Co-registration process

After co-registering the 501 days of SAR data available for the test site of the Sion Valley it has been observed that the typical values of shift displacement according to (5.15) are dshifttyp = 2 bins, whereas maximum values are dshiftmax = 10 bins. Figure 5.11 shows an

example of the shift displacement values for January 15th, 2004.

Fig. 5.11. Shift displacement values in zero-padded azimuth bins for January 15th_{, 2004, function of time.} The typical and maximum shift displacement values entail an azimuth rotation of 1.6 m and 8.3 m respectively, which are under the cross-range resolution cell of the system (see Section 4.2.3). At 2000 m range, the equivalent typical and maximum azimuth rotation are of 0.045 deg and 0.238 deg approximately.

Even if the co-registration technique proposed in 5.3.2 accounts for the rotation of the scatterer but not for its associated phase, according to the results obtained the effects of this step on the interferometric phase for the snow height retrieval have been found to be minimal. In addition, the spatial averaging applied in the computation of the coherence -3×3 pixels, see Section 5.3.3 and (2.21)- and in the computation of the interferometric phase -20×20 pixels, see Section 5.3.4- minimizes even more the effects of the co- registration step.

Figure 5.12 shows two examples of the coherence magnitude improvement obtained after the co-registration process. The plots correspond to the same day, January the 15th, 2004. Figure 5.12-a shows the results in the test point 1, where the coherence of each of the 20×20 pixels of the area under study is plotted for all the interferograms computed that day. Similarly, Figure 5.12-b shows the same results for the test point 2.

a) b)

Fig. 5.12. Coherence improvement after the co-registration process for a) test point 1; and b) test point 2.

The results in Figure 5.12 have different interpretations. First of all, as shown on the axes labels, after the co-registration process 43% of the pixels improve their coherence while 42% degrade it in the test point 1. In the test point 2 the effects of the co-registration process are a bit more notable, with a 47% of pixels that improve their coherence and a 38% that degrade it. The rest of pixels up to the 100% maintain their coherence magnitude unmodified. These results confirm the low impact on the co-registration process as already derived from the maximum shift displacements obtained. It is also observed that the co- registration process introduces a degradation of the coherence in an important number of the pixels in the image. This is due to the fact that the proposed co-registration method statistically finds the best shift displacement over the whole radar image by compressing the whole azimuth and range dimensions to a single displacement value according to (5.15) and this does not guarantee an improvement on the coherence on every single pixel. The trade-off between the pixels’ coherence degradation and improvement, hence, needs to be considered and the co-registration process should not be applied indiscriminately, but only when decorrelation degrades substantially the interferometric information and there is no better alternative to improve the imagery. As mentioned, this is not the case of the data

acquired by the LISA instrument in the Sion Valley, particularly because of the high image acquisition rate that naturally minimizes temporal decorrelation.

Notably, the coherence magnitude level observed over the whole day for both test points is above 0.7. In the first case the coherence for the selected pixels is mainly distributed above 0.6 while on the second test point it is more concentrated above 0.8. These results confirm, in line with those obtained for most of the days analyzed, the high phase stability of the LISA instrument and the feasibility of using the interferometric phase for retrieving the snow cover depth. The coherence magnitude is stably high, permitting the use of interferometric techniques even under snow fall conditions, as shown in the ground-truth information of Figure 5.13.

Fig. 5.13. Meteorological conditions for January 15th_{, 2004, provided by the automatic meteorological}

station of Donin Du Jour function of time: snow depth, temperature of air and relative humidity.

Nevertheless, even if both test points are on the same slope and separated only some 1300 m, the spatial and temporal variability on the coherences obtained evidence the different atmospheric conditions to which each test area is subject to. Unfortunately this phenomenon entails a very difficult solution. Therefore, temporal and spatial averaging, when available, are shown to be the most effective tools in order to improve the coherence. GB-SAR systems, contrary to satellite- and air-borne sensors, are optimal instruments in terms of image acquisition rate, instrumental for effectively applying temporal averaging techniques.

5.4.4. Snow height retrieval

The snow height retrieval technique presented in the preceding sections has been applied to the data available on the months of December, January, February and March of the three years of field campaign in the Sion Valley. The full table of results can be consulted in Annex F, where the calibration parameters and the mean and standard

deviation of the differences between the ground-truth snow depth and that retrieved with DInSAR are tabulated for each of the two test points analyzed on a daily basis.

Note that colder months were selected for the assessment of the snow height retrieval technique so that the dry snow model is valid. In fact the plots presented together with the snow height estimates include, as do those in Figure 5.14, an upper graphic entitled “Quality indicators” that quantifies the quality of the snow height retrieval technique by means of 3 indicators:

a) #(pixThr)/#(pixTot) is the ratio between the number of pixels with coherence magnitude above the defined threshold (0.7) and the total number o pixels in the test area (20×20 pixels as stated in Section 5.3.4).

b) avg(coh) is the averaged coherence magnitude in the 20×20 pixels test area of all pixels above the threshold defined (Thr = 0.7).

c) Dry snow is a binary indicator that equals to 1 when the air temperature is under 0 °C and, thus, the snow cover can be considered mostly dry.

All three indicators range from 0 to 1, 0 being a low confidence in the retrieved snow depth because one or more constraints are not fulfilled and 1 high probability of success.

The main constraints on the application of this technique are, hence, summarized on the three points above: sufficient number of pixels with a high coherence magnitude in order to have an adequate SNR in the interferometric phase; sufficient number of pixels in order to effectively increase the SNR of the interferometric phase by spatial averaging; and dry snow conditions on the area monitored.

Fig. 5.14. Snow depth retrieval for January 20th_{, 2004, function of time. a) Test point 1; and b) Test point 2.} Figure 5.14 presents the results of the snow height retrieval by DInSAR for January 20th, 2004, in both test points. As stated in 5.3.6, the calibration parameters α and β have been found by fitting the ground-truth snow height evolution over the whole day to the cumulative interferometric phase cum( )

s t

ϕ

Δ . The bottom plots show how the estimated snow cover depth matches the ground-truth heights in both test points. According to the tables in Annex F, the mean and standard deviation of the differences between ground-

truth and estimated values of snow height are 1.3 cm and 1.2 cm respectively for the test point 1 and 1.5 cm and 1.4 cm, respectively, for the test point 2.

Note on the quality indicators that the dry snow condition is satisfied for the whole day. Regarding the coherence of the pixels selected for spatial averaging of the interferometric phase on both test points the values are well over 0.8, which guarantees a high SNR in the interferometric phase. Regarding the ratio of pixels with coherence above the threshold, instead, significant differences can be appreciated depending on the test point. In the first test point, Figure 5.14-a, the ratio indicates that the number of high coherent pixels in the test rectangle is of 60% on several instants of time, with a mean value of 70-80% for the whole day. In the second test point instead, Figure 5.14-b, during the whole day the coherence is over the threshold in 90% of the pixels of the test area.

The ratio of pixels with coherence above the threshold has a double interpretation. First of all, 60% of pixels with coherence magnitude above 0.7 in a 20×20 pixels rectangle means that the spatial averaging will be carried out over some 240 pixels, which is a representative number of pixels to expect a substantial improvement on the interferometric phase SNR. Hence, the snow depth retrieval technique is expected to work properly under these circumstances. Secondly, the fact that coherence values are so different in both test points confirms that different atmospheric phenomena in the form of temperature gradients, precipitation, wind conditions, etc. in each test point. This fact was already noticed on Figure 5.12 but here it is repeated again since this is an extremely important issue that needs to be considered when comparing the retrieved snow cover depth with ground-truth data: ground-truth data for the complete assessment of this technique should be available in the exact location of the test points and not 2 km away from them. Differences on the estimates of the snow height are, thus, expected not only between the test points and the ground-truth data coming from the meteorological station, but also between the test points themselves. The causes for these differences, as stated, are the different atmospheric conditions that affect each point at local scale and to which the interferometric phase is highly sensitive.

Unfortunately no ground-truth information on the snow cover depth on any point of the slope covered by the radar FOV is available. Actually, the traditional mean of remotely measuring the snow height on areas where no meteorological station is present is by visual observation of the horizontal marks painted on a stick driven in the ground. This methodology is conditional on the accessibility to the areas of interest and by the stability of the stick, which may fall down because of the wind or avalanches.

Regarding the calibration parameters they can be read on the titles of the snow height plots under the [cal] label. In Figure 5.14-a α = 1.63 cm/rad and β = 295.8 cm while in Figure 5.14-b it can be read that α = 1.81 cm/rad and again β = 295.8 cm. As already analyzed in Section 5.4.2 the α parameter fits in the expected range for both test points, and very similar values are obtained at each of the test points, so these are additional qualitative proofs that show that the technique is correctly yielding the snow cover depth. According to the plot in Figure 5.10, the real part of the permittivity is approximately ε' = 1.20 in the first test point and ε' = 1.20 also on the second one. These permittivities are translated to the snow density ρs = 0.12 g/cm3 according to (5.2) and in agreement with the data

reported in [52].

Figure 5.15 shows similar results for both test points but in this occasion for a period of three consecutive days, from January the 18th to the 20th, 2005. Note on the upper plots that the #(pixThr)/#(pixTot) ratio is equal to zero at the first image of every day since the

differential interferometric phase and the quality indicators are computed on a daily basis and the first instantaneous value of every day is initialized to zero. The cumulative interferometric phase, derived as shown in Figure 5.5, does not present these discontinuities among different periods of time. Note also that the horizontal axis is labelled in these sequences DDTHH, where DD stands for the day in the month and HH for the hour in 24h format of the corresponding datum.

Fig. 5.15. Snow depth retrieval for January 18th_-20th_{, 2005 in a) test point 1; and b) test point 2.} The quality indicators for the three days time series of snow cover depth show excellent values on both test points. The second test point (Figure 5.15-b), though, shows again a slight higher coherence magnitude and a higher proportion of high coherent pixels on the test rectangle than the first test point (Figure 5.15-a). This could seem contradictory since the second test point according to Table 5.1 is at a higher elevation (2621 m versus 1942 m) and has a more pronounced inclination (36 deg versus 18 deg). In addition the second test point is very close to the mountain crest, so more exposed in theory to winds coming from the other side of the mountain that can also carry loose snow particles.

Even if both curves of the estimated snow height may appear very similar, the best fitted calibration parameter α is equal to 1.24 cm/rad on the first test point and 0.96 cm/rad on the second one. This difference is not surprising since the parameter α, as defined in (5.5), depends on the incidence angle θi and on the dry snow density which are different in

every test point. According to the Figure 5.10 the real part of the permittivity is approximately ε' = 1.30 in the first test point and ε' = 1.45 on the second one. These permittivities are translated to the snow densities ρs = 0.18 g/cm3 and ρs = 0.26 g/cm3

respectively according to (5.2), which represents 44% difference. Contrary to what was observed in Figure 5.14 where the snow densities of both test points were practically identical at the same instant of time, in this example the densities retrieved are different by 44%. These results confirm the fact that the snow pack changes at local scale because of the topography and also because of the local atmospheric conditions.

Similar results are presented in Figure 5.16 for the winter 2005-2006 this time with a series of four consecutive days: from February 18th to 21st, 2006. The quality indicators present high values for all the days in both test sites. Nevertheless, the curves of the snow height estimated with DInSAR slightly diverge from one test point to the other one. The highest difference is found during the first day of the second test point. Even if the cumulative interferometric phase increases as does the ground-truth snow height, the α

factor estimated for the whole period is smaller than that required to accurately estimate the snow height absolute values during the first day.

Fig. 5.16. Snow depth retrieval for February 18th-21st, 2006 in a) test point 1; and b) test point 2.

Figure 5.17 confirms this point when estimating the α parameter on a daily basis instead on the longer period of 4 days in the example above. In fact the estimated snow heights on both test points fit perfectly the ground-truth data, but the calibration parameters are significantly different: α = 2.65 cm/rad in the first test point while α = 4.20 cm/rad on the second one. These calibration parameters translate into almost identical permittivities, that is ε' = 1.10 in the first test point and ε' = 1.08 in the second one, which indicates similar snow conditions on both test points for that day. When trying to use a single calibration parameter α for a longer period, results show that the snow conditions are kept approximately constant in the first test point (Figure 5.16-a) and the same single calibration parameter can be used during all four days. On the second test point (Figure 5.16-b), instead, the snow density varies during the period analyzed and the use of a single calibration parameter during the whole time series provides a slightly poorer accuracy even if the quality indicators are higher than in the first test point.

Since no ground-truth data is available for the snow height at the precise location of the test points, it is impossible to determine whether the calibration parameter α cannot be extended to longer periods. The discrepancies may be because of changes in the snow cover properties or because the calibration parameters may have been properly estimated but the ground-truth snow depth curve that should be used in the assessment has not been measured in the right place.