Evaluation of a scaling cascade model for temporal rain- fall disaggregation

Abstract. The possibility of modelling the temporal structure of rainfall in southern Sweden by a simple cascade model is tested. The cascade model is based on exact conservation of rainfall volume and has a branching number of 2. The weights associated with one branching are 1 and 0 with probability P(1/0), 0 and 1 with P(0/1), and W_x/x, and 1 - W_x/x, 0 < W_x/x, < 1, with P(x/x), where W_x/x is associated with a theoretical probability distribution. Furthermore, the probabilities p are assumed to depend on two characteristics of the rainy time period (wet box) to be branched: rainfall volume and position in the rainfall sequence. In the first step, analyses of 2 years of 8-min data indicates that the model is applicable between approximately 1 hour and 1 week with approximately uniformly distributed W_x/x values. The probabilities P show a clear dependence on the box characteristics and a slight seasonal nonstationarity. In the second step, the model is used to disaggregate the time series from 17- to 1-hour resolution. The model-generated data reproduce well the ratio between rainy and nonrainy periods and the distribution of individual volumes. Event volumes, event durations, and dry period lengths are fairly well reproduced, but somewhat underestimated, as was the autocorrelation. From analyses of power spectrum and statistical moments the model preserves the scaling behaviour of the data. The results demonstrate the potential of scaling-based approaches in hydrological applications involving rainfall disaggregation.