Estimation of Historical-Annual and Historical-Monthly Scale-Invariant Flow Duration Curves with Implementation for Iowa

Abstract

This paper presents a procedure to derive historical-annual and historical-monthly flow duration curves (FDC) that are monotonic and continuous for agricultural, unregulated, ungauged sites. The authors explore the performance and the regional dependence of four different regression models for the estimation of daily flow quantiles (Qp), with probabilities of exceedance (p) ranging from .1 to .99. The construction and analysis of the four regression models is based on scale-invariance of Qp with respect to drainage area (A) or mean annual flow (Q¯). The authors implemented the procedure using data from 74 gauged sites in the state of Iowa. The study concludes that the multi-scaling framework of Qp with respect to Q¯ provides the most accurate FDC estimates, which are region-independent within the physical characteristics of Iowa. The authors developed a piecewise continuous function to estimate the scaling parameters as a function of p, allowing estimations of continuous FDCs using independent estimates of Q¯. A validation test using data from 4 gauges not employed in developing the regression equations shows that the methodology performs similarly for historical-annual FDC estimates when compared to that developed for Iowa by the US Geological Survey. For discharges with p values larger than .6, the proposed methodology exhibits lower, but still acceptable, performance. Two features make the proposed methodology attractive for FDC estimation: first, it is simpler to use and implement than the USGS methodology because it only requires estimates of Q¯; and second, it provides reliable FDC estimates at monthly scales, which are otherwise unavailable. The authors present an application example in which FDC estimates at ungauged sites are used to create maps of streamflow frequency to categorize flows predicted in real time by a distributed hydrologic model implemented for Iowa.