Validation of Monthly-Mean Streamflow Equations

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The U.S. Geological Survey, in cooperation with the Colorado Water Conservation Board, evaluated the predictive uncertainty of mean-monthly streamflow-regression equations representative of natural streamflow conditions in Colorado. This study evaluates the predictive uncertainty of mean-monthly streamflow-regression equations developed in a 2009 U.S. Geological Survey study using streamflow data collected over the entire period of record at each streamgage through calendar year 2013. The study area for this report is limited to the Mountain, Northwest, Rio Grande, and Southwest hydrologic regions of Colorado.

Data collected from the beginning of the period of record through calendar year 2013 were used to evaluate the mean-monthly streamflow equations using the same basin characteristics as in the 2009 study. U.S. Geological Survey and Colorado Division of Water Resources streamgages with at least 10 years of streamflow record and identified as representative of natural streamflow conditions were selected for this study. During the streamgage selection process, a total of 432 streamgages, composed of 278 from the 2009 study and 154 new streamgages, were identified.

The updated standard error of prediction and adjusted coefficient of determination values that correspond to the mean-monthly streamflow equations developed in the 2009 study are in close agreement with the results of this study. The old streamgages performed slightly better than the new streamgages, with approximately 88 and 85 percent of the data within the prediction intervals, respectively. This result was expected because the streamgages used to develop the regression equations should yield a better performance than the new streamgages.

For all hydrologic regions, approximately 87 percent of the data are within the 95-percent prediction intervals. The explanation for why fewer than 95 percent of the data are within the prediction intervals is that the data do not conform perfectly to the regression assumptions required to accurately estimate performance metrics. The equations for the Rio Grande hydrologic region had the best fit with the parametric prediction-interval assumptions, with approximately 91.8 percent of the data within the prediction interval (average 12 months). The Mountain, Northwest, and Southwest hydrologic regions had 87.8, 84.9, and 83.5 percent of the data contained within the prediction interval, respectively.

Monthly adjusted coefficient of determination values were computed and have the same general pattern for all four hydrologic regions. The largest values usually occur in March or April, and the lowest values usually occur in August or September. Only the Rio Grande hydrologic region deviates from this seasonal pattern, exhibiting a decrease in adjusted coefficient of determination values in August and September, with the lowest values occurring in the winter months (December, January, and February). Generally, the adjusted coefficient of determination values for this report are just slightly less (0.76 compared to 0.79) than the values computed in the 2009 study. The similarity of values, even when tested with data not used to originally develop the mean-monthly streamflow-regression equations, provides confidence that the predictive uncertainty of mean-monthly regression equations in the 2009 study are accurate. The fact that the results for the two datasets are very similar provides assurance that when these equations are applied to locations not used to develop the equations, the standard error of prediction and adjusted-coefficient of determination error metrics should be similar to those established in the 2009 study for locations with natural streamflow.

The median absolute differences between the observed and computed mean-monthly streamflow for Mountain, Northwest, and Southwest hydrologic regions are fairly uniform throughout the year, with the exception of late summer and early fall (July, August, and September), when each hydrologic region exhibits a substantial increase in median absolute percent difference. The greatest difference occurs in the Northwest hydrologic region, and the smallest difference occurs in the Mountain hydrologic region. The Rio Grande hydrologic region shows seasonal variation in median absolute percent difference with March, April, August, and September having a median absolute difference near or below 40 percent, and the remaining months of the year having a median absolute difference near or above 50 percent. In the Mountain, Northwest, and Southwest hydrologic regions, the mean-monthly streamflow equations perform the best during spring (March, April, and May). However, in the Rio Grande hydrologic region, the mean-monthly streamflow equations perform the best during late summer and early fall (August and September).