Streamflow data, basin characteristics, and rainfall data from 39 streamflow-gaging stations for urban areas in and adjacent to Missouri were used by the U.S. Geological Survey in cooperation with the Metropolitan Sewer District of St. Louis to develop an initial abstraction and constant loss model (a time-distributed basin-loss model) and a gamma unit hydrograph (GUH) for urban areas in Missouri. Study-specific methods to determine peak streamflow and flood volume for a given rainfall event also were developed.

Distinct basin characteristics were evaluated and selected for use on the basis of their theoretical relation to flow, results from previous studies, and the ability to reliably measure the basin characteristic using digital datasets and geographic information system (GIS) technology. The key basin characteristics determined or computed for each of the 39 basins upstream from the streamflow-gaging stations were drainage area, percent impervious area, main-channel slope based on the 10- and 85-percent length method, percentage of the basin area in storage (lakes, ponds, reservoirs, wetlands), the composite Natural Resources Conservation Service curve number estimated from a combination of the soil type data and land-use characteristics, and the streamflow variability index developed for the recently completed study of low-flow regression in Missouri.

Characteristics of spatial and temporal rainfall distribution came from the next generation weather radar (NEXRAD) network. Procedures were developed for this study to convert the variable radar sweep rate into a 5-minute total rainfall hyetograph using data from the radar bin at the centroid of a given basin. Additional characteristics determined for each storm on the basin included the 5-day and 14-day antecedent rainfall, estimated from the mean of daily rainfall values from various rain gages in the area.

The database of observed rainfall and runoff events for the 39 basins upstream from the streamflow-gaging stations was analyzed to compute the optimal storm-specific initial abstraction and constant loss values, as well as the time to peak, peak streamflow, and shape factor values of the GUH. The optimal storm-specific values were used to develop a regional regression equation for initial abstraction; conversely, the constant loss was estimated not by regression but from either a generalized or specific regional mean value. The optimal storm-specific values of GUH time to peak, GUH peak streamflow, and GUH shape factor were used to develop regression equations for the GUH.

The regression equations for the GUH initially were tested alone, and then were combined with the appropriate regional regression equation for initial abstraction and both the generalized regional and specific regional mean constant loss values. For the GUH regression equations, the interquartile range was substantially smaller than the range spanned by the minimum and maximum values, which indicates most of the errors have much smaller variation, and the minimum and maximum values may be extreme outliers. The central tendency of the regressed errors for peak streamflow and runoff hydrograph volume were both approximately zero, which implies a generally unbiased estimation of these values. The mean and median of the regressed errors for time to peak streamflow were both small but greater than zero, which implies the GUH regression equations create a hydrograph that has a peak that is later in time than observed. Specifically, the regressed times indicate an offset of about 10 minutes, on average, from observed. The mean and median of the regressed errors for widths of the runoff hydrograph at 50 and 75 percent were less than zero, which implies the GUH tends to slightly underestimate these widths compared to the observed.

The appropriate regional initial abstraction regression equation was combined with both the generalized and the specific regional mean constant loss values and the GUH regression equations. Both the generalized regional mean constant loss and specific regional mean constant loss forms of the basin-loss model worked equally well to model the observed runoff hydrograph based on the error analysis, and neither model seems to make a consistently better approximation. Both initial abstraction and constant loss models combined with the GUH regression equations were further validated using several storms available after the start of the project in early 2011 with similar but consistently higher error results. If these methods are used in an urban area in Missouri other than those examined in this study, advice to the user is given to consider using the generalized regional mean values. If these methods are used in an urban area that is a subbasin of one of the basins in this study, advice to the user is given to consider using the specific regional mean values.

The rainfall-runoff pairs from the storm-specific GUH analysis were further analyzed against various basin and rainfall characteristics to develop equations to estimate the peak streamflow and flood volume based on a quantity of rainfall on the basin.