![]() ![]() However, one must exercise caution in attributing causality. The computed coherence (figure 1) indicates that at most of the major ocean tidal frequencies the variation of groundwater level at this particular site is over 90% due to the forcing of the ocean tides. We further assume that the ocean surface height controls the groundwater levels so that we take the ocean surface height as the input variable, and the groundwater well height as the output variable. Let us assume that there is a linear relationship between the ocean surface height and the groundwater levels. To estimate the extent at which the groundwater levels are influenced by the ocean surface levels, we compute the coherence between them. It is clear that variation of the groundwater levels have significant power at the ocean tidal frequencies. The coherence (sometimes called magnitude-squared coherence) between two signals x(t) and y(t) is a real-valued function that is defined as: C x y ( f ) = | G x y ( f ) | 2 G x x ( f ) G y y ( f ) provides a spectral quantification of the output power that is uncorrelated with noise or other inputs.įigure 4: Autospectral density of groundwater well level. If the signals are ergodic, and the system function is linear, it can be used to estimate the causality between the input and output. It is commonly used to estimate the power transfer between input and output of a linear system.
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