Predicting the probability distribution of yield from multiple boreholes in crystalline bedrock

In many hard rock lithologies, the distribution of borehole yields can often be regarded as being derived from a log-normally distributed population, characterized by the median yield (m(1)), and standard deviation of ln-transformed values (sigma(1)). By means of numerical techniques using standard spreadsheet software, the distribution of total yield from two or more boreholes can be calculated, assuming that the yields of the boreholes are statistically independent variables and that there is no significant hydraulic interference between boreholes. The results are not necessarily obvious: (1) the median total yield for a group of y noninterfering boreholes (m(y)) is greater than y.m(1). The ratio m(y)/y.m(1) increases with increasing y and with increasing sigma(1); and (2) the standard deviation sigma(1) of ln-transformed yield distributions for water systems consisting of y multiple boreholes is less than the standard deviation sigma(1) of the ln-transformed yield distribution far single boreholes. The standard deviation decreases as the number of boreholes in the group increases.