A J Lloyd

SUMMARY Reciprocity theorems are established for the elastic sea level fingerprint problem including rotational feedbacks. In their simplest form, these results show that the sea level change at a location x due to melting a unit point mass of ice at x′ is equal to the sea level change at x′ due to melting a unit point mass of ice at x. This identity holds irrespective of the shoreline geometry or of lateral variations in elastic Earth structure. Using the reciprocity theorems, sensitivity kernels for sea level and related observables with respect to the ice load can be readily derived. It is notable that calculation of the sensitivity kernels is possible using standard fingerprint codes, though for some types of observable a slight generalization to the fingerprint problem must be considered. These results are of use within coastal hazard assessment and have a range of applications within studies of modern-day sea level change. To illustrate the latter point, we use sensitivity kernels to investigate two widely used methods for estimating, respectively, ice sheet mass loss from satellite gravity, and rates of global mean sea level rise from satellite altimetry. Though our analysis is idealized in some respects, we identify systematic errors of order 5 per cent due to the use of simplified sea level physics. Crucially, calculation of the relevant sensitivity kernels provides not only a means for understanding sources of bias in existing methods, but will aid in the design of new and improved data-assimilation techniques.