sensitivity analysis 2

Calculating the energy absorbed by the ground at a given time using the energy balance and the equations discussed in the previous sections requires a substantial number of inputs. It can be useful, therefore, to know which ones are those that can have a larger effect on the final results and which ones might, instead, require less accuracy.
Table 1 summarises the inputs needed in this part of the analysis. Considering that some of them are variables that are updated during the analysis and some others are meteorological data from external sources, the sensitivity analysis has focussed on the inputs that the user is required to input directly.

Fixed	During analysis	From Met. Station
Latitude	Time of day	Air temperature
Cloud base factor	Day of year	% of cloud cover
Vapour pressure	Surface temperature	Wind speed
S. s. w. absorptivity
S. emissivity

Table 1: Inputs to the temperature model
The structure analysed is given in Table 2. The meteorological data used in this case were extracted from an ME-PDG analysis for a location with the characteristics specified in Table 3.

Layer	Thickness [m]	Specific Heat [J kg-1 K-1]	Thermal Cond. [J m-1 s-1 K-1]	Density [kg m-3]
HMA	0.2	921	1.16	3200
Granular	0.4	754	0.38	2700
Granular	0.4	754	0.38	2700
Granular	5.0	754	0.38	2700

Table 2: Sensitivity analysis – pavement structure

Latitude	33.26º
Cloud base factor	0.9
Vapour pressure	1.33mbar
S. s. w. absorptivity	0.85
S. emissivity	0.93

Table 3: Sensitivity analysis – initial inputs
These values have been kept as the basis for the sensitivity analysis, varying them one at the time while keeping the others constant. Their effect on the simulated surface temperature is shown in Figure 1to Figure 5and is summarised in Table 4.
Figure 1: Sensitivity to latitude
Figure 2: Sensitivity to cloud base factor
Figure 3: Sensitivity to vapour pressure of air
Figure 4: Sensitivity to short wave absorptivity
Figure 5: Sensitivity to surface emissivity

Parameter	Range	Change [ºC] (Summer)	Change [ºC] (Winter)
Latitude	0 – 70 [º]	2.5	9.0
Cloud base factor	0.8 – 0.9	0.9	0.4
Vapour pressure	1.33 – 13.3 [mbar]	7.0	6.0
S. s. w. absorptivity	0.8 – 0.98	2.5	1.0
S. emissivity	0.8 - 1	2.5	2.0

Table 4: Sensitivity analysis – results (surface)
The effect of these parameters on the temperatures calculated at the bottom of the asphalt layer (depth of 0.2m) is, as expected, very similar, but these temperatures also affected by the material parameters such as thermal conductivity k and specific heat c. As shown in Table 5, the effect of varying k and c within the range suggested in the ME-PDG is quite small.

Parameter	Range	Change [ºC] (Summer)	Change [ºC] (Winter)
Specific heat	0.10 – 0.65 [J kg-1 K-1]	0.4	0.6
Thermal conductivity	0.44 – 0.81 [J m-1 s-1 K-1]	0.6	0.7

Table 5: Sensitivity analysis – results (bottom of asphalt layer)

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