= Infrared absorber sensitivity kernel
{title2=$\delta L=\int K_p(p)\,\delta x(p)\,dp$}
The derivative of outgoing spectral <radiance> with respect to a pressure-resolved absorber abundance defines a kernel once the vertical measure is fixed. In an optically thin column with $k\propto p$ and $B/B_0=p/p_0$, $K_p=[k_0B_0/(p_0gM)]p(p/p_0-1)$. It is negative inside the atmosphere and zero at both endpoints. Its largest magnitude lies at $p_0/2$, whereas the logarithmic-pressure kernel $pK_p$ peaks in magnitude at $2p_0/3$. A uniformly perturbed abundance instead has one integrated derivative, not a pressure location.
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