THE VARIABILITY OF WINTER DRAINAGE IN ENGLAND AND WALES

Estimates of winter drainage, D, are available for 82 locations in England and Wales for each winter during the 35-year period, 1940/1 to 1974/5. At each location, D is approximately normally distributed. The variability, expressed as a coefficient of variation, is approximately inversely proportional to the average drainage, DBAR; it is large, ranging from 20-30% in Wales and the uplands of northern and western England to 60-70% in eastern England. Assuming a normal distribution, the probability of exceeding a given amount of drainage is easily found. The proportion, f, of solute initially in the soil that is leached each winter can be calculated using these estimates of D in a simple layer model. However, f is not normally distributed, but can be fitted by the Type-1 extreme-value distribution. If there are n years of data, and m is the rank of a value in order of decreasing size, the estimation of the probability, P, of exceeding the mth largest value, f(m), is P (f greater-than-or-equal-to f(m)) = m/(n + 1), and the return period, t, is 1/P years. Using the transform, W = ln[-ln P], graphs of f against W yield families of lines that, for a given location and depth in the soil, depend only on soil type, and from which extreme values likely to be encountered in a given return period can be forecast. Results are discussed for Mildenhall, Suffolk (DBAR = 99 +/- 68 mm), Cockle Park, Northumberland (DBAR = 275 +/- 125 mm), Welshpool, Powis (DBAR = 373 +/- 121 mm), Carmarthen, Dyfed (DBAR = 764 +/- 196 mm) and Ambleside, Cumbria (DBAR = 1280 +/- 276 mm).