Characterization of the climatological variability of mean areal rainfall through fractional coverage

The role of fractional coverage in climatological variability of mean areal rainfall is investigated. Under second-order homogeneity assumptions, climatological variability of mean areal rainfall, as measured by its coefficient of variation, is shown to be a function of mean fractional coverage, conditional coefficient of variation of point rainfall and two correlation scales associated with inner variability and intermittency of point rainfall. To verify the analytical results, empirical analyses are performed using hourly rainfall data from nine Weather Surveillance Radar- 1988 Doppler (WSR-88D) radars in the southern plains, United States. The results indicate that given the local rainfall climatology there exists a catchment scale at which the climatological variability of mean areal rainfall is at its maximum. Existence of such a scale has been hypothesized and demonstrated via an analytical treatment of an idealized situation by Eagleson and Wang [1985], but only in climatological variability of fractional coverage (i.e., variability due only to intermittency). Sensitivity analyses for the correlation-scale parameters indicate that intermittency plays as important a role as inner variability in shaping the catchment scale-climatological variability relationship of mean areal rainfall. Decomposition of total variability indicates that over the range of catchment scales that fall within a single WSR-88D radar umbrella (effective radius of 230 km) the integrated contribution from intermittency is almost as large as that from inner variability.