GIS-Based Models as Tools for Environmental Issues: Applications in the South of Portugal - Cartography: A Tool for Spatial Analysis - page 262

where: P i is the monthly rainfall at month i (mm) and P t is the annual rainfall (mm).

Monthly rainfall data observed from 01.01.1911 to 31.12.2010 on 30 weather stations were
used as an input to the MFI model.

Rainfall distribution is highly variable in space and time. In this study the precipitation data
are insufficient and poorly distributed. Thus, for creating the MFI model other variables
which are correlated with precipitation were used such as hillshading, aspect, distance to
coastline, latitude and elevation. The software Statistica 6.0 (Statsoft, 2001) was used to
establish a multilinear regression with t critical=1.711 for a significance of 95% ( = 0.05).
Aspect model was created based on DEM, by Eq. (8).

 

dz dz

Aspect  atan2 , 



(8)

 

dy dx



dz
dy

is the variation of height in latitude and dz
dx

where: is the variation of height in longitude.

Models of hillshading created refer to solstice and equinox. These models represent the
hillshading for a given solar declination and azimuth. These variables were calculated using
the equations described by Díez-Herrero et al. (2006). Hillshading models were calculated
with Eq. (9).

 

 

HS  255 Sin (  Cos D ( )  Cos ( )  Sin D Cos ( ) (   A )



(9)



where: HS is the hillshading,  (º) is the elevation of the sun above the horizon, D (º) is the
declination of the sun,  (º) is the solar azimuth and A (º) is de aspect.

While mapping of the MFI various models were created and the respective outputs analysed
such as Cook's distance, consistency, independence and normality. The best model found
was that in which the independent variables were latitude, elevation, and distance to
coastline, spring hillshading and aspect:

(10)

R  1.1708 E  0.0009 L  708.8582 SHS  0.1225 A  0.0032 DC  3,432.4703

where: R (mm) is rainfall, E (º) is elevation, L (º) is latitude, SHS is spring hillshading, A (º) is
aspect and DC (m) is a distance to coastline.

Classes Range Classification

1 <60 Very low

2 60-90 Low

3 90-120 Moderate

4 120-160 High

5 >160 Very high

Table 6. MFI values according CORINE - CEC (1992).