An efficient optimum interpolation scheme for objective analysis over Indian region

In the optimum interpolation scheme, the weights for the observations are computed by solving a set of linear equations for every grid point. As the number of observations increases particularly over data-rich regions, the matrix dimension increases and the computer time required to solve these equations to determine weights increases considerably. In order to reduce the computer time for computing the weights, Tanguay and Robert suggested schemes in which the gaussian function representing the autocorrelation function has been approximated by a second-order and also by a fourth-order Taylor series expansion. This resulted in the solution of matrices of order 4 or 9 respectively to obtain weighting functions irrespective of the number of observations used in the analysis. In the present study, the analyses of mean sea level pressure and geopotential height at 700 mbar level have been carried out for five days using the above two schemes and the regular OI scheme. The analyses are found to be similar in all the three cases suggesting that a lot of computer time could be saved without sacrificing the analysis accuracy by using the modified scheme in which the second-order approximation is utilized.