Climatic data and bioclimatic indexes have been used to study plants, animals and ecosystem distribution. GIS-based maps of climatic and bioclimatic data can be obtained by interpolating values observed at measurement stations.

Since no single method can be considered as optimal for all observed regions, a major task was to propose comparisons between results obtained using different methods applied to the same data set of climate variables. We compared three methods that have been proved to be useful at regional scale:

1 - a local interpolation method based on de-trended inverse distance weighting (D-IDW),

2 - universal kriging (i.e. simple kriging with trend function defined on the basis of a set of covariates) which is optimal (i.e. BLUP, best linear unbiased predictor) if spatial association is present,

3 - multilayer neural networks trained with backpropagation (representing a complex nonlinear fitting).

We used the following independent variables as predictors: longitude, latitude, elevation, aspect, slope, continentality and estimated solar radiation.

Long-term (1955-1990) average monthly data were obtained from weather stations measuring precipitation (317 sites) and temperature (154 sites). Twelve climatic variables (temperature and precipitation) and nine bioclimatic indexes were analysed.

List of climatic variables and bioclimatic indexes

*Bioclimatic indexes*

1. Emberger pluviothermic quotient:

where:

P = annual precipitation

Tmax = mean maximum temperature of the hottest month

Tmin = mean minimum temperature of the coldest month

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2. Mitrakos summer drought stress:

where:

= mean precipitation of June, July and August

If P = 0 then MDS = 100

If P ≥ 50 then MDS = 0

3. Mitrakos winter cold stress:

where:

= mean of minimum temperature of December, January and February

4. Ombrothermic index:

where:

YPP = sum of the average precipitation of months whose average temperature is higher than 0 °C

and

YPT = sum of the average temperature of months whose average temperature is higher than 0 °C.

5. Compensated Summer Ombrothermic Index:

6. Continentality index:

where:

Tmax and Tmin are respectively the mean temperature of the hottest and the coldest month.

7. Thermicity index:

where:

T = yearly mean temperature

m = mean of minimum temperature of the coldest month

M = mean of maximum temperature of the coldest month

### 8. De Martonne aridity index:

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where:

P = annual precipitation

T = mean annual temperature

p = precipitation of the driest month

t = mean temperature of the driest month.

9. Box moisture index:

Where:

P = mean annual precipitation

ETp = potential evapotranspiration.

ETp has been calculated using the Jensen-Haise equation (Jensen and Haise, 1963) which is considered more robust in arid and semi-arid areas than other ways of calculating evapotranspiration:

where

RS = annual solar radiation (KiloJoule)

T = mean annual temperature.

Based on the root mean square errors from cross-validation tests, we ranked the best method for each variable data set. Universal kriging with external drift obtained the best performances for seventeen variables of the twenty-one analysed, neural network interpolator has proven to be more efficient for three variables and D-IDW for only one. Based on these results, we used the universal kriging estimates to produce the climatic and bioclimatic maps aimed at defining the bioclimatic envelope of species