Climate-Related Trends of Within-Storm Intensities Using Dimensionless Temporal-Storm Distributions

Huff curves are probabilistic time distributions of rainfall expressed as dimensionless cumulative percentages of storm depth and duration. Previous studies have documented development factors, spatial robustness, and the utility of Huff curves in practical applications. However, the effects of trending rainfall on Huff curve intensity patterns have not yet been studied. The goal of this paper is to fill this gap by studying Huff curve patterns in a watershed with demonstrated increasing trends of temperature and precipitation, with the intention that it can be generalized to other areas in the US and the world. To achieve this goal, the high temporal resolution precipitation data collected from a high spatial density, 72-year precipitation-gauge network on the $4.25\text{-}{\mathrm{km}}^2$ North Appalachian Experimental Watershed in east-central Ohio were used. Seasonal storm pattern trends from 1939 to 2010 were investigated using dimensionless depth (with the frequency of 50%, $d_{50}$) and the curve variability ($V=d_{80}-d_{20}$) at three dimensionless within-storms time periods (three verticals). The Spearman rank correlation procedure (correlation coefficient, $\rho$ and significance probability, $p$) was used to statistically determine trends over time using 8 periods of 4-season sets of Huff curves over the 72 years. Two averages of $\rho$ and $p$ were computed: (1) by averaging the individual $\rho$ and $p$ obtained from 10 gauges (AvgI); and (2) by grouped averaging of all individual gauge values of $d_{50}$ and $V$ and then computing $\rho$ and $p$ (AvgG). The test results of individual gauges showed that 4 cases for $d_{50}$ and 23 cases for $V$ were significant for all seasons and verticals (total of 120 cases for each variable). The test results of AvgI for $d_{50}$ and $V$ and AvgG for $d_{50}$ showed no significant trends in all seasons and verticals. Only the AvgG for $V$ led to a significant trend for $V$ in spring and fall at different times within storm patterns. The data do not provide sufficient evidence at the $p=0.05$ significance level to reject the null hypothesis of unchanging position of the dimensionless depth of the 50% Huff curves for individual or averages for all seasons and verticals. Also, there is insufficient evidence to reject the null hypothesis of unchanging variability, $V$, using the average $\rho$ of individual gauges (AvgI for $V$) for all seasons and verticals. AvgG results showed a significant trend in $V$; however, this analysis may be affected by the nonindependence of storm data. The results suggest that it is likely that there is little if any effect of trending climate over approximately 70 years on Huff curve patterns. The results of this study add to the robustness characteristics of Huff curves and to their potential use in hydrological practice as design storms, as the foundation of stochastic storm generation, and for storm disaggregation, and they deserve further investigation. These different forms of inputs to watershed models have the potential to improve runoff estimation. The results suggest that, if verified in other studies, they have applicability to provide useful stationary precipitation patterns across the US and other areas of the world in areas of nonstationary climate. Also, individual rain gauge data may not be representative of trends even over small areas, and seasonal differences were noticeable as found in other studies. Recommendations are provided.