In addition to the normal Ku-band, the Topex altimeter operates at a second frequency, C-band, in order to make better corrections for ionospheric delay and thus improve the height estimate of the altimeter. However, sigma0 and SWH estimates are also available from the C-band waveforms, and these may sometimes be more useful than those from the Ku-band altimeter, as C-band radar is known to be less sensitive to the effects of atmospheric liquid water (LW).
Figure 1 (above) shows the scatter diagram for colocated C-band and Ku-band sigma0s. The data displayed correspond only to points for which the Topex Microwave radiometer (TMR) indicates the atmospheric LW to be low. The data are grouped in 0.05dB bins, averaged, and then a series of lines (shown in black) fitted to yield a simple monotonic conversion between C-band sigma0s and their equivalent Ku values; this empirical relation is used later. Note that there is an approximate 3.5-4.0dB offset (C > Ku), but that different regimes in the graph exist according to whether or not the length scale of the sea surface roughness is comparable to that of the C-band radar (5.7cm) and secondly of Ku-band (2.2cm). The upper plot in Figure 1 shows that a) most of the data lies in the range 13-17dB, and b) that the s.d. of values in the 0.05dB bins in this range is typically less than 0.2dB.
Figure 2 (above) shows a Topex transit across a fairly extreme rain event - a typhoon in the NW Pacific. The red and pink curves show the good agreement between Ku- and C-band SWHs. Similarly the blue and green curves show that, once C-band values are rescaled as above, there is generally good agreement. However in the thick of the storm (admittedly using an extrapolation of the curve in Fig. 1), there is great disparity in sigma0 values. This is consistent with the Ku-band signal having suffered significant attenuation by atmospheric LW (the TMR data indicate a high water content).
Farrow (1975) has shown that simply for "moderate rain" a 2-way attenuation of 2dB would be expected at Ku-band; the expected equivalent effect at C-band is only one tenth the magnitude. The effect here is a lot greater indicating torrential rain. Clearly an estimated wind speed profile across this storm using Ku sigma0s would be somewhat awry. Not only will this attenuation of Ku-band affect the study of individual storms, but also the estimate of mean climatological winds, as high atmospheric LW contents occur preferentially in certain areas. It is believed that a much more reliable estimate could be obtained using the C-band values converted to Ku equivalents.
Figure 3 (above) shows the locations in a 2-month period (Sept-Oct 93) during which Ku-band sigma0s were more than 0.5dB below that expected from converting C-band values to their Ku equivalent (i.e. a significant departure below the black curve of Fig. 1). The banded structure present in Fig. 3 relates very well to the known locations of the Inter Tropical Convergence Zone (here lying along the Equator) and the South Pacific Convergence Zone (running from Cape Horn to Indonesia). Similar plots for different parts of the year show different areas may be affected e.g. the ITCZ is much further south in Mar-Apr and altimetric work over the NW. Indian Ocean will be more problematical in certain phases of the monsoon.
Despite C-band's supposed tolerance to atmospheric LW, large spikes in the C-band SWH are present in the data record (see Fig. 2 for example). An understanding of their cause may be learnt from examination of the waveform data and of the algorithm used to compute SWH.
Figure 4 (above) illustrates typical Ku- and C-band waveforms in non-raining conditions. For the Ku waveform, the half power point on the leading edge of the waveform lies halfway between bins 24 and 25 of the condensed data set; for C-band this point occurs 3 bins later due to the longer internal plumbing within the satellite.
An intermediate product, the SWH-related voltage, V_SWH, is calculated according to
V_SWH = 256. * (Li-Ei) / (L6-E6)
where i is the gate index and Li, Ei are the average powers in the late and early gates, whose positions (see Marth et al., 1993) are indicated in Fig. 4. SWH is then calculated from SWH.
When severe attenuation occurs, the Ku waveform is badly distorted, losing its characteristic shape. In such a case, the on-board tracker has difficulty predicting the true location of the return from the mean sea surface, and consequently shifts the tracker window. A series of waveforms from the section across the typhoon of Fig. 2 are illustrated in Fig. 5 (below). The left hand column displays the Ku waveforms; the right hand, the C-band (both sampled at 2.5Hz).
Because the positions of the gates are explicitly coded into the algorithm, when the tracker point is positioned well to the right of the desired half-power point, the mean value in the Li, Ei gates are similar. Consequently the V_SWH is low, and the derived SWH high. As the location of the C-band window is fixed relative to the position of the Ku tracker, the C-band waveform is poorly positioned in its window, despite suffering little distortion. Running a simple retracker, calculating V_SWH about the half-power point rather than about gate 24.5 (27.5 for C-band) yields much improved results as shown in Fig. 6 (below).
The red and blue curves show the SWH values for Ku- and C-band, based on the V_SWH values supplied on the Sensor Data Record. [ The section shown is 30N-32N of Fig. 2. ] The magenta and green lines show the result of the retracking exercise. A good improvement is shown for Ku-band (magenta), whilst C-band (green) shows no disturbance whatsoever on passing across this storm.
Thanks to Colin Johnson (MSSL) for setting up the software for plotting waveforms and to Phil Callahan and George Hayne or advice on interpretation of the Sensor Data Record. Parts of this work have been submitted for publication (Quartly et al., 1996, Quartly, 1996).
References
Farrow J.B. (1975) 'The influence of the atmosphere on remote sensing at microwave and radio wavelengths' [prepared for ESRO under ESTEC contract no. 1838/72 ESA]
Quartly G.D. 1996, 'Achieving Accurate Altimetry Across Storms: Improved Wind and Wave Estimates from C-band' (accepted by JAOT).
Quartly G.D., Guymer T.H. & Srokosz M.A. 1996, 'The Effects of Rain on Topex radar altimeter data' JAOT 13, 1209-1229 (to appear)
Marth P.C. et al. (1991) 'Prelaunch performance of the NASA altimeter for the TOPEX/POSEIDON project' IEEE Geosci. & Rem Sensg 31, 315-331