Detecting climate transitions, their relative duration and midpoint, together with confidence bounds, is an important application of time series analysis methods. Here is a MATLAB example of a nonlinear fit of a sigmoid function to noisy data with a transition.
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MRES 5th Edition Errata File
This is the Errata File for MATLAB Recipes for Earth Sciences (Springer 2020). The authors apologize for these errors, which were unintentional. The file is constantly updated on this webpage.