Neural networks are used to forecast hydrogeological risks, such as droughts and floods. However, uncertainties generated by these models are difficult to assess, possibly leading to a low use of these solutions by water managers. These uncertainties are the result of three sources: input data, model architecture and parameters and their initialization. The aim of the study is, first, to calibrate a model to predict Champagne chalk groundwater level at Vailly (Grand-Est, France), and, second, to estimate related uncertainties, linked both to the spatial distribution of rainfalls and to the parameter initialization. The parameter uncertainties are assessed following a previous methodology, using nine mixed probability density functions (pdf), thus creating models of correctness. Spatial distribution of rainfall uncertainty is generated by swapping three rainfall inputs and then observing dispersion of 27 model outputs. This uncertainty is incorporated into models of correctness. We show that, in this case study, an ensemble model of 40 different initializations is sufficient to estimate parameter uncertainty while preserving quality. Logistic, Gumbel and Raised Cosine laws fit the distribution of increasing and decreasing groundwater levels well, which then allows the establishment of models of correctness. These models of correctness provide a confidence interval associated with the forecasts, with an arbitrary degree of confidence chosen by the user. These methodologies have proved to have significant advantages: the rigorous design of the neural network model has allowed the realisation of models able to generalize outside of the range of the data used for training. Furthermore, it is possible to flexibly choose the confidence index according to the hydrological configuration (e.g., recession or rising water table).

中文翻译：

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使用神经网络进行水文地质预报的不确定性估计：降雨空间分布的影响和模型的随机初始化

神经网络用于预测水文地质风险，例如干旱和洪水。然而，这些模型产生的不确定性很难评估，可能导致水资源管理者对这些解决方案的使用率很低。这些不确定性是三个来源的结果：输入数据、模型架构和参数及其初始化。该研究的目的是，首先，校准一个模型来预测 Vailly（法国东部大区）香槟白垩地下水位，其次，估计相关的不确定性，与降雨的空间分布和参数相关初始化。参数不确定性是按照先前的方法评估的，使用九个混合概率密度函数 ( pdf)，从而创建正确性模型。降雨不确定性的空间分布是通过交换三个降雨输入然后观察 27 个模型输出的离散来生成的。这种不确定性被纳入正确性模型中。我们表明，在本案例研究中，40 个不同初始化的集成模型足以在保持质量的同时估计参数不确定性。Logistic、Gumbel 和升余弦定律很好地拟合了地下水位增加和减少的分布，从而可以建立正确的模型。这些正确性模型提供了与预测相关的置信区间，用户可以选择任意程度的置信度。这些方法已被证明具有显着优势：神经网络模型的严格设计使得模型能够在用于训练的数据范围之外泛化。此外，可以根据水文配置（例如，衰退或上升的地下水位）灵活选择置信指数。