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This paper presents a novel methodology for Climate Network (CN) construction based on the Kullback-Leibler divergence (KLD) among Membership Probability (MP) distributions, obtained from the Second Order Data-Coupled Clustering (SODCC) algorithm. The proposed method is able to obtain CNs with emergent behaviour adapted to the variables being analyzed, and with a low number of spurious or missing links. We evaluate the proposed method in a problem of CN construction to assess differences in wind speed prediction at different wind farms in Spain. The considered problem presents strong local and mesoscale relationships, but low synoptic scale relationships, which have a direct influence in the CN obtained. We carry out a comparison of the proposed approach with a classical correlation-based CN construction method. We show that the proposed approach based on the SODCC algorithm and the KLD constructs CNs with an emergent behaviour according to underlying wind speed prediction data physics, unlike the correlation-based method that produces spurious and missing links. Furthermore, it is shown that the climate network construction method facilitates the evaluation of symmetry properties in the resulting complex networks. [ABSTRACT FROM AUTHOR]