The Sea Level Equation
摘要
The first section of this chapter is devoted to a general discussion about the actual meaning of the Sea Level Equation (SLE). In particular, using qualitative arguments, the role of the SLE in the Earth’s system is addressed, with emphasis on the physical interactions between the Solid Earth, the oceans and the cryosphere. The regional patterns of sea level—which define the so-called sea-level zones—and of all geophysical variables associated with the SLE ultimately result from these incessant interactions. In the second section, the theory of the Sea Level Equation is illustrated in detail in a crescendo of complexity, starting from the most basic form to the final pseudo-spectral form that accounts for rotational effects on sea level and a time-varying ocean function. Since the classical version of the SLE, introduced by Farrell and Clark (1976), does not account for these features, it is considered as a special case. The implicit nature of the SLE is also discussed, suggesting a possible approach to its solution. In its more general form, the SLE is non-linear, and the implications of this feature are briefly enlightened. Last, some very special versions of the SLE are formulated and discussed. The eustatic solution, corresponding to the ideal case of a non-deformable and non-gravitating Earth, is introduced first. Second, the Woodward SLE has is illustrated, which allows to appreciate the role of the gravitational interactions between the oceans and the ice sources, assuming again a rigid Earth. Last, from Farrell and Clark (1976) we present the case in which the ice sources are added “from outside the Earth”, rather than coming from a melting ice sheet, only taking the elastic deformations into account.