= Solution
Assume a plane-parallel atmosphere in <local thermodynamic equilibrium>, negligible infrared <scattering>, a <Blackbody>[black surface], and surface <temperature> equal to the adjacent air <temperature>. For a specified ray, let $\mathfrak T$ be its <transmittance> from a level to space, increasing from $\mathfrak T_0$ at the surface to one at the top. The formal <radiative transfer> solution is
$$
L=B_0\mathfrak T_0+\int_{\mathfrak T_0}^{1}B\,d\mathfrak T.
$$
Using $\mathfrak T_0+\int_{\mathfrak T_0}^1d\mathfrak T=1$ yields
$$
\boxed{L=B_0+\int_{\mathfrak T_0}^1(B-B_0)\,d\mathfrak T.}
$$
This expresses <absorption> and re-emission together: <opacity> does not simply remove surface radiation without adding atmospheric radiation. An absorber close to a thermally coupled surface has nearly the same <Planck function> as that surface, so $B-B_0$ is small. Its emission nearly compensates the surface radiation it absorbs, giving weak <radiance> sensitivity to near-surface concentration. In an exactly <Atmosphere>[isothermal atmosphere] at surface <temperature>, $L=B_0$ for every <optical depth>, a concrete example of complete concentration ambiguity in this thermal measurement. Finite surface emissivity, reflection, <scattering> or a surface-air <temperature> discontinuity would require additional terms.
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