Rainfall intensity-duration-frequency (IDF) models have been extensively used in water resources planning and design. The choice of suitable model for a proper data range and accurate estimation of model parameters are essential for sound design. Due to the fact that IDF models involve return period, they are probabilistic models. In this thesis, the unconditional and conditional cumulative distribution function (CDF) and probability density function (PDF) of rainfall quantity corresponding to an IDF model are derived. Also, an inherent lower bound constraint associated with an IDF model is found....[ Read more ]

Rainfall intensity-duration-frequency (IDF) models have been extensively used in water resources planning and design. The choice of suitable model for a proper data range and accurate estimation of model parameters are essential for sound design. Due to the fact that IDF models involve return period, they are probabilistic models. In this thesis, the unconditional and conditional cumulative distribution function (CDF) and probability density function (PDF) of rainfall quantity corresponding to an IDF model are derived. Also, an inherent lower bound constraint associated with an IDF model is found.

In parameter estimation, the conventional approach fits the extracted rainfall quantities of some selected return periods and storm durations from a frequency analysis. The approach suffers three drawbacks: (1) indirectly uses the observed annual maximum rainfall data; (2) does not consider inherent lower bound constraint associated with the IDF model under consideration; and (3) cannot utilize the well-established criteria, such as likelihood and entropy, to estimate rainfall IDF model parameters. Numerical illustrations show that the optimal parameters obtained from the conventional approach without considering the lower bound constraint often results in negative probability for some observed data.

To overcome these shortcomings, the conventional approach is modified by incorporating the inherent lower bound constraint. Furthermore, a new approach is proposed by which observed annual maximum rainfall data are directly utilized in conjunction with seven goodness-of-fit criteria for estimating IDF model parameters. Numerical results indicate that the proposed approach produces far better fit than the conventional approach using any of the three IDF models considered.

It is also observed that all three IDF models considered are not suitable to fit the entire range of the observed rainfall data at Hong Kong Observatory (HKO). However, satisfactory result can be achieved in a piece-wise fashion by which observed annual maximum rainfall quantities of individual duration are segmented with proper choice of frequency points so that, within each frequency range, the rainfall quantity and return period has nearly linear relationship in log-log space.

Since different models, along with different fitting criteria, can be used to establish at-site IDF relationship, this thesis also addresses the issue on the evaluation and selection of proper model and fitting criterion. Based on the proposed approach, the relative performance of the three commonly used IDF models and seven fitting criteria are evaluated. In this study, two transformations, namely, normalization and standardization, are used to remove the effect of magnitude of different objective function. Evaluation procedures are developed using the Euclidean distance between the best and individual performance vectors as the performance indicator. According to the shortest-Euclidean-distance criterion, the best model-based criterion, and the best criterion-based model, as well as the best model and criterion for all fitting criteria and models, are also identified for HKO.