6 Scatterometer’s Unique Capability in Measuring Ocean Surface Stress
105
where χ is the relative azimuthal angle between the plane of incidence of the radar
beam and the wind direction, θ is the incidence angle (relative to nadir) and p represents the polarization. At fixed χ , σ 0 (in dB) increases approximately linearly with
log (U N ). The azimuthal variation of σ 0 can be characterized as harmonics with
“upwind-downwind asymmetry” and “up- wind-crosswind modulation”. It has been
demonstrated that the azimuthal angle dependence can be separated from the incidence angle and U N functions using the 3-term Fourier series (Wentz et al., 1984;
Freilich, 1996):
σ 0 = A 0 (U N ,θ) + A 1 (U N ,θ ) cos (χ ) + A 2 (U N ,θ) cos (2χ )
(6.8)
The core of GMF-W is consisted of the A coefficients as tabulated empirical data.
The forward GMF-W accepts U N vector as input and gives σ 0 as output. The inverse
GMF, however, is not unique. A single measurement of σ 0 generates a range of
potential wind vectors, all of which would have given rise to the observed backscatter. To solve the inverse problem, σ 0 at multiple azimuth angles are used. At least
three collocated observations of σ 0 differing in “look”, i.e. geometry (χ , θ ), allows
the determination of a unique wind vector. Theoretically, the solution could be found
from data without noise. Noise complicates the solution and a maximum likelihood
estimator (MLE) has to be used (Pierson, 1984). A common practice is to keep
several ambiguous solutions at each wind vector cell. In order to select the proper
ambiguity, we assume that the wind is unlikely to shift radically from one cell to the
next and a median filter technique has been used (Shaffer et al., 1991). The median
filter technique is an iteration procedure generally initialized by the NWP field in
the so called “nudging”.
6.4.2 Stress Retrieval
There are many reasons for a GMF-S to retrieve stress (or U ∗ ) directly rather than
the present GMF-W to retrieve U N . A first reason lies in the present GMF-W, which
should be developed and calibrated with U N computed from research-quality in-situ
wind measurements, using methods based on the similarity relations of Liu et al.
(1979), as in Section 6.2. Indeed, such computation of U N was performed before
credible ocean surface wind products became available from operational NWP
centers. Most of the tuning of the revised GMF after Seasat was based on NWP
products (e.g. Wentz and Smith, 1999) that are not U N (not corrected for stability
dependence). The resulting errors are not reversible and difficult to gauge.
Ideally, stress could be derived from U N retrieved from scatterometer, using a
neutral drag coefficient. However, if the drag coefficient is not the same as that
used to derive U N for development of the GMF, an error will be introduced through
the uncertainty of the drag coefficient. This is the second reason for a GMF-S.
Weissman and Graber (1999) provide an example of the very few attempts to tabulate stress instead of U N in the A coefficients of Equation (6.8). Two additional
105
where χ is the relative azimuthal angle between the plane of incidence of the radar
beam and the wind direction, θ is the incidence angle (relative to nadir) and p represents the polarization. At fixed χ , σ 0 (in dB) increases approximately linearly with
log (U N ). The azimuthal variation of σ 0 can be characterized as harmonics with
“upwind-downwind asymmetry” and “up- wind-crosswind modulation”. It has been
demonstrated that the azimuthal angle dependence can be separated from the incidence angle and U N functions using the 3-term Fourier series (Wentz et al., 1984;
Freilich, 1996):
σ 0 = A 0 (U N ,θ) + A 1 (U N ,θ ) cos (χ ) + A 2 (U N ,θ) cos (2χ )
(6.8)
The core of GMF-W is consisted of the A coefficients as tabulated empirical data.
The forward GMF-W accepts U N vector as input and gives σ 0 as output. The inverse
GMF, however, is not unique. A single measurement of σ 0 generates a range of
potential wind vectors, all of which would have given rise to the observed backscatter. To solve the inverse problem, σ 0 at multiple azimuth angles are used. At least
three collocated observations of σ 0 differing in “look”, i.e. geometry (χ , θ ), allows
the determination of a unique wind vector. Theoretically, the solution could be found
from data without noise. Noise complicates the solution and a maximum likelihood
estimator (MLE) has to be used (Pierson, 1984). A common practice is to keep
several ambiguous solutions at each wind vector cell. In order to select the proper
ambiguity, we assume that the wind is unlikely to shift radically from one cell to the
next and a median filter technique has been used (Shaffer et al., 1991). The median
filter technique is an iteration procedure generally initialized by the NWP field in
the so called “nudging”.
6.4.2 Stress Retrieval
There are many reasons for a GMF-S to retrieve stress (or U ∗ ) directly rather than
the present GMF-W to retrieve U N . A first reason lies in the present GMF-W, which
should be developed and calibrated with U N computed from research-quality in-situ
wind measurements, using methods based on the similarity relations of Liu et al.
(1979), as in Section 6.2. Indeed, such computation of U N was performed before
credible ocean surface wind products became available from operational NWP
centers. Most of the tuning of the revised GMF after Seasat was based on NWP
products (e.g. Wentz and Smith, 1999) that are not U N (not corrected for stability
dependence). The resulting errors are not reversible and difficult to gauge.
Ideally, stress could be derived from U N retrieved from scatterometer, using a
neutral drag coefficient. However, if the drag coefficient is not the same as that
used to derive U N for development of the GMF, an error will be introduced through
the uncertainty of the drag coefficient. This is the second reason for a GMF-S.
Weissman and Graber (1999) provide an example of the very few attempts to tabulate stress instead of U N in the A coefficients of Equation (6.8). Two additional