In many studies involving complex representation of the Earth's climate, the number of runs for the particular model is highly restricted and the designed set of input scenarios has to be reduced correspondingly. Furthermore, many integrated assessment models, in particular those focusing on intrinsic uncertainty in social decision-making, suffer from poor representations of the climate system ue to computational constraints.In this study, using emission scenarios as input and the temperature anomaly as a predicted response variable, we construct low-dimensional approximations of high-dimensional climate models, as represented by MAGICC. In order to extract as much explanatory power as possible from the high-dimensional climate models, we construct orthogonal emissions scenarios that carry minimum repetitive information. Our method is especially useful when there is pressure to keep the number of scenarios as low as possible. We demonstrate that temperature levels can be inferred immediately from the CO2 emissions data within a one-line model that performs very well on conventional scenarios. Furthermore, we provide a system of equations that is ready to be deployed in macroeconomic optimization models. Thus, our study enhances the methodology applied in the emulation of complex climate models and facilitates the use of more realistic climate representations in economic integrated assessment models.