A chaotic approach to rainfall disaggregation (original) (raw)

2001, Water Resources Research

The importance of high-resolution rainfall data to understanding the intricacies of the dynamics of hydrological processes and describing them in a sophisticated and accurate way has been increasingly realized. The last decade has witnessed a number of studies and numerous approaches to the possibility of transformation of rainfall data from one scale to another, nearly unanimously pointing to such a possibility. However, an important limitation of such approaches is that they treat the rainfall process as a realization of a stochastic process, and therefore there seems to be a lack of connection between the structure of the models and the underlying physics of the rainfall process. The present study introduces a new framework based on the notion of deterministic chaos to investigate the behavior of the dynamics of rainfall transformation between different temporal scales aimed toward establishing this connection. Rainfall data of successively doubled resolutions (i.e., 6, 12, 24, 48, 96, and 192 hours) observed at Leaf River basin, in the state of Mississippi, United States of America, are studied. The correlation dimension method is employed to investigate the presence of chaos in the rainfall transformation. The finite and low correlation dimensions obtained for the distributions of weights between rainfall data of different scales indicate the existence of chaos in the rainfall transformation, suggesting the applicability of a chaotic model. The formulation of a simple chaotic disaggregation model and its application to the Leaf River rainfall data provides encouraging results with practical potential. The disaggregation model results themselves indicate the presence of chaos in the dynamics of rainfall transformation, providing support for the results obtained using the correlation dimension method. 1. Introduction The lack of high-resolution temporal and spatial rainfall data has been one of the most prominent limiting factors in hydrological, meteorological, and agricultural calculations. The recent shift of our focus to deal with complex problems, such as pollution transport, rainfall-related pollution effects on treatment plants, runoff-induced washoff from impermeable surfaces, soil water infiltration movement, and water erosion, only indicates the added uncertainties on the outcomes if the required quality of data is not available. One possible way to solve this problem is to collect high-resolution data relevant for the problem in question. However, this is costly and timeconsuming and therefore hardly a competitive alternative in practice. As a result, the only alternative seems to be to try to transform the available data from one time and space scale to another. The last decade has witnessed a number of studies investigating the possibility of transformation of rainfall data from one scale to another [e.g., Hershenhorn and Woolhiser, 1987;