Temporal rainfall disaggregation using a multiplicative cascade model for spatial application in urban hydrology

Abstract

Rainfall time series of high temporal resolution and spatial density are crucial for urban hydrology. The multiplicative random cascade model can be used for temporal rainfall disaggregation of daily data to generate such time series. Here, the uniform splitting approach with a branching number of 3 in the first disaggregation step is applied. To achieve a final resolution of 5 min, subsequent steps after disaggregation are necessary. Three modifications at different disaggregation levels are tested in this investigation (uniform splitting at Δt = 15 min, linear interpolation at Δt = 7.5 min and Δt = 3.75 min). Results are compared both with observations and an often used approach, based on the assumption that a time steps with Δt = 5.625 min, as resulting if a branching number of 2 is applied throughout, can be replaced with Δt = 5 min (called the 1280 min approach). Spatial consistence is implemented in the disaggregated time series using a resampling algorithm. In total, 24 recording stations in Lower Saxony, Northern Germany with a 5 min resolution have been used for the validation of the disaggregation procedure. The urban-hydrological suitability is tested with an artificial combined sewer system of about 170 hectares. The results show that all three variations outperform the 1280 min approach regarding reproduction of wet spell duration, average intensity, fraction of dry intervals and lag-1 autocorrelation. Extreme values with durations of 5 min are also better represented. For durations of 1 h, all approaches show only slight deviations from the observed extremes. The applied resampling algorithm is capable to achieve sufficient spatial consistence. The effects on the urban hydrological simulations are significant. Without spatial consistence, flood volumes of manholes and combined sewer overflow are strongly underestimated. After resampling, results using disaggregated time series as input are in the range of those using observed time series. Best overall performance regarding rainfall statistics are obtained by the method in which the disaggregation process ends at time steps with 7.5 min duration, deriving the 5 min time steps by linear interpolation. With subsequent resampling this method leads to a good representation of manhole flooding and combined sewer overflow volume in terms of hydrological simulations and outperforms the 1280 min approach.