We have analyzed the properties of metals in the high-redshift intergalactic medium using a novel objective pixel optical depth technique on a sample of extremely high signal-to-noise ratio Keck HIRES and ESI spectra of 26 quasars between redshifts 2.1 and 6.4. The technique relies on using the doublet nature of the common ions C IV and Si IV, which are the principal metal tracers in the intergalactic medium outside of the Ly alpha forest. Optical depths are statistically corrected for contamination by other lines, telluric absorption, bad pixels, continuum fitting, etc. and for incompleteness, and we achieve in this way an increased sensitivity of approximately 0.5 dex over previous analyses. As with existing pixel optical depth analyses, the method is completely objective and avoids subjective cloud selection and Voigt profile fitting, but, unlike existing techniques, we do not compare the ion optical depths with H I optical depths to determine the ion optical depth distributions; we therefore avoid problems arising from different velocity widths in the ion and H I. We have shown how the conventional analysis can be reproduced using a percolation method to generate pseudoclouds from ion optical depths. Using this set of pseudoclouds, we have generated C IV column density distributions and have confirmed that the shape of the C IV column density distribution remains essentially invariant, with slope - 1.44, from z = 1.5 to 5.5. This in turn confirms the lack of redshift evolution of Omega( C IV) for z = 2-5, both for all absorbers with column density log N = 12-15 and for stronger absorbers with log N = 13-14. The generation of pseudoclouds from the optical depth vectors also gives information on the column density environment of a given optical depth. We find that for the higher resolution HIRES data there is a tight relation, tau similar to N-0.7, between the peak optical depth and the column density. We have then analyzed the ion redshift evolution directly and model-independently from the optical depth vectors themselves and show that there is little evolution in the total amount of C IV from z = 2 to 5, although there is a turndown of at least a factor of 2 in Omega(C IV) above z = 5. We do, however, see substantial evolution in the ratio Si IV/C IV. In two subsequent papers in this series, we will use this technique to investigate what fraction of the absorbers lie in galactic wind outflows ( Paper II) and what metallicity is associated with regions of tau(Ly alpha) < 1 ( Paper III).
