Analysis of Reaeration Equations Using Mean Multiplicative Error

D. B. Moog, G. Jirka
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引用次数: 84

Abstract

Numerous equations employing depth, velocity, and slope have been developed to estimate the stream reaeration coefficient. These have been evaluated previously using statistics based on differential errors, which are shown to be biased toward underprediction. A new metric, the mean multiplicative error (MME), overcomes this defect and offers other advantages, including identical results for both reaeration and gas transfer coefficients and less sensitivity to extreme errors. It is equal to the geometric mean of the factors, greater than unity, by which the estimates would have to be multiplied or divided to equal the corresponding measurements. With the use of the MME to test 10 selected equations, against a compilation of field measurements based on gas tracers, current equations are shown to be of little value at low slopes, whereas some frequently used equations are shown to have little general value. Slope is found to be an essential component of reaeration equations. Recommendations are made for estimating the reaeration coefficient.
利用平均乘法误差分析再生方程
许多利用深度、流速和坡度的方程已经被开发出来来估计水流再循环系数。以前已经使用基于差异误差的统计来评估这些,这表明偏向于低估。一种新的度量,即平均乘法误差(MME),克服了这一缺陷,并具有其他优点,包括再生和气体传递系数的结果相同,对极端误差的敏感性较低。它等于因子的几何平均值,大于1,估计值必须乘以或除以相应的测量值。利用MME测试了10个选定的方程,对比了基于气体示踪剂的现场测量结果,目前的方程在低斜率下几乎没有价值,而一些经常使用的方程在一般情况下几乎没有价值。发现斜率是再生方程的重要组成部分。对再生系数的估计提出了建议。
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