Stone cover on desert hillslopes: Extent of bias in diameters estimated from grid samples and procedures for bias correction

Grid-based samples of surface stone covers are widely employed for the determination of grain properties such as mean diameter. However, this method has an inherent bias that is related to clast size. Studies failing to correct for this effect have inadvertently reported stone diameters weighted by the area that each stone exposed on the sampling plane. Monte Carlo methods are used ta generate and sample synthetic veneers of surface stones, like those found on many dryland hillslopes, but having pre-determined population distribution characteristics. Uncorrected grid samples from such stone veneers are shown to yield estimates of mean diameter that are in error by up to several hundred per cent. Formulae are provided which permit accuracy of a few per cent to be obtained with samples of 100-300 stones. Slightly larger samples are required accurately to estimate edge length- and area-weighted mean diameters than for traditional volume-weighted means.