Hydraulic flow infrastructure is conventionally designed under the guidance of historic rainfall intensity-duration-frequency (IDF) curves that assume climate stationarity. However, climate change has altered, and will continue to modify, rainfall characteristics in many regions, particularly in coastal areas such as the Chesapeake Bay Watershed. As a result, the stationarity assumption will likely become invalid, making the existing deterministic IDF curves inadequate in accordance with relevant engineering design standards. To resolve this issue, next-generation probability-based IDF curves that can reflect the non-stationarity at temporal and spatial scales are needed to improve future Department of Defense (DoD) infrastructure planning processes and prevent over- or under-committing resources. In present, such probability-based IDF curves are lacking. The objectives of this project were to: 1) develop an innovative approach for creating next-generation IDF curves that consider nonstationary rainfall, and 2) use this approach to create probability-based IDF curves for the state of Virginia, most of which is located within the Chesapeake Bay Watershed.

Technical Approach

This project used 15-min rainfall data for the historical (prior 2013) periods of 57 rain gauges in Virginia and the projected precipitation time series by twelve pairs of Regional Climate Model (RCM) and Global Circulation Model (GCM).

The approach consisted of five steps. First, the missing values at each of the rain gauges were filled using advanced geostatistical techniques, such as inverse distance weighting and Kriging. For a given gauge and its record period, the missing-filled time series was used to formulate a dataset of historical annual maximum rainfall intensity. Second, for each gauge with a record period longer than 30 years, the time series were used to detect possible temporal trends using a modified Mann-Kendall technique. Herein, the non-stationarity was defined in terms of cumulative deviations from the mean. Third, in accordance to Gumbel, Fréchet, and Weibull statistical distributions, a best distribution was chosen for each of the 57 gauges. Fourth, statistical methods were developed and used to downscale the 3-h predictions of the RCM-GCM models to the gauges. Datasets of projected annual maximum rainfall intensities for selected twelve durations from 15 min to 72 h were created. Fifth, the best statistical distribution was applied to the historical and projected datasets to create gauge-level IDF curves.

In addition, the boundaries of the 53 Virginia eight-digit watersheds were extracted from the National Hydrography Dataset. Each watershed was subdivided into several Thiessen polygons in ArcGIS® to compute the areal rainfall intensities, which in turn were used to formulate the datasets of historical and projected annual maximum rainfall intensities. The best statistical distribution for this watershed, which was assumed to be same as that of the gauge with a largest Thiessen polygon area, was applied to the datasets to create the watershed-level IDF curves.


To facilitate the development of such an innovative approach, this project created several Microsoft® Excel spreadsheets and computer scripts in Visual Basic for Applications and R function. They proved to be efficient in manipulating large-size datasets for creating next-generation IDF curves. While no significant step changes were detected across Virginia, the historical annual maximum rainfall intensity was detected to have a significant (at a significance level of α = 0.05) decreasing trend at 11 gauges and a non-significant decreasing trend at another 46 gauges. For four gauges, the significant decreasing trends have led to the significant non-stationarity of annual maximum rainfall intensity. Given that the continuation of current climate trends would result in significant non-stationarity of annual maximum rainfall intensity at more gauges, it is imperative to develop probability-based IDF curves.

For a gauge with significant non-stationarity, each of its datasets of annual maximum durational rainfall intensity was iteratively subdivided into two or more sub-datasets until all sub-datasets were stationary. The sub-datasets were then used to develop IDF curves for this gauge. The annual maximum rainfall intensities at 30 gauges best fitted Gumbel distribution, while those at another 23 gauges best fitted Weibull distribution. These two distributions were found to be equally accurate for the remaining four gauges. Using the best distributions, this project generated 61 historical IDF curves for the rain gauges and 68 sets of historical IDF curves for the watersheds of Virginia. The gauge-level historical IDF curves were visually comparable with the Point Precipitation Frequency Estimates (PPFEs) of the National Oceanic and Atmospheric Administration (NOAA). Nevertheless, limited by the project period, probability-based IDF curves were created for eight gauges and one watershed only. For other gauges and watersheds, the relevant datasets were formulated for creating probability-based IDF curves.


The results of this project demonstrated the inevitable need for probability based IDF curves. An innovative approach for the development of such curves was developed and then applied to the state of Virginia. The project results can be a useful tool for the planning, design, and management of DoD, as well as civic, infrastructure.