I am trying to predict the amount of rainfall using weather measurements (temperature, precipitation, humidity, wind speed, surface radiation). For long term, midterm, and short term predictions, which lags (lags of how far long ago) affect the amount of precipitation? For example, the amount of temperature of how long ago affects the amount of precipitation of today? (I am asking for lags for each of temperature, precipitation, humidity, wind speed, surface radiation)
If you can suggest me some papers or material to study as well that would be good.