A Diabatic Lagrangian Technique for the Analysis of Convective Storms. Part I: Description and Validation via an Observing System Simulation Experiment

A diabatic Lagrangian analysis (DLA) technique for deriving potential temperature, water vapor and cloud water mixing ratios, and virtual buoyancy from three-dimensional time-dependent Doppler radar wind and reflectivity fields in storms is presented. The DLA method proceeds from heat and water substance conservation along discrete air trajectories via microphysical diabatic heating/cooling and simple damping and surface flux parameterizations in a parcel-following ground-relative reference frame to thermodynamic fields on a regular grid of trajectory endpoints at a common analysis time. Rain and graupel precipitation size distributions are parameterized from observed reflectivity at discrete Lagrangian points to simplify the cloud model based microphysically driven heating and cooling rate calculations. The DLA approximates the precipitation size distributions from reflectivity assuming conventional inverse exponential size distributions and prescribed input intercept parameter values based on the output of a mature simulated storm. The DLA is demonstrated via an observing system simulation experiment (OSSE), and its analysis compares favorably with the known output buoyancy and water substance fields in the simulated storm case. The DLA-analyzed thermal-solenoidal horizontal vorticity tendency is of comparable magnitude to the corresponding modeled solenoidal vorticity tendency. A test application of the DLA to a radar-observed storm is presented in a companion paper (Part II).