A means of measuring the submergence velocity or emergence velocity of the glacier surface by anchoring a stand for a global navigation satellite system (GNSS; usually a Global Positioning System) rec
eiver to the body of the glacier, using a suitable object (such as a coffee can) as an anchor connected to the surface by a cable under tension. The essence of the method is that measured changes in the exposed length of the cable (or equivalent measurements of the local surface mass balance), and in the surface elevation (measured by the GNSS receiver), yield two of the three terms in the continuity equation and allow the third term, the submergence or emergence velocity (that is, the flux divergence) to be determined. Corrections may be needed for the densification (that is, settling) of firn beneath the anchor and for downslope advection of the anchor. The coffee-can method has been used mainly in the accumulation zones of ice sheets, where the surface mass balance can be obtained by ice-core stratigraphy. However in the ablation zone the emergence of cables emplaced for other reasons, such as the measurement of temperature profiles, can serve a similar purpose.
The coherence, Cxy, between two signals x(t)and y(t) is a real-valued function. The square of the coherence is definedby using: Cxy^2 = |Gxy(f)|^2 / Gxx(f)Gyy(f) where Gxy(f) is equal to thecross-spec
tral density between two time series denoted as x and y,respectively, and Gxx(f) and Gyy(f) are equal to the auto-spectral densitiesof the same two time series. Values of Cxy 2 always lie in the range betweenzero and one, 0 = Cxy 2 = 1, in accordance with the Cauchy-Schwarzinequality.