论文标题
使用流体力学理论和贝叶斯分层建模对幂律等级曲线的概括
Generalization of the power-law rating curve using hydrodynamic theory and Bayesian hierarchical modeling
论文作者
论文摘要
幂律等级曲线已广泛用于液压实践和水文学中。它由$ q（h）= a（h-c）^b $，其中$ q $要排出，$ h $是水高程，$ a $，$ b $和$ c $是未知参数。我们提出了幂律等级曲线的新扩展，称为广义幂律等级曲线。它是通过将开放通道流的物理学链接到表单$ q（h）= a（h-c）^{f（h）} $的模型来构建的。功能$ f（h）$称为幂律指数，这取决于水升高。提出的模型和幂律模型拟合在贝叶斯分层模型的框架内。通过探索拟议的额定曲线及其幂律指数的属性，我们发现在自然界中可能会发现的横截面形状使得powerlaw指数$ f（h）$通常在间隔$ [1.0,2.67] $中。此事实用于用于模型参数的先前密度。提出了有效的马尔可夫链蒙特卡洛采样方案，该方案提出了两个模型在数据水平上使用对数正态分布假设，而在潜在水平的高斯假设。两个统计模型应用于四个数据集。在三个数据集的情况下，广义的幂律等级曲线比幂律等级曲线更好地拟合，而在第四种情况下，两个模型拟合得同样拟合，并且广义的幂律等级曲线模仿了幂律等级曲线。
The power-law rating curve has been used extensively in hydraulic practice and hydrology. It is given by $Q(h)=a(h-c)^b$, where $Q$ is discharge, $h$ is water elevation, $a$, $b$ and $c$ are unknown parameters. We propose a novel extension of the power-law rating curve, referred to as the generalized power-law rating curve. It is constructed by linking the physics of open channel flow to a model of the form $Q(h)=a(h-c)^{f(h)}$. The function $f(h)$ is referred to as the power-law exponent and it depends on the water elevation. The proposed model and the power-law model are fitted within the framework of Bayesian hierarchical models. By exploring the properties of the proposed rating curve and its power-law exponent, we find that cross sectional shapes that are likely to be found in nature are such that the power-law exponent $f(h)$ will usually be in the interval $[1.0,2.67]$. This fact is utilized for the construction of prior densities for the model parameters. An efficient Markov chain Monte Carlo sampling scheme, that utilizes the lognormal distributional assumption at the data level and Gaussian assumption at the latent level, is proposed for the two models. The two statistical models were applied to four datasets. In the case of three datasets the generalized power-law rating curve gave a better fit than the power-law rating curve while in the fourth case the two models fitted equally well and the generalized power-law rating curve mimicked the power-law rating curve.
