Solutions of the balance equation with minimum correction of the mass field

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If the balance equation is solved for the stream function by conventional methods, the mass field has to satisfy a condition of ellipticity. In this paper we present a method to find a stream function when this condition is not satisfied. The method is an iterative method presented by Fjørtoft (1962). It is shown that if this method converges, it gives a solution where the residual of the balance equation is a minimum. The method is tried on a height analysis of 300 mb which contains rather large hyperbolic areas. The convergence of the method is very slow, and a solution using a conventional method is used as a first guess. From the solution found we find a height field in balance with this stream function by solving the balance equation for the height field. It is shown that this field is a better approximation to the original height field than an elliptic field found after correction by a standard method. The new height field does not satisfy the condition of ellipticity with respect to the balance equation.DOI: 10.1111/j.2153-3490.1977.tb00762.x
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