• Bean, B. R., , and Dutton E. J. , 1966: Radio Meteorology. National Bureau of Standards Monograph, No. 92, U.S. Government Printing Office, 435 pp.

  • Caumont, O., and et al. , 2006: A radar simulator for high-resolution nonhydrostatic models. J. Atmos. Oceanic Technol., 23, 10491067, doi:10.1175/JTECH1905.1.

    • Search Google Scholar
    • Export Citation
  • Chen, C.-N., , Wang J.-L. , , Chu C.-M. , , and Lu F.-C. , 2009: Ray-trace of an abnormal radar echo using geographic information system. Def. Sci. J., 59, 6372, doi:10.14429/dsj.59.1487.

    • Search Google Scholar
    • Export Citation
  • Doviak, R. J., , and Zrnić D. S. , 1993: Doppler Radar and Weather Observations. 2nd ed. Academic Press, Inc., 562 pp.

  • Freehafer, J. E., 1951: Geometrical optics. Propagation of Short Radio Waves, D. E. Kerr, Ed., McGraw-Hill, 41–58.

  • Gao, J., , Brewster K. , , and Xue M. , 2006: A comparison of the radar ray path equations and approximations for use in radar data assimilation. Adv. Atmos. Sci., 23, 190198, doi:10.1007/s00376-006-0190-3.

    • Search Google Scholar
    • Export Citation
  • Hartree, D. R., , Michel J. G. L. , , and Nicolson P. , 1946: Practical methods for the solution of the equations of tropospheric refraction. Meteorological Factors in Radio-Wave Propagation, The Physical Society, 127–168.

  • Kerr, D. E., Ed., 1951: Propagation of Short Radio Waves. McGraw-Hill, 728 pp.

  • Perntner, J. M., , and Exner F. M. , 1922: Meteorologische Optik. 2nd ed. Verlag Wilhelm Braumüller, 907 pp.

  • Press, W. H., , Teukolsky S. A. , , Vetterling W. T. , , and Flannery B. P. , 1992: Numerical Recipes in Fortran 77: The Art of Scientific Computing, Vol. 1, Fortran Numerical Recipes, Cambridge University Press, 933 pp.

  • Schelleng, J. C., , Burrows C. R. , , and Ferell E. B. , 1933: Ultra-short-wave propagation. Proc. IRE, 21, 427463.

  • Turton, J. D., , Bennetts D. A. , , and Farmer S. F. G. , 1988: An introduction to radio ducting. Meteor. Mag., 117, 245254.

  • van der Werf, S. Y., 2003: Ray tracing and refraction in the modified US1976 atmosphere. Appl. Opt., 42, 354366, doi:10.1364/AO.42.000354.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 287 287 57
PDF Downloads 293 293 53

Radar Beam Tracing Methods Based on Atmospheric Refractive Index

View More View Less
  • 1 Institute for Meteorology and Climate Research, Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen, Germany
  • | 2 Deutscher Wetterdienst, Offenbach, Germany
  • | 3 Institute for Water and River Basin Management, Karlsruhe Institute of Technology, Karlsruhe, Germany
  • | 4 Institute for Meteorology and Climate Research, Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen, Germany
© Get Permissions
Restricted access

Abstract

Simulation of radar beam propagation is an important component of numerous radar applications in meteorology, including height assignment, quality control, and especially the so-called radar forward operator. Although beam propagation in the atmosphere depends on the refractive index and its vertical variation, which themselves depend on the actual state of the atmosphere, the most common method is to apply the 4/3 earth radius model, based on climatological standard conditions. Serious deviations from the climatological value can occur under so-called ducting conditions, where radar beams at low elevations can be trapped or propagate in a waveguide-like fashion, such that this model is unsuitable in this case. To account for the actual atmospheric conditions, sophisticated methods have been developed in literature. However, concerning the practical implementation of these methods, it was determined that the description in the literature is not always complete with respect to possible pitfalls for practical implementations.

In this paper, a revised version of an existing method (one example for the above-mentioned “pitfall” statement) is introduced that exploits Snell’s law for spherically stratified media. From Snell’s law, the correct sign of the local elevation is a priori ambiguous, and the revised method explicitly applies (i) a total reflection criterion and (ii) another ad hoc criterion to solve the problem.

Additionally, a new method, based on an ordinary differential equation with respect to range, is proposed in this paper that has no ambiguity.

Sensitivity experiments are conducted to investigate the properties of these three methods. The results show that both the revised and new methods are robust under nonstandard conditions. But considering the need to catch an elevation sign ambiguity in the revised method (which cannot be excluded to fail in rare instances), the new method is regarded as more robust and unproblematic, for example, for applications in radar forward operators.

Current affiliation: Deutscher Wetterdienst, Offenbach, Germany.

Corresponding author address: Yuefei Zeng, Deutscher Wetterdienst, Frankfurter Str. 135, 63067 Offenbach, Germany. E-mail: yuefei.zeng@dwd.de

Abstract

Simulation of radar beam propagation is an important component of numerous radar applications in meteorology, including height assignment, quality control, and especially the so-called radar forward operator. Although beam propagation in the atmosphere depends on the refractive index and its vertical variation, which themselves depend on the actual state of the atmosphere, the most common method is to apply the 4/3 earth radius model, based on climatological standard conditions. Serious deviations from the climatological value can occur under so-called ducting conditions, where radar beams at low elevations can be trapped or propagate in a waveguide-like fashion, such that this model is unsuitable in this case. To account for the actual atmospheric conditions, sophisticated methods have been developed in literature. However, concerning the practical implementation of these methods, it was determined that the description in the literature is not always complete with respect to possible pitfalls for practical implementations.

In this paper, a revised version of an existing method (one example for the above-mentioned “pitfall” statement) is introduced that exploits Snell’s law for spherically stratified media. From Snell’s law, the correct sign of the local elevation is a priori ambiguous, and the revised method explicitly applies (i) a total reflection criterion and (ii) another ad hoc criterion to solve the problem.

Additionally, a new method, based on an ordinary differential equation with respect to range, is proposed in this paper that has no ambiguity.

Sensitivity experiments are conducted to investigate the properties of these three methods. The results show that both the revised and new methods are robust under nonstandard conditions. But considering the need to catch an elevation sign ambiguity in the revised method (which cannot be excluded to fail in rare instances), the new method is regarded as more robust and unproblematic, for example, for applications in radar forward operators.

Current affiliation: Deutscher Wetterdienst, Offenbach, Germany.

Corresponding author address: Yuefei Zeng, Deutscher Wetterdienst, Frankfurter Str. 135, 63067 Offenbach, Germany. E-mail: yuefei.zeng@dwd.de
Save