TECHNICAL NOTE: The representation of rainfall drop-size distribution and kinetic energy

Abstract

To relate observed rainfall rates (R) to the kinetic energy flux (E) that affects soil erosion it is necessary to develop relationships between the two. This paper explores theoretical ER relationships based on gamma distributions of drop size. The relationship is poorly defined unless assumptions are made about changes in the shape of the drop-size distribution (DSD) with rainfall rate. The study suggests that the assumption of an exponential DSD leads to overestimation of kinetic energy flux. Further, incorporation of a horizontal component of kinetic energy allows for a clearer relationship between kinetic energy and rainfall intensity to be defined, but a question remains regarding the most appropriate definition of the horizontal component of drop velocity.

Effect of raindrop size distribution and rain rate inhomogeneity on the relationship between attenuation and depolarization

“… where N(D) is the DSD for the particular model and v(D) is the falling velocity of the rain, which is defined according to Ulbrich .…”

“…† E-mail: peeramedc@gmail.com In a parallel study, Nowland et al [12] proposed a formula for the relationship between rain attenuation and XPD by using a small argument approximation. The cross-polarization can be calculated theoretically, using the rainfall rate, the attenuation due to rain, the DSD, the forward scattering amplitude of the raindrops [13,14], the velocity of the rainfall [15], and the raindrop diameters [16]. Then, Fukuchi [17,18] improved Nowland's equation by using many DSDs, such as the MP DSD, the Joss thunderstorm DSD, and the Joss drizzle DSD, which they calculated up to 40 GHz.…”

Experimental study and modelling of rain drop size distribution in southern England

“…Many researchers use the accuracy of the rainfall or other predictions derived from the DSD, as proxy measures for goodness-of-fit of the model [1,3,4,5,6,11,12,15,17,18]. A number of researchers use some variant of the sum of squared errors (SSE) [3,6,11,12].…”

Toward elucidating the microstructure of warm rainfall: A survey

“…Understanding the DSD evolution with height is the key for developing the capability of extending/extrapolating polarimetric radar DSD estimations to different heights. Note that such a capability has important applications such as soil erosion studies [ Fox , 2004; Fornis et al , 2005], air pollution studies [ Mircea et al , 2000], telecommunications [ Panagopoulos and Kanellopoulos , 2002], etc., besides improving DSD retrieval methods as discussed above. The evolution of DSD in clouds is shaped by various processes such as drop breakup/coalescence, evaporation/condensation, size sorting due to updraft/downdraft, etc.…”