distance between the normalized target and synthetic flux, using a reduced $\chi^{2}$ statistical criterion. The parameter search over the grid is carried out by the IDL function minimization routine MPFIT (Markwardt 2009). In this search, we fix [$T_{\rm eff}$]{} and [$\log~g$]{} to the value determined (previously) by the SSPP, and change [\[Fe/H\]]{} and [\[C/Fe\]]{} simultaneously to generate a trial model spectrum by spline interpolation from the existing grid, rather than vary all four parameters at once. Since the temperature has the greatest influence on the spectral features over the wavelength range we consider, holding it constant permits the more subtle variations associated with the other parameters to be explored. We also find that the metallicity has a greater impact on measuring \[C/Fe\] than the surface gravity. Therefore, we allow \[Fe/H\] to vary, but not [$\log~g$]{}. The errors in [\[Fe/H\]]{} and [\[C/Fe\]]{} estimated by this approach are determined by the square root of diagonal elements of the resulting covariance matrix.

Even though the $\chi^{2}$ minimization approach reproduces [\[C/Fe\]]{} well, we seek to improve the accuracy of the carbon measurement so that there are not spurious detections of carbon-rich stars. Thus, we include an additional step to check on the estimated \[C/Fe\]. 