where the superscript II indicates that the definition applies to region II with two moving layers, and the subscripts indicate the individual layers.
It is important to note that fi in these relations is not necessarily a constant. In fact, we can write it in the formfi (Hi), which indicates thatfi depends on the latitude of the outcrop line by tracing backward along the streamline Hi = const. Therefore, in our discussion hereafter, we can write alternately fi ^ fi + Sfi, where we imagine that Sfi represents the outcrop line perturbations induced by a heating or cooling anomaly. If Sfi < 0, this implies that the outcrop line moves equatorward from its constant value offi, representing a cooling anomaly.
Since, along the first outcrop line, it can readily be seen that Hj2(x) = Hf0(x)+O(Sfi), whereHi0(x) is the total layer thickness along the unperturbed outcrop line. Thus, to the lowest-order approximation, the functional relation between Hi and x remains unchanged. Using this relation we can calculate x and Sfa(x) for a given hi in order to complete the necessary inversion to determine fi(Hi) to the lowest order. Accordingly, the solution in region II can be calculated either by solving the nonlinear equations (4.530) and (4.53i) or by using their linearized versions.
Cooling can be represented by a equatorward perturbation of the first outcrop line,
Climate variability induced by surface cooling
Therefore, the cooling-induced changes in the layer depth are
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