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Halberstam, I., 1974: A study of three finite-difference schemes and their role in asynoptic meteorological data assimilation. J. Atmos. Sci., 31, 1964-1973, doi:10.1175/1520-0469(1974)031<1964:ASOTFD>2.0.CO;2.
An investigation of three finite-difference methods and their response to the insertion of simulated satellite data is presented. A simple one-level barotropic model is used as the "forecast" model, while the Mintz-Arakawa two-layer model is used to furnish the initial field, the verification fields, and the simulated satellite data. The schemes tested are the Shuman, the Matsuno-TASU, and an implicit scheme devised by McPherson. Results indicate that the schemes react to inserted data as they would react to unfiltered initial fields. The schemes which contain significant implicit viscosity are capable of damping the high-frequency oscillations which occur after insertions, but such schemes may cause a loss of information. The schemes which contain less damping capability produce "shock" waves which damage the forecasts. It is also found that insertion of winds along with temperature data improves the forecast considerably.
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