Methods for Estimating Drought Streamflow Probabilities for Virginia Streams
Maximum likelihood logistic regression model equations used to estimate drought flow probabilities for Virginia streams are presented for 259 hydrologic basins in Virginia. Winter streamflows were used to estimate the likelihood of streamflows during the subsequent drought-prone summer months. The maximum likelihood logistic regression models identify probable streamflows from 5 to 8 months in advance. More than 5 million streamflow daily values collected over the period of record (January 1, 1900 through May 16, 2012) were compiled and analyzed over a minimum 10-year (maximum 112-year) period of record. The analysis yielded the 46,704 equations with statistically significant fit statistics and parameter ranges published in two tables in this report. These model equations produce summer month (July, August, and September) drought flow threshold probabilities as a function of streamflows during the previous winter months (November, December, January, and February). Example calculations are provided, demonstrating how to use the equations to estimate probable streamflows as much as 8 months in advance.
Methods and Equations for Estimating Peak Streamflow Per Square Mile in Virginia’s Urban Basins
Models are presented that describe Virginia urban area annual peak streamflow per square mile based on
basin percent urban area and basin drainage area. Equations are provided to estimate Virginia urban peak
flow per square mile of basin drainage area in each of the following annual exceedance probability
categories: 0.995, 0.99, 0.95, 0.9, 0.8, 0.67, 0.5, 0.43, 0.2, 0.1, 0.04, 0.02, 0.01, 0.005, and 0.002
(recurrence intervals of 1.005, 1.01, 1.05, 1.11, 1.25, 1.49, 2.0, 2.3, 5, 10, 25, 50, 100, 200, and 500
years, respectively). Equations apply to Virginia drainage basins ranging in size from no less than
1.2 mi2 to no more than 2,400 mi2 containing at least 10 percent urban area, and
not more than 96 percent urban area. A total of 115 Virginia drainage basins were analyzed.
Actual-by-predicted plots and leverage plots for response variables and explanatory variables in
each peak-flow annual exceedance probability category indicate robust model fits and significant
explanatory power. Equations for 8 of 15 urban peak-flow response surface models yield R-square values
greater than 0.8. Relations identified in statistical models, describing significant increases in urban
peak stream discharges as basin urban area increases, affirm empirical relations reported in past
studies of change in stream discharge, lag times, and physical streamflow processes, most notably those
detailed for urban areas in northern Virginia.