Generating the Urbanisation Change Factors
The generation of the urbanisation change factors applied to the weather generator used in
this analysis are described below. The basis for these is the regional climate model HadRM3
including an urban land surface scheme as described in McCarthy et al. 2012 (M12). Figure
2 of M12 shows empirical fit of warming against urban land use fraction and anthropogenic
heat flux (AHF) as a second order polynomial. In this analysis an alternative model is used
to ensure a converging solution to prevent users creating unrealistic solutions. Therefore the
urban warming component is determined as:
𝑦 = 𝑎(1 − 𝐸𝑋𝑃(𝑏𝑥))
Where y is Tmean or DTR, x is urban fraction cover or AHF and the regression has been
undertaken against mean Temperature (Tmean) and Diurnal Temperature Range (DTR)
rather than the max and min temperatures. The coefficients are provided in table A1. From
equation (1) and Table A1 we can then determine that the greatest possible impact of urban
land cover on the mean climate is 1.2 oC rise in Tmean and 1.4 oC reduction in DTR. The
highest AHF value used by M12 was 75 Wm-2 which would give rise to 1.4oC rise in Tmean
and 0.7oC fall in DTR in this formulation.
Seasonality is treated as a separate weighting term based on the simulated seasonal cycle
of UHI in the model in response to urban land and AHF. For each month of the year the
estimated urban temperature effect from equation 1 and table A1 is adjusted by a seasonal
weighting provided in table A2. This shows a peak in the UHI from urban land use in June
and July. The DTR effect peaks one month later in August. The AHF has less of a seasonal
cycle in Tmean, but does show peaks in the DTR effect in Spring and Autumn months.
To simplify the model the AHF is defined as a fixed value per unit area of impervious surface.
In the original M12 simulations a value of 25 W m-2 was used. The M12 interpretation of land
cover map (LCM, 1990 and see discussion in M12) gives an estimate of the impervious
fraction for London of 0.407. This gives a heat flux density per unit urban area of 28 W m-2
(LECI). Comparable values are obtained with alternative estimates from Iamarino et al.
(2011) and Hamilton (2009). Given the scale of HadRM3 and the weather generator it is
unknown how extreme levels of AHF in excess of 100 Wm-2 in the most central areas of
London would be mixed with the wider environment and therefore such localised impacts are
not considered in this method.
Iamarino et al. (2011) also separate the budget into sensible heat (80.7%), latent heat
(7.3%), and waste water (12%) outputs. Applying this to the estimate above and taking only
the sensible heat component yields a heat flux density of 22.6 W m-2. Therefore a grid cell
that is 50 % urban would have a net AHF of 11.3 Wm-2. The formulation could be easily
adapted to allow AHF to vary independently of urban fraction, but for the purposes of this
analysis the net AHF only varies as a consequence of changing urban cover.
The urbanised weather generator requires only the input of a change factor (cf) relative to
present day. This is calculated as a function of the baseline urban fraction for each grid cell
(x) and a change multiplier (m). Coefficients a and b from table A1 and s from table A2.
𝑐𝑓𝑢𝑟𝑏 = 𝑠. 𝑎𝑢𝑟𝑏 (𝐸𝑋𝑃(𝑏𝑢𝑟𝑏 (𝑥)) − 𝐸𝑋𝑃(𝑏𝑢𝑟𝑏 (𝑚. 𝑥)))
𝑐𝑓𝐴𝐻𝐹 = 𝑠. 𝑎𝐴𝐻𝐹 (𝐸𝑋𝑃(𝑏𝐴𝐻𝐹 (22.6𝑥)) − 𝐸𝑋𝑃(𝑏𝐴𝐻𝐹 (22.6(𝑚. 𝑥)))
The factor m.x is also constrained to not exceed a value of 0.95. As an example x = 0.5 and
m = 1.5 represents a 50% increase in urbanisation for a cell with a baseline 50 % land,
yielding cfurb= 0.44 oC and cfAHF = 0.13 oC for July.
Table A1: Coefficients, Standard Error, and R2 values for estimating urban impact on
temperature.
R2
-0.097
Standard
Error (oC)
0.05
-5.327
-0.311
0.11
0.78
2.590
-0.011
0.15
0.5
-1.571
-0.008
0.1
0.38
Parameter
a
b
Tmean against
urban fraction
DTR against urban
fraction
Tmean against
AHF (Wm-2)
DTR against AHF
(Wm-2)
13.176
0.92
Table A2: Seasonal weighting relative to the mean value.
Month
January
February
March
April
May
June
July
August
September
October
November
December
Tmean: Urban
0.607
0.673
0.85
1.061
1.275
1.405
1.451
1.367
1.129
0.881
0.685
0.616
DTR : urban
0.520
0.588
0.784
1.018
1.167
1.270
1.388
1.479
1.379
1.074
0.767
0.567
Tmean : AHF
1.095
1.126
0.911
0.819
0.851
0.970
0.950
0.970
1.043
1.136
1.053
1.076
DTR : AHF
0.702
0.928
1.196
0.894
0.797
0.487
1.030
1.341
1.638
1.374
0.934
0.678