The climate system, as a nonlinear system, has very high dimensionality and thus, understanding and quantifying its predictability requires simplification of the system, for both conceptual and practical reasons. This issue has led the climate research community to use a range of models, from simple to complex (1D EBM to 3D GCM) to explore behavior ranging from global-mean to regional temperatures. Here, we employ two methods of ``intermediate complexity'' in both modeling and diagnostics to assign quantitative answers, in terms of probabilities, to questions regarding uncertainty in climate predictions, that are themselves {\it conditional} on uncertainties in the assumed future forcings. We employ the MIT 2D climate model (Sokolov and Stone, 1998, {\it Clim. Dyn.}, {\bf 14}, 291-303) which allows us to address uncertainties in three key properties of the system: the equilibrium climate sensitivity to a doubling of CO$_2$, the rate of heat uptake by the deep ocean, and the net aerosol forcing. The combination of these three properties largely determines the modeled climate system's global mean response to prescribed changes in greenhouse gas concentrations and aerosol loadings. To assess probabilistic ranges of these properties and thus, explore uncertainty in future climate changes, we force the climate model with anthropogenic forcings (changes in greenhouse gas, aerosol, and ozone concentrations) and compare observations with modeled temperature changes to explore the regions of the model parameter space for which the simulations and observations are consistent (see Forest et al. (2000) (GRL, {\bf 27}, 4, 569--572). To reduce the dimensionality in the data comparison, data are compared using optimal climate-change detection diagnostics and the resulting goodness-of-fit statistics provide constraints on model properties. Here, we will present two aspects of this problem that reflect the non-linear nature of the problem. First, we explore the relation between model forcings and response and how this affects the interpretation of climate-change attribution results. Second, we present the results as an example of how model uncertainty relates to the uncertainty of future climate projections.