Variational Estimation of the Wind Stress Drag Coefficient and the Oceanic Eddy Viscosity Profile

Abstract

A variational Optimal control technique is uIed to allimilate ~ meteoroI~ and ~ oIRrvations into an oceanic: Ekman layer mOOd. An identical twin experiment is di-=ussed first in wbic:h the "observations" ~ Cleated by tile dynamic: mcxie1. The field IDe8SUmDeDU from tile LOWS-3 (Long-Term Upper Ocean Study-3) buoy ~ then ana1yzed. By 6Uine tile mcxie1 rauJts to tile data, tile unknown bouOOary condition (tile wind stres draa coefficient) and tile unknown Yertic:aI eddy vi.:oIity distribution ~ deduced simultaneously from the data, and an Optimal estimate of the cunent field is obtained.ThOUIh tile m<xIeI is simple, tile results show that tile variational aaimiIation tec:bnMIue is ~ of extracting from tile available ot.rvations a reaI()nabie wind sties draa coeft'x:ient and Yertic:aI eddy vi.:oIity diSlritMltion.

Specifying Air-Sea Exchange Coefficients in the High-Wind Regime of a Mature Tropical Cyclone by an Adjoint Data Assimilation Method

“…For example, the terms associated with sound waves and microphysics are excluded. The gradients with respect to C D,i and C E,i are calculated as follows (see Yu and O'Brien (1991) for a derivation):…”

“…The control variables are determined to minimize the cost function leading to optimal estimates of the model fields. Here, air-sea exchange coefficients, together with the initial state of the assimilation window, are chosen as control variables as in Yu and O'Brien (1991), though the initial state alone is usually employed in operational forecasts. Using this method, observational data outside the boundary layer such as wind velocity, the mixing ratio of water vapor, and ocean mixed layer (ML) momentum, which are relatively accessible compared to the direct eddy correlation measurements within the boundary layer, are assimilated into the model in order to evaluate C D and C K values suitable for the actual state through the model physics.…”

Development of a four‐dimensional variational coupled data assimilation system for enhanced analysis and prediction of seasonal to interannual climate variations

“…A 4D-VAR CDA system has the further advantage of supporting an optimal parameter estimation for the bulk formulae that determine air-sea-land surface fluxes. This is very useful for reducing the coupled model errors as shown by Yu and O'Brien [1991] for an Ekman layer case. These facts set the 4D-VAR CDA method apart from other familiar assimilation techniques.…”

Adjoint free four-dimensional variational data assimilation for a storm surge model of the German North Sea

“…Adjoint equations are powerful tools in 4Dvar in that it facilitates the computation of gradient of cost functions with respect to the control variables with large dimension. Yu and O'Brien (1991) used 4Dvar to estimate the C d values; they found that after 11 iterations C d converges to 0.00126. Peng et al (2013) used a threedimensional ocean model and its adjoint model to adjust C d ; it was found that the adjustment of C d can compensate for the wind data errors and improve the simulation of storm surges.…”