Editorial Type:
Article
Article Type:
Research Article

An Adaptation of the Barnes Filter Applied to the Objective Analysis of Radar Data

Mark A. Askelson School of Meteorology, University of Oklahoma, Center for Analysis and Prediction of Storms, and NOAA/National Severe Storms Laboratory, Norman, Oklahoma

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Jean-Pierre Aubagnac NOAA/National Severe Storms Laboratory and School of Meteorology, University of Oklahoma, Norman, Oklahoma

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Jerry M. Straka School of Meteorology, University of Oklahoma and Center for Analysis and Prediction of Storms, Norman, Oklahoma

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Print Publication:
01 Sep 2000
DOI:
https://doi.org/10.1175/1520-0493(2000)128<3050:AAOTBF>2.0.CO;2
Page(s):
3050–3082
Restricted access

Abstract

Spatial objective analysis is routinely performed in several applications that utilize radar data. Because of their relative simplicity and computational efficiency, one-pass distance-dependent weighted-average (DDWA) schemes that utilize either the Cressman or the Barnes filter are often used in these applications. The DDWA schemes that have traditionally been used do not, however, directly account for two fundamental characteristics of radar data. These are 1) the spacing of radar data depends on direction and 2) radar data density systematically decreases with increasing range.

A DDWA scheme based on an adaptation of the Barnes filter is proposed. This scheme, termed the adaptive Barnes (A-B) scheme, explicitly takes into account radar data properties 1 and 2 above. Both theoretical and experimental investigations indicate that two attributes of the A-B scheme, direction-splitting and automatic adaptation to data density, may facilitate the preservation of the maximum amount of meaningful information possible within the confines of one-pass DDWA schemes.

It is shown that in the idealized situation of infinite, continuous data and for an analysis in rectangular-Cartesian coordinates, a direction-splitting scheme does not induce phase shifts if the weight function is even in each direction. Moreover, for radar data that are infinite, collected at regular radial, azimuthal, and elevational increments, and collocated with analysis points, the direction-splitting design of the A-B filter removes gradients in the analysis weights. This is a beneficial attribute when considering the treatment of gradient information of rectangular Cartesian data by an analysis system because then postanalysis gradients equal the analysis of gradients. The direction-splitting design of the A-B filter is unable, however, to circumvent the impact of the varying physical distances between adjacent measurements that are inherent to the spherical coordinate system of ground-based weather radars. Because of this, even with the direction-splitting design of the A-B filter postanalysis gradients do not equal the analysis of gradients.

Ringing in the response function of a one-dimensional Barnes filter is illustrated. The negative impact of data windows on the main lobe of the response function is found to decrease rapidly as the window is widened relative to the weight function. Unless an analysis point is near a data boundary, in which case both ringing and phase shifting will adversely affect the analysis, window effects are unlikely to be significant in applications of the A-B filter to radar data.

The A-B filter has potential drawbacks, the most significant of which is misinterpretations owing to the use of the A-B filter without comprehension of its direction- and range-dependent response function. Despite its drawbacks, the A-B filter has the potential to improve analyses owing to the aforementioned attributes and thus to aid research efforts in areas such as multiple-Doppler wind analyses, pseudo-dual-Doppler analyses, and retrieval studies.

* Current affiliation: Météo-France, Toulouse, France.

Corresponding author address: Mark A. Askelson, School of Meteorology, University of Oklahoma, Energy Center, 100 East Boyd St., Norman, OK 73019.

Email: maaskels@enterprise.nssl.noaa.gov

Abstract

Spatial objective analysis is routinely performed in several applications that utilize radar data. Because of their relative simplicity and computational efficiency, one-pass distance-dependent weighted-average (DDWA) schemes that utilize either the Cressman or the Barnes filter are often used in these applications. The DDWA schemes that have traditionally been used do not, however, directly account for two fundamental characteristics of radar data. These are 1) the spacing of radar data depends on direction and 2) radar data density systematically decreases with increasing range.

A DDWA scheme based on an adaptation of the Barnes filter is proposed. This scheme, termed the adaptive Barnes (A-B) scheme, explicitly takes into account radar data properties 1 and 2 above. Both theoretical and experimental investigations indicate that two attributes of the A-B scheme, direction-splitting and automatic adaptation to data density, may facilitate the preservation of the maximum amount of meaningful information possible within the confines of one-pass DDWA schemes.

It is shown that in the idealized situation of infinite, continuous data and for an analysis in rectangular-Cartesian coordinates, a direction-splitting scheme does not induce phase shifts if the weight function is even in each direction. Moreover, for radar data that are infinite, collected at regular radial, azimuthal, and elevational increments, and collocated with analysis points, the direction-splitting design of the A-B filter removes gradients in the analysis weights. This is a beneficial attribute when considering the treatment of gradient information of rectangular Cartesian data by an analysis system because then postanalysis gradients equal the analysis of gradients. The direction-splitting design of the A-B filter is unable, however, to circumvent the impact of the varying physical distances between adjacent measurements that are inherent to the spherical coordinate system of ground-based weather radars. Because of this, even with the direction-splitting design of the A-B filter postanalysis gradients do not equal the analysis of gradients.

Ringing in the response function of a one-dimensional Barnes filter is illustrated. The negative impact of data windows on the main lobe of the response function is found to decrease rapidly as the window is widened relative to the weight function. Unless an analysis point is near a data boundary, in which case both ringing and phase shifting will adversely affect the analysis, window effects are unlikely to be significant in applications of the A-B filter to radar data.

The A-B filter has potential drawbacks, the most significant of which is misinterpretations owing to the use of the A-B filter without comprehension of its direction- and range-dependent response function. Despite its drawbacks, the A-B filter has the potential to improve analyses owing to the aforementioned attributes and thus to aid research efforts in areas such as multiple-Doppler wind analyses, pseudo-dual-Doppler analyses, and retrieval studies.

* Current affiliation: Météo-France, Toulouse, France.

Corresponding author address: Mark A. Askelson, School of Meteorology, University of Oklahoma, Energy Center, 100 East Boyd St., Norman, OK 73019.

Email: maaskels@enterprise.nssl.noaa.gov

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  • Baer, F., and J. J. Tribbia, 1976: Spectral fidelity of gappy data. Tellus,28, 215–227.

  • Baker, W. E., 1983: Objective analysis and assimilation of observational data from FGGE. Mon. Wea. Rev.,111, 328–342.

  • Barnes, S. L., 1964: A technique for maximizing details in numerical weather map analysis. J. Appl. Meteor.,3, 396–409.

  • ——, 1973: Mesoscale objective map analysis using weighted time-series observations. NOAA Tech. Memo. ERL NSSL-62, 60 pp. [Available from NSSL Library, 1313 Halley Circle, Norman, OK 73069.].

  • Berger, M. I., and R. J. Doviak, 1979: An analysis of the clear air planetary boundary layer wind synthesized from NSSL’s dual Doppler-radar data. NOAA Tech. Rep. ERL NSSL-87, 55 pp. [Available from NSSL Library, 1313 Halley Circle, Norman, OK 73069.].

  • Bracewell, R., 1965: The Fourier Transform and its Applications. McGraw-Hill Electrical and Electronic Engineering Series, McGraw-Hill, 381 pp.

  • Brandes, E. A., 1977: Flow in severe thunderstorms observed by dual-Doppler radar. Mon. Wea. Rev.,105, 113–120.

  • Buzzi, A., D. Gomis, M. A. Pedder, and S. Alonso, 1991: A method to reduce the adverse impact that inhomogeneous station distributions have on spatial interpolation. Mon. Wea. Rev.,119, 2465–2491.

  • Caracena, F., S. L. Barnes, and C. A. Doswell III, 1984: Weighting function parameters for objective interpolation of meteorological data. Preprints, 10th Conf. on Weather Forecasting and Analysis, Clearwater Beach, FL, Amer. Meteor. Soc., 109–116.

  • Carbone, R. E., M. J. Carpenter, and C. D. Burghart, 1985: Doppler radar sampling limitations in convective storms. J. Atmos. Oceanic Technol.,2, 357–361.

  • Carr, F. H., P. L. Spencer, C. A. Doswell III, and J. D. Powell, 1995:A comparison of two objective analysis techniques for profiler time–height data. Mon. Wea. Rev.,123, 2165–2180.

  • Cochran, J. A., H. C. Wiser, and B. J. Rice, 1987: Advanced Engineering Mathematics. 2d ed. Brooks/Cole, 659 pp.

  • CRC, 1987: CRC Standard Mathematical Tables. 28th ed. CRC Press, 674 pp.

  • Cressman, G. P., 1959: An operational objective analysis system. Mon. Wea. Rev.,87, 367–374.

  • Daley, R., 1991: Atmospheric Data Analysis. Cambridge University Press, 457 pp.

  • Doswell, C. A., III, 1977: Obtaining meteorologically significant surface divergence fields through the filtering property of objective analysis. Mon. Wea. Rev.,105, 885–892.

  • ——, and F. Caracena, 1988: Derivative estimation from marginally sampled vector point functions. J. Atmos. Sci.,45, 242–253.

  • ——, and S. Lasher-Trapp, 1997: On measuring the degree of irregularity in an observing network. J. Atmos. Oceanic Technol.,14, 120–132.

  • Doviak, R. J., and D. S. Zrnić, 1993: Doppler Radar and Weather Observations. 2d ed. Academic Press, 562 pp.

  • ——, P. S. Ray, R. G. Strauch, and L. J. Miller, 1976: Error estimation in wind fields derived from dual-Doppler radar measurement. J. Appl. Meteor.,15, 868–878.

  • Endlich, R. M., and R. L. Mancuso, 1968: Objective analysis of environmental conditions associated with severe thunderstorms and tornadoes. Mon. Wea. Rev.,96, 342–350.

  • Gal-Chen, T., 1982: Errors in fixed and moving frame of references:Applications for conventional and Doppler radar analysis. J. Atmos. Sci.,39, 2279–2300.

  • Gandin, L., 1965: Objective Analysis of Meteorological Fields. Israel Program for Scientific Translation, 242 pp.

  • Hamming, R. W., 1998: Digital Filters. 3d ed. Dover, 284 pp.

  • Heymsfield, G. M., 1976: Statistical objective analysis of dual-Doppler radar data from a tornadic storm. J. Appl. Meteor.,15, 59–68.

  • James, R. C., and G. James, 1992: Mathematics Dictionary. 5th ed. Chapman and Hall, 548 pp.

  • Jorgensen, D. P., T. Matejka, and J. D. DuGranrut, 1996: Multi-beam techniques for deriving wind fields from airborne Doppler radars. Meteor. Atmos. Phys.,59, 83–104.

  • Lhermitte, R. M., and L. J. Miller, 1970: Doppler radar methodology for the observation of convective storms. Preprints, 14th Conf. on Radar Meteorology, Tucson, AZ, Amer. Meteor. Soc., 133–138.

  • Mohr, C. G., and R. L. Vaughan, 1979: An economical procedure for Cartesian interpolation and display of reflectivity factor data in three-dimensional space. J. Appl. Meteor.,18, 661–670.

  • Nelson, S. P., and R. A. Brown, 1987: Error sources and accuracy of vertical velocities computed from multiple-Doppler radar measurements in deep convective storms. J. Atmos. Oceanic Technol.,4, 233–238.

  • Oye, D., and M. Case, 1995: REORDER: A program for gridding radar data. Installation and use manual for the UNIX version. NCAR/ATD, 30 pp.

  • Papoulis, A., 1962: The Fourier Integral and its Applications. McGraw-Hill Electronic Sciences Series, McGraw-Hill, 318 pp.

  • Pauley, P. M., 1990: On the evaluation of boundary errors in the Barnes objective analysis scheme. Mon. Wea. Rev.,118, 1203–1210.

  • ——, and X. Wu, 1990: The theoretical, discrete, and actual response of the Barnes objective analysis scheme for one- and two-dimensional fields. Mon. Wea. Rev.,118, 1145–1163.

  • Sasaki, Y., 1970: Some basic formalisms in numerical variational analysis. Mon. Wea. Rev.,98, 875–883.

  • ——, 1971: A theoretical interpretation of anisotropically weighted smoothing on the basis of numerical variational analysis. Mon. Wea. Rev.,99, 698–707.

  • Skolnik, M. I., 1962: Introduction to Radar Systems. McGraw-Hill, 648 pp.

  • Srivastava, R. C., and D. Atlas, 1974: Effect of finite radar pulse volume on turbulence measurements. J. Appl. Meteor.,13, 472–480.

  • Stephens, J. J., and A. L. Polan, 1971: Spectral modification by objective analysis. Mon. Wea. Rev.,99, 374–378.

  • Sun, J., and N. A. Crook, 1998: Dynamical and microphysical retrieval from Doppler radar observations using a cloud model and its adjoint. Part II: Retrieval experiments of an observed Florida convective storm. J. Atmos. Sci.,55, 835–852.

  • Takacs, L. L., 1985: A two-step scheme for the advection equation with minimized dissipation and dispersion errors. Mon. Wea. Rev.,113, 1050–1065.

  • Testud, J., and M. Chong, 1983: Three-dimensional wind field analysis from dual-Doppler radar data. Part I: Filtering, interpolating and differentiating the raw data. J. Climate Appl. Meteor.,22, 1204–1215.

  • Thiébaux, H. J., and M. A. Pedder, 1987: Spatial Objective Analysis:With Applications in Atmospheric Science. Academic Press, 299 pp.

  • Trapp, R. J., and C. A. Doswell III, 2000: Radar data objective analysis. J. Atmos. Oceanic Technol.,17, 105–120.

  • Weaver, H. J., 1983: Applications of Discrete and Continuous Fourier Analysis. J. Wiley and Sons, 375 pp.

  • Weygandt, S., 1998: The retrieval of initial forecast fields from single Doppler observations of a supercell thunderstorm. Ph.D. dissertation, University of Oklahoma, 257 pp. [Available from School of Meteorology, University of Oklahoma, 100 E. Boyd, Norman, OK 73019.].

  • Zrnić, D. S., and R. J. Doviak, 1976: Effective antenna pattern of scanning radars. IEEE Trans. Aerosp. Electron. Syst.,AES-12, 551–555.

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