In this study the relationship between two families of pairwise associated functions, describing boundary wetting and drying curves, is modelled. This relationship includes both regular and random constituents, and it is represented by a limited dataset of N known pairs of these curves, which pertain to N different soils. Using the dependent domain theory of hysteresis, we show that the regular constituent in this relationship can be described by a linear integral operator that, for a given input measured boundary wetting curve, predicts its associated boundary drying curve. The operator is optimized to reduce the influence of the random scattering of the pairs of curves. The optimization of the operator is performed with respect to the given input measured boundary wetting curve using a representative calibration dataset of k (k≤N) pairs of curves, which are a part of the N available measured pairs. The optimized operator should satisfy two opposite conditions: (i) the best possible accuracy at reproducing the boundary drying curves used for operator optimization, and (ii) the least possible sensitivity with respect to excluding any one pair from the calibration dataset.

We also apply the suggested modelling approach for derivation of the inverse operator model that predicts the boundary wetting curves from their associated measured boundary drying curves, with possibility of verification of the predictive reliability. The predictive performance of both operator models is mainly good, and their reliability can be permanently enhanced by updating them with new incoming measured data.

在这项研究中，对描述边界润湿和干燥曲线的两个成对关联函数系列之间的关系进行了建模。这种关系包括规则成分和随机成分，它由这些曲线的 N 对已知对的有限数据集表示，这些曲线与 N 种不同的土壤有关。使用滞后的依赖域理论，我们表明这种关系中的规则成分可以由线性积分算子描述，对于给定的输入测量边界润湿曲线，预测其相关的边界干燥曲线。优化算子以减少曲线对随机散射的影响。使用具有代表性的校准数据集，针对给定的输入测量边界润湿曲线执行算子的优化k ( k≤ N) 对曲线，它们是 N 个可用测量对的一部分。优化后的算子应满足两个相反的条件：(i) 再现用于算子优化的边界干燥曲线时的最佳可能精度，以及 (ii) 从校准数据集中排除任何一对的可能灵敏度最低。

我们还应用建议的建模方法来推导逆算子模型，该模型根据相关的测量边界干燥曲线预测边界润湿曲线，并有可能验证预测可靠性。两种算子模型的预测性能主要是好的，并且可以通过使用新传入的测量数据更新它们来永久增强它们的可靠性。