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.

In this study real time data have been used to compare the standard and triangle method by performing the objective analysis of mean sea level pressure.In the standard method,derivative fields are obtained from the grid point data using finite difference scheme whereas in the triangle method,a set of non-overlapping triangles are formed from the observations and the scalar and the spatial derivatives are computed directly at the centroid of each of the non-overlapping triangles.These scalars and their derivatives are then mapped to uniform grids by using the standard method.It has been found that objectively analysed scalar field obtained using standard method is superior to the scalar field derived by the triangle method,whereas the derivative fields produced by triangle method are superior to the derivative fields produced using standard method. A variational objective analysis scheme has been developed and an experiment has been carried out with depression case of June (11 –15)2004.It is found that the new scheme (variational)is able to extract the better parts of both triangle and standard methods.The results of this study will be useful in carrying out diagnostic calculations that involve derivative estimates.