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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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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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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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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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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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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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Shu-Chih Yang, Eugenia Kalnay, and Takemasa Miyoshi

Abstract

A mesoscale ensemble Kalman filter (EnKF) for a regional model is often initialized from global analysis products and with initial ensemble perturbations constructed based on the background error covariance used in the three-dimensional variational data assimilation (3DVar) system. Because of the lack of proper mesoscale information, a long spinup period of typically a few days is required for the regional EnKF to reach its asymptotic level of accuracy, and thus, the impact of observations is limited during the EnKF spinup. For the case of typhoon assimilation, such spinup usually corresponds to the stages of generation and development of tropical cyclones, when observations are important but limited over open waters. To improve the analysis quality during the spinup, the “running in place” (RIP) method is implemented within the framework of the local ensemble transform Kalman filter (LETKF) coupled with the Weather Research and Forecasting model (WRF). Results from observing system simulation experiments (OSSEs) for a specific typhoon show that the RIP method is able to accelerate the analysis adjustment of the dynamical structures of the typhoon during the LETKF spinup, and improves both the accuracy of the mean state and the structure of the ensemble-based error covariance. These advantages of the RIP method are found not only in the inner-core structure of the typhoon but also identified in the environmental conditions. As a result, the LETKF-RIP analysis leads to better typhoon prediction, particularly in terms of both track and intensity.

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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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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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Guo-Yuan Lien, Takemasa Miyoshi, and Eugenia Kalnay

Abstract

Current methods of assimilation of precipitation into numerical weather prediction models are able to make the model precipitation become similar to the observed precipitation during the assimilation, but the model forecasts tend to return to their original solution after a few hours. To facilitate the precipitation assimilation, a logarithm transformation has been used in several past studies. Lien et al. proposed instead to assimilate precipitation using the local ensemble transform Kalman filter (LETKF) with a Gaussian transformation technique and succeeded in improving the model forecasts in perfect-model observing system simulation experiments (OSSEs).

In this study, the method of Lien et al. is tested within a more realistic configuration: the TRMM Multisatellite Precipitation Analysis (TMPA) data are assimilated into a low-resolution version of the NCEP Global Forecast System (GFS). With guidance from a statistical study comparing the GFS model background precipitation and the TMPA data, some modifications of the assimilation methods proposed in Lien et al. are made, including 1) applying separate Gaussian transformations to model and to observational precipitation based on their own cumulative distribution functions; 2) adopting a quality control criterion based on the correlation between the long-term model and observed precipitation data at the observation location; and 3) proposing a new method to define the transformation of zero precipitation that takes into account the zero precipitation probability in the background ensemble rather than the climatology. With these modifications, the assimilation of the TMPA precipitation data improves both the analysis and 5-day model forecasts when compared with a control experiment assimilating only rawinsonde data.

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