Introduction of k-means clustering into random cascade model for disaggregation of rainfall from daily to 1-hour resolution with improved preservation of extreme rainfall

Abstract

Temporal disaggregation of rainfall has been of particular focus because of the non-availability of higher-resolution rainfall data for a long-duration period. Fine temporal resolution rainfall is used in a multitude of hydrological applications. Researchers have proposed various disaggregation models to disaggregate coarse temporal resolution rainfall. In this paper, firstly, the microcanonical multiplicative random cascade (MMRC) model is applied for disaggregation from daily rainfall to a one-hour scale. The model is applied in four different rainfall stations for disaggregation having varying rainfall patterns and characteristics. It is observed that the MMRC model can generate statistically reliable rainfall time series; however, the extreme rainfall characteristics are not well conserved by the model for all the stations.This paper describes a new model based on a random multiplicative cascade process where classification and parameter generation is done by k-means clustering such that it can better conserve extreme rainfall conditions and generate a reliable rainfall time series (MMRC-K). K-means clustering is a vector quantization method that divides the observations into a particular number of clusters based on the nearest mean called cluster centroid. The novel approach is tested with the same four Indian cities. The use of k-means clustering has made the classification and parameter generation of the model robust such that it can work with data sets of varying characteristics. It is found that MMRC-K provides improved conservation of extreme rainfall characteristics compared to the MMRC model for all four stations. The MMRC-K model reproduces the IDF curves of Delhi and Mumbai stations quite well; however, a little discrepancy was observed at higher resolution and larger return periods in Kolkata and Chennai stations. Extreme rainfall at finer resolution is used in various hydrological analyses and design problems like urban drainage design, stormwater management, etc. The overall superior conservation of the extreme rainfall characteristics in the model-generated rainfall time series by the MMRC-K model compared to the MMRC model supports the potential applicability of the model for temporal disaggregation.