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. Expectiles are new risk measures in hydrology. They are least square analogues of quantiles and can characterize the probability distribution in much the same way as quantiles do. To this end, we propose calibrating hydrological models using the expectile loss function, which is 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 0.500, 0.900, 0.950 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.
翻译:水文模型的预测应具有概率性。 我们的目标是采用一种方法,利用预测来直接估计水文模拟的不确定性,从而补充以前以孔数为基础的直接方法。 期望是水文中新的风险度量。 期望是孔数中最不平的类比,其概率分布特征与孔数大致相同。 为此,我们建议使用预期损失函数来校准水文模型,这对预期损失功能是一致的。 我们用我们的方法对毗连美国的511个盆地进行估算,并以GR4J、GR5J和GR6J水文模型在预期值0.500、0.900、0.950和0.975的水平提供水文模拟的预测值。 一项诚实的实证评估证明,GR6J模型在所有预期值级别上都超越了其他两个模型。 我们提供了超越水文模型平均值的极大机会,只需调整客观功能。