On manifolds, climate reconstruction and bivalve shells

To estimate the past climate, for example the ocean temperature 1000 years ago, one has to turn to naturally occurring climate recorders. There exist a number of climate recorders in nature from which the past temperature can be extracted. However, only a few natural archives are able to record climate fluctuations with high enough resolution so that the seasonal variations can be reconstructed. One such archive is a bivalve shell. The chemical composition of a shell of a bivalve depends on a number of chemical and physical parameters of the water in which the shell was composed. Of these parameters, the water temperature is probably the most important one. It should therefore be possible to estimate the water temperature for the years the shell was built, from measurements of the shell´s chemical composition. In this paper, we explore this possibility. We do this by first observing that the chemical compositions lie on a one-dimensional manifold parameterized by the water temperature. This manifold is then utilized in the regression to obtain accurate estimates of past water temperatures.