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wave range. Based on this wave spectrum, they obtained the following ana-
lytical relation for the MSS function,
δ 2 =2 αC 1 / 2
D
β 1
ln a + a 2 +81 g 2 / ( βV 10 ) 4
9 g/ ( βV 10 ) 2
,
ln a + a 2 + k d
k d
+ 3
2 αC 1 / 2
β 1
D
(4)
here C D is the drag coecient of the sea surface. β = c p /V 10 is the wave
age with c p = g/ω p as the phase speed of waves corresponding to the peak
frequency ω p and V 10 is the local wind speed a 10 m above sea level, k d is
the cut-off wave number for high wave numbers (in the near-IR the last
term of Eq. (4) is negligible) and a = g/γ s is used for convenience in
the notation. For convenience on the interpretation of wave slopes, we have
plotted (Fig. 1) the more intuitive root mean square slope (RMSS) to have
a better idea of the tilting caused by the wind interaction with the sea
surface. For further discussion and details about algorithm validation and
comparison with experimental data, the reader is encouraged to see Ref. 4.
Several studies 8 - 10 suggested that there was evidence of nonwind-
dependent factors on the determination of the MSS from altimeter mea-
surements. The largest factor appears to be the degree of sea develop-
ment which is known as wave age (characterized by the phase speed of
the dominant wave and the wind speed measured at a height of 10 m).
Fig. 1. Root mean-square slope from Eq. (4) for several wave ages ( β 's) including a
comparison with Cox and Munk empirical RMSS of the sea surface.
 
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