PROBLEMS AND SOLUTIONS FOR INSAR DIGITAL ELEVATION MODEL GENERATION OF MOUNTAINOUS TERRAIN

M. Eineder

German Aerospace Center (DLR), Oberpfaffenhofen, D-82234 Wessling, Germany, Email: Michael.Eineder@dlr.de

ABSTRACT

During the last decade, the techniques to generate digital elevation models (DEM) from SAR interferometry have been demonstrated and refined to a quasi-operational status using data from the ERS tandem mission. With this experience and an improved single-pass system concept, data from the Shuttle Radar Topography Mission (SRTM) acquired in 2000 have been used to produce a global DEM with unprecedented quality. However, under the extreme viewing conditions in mountainous terrain both ERS and SRTM suffer from or even fail due to the radar specific layover and shadow effect that leaves significant areas uncovered and poses severe problems to phase unwrapping. The paper quantifies the areas leading to layover and shadow, and shows innovative ways to overcome shadow and improve phase unwrapping in general. The paper is organized in three major sections. Firstly, the problem to map slopes is addressed in a simplified statistical way. Strategies to optimize the incidence angle for single and multiple observations are proposed. Secondly, a new algorithm is presented that makes the best from shadow by actively using it to help phase unwrapping. Thirdly, an outlook on the use of delta-k interferometry for phase unwrapping is given. The paper aims to improve the understanding of the mapping geometry of radar systems and the data currently available and to improve the concepts of future systems and missions.

range

azimuth

Fig. 1: Shadow areas visible as dark regions in an SRTM X-SAR intensity image of a mountain in Ötztal / Austria.

Fig. 2: The interferometric phase in the shadow areas is random noise. (SRTM X-SAR, Ötztal / Austria)

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Proc. of FRINGE 2003 Workshop, Frascati, Italy,1 – 5 December 2003 (ESA SP-550, June 2004) 33_eineder

1. INTRODUCTION

The generation of digital elevation models (DEMs) from interferometric SAR data has become an important application of SAR technology. Compared to conventional optical stereo techniques SAR interferometry is particularly attractive because it works independent from scene contrast and illumination and under almost all weather conditions. However, when it comes to mapping mountains with high slopes and large altitude variations then SAR interferometry is confronted with specific problems that are not yet completely solved. Shadow and layover effects prevent the radar from seeing a large percentage of mountainous terrain. Even if these hidden areas are not of interest, the resulting phase unwrapping problems may cause large height errors in the visible areas. and demonstrate that shadow causes interferometric phase noise in SRTM X-SAR data with a rather flat incidence angle of 54.5°. In contrast, ERS-1 and ERS-2 look rather steeply with 23° leading to even larger areas of layover as shown in and . Because of the viewing geometry the layover areas are compressed in slant range geometry and become much larger when transformed to ground range.

Fig. 1 Fig. 2

Fig. 3 Fig. 4

range

azimuth +π

-πFig. 3: Layover areas visible as bright areas in an ERS intensity image of a mountain in Ötztal / Austria.

Fig. 4: The interferometric phase in the layover areas is noise or even ambiguous with reverse fringe frequency. (ERS, Ötztal / Austria).

2. WHAT THE RADAR CAN “SEE”

Fig. 5 illustrates the viewing geometry of a SAR system. The antenna moves with velocity vector Vr

and looks in

direction Lr

onto a terrain facet characterized by the normal vector Nr

. The vector Mr

is defined orthogonal to Lr

and Vr

, i.e., rr

. Three conditions must be met for successful imaging. Firstly, the facet must be visible, i.e., tilted towards the radar system:

V×LMr

=

. (1) 0<⋅ NLrr

If this condition is not fulfilled, the facet is viewed from the backside and must be hidden by some other facet because the SAR antenna is located outside of the body of the earth. Secondly, the facet must be upright in range direction:

, (2) 0>⋅ NMrr

otherwise the facet is imaged reversely and will be “laid over” by another facet when the slope decreases again with increasing range. Thirdly, the facet must not be hidden by another facet. This condition can not be described by the local slope alone. Ray tracing must be performed to secure this condition as done in ]. Here, this effect is neglected for simplicity even if it accounts for a significant percentage of blind areas.

[4

y Nr

Lr

x

z

Mr

Vr

aspect

slope

SAR antenna

Fig. 5: Schematic viewing geometry of a SAR. Fig. 6: A dome contains all possible combinations of aspect and slope. The visible areas are marked in light gray.

Fig. 6

In geophysical applications the slope and aspect angles are generally used instead of the normal vector. Slope is defined as an angle between 0° and 90° measured between the horizontal plane and the surface and aspect is defined as the orientation angle of the slope measured clockwise with respect to north direction. A dome as shown in contains all relevant combinations of aspect and slope conveniently arranged in a polar diagram. shows a polar diagram of the eye-shaped combinations of slope and aspect angles that are visible to a SAR looking with 45° incidence angle to the right and flying northwards.

Fig. 7

Fig. 7: Polar diagram of the aspect and slope angle combinations visible to a radar flying northward and looking with an incidence angle of 45°.

shadow slopes

layover

slopes

useful slopes

aspect

slope

3. DISTRIBUTION OF SLOPES IN MOUNTAINOUS TERRAIN

In order to assess quantitatively the percentage of the surface that can not be mapped by a single SAR observation, knowledge of the distribution of the slopes is required. Two test areas with slightly different characteristics are examined for that purpose. Firstly, the valley of the Rhine and Tessin in Switzerland. Secondly, the Ötztal valley in Austria. The Switzerland site is a larger area with moderate to rough alpine topography. It is assumed to represent the majority of mountainous regions in the world. Ötztal is an extremely rugged area representative for the most critical regions of the world. Switzerland test area: For this area shown in a reference DEM with 100 m spacing is available. The area extends between 8030’ to 100 East and 46030’ to 470 North. North.

Fig. 8

Fig. 9Fig. 9

g. 10

g. 10 Fig. 11Fig. 11

*Rhine *Chur

*Tiefencastel

Fig. 8: Shaded view of Switzerland test area. Fig. 9: Shaded view of Ötztal test area-

Fig. 10: Slope PDF of Switzerland test area. 99 % of the slopes are smaller than 52°.

Fig. 11: Slope PDF of Ötztal test area. 99 % of slopes are smaller than 55°.

Ötztal test area: The Ötztal site shown in is selected because it contains some extremely rugged mountains and because it is very well known from other glaciological and hydrological studies performed at the University of Innsbruck. The available DEM covers the area between 10°30’ and 11°0’ East and from 46°45’ to 47° North covering an area of about 40 by 25 square kilometers. The DEM is regularly sampled at intervals of 12.5 m and quantized at 1 m levels. It has been generated from several aerial photos taken between 1960 and 1970. Unfortunately, the accuracy of this DEM is not completely known. However, high resolution DEMs of such areas are rare and this DEM proved to be a valuable source for this study. The high quality could be confirmed in ].

Ötztal test area: The Ötztal site shown in is selected because it contains some extremely rugged mountains and because it is very well known from other glaciological and hydrological studies performed at the University of Innsbruck. The available DEM covers the area between 10°30’ and 11°0’ East and from 46°45’ to 47° North covering an area of about 40 by 25 square kilometers. The DEM is regularly sampled at intervals of 12.5 m and quantized at 1 m levels. It has been generated from several aerial photos taken between 1960 and 1970. Unfortunately, the accuracy of this DEM is not completely known. However, high resolution DEMs of such areas are rare and this DEM proved to be a valuable source for this study. The high quality could be confirmed in ]. [3[3 From each DEM the probability distribution function (PDF) of slope and aspect is estimated using the 8 directions between adjacent pixels as described in ]. The 2-dimensional PDF is rather rough because of DEM quantization and other non-isotropic effects caused by DEM generation. Therefore the PDF is averaged over all aspect values assuming an isotropic distribution. Fi

and show the estimated slope PFDs for both test areas.

From each DEM the probability distribution function (PDF) of slope and aspect is estimated using the 8 directions between adjacent pixels as described in ]. The 2-dimensional PDF is rather rough because of DEM quantization and other non-isotropic effects caused by DEM generation. Therefore the PDF is averaged over all aspect values assuming an isotropic distribution. Fi

and show the estimated slope PFDs for both test areas.

[1[1

90 %

99 % 99.9 %

90 % 99 %

99.9 %

°

4. OPTIMIZATION OF A SINGLE SAR ACQUISITION WITH RESPECT TO SLOPE

e distribution, the optimal SAR

where

Knowing the eye-shaped mask of visible slopes in the polar PDF from Fig. 7 and the actual slopincidence angle can be estimated by maximizing the coverage integral

∫∫ ⋅= βαβαβα ddmaskPDFc ),(),( , (3)

α and β

exampl of ge oded radar images with varying ce angles and visualize that an ENVISAT/ASAR beam 6 acquisition with 41° reveals much less layover and shadow distortions than those of ERS and SRTM/X-SAR.

exampl of ge oded radar images with varying ce angles and visualize that an ENVISAT/ASAR beam 6 acquisition with 41° reveals much less layover and shadow distortions than those of ERS and SRTM/X-SAR.

are the aspect and slope angles. Fig ce angle. Note that the curve is an upper bound as it does not include the areas shaded or laid over by other facets. Fig. 13 to Fig. 15 show

es oc

ce angle. Note that the curve is an upper bound as it does not include the areas shaded or laid over by other facets. Fig. 13 to Fig. 15 show

es oc

. 12 shows that the maximum coverage is achieved at 45° incidenen

inciden inciden

Fig. 12:: Achievable coverage of alpine terrain with incidence angles between 10° and 75°.

ASAR 41°

. OPTIM AR ACQUISITION W O SLOPE

Fig. 13: Geocoded ERS SAR image of Ötztal area.

ERS 23° Layover

Fig. 14: Geocoded ENVISAT/ASAR image of Ötztal area.

IZATION OF MULTIPLE S ITH RESPECT T

Assuming that data more than one acquisition can be combined to achieve maximum coverage, it may be favorable to use a ) at slightly steeper incidence

where s the logical set union of the obser e

ationcircle marking 99% of all slopes can be covered with ERS date if left and right looking or ascending and descending observations

Fig. 15: Geocoded SRTM/X-SAR image of Ötztal area.

SRTM 54° Shadow

5

slightly different incidence angle than 45° in order to obtain a better signal to noise ratio (SNRangles or to get a better total coverage of the PDF. Several acquisitions can be optimized similar to (3) by optimizing the integral

∫∫ ⋅ ββαβα dadmaskPDF U ),(),( , (4) i

i

vation maps. Figures Fig. 16 to Fig. 18 show a number of reasonablUi

i

combin s of two pass slope masks of existing sensors even if left looki for ypothetic. It can be seen that the

are combined. However, it is not completely covered by the combination of ascending and descending SRTM data.

ng mode ERS is h

Fig. 16: Slope mask of (virtual) left and right looking ERS ascending passes f r

Fig. 17: Slope mask of right looking ascending and descending passes for

Fig. 18: Slope mask of ascending and descending SRTM left looking pass s

It proposed metho bound for the enient and illustrative method to assess the viewing geometry of different radar observations.

e appropriate incidence angle for a certain rrain type. However the data from ERS and SRTM is acquired with a fixed, non optimal angle. In the following a method is

. This random phase may lead to and phase consistency problems.

α

oθ=23°. Coverage: 99.98 %.

is emphasized again that the

θ=23°. Coverage: 99.98%.

d is not precise but an upper

ewith θ=54°. Coverage: 99.7 %.

achievable coverage. It is a conv

With ENVISAT/ASAR there is the possibility to optimize the coverage by selecting thtepresented that at least allows to overcome the destructive phase noise in shadow regions. 6. A TECHNIQUE TO HANDLE RADAR SHADOW IN SAR INTERFEROMETRY

Shadow in SAR data contains no echo signal and hence the interferometric phase is randomsevere phase unwrapping problems and consequently, even if masked out, to coverage Understanding that the interferometric phase gradient along the shadow line is zero helps phase unwrapping significantly. Firstly, the shadow area is no more a nuisance but actively helps the phase unwrapping algorithm to “climb” mountains from the shadowed backside. Secondly, the shadowed areas in the DEM can at least be filled with height values along the shadow line that are more reasonable than pure noise. The algorithm is described in detail in [5] and shortly illustrated in Fig. 19. Antenna 2 The eleva n angle along the shadow onst

Antenna 1

ζ(r) r1

r2

B⊥

r

ant:

tio line is c

)()( 21 rr ζζ = , (5) and hence the in e phase

radient is zero.

nderstood by using the formula for the fringe equency from [7]:

terferometric phase is constant, i.e., thg This can also be ufr

( ) 0tan2

≈−αζλr

−=∆ ⊥cBf , (6)

because °−= 90ζα (7).

Fig. 19: Interferometric shadow reconstruction.

n in Fig. 20 xtreme slopes of Nanga Parbat (8125 m) could only be nwrapped correctly after correction of the phase gradients in the shadow regions.

An application example for the algorithm is show . The eu

Fig. 20: Perspective view Nanga Parbat mountain (8125 m) from SRTM/X-SAR data. Despite the large shadow areas the phase of this steep terrain could be recovered by interferometric shadow reconstruction technique. The linear geometric interpolation

ledge of the integer phase ambiguity requires phase unwrapping which gets more ifficult as the baseline is increased in order to increase accuracy. A solution to avoid phase unwrapping by direct estimation of

PING

EM reconstruction is inherently limited by the phase quency operation. The fundamentals of an approach to

2 with SRTM -SAR data. Due to the rather small usable bandwidth B/2=4 MHz, this configuration is equivalent to an additional wavelength of

along the dark shadow areas is clearly visible. Still, DEM reconstruction without a-priori knowdthe absolute phase for each pixel could be delta-k interferometry. 7. USING DELTA-K TECHNIQUE FOR PHASE UNWRAP

Using an interferometric SAR for precise ranging as in the case of Dambiguity introduced by the small bandwidth and by the single carrier freovercome this limitation have been proposed in [8], [9], [10] by exploiting the frequency dispersion available in the range bandwidth. If the bandwidth B is divided into two sub-bands with bandwidth B/2 separated by B/2, then a differential interferogram can be formed from the sub-band in fe gra with a synthesized wavelength of 2c/B. For the small bandwidth systems currently in space this synthesized wavelength is so small compared to the natural wavelength λ=c/f0 that this method has little practical significance. The reason is that the small differential phase information contained in the upper and lower sub-band is very noisy when scaled to the wavelength λ. Nevertheless this method has found application in interferometric co-registration [11] and, recently for phase unwrapping of single bright targets for the estimation of snow water equivalent [6].

technique could in principle be used for phase unwrapping of distributed targets as shown in Fig. 21 and Fig. 2

ter ro ms

TheX74 meters besides the 3.1 centimeter X-band wavelength or to an additional baseline of 2.5 centim ith th nal 60 meter mast. Because of these bad conditions the DEM reconstructed from delta-k technique is very noisy and must be averaged over large areas to reduce the error. The key factor for the usability of delta-k technique for phase unwrapping is the ratio between carrier frequency f0 and bandwidth B. For SRTM X-SAR this is 1200, for ERS it is 341.

eters w e nomi

Fig. 22: SRTM X-SAR DEM, processed using delta-k

Fig. 21: SRTM X-SAR DEM of data take 153.260 over

mountains in Iran. The wavelength is 3.1 cm, the resolution ca. 30 meters.

technique - without phase unwrapping. The synthesized wavelength is 74 meters, the resolution is reduced to ca. 6 km in order to reduce the error enough so that the terrain gets visible.

uture high bandwidth systems like TerraSAR-X or TerraSAR-L will have carrier to bandwidth ratios of 32 or 16, respectively.

. SUMMARY

odels from SAR interferometry have shown excellent results over moderate terrain so far. Over rugged

. REFERENCES

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NVISAT Interferograms,

R interferograms of large areas and of rugged terrain, Geoscience and Remote

FThis means that the synthesized wavelength is much closer to the natural one and can be used like a second carrier frequency for phase unwrapping. The high bandwidth transmit and receive components of future SAR systems should be optimized to use two relatively small bandwidths separated as far possible. Only one receiver and analog digital converter are required to sample these dual band signals. Such split bandwidth systems could simplify phase unwrapping enormously and provide enormous benefit to all disciplines of SAR interferometry. 8

Digital elevation mmountains the interferometric technique still has to be improved to overcome SAR specific problems from layover, shadow and especially from phase unwrapping. Promising techniques exist that can be further developed for future, improved systems. An interferometric system optimized for mountains should operate with an incidence angle close to 45° and with dual frequency bands. 9

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