The Global Ocean Circulation Estimated from TOPEX/POSEIDON Altimetry and the MIT General Circulation Model

One of the major reasons for observing the global ocean is to infer the transport properties of quantities important to climate, including heat, freshwater, carbon, oxygen, etc. Given the disparate observational techniques which formed the World Ocean Circulation Experiment, the only feasible approach to these inferences is to combine the data with general circulation models (GCMs) to produce the required estimates. We demonstrate here the beginning of such a global ocean circulation estimate. It is based on an OGCM which is being brought to full consistency with a variety of global data sets. The resulting model state will be employed to study the consequences of the circulation and its temporal variability on a host of oceanographic problems. Quantitative estimates of the uncertainty of the results and their sensitivity to observational strategies are in preparation, which are further important elements in determining what is known about climate change and of utmost importance in designing future observational programs to reduce the remaining uncertainty. The quantitative combination of an OGCM with observations leads to the initialization of the climate models --an essential step should one wish to undertake climate forecasting, probably in conjunction with a coupled atmospheric model.

    Our present focus is on the time-evolving global circulation as it emerges primarily from altimetric measurements and an ocean general circulation model. Computations are ongoing during which the MIT circulation model is constrained over the 6 year period 1992 through 1997. Data constrains include the absolute and time-varying T/P data (relative to the EGM-96 geoid model; see Lemoine et al., [1997]) from October 1992 through December 1997, SSH anomalies from the ERS-1 and ERS-2 satellites, monthly mean SST data (Reynolds and Smith, 1994), and the time-varying NCEP Re-Analysis fluxes of momentum, heat and freshwater. Monthly means of the model state are required to remain within assigned bounds of the monthly mean Levitus et al. (1994) climatology, and NSCAT estimates of wind stress errors (D. Chelton, pers. communication, 1997) are being employed.

    To bring the model into consistency with the observations, the following control parameters are modified: the initial potential temperature ($\theta$) and salinity (S) fields, as well as the surface forcing fields over the entire 6 year period.
 

Figure: Schematic of the ongoing optimization. While the middle part of the figures shows the data constraints and their distribution in time, the lower part shows the ''control`` parameters, which are being adjusted to bring the model into consistancy with the data. The top part shos the data currently being used for comparison and testing. Those data will be also used as constraints in the next optimization.

 

    As compared to previous attemps (Stammer et al., 1997;
see also http://puddle.mit.edu/ detlef/OSE/report_0/index.html), improvements in the present experiment include an increased model resolution to 1$^{\circ}$ , as well as more accurate representations of straits and sills in the topography. Equally important, a complete mixed layer model (Large et al., 1994) and an eddy parameterization (Gent and McWilliams, 1990) have been incorporated into the model. A full (non-diagonal) geoid error covariance matrix is being used now as well as other improvements in the remaining weights.

    Both the forward model and its adjoint have been developed recently at the Massachusetts Institute of Technology. The forward component is the M.I.T. general circulation model which is based on the incompressible Navier-Stokes equations on a sphere under the Boussinesq approximation and was developed recently by John Marshall and his group (Marshall et al.; 1997a,b). While the forward model by itself predicts the observations and determines the misfits between model and observations, the adjoint of the original model measures the misfit gradient relative to the uncertain model parameters, and is used to bring the forward component into accord with the data. The coding of the M.I.T. model rendered it possible to obtain the adjoint component from the forward code in a semi-automatic way by using the Tangent Linear and Adjoint Model Compiler (TAMC) of Ralf Giering [Giering and Kaminsky, 1998].

    Currently the model is being run on a 2$^{\circ}$ grid with the convective adjustment scheme. In particular, no KPP model and no GM eddy parametrization are yet used. KPP will switched on after the surface fluxes have been adjusted and the model is more stable than is the present case. Stability is anticipated after about 15 iterations. The Gent/McWilliams parametrization will be included as the last step. Once the optimization is converged on a 2 $^{\circ}$ horizontal grid, the optimization will be continued at 1$^{\circ}$ , globally.

    At this time, 10 iterations have been completed. The iteration labelled ``-1'' below is the first guess which results from running the model forward for 6 years while forcing it with NCEP surface flux fields. In the iteration labelled ``0'' a first guess flux correction was added to the control vector. This first guess corrections resulted from running the model forward forced by surface fluxes and a relaxation term toward Levitus monthly T and S fields. The 6 year mean relaxation contribution was used as a first guess flux correction in heat and freshwater.

An animation of 6 years of model SSH anomaly fields obtained from last iteration of the ongoing optimization can be viewed at http://puddle.mit.edu/ detlef/OSE/psbar11.mpeg

1999-01-08