Probabilities and statistics for backscatter estimates obtained by a scatterometer with applications to new scatterometer design data

The values of the Normalized Radar Backscattering Cross Section (NRCS), sigma (o), obtained by a scatterometer are random variables whose variance is a known function of the expected value. The probability density function can be obtained from the normal distribution. Models for the expected value obtain it as a function of the properties of the waves on the ocean and the winds that generated the waves. Point estimates of the expected value were found from various statistics given the parameters that define the probability density function for each value. Random intervals were derived with a preassigned probability of containing that value. A statistical test to determine whether or not successive values of sigma (o) are truly independent was derived. The maximum likelihood estimates for wind speed and direction were found, given a model for backscatter as a function of the properties of the waves on the ocean. These estimates are biased as a result of the terms in the equation that involve natural logarithms, and calculations of the point estimates of the maximum likelihood values are used to show that the contributions of the logarithmic terms are negligible and that the terms can be omitted.

[1]  The impact of Seasat-A scatterometer data on the numerical prediction of the Queen Elizabeth II storm , 1986 .

[2]  L. Hasse.  On Charnock’s Relation for the Roughness at Sea , 1986 .

[3]  L. Schroeder,et al.  AAFE RADSCAT 13.9-GHz measurements and analysis: Wind-speed signature of the ocean , 1985, IEEE Journal of Oceanic Engineering.

[4]  Fuk-kwok Li,et al.  Radar Backscatter Measurement Accuracies Using Digital Doppler Processors in Spaceborne Scatterometers , 1986, IEEE Transactions on Geoscience and Remote Sensing.

[5]  David G. Long,et al.  Roundoff noise analysis for digital signal power processors using Welch's power spectrum estimation , 1987, IEEE Trans. Acoust. Speech Signal Process..

[6]  Aspects of the determination of winds by means of scatterometry and of the utilization of vector wind data for meteorological forecasts , 1986 .

[7]  R. Moore,et al.  The radar radiometer , 1969 .

[8]  F. Li,et al.  Nross Scatterometer An Instrument For Global Oceanic Wind Observations , 1984, Other Conferences.

[9]  P. Woiceshyn,et al.  A new parameterization of an empirical model for wind/ocean scatterometry , 1984 .

[10]  E. Bahar.  Review of the full wave solutions for rough surface scattering and depolarization , 1987 .

[11]  F. J. Wentz,et al.  A model function for ocean radar cross sections at 14.6 GHz , 1984 .

[12]  W. Pierson,et al.  The relationship between wind vector and normalized radar cross section used to derive SEASAT‐A satellite scatterometer winds , 1982 .

[13]  S. Durden,et al.  A physical radar cross-section model for a wind-driven sea with swell , 1985, IEEE Journal of Oceanic Engineering.

[14]  J. Mitchell,et al.  Flight measurement and analysis of AAFE RADSCAT wind speed signature of the ocean , 1984 .

[15]  Franklin A. Graybill,et al.  Introduction to the Theory of Statistics, 3rd ed. , 1974 .

[16]  W. Pierson.  Highlights of the SEASAT-SASS program - A review , 1983 .

[17]  W. Pierson,et al.  Synoptic Scale Wind Field Properties From The SEASAT SASS , 1983, Proceedings OCEANS '83.

[18]  W. L. Grantham,et al.  Seasat-A satellite scatterometer instrument evaluation , 1980 .

[19]  Robert E. Fischer,et al.  Standard Deviation of Scatterometer Measurements from Space , 1972 .

[20]  W. Plant.  A two-scale model of short wind-generated waves and scatterometry , 1986 .

[21]  Response to “Review of the full wave solutions for rough surface scattering and depolarization: Comparisons with geometric and physical optics, perturbation, and two‐scale hybrid solutions” by E. Bahar , 1987 .

[22]  M. Donelan,et al.  Radar scattering and equilibrium ranges in wind‐generated waves with application to scatterometry , 1987 .

[23]  W. J. Pierson.  A Monte Carlo comparison of the recovery of winds near upwind and downwind from the SASS-1 model function by means of the sum of squares algorithm and a maximum likelihood estimator , 1984 .

[24]  W. Pierson,et al.  The measurement of the synoptic scale wind over the ocean , 1983 .

[25]  David G. Long,et al.  The design of an onboard digital Doppler processor for a spaceborne scatterometer , 1988 .

[26]  F. J. Wentz,et al.  New algorithms for microwave measurements of ocean winds , 1984 .

[27]  W. Linwood Jones,et al.  The Seasat-A satellite scatterometer - The geophysical evaluation of remotely sensed wind vectors over the ocean , 1982 .

[28]  E. H. Fooks,et al.  On the microwave reflectivity of small-scale breaking water waves , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[29]  Fuk K. Li,et al.  Studies of the location of azimuth modulation minima for Ku band ocean radar backscatter , 1988 .

[30]  G. Valenzuela.  Theories for the interaction of electromagnetic and oceanic waves — A review , 1978 .

[31]  A. L. Maffett,et al.  The Contribution of Wedge Scattering to the Radar Cross Section of the Ocean Surface , 1983, IEEE Transactions on Geoscience and Remote Sensing.

[32]  B. Lake,et al.  A deterministic, coherent, and dual-polarized laboratory study of microwave backscattering from water waves, Part I: Short gravity waves without wind , 1984, IEEE Journal of Oceanic Engineering.