Spatially variable advection correction of radar data. Part I: Theoretical considerations

Journal of the Atmospheric Sciences

Volumn 67, Issue 11, 2010, Pages 3445-3456

  Shapiro, Alan ^a   Willinghamm, Katherine M ^a   Potvin, Corey K ^a  

^a UNIVERSITY OF OKLAHOMA   (United States)

Author keywords

Advection; Algorithm; Error analysis; Radar Radar observations

Indexed keywords

ACCUMULATED RAINFALL; CONSTANT SPEED; CORRECTION PROCEDURE; DOPPLER WINDS; EULER-LAGRANGE EQUATIONS; NONUNIQUENESS; NUMERICAL PROCEDURES; RADAR DATA; RADAR/RADAR OBSERVATIONS; RADIAL VELOCITY; SMOOTHNESS CONSTRAINTS; SUBSTANTIAL ERRORS; TEMPORAL SAMPLING; VARIATIONAL PROBLEMS;

ERROR ANALYSIS; EULER EQUATIONS; RADAR; REFLECTION; SAMPLING;

ADVECTION;

ALGORITHM; DATA PROCESSING; DOPPLER RADAR; ERROR ANALYSIS; METEOROLOGY; OBSERVATIONAL METHOD; SPATIAL ANALYSIS; TEMPORAL ANALYSIS; THEORETICAL STUDY;

EID: 78649456124     PISSN: 00224928     EISSN: None     Source Type: Journal    
DOI: 10.1175/2010JAS3465.1     Document Type: Article

References (73)

1. Anagnostou, E. N., and W. F. Krajewski, 1999: Real-time radar rainfall estimation. Part I: Algorithm formulation. J. Atmos. Oceanic Technol., 16, 189-197.
2. Andrejczuk, M., S. Moszkowicz, K. Haman, and T. Szoplik, 2003: Radar-echo tracking by use of invariant moments. Appl. Opt., 42, 5891-5896.
3. Austin, G. L., and A. Bellon, 1974: The use of digital weather radar records for short-term precipitation forecasting. Quart. J. Roy. Meteor. Soc., 100, 658-664.
4. Austin, P. M., 1987: Relation between measured radar reflectivity and surface rainfall. Mon. Wea. Rev., 115, 1053-1070.
5. Biggerstaff, M. I., and Coauthors, 2005: The Shared Mobile Atmospheric Research and Teaching Radar: A collaboration to enhance research and teaching. Bull. Amer. Meteor. Soc., 86, 1263-1274.
6. Caillault, K., and Y. Lemaitre, 1999: Retrieval of threedimensional wind fields corrected for the time-induced advection problem. J. Atmos. Oceanic Technol., 16, 708-722.
7. Carbone, R. E., 1982: A severe frontal rainband. Part I: Stormwide hydrodynamic structure. J. Atmos. Sci., 39, 258-279.
8. Caya, A., S. Laroche, I. Zawadzki, and T. Montmerle, 2002: Using single-Doppler data to obtain a mesoscale environmental field. J. Atmos. Oceanic Technol., 19, 21-36.
9. Chong, M., J. Testud, and F. Roux, 1983: Three-dimensional wind field analysis from dual-Doppler radar data. Part II: Minimizing the error due to temporal variation. J. Climate Appl. Meteor., 22, 1216-1226.
10. Clarke, T. L., F. I. Harris, and C. G. Mohr, 1980: Errors in wind fields derived from multiple-Dopper radars: Random errors and temporal errors associated with advection and evolution. J. Appl. Meteor., 19, 1273-1284.
11. Courant, R., and D. Hilbert, 1953: Methods of Mathematical Physics. Vol. 1. Wiley-Interscience, 560 pp.
12. Crook, A., 1994: Numerical simulations initialized with radarderived winds. Part I: Simulated data experiments. Mon. Wea. Rev., 122, 1189-1203.
13. Crum, T. D., and R. L. Alberty, 1993: The WSR-88D and the WSR-88D Operational Support Facility. Bull. Amer. Meteor. Soc., 74, 1669-1687.
14. Dixon, M., and G. Wiener, 1993: TITAN: Thunderstorm Identification, Tracking Analysis and Nowcasting-A radar-based methodology. J. Atmos. Oceanic Technol., 10, 785-797.
15. Dowell, D. C., and H. B. Bluestein, 1997: The Arcadia, Oklahoma, storm of 17 May 1981: Analysis of a supercell during tornadogenesis. Mon. Wea. Rev., 125, 2562-2582.
16. Dowell, D. C., and H. B. Bluestein, 2002: The 8 June 1995McLean, Texas, Storm. Part I: Observations of cyclic tornadogenesis. Mon. Wea. Rev., 130, 2626-2648.
17. Fabry, F., A. Bellon, M. R. Duncan, and G. L. Austin, 1994: High resolution rainfall measurements by radar for very small basins: The sampling problem reexamined. J. Hydrol., 161, 415-428.
18. Flanigan, F. J., 1983: Complex Variables. Dover, 353 pp.
19. Fulton, R., J. Breidenbach, D.-J. Seo, D. Miller, and T. O'Bannon, 1998: The WSR-88D rainfall algorithm. Wea. Forecasting, 13, 377-395.
20. Gal-Chen, T., 1978: A method for the initialization of the anelastic equations: Implications for matching models with observations. Mon. Wea. Rev., 106, 587-606.
21. 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.
22. Gao, J., M. Xue, A. Shapiro, Q. Xu, and K. K. Droegemeier, 2001: Three-dimensional simple adjoint velocity retrievals from single Doppler radar. J. Atmos. Oceanic Technol., 18, 26-38.
23. Germann, U., and I. Zawadzki, 2002: Scale-dependence of the predictability of precipitation from continental radar images. Part I: Description of the methodology. Mon. Wea. Rev., 130, 2859-2873.
24. Gerstner, E.-M., and G. Heinemann, 2008: Real-time areal precipitation determination from radar by means of statistical objective analysis. J. Hydrol., 352, 296-308.
25. Hane, C. E., 1993: Storm-motion estimates derived from dynamicretrieval calculations. Mon. Wea. Rev., 121, 431-443.
26. Hane, C. E., R. B. Wilhelmson, and T. Gal-Chen, 1981: Retrieval of thermodynamic variables within deep convective clouds: Experiments in three dimensions. Mon. Wea. Rev., 109, 564-576.
27. Heymsfield, G. M., 1978: Kinematic and dynamic aspects of the Harrah tornadic storm analyzed from dual-Doppler radar data. Mon. Wea. Rev., 106, 233-254.
28. Islam, M. R., and P. F. Rasmussen, 2008: Improved high-resolution radar-based rainfall estimation. J. Hydrol. Eng., 13, 910-913.
29. Johnson, J., P. MacKeen, A. Witt, E. Mitchell, G. Stumpf, M. Eilts, and K. Thomas, 1998: The storm cell identification and tracking algorithm: An enhanced WSR-88D algorithm. Wea. Forecasting, 13, 263-276.
30. Klazura, G. E., and D. A. Imy, 1993: A description of the initial set of analysis products available from the NEXRAD WSR-88D system. Bull. Amer. Meteor. Soc., 74, 1293-1311.
31. Lakshmanan, V., R. Rabin, and V. DeBrunner, 2003: Multiscale storm identification and forecast. Atmos. Res., 67-68, 367-380.
32. Lakshmanan, V., T. Smith, K. Hondl, G. J. Stumpf, and A. Witt, 2006: A realtime, three-dimensional, rapidly updating, heterogeneous radar merger technique for reflectivity, velocity, and derived products. Wea. Forecasting, 21, 802-823.
33. Lanczos, C., 1986: The Variational Principles of Mechanics. Dover, 418 pp.
34. Langston, C., J. Zhang, and K. Howard, 2007: Four-dimensional dynamic radar mosaic. J. Atmos. Oceanic Technol., 24, 776-790.
35. Laroche, S., and I. Zawadzki, 1995: Retrievals of horizontal winds from single-Doppler clear-air data by methods of cross correlation and variational analysis. J. Atmos. Oceanic Technol., 12, 721-738.
36. Lazarus, S., A. Shapiro, and K. Droegemeier, 2001: Application of the Zhang-Gal-Chen single-Doppler velocity retrieval to a deep convective storm. J. Atmos. Sci., 58, 998-1016.
37. Liou, Y.-C., 1999: Single radar recovery of cross-beam wind components using a modified moving frame of reference technique. J. Atmos. Oceanic Technol., 16, 1003-1016.
38. Liou, Y.-C., 2001: The derivation of absolute potential temperature perturbations and pressure gradients from wind measurements in three-dimensional space. J. Atmos. Oceanic Technol., 18, 577-590.
39. Liou, Y.-C., and I.-S. Luo, 2001: An investigation of the moving-frame single-Doppler wind retrieval technique using Taiwan Area Mesoscale Experiment low-level data. J. Appl. Meteor., 40, 1900-1917.
40. Liu, C., and W. F. Krajewski, 1996: A comparison of methods for calculation of radar-rainfall hourly accumulations. Water Resour. Bull., 32, 305-315.
41. Liu, S., C. Qiu, Q. Xu, and P. Zhang, 2004: An improved time interpolation for three-dimensional Doppler wind analysis. J. Appl. Meteor., 43, 1379-1391.
42. Lu, H., and Q. Xu, 2009: Trade-offs between measurement accuracy and resolutions in configuring phased-array radar velocity scans for ensemble-based storm-scale data assimilation. J. Appl. Meteor. Climatol., 48, 1230-1244.
43. Matejka, T., 2002: Estimating themost steady frame of reference from Doppler radar data. J. Atmos. Oceanic Technol., 19, 1035-1048.
44. Michelson, M., W. W. Shrader, and J. G. Wieler, 1990: Terminal Doppler weather radar. Microwave J., 33, 139-148.
45. Miller, L. J., and R. A. Kropfli, 1980: The multiple Doppler radar workshop, November 1979. Part II: Experimental design and procedures. Bull. Amer. Meteor. Soc., 61, 1173-1177.
46. Mohr, C. G., L. J. Miller, R. L. Vaughan, and H. W. Frank, 1986: The merger of mesoscale datasets into a common Cartesian format for efficient and systematic analyses. J. Atmos. Oceanic Technol., 3, 143-161.
47. NOAA/NWS, 2005: TDWR interface control and specifications documentation for the NWS supplemental product generator, version 4.3, 42 pp. [Available online at http://wdtb.noaa.gov/buildTraining/TDWR/TDWR_SPG_ICD_v43.pdf.]
48. Parsons, D. B., C. G. Mohr, and T. Gal-Chen, 1987: A severe frontal rainband. Part III: Derived thermodynamic structure. J. Atmos. Sci., 44, 1615-1631.
49. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, 1992: Numerical Recipes in FORTRAN: The Art of Scientific Computing. 2nd ed. Cambridge University Press, 963 pp.
50. Protat, A., and I. Zawadzki, 1999: A variational method for realtime retrieval of three-dimensional wind field from multiple-Doppler bistatic radar network data. J. Atmos. Oceanic Technol., 16, 432-449.
51. Ray, P. S., M. Gilet, and K. W. Johnson, 1980: The multiple Doppler radar workshop, November 1979. Part IV: Motion field synthesis and radar placement. Bull. Amer. Meteor. Soc., 61, 1184-1189.
52. Rosenfeld, D., 1987: Objective method for analysis and tracking of convective cells as seen by radar. J. Atmos. Oceanic Technol., 4, 422-434.
53. Roux, F., 1985: Retrieval of thermodynamic fields from multiple-Doppler radar data using the equations of motion and the thermodynamic equation. Mon. Wea. Rev., 113, 2142-2157.
54. Sasaki, Y., 1970: Some basic formalisms in numerical variational analysis. Mon. Wea. Rev., 98, 875-883.
55. Sasaki, Y., 1971: Atheoretical interpretation of anisotropically weighted smoothing on the basis of numerical variational analysis. Mon. Wea. Rev., 99, 698-707.
56. Shapiro, A., S. Ellis, and J. Shaw, 1995: Single-Doppler velocity retrievals with Phoenix II data: Clear air and microburst wind retrievals in the planetary boundary layer. J. Atmos. Sci., 52, 1265-1287.
57. Shapiro, A., P. Robinson, J. Wurman, and J. Gao, 2003: Single-Doppler velocity retrieval with rapid scan radar data. J. Atmos. Oceanic Technol., 20, 1758-1775.
58. Shapiro, A., K. M. Willingham, and C. K. Potvin, 2010: Spatially variable advection correction of radar data. Part II: Test results. J. Atmos. Sci., 67, 3457-3470.
59. Sun, J., and R. A. Houze Jr., 1992: Validation of a thermodynamic retrieval technique by application to a simulated squall line with trailing stratiform precipitation. Mon. Wea. Rev., 120, 1003-1018.
60. Sun, J., and N. A. Crook, 1994: Wind and thermodynamic retrieval from single-Doppler measurements of a gust front observed during Phoenix II. Mon. Wea. Rev., 122, 1075-1091.
61. Sun, J., and N. A. Crook, 2001: Real-time low-level wind and temperature analysis using single WSR-88D data. Wea. Forecasting, 16, 117-132.
62. Tabary, P., 2007: The new French operational radar rainfall product. Part I: Methodology. Wea. Forecasting, 22, 393-408.
63. Taylor, G. I., 1938: The spectrum of turbulence. Proc. Roy. Soc. London, 164A, 476-490.
64. Tuttle, J. D., and G. B. Foote, 1990: Determination of the boundary layer airflow from a single Doppler radar. J. Atmos. Oceanic Technol., 7, 218-232.
65. Vasiloff, S. V., 2001: Improving tornado warnings with the Federal Aviation Administration's terminal Doppler weather radar. Bull. Amer. Meteor. Soc., 82, 861-874.
66. Villarini, G., and W. F. Krajewski, 2010: Review of the different sources of uncertainty in single-polarization radar-based estimates of rainfall. Surv. Geophys., 31, 107-129.
67. Wurman, J., J. Straka, E. Rasmussen, M. Randall, and A. Zahrai, 1997: Design and deployment of a portable, pencil-beam, pulsed, 3-cm Doppler radar. J. Atmos. Oceanic Technol., 14, 1502-1512.
68. Xu, Q., H. Gu, and C. Qiu, 2001a: Simple adjoint retrievals of wetmicroburst winds and gust-front winds from single-Doppler radar data. J. Appl. Meteor., 40, 1485-1499.
69. Xu, Q., H. Gu, and S. Yang, 2001b: Simple adjoint method for threedimensional wind retrievals from single-Doppler radar. Quart. J. Roy. Meteor. Soc., 127, 1053-1067.
70. Yang, H., J. Zhang, and C. Langston, 2009: Synchronization of radar observations with multi-scale storm tracking. Adv. Atmos. Sci., 26, 78-86.
71. Zawadzki, I. I., 1973: Statistical properties of precipitation patterns. J. Appl. Meteor., 12, 459-472.
72. Zhang, J., and T. Gal-Chen, 1996: Single-Doppler wind retrieval in the moving frame of reference. J. Atmos. Sci., 53, 2609-2623.
73. Zrnic, D. S., and Coauthors, 2007: Agile-beam phased array radar for weather observations. Bull. Amer. Meteor. Soc., 88, 1753-1766.