## Modelling UHI

Dr. Roy Spencer from UHA has a very interesting article on how UHI could contaminate the GHCN (Global Historic Data Net) temperature series that form the basis for  GISS and HADCrut3 . From his graph showing the decadal trend versus population density I extracted the following 4 data couples (first column = population density, last column = temperature trend in °C/decade).

pop        dT
___________

10       0.093
50       0.135
200    0.190
980    0.215

Dr. Spencer gives a logarithmic fit of the form dT = a + b*log(pop). The problem with this type of fit is that log(0) is minus infinite, and as such can not give a mathematical plausible answer to the question: what would have the warming if population density had been zero?

I tried another model, based on a fractional power of population density:  dT = a + b* pop^c
For a comparison, here are the 2 fits with their R2 score (R2 = percentage of variance explained by the model):

Clearly the power model gives a much better R2 score (it is a tremendous result!): the model explains more than 97% of the observed variability!

Four data points are not too many for such an analysis, so please take these results with a grain of salt. The power model suggests that true US temperature change would have been a warming of -2.4174 + 2.45104 = 0.033   °C/decade for the period 1973-2009 if there had been no UHI ( i.e. pop = 0).

Conclusion: no UHI, no warming!