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Chengsi Liu, Ming Xue, and Rong Kong

Abstract

Despite the well-known importance of background error covariance in data assimilation, not much study has been focused on its impact on the assimilation of radar reflectivity within a three-dimensional variational (3DVar) framework. In this study, it is shown that unphysical analysis increments of hydrometeors are produced when using vertically homogeneous background error variance. This issue cannot be fully solved by using the so-called hydrometeor classification in the reflectivity observation operator. Alternatively, temperature-dependent background error profiles for hydrometeor control variables are proposed. With such a treatment, the vertical background error profiles are specified to be temperature dependent, allowing for more physical partitioning of radar-observed precipitation information among the liquid and ice hydrometeors. The 3DVar analyses using our treatment are compared with those using constant background error or “hydrometeor classification” through observing system simulation experiments with a simulated supercell storm. Results show that 1) 3DVar with constant hydrometeor background errors produces unphysical rainwater at the high levels and unphysical snow at the low levels; 2) the hydrometeor classification approach reduces unphysical rainwater and snow at those levels, but the analysis increments are still unphysically spread in the vertical by the background error covariance when the vertically invariant background errors are used; and 3) the temperature-dependent background error profiles enable physically more reasonable analyses of liquid and ice hydrometeors from reflectivity assimilation.

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Rong Kong, Ming Xue, and Chengsi Liu

Abstract

A hybrid ensemble–3DVar (En3DVar) system is developed and compared with 3DVar, EnKF, “deterministic forecast” EnKF (DfEnKF), and pure En3DVar for assimilating radar data through perfect-model observing system simulation experiments (OSSEs). DfEnKF uses a deterministic forecast as the background and is therefore parallel to pure En3DVar. Different results are found between DfEnKF and pure En3DVar: 1) the serial versus global nature and 2) the variational minimization versus direct filter updating nature of the two algorithms are identified as the main causes for the differences. For 3DVar (EnKF/DfEnKF and En3DVar), optimal decorrelation scales (localization radii) for static (ensemble) background error covariances are obtained and used in hybrid En3DVar. The sensitivity of hybrid En3DVar to covariance weights and ensemble size is examined. On average, when ensemble size is 20 or larger, a 5%–10% static covariance gives the best results, while for smaller ensembles, more static covariance is beneficial. Using an ensemble size of 40, EnKF and DfEnKF perform similarly, and both are better than pure and hybrid En3DVar overall. Using 5% static error covariance, hybrid En3DVar outperforms pure En3DVar for most state variables but underperforms for hydrometeor variables, and the improvement (degradation) is most notable for water vapor mixing ratio q υ (snow mixing ratio q s). Overall, EnKF/DfEnKF performs the best, 3DVar performs the worst, and static covariance only helps slightly via hybrid En3DVar.

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Chengsi Liu, Ming Xue, and Rong Kong

Abstract

Radar reflectivity (Z) data are either directly assimilated using 3DVar, 4DVar, or ensemble Kalman filter, or indirectly assimilated using, for example, cloud analysis that preretrieves hydrometeors from Z. When directly assimilating radar data variationally, issues related to the highly nonlinear Z operator arise that can cause nonconvergence and bad analyses. To alleviate the issues, treatments are proposed in this study and their performances are examined via observing system simulation experiments. They include the following: 1) When using hydrometeor mixing ratios as control variables (CVq), small background Z can cause extremely large cost function gradient. Lower limits are imposed on the mixing ratios (qLim treatment) or the equivalent reflectivity (ZeLim treatment) in Z observation operator. ZeLim is found to work better than qLim in terms of analysis accuracy and convergence speed. 2) With CVq, the assimilation of radial velocity (V r) is ineffective when assimilated together with Z data due to the much smaller cost function gradient associated with V r. A procedure (VrPass) that assimilates V r data in a separate pass is found very helpful. 3) Using logarithmic hydrometeor mixing ratios as control variables (CVlogq) can also avoid extremely large cost function gradient, and has much faster convergence. However, spurious analysis increments can be created when transforming the analysis increments back to mixing ratios. A background smoothing and a lower limit are applied to the background mixing ratios, and are shown to be effective. Using CVlogq with associated treatments produces better reflectivity analysis that is much closer to the observation without resorting to multiple analysis passes, and the cost function minimization also converges faster. CVlogq is therefore recommended for variational radar data assimilation.

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Rong Kong, Ming Xue, Chengsi Liu, and Youngsun Jung

Abstract

In this study, a hybrid En3DVar data assimilation (DA) scheme is compared with 3DVar, EnKF, and pure En3DVar for the assimilation of radar data in a real tornadic storm case. Results using hydrometeor mixing ratios (CVq) or logarithmic mixing ratios (CVlogq) as the control variables are compared in the variational DA framework. To address the lack of radial velocity impact issues when using CVq, a procedure that assimilates reflectivity and radial velocity data in two separate analysis passes is adopted. Comparisons are made in terms of the root-mean-square innovations (RMSIs) as well as the intensity and structure of the analyzed and forecast storms. For pure En3DVar that uses 100% ensemble covariance, CVlogq and CVq have similar RMSIs in the velocity analyses, but errors grow faster during forecasts when using CVlogq. Introducing static background error covariance B at 5% in hybrid En3DVar (with CVlogq) significantly reduces the forecast error growth. Pure En3DVar produces more intense reflectivity analyses than EnKF that more closely match the observations. Hybrid En3DVar with 50% B outperforms other weights in terms of the RMSIs and forecasts of updraft helicity and is thus used in the final comparison with 3DVar and EnKF. The hybrid En3DVar is found to outperform EnKF in better capturing the intensity and structure of the analyzed and forecast storms and outperform 3DVAR in better capturing the intensity and evolution of the rotating updraft.

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Lianglyu Chen, Chengsi Liu, Ming Xue, Gang Zhao, Rong Kong, and Youngsun Jung

Abstract

When directly assimilating radar data within a variational framework using hydrometeor mixing ratios (q) as control variables (CVq), the gradient of the cost function becomes extremely large when background mixing ratio is close to zero. This significantly slows down minimization convergence and makes the assimilation of radial velocity and other observations ineffective because of the dominance of the reflectivity observation term in the cost function gradient. Using logarithmic hydrometeor mixing ratios as control variables (CV logq) can alleviate the problem but the high nonlinearity of logarithmic transformation can introduce spurious analysis increments into mixing ratios. In this study, power transform of hydrometeors is proposed to form new control variables (CVpq) where the nonlinearity of transformation can be adjusted by a tuning exponent or power parameter p. The performance of assimilating radar data using CVpq is compared with those using CVq and CV logq for the analyses and forecasts of five convective storm cases from the spring of 2017. Results show that CVpq with p = 0.4 (CVpq0.4) gives the best reflectivity forecasts in terms of root-mean-square error and equitable threat score. Furthermore, CVpq0.4 has faster convergence of cost function minimization than CVq and produces less spurious analysis increment than CV logq. Compared to CVq and CV logq, CVpq0.4 has better skills of 0–3-h composite reflectivity forecasts, and the updraft helicity tracks for the 16 May 2017 Texas and Oklahoma tornado outbreak case are more consistent with observations when using CVpq0.4.

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Rong Kong, Ming Xue, Alexandre O. Fierro, Youngsun Jung, Chengsi Liu, Edward R. Mansell, and Donald R. MacGorman

Abstract

The recently launched Geostationary Operational Environmental Satellite “R-series” (GOES-R) satellites carry the Geostationary Lightning Mapper (GLM) that measures from space the total lightning rate in convective storms at high spatial and temporal frequencies. This study assimilates, for the first time, real GLM total lightning data in an ensemble Kalman filter (EnKF) framework. The lightning flash extent density (FED) products at 10-km pixel resolution are assimilated. The capabilities to assimilate GLM FED data are first implemented into the GSI-based EnKF data assimilation (DA) system and tested with a mesoscale convective system (MCS). FED observation operators based on graupel mass or graupel volume are used. The operators are first tuned through sensitivity experiments to determine an optimal multiplying factor to the operator, before being used in FED DA experiments FEDM and FEDV that use the graupel-mass or graupel-volume-based operator, respectively. Their results are compared to a control experiment (CTRL) that does not assimilate any FED data. Overall, both DA experiments outperform CTRL in terms of the analyses and short-term forecasts of FED and composite/3D reflectivity. The assimilation of FED is primarily effective in regions of deep moist convection, which helps improve short-term forecasts of convective threats, including heavy precipitation and lightning. Direct adjustments to graupel mass via observation operator as well as adjustments to other model state variables through flow-dependent ensemble cross covariance within EnKF are shown to work together to generate model-consistent analyses and overall improved forecasts.

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