Renewable energy development is closely related to natural meteorological properties. Hence, the identification of climate change and its underlying physical mechanisms across the globe is indispensable. Meteorological stations provide a wealth of high-quality data for observing global meteorological changes. However, there is no research focusing on the long-term development mechanisms and operation of meteorological stations. This study explores the operation and distribution of meteorological stations in 181 countries from 1800 to 2018 and analyzes the relationship between the number of active stations and development indicators by correlation analysis, least squares regression, and machine learning interpretable modeling based on station data from 25 countries. The results indicate that Gross Domestic Product (GDP) and government spending are the main factors influencing the number of active stations in each country, while GDP per capita and agricultural land area have weaker effects. Meanwhile, most of the meteorological stations are located in developed countries. In addition, machine learning models, including Multilayer Perceptron, Long Short-Term Memory (LSTM) neural network, Gated Recurrent Unit (GRU) neural network, and Broad Learning System, are developed to predict the number of active stations in a country. The experimental results show that GRU and LSTM models achieve better performance than other models.