Tidally forced under-ice Ekman layers observed by an acoustic Doppler current profiler

Abstract

A simple, tidally forced Ekman model is fit to acoustic Doppler current profiler observations of the horizontal velocity field sampled during the Resolute portion of the SARES project. An assimilation inversion technique is demonstrated that does not require the use of Lagrange multipliers or an adjoint equation. The gradient of the cost function is obtained through direct differentiation of the equations of motion and associated boundary conditions. Both the standard depth-independent pressure gradient and a new depth-dependent pressure gradient are assimilated into the model. The depth-dependent pressure gradient reduced the residual error over the depth-independent case and produced estimates of eddy viscosities and drag coefficients that were consistent with a marked change in the stratification observed during the course of the experiment. The results suggest that a depth-dependent pressure gradient may be more important than a depth-dependent eddy viscosity in describing under-ice tidally forced Ekman layers. A maximum value of 4.75 × 10 −3 m 2 s −1 is obtained for the vertical eddy viscosity, which implies a nutrient transport 50 times less than that required to meet ice-algal demand. This result suggests that turbulence associated with the passage of high frequency internal waves, rather than the background tide, is likely responsible for bringing nutrients to the ice-water interface.