAR reanalysis are performed, and the forecasts are compared with their own analyses. The 48-h forecast verifications suggest a similar level of accuracy when comparing LETKF to the operational systems. Overall, LETKF shows encouraging results in this study.

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Shigenori Otsuka
and
Takemasa Miyoshi

Abstract

Multimodel ensemble data assimilation may account for uncertainties of numerical models due to different dynamical cores and physics parameterizations. In the previous studies, the ensemble sizes for each model are prescribed subjectively, for example, uniformly distributed to each model. In this study, a Bayesian filter approach to a multimodel ensemble Kalman filter is adopted to objectively estimate the optimal combination of ensemble sizes for each model. An effective inflation method to make the discrete Bayesian filter work without converging to a single imperfect model was developed.

As a first step, the proposed approach was tested with the 40-variable Lorenz-96 model. Different values of the model parameter F are used to mimic the multimodel ensemble. The true F is first chosen to be , and the observations are generated by adding independent Gaussian noise to the true time series. When the multimodel ensemble consists of , 7, 8, 9, and 10, the Bayesian filter finds the true model and converges to quickly. When , 7, 9, and 10, the closest two models, and F = 9, are selected. When the true F has a periodic variation about with a time scale much longer than the observation frequency, the proposed system follows the temporal change, and the error becomes less than that of the time-invariant optimal combination. Sensitivities to several parameters in the proposed system were also investigated, and the system was found to show improvements in a wide range of parameters.

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Keiichi Kondo
and
Takemasa Miyoshi

Abstract

The ensemble Kalman filter (EnKF) with high-dimensional geophysical systems usually employs up to 100 ensemble members and requires covariance localization to reduce the sampling error in the forecast error covariance between distant locations. The authors’ previous work pioneered implementation of an EnKF with a large ensemble of up to 10 240 members, but this method required application of a relatively broad covariance localization to avoid memory overflow. This study modified the EnKF code to save memory and enabled for the first time the removal of completely covariance localization with an intermediate AGCM. Using the large sample size, this study aims to investigate the analysis and forecast accuracy, as well as the impact of covariance localization when the sampling error is small. A series of 60-day data assimilation cycle experiments with different localization scales are performed under the perfect model scenario to investigate the pure impact of covariance localization. The results show that the analysis and 7-day forecasts are much improved by removing covariance localization and that the long-range covariance between distant locations plays a key role. The eigenvectors of the background error covariance matrix based on the 10 240 ensemble members are explicitly computed and reveal long-range structures.

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Koji Terasaki
and
Takemasa Miyoshi

Abstract

Densely observed remote sensing data such as radars and satellites generally contain significant spatial error correlations. In data assimilation, the observation error covariance matrix is usually assumed to be diagonal, and the dense data are thinned or spatially averaged to compensate for neglecting the spatial observation error correlation. However, in theory, including the spatial observation error correlation in data assimilation can make better use of the dense data. This study performs perfect model observing system simulation experiments (OSSEs) using the nonhydrostatic icosahedral atmospheric model (NICAM) and the local ensemble transform Kalman filter (LETKF) to assess the impact of assimilating horizontally dense and error-correlated observations. The condition number of the observation error covariance matrix, defined as the ratio of the largest to smallest eigenvalues, is important for the numerical stability of the LETKF computation. A large condition number makes it difficult to compute the ensemble transform matrix correctly. Reducing the condition number by reconditioning is found effective for stable computation. The results show that including the horizontal observation error correlation with reconditioning makes the analysis more accurate but requires 6 times more computations than the case with the diagonal observation error covariance matrix.

Significance Statement

It is important to effectively utilize observations in data assimilation for more accurate weather prediction. Spatially dense observations are known to have an error correlation that is ignored in the data assimilation. This study explores assimilating dense observations by explicitly including observation error correlations with an idealized experiment. The results shows that the analysis is improved by including the observation error correlations. Also, the condition number of the observation error covariance matrix is essential for stable computations.

Open access
Masaru Kunii
and
Takemasa Miyoshi

Abstract

Sea surface temperature (SST) plays an important role in tropical cyclone (TC) life cycle evolution, but often the uncertainties in SST estimates are not considered in the ensemble Kalman filter (EnKF). The lack of uncertainties in SST generally results in the lack of ensemble spread in the atmospheric states near the sea surface, particularly for temperature and moisture. In this study, the uncertainties of SST are included by adding ensemble perturbations to the SST field, and the impact of the SST perturbations is investigated using the local ensemble transform Kalman filter (LETKF) with the Weather Research and Forecasting Model (WRF) in the case of Typhoon Sinlaku (2008). In addition to the experiment with the perturbed SST, another experiment with manually inflated ensemble perturbations near the sea surface is performed for comparison. The results indicate that the SST perturbations within EnKF generally improve analyses and their subsequent forecasts, although manually inflating the ensemble spread instead of perturbing SST does not help. Investigations of the ensemble-based forecast error covariance indicate larger scales for low-level temperature and moisture from the SST perturbations, although manual inflation of ensemble spread does not produce such structural effects on the forecast error covariance. This study suggests the importance of considering SST perturbations within ensemble-based data assimilation and promotes further studies with more sophisticated methods of perturbing SST fields such as using a fully coupled atmosphere–ocean model.

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Takumi Honda
,
Yousuke Sato
, and
Takemasa Miyoshi

Abstract

Lightning flash observations are closely associated with the development of convective clouds and have a potential for convective-scale data assimilation with high-resolution numerical weather prediction models. A main challenge with the ensemble Kalman filter (EnKF) is that no ensemble members have nonzero lightning flashes in the places where a lightning flash is observed. In this situation, different model states provide all zero lightning, and the EnKF cannot assimilate the nonzero lightning data effectively. This problem is known as the zero-gradient issue. This study addresses the zero-gradient issue by adding regression-based ensemble perturbations derived from a statistical relationship between simulated lightning and atmospheric variables in the whole computational domain. Regression-based ensemble perturbations are applied if the number of ensemble members with nonzero lightning flashes is smaller than a prescribed threshold (N min). Observing system simulation experiments for a heavy precipitation event in Japan show that regression-based ensemble perturbations increase the ensemble spread and successfully induce the analysis increments associated with convection even if only a few members have nonzero lightning flashes. Furthermore, applying regression-based ensemble perturbations improves the forecast accuracy of precipitation although the improvement is sensitive to the choice of N min.

Significance Statement

This study develops an effective method to use lightning flash observations for weather prediction. Lightning flash observations include precious information of the inner structure of clouds, but their effective use for weather prediction is not straightforward since a weather prediction model often misses observed lightning flashes. Our new method uses ensemble-generated statistical relationships to compensate for the misses and successfully improves the forecast accuracy of heavy rains in a simulated case. Our future work will test the method with real observation data.

Open access
Takemasa Miyoshi
,
Yoshiaki Sato
, and
Takashi Kadowaki

Abstract

The local ensemble transform Kalman filter (LETKF) is implemented and assessed with the experimental operational system at the Japanese Meteorological Agency (JMA). This paper describes the details of the LETKF system and verification of deterministic forecast skill. JMA has been operating a four-dimensional variational data assimilation (4D-Var) system for global numerical weather prediction since 2005. The main purpose of this study is to make a reasonable comparison between the LETKF and the operational 4D-Var.

Several forecast–analysis cycle experiments are performed to find sensitivity to the parameters of the LETKF. The difference between additive and multiplicative error covariance inflation schemes is investigated. Moreover, an adaptive bias correction method for satellite radiance observations is proposed and implemented, so that the LETKF is equipped with functionality similar to the variational bias correction used in the operational 4D-Var. Finally, the LETKF is compared with the operational 4D-Var. Although forecast verification scores of the two systems relative to each system’s own analyses and to radiosonde observations show some disagreement, the overall conclusion indicates that the LETKF and 4D-Var have essentially comparable performance. The LETKF shows larger temperature bias in the lower troposphere mainly over the ocean, which is related to a well-known JMA model bias that plays an important role in the significant degradation of the forecast scores in the SH. The LETKF suffers less of a performance degradation than 4D-Var in the absence of satellite radiance assimilation. This suggests that better treatment of satellite radiances would be important in future developments toward operational use of the LETKF. Developing both LETKF and 4D-Var at JMA has shown significant benefits by the synergistic effect and is the recommended strategy for the moment.

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Masaru Kunii
,
Takemasa Miyoshi
, and
Eugenia Kalnay

Abstract

The ensemble sensitivity method of Liu and Kalnay estimates the impact of observations on forecasts without observing system experiments (OSEs), in a manner similar to the adjoint sensitivity method of Langland and Baker but without using an adjoint model. In this study, the ensemble sensitivity method is implemented with the local ensemble transform Kalman filter (LETKF) and the Weather Research and Forecasting (WRF) model with real observations. The results in the case of Typhoon Sinlaku (2008) show that upper-air soundings have the largest positive impact on the 12-h forecasts, and that the targeted impact evaluation performs as expected and is computationally efficient. Denying negative-impact observations improves the forecasts, validating the estimated observation impact.

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Shigenori Otsuka
,
Shunji Kotsuki
, and
Takemasa Miyoshi

Abstract

Space–time extrapolation is a key technique in precipitation nowcasting. Motions of patterns are estimated using two or more consecutive images, and the patterns are extrapolated in space and time to obtain their future patterns. Applying space–time extrapolation to satellite-based global precipitation data will provide valuable information for regions where ground-based precipitation nowcasts are not available. However, this technique is sensitive to the accuracy of the motion vectors, and over the past few decades, previous studies have investigated methods for obtaining reliable motion vectors such as variational techniques. In this paper, an alternative approach applying data assimilation to precipitation nowcasting is proposed. A prototype extrapolation system is implemented with the local ensemble transform Kalman filter and is tested with the Japan Aerospace Exploration Agency’s Global Satellite Mapping of Precipitation (GSMaP) product. Data assimilation successfully improved the global precipitation nowcasting with the real-case GSMaP data.

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