  We present K band spectra for 133 nearby (d < 33 parsecs) M dwarfs, including
18 M dwarfs with reliable metallicity estimates (as inferred from an FGK type
companion), 11 M dwarf planet hosts, more than 2/3 of the M dwarfs in the
Northern 8 pc sample, and several M dwarfs from the LSPM catalog. From these
spectra, we measure equivalent widths of the Ca and Na lines, and a spectral
index quantifying the absorption due to H2O opacity (the H2O-K2 index). Using
empirical spectral types standards and synthetic models, we calibrate the
H2O-K2 index as an indicator of an M dwarf's spectral type and effective
temperature. We also present a revised relationship that estimates the [Fe/H]
and [M/H] metallicities of M dwarfs from their Na I, Ca I, and H2O-K2
measurements. Comparisons to model atmosphere provide a qualitative validation
of our approach, but also reveal an overall offset between the atomic line
strengths predicted by models as compared to actual observations. Our
metallicity estimates also reproduce expected correlations with Galactic space
motions and H alpha emission line strengths, and return statistically identical
metallicities for M dwarfs within a common multiple system. Finally, we find
systematic residuals between our H2O-based spectral types and those derived
from optical spectral features with previously known sensitivity to stellar
metallicity, such as TiO, and identify the CaH1 index as a promising optical
index for diagnosing the metallicities of near-solar M dwarfs.
