Theoretical relationships between rainfall intensity and kinetic energy variants associated with stormwater particle washoff

Abstract

Previous studies have identified rainfall intensity as a contributing factor to the amount of suspended particles washed from urban areas during storms. Moreover, it has been postulated that the square of rainfall intensity (I 2) provides a measure of the rainfall kinetic energy (KE) available for washoff processes. This paper provides a theoretical analysis of the potential inter-relationships between I 2 and rainfall KE. A hypothetical raindrop size distribution (DSD) was used to derive rainfall energy characteristics. A special form of the Marshall-Palmer DSD was developed that ensured conservation of rainfall mass over the analyzed range of rainfall intensities. This ‘conserved rainfall mass’ DSD was used to calculate the specific KE variants of rainfall (the time-specific KEI and the volume-specific KEP). It was found that KEI has a loge-based relationship with rainfall intensity. Empirical relationships widely used in soil erosion studies have generally adopted a log10 basis. A direct relationship between the two KE variants and I2 appears to be absent. A new KE variant (KEIA) is proposed and it is demonstrated that this variant supports the hypothesis that I2 is a measure of the KE of rainfall. KEIA is the kinetic energy potentially transferred from raindrops to the proportion of the unit area impacted at a specific instant in time. It is a function of KEI and raindrop circumferential area. Relationships based on variants of rainfall momentum M are also investigated. The relationship between MI and KEI is nearly linear as a fitted power function has an exponent close to unity (equal to 0.93). This suggests KE and M could be effectively interchangeable if used in particle washoff estimation.