Statistics of Blended Winds

Monthly zonal mean, variance, skewness, and kurtosis are computed for pseudo windstress of blended winds (version 4), and are compared with QSCAT rev data. In generating blended winds, QSCAT rev data are used with the following exceptions: the outermost 3 wind vector cells (WVC) are eliminated, and all rain-flagged WVC with wind speeds < 15 m/s are eliminated. When deriving QSCAT only statistics the same quality criteria are used. In the blended product, all land values are masked out.

The statistical moments of values x1, ..., xN, are defined as follows:

Mean

av = 1/N &sum j=1,N (xj)
Variance
var = 1/(N-1) &sum j=1,N (xj-av) 2
Standard Deviation

&sigma = sqrt ( var )
Skewness
skew = 1/N &sum j=1,N [(xj-av)/&sigma ] 3
Kurtosis
kurt = &lang 1/N &sum j=1,N [(xj-av)/&sigma ] 4 &rang - 3

Pseudo windstress is defined as
pws = ( u ² + v ² ) * (sign of u)

In the figures below, monthly zonal statistics are plotted for blended winds (left panels) and QSCAT (right panels): mean in m2s-2; variance in 10 3 m4s-4, Number of data at each latitude (Ndat, as dashed line); skewness; and kurtosis. Click on the figures for an enlarged plot.

Fig. 1: September 1999, blended winds (left panel) and QSCAT (right)


Fig. 2: January 2000, blended winds (left panel) and QSCAT (right)


Overall, the statistics of the blended product are very similar to the QSCAT rev statistics. Skewness (in absolute terms) and kurtosis are slightly higher for QSCAT than for the blended product. Those higher moments, however, are very sensitive to outliers in the data distribution.

To illustrate this sensitivity, consider the kurtosis in January 2000. The kurtosis for QSCAT reaches a peak value of 48 at 20 ° S (Fig. 2, right panel). Closer examination of the data at this latitude shows that out of 95,591 data points there are 7 data with pseudo windstress values more than 20 standard deviations away from the mean (at 20° S, the pws mean is -34, and the standard deviation is 54 m2s-2). Six data points have corresponding wind speeds of about 27 m/s, and one value has a speed of almost 40 m/s. These are high wind speeds, but not necessarily unrealistic. Eliminating those 7 data, and re-computing statistics for the remaining 95,584 data results in an increase of skewness from -0.9 to 1.3, and a decrease of kurtosis from 48 to 24.

last modified on September 10, 2003
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