  Recently, D. Zhou et al. 2015 studied empirically the land surface
temperature of 32 Chinese cities and reported an exponentially decaying
residual effect of the urban heat island (UHI) around the cities. Here we show
analytically that such a form is equivalent to a previously proposed
two-dimensional Gaussian function. The reason for this seeming contradiction is
the way how the distance from the considered city is defined. While in the
former, consecutive equal area belts around the city are used, in the latter it
is the euclidean distance. In simplified terms, the definition of the belts
implies a transformation of the independent variable $\rho\sim d^{\alpha}$ with
$\alpha\approx 1/2$, where $\rho$ is the euclidean distance from the center and
$d$ is the index of the belt. Since the belts have equal area, outer ones
become more narrow. As a consequence, the Gaussian function $\sim
\mathrm{e}^{-\rho^2}$ becomes an exponential cone $\sim \mathrm{e}^{-d}$. This
paper provides an explicit derivation of the equivalence.
