Propiedades tecnofuncionales de las proteínas

We have learnt that the bias of the re tracked surfaces is due to the speckle noise and topographic effects. The effect of surface topography on the accuracy of the measurement can be easily observed from table.5.1 because three surfaces of different

horizontal scales have been retrieved. However, the effect of the speckle noise on the measurement has not been clearly examined. Hence, in this section, the speckle noise level in the altimeter echoes will be varied and the surface retrieval process will be repeated.

In the above sections, the parameter N=50 (2.42) is used to reduce the speckle noise. Echoes with large speckle noise, N=5, and speckle-free echoes are used for the surface retrieval process in this section. The filtering process of the echoes here is the approximation of the on-board filtering which has been described in §.5.2. Losing surface information due to the filtering has been neglected so far. Two surfaces are selected to recover in this section. They are surface (a) of L=25km and surface (b) of L=8km shown in fig.5.1. The RMS error of the retrieved surfaces from the retracking method by processing the noisy speckled echoes and speckle-free echoes will be presented here.

I 1

Fig.5.13 Samples of speckled and speckle-free altimeter echoes. The echo indicated by the solid curve is the speckled altimeter echo with parameter N=5, the echo indicated by the dotted curve is the speckle-free echo and the straight solid line is the surface height relative to the range window. Echoes (a) are returned from surface (a); and echoes (b) are returned from surface (b). The surfaces are illustrated in fig.5.1.

The speckled echoes for N=5 and the speckle-free echoes are presented in fig.5.13. The speckled echoes for N=5 are shown by the solid line and the speckle- free echoes are shown by the dotted line. The straight line represents the location of the surface height relative to the echo. In this figure, we can easily observe how the

speckle noise distorts the echo profile from its mean value. We have shown in fig.5.4 that the speckled altimeter echoes for N=50 the speckled fluctuation is obviously less than for the speckled echoes with N=5, but the noisy component in the echoes with N=50 is still apparent in comparison to the speckle-free echoes in fig.5.13.

Table.5.2 compares the RMS errors of two retrieved surfaces by retracking the altimeter echoes from three different speckle noise levels. Surface (a) has large correlation length L=25km, the altimeter echoes from this surface are simple ocean­ like with a single ramp in the earlier part of the echo (see fig.5.4a). It can be seen from table.5.2 that the RMS error of surface (a) has increased rapidly when the speckle noise increases. This phenomenon can be explained in fig.5.14. Two speckled echoes with N=5 are shown in this figure. The echo parameter function has a smooth profile. The retracked height determined by the parameter model (2.62) is indicated by the straight dotted line, and the true surface height is indicated by the straight solid line. It can be seen that the re tracked heights depart from the half power point of the leading

Retracking method N=5 N=50 Speckle-free 1st rarap^^”^^^ ^„,.^^nd rami 1st r a m p ^ ^ ^^^^"^"2nd ram 1st ram p"'"^ ram; Surface(a) CJs=20m, L=25km 17.58pT 3 . 9 4 r n / ^ Surface(b) as=20m. 1 6 .2 5 m / ^ 1 5 . 2 4 y / ^ 14.89m % ^ L=8km _{[5.05m [5.63m}

Table.5.2 The RMS error of the retracked surfaces obtained from the re tracking method. The first column shows the RMS error by processing the echoes with speckle noise level N=5; the second column with speckle noise level N=50; and the third column is the RMS error by processing the speckle-free echoes.

I ---- T7\--- n 1 I 0 .5 CO .E 0 0 .5 0 - 5 0 0 5 0 - 5 0 0 50 R a n g e in metre

Fig.5.14 Speckled altim eter echoes and the echo param eter function after the least square fit of the echoes into the single-ramp model in the retracking method. The straight solid line is the true surface height and the dotted line is the retracked height.

edge of the param eter model. This departure increases when the echo distortion increases and is shown in fig.5.14.

Wlien the speckle noise level decreases, the RMS error in retrieving surface (a) decreases, as shown in table.5.2. The RMS error of surface (a) from retracking the speckle-free echoes is 2.8m. This has confirmed that the speckle noise level of N=50 has caused about Im height bias in the m easurem ent, and topographic effect of L=25km and the range resolution has caused about 2.8m of height bias.

The distortion of the echo profile is mainly due to the speckle noise and the topographic effect. When the surface topography is relatively smooth and the speckle noise level is moderate, the bias of the re tracked surface is caused equally by both effects. H owever, when the surface has rougher undulations, the bias w ill be dominated by the topographic effect. When the echoes have been seriously distorted by the surface topography, a further increase or decrease in the distortion caused by the speckle noise will not make any significant difference. This point can be easily verified in table.5.2. Here, the retracked surfaces with L=8km from the echoes with three different levels of speckle noise do not show significant differences in their RMS error, w hereas the RMS errors o f the retracked surfaces of L=25km show a considerable difference from the three different speckle noise levels.