Understanding the complex dynamics of climate patterns under different anthropogenic emissions scenarios is crucial for predicting future environmental conditions and formulating sustainable policies. Using Dynamic Mode Decomposition with control (DMDc), we analyze surface air temperature patterns from climate simulations to elucidate the effects of various climate-forcing agents. This improves upon previous DMD-based methods by including forcing information as a control variable. Our study identifies both common climate patterns, like the North Atlantic Oscillation and El Niño Southern Oscillation, and distinct impacts of aerosol and carbon emissions. We show that these emissions’ effects vary with climate scenarios, particularly under conditions of higher radiative forcing. Our findings confirm DMDc’s utility in climate analysis, highlighting its role in extracting modes of variability from surface air temperature while controlling for emissions contributions and exposing trends in these spatial patterns as forcing scenarios change.