 Solution

Let ${\tau }_t$ be the tropopause optical depth and linearize $B$ with positive derivative $B_T$. In the troposphere $T=T_t+\Gamma H_{\tau }\log (\tau /{\tau }_t)$, so the requested schematic isIt is constant in the isothermal stratosphere and rises linearly with $\log \tau$ below it. At unchanged temperatures and a multiplicative abundance change $a$, optical depth at each height changes to $a\tau$, hence $\boxed{B_a(\tau )=B_{\mathrm{old}}(\tau /a)}$. Doubling moves the tropopause kink to $2{\tau }_t$ and gives colder emission temperatures at a fixed optical depth; halving does the opposite.