# URBAN FORM ANALYSIS EMPLOYING LAND COVER AND SPATIAL METRICS THE CASE OF THE LISBON METROPOLITAN AREA

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7 CVVP MCENT CVCENT MCOMP CVCOMP VP CVVP 100 MVP σvp = Stadard deviatio of the muicipality earest eighbour idex MVP = Muicipality mea earest eighbour idex MCENT i1 Dist / R Dist i = The distace from the cetroid of patch i to the major muicipality tow R = Radius of a circle with area equal to the total muicipality area = total umber of patches i the muicipality CENT CVCENT 100 MCENT σcent = Stadard deviatio of the muicipality cetrality idex MCENT = Muicipality mea cetrality idex MCOMP i1 i COMP COMP i = patch i perimeter divided by the miimum perimeter possible for a maximally compact patch of the correspodig patch i area = total umber of patches i the muicipality COMP CVCOMP 100 MCOMP σcomp = Stadard deviatio of the muicipality compactess idex MCOMP = Muicipality mea compactess idex i CVVP is equal to the stadard deviatio of the muicipality earest eighbour idex divided by the muicipality mea earest eighbour idex the multiplied by 100 to be expressed i percetage Uit: Percet Rage: CVVP 0, without limit MCENT is the average distace amog the muicipality patches, to the major muicipality tow To miimize the bias of the urba scale, the average distace was divided by the radius of a circle with the total muicipality area Uit: Meters Rage: MCENT 0, without limit CVCENT is equal to the stadard deviatio of the muicipality cetrality idex, divided by the muicipality mea cetrality idex, the multiplied by 100 to be expressed i percetage Uit: Percetage Rage: CVCENT 0, without limit MCOMP equals patch perimeter divided by the miimum perimeter possible for a maximally compact patch of the correspodig patch area. MCOMP = 1 whe the patches are maximally compact ad icreases without limit as patch shape becomes more irregular Uit: Noe Rage: MCOMP 1, without limit CVCOMP is equal to the muicipality stadard deviatio compactess idex, divided by the mea muicipality compactess idex the multiplied by 100 to be expressed i percetage Uit: Percetage Rage: CVCOMP 0, without limit Source: Adapted after Mcgarigal, et al., (2002); Huag, et al., (2007) Thus, the spatial metrics were calculated for the patches from the aggregatio of CLC classes. 139

10 Figure 7. Rate of chage i the average (MCENT) ad coefficiet of variatio (CVCENT) of the cetrality idex, betwee 1990 ad (%) ODI ALC MON VFX ALM MAF CAS OEI MOI SIN SET SEI LOU LIS BAR PAL AMA SES MCENT CVCENT Source: Table 2 Fially, figure 8 graphically represets the rate of chage for the compactio idex. We see that the idex has ot chaged very sigificatly, still there was a tedecy for dispersio. With the majority of the muicipalities with positive rates of chage for the idex mea, otig a icrease i dispersio for their urba patches, oticeable Moita, Oeiras, Sitra ad Alcochete. 50 Figure 8. Rate of chage i the mea (MCOMP) ad coefficiet of variatio (CVCOMP) of the compactess idex, betwee 1990 ad (%) LIS LOU AMA SET CAS PAL BAR ALM VFX MON MAF ODI SES SEI MOI OEI SIN ALC MCOMP CVCOMP Source: Table 2 For the last step o this study, we used a techique of multidimesioal data aalysis: clusters aalysis. This aalysis was meat to classify the muicipalities uder aalysis agaist the calculated spatial metrics. I terms of geographical aalysis, the clusters defie regios with clustered similar characteristics. The techique adopted was the hierarchical clusterig. The startig poit of this techique is based o buildig a matrix of similarities or differeces betwee the muicipalities, with a iitial group, equal to the umber of uits i aalysis (18), which describes the degree of similarity, or differece, betwee ay two pairs of muicipalities. The selected method of aggregatio was the group average. I this method the distace betwee two classes, "a" ad "b" is the average of the distaces betwee all elemets of "a" ad all elemets of "b", oe process widely used i a umerical taxoomy because of the clearess of its meaig. The resultig clusters represet groups of muicipalities give the similarity of shared values with the spatial metrics of urba form. 142

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