Night-time minimum air temperature from maximum temperature, dew point, overnight wind and cloud · McKenzie's method, Met Office Forecasters' Reference Book §2.4.2.1, Table 2.8, with a 1000-member Monte Carlo uncertainty cloud
Tmin = 0.5 (Tmax + Td) − K, where Tmax is the representative maximum temperature, Td the air-mass dew point at the time of Tmax, and K a local constant depending on forecast mean overnight surface wind and average low cloud.
K is read from the station table (default: Birmingham Airport, Table 2.8(a)) and then corrected for the month and for good (A) or poor (B) radiation nights (Table 2.8(b)). The correction is added to K, so a negative correction raises Tmin.
The uncertainty cloud draws 1000 perturbed sets of inputs from independent Gaussians centred on your values. Wind and cloud are rounded to whole knots/oktas, clamped (wind ≥ 0, above 21 kn uses the 17–21 kn row; cloud 0–8) and binned. Perturbed dew point is capped at the perturbed Tmax. The random draws are seeded so the cloud stays stable until you press Resample.
K values are specific to a site. Use your local forecast office's table for other stations and save it with a name.