## 5 Results and Discussion
### Training SOM  
The SOM component planes of the functional attributes are displayed in Figure 5. This method, allows visualizing multiple variables simultaneously and their relationship, being and efficient way to analyze the effect of each variable on the patterning input dataset. The 19 subfigures are linked by position: in each subfigure, the hexagon in a certain position corresponds to the same map unit, and the color of each hexagon informs on the value of the component in that neuron--warm colors for high values and cold colors for low values. Figure 4: Example of several functional variables (Date of maximum Normalized Difference Vegetation Index (DNDVI), Normalized Difference Vegetation Index (NDVI), Mean Land Surface Temperature (MeanLST), IAlbedo, Aridity Index). Comparing the color gradient of the component planes some correlation patterns among the variables could be discerned, indicating a number of general features summarized below. First, multiple variables exhibit a similar color indicating a strong positive correlation, such as precipitation, humidity and moisture indices, demonstrating that a decrease in the precipitation encompasses a decrease of moisture index [84]. Moreover, the integrals and mean values of variables (e.g., MeanLST and ILST) also show the same pattern, confirming that the information provided is similar and corroborating that SOM patterns make physical sense. Hence, these variables have the same relative influence in the characterization of the ecosystem function. For this reason, and to avoid redundancy, only one of the related variables in each category may be needed to adequately describe the ecosystem. Second, several attributes have a strong negative correlation (same pattern but opposite colors). For example, between aridity index and precipitation as previously pointed out in the Mediterranean region [85], especially during the warm season. Third, several attributes present very homogeneous patterns, so these variables contribute little to discriminate among EFTs, e.g., RLST and RAlbedo. Figure 6 shows the final variables chosen for deriving EFTs based on the SOM maps presented in Figure 5 and following two criteria: (i) avoid variables which are redundant (_i.e._, MeanLST and ILST) and (ii) include all the representative attributes involved in ecosystem functioning (e.g., attributes concerning the biomass production (NDVI) and heat fluxes (LST)). One of the most appealing characteristic of SOM is its faithful representation of the original data, e.g., two data points are represented close to each other in the resulting map when they have similar features. Figure 5: Visualization of the two-plane components of the Self-Organizing Map (SOM) trained from time series of NDVI, Albedo, LST and climatic data of Spain. Several SOM neural network architectures were evaluated through the _Qe_ and _Te_ errors in order to optimize performance. The main discrepancies in these error parameters appear to regard the number of neurons. Since no strict rules to determine the optimal number of neurons exist, different map sizes were evaluated (Table 1) resulting in a mild drop of the _Qe_ with increasing number of neurons. _Qe_ is expected to decrease because a large number of dimensions better represent the sample; more neurons produce a better-input pattern because each data vector will be closer to its best matching unit. Nevertheless, a large number of neurons may cause over-fitting, while a small number can cause insufficient learning. _Te_ represents the proportion of all data vectors for which first and second BMUs are not adjacent. The lower the _Te_ is, the better the SOM preserves the topology. However, _Te_ exhibits a tendency to increase with increasing SOM dimensionality due to a large number of non-neighbors in a large SOM matrix. Here the optimum size of 600 neurons was selected based on a compromise between _Qe_ and _Te_[86]. For the rest of the parameters, the best fit was achieved by those parameters proposed by [41].