Surface of 8km correlation length.

The altim eter echoes in fig.5.4b returning from surface (b) in fig.5.1 have m ultiple profiles. The correlation length of this surface is 8km which is about three tim es smaller than the previous surface. Some of the returned echoes from surface (b) are ocean-like (fig.2.8a), some are double-ramped (fig.2.8b) and others are irregular an d do not strictly fall into any category of the echo models. Fig.5.8 illustrates the RM S error of the across-track distance of surface (b) in fig.5.1. The RMS error is

calculated from the retracked heights in the along-track distance. Tie RM S error retracked from the first leading edge is indicated by the circled line. The retracked heights of this curve are determined from the first leading edge of the echo by fitting the echoes either into the ocean-like (2.62) or the double-ramp model (264).

m 3 0 o 2 5 5 20 20 100 A c r o s s-tr a c k d is ta n c e (x - a x is ) in km

Fig.5.8 The RMS error of retrieving the surface of L=8km. The retrieved surface is obtained from the retracking method, and the true surface is tie surface (b) with correlation length L=8km as shown in fig.5.1. The RMS error is calculated from the bias in the along-track distance. In the figure, the RMS error of the retracked surface which is determined from the firsi leading edge of the echoes is indicated by the circled symbols, "o"; the re tricked surface from the second leading edge is indicated by the plus symbols, '+".

The echoes returned from surface(b) are subject to speckle-noise and topographic distortion. Som etim es, the features of the echoes cannot be easily distinguished as to whether they are single-ramp or double-ramp in origin. Hence, all the echoes will also be fitted into a double-ramp model. The curve indicated by the "-h" line shown in fig.5.8 is the RMS error of the retracked surface which is cetermined by

the second leading edge of the echoes. When the retracked heights from the second leading edge coincide with the retracked heights from the first leading edge, this implies the echoes are single-ramp in origin. It can be seen in fig.5.8 that the surface height is neither at the first nor second leading edge of the echo. Such a high bias as shown in fig.5.8 verifies that the relationship between the surface height and the echo profile assumed in the retracking method becomes invalid when the surface correlation length is less than the antenna footprint.

We present in fig.5.9 a comparison of a one dimensional profile of the retracked surface and the true surface. The true surface profile is extracted from surface (b) shown in fig.5.1 and the location of this profile is at an along-track distance of about 18km. Fig.5.9a shows the retracked heights determined from the first leading edge of the echo. The true surface height is indicated by the solid line and the retracked heights are indicated by the circled line. Fig.5.9b shows the retracked heights from the second leading edge of the echo which is drawn in "-I-" symbols. The bias of the retracked surface consists of two components. The noise-like component is due to the speckle noise. As said earlier, this noise in the echoes is uncorrelated. This gives rise to uncorrelated noisy features in the retracked surface. Another bias component is due to the topographic effect in which the echo profile is distorted, and the surface height departs from the leading edge of the echo.

In fig.5.8, a sudden rise in the RMS error is seen along the across-track distance between 80-100km. The high bias in this region is also seen in the single profile of the retracked surface in fig.5.9. This high bias is caused by the rough surface undulations in the along-track distance, as shown in fig.5.10. The figure illustrates one-dimensional surface undulations with the along-track distance at an across-track location of 95km. For ease of comparison, the diagram is drawn on the same scale as in fig.5.9. It can be seen in fig.5.10 that the along-track distance changes in the vertical by 100m over a horizontal distance of 7km. The altimeter tends to lock onto the hill in that region which causes a forward shift of the leading edge of the echoes in the vicinity. In consequence, the re tracked surface under-estimates the depth of the valley (80-100km) shown in fig.5.9a, and gives rise to a high RMS error

-2 0 - 3 0 - 4 0 0 20 40 6 0 8 0 100 120 A c r o ss-tr a c k location in km -g - 1 0 -20 - 3 0 - 4 0 8 0 0 20 40 6 0 100 120 A c r o s s-tr a c k location in km

Fig.5.9 Comparison of an one dimensional profile of the retracked surface and the true surface. The true surface is at 40km of the along-track distance of surface (b) with L=8km as shown in fig.5.1. The re tracked surface profile is determined from (a) the first leading edge of the echoes; (b) the second leading edge of the echoes.

near that region, as shown in fig.5.8.