How can we optimally combine the information provided by proxy records and model results ?

How can we optimally combine the information provided by proxy records and model results ? Hugues Goosse Université catholique de Louvain, Belgium

Assimilation of observations Data assimilation could be mathematically represented by: Wherexa is the analysis, y0 is the observed variables, xb is the background field, generally obtained by a model integration, H the observation operator and W is a weight matrix. xa, y0 and xb 3-D vectors. is often called the innovation or observation increment

Assimilation of observations Pessimistic view: Models are not good enough, sophisticated models are too expansive to perform data assimilation We do not have enough proxy records for the last millennium Proxy and model results are difficult to compare. Classical data assimilation techniques could not be used directly to the analysis past millennium climate It is too early to make data assimilation.

Assimilation of observations Optimistic view: Models are not perfect but include some realistic features There is now a reasonable amount proxy records for the last millennium Some simple comparison between proxy data and model results are possible. We could try first very simple methods It is worthwhile to make first attempts and then improve all the steps of the procedure.

One example: using paleoclimate proxy-data to select the best realisation in an ensemble Simulation of the climate of the last 1000 years : selecting among a relatively large ensemble of simulations (> 100) the one that is the closest to the observed climate. The experiment selected is the one that minimise a cost function CF for a particular period : Where n is the number of reconstructions used in the model/data comparison. Fobs is the reconstruction of a variable F, while Fmod is the simulated value of the corresponding variable. wi is a weight factor. Goosse et al. 2006

Using paleoclimate proxy-data to select the best realisation in an ensemble Selecting among a relatively large ensemble of simulations the one that is the closest to the observed climate : example Summer temperature in Fennoscandia Temperature in the Arctic The black line corresponds to the mean over the 105 simulations while the grey lines are the ensemble mean plus and minus two standard deviations. The red line is the succession of the states that produce the minimum of the cost function (i.e., the ‘best pseudo-simulation’). The blue lines are the proxy reconstruction for the region (Briffa et al. 1992, Overpeck et al. 1997). The reference period is the years 1600-1950. Goosse et al. 2006

Using paleoclimate proxy-data to select the best realisation in an ensemble Normalized winter (DJF) temperature anomaly during the period 1690-1700 AD in the reconstruction of Luterbacher et al. (2004) in the best pseudo-simulation. Reconstruction Best Simulation Goosse et al. 2006

Using paleoclimate proxy-data to select the best realisation in an ensemble Anomaly in surface ocean current (m/s) during the period 1690-1700 AD in the best simulation. Goosse et al. 2006

How can we optimally combine the information provided by proxy records and model results ?