How much of the historical global mean surface temperature record is needed to well constrain projections of future warming?

Observational constraints are widely used to reduce uncertainty in multi-model projections and have been proven to be effective. Implementations of constraints vary widely, ranging from using temperature trends over different time periods to incorporate the full evolution of the historical climate time series and even a range of covariates. In this study we consider two Bayesian approaches to developing a constraint on future global warming, using the historical time evolution of global mean surface temperature (GMST) in one case, and historical GMST trends during recent decades in another. We also consider which period in the historical GMST record provides the most effective constraint on future projections. We conduct our studying using large ensemble simulations from climate models with different sensitivities.  When using a time series of annual GMST values, we find an effective constraint only becomes possible when data from the recent period of rapid transient climate change are included in the analysis. Furthermore, incorporating the full transition from a quasi-equilibrium pre-industrial state to the recent strong transient response results in a better constrain. Using a simple linear warming trend from recent decades does improve upon unconstrained projections but to a lesser extent than using the full time series for the same period. Accounting for the intercept obtained in linear trend estimation, which provides information about the warming that occurred before the trend estimation period and thus how represents the Earth system transitioned from a quasi-stationary state to its current state of rapid transient response, improves the skill of trend based constraints. Nevertheless, a constraint based on both the trend (the recent rate of warming) and intercept (the accumulated warming prior to the trend period) does not perform as well as a constraint that uses the entire historical GMST record from 1850 to present.