  Stellar loci are widely used for selection of interesting outliers, reddening
determinations, and calibrations. However, hitherto the dependence of stellar
loci on metallicity has not been fully explored and their intrinsic widths are
unclear. In this paper, by combining the spectroscopic and re-calibrated
imaging data of the SDSS Stripe 82, we have built a large, clean sample of
dwarf stars with accurate colors and well determined metallicities to
investigate the metallicity dependence and intrinsic widths of the SDSS stellar
loci. Typically, one dex decrease in metallicity causes 0.20 and 0.02 mag
decrease in colors u-g and g-r, and 0.02 and 0.02 mag increase in colors r-i
and i-z, respectively. The variations are larger for metal-rich stars than for
metal-poor ones, and for F/G/K stars than for A/M ones. Using the sample, we
have performed two dimensional polynomial fitting to the u-g, g-r, r-i, and i-z
colors as a function of color g-i and metallicity [Fe/H]. The residuals, at the
level of 0.029, 0.008, 0.008 and 0.011 mag for the u-g, g-r, r-i, and i-z
colors, respectively can be fully accounted for by the photometric errors and
metallicity uncertainties, suggesting that the intrinsic widths of the loci are
at maximum a few mmag. The residual distributions are asymmetric, revealing
that a significant fraction of stars are binaries. In a companion paper, we
will present an unbiased estimate of the binary fraction for field stars. Other
potential applications of the metallicity dependent stellar loci are briefly
discussed.
