Estimating the annual mean screen temperature empirically

We have examined station data from around the world to study the separate effects of the latitude (between 60° N-40° S), elevation and distance inland, on the annual-mean screen temperature. In the first 200-400 km from some west coasts, screen temperatures (after adjustment for elevation) rise inland, reaching a maximum called the 'thermal-ridge temperature' Tr. The rise of temperature within this littoral fringe (of width F) depends mainly on the difference between the sea-surface temperature off the west coast and the zonal mean. Further inland than such a fringe, adjusted temperatures generally decline eastwards, approximately linearly, at a rate C. The rate is related to hemisphere and latitude. Empirical relationships between latitude and the observed coastal sea-surface temperature, the near-shore screen temperature, Tr, C and F for each continent are used to estimate annual mean temperatures on land. Independent estimates of this kind for 48 places, using a look-up table, differ overall by only 0.7 K from the actual long-term average annual mean temperatures. This is less than half the error resulting from an assumption of zonal-mean temperatures. Basing estimates on coastal sea-surface temperatures, instead of the look-up table, results in an average error of 1.0 K for the 48 places. The errors are comparable with the standard deviation of annual mean temperatures during 30 years or so.