While the detailed approach may vary, the basic principal is to compare the contribution, in terms of information, of each rain gauge to your quantitative objective. You can then eliminate the gauge that contributes the least information. This process can be repeated until a minimum network that meets the project objective is arrived at. Computationally refining this method to look at all possible combinations of subsamples is usual. I.e. for a 10 gauge network you would look at all combinations of 9 gauges, then of 8 etc. until the objectives were met.

A similar approach can be used to add gauges to a network, by looking at the correlations between adjacent rain gauges and siting gauges in areas of poor spatial correlation.

«A New Approach for Optimizing Rain Gauge Networks: A Case Study in the Jinjiang Basin» by Wu et al. is a good worked example of this process using geostatistics. Its reference list provides links to many other case studies.

Reference:

Wu, H.; Chen, Y.; Chen, X.; Liu, M.; Gao, L.; Deng, H. Water 2020, 12, 2252; (https://doi.org/10.3390/w12082252, open access).