Estimating 7Q10 Confidence Limits from Data: A Bootstrap Approach

7Q10 streamflow estimates used to support modeling and data analysis under the Clean Water Act national pollution discharge elimination system and total maximum daily load programs can have direct environmental and economic impacts. Thus it is important that 7Q10 streamflow always be reported together with confidence limits indicating the reliability of the estimate. In practice this is rarely done. This technical note presents a bootstrap approach for computing 7Q10 confidence limits from data and compares it to an empirical method. A case study using randomly selected subsets of data from five rivers in Idaho is used to evaluate the two methods. While both methods exhibit the expected increase in confidence interval as fewer years of data used, the bootstrap approach generally results in wider confidence intervals than does the empirical method. The opposite appears to be true in cases where fewer than $15\text{years}$ of data are used or when the data are positively skewed. As most streamflow data are positively skewed short records, the bootstrap approach can generally be thought of as a more conservative means for estimating 7Q10 confidence intervals.