Center for Coastal & Land-Margin Research

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Aliasing Effects: In order to adequately reproduce a signal of period T using discreet samples, the signal must be sampled on the order of T or smaller. Failing this, the analysis will misassign energy into other frequnecies not present in the original signal. In simple terms, the analysis will build an entirely new record which is a false image, or "alias" of the original.

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This effect can be seen in the following simple example. Consider a straight, flat channel of constant depth and constant velocity from left to right. In this channel, an 8-hour pulse of "contaminant" is introduced at the left boundary and allowed to move (but not diffuse) with the moving water.

This is the simplest of all possible cases. All confounding factors of variable geometry and flow velocities have been eliminated, along with any transformations or diffusion of the imaginary pollutant. In this laboratory-clean environment, data aliasing effects are easy to see.

• First Click here to see an animation of the imaninary plume being moved from left to right by the movement of the water.

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Now we can sample this plume at varying intervals and check the resulting record:

• One hour sampling interval: This sampling scheme reproduces the pulse well and can be considered a base-line case.

• Four hour sampling interval: The record is begining to be distorted, but the general behavior is still being adequately reproduced.

• Eight hour sampling interval: At this level of resolution, the signal is highly distorted, though some reasonable estimate of break-through time and peak concentration can still be obtained.

• Sixteen hour sampling interval: In this case, the signal has been complete lost.

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In this case, the ratio of sampling interval to pulse duration varied from .125 to 2.0, where, at 2.0, the signal was not resolved at all. In the case of fecal coliform sampling on Tillamook Bay, that same ratio is on the order of 40 to 80.

• Click here for a snapshot of a typical record of Wilson River gauge levels compared to a typical water quality sampling interval.

This simple analysis suggests that discreet samples taken at 40 day intervals have no hope of reproducing the real response signal of the bay to fecal contamination events and leads to the realization that:

Fluxes on the Wilson River may in fact be a key indicator of fecal coliform levels on Tillamook Bay. However, temporal sparseness in the existing data set strictly limits our ability to evaluate this or any other correlation, temporal or spatial trend, or causal relationship.

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E-mail to: Pearson Baptista
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