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A parameterization of momentum roughness length and displacement height for a wide range of canopy densities

机译:广泛的冠层密度的动量粗糙度长度和位移高度的参数化

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Values of the momentum roughness length, z0 , and displacement height, d , derived from wind profiles and momentum flux measurements, are selected from the literature for a variety of sparse canopies. These include savannah, tiger-bush and several row crops. A quality assessment of these data, conducted using criteria such as available fetch, height of wind speed measurement and homogeneity of the experimental site, reduced the initial total of fourteen sites to eight. These datapoints, combined with values carried forward from earlier studies on the parameterization of z0 and d , led to a maximum number of 16 and 24 datapoints available for d and z0 , respectively. The data are compared with estimates of roughness length and displacement height as predicted from a detailed drag partition model, R92 (Raupach, 1992), and a simplified version of this model, R94 (Raupach, 1994). A key parameter in these models is the roughness density or frontal area index, λ. Both the comprehensive and the simplified model give accurate predictions of measured z0 and d values, but the optimal model coefficients are significantly different from the ones originally proposed in R92 and R94. The original model coefficients are based predominantly on measured aerodynamic parameters of relatively closed canopies and they were fitted `by eye'. In this paper, best-fit coefficients are found from a least squares minimization using the z0 and d values of selected good-quality data for sparse canopies and for the added, mainly closed canopies. According to a statistical analysis, based on the coefficient of determination ( r2 ), the number of observations and the number of fitted model coefficients, the simplified model, R94, is deemed to be the most appropriate for future z0 and d predictions. A CR value of 0.35 and a cd1 value of about 20 are found to be appropriate for a large range of canopies varying in density from closed to very sparse. In this case, 99% of the total variance occurring in the d -data across 16 selected canopies can be explained, whereas the analogous value for the z0 -data (24 datapoints available) is 81%. This makes the R94 model, with only two coefficients and its relatively simple equations, a useful universal tool for predicting z0 and d values for all kinds of canopies. For comparison, a similar fitting exercise is made using simple linear equations based on obstacle height only (e.g. Brutsaert, 1982) and another formula involving canopy height as well as roughness density (Lettau, 1969). The fitted Brutsaert equations explain 98% and 62% of the variance in the d and z0 -data, respectively. Lettau's equation for prediction of z0 performs unsatisfactorily ( r2 values <0, even after fitting of the coefficient) and so it is concluded that the drag partition model is definitely the most effective for prediction of the momentum roughness lengths for a wide rang of canopy densities.
机译:从风廓线和动量通量测量中得出的动量粗糙度长度z 0 和位移高度d的值是从各种稀疏顶篷的文献中选取的。这些包括大草原,老虎灌木和几行庄稼。对这些数据的质量评估使用可获取的标准,风速测量高度和实验地点的均匀性等标准进行,将最初的14个地点减少到了8个。这些数据点,再加上先前对z 0 和d的参数化研究得出的值,导致d和z 0 最多可使用16和24个数据点, 分别。将数据与根据详细的阻力分配模型R92(Raupach,1992)和该模型的简化版本R94(Raupach,1994)所预测的粗糙度长度和位移高度的估计值进行比较。这些模型中的关键参数是粗糙度密度或正面面积指数λ。综合模型和简化模型都可以准确预测z 0 和d值的测量值,但是最优模型系数与R92和R94最初提出的系数有很大不同。原始模型系数主要基于相对封闭的机盖的空气动力学参数,并且“用眼睛”拟合。在本文中,使用选定的优质数据的z 0 和d值的最小二乘最小化找到了最佳拟合系数,这些数据用于稀疏树冠和添加的,主要是封闭树冠。根据统计分析,基于确定系数(r 2 ),观察次数和拟合模型系数的数目,简化模型R94被认为最适合未来的z 0 和d个预测。发现C R 值为0.35,c d1 值为大约20,适用于密度从封闭到非常稀疏的大范围顶篷。在这种情况下,可以解释出现在16个选定树冠的d数据中的总方差的99%,而z 0 -data(24个可用数据点)的相似值为81%。这使得仅具有两个系数及其相对简单的方程的R94模型成为预测各种树冠的z 0 和d值的有用的通用工具。为了进行比较,使用仅基于障碍物高度的简单线性方程式(例如Brutsaert,1982)和涉及冠层高度以及粗糙度密度的另一个公式(Lettau,1969)进行了类似的拟合练习。拟合的Brutsaert方程分别解释了d和z 0 -数据中98%和62%的方差。预测z 0 的Lettau方程的执行效果不理想(即使在系数拟合后,r 2 值<0),因此得出的结论是,拖动分区模型肯定是最有效地预测各种树冠密度下的动量粗糙度长度。

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