Derivation of rainfall IDF relations by third-order polynomial normal transform

Establishing the rainfall intensity–duration–frequency (IDF) relations by the conventional method, the use of parametric distribution models has the advantage of automatic compliance of monotonicity condition of rainfall intensity and frequency. However, fitting rainfall data to a distribution separ...

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Bibliographic Details
Published in:Stochastic environmental research and risk assessment 2018-08, Vol.32 (8), p.2309-2324
Main Authors: You, Lingwan, Tung, Yeou-Koung
Format: Article
Language:English
Subjects:
Aquatic Pollution
Chemistry and Earth Sciences
Computational Intelligence
Computer Science
Earth and Environmental Science
Earth Sciences
Environment
Environmental research
Hydrologic data
Math. Appl. in Environmental Science
Mathematical models
Methods
Original Paper
Physics
Polynomials
Probability Theory and Stochastic Processes
Rain
Rain gauges
Rainfall
Rainfall intensity
Random variables
Risk assessment
Statistics for Engineering
Stormwater management
Waste Water Technology
Water Management
Water Pollution Control
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Summary:Establishing the rainfall intensity–duration–frequency (IDF) relations by the conventional method, the use of parametric distribution models has the advantage of automatic compliance of monotonicity condition of rainfall intensity and frequency. However, fitting rainfall data to a distribution separately by individual duration may possibly produce undulation and crossover of IDF curves which does not comply physical reality. This frequently occurs when rainfall record length is relatively short which often is the case. To tackle this problem this study presents a methodological framework that integrates the third-order polynomial normal transform (TPNT) with the least squares (LS) method to establish rainfall IDF relations by simultaneously considering multi-duration rainfall data. The constraints to preserve the monotonicity and non-crossover in the IDF relations can be incorporated easily in the LS-based TPNT framework. Hourly rainfall data at Zhongli rain gauge station in Taiwan with 27-year record are used to establish rainfall IDF relations and to illustrate the proposed methodology. Numerical investigation indicates that the undulation and crossover behavior of IDF curves can be effectively circumvented by the proposed approach to establish reasonable IDF relations.
ISSN:1436-3240
1436-3259
DOI:10.1007/s00477-018-1583-4