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Finally, two sets of MP–CD relationships are applied to assess uncertainty in the regionalisation models (see Table 3). The first set of MP–CD relationships considers that there may be many equally optimal sets of regression coefficients arising from MP equifinality. Therefore, here the original CDs are maintained but their coefficients are allowed to vary; hence this set is consistent with the physically meaningful relationships of Table 4 in Pechlivanidis et al. (2010). These relationships were generated using randomly selected equifinal MP sets (in here the 10th optimum parameter set). The second set omits the constraint of generating physically meaningful relationships and is solely based on statistical significance. Therefore, the empirical regression model aimed at maximising its performance (i.e., coefficient of determination) without any constraint upon combinations of CDs for each MP. Hence, inter-dependency between CDs could exist, so that the inclusion of different CDs may be giving essentially the same relationship.

Table 3

Alternative MP–CD relationships to assess the effect of regional relationships on results

Equation
Set 1 
 Cmax=117.6+56.7 log(AREA)1140.7 URBEXT+4.14 DPSBAR 
 Kq=−43.6+126.4 BFIHOST+156.6 URBEXT 
 TP=233.232.2 URBEXT +0.175 DPLBAR81.7log(SAAR) 
Set 2 
 Cmax=2111168.1 URBEXT+0.12 AREA+259.3 BFIHOST 
 Kq=−812.5+1.56 SAAR3.26 DPSBAR+12.01 log(URBEXT) 
 TP=4.2634.69 URBEXT+1.78 log(AREA) 
Equation
Set 1 
 Cmax=117.6+56.7 log(AREA)1140.7 URBEXT+4.14 DPSBAR 
 Kq=−43.6+126.4 BFIHOST+156.6 URBEXT 
 TP=233.232.2 URBEXT +0.175 DPLBAR81.7log(SAAR) 
Set 2 
 Cmax=2111168.1 URBEXT+0.12 AREA+259.3 BFIHOST 
 Kq=−812.5+1.56 SAAR3.26 DPSBAR+12.01 log(URBEXT) 
 TP=4.2634.69 URBEXT+1.78 log(AREA) 

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