Infrared stellar photometry from the Two Micron All Sky Survey (2MASS) and spectral line imaging observations of 12 CO and 13 CO J = 1-0 line emission from the Five College Radio Astronomy Observatory (FCRAO) 14m telescope are analysed to assess the variation of the CO abundance with physical conditions throughout the Orion A and Orion B molecular clouds. Three distinct A v regimes are identified in which the ratio between the 13 CO column density and visual extinction changes corresponding to the photon dominated envelope, the strongly self-shielded interior, and the cold, dense volumes of the clouds. Within the strongly self-shielded interior of the Orion A cloud, the 13 CO abundance varies by 100% with a peak value located near regions of enhanced star formation activity. The effect of CO depletion onto the ice mantles of dust grains is limited to regions with A v > 10 mag and gas temperatures less than ∼20 K as predicted by chemical models that consider thermal-evaporation to desorb molecules from grain surfaces.Values of the molecular mass of each cloud are independently derived from the distributions of A v and 13 CO column densities with a constant 13 CO-to-H 2 abundance over various extinction ranges. Within the strongly self-shielded interior of the cloud (A v > 3 mag), 13 CO provides a reliable tracer of H 2 mass with the exception of the cold, dense volumes where depletion is important. However, owing to its reduced abundance, 13 CO does not trace the H 2 mass that resides in the extended cloud envelope, which comprises 40-50% of the molecular mass of each cloud. The implied CO luminosity to mass ratios, M/L CO , are 3.2 and 2.9 for Orion A and Orion B respectively, which are comparable to the value (2.9), derived from γ-ray observations of the Orion region. Our results emphasize the need to consider local conditions when applying CO observations to derive H 2 column densities.