Currently, we implement an approximate solution to the two-box energy balance model, which is really more of a 1.5 box solution which assumes the upper-box equilibrates instantly with the forcing. I did this because I did not know how to solve the full two-box equations but thankfully Geoffroy et al. 2013 did this for us and the solution is just a sum of exponential green's functions.
Currently, we implement an approximate solution to the two-box energy balance model, which is really more of a 1.5 box solution which assumes the upper-box equilibrates instantly with the forcing. I did this because I did not know how to solve the full two-box equations but thankfully Geoffroy et al. 2013 did this for us and the solution is just a sum of exponential green's functions.