Abstract

Non-Gaussian probability density functions (PDFs) in convection initiation (CI) and development were investigated using a particle filter with a storm-scale numerical prediction model and an adaptive observation error estimator (NHM-RPF). An observing system simulation experiment (OSSE) was conducted with a 90-min assimilation period and 1000 particles at a 2-km grid spacing. Pseudosurface observations of potential temperature (PT), winds, water vapor (QV), and pseudoradar observations of rainwater (QR) in the lower troposphere were created in a nature run that simulated a well-developed cumulonimbus. The results of the OSSE (PF) show a significant improvement in comparison to ensemble simulations without any observations. The Gaussianity of the PDFs for PF in the CI area was evaluated using the Bayesian information criterion to compare goodness-of-fit of Gaussian, two-Gaussian mixture, and histogram models. The PDFs are strongly non-Gaussian when NHM-RPF produces diverse particles over the CI period. The non-Gaussian PDF of the updraft is followed by the upper-bounded PDF of the relative humidity, which produces non-Gaussian PDFs of QV and PT. The PDFs of the cloud water and QR are strongly non-Gaussian throughout the experimental period. We conclude that the non-Gaussianity of the CI originated from the non-Gaussianity of the updraft. In addition, we show that the adaptive observation error estimator significantly contributes to the stability of PF and the robustness to many observations.

Abstract

In sensitivity analysis, ensemble sensitivity is defined as the regression coefficients resulting from a simple linear regression of changes of a response function on initial perturbations. One of the interpretations for ensemble sensitivity considers this a simplified version of regression-based adjoint sensitivity called univariate ensemble sensitivity whose derivation involves the so-called diagonal approximation. This approximation, which replaces the analysis error covariance matrix by a diagonal matrix with the same diagonal, helps to avoid inversion of the analysis error covariance, but, at the same time causes confusion in understanding and practical application of ensemble sensitivity. However, some authors have challenged such a controversial interpretation by showing that univariate ensemble sensitivity is multivariate in nature, which raises the necessity for the foundation of ensemble sensitivity. In this study, we have tried to resolve the confusion by establishing a robust foundation for ensemble sensitivity without relying on the controversial diagonality assumption. As employed in some studies, we adopt an impact-based definition for ensemble sensitivity by taking into account probability distributions of analysis perturbations. The mathematical results show that standardized ensemble sensitivity carries in itself three important quantities at the same time: 1) standardized changes of the forecast response with one standard deviation changes of individual state variables, 2) correlations between the forecast response and individual state variables, and 3) the most sensitive analysis perturbation. The theory guarantees validity of ensemble sensitivity, demonstrates its multivariate nature, and explains why ensemble sensitivity is effective in practice.

Abstract

We investigated the effect of flow dependency in the assimilation of high-density, high-frequency observations. Radial winds from a Doppler radar are assimilated using a regional hybrid four-dimensional variational data assimilation (4D-Var) scheme with a flow-dependent background error covariance. To consistently assimilate 5 km × 5.625° cell-averaged radial winds at an interval of 10 min, the spatial and temporal correlations of the observation error are statistically diagnosed to be incorporated into the hybrid 4D-Var. The spatial correlation width is larger than that expected from instrument error, suggesting a contribution from representation error whose propagation is also considered to lead to temporal correlation, the width of which is diagnosed to increase with forecast time. The background error covariance also has an important role in incorporating observational information into the analysis. Single observation experiments show that the hybrid 4D-Var has more small-scale structure in its flow-dependent background error correlation than the 4D-Var limited from the climatological background error covariance mainly in the former part of the assimilation window. This suggests the higher potential of the hybrid 4D-Var to allow more higher-wavenumber components in the increment. A case study shows that the hybrid 4D-Var makes better use of the dense and frequent observations, reflecting more detailed representation of flow throughout the assimilation window, leading to promising results in the forecast. Sensitivity experiments also show that it is important to use the optimal observation error correlation. It is suggested that the flow-dependent background error becomes necessary to effectively use high-resolution, high-frequency observations.

Abstract

A cloud-resolving nonhydrostatic four-dimensional variational data assimilation system (NHM-4DVAR) was modified to directly assimilate radar reflectivity and applied to a data assimilation experiment using actual observations of a heavy rainfall event. Modifications included development of an adjoint model of the warm rain process, extension of control variables, and development of an observation operator for radar reflectivity.

The responses of the modified NHM-4DVAR were confirmed by single-observation assimilation experiments for an isolated deep convection, using pseudo-observations of rainwater at the initial and end times of the data assimilation window. The results showed that the intensity of convection could be adjusted by assimilating appropriate observations of rainwater near the convection and that undesirable convection could be suppressed by assimilating small or no reflectivity.

An assimilation experiment using actual observations of a local heavy rainfall in the Tokyo, Japan, metropolitan area was conducted with a horizontal resolution of 2 km. Precipitable water vapor derived from global positioning system data was assimilated at 5-min intervals within 30-min assimilation windows, and surface and wind profiler data were assimilated at 10-min intervals. Doppler radial wind and radar-reflectivity data below the elevation angle of 5.4° were assimilated at 1-min intervals.

The 4DVAR assimilation reproduced a line-shaped rainband with a shape and intensity consistent with the observation. Assimilation of radar-reflectivity data intensified the rainband and suppressed false convection. The simulated rainband lasted for 1 h in the extended forecast and then gradually decayed. Sustaining the low-level convergence produced by northerly winds in the western part of the rainband was key to prolonging the predictability of the convective system.

Abstract

The authors evaluated the effects of assimilating three-dimensional Doppler wind lidar (DWL) data on the forecast of the heavy rainfall event of 5 July 2010 in Japan, produced by an isolated mesoscale convective system (MCS) at a meso-gamma scale in a system consisting of only warm rain clouds. Several impact experiments using the nonhydrostatic four-dimensional variational data assimilation system (NHM-4DVAR) and the Japan Meteorological Agency nonhydrostatic model with a 2-km horizontal grid spacing were conducted in which 1) no observations were assimilated (NODA), 2) radar reflectivity and radial velocity determined by Doppler radar and precipitable water vapor determined by GPS satellite observations were assimilated (CTL), and 3) radial velocity determined by DWL were added to the CTL experiment (LDR) and five data denial and two observational error sensitivity experiments. Although both NODA and CTL simulated an MCS, only LDR captured the intensity, location, and horizontal scale of the observed MCS. Assimilating DWL data improved the wind direction and speed of low-level airflows, thus improving the accuracy of the simulated water vapor flux. The examination of the impacts of specific assimilations and assigned observation errors showed that assimilation of all data types is important for forecasting intense MCSs. The investigation of the MCS structure showed that large amounts of water vapor were supplied to the rainfall event by southerly flow. A midlevel inversion layer led to the production of exclusively liquid water particles in the MCS, and in combination with the humid airflow into the MCS, this inversion layer may be another important factor in its development.

Abstract

This paper discusses the benefits of using a hybrid ensemble Kalman filter and four-dimensional variational (4D-Var) data assimilation (DA) system rather than a 4D-Var system employing the National Meteorological Center (NMC, now known as NCEP) method (4D-Var-Bnmc) to predict severe weather events. An adjoint-based 4D-Var system was employed with a background error covariance matrix constructed from the NMC method and perturbations in a local ensemble transform Kalman filter system. The DA systems are based on the Japan Meteorological Agency’s nonhydrostatic model. To reduce the sampling noise, three types of implementation (the spatial localization, spectral localization, and neighboring ensemble approaches) were tested. The assimilation of a pseudosingle observation of sea level pressure located at a tropical cyclone (TC) center yielded analysis increments physically consistent with what is expected of a mature TC in the hybrid systems at the beginning of the assimilation window, whereas analogous experiments performed using the 4D-Var-Bnmc system did not. At the end, the structures of the 4D-Var-based increments became similar to one another, while the analysis increment by the 4D-Var-Bnmc system was broad in the horizontal direction. Realistic DA experiments showed that all of the hybrid systems provided initial conditions that yielded more accurate TC track and intensity forecasts than those achievable by the 4D-Var-Bnmc system. The hybrid systems also yielded some statistically significant improvements in forecasting local heavy rainfall events in terms of fraction skill scores when a 160 km × 160 km window size was used. The overall skills of the hybrid systems were relatively independent of the choice of implementation.