Pattern of recent vertical crustal movements in Canada

We used the method of smooth piecewise algebraic approximation to automatically compute a smooth approximation of large functional scattered re-levelling data and historical tide gauge records given over Canada and northern US to thereby compile a unified map of vertical crustal movements (VCM). The area of study is divided into pieces and piecewise algebraic surfaces are fitted to the tide gauge trends and to the height difference differences, computed from monthly mean sea-level and re-levelling segments, respectively. When the surfaces are fitted to the data, a set of continuity and smoothness constraints is imposed in such a way that rather than the surfaces being fitted sequentially, they are fitted simultaneously, using the constraints as a set-conditions which the parameters of the surfaces must also satisfy.