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Isidore Halberstam

Abstract

A possible method for assimilating large quantities of asynoptic data, such as satellite observations, into numerical weather forecasts, is investigated. The method is based on a transformation of the time coordinate to coincide with satellite paths, and a well-posed problem is solved in order to obtain forecasts beyond the time of data acquisition. Simulated barotropic forecasts based on the proposed technique are compared with forecasts derived from the direct insertion of data. Results indicate that only in ideal situations, when asynoptic data are obtained both continuously and accurately, will the method function well as compared with direct insertion techniques.

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Isidore Halberstam

Abstract

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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Isidore Halberstam

Abstract

A study is made of the geophysical algorithms relating the Seasat-A scatterometer (SASS) backscatter measurements σ° with a wind parameter. It is shown that although σ° is closely related to surface features, identification with surface layer parameters such as friction velocity u* or the roughness length z 0 is difficult from both theoretical and practical considerations. It is shown how surface truth in the form of wind speeds and coincident stability can be used to derive either u* or the equivalent neutral wind uN at an arbitrary height. It is also shown that derived u* values are sensitive to contested formulations relating u* to z 0, while derived uN values are not. Also, derived quantities are seen to be more sensitive to changes in positive stability than to change in unstable conditions. Examples of geophysical verification is demonstrated using values obtained from the Gulf of Alaska Seasat Experiment (GOASEX). Results of this verification show very little sensitivity to the type of wind parameter employed. It is suggested that this insensitivity is due mainly to large scatter in the SASS and surface truth data.

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Isidore Halberstam and John P. Schieldge

Abstract

During March, 1978 on a snow-covered field near Lee Vining, California, measurements were made that included: 1) variations above the snow surface of the net radiative flux and the profile of wind speed, air temperature and relative humidity; and 2) variations beneath the snow surface of the conductive heat flux and the temperature profile. The period was marked by clear skies, warm air and calm winds during the day, and cold air and moderate winds at night. During the day, a highly stable sublayer formed near the surface, with a persistent warm layer at ∼0.5 m above the surface. At night, profiles agreed more with classical log-linear forms found in stable air. Numerical simulation of long and shortwave radiative fluxes near the surface, using observed humidity profiles, produced the daytime warm level in agreement with observations. It was concluded that in the absence of turbulent mixing, strong solar radiation and a supply of moisture from the snow will cause a raised maximum of temperature during the day.

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Isidore Halberstam and Shu-Lin Tung

Abstract

Objective analysis can he performed on irregularly spaced observation points by fitting selected functions to the observations. A simple least-squares fit is found to be both impractical and ill-conditioned, the latter because of gaps in the data exceeding the smallest wavelengths of the fitting functions. Alternative fits can be made practical either by breaking down the least-squares fit into a step-wise fitting of several subsets or by imposing a “finality” condition that yields errors greater than least-squares, but are nevertheless bounded by a number related to the distribution of the data points. The method of finality involves sequential subtraction of each vector's successive contribution. Ordering of the vectors efficiently then becomes rather crucial. The ill-conditioned behavior of thew fits can be suppressed by adding first-guess information in areas that lack data. Tests of the methods using Hough functions evaluated at observation sites as the basis vectors and data from FGGE Ila and Illa as well as from a forecast field from the Air Force Geophysics Laboratory's global, spectral model show that the finality method is a viable alternative analysis procedure worth exploring. The step-wise least-square method is also a practical method if sufficient realistic data are distributed throughout the domain. Using residuals (forecast minus observation values) proves to be a more accurate procedure than using observed and forecast values themselves.

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