No abstract

Four-dimensional variational data assimilation (4DVar) is one of the most promising methods to provide optimal analysis for numerical weather prediction (NWP). Five national NWP centers in the world have successfully applied 4DVar methods in their global NWPs, thanks to the increment method and adjoint technique. However, the application of 4DVar is still limited by the computer resources available at many NWP centers and research institutes. It is essential, therefore, to further reduce the computational cost of 4DVar. Here, an economical approach to implement 4DVar is proposed, using the technique of dimensionreduced projection (DRP), which is called "DRP-4DVar." The proposed approach is based on dimension reduction using an ensemble of historical samples to define a subspace. It directly obtains an optimal solution in the reduced space by fitting observations with historical time series generated by the model to form consistent forecast states, and therefore does not require implementation of the adjoint of tangent linear approximation.To evaluate the performance of the DRP-4DVar on assimilating different types of mesoscale observations, some observing system simulation experiments are conducted using MM5 and a comparison is made between adjoint-based 4DVar and DRP-4DVar using a 6-hour assimilation window.

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 qυ (snow mixing ratio qs). Overall, EnKF/DfEnKF performs the best, 3DVar performs the worst, and static covariance only helps slightly via hybrid En3DVar.

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.