Optimal sensor placement using learning models

Measuring data efficiently in the framework of geosciences has proven to be more cumbersome than expected, despite technological advances. While remote sensing techniques, such as satellite observations, provide extraordinary spatial coverage, they still lack the fine spatial and temporal resolution of in situ measuring techniques. Naturally, the level of coverage obtained by remote sensing techniques could be replicated with physical measuring
stations and devices, however, the financial cost would be immense. Therefore, if we are to broaden the spatial coverage while retaining both resolutions and minimising cost, we need to strategically deploy as few sensors as possible. In order to tackle this problem, we have
utilised three unsupervised learning (clustering) methods not only to demonstrate how a smaller subset of sensors can provide significant measurement accuracy, but also to show that there exists an optimal sensor placement (as opposed to random placement). Data used for this
demonstration is ERA5 wind components at 10m height from 1979 to 2019 over the Mediterranean sea, at a spatial resolution of 0.5° × 0.5° every 6 hours.
Clustering methods used are K-means clustering, Self-Organising Maps (SOM) and Growing Neural Gas (GNG). We have clustered the data into 5, 10, 20, 50, 100, 200 and 500 groups and treated the median centers of the resulting domains as the optimal placement for sensors. After the clustering was completed, we have attempted to reconstruct the missing data using two regression models: linear and K-Nearest Neighbours. Reconstructed data was compared (in both size and angle) to original data, and the results show that with just 5 points (out of a grand total of 1244 wet points), reconstruction accuracies are as follows: 65.6, 65 and 62.5% for linear regression reconstruction and 71.6, 71.2 and 70.5% for KNN reconstruction, when applied to GNG, K-means and SOM respectively. Increasing the number of points has diminishing returns (especially in excess of 100 points), with linear regression reconstruction accuracy peaking at ≈ 95% and KNN reconstruction remaining in the high 70%. As demonstrated, GNG and K-means performed slightly better than SOM, due to the nature of SOM’s rigid algorithm.

This work has been supported by Croatian Science Foundation under the project UIP-2019-04-1737.