Sensitivity test of the input parameters to the surface temperature model
The information provided here should help users to determine how accurate they need to be with the input parameters to the STAR tools.
This information is taken from: Gill, S.E. (2006). Climate change and urban greenspace. PhD thesis, The University of Manchester.
www.ginw.co.uk/resources/Susannah_PhD_Thesis_full_final.pdf. It refers to the parameters as they were named, set and used in this thesis; however this is very similar to their names, default values and use in the STAR tools. It sometimes refers to other sections of the thesis, which can be accessed at the weblink above if desired.
From Gill (2006):
5.4. Sensitivity Tests
Sensitivity tests were undertaken in order to gain an increased understanding of how the model worked, as well as to test the relative sensitivity of the maximum surface temperature output to the different parameters. The sensitivity tests were undertaken using the parameters as determined for the 1961-1990 baseline climate model runs (Section 5.3). All sensitivity analyses were undertaken with the town centre and woodland UMTs, as these are the categories with the highest and lowest maximum surface temperatures (Section 5.5.1.1). Each input parameter was taken in turn and altered by ±10%, or another suitable value, whilst all the other parameters were held constant. A detailed analysis of the sensitivity tests can be found in
Appendix D. In this section, the sensitivities of the various parameters are compared to each other.
The ranking of the parameters according to the magnitude of change in maximum surface temperature varies slightly depending on whether it is a plus or minus 10% change and whether it is the town centre or woodland UMT (Tables 5.8 to 5.11). The tests reveal that sensitive parameters include the peak insolation, wind velocity at the SBL, density of the air, and temperature at the SBL. The evaporative fraction is also very important, especially in woodlands, where it is the most sensitive parameter when decreased by 10% (Table 5.11). Unfortunately, it was not possible to increase the evapotranspiring cover in woodland by 10% (or to increase the fraction by 0.098) as this took the evaporating fraction above 1.0. However, even just increasing the evaporating fraction by 0.02, from 0.98 to 1.0, decreased the maximum surface temperature by 0.16°C. Such a change would rank the evaporating fraction at number 9 in table 5.9, below the reference temperature and above the specific humidity at the SBL.
The five least important parameters for town centres are night radiation, bulk density of the soil, specific heat capacity of the soil, soil depth at level s, and soil thermal conductivity. The five least important parameters for woodlands are night radiation, building mass per unit of land, specific heat of concrete, bulk density of the soil, and specific heat capacity of the soil.
Table 5.8. Absolute change in maximum surface temperature resulting from a 10% increase in the respective input parameters in town centres. Parameters listed according to magnitude of change.
Table 5.9. Absolute change in maximum surface temperature resulting from a 10% increase in the respective input parameters in woodlands. Parameters listed according to magnitude of change.
Table 5.10. Absolute change in maximum surface temperature resulting from a 10% decrease in the respective input parameters in town centres. Parameters listed according to magnitude of change.
Table 5.11. Absolute change in maximum surface temperature resulting from a 10% decrease in the respective input parameters in woodlands. Parameters listed according to magnitude of change.
Appendix D. Energy Exchange Model Sensitivity Tests
The sensitivity tests were undertaken using the model runs set up for the 1961-1990 baseline climate. All sensitivity analyses were undertaken with the town centre and woodland UMTs, as these are the categories with the highest and lowest maximum surface temperatures. The input parameters are identical for the two UMTs, except for the evaporating fraction which is 0.20 in town centres and 0.98 in woodlands, and the building mass per unit of land which is 342.20 kg/m² in town centres and 6.58 kg/m² in woodlands. The sensitivity of the maximum surface temperatures to the input parameters are considered on the following pages. Current input values (i.e. those used by Gill, 2006) are marked on figures D.1 to D.20 by grey dotted lines.
Input parameters considered are:
D.1 Soil Temperature
D.2 Reference Temperature
D.3 Air Temperature at SBL
D.4 Wind Speed at SBL
D.5 Surface Roughness Length
D.6 Height of SBL
D.7 Density of Air
D.8 Density of Soil
D.9 Peak Insolation
D.10 Night Radiation
D.11 Specific Heat of Air
D.12 Specific Heat of Concrete
D.13 Specific Heat of Soil
D.14 Soil Depth at Level s
D.15 Soil Thermal Conductivity
D.16 Latent Heat of Evaporation
D.17 Specific Humidity at SBL
D.18 Hours of Daylight
D.19 Building Mass per Unit of Land
D.20 Evaporating Fraction
D.1 Soil Temperature
The soil temperature at 20 cm (T
_{b}) is used in the finite difference form of the conductive heat flux term (G) (Equation 5.15) of the energy balance equation. This equation is used as one of the set of simultaneous equations solved to find analytical solutions for the surface temperature (T
_{0}) and the soil temperature at level s (T
_{s}).
Currently soil temperature is set at 20°C, and maximum surface temperatures are 31.2°C in town centres and 18.4°C in woodlands (Figure D.1). Increasing soil temperatures leads to warmer maximum surface temperatures and vice versa. This effect appears to be linear. Changing the soil temperature has a greater effect in town centres rather than woodlands. For example, changing the soil temperature (from the current temperature) by 1°C alters the maximum surface temperature by ±0.11°C in town centres and ±0.05°C in woodlands. Similarly, changing the soil temperature (from the current temperature) by 5°C alters the maximum surface temperature by ±0.55°C in town centres and ±0.25°C in woodlands. If soil temperature is set at 14.3°C, equivalent to the mean summer temperature for Ringway (BETWIXT) minus 0.6°C, the maximum surface temperature is 0.6°C and 0.3°C less in town centres and woodlands, respectively. Whilst town centres have 6% bare soil compared to 0% in woodlands, the change in maximum surface temperatures in the two UMTs as a result of altering soil temperature is not due to the amount of bare soil. The amount of bare soil is not a term in the finite difference heat conduction equation (Equation 5.15). In addition, a further sensitivity test using refuse disposal, which has the highest amount of bare soil cover (58%), found changes of approximately ±0.08°C in maximum surface temperature as a result of changing soil temperatures by ±1°C. The soil temperature appears to have the greatest impact on maximum surface temperature in UMTs where there is a low evaporating cover. This suggests that much more heat is lost to the air by convection and evapotranspiration than to the soil by conduction.
As the soil temperature increases, the difference between the maximum surface temperatures of town centres and woodlands also increases. At soil temperatures of 15°C, 20°C and 25°C, the difference between the maximum surface temperatures in these UMTs is 12.5°C, 12.8°C, and 13.1°C, respectively. The soil temperature appears to have no effect on the timing of the maximum surface temperature.
D.2 Reference Temperature
The reference temperature (T
_{f}) does not appear in any of the terms of the energy balance equation as such. The specific humidity, which appears in the latent heat flux (LE) is linearised around the reference temperature.
Currently the reference temperature is set at 20.6°C, and maximum surface temperatures are 31.2°C in town centres and 18.4°C in woodlands (Figure D.2). The relationship between the reference temperature and the maximum surface temperature is quadratic. This is because the specific humidity is linearised by taking the first term of the expansion around the reference temperature. If the reference temperature is equal to the surface temperature there is no error. However, if the reference temperature is higher or lower than the surface temperature the squared term of the expansion (which is always positive) becomes more significant. Therefore at higher and lower temperatures the latent heat loss is underestimated and the calculated maximum surface temperature rises.
The minimum point of the quadratic curves differs for the two UMTs, with woodland being at a lower reference temperature (around 18.6°C) than town centre (around 30.6°C). This is because woodland has lower surface temperatures than town centres. Thus, in woodlands, the point at which the reference temperature is equal to the surface temperature, and hence there is no error in the linearisation of the specific humidity, is lower.
Increasing the reference temperature by 1°C to 21.6°C decreases the maximum surface temperature in town centres by 0.1°C and increases it in woodlands by the same amount. When the reference temperature is decreased by 1°C to 19.6°C, the maximum surface temperature increases in town centres and decreases in woodlands, each by 0.1°C.
Changing the reference temperature alters the timing of the maximum surface temperatures in town centres more significantly than in woodlands.
D.3 Air Temperature at SBL
The air temperature at the SBL (T
_{2}) is used in the sensible heat flux term (H) of the energy balance equation. Increased air temperatures at the SBL increase the magnitude of this term and vice versa.
Currently the air temperature at the SBL is set at 15.4°C, and maximum surface temperatures are 31.2°C in town centres and 18.4°C in woodlands (Figure D.3). Increasing air temperatures at the SBL leads to warmer maximum surface temperatures and vice versa. This effect appears to be linear. Changing the air temperature at the SBL has a greater effect on the maximum surface temperature in town centres rather than woodlands. This is because more energy is lost by convection in town centres which have less evapotranspiring surface. For example, changing the soil temperature (from the current temperature) by 1°C alters the maximum surface temperature by ±0.58°C in town centres and ±0.26°C in woodlands. Similarly, changing the soil temperature (from the current temperature) by 5°C alters the maximum surface temperature by ±2.9°C in town centres and ±1.3°C in woodlands. These changes are much greater than those for the soil temperature.
As the air temperature at the SBL increases, the difference between the maximum surface temperatures of town centres and woodlands also increases. At air temperatures at the SBL of 10.4°C, 15.4°C and 20.4°C, the difference between the maximum surface temperatures in these UMTs is 11.2°C, 12.8°C, and 14.4°C, respectively. The air temperature at the SBL appears to have no effect on the timing of the maximum surface temperature.
D.4 Wind Speed at SBL
Wind speed at the SBL (U
_{2}) is used in the sensible (H) and latent heat flux (LE) terms (Equations 5.9 and 5.10). Increasing wind speed increases the magnitude of these terms and vice versa.
Currently wind speed at the SBL is set at 5 m/s, and maximum surface temperatures are 31.2°C in town centres and 18.4°C in woodlands (Figure D.4). Increasing wind speed leads to cooler maximum surface temperatures and vice versa. The effect of decreasing wind speed is slightly stronger than that of increasing it. Changing wind speed has a greater effect on the maximum surface temperature in town centres rather than woodlands. This is because more energy is lost by convection in town centres which have less evaporating surface. For example, increasing the wind speed (from the current speed) by 0.5 m/s to 5.5 m/s (a 10% increase) alters the maximum surface temperature by -1.1°C in town centres and -0.7°C in woodlands. Similarly, decreasing the wind speed by 0.5 m/s to 4.5 m/s (a 10% decrease) alters the maximum surface temperature by +1.3°C in town centres and +0.8°C in woodlands.
As the wind speed increases, the difference between the maximum surface temperatures of town centres and woodlands decreases. At wind speeds of 4 m/s, 5 m/s and 6 m/s, the difference between the maximum surface temperatures in these UMTs is 13.8°C, 12.8°C, and 11.9°C, respectively. Wind speed appears to have no effect on the timing of the maximum surface temperature in woodlands, but in town centres increasing the wind speed brings forward the timing of the maximum surface temperature and vice versa.
D.5 Surface Roughness Length
The surface roughness length (Z
_{0}) is used in the sensible (H) and latent heat flux (LE) terms (Equations 5.9 and 5.10). Increasing surface roughness increases the magnitude of these terms and vice versa.
Currently the surface roughness length is set at 2 m, and maximum surface temperatures are 31.2°C in town centres and 18.4°C in woodlands (Figure D.5). Increasing the surface roughness length leads to cooler maximum surface temperatures and vice versa. The effect of decreasing the surface roughness length is stronger than that of increasing it. Changing the surface roughness length has a slightly greater effect on the maximum surface temperature in town centres rather than woodlands. For example, increasing the surface roughness length (from the current length) by 0.2 m to 2.2 m (a 10% increase) alters the maximum surface temperature by -0.39°C in town centres and -0.23°C in woodlands. Similarly, decreasing the surface roughness length by 0.2 m to 1.8 m (a 10% decrease) alters the maximum surface temperature by +0.43°C in town centres and +0.26°C in woodlands.
As the surface roughness length increases, the difference between the maximum surface temperatures of town centres and woodlands decreases. At surface roughness lengths of 1 m, 2 m and 3 m, the difference between the maximum surface temperatures in these UMTs is 13.8°C, 12.8°C, and 12.1°C, respectively. The surface roughness length appears to have no effect on the timing of the maximum surface temperature in woodlands, but in town centres increasing the surface roughness length brings forward the timing of the maximum surface temperature and vice versa.
D.6 Height of SBL
The height of the SBL (Z
_{2}) is used in the sensible (H) and latent heat flux (LE) terms (Equations 5.9 and 5.10). Increasing the height of the SBL decreases the magnitude of these terms and vice versa.
Currently the height of the SBL is set at 800 m, and maximum surface temperatures are 31.2°C in town centres and 18.4°C in woodlands (Figure D.6). Increasing the height of the SBL leads to warmer maximum surface temperatures and vice versa. The effect of decreasing the height of the SBL is slightly stronger than that of increasing it. Changing the height of the SBL has a slightly greater effect on the maximum surface temperature in town centres rather than woodlands. For example, increasing the height of the SBL (from the current height) by 80 m to 880 m (a 10% increase) alters the maximum surface temperature by +0.39°C in town centres and +0.24°C in woodlands. Similarly, decreasing the height of the SBL to 720m (a 10% decrease) alters the maximum surface temperature by -0.43°C in town centres and -0.26°C in woodlands.
As the height of the SBL increases, the difference between the maximum surface temperatures of town centres and woodlands increases slightly. At SBL heights of 600 m, 800 m and 1000 m, the difference between the maximum surface temperatures in these UMTs is 12.3°C, 12.8°C, and 13.1°C, respectively. The height of the SBL appears to have no effect on the timing of the maximum surface temperature in woodlands, but in town centres increasing the SBL height makes the timing of the maximum surface temperature later and vice versa.
D.7 Density of Air
The density of the air (ρ
_{a}) is used in the sensible (H) and latent heat flux (LE) terms (Equations 5.9 and 5.10). Increasing the density of the air increases the magnitude of these terms and vice versa.
Currently the density of the air is set at 1.208 kg/m³, and maximum surface temperatures are 31.2°C in town centres and 18.4°C in woodlands (Figure D.7). Increasing the air density leads to cooler maximum surface temperatures and vice versa. The effect of decreasing the air density is slightly stronger than that of increasing it. Changing the density of the air has a greater effect on the maximum surface temperature in town centres rather than woodlands. For example, increasing the density of the air to 1.3288 kg/m³ (a 10% increase from current settings) alters the maximum surface temperature by -1.13°C in town centres and -0.67°C in woodlands. Similarly, decreasing the density of the air to 1.0872 kg/m³ (a 10% decrease from current settings) alters the maximum surface temperature by +1.32°C in town centres and +0.81°C in woodlands. It should be noted that these changes are outside the range of interest, air densities of 1.3288 kg/m³ and 1.0872 kg/m³ would be found at temperatures of about -5°C and 52°C, respectively (Holman, 1997, p. 646). Changes to air density of plus or minus 1% would be more likely (1.220 kg/m³ and 1.196 kg/m³), occurring at temperatures of about 23°C and 18°C, respectively (Holman, 1997, p. 646). With a ±1% change in air density, the change in maximum surface temperature is at most ±0.12°C.
As the density of the air increases, the difference between the maximum surface temperatures of town centres and woodlands decreases slightly. At air densities of 1.0872 kg/m³, 1.208 kg/m³ and 1.3288 kg/m³, the difference between the maximum surface temperatures in these UMTs is 13.3°C, 12.8°C, and 12.3°C, respectively. The density of the air appears to have no effect on the timing of the maximum surface temperature in woodlands, but in town centres increasing the air density brings forward the timing of the maximum surface temperature later and vice versa.
D.8 Density of Soil
The density of the soil (ρ
_{s}) is used in the finite difference form of the heat conduction equation (G) (Equation 5.15). Increasing the density of the soil decreases the magnitude of this term and vice versa.
Currently the density of the soil is set at 1800 kg/m³, and maximum surface temperatures are 31.2°C in town centres and 18.4°C in woodlands (Figure D.8). Changing the soil density has very little effect on the maximum surface temperature. An increase in soil density leads to very slight decreases in the maximum surface temperatures and vice versa. The effect is approximately linear and is slightly more noticeable in town centres than in woodlands. For example, changing the density of the soil by ±10% (to 1980 kg/m³ and 1620 kg/m³) alters the maximum surface temperature by ±0.04°C in town centres and ±0.01°C in woodlands. When the lowest soil density value for dry peat soils (300 kg/m³) is used (Oke, 1987, p. 44) the change in maximum surface temperature is +0.39°C and +0.07°C in town centres and woodland, respectively. Similarly, when the highest soil density value for saturated sandy and clay soils (2000 kg/m³) is used (Oke, 1987, p. 44) the change in maximum surface temperature is -0.04°C and -0.01°C in town centres and woodland, respectively.
As the density of the soil increases, the difference between the maximum surface temperatures of town centres and woodlands decreases very slightly, but the effect is marginal. Similarly, the density of the soil appears to have very little effect on the timing of the maximum surface temperature in both woodlands and town centres.
D.9 Peak Insolation
Peak insolation (a
_{3}) is used in the net radiation flux term (R) (Equation 5.4). Increasing the peak insolation increases the magnitude of this term.
Currently peak insolation is set at 802.5 W/m², and maximum surface temperatures are 31.2°C in town centres and 18.4°C in woodlands (Figure D.9). Increasing the peak insolation leads to warmer maximum surface temperatures and vice versa. This effect is linear. Changing the peak insolation has a greater effect on the maximum surface temperature in town centres rather than woodlands. For example, changing peak insolation by ±10% (to 882.75 W/m² and 722.25 W/m², respectively) alters the maximum surface temperature by ±1.51°C in town centres and ±0.74°C in woodlands.
As the peak insolation increases, the difference between the maximum surface temperatures of town centres and woodlands increases. With peak insolations of 702.5 W/m², 802.5 W/m², and 902.5 W/m², the difference between the maximum surface temperatures in these UMTs is 11.8°C, 12.8°C, and 13.8°C, respectively. The peak insolation appears to have no effect on the timing of the maximum surface temperature in both woodlands and town centres.
D.10 Night Radiation
Night radiation (a'
_{3}) is used for the night net radiation flux (R) (Equation 5.5). Increasing the night radiation increases the magnitude of this term and vice versa.
Currently night radiation is set at -93 W/m², and maximum surface temperatures are 31.2°C in town centres and 18.4°C in woodlands (Figure D.10). Changing the night radiation has very little effect on maximum surface temperatures. The effect is linear and is slightly greater in town centres than woodlands. As the magnitude of night radiation increases, the difference between the maximum surface temperatures of town centres and woodlands decreases very slightly. In addition, night radiation appears to have very little effect on the timing of the maximum surface temperature in both woodlands and town centres.
D.11 Specific Heat of Air
The specific heat of the air (C
_{a}) is used in the sensible flux term (H) (Equation 5.9). Increasing the specific heat of the air increases the magnitude of this term and vice versa.
Currently the specific heat of the air is set at 1006 J/kg/°C, and maximum surface temperatures are 31.2°C in town centres and 18.4°C in woodlands (Figure D.11). Increasing the specific heat of the air leads to cooler maximum surface temperatures and vice versa. The effect of changing the specific heat of the air is approximately linear, with the effect of a decrease being slightly stronger than an increase. Changing the specific heat of the air has a greater effect on the maximum surface temperature in town centres rather than woodlands. For example, increasing the specific heat of the air to 1106.6 J/kg/°C (a 10% increase from current settings) alters the maximum surface temperature by -0.77°C in town centres and -0.08°C in woodlands. Similarly, decreasing the specific heat of the air to 905.4 J/kg/°C (a 10% decrease from current settings) alters the maximum surface temperature by +0.85°C in town centres and +0.08°C in woodlands. It should be noted that there is little point in testing the sensitivity of the model to changes of ±10% to the specific heat of air. This is because a +10% change would occur between 527°C and 577°C, whilst a -10% change goes off the temperature scale (Holman, 1997, p. 646). The specific heat of the air changes very little at the temperatures of interest and its effect on maximum surface temperature is marginal.
As the specific heat of the air changes there is very little change to the difference between the maximum surface temperatures of town centres and woodlands. If anything, as it increases the difference decreases, but the effect is negligible. The specific heat of the air also appears to have very little effect on the timing of the maximum surface temperature in both woodlands and town centres.
D.12 Specific Heat of Concrete
The specific heat of concrete (C
_{c}) is used in the heat flux to storage in the built environment term (G) (Equation 5.16). Increasing the specific heat of concrete increases the magnitude of this term and vice versa.
Currently the specific heat of the concrete is set at 880 J/kg/°C, and maximum surface temperatures are 31.2°C in town centres and 18.4°C in woodlands (Figure D.12). Increasing the specific heat of concrete leads to slightly cooler maximum surface temperatures and vice versa. The effect of changing the specific heat of concrete is linear. Changing the specific heat of concrete has a greater effect on the maximum surface temperature in town centres rather than woodlands. For example, a ±10% change (to 968 J/kg/°C and 792 J/kg/°C, respectively) alters the maximum surface temperature by ±0.14°C in town centres whereas the effect in woodlands is negligible. Oke (1987, p. 259) lists the thermal properties of different materials. The material listed with the lowest specific heat is steel at 500 J/kg/°C whilst the highest is dense wood at 1880 J/kg/°C. When these values are used the change in the maximum surface temperatures in town centres is +0.55°C for steel and -1.76°C for dense wood. In both cases there is still negligible change in woodlands.
As the specific heat of concrete increases the difference between the maximum surface temperatures of town centres and woodlands decreases, from 13.3°C to 11.0°C, when the specific heat is 500 J/kg/°C and 1880 J/kg/°C, respectively. The specific heat of the air appears to have little effect on the timing of the maximum surface temperature in woodlands, but as it increases the timing of the maximum surface temperature becomes later in town centres.
D.13 Specific Heat of Soil
The specific heat of soil (C
_{s}) is used in the finite difference form of the heat conduction equation (Equation 5.15). Increasing the specific heat of soil decreases the magnitude of this term and vice versa.
Currently the specific heat of the soil is set at 1180 J/kg/°C, and maximum surface temperatures are 31.2°C in town centres and 18.4°C in woodlands (Figure D.13). The effect of changing the specific heat of the soil on maximum surface temperatures is very small. Increasing it leads to slightly cooler temperatures and vice versa. The result of changing the specific heat of soil is approximately linear and has a slightly greater effect on the maximum surface temperature in town centres rather than woodlands. For example, a ±10% change (to 1298 J/kg/°C and 1062 J/kg/°C, respectively) alters the maximum surface temperature by ±0.04°C in town centres and ±0.01°C woodlands. Oke (1987, p. 44) lists the thermal properties of different soils. Dry sandy soil has the lowest specific heat at 800 J/kg/°C whilst saturated peat soil has the highest specific heat at 3650 J/kg/°C. When these values are used the change in the maximum surface temperatures in town centres is +0.14°C for dry sand and -0.33°C for saturated peat, whilst in woodlands maximum surface temperatures are +0.03°C for dry sand and -0.11°C for saturated peat.
The specific heat of soil has very little effect on the difference between the maximum surface temperatures of town centres and woodlands. As it increases the difference becomes slightly less, from 12.9°C to 12.5°C, when the specific heat is 800 J/kg/°C and 3650 J/kg/°C, respectively. The specific heat of the soil appears to have little effect on the timing of the maximum surface temperature in both woodlands and town centres.
D.14 Soil Depth at Level s
The soil depth at level s (d) is used in both the conductive heat flux term (G) as well as in the finite difference form of the heat conduction equation (Equations 5.14 and 5.15). Increasing the soil depth decreases the magnitude of these terms and vice versa.
Currently the soil depth at level s is set at 0.1 m, and maximum surface temperatures are 31.2°C in town centres and 18.4°C in woodlands (Figure D.14). In town centres, increasing the soil depth increases the maximum surface temperature and vice versa. On the other hand, in woodlands, increasing the soil depth decreases maximum surface temperatures and vice versa. In both UMTs the effect of decreasing soil depth is slightly greater than the effect of increasing soil depth. The effect is also greater in town centres than woodlands. For example, at soil depths of 0.11 m (a 10% increase from current depths) alters the maximum surface temperature by +0.06°C in town centres and -0.02°C woodlands. Similarly, at soil depths of 0.09 m (a 10% decrease from current depths) alters the maximum surface temperature by -0.07°C in town centres and +0.02°C woodlands.
An increase in the soil depth leads to an increase in the difference between the maximum surface temperatures of town centres and woodlands. The difference is 11.9°C and 13.2°C at soil depths of 0.05 m and 0.15 m, respectively. The soil depth has little effect on the timing of the maximum surface temperature in woodlands, but in town centres increasing it leads to later maximum surface temperatures.
D.15 Soil Thermal Conductivity
Soil thermal conductivity (k
_{s}) is used in the conductive heat flux term (G) as well as in the finite difference form of the heat conduction equation (Equations 5.14 and 5.15). Increasing the soil thermal conductivity increases the magnitude of both these terms and vice versa.
Currently the soil thermal conductivity is set at 1.083 W/m/°C, and maximum surface temperatures are 31.2°C in town centres and 18.4°C in woodlands (Figure D.15). In town centres, increasing the soil thermal conductivity decreases the maximum surface temperature and vice versa. On the other hand, in woodlands, increasing the soil thermal conductivity increases maximum surface temperatures and vice versa. The effect of changing soil thermal conductivity is more or less linear. The effect is also greater in town centres than woodlands. For example, a ±10% change (to 1.1913 W/m/°C and 0.9747 W/m/°C, respectively) alters the maximum surface temperature by ±0.1°C in town centres and ±0.01°C woodlands. Oke (1987, p. 44) lists the thermal properties of different soils. Saturated peat soil has the lowest thermal conductivity at 0.06 W/m/°C whilst saturated sandy soil has the highest thermal conductivity at 2.2 W/m/°C. When these values are used the change in the maximum surface temperatures in town centres is +1.55°C for saturated peat and -0.95°C for saturated sand, whilst in woodlands maximum surface temperatures are -0.01°C for saturated peat and +0.10°C for saturated sand.
Increasing soil thermal conductivity leads to a decrease in the difference between the maximum surface temperatures of town centres and woodlands, from 14.3°C to 11.7°C, when the thermal conductivity is 0.06 W/m/°C and 2.2 W/m/°C, respectively. Soil thermal conductivity has little effect on the timing of the maximum surface temperature in both woodlands and town centres.
D.16 Latent Heat of Evaporation
The latent heat of evaporation (L) is used in the latent heat flux (LE) (Equation 5.10). Increasing the latent heat of evaporation increases the magnitude of this term and vice versa.
Currently the latent heat of evaporation is set at 2452000 J/kg, and maximum surface temperatures are 31.2°C in town centres and 18.4°C in woodlands (Figure D.16). Increasing the latent heat of evaporation leads to lower maximum surface temperatures and vice versa. The effect of the latent heat of evaporation is more or less linear, with decreases resulting in a slightly greater change. The effect is also greater in woodlands than town centres. For example, an increase of 10% (to 2697200 J/kg) alters the maximum surface temperature by -0.40°C in town centres and -0.62°C woodlands. Similarly, a decrease of 10% (to 2206800 J/kg) alters the maximum surface temperature by +0.42°C in town centres and +0.71°C woodlands. It should be noted that there is little point in testing the sensitivity of the model to changes of ±10% in the latent heat of evaporation, as such changes occur at temperatures below -30°C and above 45°C (Oke, 1987, p. 392). Changes of ±1% in the latent heat of evaporation occur between temperatures of about 10°C and 35°C. These lead to maximum surface temperature changes of ±0.04°C in town centres and ±0.07°C in woodlands.
Increasing the latent heat of evaporation leads to a slight increase in the difference between the maximum surface temperatures of town centres and woodlands. The latent heat of evaporation has little effect on the timing of the maximum surface temperature in both woodlands and town centres.
D.17 Specific Humidity at SBL
The specific humidity at the SBL (q
_{2}) is used in the latent heat flux term (LE) (Equation 5.10). Increasing the specific humidity at the SBL increases the magnitude of this term and vice versa.
Currently the specific humidity at the SBL is set at 0.002 (dimensionless units), and maximum surface temperatures are 31.2°C in town centres and 18.4°C in woodlands (Figure D.17). Increasing the specific humidity at the SBL leads to warmer maximum surface temperatures and vice versa. The effect of changing the specific humidity at the SBL is linear and is greater in town centres than woodlands. For example, a ±10% change to the specific humidity at the SBL (to 0.0022 and 0.0018, respectively) alters the maximum surface temperature by ±0.28°C in town centres and ±0.13°C in woodlands.
An increase in the specific humidity at the SBL leads to an increase in the difference between the maximum surface temperatures of town centres and woodlands. The difference is 12.0°C and 13.6°C at specific humidities of 0.001 and 0.003, respectively. The specific humidity at the SBL has little effect on the timing of the maximum surface temperature in both woodlands and town centres.
D.18 Hours of Daylight
The hours of daylight (hoD) are used to specify ω in the net radiation flux term (R) (Equation 5.4). Increasing the hours of daylight will increase the period of the sine curve and vice versa. It makes sense when changing the hours of daylight to also change the sunrise and sunset times accordingly. Thus, with the current setting of 16 hours of daylight, the sunrise and sunset times are 04:00 and 20:00, respectively. An increase of 10% in the daylight hours to 17.6 hours, gives sunrise and sunset times of 3.2 (03:12) and 20.8 (20:48), respectively. Similarly, a decrease of 10% in the daylight hours to 14.4 hours, gives sunrise and sunset times of 4.8 (04:48) and 19.2 (19:12), respectively.
With the current setting of 16 hours of daylight, the maximum surface temperatures are 31.2°C in town centres and 18.4°C in woodlands (Figure D.18). Increasing the hours of daylight leads to slightly warmer maximum surface temperatures and vice versa. A decrease in the hours of daylight has a slightly greater effect on the maximum surface temperature than an increase does. The effect of changing the hours of daylight is also slightly greater in town centres than woodlands. For example, an increase of 10% in daylight hours (to 17.6 hours) alters the maximum surface temperature by +0.18°C in town centres and +0.01°C in woodlands. Similarly, a decrease of 10% in daylight hours (to 14.4 hours) alters the maximum surface temperature by -0.22°C in town centres and -0.01°C in woodlands.
An increase in the hours of daylight increases the difference between the maximum surface temperatures of town centres and woodlands. The difference is 12.5°C and 13.0°C with daylight hours of 14 and 18 hours, respectively. The hours of daylight have little effect on the timing of the maximum surface temperature in both woodlands and town centres.
D.19 Building Mass per Unit of Land
The building mass per unit of land (m
_{c}) is used in the heat flux to storage in the built environment term (M) (Equation 5.16). Increasing the building mass increases the magnitude of this term and vice versa.
The building mass per unit of land varies between the UMTs according to the proportions of buildings and other impervious surfaces. Thus, in town centres it is currently set at 342.20 kg/m² whilst in woodlands it is 6.58 kg/m². Maximum surface temperatures are 31.2°C in town centres and 18.4°C in woodlands (Figure D.19). Increasing the building mass leads to slightly cooler maximum surface temperatures and vice versa. Changing the building mass of town centres by ±10% (to 376.42 kg/m² and 307.98 kg/m², respectively) leads to changes in maximum surface temperatures of ±0.1°C. Changing the building mass of woodlands by ±10% (to 7.238 kg/m² and 5.922 kg/m², respectively) has negligible effects.
An increase in the building mass per unit of land decreases the difference between the maximum surface temperatures of town centres and woodlands. The difference is 13.7°C and 12.3°C with building masses of 1.28 kg/m² (equivalent to the mass in unimproved farmland, the UMT category with the lowest building mass) and 492.11 kg/m² (equivalent to the mass in major roads, the UMT category with the highest building mass), respectively. Increasing the building mass means that maximum surface temperatures occur later in the day, in both woodlands and town centres.
D.20 Evaporating Fraction
The evaporating fraction (E
_{f}) is used in the latent heat flux term (LE) to define q
_{0}, the specific humidity of the atmosphere (Equation 5.13). Increasing the evaporating fraction increases the magnitude of q
_{0} and vice versa.
The evaporating fraction varies between the UMTs. In town centres it is currently set at 0.2 whilst in woodlands it is 0.98. Maximum surface temperatures are 31.2°C in town centres and 18.4°C in woodlands (Figure D.20). Increasing the evaporating fraction leads to cooler maximum surface temperatures and vice versa. Increasing the evaporating fraction of town centres by 10%, to 0.22, leads to a change in the maximum surface temperature of -0.67°C. Similarly, decreasing the evaporating fraction of town centres by 10%, to 0.18, leads to a change in the maximum surface temperature of +0.71°C. It is not possible to increase the evaporating fraction of woodlands by 10% at this would take it over 1.0, however decreasing the evaporating fraction by 10%, to 0.882, leads to a change in the maximum surface temperature of +0.85°C.
The two UMTs have very similar maximum surface temperatures to each other when they are set with the same evaporating fractions. This highlights the importance of the evaporating fraction in cooling the UMTs. In fact, with evaporating fractions of 0.01 and 1.0, woodlands are 2.2°C and 0.1°C warmer than town centres, respectively. Increasing the evaporating fraction also leads to slightly earlier maximum surface temperatures in both woodlands and town centres.