Errors from hydrological simulations have substantial influence on hydrological applications. There are increasing interests to incorporate statistical models of the errors (error models) into hydrological applications to improve simulations. However, conventional error models are usually temporally unvaried and may be inadequate to handle model simulation errors when the underlying error statistics are strongly seasonal. To overcome this problem, the use of temporally varied error models in both prediction and forecasting applications are investigated. We analyze different levels of temporal granularity to identify the optimal temporally varied error model to best improve simulations and to quantify uncertainty. The Error Reduction and Representation In Stages (ERRIS) model is adapted in this study to improve streamflow simulations produced by the Variable Infiltration Capacity model for the Yarlung Tsangbo River basin. Well-marked seasonal and sub-seasonal variations in error statistics are found. Accordingly, three temporally varied ERRIS models are constructed at semi-annual (ERRIS-H), seasonal (ERRIS-S) and monthly (ERRIS-M) temporal granularity and compared with a benchmark model, the temporally unvaried model (ERRIS-A). Results show that the temporally varied ERRIS models are considerably more effective than the temporally unvaried one, with 34% reduction in continuous ranked probability score (CRPS) and 23% increase in Nash-Sutcliffe Efficiency (NSE) for prediction applications. With respect to forecasting applications, improvements of about 7% in CRPS are achieved by the temporally varied models. The performance of different temporally varied error models roughly follows the same order as the level of temporal granularity. Generally, ERRIS-S and ERRIS-M are similarly effective, with ERRIS-M providing additional improvement by more than 15% in CRPS for the spring season and by at least 30% for the autumn season. It is concluded that the consistency of temporal granularity between error models and variations of error statistics is the key to effective error reduction and uncertainty quantification. When complicated hydrological processes exist, hydrological model tends to produce seasonally and even sub-seasonally varied error statistics. Consequently, temporally finer error models are expected to lead to higher accuracy and reliability.

中文翻译：

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用于改进模拟和量化不确定性的时变误差建模

水文模拟的误差对水文应用有重大影响。将误差的统计模型（误差模型）纳入水文应用以改进模拟的兴趣越来越大。然而，传统的误差模型通常在时间上是不变的，当基础误差统计具有很强的季节性时，可能不足以处理模型模拟误差。为了克服这个问题，研究了在预测和预测应用中使用随时间变化的误差模型。我们分析了不同级别的时间粒度，以确定最佳的时间变化误差模型，以最好地改进模拟并量化不确定性。本研究采用了误差减少和阶段表示 (ERRIS) 模型，以改进雅鲁藏布江流域可变入渗容量模型产生的流量模拟。发现错误统计中明显的季节性和次季节性变化。因此，在半年 (ERRIS-H)、季节性 (ERRIS-S) 和每月 (ERRIS-M) 时间粒度上构建了三个随时间变化的 ERRIS 模型，并与基准模型、时间不变模型 (ERRIS-A) 进行了比较. 结果表明，时间变化的 ERRIS 模型比时间不变的模型更有效，连续排名概率得分 (CRPS) 降低 34%，纳什-萨特克利夫效率 (NSE) 提高 23%，用于预测应用。在预测应用方面，通过随时间变化的模型实现了 CRPS 约 7% 的改进。不同的时间变化误差模型的性能大致遵循与时间粒度级别相同的顺序。一般来说，ERRIS-S 和 ERRIS-M 的效果相似，ERRIS-M 在春季提供额外的 CRPS 改善 15% 以上，在秋季提供至少 30% 的额外改善。得出的结论是，误差模型和误差统计变化之间时间粒度的一致性是有效减少误差和不确定性量化的关键。当存在复杂的水文过程时，水文模型往往会产生季节性甚至亚季节变化的误差统计。因此，预计时间上更精细的误差模型将导致更高的准确性和可靠性。