Aims. The very high main beam efficiency (90%) of the telescope on the sub-millimetre wave satellite Odin, in combination with the small calibration errors in the absence of atmospheric attenuation, assures that observed line brightness temperatures are very accurately determined. Based on this, we attempt to determine the column density distribution of H 2 , and the ortho-water abundance, in the Orion KL region. Methods. We have, for the first time, mapped the 12 CO J = 5−4 emission in a 7 × 7 region covering Orion KL, observed simultaneously with a 13 CO J = 5−4 map. Also presented are C 18 O J = 5−4 emission data at four different positions and a C 17 O J = 5−4 emission spectrum detected towards the Orion KL position. The Odin mapping was performed at 1 spacing (beam full width at half maximum 126 at 557 GHz). Results. The CO J = 5−4 narrow line emission from this region mainly arises in the warm, dense gas at the interface (the photondominated region) between the M 42 H ii region and the Orion A molecular cloud, the Orion PDR. The 12 CO and 13 CO J = 5−4 emission maps have been used to determine the column density distribution of H 2 gas across the Orion KL region. The results have been verified by comparing to column densities obtained using the decidedly optically thin C 18 O emission as input to the RADEX radiative transfer code. We find H 2 column densities ranging from 5 × 10 21 cm −2 at map edges to 7× 10 22 cm −2 at the molecular ridge. The mass of the gas in the mapped region is estimated to be 480 M , of which 320 M is situated towards the molecular ridge. We estimate that about half of this mass belongs to the warm Orion PDR interface layer. Finally, based on data from the positions where C 18 O J = 5−4 has been observed, we estimate the ortho-water abundance in the Orion PDR layer to be ≥8 × 10 −8 , higher than previously estimated.