Reconstructing surface conditions over the past 2 millennia

This work is at the interface between applied mathematics and climatology, with a joint emphasis on proxy quality and the development of adequate statistical and timeseries analysis methods. Here is the general idea: consider the picture painted in the tropical Pacific by the instrumental record of the past 150 years. The temperature field varies as a function of time, latitude and longitude, but we can fold latitude and longitude into a single location index (362 points, each corresponding to a 5 by 5 degree box). The following picture is such a represensation of Kaplan SST over the tropical Pacific, smoothed with a 10-year lowpass filter to highlight slowly evolving phenomena.

As you can see, this looks rather like a tapestry. The question is: how can we weave this climate tapestry back in time ?

In the case of ENSO, I use the coarse threads provided by multiple proxies from around the tropics, and a statistical method called RegEM. The proxies are geological objects (corals, ice cores, stalagmites, sediment cores, tree rings) that sensitively record climate information like temperature and precipitation perturbations. Those are generated by ENSO even in remote regions of the Tropics. Of course, such proxies only tell us part of what we want to know, so the exercise essentially amounts to weaving only the coarsest threads of the tapestry, using statistical methods to fill in the holes. This can be achived by making use of the correlation matrix estimated over the period of overlap between instrumental meansurements and proxy measurements. The method (like any other) does introduce errors and biases, however, so it is just as critical to represent those as fairly as possible.

I am currently working on developing new ways of achieving this, using recent advances in statistics. This work straddles the boundary between geological and mathematical sciences, an example of which can be found here. A working reconstruction of tropical Pacific SST for the past 850 years is described here.