Considering the degree of spatial and temporal variation of groundcover in grazing land, it is desirable to use a simple and robust model to represent the spatial variation in cover in order to quantify its effect on runoff and soil loss. The purpose of the study was to test whether a two-parameter beta (β) distribution could be used to characterise cover variation in space at the sub-catchment scale. Twenty sub-catchments (area range 35.8–231 km²) in the Burnett–Mary region, Queensland, were randomly selected. Thirty raster layers of groundcover at 30-m resolution were prepared for these 20 sub-catchments with the average cover for the 30 layers ranging from 24% to 91%. Three methods were used to test the appropriateness of the β distribution for characterising the cover variation in space: (i) visual goodness-of-fit assessment and Kolmogorov–Smirnov (K-S) test; (ii) the fractional area with cover ≤53%; and (iii) estimated runoff amount for a given rainfall amount for the area with cover ≤53%. The K-S test on 30 × 100 samples of groundcover showed that the hypothesis of β distribution for groundcover could not be rejected at P = 0.05 for 97.5% of the cases. A comparison of the observed and β distributions in terms of the fractional area with cover ≤53% showed that the discrepancy was ≤8% for the 30 layers considered. A comparison in terms of the estimated runoff showed that results using the observed cover distribution and the β distribution were highly correlated (R² range 0.91–0.98; Nash–Sutcliffe efficiency measure range 0.88–0.99). The mean absolute error of estimated runoff ranged from 0.98 to 8.10 mm and the error relative to the mean was 4–16%. The results indicated that the two-parameter β distribution can be adequately used to characterise the spatial variation of cover and to evaluate the effect of cover on runoff for these predominantly grazing catchments.

考虑到放牧地表覆盖物的时空变化程度，为了量化其对径流和土壤流失的影响，希望使用一个简单而健壮的模型来表示覆盖物的空间变化。这项研究的目的是测试是否可以使用两参数的β（β）分布来表征亚汇水规模下的空间覆盖变化。随机选择了昆士兰州伯内特-玛丽地区的20个子汇水区（区域范围35.8–231 km ²）。为这20个子汇水区准备了30层分辨率的30层地面覆盖物的栅格，这30个层的平均覆盖率为24％至91％。三种方法用于测试β分布的适当性，以表征空间的覆盖变化：（i）视觉拟合度评估和Kolmogorov-Smirnov（KS）测试；（ii）覆盖率≤53％的分数面积；（iii）在覆盖率≤53％的地区，给定降雨量下的估计径流量。在30×100的地被样品上进行的KS测试表明， 对于97.5％的情况，在P = 0.05时不能拒绝地被的β分布假设。覆盖率≤53％的观察面积和β分布的比较表明，所考虑的30层的差异≤8％。根据估算的径流进行比较，结果表明，使用观测到的覆盖分布和β分布的结果高度相关（R ²0.91-0.98；Nash–Sutcliffe效率度量范围为0.88–0.99）。估计径流的平均绝对误差范围为0.98至8.10 mm，相对于平均值的误差为4-16％。结果表明，对于这些主要为放牧集水区，两参数β分布可以适当地用于表征覆盖物的空间变化并评估覆盖物对径流的影响。