Differences Between Explicit and Approximated Radar Ray Paths Due to Vertical Gradient of Refractivity

The radar ray path equations are used to determine the physical location of each radar measurement. These equations are necessary for mapping radar data to computational grids for diagnosis, display and numerical weather prediction (NWP). They are also used in the forward observational operators when assimilating radar data into NWP models, which map the grid-point values to radar observational locations. Typically, the four-thirds earth radius model is used for the radar ray path calculations, This model assumes that the atmosphere has a constant gradient of refractive index in the lower troposphere, as determined from the standard atmosphere. In reality, the gradient of the refractive index is seldom constant, and significant departures from the linearity assumption exist when there are strong temperature inversions and/or large vertical moisture gradient. A better understanding of the sensitivity of the path to refractive index gradient is valuable to radar data quality control, among other things. In this study, we examine the influence of different environmental temperature and moisture profiles to the radar ray path. To accurately calculate the radar ray path, a stepwise ray tracing method is used. The influence of atmospheric refractive index on the ray path at different geographical locations in the United States is examined using historic sounding data from National Weather Service. For the sample of soundings examined, we find that only a small fraction of the ray paths diverge significantly from the four-thirds earth radius model. While the problem of ducting in the presence of a temperature inversion is generally recognized, we identified vertical moisture gradient to be a more significant contributor in the Great Plains cases where significant deviations from the standard atmosphere path occur. Detailed statistics will also be reported at the conference.