Estilo de liderazgo que predomina en los directores de las instituciones educativas

The on-board filtering has been described in §2.2.4 (2.4, 2.44). The purpose of this process is to average a number of return echoes N in order to reduce the echo fluctuation due to speckle noise. Integrating N echoes will reduce the speckled variance by a factor of N. However, when the number N is too large, the filtering will

lose many details of the surface and, in consequence, increase the bias of the measurement. In this section, we shall present examples to observe how the parameter N affects the accuracy of the measurement.

We present in fig.4.8 the a posteriori error as a function of the parameter N. The error curve is calculated from the best linear estimation (3.4, 3.6) in which only 5 altimeter echoes are used. The surface parameters of this curve are L=8km and (jg=20m. It can be seen in the figure that the error decreases rapidly below N=3. Afterwards, the error curve increases slowly in comparison with the earlier part of the curve. The rapid decrease of the error shows that the reduction of the speckle-noise level in the echo has improved the accuracy of the measurement. When the error curve reaches its minimum, it then slowly increases. This illustrates the negative effect of the on-board filtering - losing details of the surface.

For a given number N, the loss of surface detail is relative to the horizontal scale of the surface undulations - a smoother surface will not lose as much surface information as a rougher surface. Hence, an increased rate of the bias after reaching the minimum point largely depends on the surface correlation length. In order to verify this point, fig.4.9 and fig.4.10 are presented. Fig.4.9 has a correlation length 2.5km and it shows that the increased rate of the bias is more rapid than the increased rate from the 8km correlation length shown in fig.4.8. In contrast, fig.4.10 has a correlation length of 20km which shows the lowest rising rate of the bias. The surface in this figure is smooth enough that the surface detail lost during the noise filtering process is too small to have an effect on the measurement.

We have found that the multi-channel processing method is relatively immune to speckle noise in comparison with the present re tracking method. This is because each convolution between the echoes and the estimator in the process of the multi­ channel processing is, to a certain extent, similar to the integration of the echoes temporally and spatially, which acts Eke a noise reduction process. This will be further verified when the simulation of the surface retrieval process is carried out in chapters 5 and 6. However, at this stage, this immunity is also reflected in fig.4.8, fig.4.9 and fig.4.10, where the a posteriori error has reached its minimum

7.6 7 . 5 7 . 4 7 . 3 m 7 . 2 6 . 9 6 . 7 6.6 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 N um ber of e c h o e s a v e ra g e d o n -b o a r d N 4 0 1 8 0 200 20

Fig.4.8 The a posteriori error as a function of param eter N. The error is calculated from the best-linear estimation (3.4, 3.6) in which only 5 echoes are used. The surface parameters are L=8km and Og=20m.

1 6 . 9 1 6 . 7 (D <U E c O 1 6 . 6 o3 CO 2 CO 1 6 . 5 1 6 . 4 1 6 . 3 1 8 0 200 1 4 0 ■board N 1 6 0 6 0 8 0 1 0 0 N um ber of e c h o e s a v e ra g e d o n - b o a r d N 120 4 0

Fig.4.9 The a posteriori error as a function of param eter N. The error is calculated from the best linear estimation (3.4, 3.6) in which only 5 echoes are used. The surface parameters are L=2.5km and Gg=20m.

5.5 o3 4 . 5 3 . 5 4 0 100 120 N um ber of e c h o e s a v e ra g e d o n -b o a r d N 6 0 Num ber 1 4 0 •board N 1 6 0 1 8 0 200 20

F ig .4 .10 The a posteriori error as a function of parameter N. The error is calculated from the best linear estimation (3.4, 3.6) where only 5 echoes are used. The surface parameters are L=20km and (jg=20m.

only when N=3. In fig.4.8, only 5 echoes are used in the estimation for calculating the a po steriori error. However, we believe that when the num ber o f echoes is increased in the estimation, the on-board filtering may not be necessary for the multi­ channel processing method, because the method has enough samples to filter out the speckle noise itself. We shall re-visit this point in §6.3.

4.6 Chapter summary.

Ice surfaces will all have different horizontal and vertical scales of height variatio ns. These two scales have opposite effects on the accuracy of the measurement. The bias increases with the vertical scale of variation Og and decreases with the surface correlation length L.

slope. In addition, a slope which is perpendicular to the selected sequence of echoes shows a higher bias than a slope parallel with the selected sequence.

When echoes are selected as an input to the estimation, the spatial and temporal patterns of these echoes have effects on the accuracy of the measurement. Given a fixed number of echoes, the spatial density and coverage of the echoes can be traded- off. The spatial density of the echoes can improve the accuracy of the measurement provided that the data extends over twice the surface correlation length. Once this criterion is met, increasing the spatial coverage of data will not improve the accuracy of the measurement. We have also found that when data in the across-track direction is not included in the best linear estimation, a further increase of the echoes in the along- track direction will not effectively improve the accuracy of the measurement

In general, the surface topography has far larger height variation than the oceans. One of the recently launched satellite altimeters, ERS-1, is equipped with an additional operating mode which is specifically designed for measuring the ice sheets. This ice mode has a 12ns temporal interval as compared with the ocean mode of 3ns interval. The results show that the accuracy of the measurement of surface topography from 12ns interval is better than from 3ns interval.

The speckle noise is currently reduced by integrating N echoes. We have found that the multi-channel processing method is a natural noise filter as far as the speckle noise is concerned. Hence, the number N required in this method is far less than is required by the present re tracking method.

Chapter 5