Probability distribution of groundcover for runoff prediction in rangeland in the Burnett–Mary Region, Queensland

Abstract

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 35.8–231km2) 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 8.10mm 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.