A diagnostic pressure equation is incorporated into a storm-scale three-dimensional variational data assimilation (3DVAR) system in the form of a weak constraint in addition to a mass continuity equation constraint (MCEC). The goal of this diagnostic pressure equation constraint (DPEC) is to couple different model variables to help build a more dynamic consistent analysis, and therefore improve the data assimilation results and subsequent forecasts. Observational System Simulation Experiments (OSSEs) are first performed to examine the impact of the pressure equation constraint on storm-scale radar data assimilation using an idealized tornadic thunderstorm simulation. The impact of MCEC is also investigated relative to that of DPEC. It is shown that DPEC can improve the data assimilation results slightly after a given period of data assimilation. Including both DPEC and MCEC yields the best data assimilation results. Sensitivity tests show that MCEC is not very sensitive to the choice of its weighting coefficients in the cost function, while DPEC is more sensitive and its weight should be carefully chosen. The updated 3DVAR system with DPEC is further applied to the 5 May 2007 Greensburg, Kansas, tornadic supercell storm case assimilating real radar data. It is shown that the use of DPEC can speed up the spinup of precipitation during the intermittent data assimilation process and also improve the follow-on forecast in terms of the general evolution of storm cells and mesocyclone rotation near the time of observed tornado.

This paper investigates the impacts of assimilating measurements of different state variables, which can be potentially available from various observational platforms, on the cycled analysis and short-range forecast of supercell thunderstorms by performing a set of observing system simulation experiments (OSSEs) using a storm-scale three-dimensional variational data assimilation (3DVAR) method. The control experiments assimilate measurements every 5 min for 90 min. It is found that the assimilation of horizontal wind V h can reconstruct the storm structure rather accurately. The assimilation of vertical velocity w, potential temperature u, or water vapor q y can partially rebuild the thermodynamic and precipitation fields but poorly retrieves the wind fields. The assimilation of rainwater mixing ratio q r can build up the precipitation fields together with a reasonable cold pool but is unable to properly recover the wind fields. Overall, V h data have the greatest impact, while q y have the second largest impact. The impact of q r is the smallest. The impact of assimilation frequency is examined by comparing results using 1-, 5-, or 10-min assimilation intervals. When V h is assimilated every 5 or 10 min, the analysis quality can be further improved by the incorporation of additional types of observations. When V h are assimilated every minute, the benefit from additional types of observations is negligible, except for q y . It is also found that for V h , w, and q r measurements, more frequent assimilation leads to more accurate analyses. For q y and u, a 1-min assimilation interval does not produce a better analysis than a 5-min interval.

Numerical experiments over the past years indicate that incorporating environmental variability is crucial for successful very short-range convective-scale forecasts. To explore the impact of model physics on the creation of environmental variability and its uncertainty, combined mesoscale-convective scale data assimilation experiments are conducted for a tornadic supercell storm. Two 36-member WRF-ARW model-based mesoscale EAKF experiments are conducted to provide background environments using either fixed or multiple physics schemes across the ensemble members. Two 36-member convective-scale ensembles are initialized using background fields from either fixed physics or multiple physics mesoscale ensemble analyses. Radar observations from four operational WSR-88Ds are assimilated into convective-scale ensembles using ARPS model-based 3DVAR system and ensemble forecasts are launched. Results show that the ensemble with background fields from multiple physics ensemble provides more realistic forecasts of significant tornado parameter, dryline structure, and near surface variables than ensemble from fixed physics background fields. The probabilities of strong low-level updraft helicity from multiple physics ensemble correlate better with observed tornado and rotation tracks than probabilities from fixed physics ensemble. This suggests that incorporating physics diversity across the ensemble can be important to successful probabilistic convective-scale forecast of supercell thunderstorms, which is the main goal of NOAA's Warn-on-Forecast initiative.

The radar ray path and beam broadening equations are important for assimilation of radar data into numerical weather prediction (NWP) models. They can be used to determine the physical location of each radar measurement and to properly map the atmospheric state variables from the model grid to the radar measurement space as part of the forward observation operators. Historically, different degrees of approximations have been made with these equations; however, no systematic evaluation of their impact exists, at least in the context of variational data assimilation. This study examines the effects of simplifying ray path and ray broadening calculations on the radar data assimilation in a 3D variational data assimilation (3DVAR) system. Several groups of Observational System Simulation Experiments (OSSEs) are performed to test the impact of these equations to radar data assimilation with an idealized tornadic thunderstorm case. This study shows that the errors caused by simplifications vary with the distance between the analyzed storm and the radar. For single time level wind analysis, as the surface range increases, the impact of beam broadening on analyzed wind field becomes evident and can cause relatively large error for distances beyond 150 km. The impact of the earth's curvature is more significant, even for distances beyond 60 km, because it places the data at the wrong vertical location. The impact of refractive index gradient is also tested. It is shown that the variations of refractive index gradient have a very small impact on the wind analysis results.Two time series of 1-h-long data assimilation experiments are further conducted to illustrate the impact of the beam broadening and earth curvature on all retrieved model variables. It is shown that all model variables can be retrieved to some degrees in all data assimilation experiments. Similar to the wind analysis experiments, the impacts of both factors are not obvious when radars are relatively close to the storm. When the radars are far from the storm (especially beyond 150 km), overlooking beam broadening degrades the accuracy of assimilation results slightly, whereas ignoring the earth's curvature leads to significant errors.

In this study, a new set of reflectivity equations are introduced into the Advanced Regional Prediction System (ARPS) cloud analysis system. This set of equations incorporates double-moment microphysics information in the analysis by adopting a set of diagnostic relationships between the intercept parameters and the corresponding mass mixing ratios. A reflectivity-and temperature-based graupel classification scheme is also implemented according to a hydrometeor identification (HID) diagram. A squall line that occurred on 23 April 2007 over southern China containing a pronounced trailing stratiform precipitation region is used as a test case to evaluate the impacts of the enhanced cloud analysis scheme.The results show that using the enhanced cloud analysis scheme is able to better capture the characteristics of the squall line in the forecast. The predicted squall line exhibits a wider stratiform region and a more clearly defined transition zone between the leading convection and the trailing stratiform precipitation region agreeing better with observations in general, when using the enhanced cloud analysis together with the twomoment microphysics scheme. The quantitative precipitation forecast skill score is also improved.