Timescale and Intensity Dependency in Multiplicative Cascades for Temporal Rainfall Disaggregation

Multiplicative random cascades (MRC) can parsimoniously generate highly intermittent patterns similar to those in rainfall. The elemental MRC model parameter is the cascade weight, which determines how rainfall at one scale is partitioned at the next smallest scale in the cascade. While it is known that the probability density of these weights may vary with both timescale and rainfall intensity, nearly all previous studies have considered either timescale or intensity separately. We examined the simultaneous dependency of the weights on both factors and assessed the impacts of explicitly including these dependencies in the MRC model. Based on the observed relationships between cascade weights and timescale and intensity, four progressively more “dependent ” models were constructed to disaggregate a long time series of daily rainfall to hourly intervals. We found that inclusion of the intensity dependency on the model parameters that generate dry intervals greatly improved performance. For the relatively small range of time scales over which the rainfall was disaggregated, varying model parameters with timescale resulted in minor improvement. 2 1