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Improving probabilistic prediction of daily streamflow by identifying Pareto optimal approaches for modeling heteroscedastic residual errors

机译：通过确定建模异方差残差误差的帕累托最优方法，提高日流量的概率预测

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摘要

Reliable and precise probabilistic prediction of daily catchment-scale streamflow requires statistical characterization of residual errors of hydrological models. This study focuses on approaches for representing error heteroscedasticity with respect to simulated streamflow, i.e., the pattern of larger errors in higher streamflow predictions. We evaluate eight common residual error schemes, including standard and weighted least squares, the Box-Cox transformation (with fixed and calibrated power parameter ) and the log-sinh transformation. Case studies include 17 perennial and 6 ephemeral catchments in Australia and the United States, and two lumped hydrological models. Performance is quantified using predictive reliability, precision, and volumetric bias metrics. We find the choice of heteroscedastic error modeling approach significantly impacts on predictive performance, though no single scheme simultaneously optimizes all performance metrics. The set of Pareto optimal schemes, reflecting performance trade-offs, comprises Box-Cox schemes with of 0.2 and 0.5, and the log scheme (=0, perennial catchments only). These schemes significantly outperform even the average-performing remaining schemes (e.g., across ephemeral catchments, median precision tightens from 105% to 40% of observed streamflow, and median biases decrease from 25% to 4%). Theoretical interpretations of empirical results highlight the importance of capturing the skew/kurtosis of raw residuals and reproducing zero flows. Paradoxically, calibration of is often counterproductive: in perennial catchments, it tends to overfit low flows at the expense of abysmal precision in high flows. The log-sinh transformation is dominated by the simpler Pareto optimal schemes listed above. Recommendations for researchers and practitioners seeking robust residual error schemes for practical work are provided.
机译：可靠和精确的概率预测日汇水规模流量需要统计表征水文模型的剩余误差。这项研究着重于代表关于模拟流量的误差异方差性的方法，即在较高流量预测中较大误差的模式。我们评估了八种常见的残差方案，包括标准和加权最小二乘，Box-Cox变换（具有固定和校准的功率参数）和log-sinh变换。案例研究包括澳大利亚和美国的17个常年流域和6个临时流域，以及两个集总水文模型。使用预测的可靠性，精度和体积偏差指标来量化性能。我们发现，选择异方差错误建模方法会对预测性能产生重大影响，尽管没有哪个方案可以同时优化所有性能指标。反映性能权衡的一组帕累托最优方案包括具有0.2和0.5的Box-Cox方案以及对数方案（= 0，仅常年流域）。这些方案甚至远远优于平均水平的其余方案（例如，在临时集水区，中位精度从观测流量的105％降低到40％，中位偏差从25％降低到4％）。对经验结果的理论解释强调了捕获原始残差的偏斜/峰度并重现零流量的重要性。矛盾的是，对的校准往往适得其反：在多年生流域，它往往过低地适合低流量，却以高流量下的精度差为代价。对数正弦变换由上面列出的更简单的Pareto最优方案控制。为研究人员和从业人员提供了建议，以为实际工作寻求鲁棒的残差方案。

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