Estimation of Raindrop Size Distribution in Mexico City by a Network of Disdrometers: Implications for Z-R Relationships

Accurate measurements and prediction of the spatial and temporal distribution of rainfall is crucial for an adequate management of urban hydrological processes. Rainfall measurement using ground-based weather radars rely on radar reflectivity (Z)-rain rate (R) relationships play a crucial role for the quantitative use of this instrument for an adequate measurement of rainfall. However, much uncertainty still remains in this process, which prevents the use of this radar-derived rainfall amounts quantitatively for hydrological purposes.

Indeed, Z and the R are related to each other via the raindrop size distribution (DSD). This DSD is defined as the mean number of raindrops in a particular diameter interval present per unit volume of air N(D) (mm-1m-3). Usually, the general exponential or gamma distributions are used to characterize DSDs. This is the most popular equation to DSD evaluation, from a pioneer study of Marshal and Palmer (1948). However, recently the normalized gamma distribution has been used in many studies, showing good performance. The general expression of the normalization of the DSD is: N(D) = Nw Fµ (D/Do), where Nw is the normalized intercept, Do represents a mean particle size (median volume diameter) and µ is confined to the description of the shape of the DSD.

On the other hand, disdrometer measurements can be used to determine the DSD at a given location and are also useful in defining the shape of the DSD. This enables a better estimation of the coefficients of Z-R relationship. In this study, a dense network of 39 optical disdrometers (OTT Parsivel2) with 1 min resolution installed in Mexico city, Mexico, is used to explore the spatial shape of the normalized DSD within the city and the enhancement/calibration /modification of a Z-R relationship considering the DSD. Disdrometer data with temporal resolution of 1-min is used to define the three parameters (Nw, µ, Do) that characterize a normalized gamma distribution of the DSD. Using these parameters, the rainfall and reflectivity are calculated as 3.67 and 6 moments of the DSD. Additionally, the Z-R relation is adjusted through a power law Z=aR^b, by applying a regression log Z- log R scatter plot, proposed by Marshal and Palmer (1948). Parameters a and b are fitted and classified according to seasons: summer and winter. Results show that the Z-R relationship presents a spatial and temporal variability. Finally, computed coefficients are used to convert measurements from a X-band dual-polarization radar to quantitative rainfall estimations.