Table 3 Frequency equations for SMD at the end of April – September.

y = {[-ln ln (1 – 1/T) – 3.3842 ] * 1.09348 * T-0.046518 } + 3.3842
where y = modified reduced variate (Rakhecha & Clark, 1999); T = return period (years).
The probability of the SMD at other times can be calculated by linear interpolation between the gradients and constants of the regression equations.
For the constant: {d/M ( k2 – k1) } + k1
For the regression slope: { d/M ( S2 – S1) } + S1
Where d = day of the month; M = length of month (days); k = regression constant; S = slope of regression; subscripts represent data for the first and second month chronologically. For example for the middle of May the regression constant would be (15.5/31) * (20.501 + 12.863) – 12.863; while the regression slope: (15.5/31) * (-18.027 + 33.662) -33.662). When correcting for other areas in Britain only the slope adjustment needs to be done. The constant is obtained from an estimate of the median SMD for the date in question and substitution into the equation SMD = Regression slope * 0.189 + constant.

 April SMD = -33.662y -12.863 r = -0.99 May SMD = -18.027y + 20.501 r = -0.98 June SMD = -29.327y + 39.886 r = -0.94 July SMD = -26.528y + 54.807 r = -0.99 August SMD = -16.615y + 39.855 r = -0.96 September SMD = -16.794y -2.6506 r = -0.99