We present wide field JHKs photometry of 16 Galactic globular clusters located towards the Galactic bulge, calibrated on the 2MASS photometric system. Differential reddening corrections and statistical field star decontamination are employed for all of these clusters before fitting fiducial sequences to the cluster red giant branches (RGBs). Observed values and uncertainties are reported for several photometric features, including the magnitude of the RGB bump, tip, the horizontal branch (HB) and the slope of the upper RGB. The latest spectroscopically determined chemical abundances are used to build distance- and reddening-independent relations between observed photometric features and cluster metallicity, optimizing the sample size and metallicity baseline of these relations by supplementing our sample with results from the literature. We find that the magnitude different between the HB and the RGB bump can be used to predict metallicities, in terms of both iron abundance [Fe/H] and global metallicity [M/H], with a precision of better than 0.1 dex in all three near-IR bandpasses for relative metal-rich ([M/H]$gtrsim$-1) clusters. Meanwhile, both the slope of the upper RGB and the magnitude difference between the RGB tip and bump are useful metallicity indicators over the entire sampled metallicity range (-2$lesssim$[M/H]$lesssim$0) with a precision of 0.2 dex or better, despite model predictions that the RGB slope may become unreliable at high (near-solar) metallicities. Our results agree with previous calibrations in light of the relevant uncertainties, and we discuss implications for clusters with controversial metallicities as well as directions for further investigation.
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