QSCAT Wavelet PSD Research Topics and Issues



QSCAT publications on-line

Milliff, R.F., M.H. Freilich, W.T. Liu, R. Atlas, and W.G. Large, 2002: "Global Ocean Surface Vector Wind Observations from Space" in Observing the Oceans in the 21st Century, C.J. Koblinsky and N.R. Smith (eds.), GODAE Project Office and Bureau of Meteorology, Melbourne., pgs. 102-119.

This chapter provides a summary of current capabilities and near-future plans for surface vector wind observation sampling frequency, record length, spatial resolution, and global coverage. These properties are put in proper physical oceanographic context by means of several examples described in the appendix.


Cross-swath power spectral density (PSD)

a. Monthly averages of PSD

In order to perform the Chin-blending method, which combines high-resolution (but sparse) scatterometer data with low-resolution (but global) weather center analyses, first the power spectral density (PSD) needs to be computed for wavelets at 8°, 4°, 2°, and 1° resolution. Empirical power law relations between PSD and wavenumber k suggest that PSD ~ k p, where the exponent p takes values between -2 at high latitudes and -5/3 (= 1.67) at the equator. Plotted on a log/log plot, the exponent p represents the slope of the PSD. The Chin-blending preserves the observed power law dependency in the blended product. When computing PSD values from QSCAT data, it appears that p depends on the cross-swath cell number: less negative values of p indicate higher small-scale variability within the nadir region as well at the outer edges of the swath. See also the plots of scatterometer wind vectors under Variability in different QSCAT products below.

The dependency of the slope on cross-swath cell number is demonstrated in the following plots. Shown are slope vs. cell number for the months of January, March, May, July, September, and November 2000. The spectral slopes are computed from nonoverlapping, along-track segments of zonal velocity spanning at least 30° of latitude. The slopes were computed for 3 different regions: North Pacific (40-50° N, 120-240° E), Subtropical Northern Pacific (20-30° N, 120-240° E), and the combined Western Tropical Pacific and Tropical Atlantic (10° S-10° N, 120-180° E and 300°-360° E. The centers of tracks are required to fall within these areas. All slopes are indicated by dots, the averages are plotted with filled circles and lines, and standard deviations at each cross-swath cell number are represented by red lines. The lower panels show bin weights vs. cell number.



























The lower slopes (i.e. less negative values) in the nadir region are visible in all geographic areas and in all seasons. This tendency is most pronounced in the Subtropical Northern Pacific. A summary plot for this area is presented below for every other month. It appears that the annual signal is as strong in the nadir region as it is in outer regions of the swath. In general, the slopes reach a minimum in July and a maximum in November and January.





b. January 2000 comparison of PSD among several QSCAT data sets and with NCEP in the Subtropical Northern Pacific

The PSD slope has been calculated for the regular QSCAT-1 data, the DIRTH product, Remote Sensing Systems' KU-2001 product, and for collocated NCEP data (4xdaily, T126 FNL Operational Analysis; courtesy of Mike Freilich and Barry Vanhoff at OSU). DIRTH slope amplitudes are systematically (though perhaps not significantly) lower than the R1 slope amplitudes for all cell numbers. They rise, however, much less in the nadir region than for the R1 product. The cell-by-cell changes in slope match between R1 and DIRTH, with a nearly constant offset of 0.2-0.3 outside the nadir region, and up to 0.5 - 0.6 around nadir. The KU-2001 slope amplitudes are as low as the DIRTH amplitudes in the "sweet-spots" (cell numbers 10-25 and 52-67), but as large as the R1 amplitudes in the nadir region.





c. Year 2000 annual average PSD in the Subtropical Northern Pacific

Annual statistics for all 12 months beginning in January 2000 are shown below for the Subtropical Northern Pacific (20-30° N, 120-240° E). Results are presented for the regular QSCAT-1 as well as the DIRTH product.

The first figure for each product shows the average slope of power spectral density (PSD) for the zonal wind component U averaged over all tracks in this region. The number of tracks averages 700-900 in the central swath region, but can be as low as 400 in the outer swath regions (cell numbers 3-9 and 68-74). Cell numbers 1, 2, 75, and 76 have no valid data. Standard deviations and the 5-point running mean are also shown. Bin weights are shown in the bottom panel of the first figure.

The second figure shows the average U PSD for wavelets 8°, 4°, 2°, and 1° at every third cell across the swath. The resulting slope at that cell number is represented by the line (linear fit to the 4 data points) and printed below the graphs. The gray background areas represent the across-swath average PSD values +/- the across-swath standard deviations. Note that the across-swath PSD standard deviations are smallest for the 8° and 4° wavelets, but larger for the 2° and even bigger for 1° wavelets. This is the case for the R1 product, but those standard deviations are almost constant (on the log plot) for the DIRTH product.

The third figure shows in four panels (with linear y-scale) the average U PSD vs. cell number. The solid line indicates the average PSD in the sweet spot regions (cell numbers 10-25 and 52-67). The dashed line represents the average of all cell numbers. Note that the PSD is almost constant with respect to cell number for the 8° and 4° wavelets, but increases in the nadir region for the 2° wavelet and shows the biggest relative nadir increase for the 1° wavelet. The same is true for the standard deviations (red bars).

The fourth figure is similar to the third figure, but shows average PSD for all wavelets in one graph on a logarithmic scale. Solid and dashed lines represent sweet spot and overall swath averages as in the third figure. The relative increases of PSD in the nadir region for 2° and 1° wavelets are more pronounced in this log plot.

Note that in the DIRTH product, the nadir region increase of PSD is eliminated for the 2° wavelet and significantly reduced for the 1° wavelet. In addition, PSD is lower in DIRTH than in R1 for every cell number and for every wavelet. The resulting sweet-spot average, however, is only 3% lower for 8° and 10% lower for 4°, but 21% lower for 2& and 32% for 1°. The bottom graph in the last figure for DIRTH (log PSD vs. cell number for the 1° wavelet) indicates that the sweet-spot region, i.e. cell numbers 10-25 and 52-67, corresponds with very constant values in PSD.
















Variability in QSCAT, "DIRTH" QSCAT, QSCAT-KU2000, and "smooth" QSCAT-KU2000

To explore the within-swath variability of different QSCAT data products, a small region of one revolution was examined. Revolution 5664 (7/21/200, 2:42, day 203.105) is plotted in the Northern Tropical Pacific Ocean. "QSCAT-1" is the Operational Standard Data Product Release from PODAAC. Both the standard product and the DIRTH product are displayed. Light-blue vectors are wind vector cells (WVC) for which the MUDH algorithm indicates rain. Also presented are Remote Sensing System's (RSS) "KU2000" products: the standard QSCAT-KU2000, as well as the smoothed QSCAT-KU2000. Light-blue vectors indicate WVCs with scatterometer derived rain.

Both QSCAT and KU2000 exhibit greater variability (noise?) in the nadir region. This region is narrower in KU2000 than in QSCAT. The very central part of the nadir region seems to be slightly less noisy in QSCAT than in KU2000. There is greater variability (true WVC-to-WVC wind variability or noise?) in the outer swath regions in QSCAT than in KU2000.

______________ QSCAT ________________   ___________ DIRTH QSCAT ___________   __________ QSCAT-KU2000 ____________   ________ smooth QSCAT-KU2000 ________



last modified on March 10, 2006
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