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Christiansen et al., 2006). The results are only valid near the meteorological mast as wind
direction cannot be assumed constant for a region.
In the case of ERS-1/2 it was possible to operate the radar in two modes: either scatterometer
or SAR. When set in scatterometer mode the radar recorded from three antennae
but when set in SAR mode the radar recorded from one antenna. Viewing of a given point
at the surface from several different incidence and/or aspect angles allowed for unambiguous
estimatesofthe windspeed and directionfrom a set ofNRCS values at different aspect angles
from the scatterometer. The Geophysical Model Functions (GMFs) were empirically developed
to establish the wind-vector-to-backscatter relationship for the C-band scatterometer
data (e.g. Stoffelen and Anderson, 1997).
The scatterometer model functions have later been proven to be suitable for SAR wind
retrievals as well.
Figure 187(right) showsthe relationshipbetweenfour GMFs forC-bandVV forupwindand
crosswind. The upwind and crosswind directions are defined from the SAR viewing geometry:
the radar look angle difference to the prevailing wind direction. The GMFs are similar for
upwind and downwind geometry but different for other angles with a minimum for crosswind.
In other words,the GMFs are more sensitive to the NRCS forthe upwind/downwindgeometry
than for the crosswind geometry. The signals are also weaker for crosswind.
The GMF for C-band SAR wind retrieval at low to moderate wind speeds CMOD4 is valid
for wind speeds of 2−24ms −1 (Stoffelen & Anderson, 1997). Forhigher wind speeds CMOD-
IFR2 (Quilfen et al., 1998) and CMOD5 (Hersbach et al., 2007) are typically used and are
valid for wind speeds of 2−36 ms −1 . CMOD4, CMOD5 and CMOD-IFR2 all have a nominal
accuracy of ±2ms −1 .
Generally, the empirical GMFs take the following form
σ 0 = U γ(θ) A(θ)[1+B(θ,U)cosφ+C(θ,U)cos2φ] (349)
where σ 0 is the normalized radar cross section (NRCS), U is wind speed at a height of 10 m
for a neutrally-stratified atmosphere, θ is the local incident angle, and φ is the wind direction
with respect to the radar look direction. The coefficients A, B, C and γ are functions of wind
speed and the local incidence angle.
Figure 187: Left: Surface wave and microwave wavelength for radar. Right: Relationship between
Normalized Radar Cross Section (NRCS) and wind speed for upwind and crosswind for
three Geophysical Model Functions CMOD-IFR2, CMOD4 and CMOD5 for a given incidence
angle.
The physical relationship between NRCS and the wind stress (friction velocity) is physically
more direct than to the 10 m wind, hence friction velocity may empirically fit better to NRCS
than 10 m wind. Most users, however, favour 10 m wind speed. Physical models describing
the relationship between NRCS, the 2D wave spectrum, and the scattering mechanisms are
complicated (Romeiser et al., 1997a; 1997b; Kudryavtsev et al., 2003). As a matter of fact,
the empirical GMFs are so far best suited for wind retrieval.
DTU Wind Energy-E-Report-0029(EN) 279