op952d.f

Gets the OPAL95 opacity from the table pre-interpolated to the surface composition (MHP 7/98: "get OPAL95 opacity from table at surface X,Z"): a two-dimensional interpolation in $\log T$ and $\log R$, where $R = \rho/T_6^3$. It is the fastest of three routines; OP953D adds $X$ and OP954D adds $X$ and $Z$.

• Inputs: the surface table CAPPAE(70,19) of $\log\kappa$ in LLOT95E_MOD, built by OP95XTAB; the indices and the Lagrange weights prepared by GETOPAL95 in OP95INTERP_MOD (formerly /OP95INDX/, /OP95FACT/ and /OP95EXT/), where $\log R$ is now named RHO_T63L (formerly RL) and its lowest table value RHO_T63LL (formerly RLL).
• Who calls it: GETOPAL95, when the point's $Z$ matches the table's ZTAB (to a relative $10^{-4}$) and its $X$ the surface table's XTAB (to $10^{-4}$), and the acoustic depth is not being computed (LADON and LACOUT, which force OP954D).
• Outputs: $\kappa$ (O), $\log\kappa$ (OL), QOD $= \partial\log\kappa/\partial\log\rho$ and QOT $= \partial\log\kappa/\partial\log T$.

At each of the four nearest temperatures $T_i$, four-point Lagrange interpolation in $\log R$ gives $\log\kappa$ and its slope: $$C_i = \sum_k b^{(D)}_{ik}\,\log\kappa_{i,k},\qquad C'_i = \sum_k b^{(D')}_{ik}\,\log\kappa_{i,k}.$$ If $\log R$ lies below the table (LEXTL) or above it at some $T_i$ (LEXH(I)), the value at the edge is extrapolated linearly, $C_i \to C_i + (\log R - \log R_\mathrm{edge})\,C'_i$. Then, in $\log T$, $\log\kappa = \sum_i b^{(T)}_i C_i$, $\partial\log\kappa/\partial\log T|_R = \sum_i b^{(T')}_i C_i$ and $\partial\log\kappa/\partial\log R|_T = \sum_i b^{(T)}_i C'_i$. Since $\log R = \log\rho - 3\log T_6$, $$\left(\frac{\partial\log\kappa}{\partial\log\rho}\right)_T = \left(\frac{\partial\log\kappa}{\partial\log R}\right)_T,\qquad \left(\frac{\partial\log\kappa}{\partial\log T}\right)_\rho = \left(\frac{\partial\log\kappa}{\partial\log T}\right)_R - 3\left(\frac{\partial\log\kappa}{\partial\log R}\right)_T .$$

The table dimensions are fixed (70 temperatures, 19 values of $\log R$), now as private parameters of LLOT95E_MOD; the routine itself no longer declares them.