How much are wave height measurements affected by the tidal currents?

​Wave height can be significantly modulated by strong currents, affecting various maritime activities and coastal dynamics. In a recent study, we leveraged the drifting Spotter wave buoy SPOT-0616 passing near Cape Reinga, at the northern tip of New Zealand's North Island. The data, kindly provided by SOFAR enabled us to analyze the complex interactions between waves and tidal currents in an area where current speeds can reach up to 4 knots.
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To undertake this study, depth-averaged tidal currents and directions were extracted from the Oceanum tidal model at a 400m resolution. The effect of the tidal current was calculated and removed using the formula described in Baschek (2005):

Where a is the wave amplitude, u is the horizontal current speed, c is the wave celerity, and variables with current interaction have no subscript, while variables with current interaction removed are marked by the subscript '0'. For example, a wave with an 8 second period traveling against a current of 1 m/s will experience an amplitude increase of approximately 23%.

The animation above illustrates the results of this analysis. The wave buoy (in black) is shown drifting near Cape Reinga. Grey arrows and color gradients represent the tidal current velocities and directions (going to). Underneath the animation,is a time series of the measured wave height (red) and the theoretical wave height with tidal effects removed (green).
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While the effects are dependent on wave period (on this day around 8s), here we see that wave heights are increased by 17% (about 0.4m) when the currents are in opposition to the tidal flows. When the wave direction and tidal currents are in the same direction, wave heights are decreased by around 19% (about 0.6m).

Baschek, B., (2005). Wave-current interaction in tidal fronts, in: Aha Hulikoa Hawaiian Winter Workshop 2005. pp. 131–138), http://www.soest.hawaii.edu/PubServices/2005pdfs/Baschek.pdf.
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Try our calculator to determine how much the wave amplitude increases or decreases based on the given wave and current parameters: