# Envisat RA-2 Individual Echoes: A Unique Dataset for a Better Understanding of Inland Water
## 4 Selected Case Studies
### Rio Nahuapa  
The first demonstration is Rio Nahuapa, a tributary of Rio Tigre, Peru. Rio Nahuapa flows south, but meanders back and forth E-W so that an altimeter nadir track is likely to intersect the river at multiple points (Figure 9). In particular, the data that we analyzed are characterized by three crossings. The North-most (upriver) intersection is labeled \"Crossing 1\" (4.39\({}^{\circ}\)S, 74.11\({}^{\circ}\)W). The next two at intervals of 4-6 km downstream along the meandering river are named \"Crossing 2\" and \"Crossing 3\". The river width increases from about 45 m at Crossing 1 to about 65 m at Crossing 3. The altimeter track cuts almost perpendicular to the river direction, simplifying the interpretation of the echo time series. Rio Tigre, which is 300 m wide in this location, is just beyond the point where the tracks terminate after Crossing 3. Envisat tracks repeat every 35 days. We have data from eight passes in the period 2007-2008. Figure 10 is the radargram from one of the eight passes (they are all very similar). The radargram has three striking flashes of specular returns corresponding to the three river crossings. The altimeter track never quite reaches Rio Tigre but some off-nadir returns from Rio Tigre are presumably seen at the far right. Figure 10: Radargram for the Rio Nahuapa case. Figure 9: Rio Nahuapa and Envisat Nominal track (IE coverage highlighted in red). Preprocessing on the data includes correction for the onboard tracker, which causes the jagged top and bottom edges. AGC adjustments are made so that echo power is on a consistent scale and comparable across all the examples. In L1B data the Doppler includes the satellite vertical velocity. This vertical velocity is known from satellite ephemerids; phases are accordingly adjusted to facilitate comparison with theoretical model expectation that Doppler is zero at CPA. It can be observed that there is only a slight mark of echo power on the hyperbola. This is because the side-lobes quickly drop >30 dB from the peak and into the background noise. Echoes from Rio Tigre begin to be detected further on a quasi-hyperbola (IE numbers > 1300, approximately). In Figure 11 the eight radargrams have been collapsed to a 1-dimension peak power plot, and mapped on a Google Earth image. Successive radar altimeter passes drift in longitude; interestingly, the effect of many passes over the area is to paint a map of the water surface. The results presented in Figure 11 show how the main lobes scale with the river width, being narrower the lobes pertaining to the wider river sections. In particular, Figure 12 shows the RCSs for Crossing 2 (left panel) and 3 (right panel). Coherently integrated bursts of 21 echoes were used to produce the plots. Each of the eight passes is a plotted with a different color. The dashed black curve is the theoretical power returned for 45 m and 65 m wide rivers, respectively. The widths were estimated from Google Earth, with an accuracy estimated as \(\pm\)5 m. The distance is from the river centerline. All passes are remarkably similar. Their power levels cluster in a narrow range 88 \(\pm\) 2 db. There is excellent agreement in both the width of the main lobe and the level of the first two or three side lobes. Crossing 2 can only be plotted on a distance interval of \(\pm\)500 m before encountering side lobes of crossing 1 and 3. Crossing 3 can be plotted a bit further out, to 800 m, and shows a remarkable agreement between data and theory up to the 5 th side lobe and a power range of 20 dB. Figure 11: Amplitude profiles of the 8 passes used in this case study (Rio Nahuapa). Figure 13 illustrates the ranging with the two-range-bins method described in Section 3.2.3 (Equation (12)) for Crossing 2. The abscissa is the same as in Figure 12. The left panel are range solutions with single echoes. The right panel presents the range solutions obtained with coherent burst integrations. Coherent integration visibly improved the range estimates.