Unbiased Estimates and Confidence Intervals of Riverine Loads for Low-Frequency Water Quality Monitoring Strategies

Abstract

Accurate estimates of riverine constituent loads are essential for water pollution control and erosion control in watersheds, but an accurate estimation method for commonly employed water quality monitoring strategies, such as calendar-based sampling with high-flow sampling, has not been established. Therefore, we propose methods for both unbiased load estimation and confidence interval construction for annual riverine loads using the Horvitz-Thompson estimator based on limited samples (12 to 20 per year) collected with commonly used water quality monitoring strategies. In addition, we propose an uncertainty reduction method to calculate efficient confidence intervals using probability resampling based on a simple rating curve due to the small sample sizes. The effectiveness of the proposed method is verified by load estimates based on 150 annual data sets of daily pairs of discharge and concentration observations of six water quality parameters from different watersheds and years. The tested sampling strategies include random sampling over time as a proxy for calendar-based sampling, random sampling with high-flow sampling, and flow-proportional sampling. The results show that the proposed methods provide unbiased load estimates for all the data sets and appropriate confidence intervals. The uncertainty reduction in the confidence interval widths obtained with probability resampling is effective for calendar-based sampling. We also explain the importance of defining proper sampling probabilities for load estimation based on samples with missing observations. The proposed method can be used to evaluate and improve existing water quality monitoring strategies for more efficient load estimation and the retrieval of accurate load estimates from existing data sets.