**3. Results**

The rainfall pattern in the case study area demonstrated certain particularities and varied greatly in both space and time, in line with the main characteristics of the climate type in the Mediterranean basin. The seasonal distribution of rainfall based on the examined meteorological stations' data is shown in Figure 2. As depicted, 35% of the annual rainfall occurs during winter, 32% in autumn, 24% in spring, and only 9% in summer.

The results of the Mann–Kendall statistics test indicated that most of the meteorological stations (around 67%) recorded a downward trend in annual rainfall, which could be considered as statistically significant for the Katafyto station. In addition, decreasing trends of rainfall time series were recorded in winter and autumn for most of the stations. During spring, half of the stations revealed a decreasing trend, whereas the other half revealed an increasing one. Finally, summer was the only time season when rainfall trends were recorded increasing in most of the stations.

Detailed results of the application of the Mann–Kendall test are given in Table 3. The upward arrow ↑ indicates an increasing trend, whereas the downward arrow ↓ indicates a decreasing one. Furthermore, the light grey cell color shows that the trend is not statistically significant (for a significance level of a = 0.05), whereas the dark grey color shows a statistically significant trend. In addition, the number within the parenthesis indicates the time of occurrence for changes in the mean of the rainfall time series.

**Figure 2.** Seasonal distribution of rainfall.


**Table 3.** Trend detection using the Mann–Kendall test and the change-point analysis.

As shown in Table 3, the rainfall non-stationarity starts to occur in the middle of 1960s for the annual, autumn, spring, and summer rainfalls and the early 1970s for the winter rainfall in most of the stations.

Moreover, Sen's slope was used to compute the trend magnitude per decade, which ranged from approximately −5.3% to +1.5% (average −1.9%) in annual rainfalls, from −14.5% to +7.5% (average −3.2%) in winter, from −4.7% to +5.5% (average +0.7%) in autumn, from −4.2% to +3.6% (average +0.2%) in spring, and from −0.3% to +4.8% (average +2.4%) in summer. Detailed results for each station are given in the next table (see Table 4).

The investigation of the relationships between the variation of rainfall and altitude showed that the derived coefficients of determination are rather low. This indicates that only a small percentage (19–25%) of rainfall variation in the study area was due to the change in altitude. Furthermore, it was observed that the power trendline performed the best fit in all cases. In the equations below (see Table 5), *y* is the rainfall (mm) and *x* is altitude (m).


**Table 4.** Trend magnitude (%) per decade using Sen's slope method.

**Table 5.** Relationship between rainfall and altitude.


For that reason, the spatial variability of both seasonal and annual rainfall was assessed using a multiple regression analysis. All the necessary factors affecting rainfalls were included into the multiple regression procedure, including longitude, latitude, and altitude. The coefficient obtained for each factor, based on a regression analysis, is given in Table 6.


**Table 6.** Coefficients of multiple regression models and statistics.

It is noteworthy that the multiple regression model can explain 62.2% of the spatial variability of the annual rainfall, 58.9% of variability in winter, 75.9% of variability in autumn, 55.1% of variability in spring, and 32.2% of variability in summer. In order to evaluate the statistical significance of the examined factors, *p*-values were estimated (see Table 7). In cases where the significant level of the examined factor is less than 95% (*p* > 0.05), the factor should be eliminated from the model and the multi-linear regression must be performed again. In this study, the *p*-values for all factors were less than 0.05, which means a strong presumption against null hypothesis.

**Table 7.** Output *p*-values of the examined coefficients.


Furthermore, regarding the results of cross validation amongst different spatial interpolation methods it was revealed that better results were achieved by Ordinary Kriging combined with spherical semivariogram (Table 8).


**Table 8.** Cross-validation results from the interpolation of annual and seasonal rainfall.

The semivariogram/covariance cloud tool shows the empirical semivariogram and covariance values for all pairs of locations within a dataset and plots them as a function of the distance that separates the two locations. It can be used to examine the local characteristics of spatial autocorrelation within a dataset and look for local outliers. The selection of lag size has an important effect on the semivariogram. If the lag size is too large, the short-range autocorrelation may be masked, whereas if the lag size is too small, there may be many empty bins. A rule of thumb is to multiply the lag size times the number of lags, which should be about half of the largest distance among all points.

Important characteristics of the semivariogram are also the nugget and the partial sill. The nugget is a parameter of covariance or semivariogram model that represents independent error, and a microscale variation at spatial scales that are too fine to detect. As for the partial sill, it is a parameter that represents the variance of a spatially autocorrelated process without any nugget effect. These parameters for the spherical variogram that was used in this study are given in the following table (see Table 9).

Regarding the semivariograms (see Figure 3), it can be assumed that the phenomenon to estimate is smooth (i.e., rainfall values change gradually with the distance). The semivariogram represents the continuity structure quite well also. Additionally, the semivariogram diagrams showed that the samples did not show autocorrelation in any direction.

**Figure 3.** Spherical semivariograms of ordinary kriging interpolation models for annual and seasonal rainfalls.


**Table 9.** Variogram Statistics.

The rainfall spatial distribution maps over the mountainous catchment of the study area were produced using ordinary kriging and are given in the following figure (see Figure 4).

**Figure 4.** *Cont.*

**Figure 4.** Spatial distribution of (**a**) annual, (**b**) winter, (**c**) autumn, (**d**) spring and (**e**) summer rainfall over the study area.

The major range of rainfall conditions within the mountainous catchment of the study area is shown in Figure 2. The rainfall range (mm) in each catchment and every season is given in Table 10.


**Table 10.** Annual and seasonal rainfall (mm) ranges in the catchments of the study area.
