Near-optimal selection of representative measuring points for robust temperature field reconstruction with the CRO-SL and analogue methods

In this paper we tackle a problem of representative measuring points selection for temperature field reconstruction. This problem is a version of the more general Representative Selection (RS) problem, well-known in computer and data science. In this particular case, the objective is to select the best set of N measuring points (i.e. N representative points), in such a way that a reconstruction error is minimized when reconstructing the monthly average temperature field. We use a novel meta-heuristic algorithm, the Coral Reefs Optimization with Substrate Layer (CRO-SL), which is an evolutionary-type method able to combine several different search procedures within a single population. The CRO-SL is combined with the Analogue Method (AM) to identify the most representative points. This approach exhibits strong performance from experiments with gridded and un-gridded temperature field datasets (European Climate Assessment & Dataset (ECA) and ERA-Interim reanalysis (ERA)). Different aspects such as the error assessment and the comparison with alternative approaches, are discussed in the experimental analysis of this article. We show that the algorithm performs better than a greedy approach, i.e. the best solution for N points is different from the N best individual predictors. The solutions obtained with the proposed methodology are climatologically consistent and include points from Scandinavia, Central and Southern Europe, the Black Sea and Central and South Western Asia as the more representative in the case of the ECA dataset; similar areas are selected for ERA. We have found out that once the number of stations/points goes over a threshold, the improvement in the model is obtained by increasing the density of data in the given zones, instead of adding data from different zones to the algorithm. The method proposed may have direct application in Palaeoclimalogy, where there are a large amount of distributed proxies with scarce information, so the proposed approach could be useful to select the most important ones to reconstruct a desired field.