The estimation of climate model parameters requires both the ability to search parameter space of a climate model and the proper use of climate-change detection statistics. Using the MIT 2D Climate model, we present a method for constraining model parameters that incorporates fingerprint statistics as the measure of fit with climate observations. In this research, we have three uncertain model parameters. The first two determine the model's climatology: the climate sensitivity (via the cloud parameterization) and the vertical diffusion of heat into the deep ocean. The third parameter is the magnitude of the aerosol forcing, parameterized as a change to the model's surface albedo, which is set separately over land and ocean for each latitude band. The MIT model consists of a zonally averaged atmospheric model coupled to a diffusive ocean model and includes parameterizations for all of the main physical processes making it capable of reproducing the nonlinear processes found in 3D AOGCMs. Because of its computational efficiency, the MIT 2D Climate model is ideal for testing the sensitivity of modeled climate changes to model parameters. We will present results from simulations of 20$^{th}$ century climate as forced by changes in greenhouse gas, aerosol, and ozone concentrations and where the three uncertain model parameters are varied. To compare simulated temperature changes with radiosonde observations for 1961-1995, we use a noise-weighted goodness-of-fit statistic which uses variability estimates from the Hadley Centre's HadCM2 control run. The distribution of this statistic is used to estimate plausible ranges of model parameters, and hence of the magnitude of the aerosol forcing over this period. For comparison, we will also estimate the effect on temperature changes of using latitude-height distributions of aerosol concentrations directly in the radiation code. The aerosol distribution will be predicted, in this case, by the Chemistry-Climate version of the MIT 2D model.