A Variational Multiple–Doppler Radar Three-Dimensional Wind Synthesis Method and Its Impacts on Thermodynamic Retrieval

Abstract

A multiple?Doppler radar synthesis method is developed to recover the three-dimensional wind field. In this method the solutions are obtained by variationally adjusting the winds to satisfy a series of constraints in weak formats. Among them, the primary ones are multiple-radar radial velocity observations, the anelastic continuity equation, the vertical vorticity equation, the background wind, and spatial smoothness terms. The retrieved wind products are at two time levels, and can be readily applied to deduce the information about the pressure and temperature through the use of the thermodynamic retrieval algorithm, in which the temporal derivatives of the wind fields are required. Experiments using model-simulated data are conducted, from which two major findings are obtained. First, the wind field along and near the radar baseline can still be recovered. This is a major advantage over the traditional approach. Therefore, the proposed method is capable of providing uninterrupted observations of a weather system as it passes the baseline. This allows for more flexibility when designing the radar deployment in field experiments. Second, if the winds are applied to infer the thermodynamic fields using the traditional dynamic retrieval method, and an extra sounding (e.g., radiosonde or dropsonde) is combined in order to specify the horizontal average of the thermodynamic perturbations, the preferable place to release this sounding is within the region of weak, rather than strong, convection. In additional to the aforementioned findings, with this method there is no need to prescribe the top or bottom boundary conditions for the vertical velocities in the traditional sense. Since the computation is performed without explicit vertical integration of the continuity equation, the problem of error accumulation due to inappropriate boundary conditions for the vertical velocities is prevented. These finding are consistent with some previous publications. Furthermore, the instability that occurs during traditional iterative dual-Doppler wind synthesis based on a Cartesian coordinate can also be avoided. Finally, data from any number of radars can be easily added to the computation. This method is also tested using the radar datasets collected during the Southwest Monsoon Experiment/Terrain-Influenced Monsoon Rainfall Experiment (SoWMEX/TiMREX), which was conducted from May to June 2008 in Taiwan, and reasonable results are obtained.