This paper provides the theoretical basis and simulated retrievals for the Cloud Height Retrieval from O2 Molecular Absorption (CHROMA) algorithm. Simulations are performed for the Ocean Color Instrument (OCI), which is the primary payload on the forthcoming NASA Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission, and the Ocean Land Colour Instrument (OLCI) currently flying on the Sentinel 3 satellites. CHROMA is a Bayesian approach which simultaneously retrieves cloud optical thickness (COT), cloud-top pressure and height (CTP and CTH respectively), and (with a significant prior constraint) surface albedo. Simulated retrievals suggest that the sensor and algorithm should be able to meet the PACE mission goal for CTP error, which is ±60 mb for 65 % of opaque (COT ≥3) single-layer clouds on global average. CHROMA will provide pixel-level uncertainty estimates, which are demonstrated to have skill at telling low-error situations from high-error ones. CTP uncertainty estimates are well-calibrated in magnitude, although COT uncertainty is overestimated relative to observed errors. OLCI performance is found to be slightly better than OCI overall, demonstrating that it is a suitable proxy for the latter in advance of PACE’s launch. CTP error is only weakly sensitive to correct cloud phase identification or assumed ice crystal habit/roughness. As with other similar algorithms, for simulated retrievals of multi-layer systems consisting of optically thin cirrus clouds above liquid clouds, retrieved height tends to be underestimated because the satellite signal is dominated by the optically thicker lower layer. Total (liquid plus ice) COT also becomes underestimated in these situations. However, retrieved CTP becomes closer to that of the upper ice layer for ice COT ≈3 or higher.
