Multifractal analysis of Drop Size Distribution parameters vertical and temporal variability

Rainfall exhibits extreme spatial and temporal variability observable across wide range of scales. This variability is not limited to precipitation totals but also concerns the microphysical structure of the rain characterized with the help of the drop size distribution (DSD). It is defined as the number of raindrops per unit volume of air with a given equivolumic diameter. The  DSD can be described through its statistical parameters (basically its moments) such as the rain rate (RR), the liquid water content (LWC), the mass-weighted mean diameter (D_m) and the total number concentration (N_t). The vertical variability of DSD remains an active field of research, particularly due to the challenges associated with observing and generalizing microphysical profiles which are used to improve rainfall ground estimates from radar measurements.

Vertically-oriented radar measurements are a valuable tool for studying the vertical variability of DSD along the precipitation column with small spatial and short temporal observation scales. In this study, nine months of a Micro Rain Radar PRO (MRR-PRO) measurements were gathered in Ecole nationale des ponts et chaussées (ENPC), Institut Polytechnique de Paris (IPP), which is located in the eastern part of the Paris region, France. The MRR-PRO is a K-band weather radar that provides high-resolution vertical profiles of precipitation features that reach more than 4 kilometers of altitude above its position with a 35 meters spatial resolution and a 10 seconds time step. Based on the collected data and simple assumptions, several parameters related to the raindrop size distribution can be estimated empirically, such as RR, LWC, D_m and N_t. The spatial and temporal variability of the DSD was studied using the Universal Multifractal (UM) framework, a physically based framework designed to characterize geophysical fields across wide  range of scales through a limited set of physically interpretable parameters.

Two types of UM analysis were conducted in this study. First, the time series of DSD statistical moments is explored at each altitude. Then, vertical profiles of these moments are examined to extract UM parameters that characterize the variability along the vertical column. The results and their interpretation within a spatiotemporal framework will be presented.

Authors acknowledge the France-Taiwan Ra2DW project for financial support (grant number by the French National Research Agency – ANR-23-CE01-0019-01).