Upwelling Index Calculator

The upwelling index estimates how much surface water wind pushes away from a coast, since that offshore volume must be replaced by water drawn up from depth. It is built from two steps. Wind stress on the sea surface follows the bulk formula tau = rho_air Cd U squared, with air density near 1.22 kg/m3 and a drag coefficient of roughly 1.1 to 1.5 times ten to the minus three at moderate wind speeds; because stress scales with the square of wind speed, a 12 m/s wind exerts more than twice the stress of an 8 m/s wind. The alongshore component of that stress is then divided by seawater density, about 1025 kg/m3, and by the Coriolis parameter f = 2 omega sin(latitude), where omega is 7.2921e-5 rad/s. The quotient is Ekman transport in m2/s, scaled here by 100 so the index reads in cubic metres per second per 100 m of coastline. Values near zero to 20 indicate weak forcing, 20 to 100 moderate, and sustained values above 100 to 200 mark strong upwelling of the kind seen off central California and Peru in summer; negative values mean onshore transport and downwelling. Upwelled water typically originates 50 to 300 m down and carries nitrate an order of magnitude above surface concentrations, which is why these margins yield a disproportionate share of the world fish catch. The method assumes a straight coast, uniform wind, steady state and no stratification, and it fails near the equator where f approaches zero. Nearshore winds are also often weaker than the offshore winds used as input.

The dynamics behind the index trace to Fridtjof Nansen, who noticed during the Fram expedition of 1893 to 1896 that drifting sea ice moved 20 to 40 degrees to the right of the wind rather than with it. He put the puzzle to Vilhelm Bjerknes, who passed it to his student Vagn Walfrid Ekman. Ekman worked out the balance between wind stress, friction and the Coriolis force in his 1902 dissertation and published the full result in 1905, deriving the spiral of current vectors that bears his name and showing that transport integrated over the wind-driven layer is directed exactly 90 degrees to the right of the wind in the Northern Hemisphere. Harald Sverdrup extended the reasoning to large-scale wind-driven circulation in the 1940s. The operational index came from Andrew Bakun, then with the National Marine Fisheries Service, who in a 1973 NOAA technical report computed Ekman transport from atmospheric pressure fields at standard positions along the west coast of North America and produced a continuous series back to 1946. Those Bakun indices, published in units of cubic metres per second per 100 m of coastline, became the standard input for fisheries recruitment studies and remain in NOAA production. Later work identified systematic biases from coarse pressure grids and neglected stratification, prompting Michael Jacox and colleagues to introduce revised transport and nutrient-based indices for the California Current in 2018, which are now published alongside the original Bakun series.