Estimates of the statistical two-dimensional spatial structure in rain over a small network of disdrometers

A R Jameson,M L Larsen

doi:10.1007/s00703-016-0438-0

Abstract

Microphysical understanding of the variability in rain requires a statistical characterization of different drop sizes both in time and in all dimensions of space. Temporally, there have been several statistical characterizations of raindrop counts. However, temporal and spatial structures are neither equivalent nor readily translatable. While there are recent reports of the one-dimensional spatial correlation functions in rain, they can only be assumed to represent the two-dimensional (2D) correlation function under the assumption of spatial isotropy. To date, however, there are no actual observations of the (2D) spatial correlation function in rain over areas. Two reasons for this deficiency are the fiscal and the physical impossibilities of assembling a dense network of instruments over even hundreds of meters much less over kilometers. Consequently, all measurements over areas will necessarily be sparsely sampled. A dense network of data must then be estimated using interpolations from the available observations. In this work, a network of 19 optical disdrometers over a 100 m by 71 m area yield observations of drop spectra every minute. These are then interpolated to a 1 m resolution grid. Fourier techniques then yield estimates of the 2D spatial correlation functions. Preliminary examples using this technique found that steadier, light rain decorrelates spatially faster than does the convective rain, but in both cases the 2D spatial correlation functions are anisotropic, reflecting an asymmetry in the physical processes influencing the rain reaching the ground not accounted for in numerical microphysical models.

Highlights

The existence of temporal and spatial structures in rain is widely recognized
We get a glimpse of just what such functions might look like over a small domain of 71 m 9 100 m defined by 19 optical disdrometers
The Fourier transform of this field times its complex conjugate yields the field of variances which can be transformed into the 2D spatial correlation function using an inverse Fourier transform

Summary

Introduction

The existence of temporal and spatial structures in rain is widely recognized. One of the primary motivations for studies of this structure has long been hydrological applications, flood predictions and flood warnings. The ground-breaking work of Tapiador et al (2010) and of Jaffrain and Berne (2012a) used observations of spatially separated optical disdrometers to compute the spatial correlations of moments of the drop size distributions (i.e., the rainfall rate, the radar reflectivity factor, mean drop size) between pairs of instruments separated by distances varying from hundreds of meters to a few kilometers as has Jameson et al (2015a) on scales less than 100 m As important as these studies are, they are only one-dimensional pair correlations, not the complete two-dimensional correlation functions over an area. A common statistical tool for studying the structure of rain in time using a disdrometer is the correlation function of counts of different sizes of drops (Kostinski and Jameson 1997; Jameson and Kostinski 2000) As useful as such studies have been, they are not equivalent to one-dimensional (1D) spatial observations (Jameson et al 2015a). Subsequent sections will briefly describe the network of instruments, a description of the data being analyzed and an example of the natural neighbor

Preliminary considerations

Data and analyses

Summary