Incorporating daily rainfalls to derive rainfall DDF relationships at ungauged sites in Hong Kong and quantifying their uncertainty

Rainfall depth-duration-frequency (DDF) relationships are essential inputs for the design and management of various hydrosystem infrastructures (e.g., urban drainages, dams, dykes, etc.). In many cases, rainfall DDF relationships are required at a location where there is no gauge. However, due to the presence of intrinsic randomness of the precipitation process, limited rainfall record, and spatial interpolation, the derived DDF relationships at ungauged sites are subject to uncertainty. This is especially true in Hong Kong with regard to record length. To enhance the utilization of available rainfall data, a daily precipitation-based DDF generation framework for conventional rain gauges in Hong Kong has been developed by the authors utilizing a scaling model. In this article, the methodological framework is extended to derive rainfall DDF relationships at ungauged sites. Owing to the nonlinearity and complexity of the modeling process, exact statistical features of derived DDF relationships are difficult to obtain. In this study, Harr’s probabilistic point estimation method, known for its computational simplicity and accuracy, is applied to quantify the uncertainty features of rainfall DDF relationships derived for ungauged sites in Hong Kong. For illustration, four locations in different geographical locations in Hong Kong are considered. The results show that the uncertainty associated with the estimated statistical moments of annual maximum daily rainfall is significant in contributing to the overall uncertainty of derived rainfall DDF relationships.