Abstract: This article focuses on the applications of new computing technologies represented by artificial intelligence (AI) and quantum computing in the fields of weather forecasting and climate prediction. The article delves into the applications of AI in meteorological data processing and analysis, as well as long - term climate prediction. Meanwhile, it expounds on the achievements of quantum computing in accelerating climate model calculations and optimizing parameters. The article holds that new computing technologies have significantly enhanced the capabilities, speed, and accuracy of weather forecasting and climate prediction. However, they also face challenges such as the weak interpretability of AI models and the slow development of quantum computing hardware and algorithms. Looking ahead, with the enhancement of the interpretability of AI algorithms and the improvement of the performance of quantum computing hardware, emerging computing technologies will provide more robust support for weather forecasting and climate prediction.