Water, Energy and Environmental Engineering Research Unit, Faculty of Technology, University of Oulu, 90014 Oulu, Finland.
Department of Biosystems and Agricultural Engineering, Oklahoma State University, 111 Agricultural Hall, Stillwater, OK 74078, USA.
Sci Total Environ. 2021 Oct 15;791:148394. doi: 10.1016/j.scitotenv.2021.148394. Epub 2021 Jun 9.
Although dimensional analysis suggests sound functional forms (FFs) to calculate longitudinal dispersion coefficient (K), no attempt has been made to quantify both reliability of the estimated K value and its sensitivity to variation of the FFs' parameters. This paper introduces a new index named bandwidths similarity factor (bws-factor) to quantify the reliability of FFs based on a rigorous analysis of distinct calibration datasets to tune the FFs. We modified the bootstrap approach to ensure that each resampled calibration dataset is representative of available datapoints in a rich, global database of tracer studies. The dimensionless K values were calculated by 200 FFs tuned with the generalized reduced gradient algorithm. Correlation coefficients for the tuned FFs varied from 0.60 to 0.98. The bws-factor ranged from 0.11 to 1.00, indicating poor reliability of FFs for K calculation, mainly due to different sources of error in the K calculation process. The calculated exponent of the river's aspect ratio varied over a wider range (i.e., -0.76 to 1.50) compared to that computed for the river's friction term (i.e., -0.56 to 0.87). Since K is used in combination with one-dimensional numerical models in water quality studies, poor reliability in its estimation can result in unrealistic concentrations being simulated by the models downstream of pollutant release into rivers.
尽管维度分析为计算纵向弥散系数（K）提供了合理的函数形式（FF），但尚未尝试量化估计的 K 值的可靠性及其对 FF 参数变化的敏感性。本文引入了一个新的指标，即带宽相似因子（bws-factor），以量化基于严格分析不同校准数据集来调整 FF 的可靠性。我们修改了自举方法，以确保每个重采样的校准数据集代表丰富的示踪剂研究全球数据库中可用数据点的代表性。通过广义缩减梯度算法调整的 200 个 FF 计算出无量纲 K 值。调整后的 FF 的相关系数从 0.60 到 0.98 不等。bws-factor 的范围从 0.11 到 1.00，表明 K 计算的 FF 可靠性较差，主要是由于 K 计算过程中存在不同的误差源。与河流摩擦项计算出的 K 值（即 -0.56 到 0.87）相比，河流纵横比的计算指数变化范围更广（即-0.76 到 1.50）。由于 K 与水质研究中的一维数值模型一起使用，因此其估计中的可靠性较差可能导致模型在河流污染物释放下游模拟出不真实的浓度。
