On the Relationships Between Radar Reflectivity and Rainfall Rate and Kinetic Energy Resulting From a Weibull Drop Size Distribution

The rainfall rate is a crucial variable in modeling runoff and water erosion. Rainfall rates present a very large spatial and temporal variability. Radars are used to estimate the spatial and temporal changes in rainfall rates during storms. The radar reflectivity is strongly affected by the drop size distribution (DSD) that results from the relative intensity of the microphysical processes involved in rainfall formation. One of the mathematical models applied to quantify the DSD is the Weibull function. Rainfall rate and kinetic energy, and radar reflectivity, are all related to different moments of the DSD. An analytical expression for these moments is proposed in the case of the Weibull distribution. The resulting relationships between radar reflectivity, rainfall rate, and kinetic energy are presented. The use of a scaled DSD that is independent of rainfall rate and characterizes a specific location allows an a priori estimate of relationships between radar reflectivity, rainfall rate, and kinetic energy that will be also characteristics of that location. Radar reflectivity can be used to estimate the kinetic energy of rainfall events. This extends the application of radar to agriculture and environmental purposes such as potential rainfall damages estimates in terms of soil loss, erosion, and sediment transport. An analytical expression of the moments of the drop size distribution corresponding to R and Z are presented for the Weibull distributionThe use of a scaled DSD characterizing a specific location allows to estimate of relationships between Z, R, and dE/dt for that locationZ can be used to estimate dE/dt; the Z (dE/dt) relationship is of a power type, but could be approximated by a linear one