The coupling between weather and climate is in the influence of the former on the absorption and reflection of sunlight, and on the outbound radiation from the earth. All are time and location dependent, but generally in a steady state and a crude spatial grid might be suffice.Weather is an initial value problem, climate is a boundary value problem (so essentially a very complex energy balance)
This means that you cannot compare weather predictions with climate predictions. It is a common misunderstanding. Weather is influenced by chaos, climate much less so. This however in no way means that climate predictions are less complex, just differently complex...