The Sequential Probability Ratio Test: An efficient alternative to exact binomial testing for Clean Water Act 303(d) evaluation

The United States’s Clean Water Act stipulates in section 303(d) that states must identify impaired water bodies for which total maximum daily loads (TMDLs) of pollution inputs into water bodies are developed. Decision-making procedures about how to list, or delist, water bodies as impaired, or not, per Clean Water Act 303(d) differ across states. In states such as California, whether or not a particular monitoring sample suggests that water quality is impaired can be regarded as a binary outcome variable, and California’s current regulatory framework invokes a version of the exact binomial test to consolidate evidence across samples and assess whether the overall water body complies with the Clean Water Act. Here, we contrast the performance of California’s exact binomial test with one potential alternative, the Sequential Probability Ratio Test (SPRT). The SPRT uses a sequential testing framework, testing samples as they become available and evaluating evidence as it emerges, rather than measuring all the samples and calculating a test statistic at the end of the data collection process. Through simulations and theoretical derivations, we demonstrate that the SPRT on average requires fewer samples to be measured to have comparable Type I and Type II error rates as the current fixed-sample binomial test. Policymakers might consider efficient alternatives such as SPRT to current procedure

Availability of high-magnitude streamflow for groundwater banking in the Central Valley, California

California's climate is characterized by the largest precipitation and streamflow variability observed within the conterminous US This, combined with chronic groundwater overdraft of 0.6-3.5 km3 yr-1, creates the need to identify additional surface water sources available for groundwater recharge using methods such as agricultural groundwater banking, aquifer storage and recovery, and spreading basins. High-magnitude streamflow, i.e. flow above the 90th percentile, that exceeds environmental flow requirements and current surface water allocations under California water rights, could be a viable source of surface water for groundwater banking. Here, we present a comprehensive analysis of the magnitude, frequency, duration and timing of high-magnitude streamflow (HMF) for 93 stream gauges covering the Sacramento, San Joaquin and Tulare basins in California. The results show that in an average year with HMF approximately 3.2 km3 of high-magnitude flow is exported from the entire Central Valley to the Sacramento-San Joaquin Delta often at times when environmental flow requirements of the Delta and major rivers are exceeded. High-magnitude flow occurs, on average, during 7 and 4.7 out of 10 years in the Sacramento River and the San Joaquin-Tulare Basins, respectively, from just a few storm events (5-7 1-day peak events) lasting for 25-30 days between November and April. The results suggest that there is sufficient unmanaged surface water physically available to mitigate long-term groundwater overdraft in the Central Valley