Looking for Scaling Laws for the Width and Source Depth of Coastal Upwelling Zones

Abstract The width of the coastal upwelling zone and the depth from which the upwelling originates are two fundamental features of eastern boundary upwelling systems as they play a significant role in determining the state of the upper ocean in these regions. Here, we aim to characterize the width and depth scales associated with the coastal upwelling zone and to identify a set of empirical scaling laws for these length scales. We estimate the length scales using high-resolution, regional ocean simulations of an idealized coastal upwelling system. Our results indicate, though, that there are two distinct horizontal length scales related to the upwelling zone: first, the width of the offshore region where upwelling occurs, which scales like ND s / f , and second, the width of the offshore region where isopycnals deform significantly from horizontal, which scales like , where τ is the wind stress, N is the stratification, D s is the upwelling source depth, and ρ 0 is the reference density. We also find that the scaling for the mean upwelling source depth does not depend on f and instead scales like . We emphasize that while these scaling behaviors provide a strong fit to the numerical results, they are incomplete as they involve coefficients that are not order one nor dimensionless. These scalings are consistent with the results of our numerical simulations as well as self-consistent with the derivation of the mean source depth that depends on the proposed length scale for isopycnal deformation.