Abstract Hydrosystems engineering designs involve analysis of hydrometric data (e.g., rainfall, floods) and use of hydrologic/hydraulic models, all of which contribute various degrees of uncertainty to the design process. Uncertainties in hydrosystem designs can be generally categorized into aleatory and epistemic types. The former arises from the natural randomness of hydrologic processes whereas the latter are due to knowledge deficiency in model formulation and model parameter specification. This study shows that the presence of epistemic uncertainties induces uncertainty in determining the design capacity. Hence, the designer needs to quantify the uncertainty features of design capacity to determine the capacity with a stipulated performance reliability under the design condition. Using detention basin design as an example, the study illustrates a methodological framework by considering aleatory uncertainty from rainfall and epistemic uncertainties from the runoff coefficient, curve number, and sampling error in design rainfall magnitude. The effects of including different items of uncertainty and performance reliability on the design detention capacity are examined. A numerical example shows that the mean value of the design capacity of the detention basin increases with the design return period and this relation is found to be practically the same regardless of the uncertainty types considered. The standard deviation associated with the design capacity, when subject to epistemic uncertainty, increases with both design frequency and items of epistemic uncertainty involved. It is found that the epistemic uncertainty due to sampling error in rainfall quantiles should not be ignored. Even with a sample size of 80 (relatively large for a hydrologic application) the inclusion of sampling error in rainfall quantiles resulted in a standard deviation about 2.5 times higher than that considering only the uncertainty of the runoff coefficient and curve number. Furthermore, the presence of epistemic uncertainties in the design would result in under-estimation of the annual failure probability of the hydrosystem and has a discounting effect on the anticipated design return period.

中文翻译：

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不确定性对基于概率的水系统设计能力的影响

摘要 水文系统工程设计涉及水文数据（例如降雨、洪水）的分析和水文/水力模型的使用，所有这些都会对设计过程产生不同程度的不确定性。水利系统设计中的不确定性通常可分为随机和认知类型。前者源于水文过程的自然随机性，而后者源于模型制定和模型参数规范方面的知识不足。这项研究表明，认知不确定性的存在会导致确定设计能力的不确定性。因此，设计者需要量化设计容量的不确定性特征，以确定在设计条件下具有规定性能可靠性的容量。以滞留池设计为例，该研究通过考虑降雨的偶然不确定性和径流系数、曲线数和设计降雨量级抽样误差的认知不确定性，说明了一个方法框架。检查了包括不同项目的不确定性和性能可靠性对设计滞留容量的影响。一个数值例子表明，滞留池设计容量的平均值随着设计重现期的增加而增加，并且无论考虑的不确定性类型如何，这种关系实际上是相同的。当受到认知不确定性的影响时，与设计能力相关的标准偏差会随着设计频率和所涉及的认知不确定性项目而增加。发现由于降雨分位数的抽样误差引起的认知不确定性不应被忽视。即使样本大小为 80（对于水文应用来说相对较大），在降雨量分位数中包含采样误差导致的标准偏差比仅考虑径流系数和曲线数的不确定性的标准偏差高约 2.5 倍。此外，设计中存在的认知不确定性会导致对水系统年故障概率的低估，并对预期的设计重现期产生贴现效应。比仅考虑径流系数和曲线数的不确定性高5倍。此外，设计中存在的认知不确定性会导致对水系统年故障概率的低估，并对预期的设计恢复期产生贴现效应。比仅考虑径流系数和曲线数的不确定性高5倍。此外，设计中存在的认知不确定性会导致对水系统年故障概率的低估，并对预期的设计恢复期产生贴现效应。