Toward parsimonious modeling of frequency of areal runoff from heavy-to-extreme precipitation in large urban areas under changing conditions: a derived moment approach

Translating changes in land surface conditions and climate into changes in precipitation, runoff and flood frequencies over a range of catchment scales is a pressing challenge for hydrologic design and flood risk management today. In this paper, we describe a novel approach for modeling areal runoff frequency from heavy-to-extreme precipitation in large urban areas using a simple but general stochastic model for runoff at point scale and bi- and univariate parametric probability distributions for positive point precipitation and areal runoff, respectively. We apply the approach to the Dallas-Fort Worth area using a 22-year historical multisensor precipitation dataset from the National Weather Service to characterize how the different factors that specify the second-order statistics of precipitation, imperviousness and soil water holding capacity at point scale may shape areal runoff frequency, and to assess how changes in precipitation climatology and land surface conditions may change areal runoff frequency as a function of catchment scale and magnitude of precipitation. The results indicate that areal runoff frequency is impacted most significantly by changes in climatological mean and coefficient of variation of positive point precipitation, water holding capacity of soil, imperviousness, and spatial correlation scale of positive point precipitation given the probability of occurrence of heavy-to-extreme precipitation, and that a very small number of low-order statistics of point precipitation may describe areal runoff frequency given the conditional probability distribution models for point precipitation and areal runoff. The approach presented hence offers a parsimonious physically-based alternative to purely numerical approaches based on integrated modeling, or empirical approaches based solely on statistical modeling toward predictive modeling of areal precipitation and runoff frequencies under changing hydroclimatological conditions.