DATA ASSIMILATION
The concept and procedure of variational data assimilation are described in Ikeda et al (1995) and briefly introduced here. A cost function J, which represents a misfit between data and a model solution, is minimized by varying control variables. The cost function is chosen to be squared differences between data and a model solution. Initial values and subsurface properties are chosen as control variables. The partial derivatives of J with respect to the control variables are efficiently calculated by integrating the equations adjoint to the governing equations backward in time.
The data to be used are listed as follows:
(1) Ocean physical properties: taken from World Ocean Atlas 94, in which the mixed-layer depth is determined by the density larger than a 10-m value by 0.1 kg m-3
(2) Atmospheric forcing: ECMWF data are used first for individual years from 85 to 90, and then, the forcing is averaged over these years
(3) Geochemical properties at the sea surface: taken from Takahashi et al (1993) only for the initial condition (July to October) and the final state (January to April), in which alkalinity is calculated from pCO2, total carbonate and temperature.
(4) Geochemical properties in the subsurface: based on the data only along 165°E in Tsunogai et al (1993), from which the total carbonate at a 100-m depth is chosen to be larger than the surface value in winter by 50μmol/kg, and alkalinity is chosen to be equal to the winter surface value. The vertical gradient of total carbonate is 50μmol/kg per 100m, and alkalinity has no vertical gradient.
RESULTS
A calculation is carried out for 6 months from October 1. The final solution of the forward calculation without data assimilation is shown in Fig. 1. The seasonal evolutions of the physical properties (temperature, salinity (not shown here) and mixed-layer depth) are well reproduced in the present model even without data assimilation. However, the chemical properties have significant discrepancies: e.g., the meridional gradient is too gentle in the western region, and total carbonate exceeds the data in the eastern region. It is possible that lack of chemical data in the subsurface ocean prevents agreement in the chemical properties. Another uncertain parameter is the piston velocity, whereas it is impossible to match the solution to the data by varying the coefficient of cubed wind speed.
The total carbonate in the mixed layer and the chemical properties below the mixed layer are shown in Fig. 2, in comparison to the forward calculation results and data. It is obvious that the surface value becomes similar to the data. In the subsurface, the meridional gradient of total carbonate becomes remarkable in the western region.
