Statistical weather prediction
You need a model. You could try to use Bayes theorem to build a model based upon conditional probabilities. See this reference from NOAA about weather forecasting: Probability Forecasting - Primer . 

If I were to try to build a Bayesian model for weather forecasting, with the intention of using a limited data set of observations I had collected myself, I would look into existing software frameworks to see if I could use one of these. For example, the Infer.NET framework is available for free, and has several examples which would be a good starting point for learning about probabilistic modeling.