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Regional regression equations for estimation of four hydraulic properties of streams at approximate bankfull conditions for different ecoregions in Texas

November 2, 2020

The U.S. Geological Survey, in cooperation with the U.S. Army Corps of Engineers, assessed statistical relations between hydraulic properties of streams at approximate bankfull conditions for different ecological regions (ecoregions) in Texas. Data from more than 103,000 records of measured discharge and ancillary hydraulic properties were assembled from summaries of discharge measurements for 424 U.S. Geological Survey streamgages in Texas. The data were subsequently subsetted at each streamgage for a streamgage-specific discharge interval centered on the estimated median annual peak discharge (0.5 annual exceedance probability) obtained from previously published regional regression equations in Texas in conjunction with the streamgage-specific sample median annual peak discharge for the period of record for each streamgage. Discharge measurements at gaged locations representing bankfull conditions (approximated from a discharge interval centered on the estimated median annual peak discharge at a given site) and associated watershed properties were subjected to rigorous statistical analysis. For most discharge measurements (where discharge is symbolically represented as Q), the following hydraulic properties are available: cross-section area (A), water-surface top width (B), and reported mean velocity (V). Statewide summary statistics were computed by using these four hydraulic properties (Q, A, B, and V) and the following five watershed properties: (1) watershed area (contributing drainage area), (2) a multiple of main-channel slope (1,000 times main-channel slope), (3) mean annual precipitation, (4) drainage density, and (5) sinuosity ratio. From the initial set of 424 streamgages, summary statistics were computed for 372 selected streamgages in Texas and constitute the subsetted measurements dataset described in this report. Eight of the 10 ecoregions in Texas are represented in the statewide summary statistics.

The resulting statistical relations, expressed as regression equations, can be used to estimate cross-section area, water-surface top width, discharge, and mean velocity of streams in different Texas ecoregions, at approximate bankfull conditions. In the regression equations, watershed properties were the independent variables for applicable watersheds, and predictions from the equations might be useful for estimating the four hydraulic properties at ungaged or unmonitored locations from selected characteristics measured at both the ungaged locations and gaged locations.

Four regression equations to estimate the four hydraulic properties were identified as the preferred equations from this study. The four preferred equations use watershed area, mean annual precipitation, and aggregated ecoregion (treated as a categorical variable) to estimate the hydraulic properties, and justification is provided for this preference. For the four equations, the proportions of variance explained by the regression equations as measured by Nash-Sutcliffe efficiency are about 71 percent for cross-section area, 36 percent for top width, 76 percent for discharge, and 25 percent for mean velocity. Residual standard error (RSEs) of the regression equations are 0.252 log10 square feet for cross-section area, 0.319 log10 feet for top width, 0.247 log10 cubic feet per second for discharge, and 0.190 log10 feet per second for mean velocity, and the corresponding standard deviations of response are 0.465 log10 square feet, 0.397 log10 feet, 0.507 log10 cubic feet per second, and 0.220 log10 feet per second, respectively. The residual standard errors are less than the standard deviations as anticipated but show that the uncertainty reduction (percent change) for cross-section area is about −46 percent, about −20 percent for top width, about −51 percent for discharge, and about −14 percent for mean velocity.