Variational method for objective analysis of scalar variable and its derivative

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.