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:

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 oCrise 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 apeak 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-2was 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 fractionfor each grid cell (x) and achange multiplier (m). Coefficients a andb from table A1 and s from table A2.

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.

Parameter / a / b / Standard Error (oC) / R2
Tmean against urban fraction / 13.176 / -0.097 / 0.05 / 0.92
DTR against urban fraction / -5.327 / -0.311 / 0.11 / 0.78
Tmean against AHF (Wm-2) / 2.590 / -0.011 / 0.15 / 0.5
DTR against AHF (Wm-2) / -1.571 / -0.008 / 0.1 / 0.38

Table A2: Seasonal weighting relative to the mean value.

Month / Tmean: Urban / DTR : urban / Tmean : AHF / DTR : AHF
January / 0.607 / 0.520 / 1.095 / 0.702
February / 0.673 / 0.588 / 1.126 / 0.928
March / 0.85 / 0.784 / 0.911 / 1.196
April / 1.061 / 1.018 / 0.819 / 0.894
May / 1.275 / 1.167 / 0.851 / 0.797
June / 1.405 / 1.270 / 0.970 / 0.487
July / 1.451 / 1.388 / 0.950 / 1.030
August / 1.367 / 1.479 / 0.970 / 1.341
September / 1.129 / 1.379 / 1.043 / 1.638
October / 0.881 / 1.074 / 1.136 / 1.374
November / 0.685 / 0.767 / 1.053 / 0.934
December / 0.616 / 0.567 / 1.076 / 0.678