Disaggregative Invariance of Daily Precipitation

Disaggregative invariance refers to stochastic independence between the total precipitation amount and its temporal disaggregation. This property is investigated herein for areal average and point precipitation amounts accumulated over a 24-h period and disaggregated into four 6-h subperiods. Statistical analyses of precipitation records from 1948 to 1993 offer convincing empirical evidence against the disaggregative invariance and in favor of the conditional disaggregative invariance, which arises when the total amount and its temporal disaggregation are conditioned on the timing of precipitation within the diurnal cycle. The property of conditional disaggregative invariance allows the modeler or the forecaster to decompose the problem of quantitative precipitation forecasting into three tasks: (i) forecasting the precipitation timing; (ii) forecasting the total amount, conditional on timing; and (iii) forecasting the temporal disaggregation, conditional on timing. Tasks (ii) and (iii) can be performed independently of one another, and this offers a formidable advantage for applications.