Preliminary Statistical Characterizations of the Lowest Kilometer Time–Height Profiles of Rainfall Rate Using a Vertically Pointing Radar

Abstract

A realistic approach for gathering high-resolution observations of the rainfall rate, R, in the vertical plane is to use data from vertically pointing Doppler radars. After accounting for the vertical air velocity and attenuation, it is possible to determine the fine, spatially resolved drop size spectra and to calculate R for further statistical analyses. The first such results in a vertical plane are reported here. Specifically, we present results using MRR-Pro Doppler radar observations at resolutions of ten meters in height over the lowest 1.28 km, as well as ten seconds in time, over four sets of observations using two different radars at different locations. Both the correlation functions and power spectra are useful for translating observations and numerical model outputs of R from one scale down to other scales that may be more appropriate for particular applications, such as flood warnings and soil erosion, for example. However, it was found in all cases that, while locally applicable radial power spectra could be calculated, because of statistical heterogeneity most of the power spectra lost all generality, and proper correlation functions could not be computed in general except for one 17-min interval. Nevertheless, these results are still useful since they can be combined to develop catalogs of power spectra over different meteorological conditions and in different climatological settings and locations. Furthermore, even with the limitations of these data, this approach is being used to gain a deeper understanding of rainfall to be reported in a forthcoming paper.

A Practical Approach for Determining Multi-Dimensional Spatial Rainfall Scaling Relations Using High Resolution Time Height Doppler Data from a Single Mobile Vertical Pointing Radar

“…This is likely important for the other data in this study as well. Thus, in the previous work, (Figure 9 of [26]) which were erroneously calculated by assuming the incorrect Va = 1 ms -1 , the values of the slopes only ranged from -2.47 to -2.74, while those below in Figure 11, calculated using the best estimates of Va , fall over a greater range of slopes between -2.71 to -3.51. However, while the maximum differences in slopes in Figure 11is about 0.8, this decreases to about 0.27 after first noting that these relations can all be scaled to the volume (Figure12).…”

“…. As explained in [26] but repeated here for readability, this is accomplished by first computing the 2D horizontal-vertical coordinate system of the original 2D power spectrum using the fft2 routine in Matlab  and then multiplying by its complex conjugate. This 2D power spectrum of values in (Δz, Δh)…”

A Practical Approach for Determining Multi-Dimensional Spatial Rainfall Scaling Relations Using High Resolution Time Height Doppler Data from a Single Mobile Vertical Pointing Radar

“…Rng z h =+ . As explained in [34] but repeated here for readability, this is accomplished by first computing the 2D horizontal-vertical coordinate system of the original 2D power spectrum using the fft2 routine in Matlab  and then multiplying by its complex conjugate. This 2D power spectrum of values in (Δz, Δh) coordinates is then converted into 2D polar coordinate system of (Δr, Δθ) values of the power spectrum.…”

A Practical Approach for Determining Multi-Dimensional Spatial Rainfall Scaling Relations Using High Resolution Time Height Doppler Data from a Single Mobile Vertical Pointing Radar

“…. As explained in [34] but repeated here for readability, this is accomplished by first computing the 2D horizontal-vertical coordinate system of the original 2D power spectrum using the fft2 routine in Matlab â and then multiplying by its complex conjugate. This 2D power spectrum of values in (Δz, Δh)…”

“…Figure10. A plot illustrating the effect of increasing advection velocity on the slope of a power fit to the radial spectral power function for the CoC data illustrating the importance of using an estimate of an optimal advection speed rather than an arbitrary assumption as was done in[34].…”