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Estimating the uncertainty in annual riverine constituent loads, which is the mass that passes through a river cross-section into a receiving water body, using infrequent water quality (WQ) observations is a difficult and unsolved task. Therefore, we propose an unbiased point estimation method and interval estimation method for river loads based on the rating curve (RC) method using importance sampling and the bootstrap method, respectively. In this paper, we first statistically explain the unbiasedness of load estimates using the proposed method. Second, the effectiveness of point and interval estimates by the proposed method is demonstrated for river loads from a small catchment and from large watersheds based on discharge and WQ data of solutes, nutrients, and suspended sediments with 10-min to daily intervals. The results show that the proposed method provides unbiased estimates and appropriate coverage of confidence intervals regardless of the RC model used. The results also reveal that the dominant cause of bias in load estimates based on ordinary RC methods, such as the Loadest model, is not due to the poor simulation of observed loading rates by the RCs or because of the nonnormality of the regression residuals but rather improper sampling strategies. The proposed method is currently not feasible for WQ monitoring sites in large rivers due to the unmanageability of missing observations or censored data and an inefficient sampling strategy, although the requirement of unbiased estimation explained here can aid in scheduling high-flow sampling for monitoring sites. |
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