Diagnostic Pressure Equation as a Weak Constraint in a Storm-Scale Three Dimensional Variational Radar Data Assimilation System

A diagnostic pressure equation is incorporated into a storm-scale three-dimensional variational (3DVAR) data assimilation 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 spin-up 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.