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CLIMATE vs WEATHER: predicting global warming is like predicting how fast a pot of water will warm if you know the power output of the stove. Predicting weather is like predicting where and when the next bubble will rise in a boiling pot.
The heating caused by the human-caused CO2 increase in the atmosphere is 2 Watts per square meter of Earth surface. That’s the analogy to the power of the stove. It is the cause of global warming.
We call that change to the planet's heat budget "radiative forcing". It is the driver of global heating. Here is a comparison of human-caused and natural radiative forcing since the year 1750, graph from the current US National Climate Assessment. 
In terms of physics, weather prediction is an initial value problem (the forecast depends on the initial conditions). Climate is a boundary condition problem, i.e. the average global temperature depends on the boundary conditions: solar radiation, greenhouse gas content etc.
