Transverse micro-erosion meter measurements; determining minimum sample size

Two transverse micro-erosion meter (TMEM) stations were installed in each of four rock slabs, a slate/shale, basalt, phyllite/schist, and sandstone. One station was sprayed each day with fresh water and the other with a synthetic sea water solution (salt water). To record changes in surface elevation (usually downwearing but with some swelling), 100 measurements (the pilot survey), the maximum for the TMEM used in this study, were made at each station in February 2010, and then at two-monthly intervals until February 2011. The data were normalized using Box-Cox transformations and analyzed to determine the minimum number of measurements needed to obtain station means that fall within a range of confidence limits of the population means, and the means of the pilot survey. The effect on the confidence limits of reducing an already small number of measurements (say 15 or less) is much greater than that of reducing a much larger number of measurements (say more than 50) by the same amount. There was a tendency for the number of measurements, for the same confidence limits, to increase with the rate of downwearing, although it was also dependent on whether the surface was treated with fresh or salt water. About 10 measurements often provided fairly reasonable estimates of rates of surface change but with fairly high percentage confidence intervals in slowly eroding rocks; however, many more measurements were generally needed to derive means within 10% of the population means. The results were tabulated and graphed to provide an indication of the approximate number of measurements required for given confidence limits, and the confidence limits that might be attained for a given number of measurements.

► Number of micro-erosion meter measurements determines mean confidence levels.
► More effective to increase a low than a high number of measurements.
► Number of measurements depends on the required accuracy and station variability.
► 10 measurements normally give reasonable estimates of rates of surface change.