Modeling Temporal Rainfall via a Fractal Geometric ApproachEPA Grant Number: R824780
Title: Modeling Temporal Rainfall via a Fractal Geometric Approach
Investigators: Puente, Carlos E.
Institution: University of California - Davis
EPA Project Officer: Packard, Benjamin H
Project Period: November 1, 1995 through October 1, 1998
Project Amount: $198,000
RFA: Water and Watersheds (1995) Recipients Lists
Research Category: Water and Watersheds , Water
Description:The goal of this work is to derive parsimonious representations of rainfall records under alternative climatic conditions so that a classification of observed rainfall patterns may be elucidated. Accurate rainfall modeling is of vital importance for the proper management of our environment. Rainfall descriptions are required, among others, to model pollution migration, to address issues related to climate change (i.e., global circulation), to estimate extreme weather events, and to manage our watersheds.
This task will be accomplished by employing the fractal-multifractal representation developed by Puente (1992) to encode rainfall records throughout the State of California as suitable fractal transformations of appropriate (turbulence-related) multifractal measures. Once the time series are represented by this approach, a classification of rainfall events will be attempted via the surrogate parameters that define the fractal transformation and the multifractal measure. This should result in a better understanding of temporal and spatial rainfall patterns within the State of California under alternative climatic conditions. Experimentation with alternative optimization methodologies, using a variety of objective functions, has been attempted in order to properly understand how to find the fractal-multifractal parameters. For a detailed storm in Boston it has been found that indeed good representations may be obtained with only five parameters. This is relevant as our best published results for the same storm required thirteen parameters. Simulations with Cantorian parent measures are being carried out and they show that the fractal-multifractal approach results in objects which resemble rainfall time series. During the next year efforts will concentrate in finding representations at the chosen sites within the State of California.
This research should lay a firm foundation for a new approach towards hydrologic dynamics in terms of surrogate geometric information. This methodology should be viable since it concentrates on capturing what is observed, i.e., the geometry of rainfall series.