Changes in marine primary productivity are key to determine how climate change might impact marine ecosystems and fisheries. Satellite ocean color sensors provide coverage of global ocean chlorophyll with a combined record length of ~ 20 years. Coupled physical-biogeochemical models can inform on expected changes and are used here to constrain observational trend estimates and their uncertainty. We produce estimates of ocean surface chlorophyll trends, by using Coupled Model Intercomparison Project (CMIP5) models to form priors as a "first guess", which are then updated using satellite observations in a Bayesian spatio-temporal model. Regional chlorophyll trends are found to be significantly different from zero in 18/23 regions, in the range ± 1.8% year-1. A global average of these regional trends shows a net positive trend of 0.08 ± 0.35% year-1, highlighting the importance of considering chlorophyll changes at a regional level. We compare these results with estimates obtained with the commonly used "vague" prior, representing no independent knowledge; coupled model priors are shown to slightly reduce trend magnitude and uncertainties in most regions. The statistical model used here provides a robust framework for making best use of all available information and can be applied to improve understanding of global change.