Climate as a pattern of weather over a long period of time. If the climate is increasingly unpredictable, I would think that it wouldn't really effect our ability to make short-term predictions, like a few days out.
But our ability to forecast weather on a longer timeline, like for industrial forecasting, is calibrated on historical weather patterns. But with weather being more erratic and unusual, I don't understand how AI will be forecasting with the models they have now.