Summary

The USGS, in cooperation with the Idaho Department of Environmental Quality (IDEQ), used multiple linear regression analyses to develop equations that can be used for estimating the 1Q₁₀, 7Q₂, 7Q₁₀, and 30Q₅ low-flow frequency statistics at ungaged, unregulated sites on streams in Idaho. As part of this process, the relevant statistics were updated for all gaging stations in Idaho and some in adjacent States that, in general, had 10 or more years of record through water year 2003 and were unaffected by regulation and/or diversions. In regions of the State where one or more of these statistics are sometimes equal to zero, logistic regression analyses were used to develop equations for estimating the probability that the annual N-day low flow is equal to zero. Various physical and climatic characteristics of the drainage basins (basin characteristics) were used as the explanatory variables in each of the equations.

The logistic regression analyses in regions 4, 6, and 7 resulted in equations that were statistically significant for estimating the annual probability of zero flows for 1-, 7-, and 30-day periods. The final probability equations correctly predicted zero-flow values for 74 to 100 percent of the gaging stations used to develop the equations, depending on the region and the N-day period. Although it is assumed that these gaging stations provide a good representation of zero‑flow characteristics in each of the regions, any variability in the zero-flow characteristics within each region that was not represented may affect the predictive accuracy of the final equations. The zero-flow probability equations should be used for sites in regions 4, 6, and 7 before low-flow frequency statistics are estimated. If the resulting probability is greater than the non-exceedance probability for the statistic of interest, then the expected value for that statistic would be zero and the low-flow frequency equations should not be used. If the resulting probability is less than the non-exceedance probability for the statistic of interest, then the low-flow frequency equations should be used to estimate the value of the required statistic.

The equations for estimating low-flow frequency statistics had standard errors of prediction with a minimum range of +26.9 to -21.2 percent and a maximum range of +311 to -75.7 percent. In general, the 7Q₂ estimating equations exhibited the lowest standard errors, whereas the 1Q₁₀ equations exhibited the largest standard errors. The equations may not yield reliable results for sites with basin‑characteristic values that are outside of the range of values used to develop the equations. The equations also are not applicable for sites on regulated streams or on streams that are affected by significant gains and(or) losses resulting from factors including spring flow, channel seepage, diversions, and irrigation returns. If desired, however, the equations could be used on regulated streams to provide an estimate of natural flow statistics for comparison with the regulated statistics.

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