Hydrological models are simplified imitations of natural and man-made water systems, and because of this simplification, always deal with inherent uncertainty. To develop more rigorous modeling procedures and to provide more reliable results, it is inevitable to consider and estimate this uncertainty. Although there are different approaches in the literature to assess the parametric uncertainty of hydrological models, their structures and results have rarely been compared systematically. In this research, two different approaches to analyze parametric uncertainty, namely direct and inverse methods are compared and contrasted. While the direct method employs a sampling simulation procedure to generate posterior distributions of parameters, the inverse method utilizes an optimization-based approach to optimize parameter sets of an interval-based hydrological model. Two different hydrological models and case studies are employed, and the models are set by two distinct mathematical operations of interval mathematics. Findings of this research show that while the choice of the interval mathematic method can affect the final results, generally, the inverse method cannot be counted on as a reliable tool to analyze the parametric uncertainty of hydrological models, and the direct method provides more accurate results.

水文模型是对自然和人造水系统的简化模仿，并且由于这种简化，总是处理固有的不确定性。为了开发更严格的建模程序并提供更可靠的结果，不可避免地要考虑和估计这种不确定性。尽管文献中有不同的方法来评估水文模型的参数不确定性，但很少系统地比较其结构和结果。在这项研究中，有两种不同的方法来分析参数不确定性，即正向和逆向方法进行比较和对比。虽然直接方法采用采样模拟过程来生成参数的后验分布，但是反方法采用基于优化的方法来优化基于间隔的水文模型的参数集。使用了两种不同的水文模型和案例研究，并且该模型是通过间隔数学的两种不同的数学运算设置的。研究结果表明，虽然区间数学方法的选择会影响最终结果，但通常不能将反演方法作为分析水文模型参数不确定性的可靠工具，而直接法则可提供更准确的结果。