Center for Ocean-Atmospheric Prediction Studies

Conversion From Wave-Relative Stress Coordinates To lat/lon Vector Components

Some applications will require the conversion of a vector stress from a wave-relative cooredinat system to zonal (West to East) and zonal (South to North) components. BVW and Bourassa (2006) stress vectors are parallel (first component) and perpendicular (second component) to the mean direction of wave propagation. Conversion to zonal and meridional components (tau_x and tau_y) requires a simple rotation. If the mean direction of wave propagation (wave_ang) is specified in a 'math coordinate' system (zero degrees to the East, and angles increasing in a counter-clockwise direction), then the equations for this rotation are:

tau_x = tau[0] * cos(wave_ang*DTR) + tau[1] * sin(wave_ang*DTR);
tau_y = -tau[0] * sin(wave_ang*DTR) + tau[1] * cos(wave_ang*DTR);

Where tau[] is the wave-relative stress vector, and DTR is a constant converting degrees to radians.

To convert from directions specified in the meteorological convection (direction the wind is moving from) use
wind_ang = 270 - wind_ang.

To convert from directions specified in the oceanographic convection (direction the wind is moving to) use
wind_ang = 90 - wind_ang.

Last update: September 22, 2012

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