Application of a dynamical two-box surface-atmosphere model to the Mount   Pinatubo cooling event
  We analyze the global temperature change due to the Mt. Pinatubo eruption using a simple two-layer model of the atmosphere and surface to obtain results consistent with satellite data. Through analytic and numerical analysis we find a principal characteristic response time of 5 to 8 months and a climate sensitivity of 0.17 to 0.20 C/(W/m^2), corresponding to a negative instantaneous feedback. Our solutions were fit to the data, reproducing the results of a one-box model, and providing somewhat more detailed information about the feedbacks related to surface layer temperature. The formalism for coupling of the surface layer to the thermocline is set up but not applied. 
Robert S. Knox and Kevin J. LaTourette