Validation of Vector Magnitude Datasets: Effects of Random Component Errors

Michael H. Freilich College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon

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Abstract

A statistically consistent and physically realistic approach for validating vector magnitude measurements is developed, based on a model for random measurement noise that explicitly satisfies a nonnegativity constraint for all “noisy” vector magnitude measurements. Numerical and analytic approximations are used to quantify the nonlinear functional dependence of sample conditional means on true values and component noise magnitudes. In particular, it is shown analytically that random component errors will result in overall vector magnitude biases. A simple nonlinear regression of measured sample conditional mean vector magnitudes (calculated from traditional collocated data) against Monte Carlo simulation results is proposed for determining both deterministic trends and random errors in the data to be validated. The approach is demonstrated using Seasat and ERS-1 scatterometer measurements and collocated buoy data. The approach accounts well for the observed qualitative features of the collocated datasets and yields realistic values of random component error magnitudes and deterministic gain and offset for each dataset. An apparent systematic insensitivity of scatterometers at low wind speeds is shown to be a consequence of random component speed errors if it is assumed that the comparison buoy measurements are error free.

Corresponding author address: Michael H. Freilich, College of Oceanic and Atmospheric Sciences, Oregon State University, 104 Ocean Admin Building, Corvallis, OR 97331-5503.

Email: mhf@oce.orst.edu

Abstract

A statistically consistent and physically realistic approach for validating vector magnitude measurements is developed, based on a model for random measurement noise that explicitly satisfies a nonnegativity constraint for all “noisy” vector magnitude measurements. Numerical and analytic approximations are used to quantify the nonlinear functional dependence of sample conditional means on true values and component noise magnitudes. In particular, it is shown analytically that random component errors will result in overall vector magnitude biases. A simple nonlinear regression of measured sample conditional mean vector magnitudes (calculated from traditional collocated data) against Monte Carlo simulation results is proposed for determining both deterministic trends and random errors in the data to be validated. The approach is demonstrated using Seasat and ERS-1 scatterometer measurements and collocated buoy data. The approach accounts well for the observed qualitative features of the collocated datasets and yields realistic values of random component error magnitudes and deterministic gain and offset for each dataset. An apparent systematic insensitivity of scatterometers at low wind speeds is shown to be a consequence of random component speed errors if it is assumed that the comparison buoy measurements are error free.

Corresponding author address: Michael H. Freilich, College of Oceanic and Atmospheric Sciences, Oregon State University, 104 Ocean Admin Building, Corvallis, OR 97331-5503.

Email: mhf@oce.orst.edu

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  • Abramowitz, A., and I. A. Stegun, 1964: Handbook of Mathematical Functions. Dover, 1046 pp.

  • Attema, E. P. W., 1991: The active microwave instrument on board the ERS-1 satellite. Proc. IEEE,79, 791–799.

    • Crossref
    • Export Citation
  • Boutin, J., and J. Etcheto, 1996: Consistency of Geosat, SSM/I, and ERS-1 global surface wind speeds—Comparison with in situ data. J. Atmos. Oceanic Technol.,13, 183–197.

    • Crossref
    • Export Citation
  • Bracalante, E. M., D. H. Boggs, W. L. Grantham, and J. L. Sweet, 1980: The SASS scattering coefficient algorithm. J. Oceanic Eng.,OE-5 (2), 145–154.

    • Crossref
    • Export Citation
  • Chelton, D. B., and F. J. Wentz, 1986: Further development of an improved altimeter wind speed algorithm. J. Geophys. Res.,91, 14 250–14 260.

    • Crossref
    • Export Citation
  • ———, A. M. Mestas-Nunez, and M. H. Freilich, 1990: Global wind stress and Sverdrup circulation from the Seasat scatterometer. J. Phys. Oceanogr.,20, 1175–1205.

    • Crossref
    • Export Citation
  • Chi, C.-Y., and F. K. Li, 1988: A comparative study of several wind estimation algorithms for spaceborne scatterometers. IEEE Trans. Geosci. Remote Sens.,GE-26, 115–121.

    • Crossref
    • Export Citation
  • Donelan, M. A., and W. J. Pierson, 1987: Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry. J. Geophys. Res.,92, 4971–5029.

    • Crossref
    • Export Citation
  • Essenwanger, O., 1976: Applied Statistics in Atmospheric Science. Developments in Atmospheric Science, Vol. 4A, Elsevier, 412 pp.

  • Freilich, M. H., 1986: Satellite scatterometer comparisons with surface measurements: Techniques and Seasat results. Proc. Workshop on ERS-1 Wind and Wave Calibration, Schliersee, Germany, ESA, ESA SP-262, 57–62.

  • ———, and R. S. Dunbar, 1993: A preliminary C-band scatterometer model function for the ERS-1 AMI instrument. Proc. First ERS-1 Symp., Cannes, France, ESA, ESA SP-359, 79–83.

  • ———, and P. G. Challenor, 1994: A new approach for determining fully empirical altimeter wind speed model functions. J. Geophys. Res.,99, 25 051–25 062.

  • Graber, H. C., N. Ebuchi, and R. Vakkayil, 1996: Evaluation of ERS-1 scatterometer winds with wind and wave ocean buoy observations. University of Miami Tech. Rep. RSMAS 96-003, 78 pp. [Available from Prof. Hans Graber, RSMAS/AMP, 4600 Rickenbacker Causeway, Miami, FL 33149.].

  • Hayes, S. P., L. J. Magnum, J. Picaut, and K. Takeuchi, 1991: TOGA-TAO: A moored array for real-time measurements in the tropical Pacific Ocean. Bull. Amer. Meteor. Soc.,72, 339–347.

    • Crossref
    • Export Citation
  • Justus, C. G., W. R. Hargraves, A. Mikhail, and D. Graber, 1978: Methods for estimating wind speed frequency distributions. J. Appl. Meteor.,17, 350–353.

    • Crossref
    • Export Citation
  • Liu, W. T., and T. V. Blanc, 1984: The Liu, Katsaros, and Businger (1979) bulk atmospheric flux computational iteration program in FORTRAN and BASIC. NRL Memo. Rep. 5291, 16 pp. [Available from Naval Research Laboratory, Code 4110, Washington, DC 20375.].

    • Crossref
    • Export Citation
  • Monaldo, F., 1988: Expected differences between buoy and radar altimeter estimates of wind speed and significant wave height and their implications on buoy-altimeter comparisons. J. Geophys. Res.,93, 2285–2302.

    • Crossref
    • Export Citation
  • Naderi, F. M., M. H. Freilich, and D. G. Long, 1991: Spaceborne radar measurement of wind velocity over the ocean—An overview of the NSCAT scatterometer system. Proc. IEEE,79, 850–866.

    • Crossref
    • Export Citation
  • Offiler, D., 1994: The calibration of ERS-1 satellite scatterometer winds. J. Atmos. Oceanic Technol.,11, 1002–1017.

    • Crossref
    • Export Citation
  • Parzen, E., 1960: Modern Probability Theory and Its Applications. John Wiley and Sons, 464 pp.

  • Pavia, E. G., and J. J. O’Brien, 1986: Weibull statistics of wind speed over the ocean. J. Climate Appl. Meteor.,25, 1324–1332.

    • Crossref
    • Export Citation
  • Pierson, W. J., 1983: The measurement of the synoptic scale wind over the ocean. J. Geophys. Res.,88, 1683–1708.

    • Crossref
    • Export Citation
  • Press, W. H., S. A. Teukolsky, W. T. Vettering, and B. P. Flannery, 1992: Numerical Recipes in FORTRAN. 2d. ed. Cambridge University Press, 963 pp.

  • Stewart, D. A., and O. M. Essenwanger, 1978: Frequency distribution of wind speed near the surface. J. Appl. Meteor.,17, 1633–1642.

    • Crossref
    • Export Citation
  • Takle, E. S., and J. M. Brown, 1978: Note on the use of Weibull statistics to characterize wind-speed data. J. Appl. Meteor.,17, 556–559.

    • Crossref
    • Export Citation
  • Wentz, F. J., S. Peteherych, and L. A. Thomas, 1984: A model function for ocean radar cross sections at 14.6 GHz. J. Geophys. Res.,89, 3689–3704.

    • Crossref
    • Export Citation
  • Woiceshyn, P. M., M. G. Wurtele, D. H. Boggs, L. F. McGoldrick, and S. Peteherych, 1986: The necessity for a new parameterization of an empirical model for wind/ocean scatterometry. J. Geophys. Res.,91, 2273–2288.

    • Crossref
    • Export Citation
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