The use of a stream function in a two‐parameter model of the atmosphere

Abstract

SuhfhfARYIn an attempt to obtain a better approximation to the horizontal flow of a non-divergent fluid than the geostrophic approximation, a Monge-Ampere type of partial differential equation, similar to that of Charney (1955), is derived to enable a stream function to be found from the contour height field. A method is given for the numerical aolution of this equation.The stream fmction has been used in place of the contour height parameter to represent the flow at the mean level in computing three 24 hr forecasts based on the Sawyer-Bushby two-parameter model of the atmosphere, and the results are compared with similar computations without the stream function.In one situation, the use of the stream function produced a marked improvement in the Computation.

Early operational Numerical Weather Prediction outside the USA: an historical introduction Part III: Endurance and mathematics – British NWP, 1948–1965

“…In parallel with their work on objective analysis, 32 Bushby & Huckle (1956a worked on replacing the geopotential field by a stream function to avoid the spurious formation of anticyclones. They were successful and the tests showed positive results.…”

“…For unknown reasons there were two approaches; see D. H. Johnson (1956Johnson ( , 1957, Bushby (1956aBushby ( , 1956b, Huckle (1956), Bushby & Huckle (1957) and Corby (1961). 33 Whereas in Bushby & Huckle (1956a) two forecasts out of three were said to have improved, in Bushby & Huckle (1956b) two cases were reported neutral and one positive. 34 This was actually two years before Lorenz's famous coffee break when the 'butterfly effect' was officially discovered.…”

A report on some experiments in numerical prediction using a stream function

“…Bushby and Huckle (1956) had already shown that there was an improvement in baroclinic forecasts when the computations proceeded from a field closely allied to the stream-function field. Accordingly, some of the cases, in which the integrations made on the basis of the Sawyer-Bushby model showed marked height errors, were selected for re-computation with winds derived from stream-function fields in place of the contour-height fields.…”

“…Shuman also contended that barotropic forecasts made by assuming that the wind field was obtainable from a stream function, and therefore strictly non-divergent, should be superior to those made assuming that the wind is geostropic, in ihat the spurious anticyclogenesis should not be so important an error; subsequent experience has shown that this is so and barotropic forecasts made by the Joint Numerical Weather Prediction Unit at Washington D.C. make use of a stream function. Bushby and Huckle (1956) had already shown that there was an improvement in baroclinic forecasts when the computations proceeded from a field closely allied to the stream-function field. Accordingly, some of the cases, in which the integrations made on the basis of the Sawyer-Bushby model showed marked height errors, were selected for re-computation with winds derived from stream-function fields in place of the contour-height fields.…”