Reconstructing bottom water temperatures from measurements of temperature and thermal diffusivity in marine sediments

Continuous monitoring of oceanic bottom water temperatures is a complicated task, even in relatively easy-to-access basins like the North or Baltic seas. Here, a method to determine annual bottom water temperature variations from inverse modeling of instantaneous measurements of temperatures and sediment thermal properties is presented. This concept is similar to climate reconstructions over several thousand years from deep borehole data. However, in contrast, the presented method aims at reconstructing the recent temperature history of the last year from sediment thermal properties and temperatures from only a few meters depth. For solving the heat equation, a commonly used forward model is introduced and analyzed: knowing the bottom water temperature variations for the preceding years and the thermal properties of the sediments, the forward model determines the sediment temperature field. The bottom water temperature variation is modeled as an annual cosine defined by the mean temperature, the amplitude and a phase shift. As the forward model operator is non-linear but low-dimensional, common inversion schemes such as the Newton algorithm can be utilized. The algorithms are tested for artificial data with different noise levels and for two measured data sets: from the North Sea and from the Davis Strait. Both algorithms used show stable and satisfying results with reconstruction errors in the same magnitude as the initial data error. In particular, the artificial data sets are reproduced with accuracy within the bounds of the artificial noise level. Furthermore, the results for the measured North Sea data show small variances and resemble the bottom water temperature variations recorded from a nearby monitoring site with relative errors smaller than 1 % in all parameters.