论文标题
基于期望的水文建模用于不确定性估计：平均值之后的寿命
Expectile-based hydrological modelling for uncertainty estimation: Life after mean
论文作者
论文摘要
水文模型的预测本质上应该是概率的。我们的目的是引入一种方法，该方法直接使用预期材料估算水文模拟的不确定性，从而补充先前基于分位数的直接方法以及概括基于平均值的方法。预期是水文学的新风险措施。与使用指定值相比过程实现频率信息的分位数相比，预期使用了超过指定值超出量的其他信息。预期是分位数的最低平方类似物，并且可以以与分位数相同的方式表征概率分布。此外，概率分布的平均值是预期级为0.5的特殊情况。为此，我们提出了使用预期损失函数进行校准的水文模型，这对于预期而言是一致的。我们将我们的方法应用于连续美国的511个盆地，并以GR4J，GR5J和GR6J水文模型的预期水平模拟提供了预期水平的预期性预期，以期望水平为0.5、0.9、0.95和0.975。从经验上，诚实的评估证明，GR6J模型在所有预期水平上都优于其他两个模型。通过简单地调整目标函数，提供了超越水文建模的平均值的巨大机会。
Predictions of hydrological models should be probabilistic in nature. Our aim is to introduce a method that estimates directly the uncertainty of hydrological simulations using expectiles, thus complementing previous quantile-based direct approaches as well as generalizing mean-based approaches. Expectiles are new risk measures in hydrology. Compared to quantiles that use information of the frequency of process realizations over a specified value, expectiles use additional information of the magnitude of the exceedances over the specified value. Expectiles are least square analogues of quantiles and can characterize the probability distribution in much the same way as quantiles do. Moreover, the mean of the probability distribution is the special case of the expectile at level 0.5. To this end, we propose calibrating hydrological models using the expectile loss function, which is strictly consistent for expectiles. We apply our method to 511 basins in contiguous US and deliver predictive expectiles of hydrological simulations with the GR4J, GR5J and GR6J hydrological models at expectile levels 0.5, 0.9, 0.95 and 0.975. An honest assessment empirically proves that the GR6J model outperforms the other two models at all expectile levels. Great opportunities are offered for moving beyond the mean in hydrological modelling by simply adjusting the objective function.
