Reciprocity and sensitivity kernels for sea level fingerprints

TL;DR

This paper establishes reciprocity theorems for elastic sea level fingerprints, enabling straightforward derivation of sensitivity kernels for ice load impacts, with applications in coastal hazard assessment and sea level change studies.

Contribution

It introduces reciprocity theorems for sea level fingerprints that are independent of shoreline geometry and Earth structure variations, facilitating easier sensitivity kernel calculations.

Findings

Reciprocity theorems for sea level change are established.

Sensitivity kernels can be derived using standard fingerprint codes.

Results are applicable to coastal hazard assessment and sea level studies.

Abstract

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 generalisation to the fingerprint problem must be considered. These results are of use within coastal hazard assessment and have a range of potential applications within studies of modern-day sea level change.