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Volume 23 Issue 2

Mar.  2006

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Article >  ADVANCES IN ATMOSPHERIC SCIENCES  > 2006 >  23(2): 190-198

A Comparison of the Radar Ray Path Equations and Approximations for Use in Radar Data Assimilation

  • 1.

    Center for Analysis and Prediction of Storms, Sarkeys Energy Center, Norman, OK 73019, U.S.A,Center for Analysis and Prediction of Storms, Sarkeys Energy Center, Norman, OK 73019, U.S.A,Center for Analysis and Prediction of Storms, Sarkeys Energy Center, Norman, OK 73019, U.S.A, School of Meteorology, University of Oklahoma, U.S.A


doi: 10.1007/s00376-006-0190-3

  • The radar ray path equations are used to determine the physical location of each radar measurement. These equations are necessary for mapping radar data to computational grids for diagnosis, display and numerical weather prediction (NWP). They are also used to determine the forward operators for assimilation of radar data into forecast models. In this paper, a stepwise ray tracing method is developed. The influence of the atmospheric refractive index on the ray path equations at different locations related to an intense cold front is examined against the ray path derived from the new tracing method. It is shown that the radar ray path is not very sensitive to sharp vertical gradients of refractive index caused by the strong temperature inversion and large moisture gradient in this case. In the paper, the errors caused by using the simplified straight ray path equations are also examined. It is found that there will be significant errors in the physical location of radar measurements if the earth’s curvature is not considered, especially at lower elevation angles. A reduced form of the equation for beam height calculation is derived using Taylor series expansion. It is computationally more efficient and also avoids the need to use double precision variables to mitigate the small difference between two large terms in the original form. The accuracy of this reduced form is found to be sufficient for modeling use.
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    • Manuscript History

    Manuscript received: 10 March 2006
    Manuscript revised: 10 March 2006
    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

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    A Comparison of the Radar Ray Path Equations and Approximations for Use in Radar Data Assimilation

    • 1. Center for Analysis and Prediction of Storms, Sarkeys Energy Center, Norman, OK 73019, U.S.A,Center for Analysis and Prediction of Storms, Sarkeys Energy Center, Norman, OK 73019, U.S.A,Center for Analysis and Prediction of Storms, Sarkeys Energy Center, Norman, OK 73019, U.S.A, School of Meteorology, University of Oklahoma, U.S.A
    • Manuscript received: 2006-03-10
    • Manuscript revised: 2006-03-10

    Abstract: The radar ray path equations are used to determine the physical location of each radar measurement. These equations are necessary for mapping radar data to computational grids for diagnosis, display and numerical weather prediction (NWP). They are also used to determine the forward operators for assimilation of radar data into forecast models. In this paper, a stepwise ray tracing method is developed. The influence of the atmospheric refractive index on the ray path equations at different locations related to an intense cold front is examined against the ray path derived from the new tracing method. It is shown that the radar ray path is not very sensitive to sharp vertical gradients of refractive index caused by the strong temperature inversion and large moisture gradient in this case. In the paper, the errors caused by using the simplified straight ray path equations are also examined. It is found that there will be significant errors in the physical location of radar measurements if the earth’s curvature is not considered, especially at lower elevation angles. A reduced form of the equation for beam height calculation is derived using Taylor series expansion. It is computationally more efficient and also avoids the need to use double precision variables to mitigate the small difference between two large terms in the original form. The accuracy of this reduced form is found to be sufficient for modeling use.

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