NSCAT Probability Distribution Study
NSCAT makes only indirect measurements of wind. The direct measurement
is is of the backscattered radar power. This signal power is contaminated
by radiometric noise so a separate measurement of the noise power
is subtracted from the signal+noise measurement to estimate the
backscattered power. Using the radar equation, sigma0 is computed
from the measured signal power. From multiple sigma0 measurements
made at different azimuth angles, the wind is estimated. In wind
retrieval, the NSCAT sigma0 measurements are assumed to have a
Gaussian probability distribution with a variance which depends
on the mean. Given this distribution model, the maximumlikelihood
estimator is formed and optimized to estimate the wind.
Because of the onboard signal processing used by NSCAT, the model
of a Gaussian distribution for sigma0 is only an approximation
to the actual distribution. Working from first principles and the
design of the NSCAT signal processor we derive the distribution
of the NSCAT measurements as a function of the surface sigma0,
the signal to noise ratio and the cell number. The resulting hypergeometric
distribution is skewed relative to the traditional Gaussian model.
The observed NSCAT probability distribution (pdf) will be the
combination (convolution) of the pdf described above and the pdf
of the sigma0 of the surface. The latter will be a function of
the pdf of the nearsurface wind field and the geophysical model
function.
From wavetank and lake experiments there is strong evidence that
sigma0 falls off rapidly at low winds. While this effect is clear
in such data, it is not as clear in spaceborne data where the radar
footprint covers 25 km**2 or more. However, if sigma0 does drop
to low values at low wind speeds the probability of seeing negative
sigma0 measurements (which occurs because of noise in the power
measurements) increases. As evidence that negative sigma0 measurements
are correlated with low wind speeds consider the following figures.
Figure 1 shows the spatial distribution of negative sigma0 measurements
over a three day period. Figure 2 shows a map of 3 days of NSCATderived
wind speeds. Figure 3 shows shows a map of the standard deviation
of NSCATderived wind speeds over the three day period. The later
image is useful in evaluting the temporal variation over the three
day period.
Figure 1: Map of the count of the number of negative sigma0 measurements
in 3 days of NSCAT data. This is a shunk down version of the
original image (58 K) which is a 1/4 deg by 1/4 deg map. In
this image, the number of measurements in each grid element are
indicated by a gray value with white as the most (thresholded to
5).
Figure 2: Map of the average NSCATderived wind speed over a three
day period. This is a shunk down version of the
original image (605 K) which is a 1/4 deg by 1/4 deg map. Whiter
values indicate higher wind speeds with pure white 18 m/s and higher.
Figure 3: Map of the average NSCATderived wind speed over a three
day period. This is a shunk down version of the
original image (608 K) which is a 1/4 deg by 1/4 deg map. Whiter
values indicate higher wind speeds with pure white 18 m/s and higher.
Figure 4: Map of the count of the number of sigma0 smaller (but
positive) than the square of root of Gamma in the quadratic Kpc
equation in 3 days of NSCAT data. This is a shunk down version of
the original image
(58 K) which is a 1/4 deg by 1/4 deg map. In this image, the
number of measurements in each grid element are indicated by a gray
value with white as the most (thresholded to 5).
Figure 5: Map of the weekly NCEP analyzed sea surface temperture
(SST). This is a shunk down version of the
original image (136 K) which is a 1/4 deg by 1/4 deg map. In
this image, the temperature is represented as a gray value from
10 to 40 deg C.
The images presented above are for JDs 810 in 1997. Full size
images for JDs 1921 are available below.
Spatial distribution
negative sigma0 image (55 K)
Wind speed image (619
K)
Wind speed standard deviation
image (621 K)
Spatial distribution
of low sigma0 values (58 K)
SST map (135 K)
