Abastecimiento de agua potable y gestión del recurso en la ciudad

Having defined the environmental and stand related factors from which variables affecting non-timber functions can be derived and inventoried the next step is to determine the meaning or significance of each value of a variable with respect to the non-timber function under consideration. Since a variable can have different meaning with respect to different functions, a significance to its values should be assigned for each non-timber function considered. To do this, knowledge of the relation between each variable and the forest function is needed. As a general rule the relationships between environmental factors and forest functions are not explicit known and they seldom are expressed with a mathematical formula, with probably the only exception of the Universal Soil Loss Equation. Nevertheless, the available scientific knowledge and practical experience permit an approximation of such relationships in qualitative terms. For example, a hydrologist can say that a vegetation cover of 20% provides a relative low protection of soil from erosion, while a coverage of 80% assures a relative high protection.

Such qualitative judgements of experts can be transformed into quantitative assessments by the use of scaling methods (MARTÍNEZ-FALERO ET AL., 1995). Scaling is the branch of measurement that employs methods for the construction of an instrument to associate qualitative concepts with quantitative metric units (TROCHIM, 1999). The instrument to be constructed is an arbitrary metric scale on the divisions of which the qualitative judgements can be allocated. Depending on the type of input variables (nominal, ordinal, cardinal) and the desired type of resulted variables different scaling methods have been developed. Detailed description of the methodological background and the practical implementation of the methods can be found among others in ZANGEMEISTER (1976) and BORTZ AND DÖRING (1995).

The objective in assigning a meaning to environmental factors with respect to a function is to derive a quantitative expression of the non-timber function which can be used further in analysis. Therefore, the output of scaling should be a cardinal variable – the degree at which a factor value contributes to the manifestation of the function. Consequently, the scaling method should use a rating scale behind which the existence of an interval scale is assumed. That is, the categories of the rating scale are to be perceived as equidistant points on an axis of values. The expert can picture the magnitude of his reaction on the various values of a variable directly through quantitative judgement, making every judgement under the same (arbitrary) scale – with the same null point and scale unit; the numerical differences between scale-values reflect then subjective distances (ZANGEMEISTER 1976). An example of interval scale is shown in figure 4. The breadth of the scale can be changed as desired. An expert is asked to allocate the values of a factor in the classes of the interval

scale based on his judgement on the influence/impact that different factor-values have on the function. Thus, the classes of the interval scale reflect different equidistant levels of function manifestation. 0 1 2 3 4 I n t e r v a l s c a l e Ratio scale -0.5 0.5 0 1.5 2.5 2.5 5.0 3.5 7.5 4.5 10 No influence Very low nfluence Low influence High influence Very high influence

Figure 4: Interval scale for the assessment of the significance of factor values

(adapted from GATZOJANNIS, 1984).

A problem that arises in the implementation of interval scales relates to the number of classes to be used and to whether an even or an odd number of classes should be applied. The more classes a scale comprises the better quantification of a function it achieves. But, the number of classes can be increased up to the differentiation ability of the experts. Consequently, the number of classes depends on the knowledge available regarding the relationship between factor and function, which permits the experts to clearly differentiate more function levels.

Scales with odd number of classes contain usually a neutral middle category. This category may however be used from the experts to evade uncertain judgements. When such evasion is suspected then an even number of classes should be used. Scales with even number of classes comprise no neutral category and force the experts to provide at least a tendency with their judgement.

In the present work a scale with four classes has been used, in order to obtain a possible clear judgement from the experts. The four classes were built from the scale in figure 4 by integrating the two lower classes (0 and 1) into one. It was thought that since the variables derived from the external and internal factors are selected to relate to the function under consideration, a variable with no influence was rather unlikely.

For the allocation of factor values into the classes of the interval scale the discrimination between quantitative and qualitative factors should be considered. For quantitative variables the limits of the classes are to be identified, while for qualitative factors a direct allocation of the factor values into a class is required. Examples for both cases are given in table 7 for the case of erosion protection function and for the parameters soil depth

(external factor "soil") and land use (external factor "human impact"), which have been developed for the testing area of this study.

Table 7: Classification of the values of "Soil depth" and "Land use type" into classes with respect to the erosion protection function.

Erosion Danger is

High Rel. high Rel. low Low

Soil depth 4 3 2 1

A. Very deep soil ( ≥ 120cm) B. Deep soil (60 - 120 cm) C. Shallow soil (30 - 60 cm) D. Very shallow soil ( < 30cm)

Land use type 4 3 2 1

A. Protected areas B. Wood production C. Recreation areas D. Grazing areas E. Agriculture

F. Wildland-urban interface, Build-up areas

Factor specific expertise from related sciences and local experience of the performance of the factors in the forest under consideration are key elements to assure consistence in the implementation of the interval scale. Knowledge of the local conditions in the area under study is important because the influence of most factors on the manifestation of a function varies from place to place. In the example of table 3 all land use types, except possibly for the type "protected areas", can be assigned to different erosion danger classes in another than the forest of Thessaloniki area. These inherent characteristics of such empirical classifications pose also limits to the transferability of them to areas not similar to the ones for which they have been developed.

3.4 Inventory design for non-timber functions and establishment of measurement