Civil supersonic aviation may return in the near future. Their emissions have been found to lead to changes in the composition of the stratosphere, affecting the ozone layer and climate. To keep up with the rapid developments in supersonic aircraft technology and alternative fuels there is an increasing need for the development of surrogate modeling methods, which requires knowledge of the sensitivities to these emissions. We present a parametric study which evaluates the first- and second-order sensitivities of the ozone column and radiative forcing (RF) to supersonic emissions across two flight corridors and three altitudes. For a given increase in global fuel burn, we find that the increase in emission of (Formula presented.) is the main driver of both the changes in the global ozone column and RF, the latter of which is linked through changes in the ozone distribution. Followed by the increase in the emission of (Formula presented.), which leads to (Formula presented.) loss and has a cooling effect. The ozone column and climate are least sensitive to increases in (Formula presented.) emissions. We also show that interactions between (Formula presented.), (Formula presented.), and (Formula presented.) emissions lead to non-linear behavior in the atmospheric response. The effect of these interactions can lead to (Formula presented.) 5% differences in the ozone column impacts and up to 7.3% increases in RF. Our results demonstrate that the majority of second-order sensitivities may be neglected in surrogate models for small errors, which could greatly simplify their development. Our results also indicate that reductions in flight altitude and fleetwide (Formula presented.) emissions may effectively reduce the environmental footprint of supersonic aviation emissions.