ANALYSIS OF SRTM DTM METHODOLOGY AND PRACTICAL RESULTS

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1 ISPRS SIPT IGU UCI CIG ACSG Table of contents Table des matères Authors ndex Index des auteurs Search Recherches Ext Sortr ANALYSIS OF SRTM DTM METHODOLOGY AND PRACTICAL RESULTS A. Koch, C. Hepke, P. Lohmann Insttute for Photogrammetry and GeoInformaton (IPI), Unversty of Hannover Nenburger Straße 1, Hannover, Germany (koch, hepke, Commsson IV, WG IV/6 KEY WORDS: DTM, DSM, Spatal Smlarty Transformaton, Systematc Errors ABSTRACT: In February 2000 the frst msson usng space-borne sngle-pass-nterferometry was launched the Shuttle Radar Topography Msson (SRTM). The goal of the msson was to survey the Earth surface and to generate a homogeneous elevaton data set of the world wth a grd spacng of 1 arcsec. Antennas wth two dfferent wavelengths were used: Besde the Amercan SIR-C the German / Italan X-SAR system was on board. Ths paper deals wth the assessment of the Interferometrc Terran Elevaton Data derved from the X-SAR system. These so called ITED-2 data were compared to reference data of hgher qualty of a well known test ste n the South of Hannover (Trgonometrc Ponts and Dgtal Terran Model). The approach used s based on a spatal smlarty transformaton wthout usng any knd of control pont nformaton. The algorthm matches the SRTM data onto the reference data n order to derve seven unknown parameters whch descrbe horzontal and vertcal shfts, rotatons and a scale dfference wth respect to the reference data. These values descrbe potentally exstng systematc errors. The standard devaton of the SRTM ITED-2 was found to be ±3,3 m n open landscape, after applyng the spatal smlarty transformaton. Maxmum horzontal systematc shfts of 4-6 m were detected, representng only % of the ITED-2 grd sze. In summary, t can be stated that the results are much better than predcted before the start of the msson. Thus, the qualty of the SRTM ITED-2 s ndeed remarkable. 1. INTRODUCTION Interferometrc SAR (IfSAR) allows to obtan nformaton about the thrd dmenson of the Earth surface. Thus, the man product of ths method s a Dgtal Terran Model (DTM) or Dgtal Surface Model (DSM) n case of usng a short wave system. The SRTM msson (Werner, 2001, Rosen et al., 2001a) has been the frst msson usng space-borne sngle-pass nterferometrc SAR. The man antenna of the system was located nsde the cargo bay of the Space Shuttle Endeavour. It transmted and receved mcrowave pulses. The outboard or slave antenna was fxed at the tp of a 60 m long mast and acted as a recever only. The mast realsed the nterferometrc baselne. The system used two dfferent wavelength. The Amercan C-band system SIR-C operated wth a wavelength of λ=6,0 cm, the wavelength of the German / Italan X-band system was λ=3,1 cm. In order to obtan a global coverage between 60 degrees north and 58 degrees south the Shuttle was flown at an alttude of 233 km and an nclnaton of 57 degrees. Because of the Earth rotaton the Shuttle surveyed the ground strp after strp. Wth C-band t was possble to cover the Earth surface completely. The C-band nterferometer operated n the so-called ScanSAR mode (Bamler, 1999). The X-band antenna operated at a fxed depresson angle of 38 degrees and a swath wdth of about 50 klometres. The advantage of X-band s the hgher relatve vertcal accuracy resultng from the shorter wavelength. The dsadvantage of the X-band system used on board SRTM was the ncomplete coverage of the Earth. There are gaps between the swaths whch became smaller wth growng lattude. The goal of the project at the Insttute for Photogrammetry and GeoInformaton (IPI) of the Unversty of Hannover was the assessment of the SRTM X-SAR data. The qualty of the data has been obtaned by comparson to reference data of hgher qualty n a well known test ste. Chapter 2 descrbes the algorthm used for the assessment of the SRTM data. The method s based on a spatal smlarty transformaton wthout usng any knd of control pont nformaton. An overvew about the test ste and the used reference and SRTM data sets s gven next (chapter 3) and the results of the valdaton process are presented n chapter 4 and 5. The paper concludes wth a short summary. A smlar nvestgaton was e.g. carred out by Kleusberg & Klaedtke (1999) for arborne IfSAR data and by Rosen et al. (2001b) for SRTM. 2. ALGORITHM FOR MATCHING DIGITAL SURFACE MODELS The developed algorthm (see also Koch & Hepke, 2001) s based on a spatal smlarty transformaton. The seven parameters of ths transformaton descrbe systematc errors of the SRTM data set detected wthn the test area. Remanng errors after havng appled the smlarty transformaton can be consdered as ether local systematc errors or random errors. Symposum on Geospatal Theory, Processng and Applcatons, Symposum sur la théore, les tratements et les applcatons des données Géospatales, Ottawa 2002

2 2.1 Mathematcal Model Sngle ponts P (X,Y,Z) contan heght nformaton about a gven area. The ponts are combned to vectors: { L L } G1 = P11 P12 P1 P1 n G = P P P P { L j L m} The reference data set G 1 contans n regularly or rregularly dstrbuted ponts. G 2 conssts of m ponts, whch descrbe the same physcal surface as G 1. G 2 s the data set to be nvestgated. For the remander of ths paper we consder ponts P 1 and P 2 to have the same planmetrc coordnates. If for a pont P 1 no such correspondng pont P 2 exsts a pror (or vce versa) a heght Z 2 must be nterpolated from the other data set at the poston X 2,Y 2 usng e.g. a blnear nterpolaton. In the deal case the followng equaton s fulflled under the above mentoned assumptons: (, ) = (, ) (1) Z X Y Z X Y (2) Because of possble global systematc errors the two elevaton data sets can be shfted and rotated aganst each other and can have dfferent scale factors. Consequently a spatal smlarty transformaton s ntroduced: where (, ) = 0+ ( 1+ ) 3 2 Z X Y Z m r X (3) X = + ( 1+ ) X r m X Y Y 0 r X X Y Z R r r r 1 2 T 2 = ( 2 2 2) T = ( 1 2 3) In ths way the ponts P 2 are transformed nto the coordnate system of the reference data set by means of the seven parameters of the spatal smlarty transformaton. Z0 s the heght translaton, (1+m) s the scale. The vector r 3 contans the rotatons ω, ϕ and κ, t s the thrd row of the rotaton matrx R of the spatal smlarty transformaton. Note that we use the rotaton sequence ω, ϕ and κ. The centre pont of rotaton s the centre of the test ste. Z 1 on the left sde of equaton (3) s the correspondng heght value of the reference data set wth the planmetrc coordnates X 1, Y 1. X 1 and Y 1 are computed accordng to equaton (4) by transformng the coordnates X 2, Y 2, Z 2 of the nvestgated data set by means of the seven parameters. The vectors r 1 and r 2 are the frst two rows of the rotaton matrx R. X0 and Y0 are the planmetrc translatons of the smlarty transformaton. In order to determne Z 1 n general the mentoned nterpolaton must be carred out, snce we cannot assume that for the 2 (4) computed planmetrc poston (X 1,Y 1 ) a value Z 1 exsts n the reference data set. 2.2 Least squares adjustment Equatons (3) and (4) form the base of a least squares adjustment. We ntroduce the heghts Z 2 (X 2, Y 2 ) as observatons and consder the parameters of the smlarty transformaton as unknowns. The observatons are assumed to be ndependent of each other and of equal accuracy resultng n an dentty matrx for the covarance matrx of the observatons. Equatons (3) and (4) can then be formulated as observaton equatons, one for each heght value Z 2 : v ( Z2) = Z1 ( X0 ( 1 m) r1x 2, Y0 ( 1 m) r2x 2) ( Z0+ ( 1+ m) r3x 2 ) Ths equaton s the fundamental equaton for calculatng the unknown parameters of the spatal smlarty transformaton. Because of the non-lnearty of equaton (5) t has to be expanded nto a Taylor seres, and the unknowns are computed teratvely startng from approxmate values. The desgn matrx of the least squares adjustment contans the partal dervatves of the observaton equatons wth respect to the unknown transformaton parameters. It should be noted that the explaned method reles on heght varatons wthn the area under consderaton, because wth the excepton of v Z 0 - the partal dervatves all depend on Z X or Z Y (see equaton 6). v Z1 = X0 X1 v Z1 = Y0 Y1 v = 1 Z0 v Z1 Y1 Z2 = ω Y1 ω ω v Z1 X1 Z1 Y1 Z2 = + ϕ X1 ϕ Y1 ϕ ϕ v Z1 X1 Z1 Y1 Z2 = + κ X1 κ Y1 κ κ v Z1 X1 Z1 Y 1 Z2 = + m X1 m Y1 m m ( ) Z = Z0+ 1+ m r X s the transformed heght value The unknown parameters are then computed accordng to the well-known equatons of the least squares adjustment. The standard devaton of unt weght s dentcal to the standard devaton of the heght dfferences after applyng the transformaton. (5) (6)

3 2.3 Specal case of unknown shft Z0 The algorthm was mplemented such that dfferent unknown parameters can be ntroduced. If only a vertcal shft Z0 s to be obtaned the algorthm can be smplfed. The obtaned transformaton parameter Z0 s dentcal to the mean value of the heght dfferences between the two data sets. The observaton equatons have the followng form: about 20 m. The avalable data set conssts of 5,5 mllon ponts. ( 2 ) = 1 ( 2, 2 ) ( ( 2, 2 )) v Z Z X Y Z Z X Y (7) The result of the algorthm ntroducng only a vertcal shft Z0 corresponds wth calculatng a dfference DTM. 3. TEST SITE AND USED DATA SETS As mentoned before the am of the project was the assessment of the SRTM X-SAR elevaton data set. Ths task can be accomplshed by comparng the data wth reference data of a well known test ste. The test ste of IPI s stuated n the south of Hannover. The north-eastern part of the area s characterzed by urban regons and flat terran. The south-western part s more undulated, forest and agrgultural regons cover the area. The sze of the test ste s 50x50 km². The maxmum heght dfference s about 450 m. The accuracy of the reference data - provded by the surveyng authorty of Lower Saxony "Landesvermessung und Geobassnformaton Nedersachsen LGN" n our case - has to be at least one order of magntude better than the SRTM data. The expected vertcal accuracy of the SRTM data s several meters. Thus, hghly accurate coordnates of Trgonometrc Ponts (TP) and the Dgtal Terran Model of LGN, the ATKIS DGM5, had to be used as reference data sets. Trgonometrc Ponts are part of the fundamental network of the surveyng authortes of Germany. The planmetrc coordnates are Gauß-Krüger coordnates, the heghts are normal heghts. The horzontal and vertcal accuracy s 1-3 cm. The DGM5 s a data set representng the terran surface. The data consst of regularly dstrbuted ponts wth a grd spacng of 12,5 m. Together wth morphologcal nformaton the data represent a hybrd DTM. The vertcal accuracy s about 0,5 m and depends on the terran undulaton. The DGM5 covered parts of the test ste, altogether 4,7 mllon DGM5 ponts were avalable. The SRTM ITED-2 data (Fgure 1) represent the surface ncludng vegetaton and buldngs because of usng a shortwave X-band system. Thus, the data set s a Dgtal Surface Model n contrast to the reference Dgtal Terran Model. The data are gven n ellpsodal coordnates referrng to the geocentrc ellpsod WGS84. The grd spacng s 1 arcsec n both drectons. For comparng the data sets the ITED-2 data were transformed nto the coordnate system of the reference data set. A datum transformaton between the two ellpsods WGS84 and Bessel was carred out, addtonally the ellpsodal heghts were corrected usng geod undulatons. The geod has an extent of m n the test ste. After these transformaton steps the ITED-2 data are approxmately dstrbuted n a rectangular grd. The grd spacng n north-south drecton s about 30 m, the grd spacng n east-west drecton depends on the ellpsodal lattude. The test area s stuated at a lattude of about 52. Therefore the grd spacng n east-west drecton s Fgure 1. The test ste, SRTM ITED-2 data 4. QUALITY ASSESSMENT BY USING COORDINATES OF TRIGONOMETRIC POINTS The frst experments were performed by usng the coordnates of Trgonometrc Ponts (TPs) TPs were avalable n our test ste whch are covered by the SRTM ITED-2 data. To obtan the vertcal accuracy only those TPs were consdered whch le clear of vegetaton and buldngs. To classfy the TPs a Dgtal Landscape Model (DLM) of the surveyng authorty LGN (ATKIS Bass DLM) was used. The DLM s a twodmensonal representaton of the topography. 368 ponts n urban regons, nsde or near forests were excluded. Values Z0 [m] +3,18 s [m] ±4,27 s Z0 [m] ±2,86 n 700 Table 1. Qualty measures usng TPs By means of the planmetrc postons of the TPs the correspondng heght values of the ITED-2 data set were

4 obtaned. The heght dfferences were calculated and the qualty measures were obtaned (see equaton 7). Any knd of planmetrc systematc error or errors n rotaton or scale were neglected. Table 1 shows the results. The postve value Z0 means that the heght level of the SRTM ITED-2 data s lower than the heght level of the TPs. The data set contans a systematc vertcal shft of +3,2 m. The standard devaton of the heght dfferences s s ±4,3 m. After consderng the mean value, the standard devaton s Z0 s ±2,9 m. These values confrm the hgh vertcal accuracy of the SRTM ITED-2 data. Unfortunately, a conclusve reason for the shft cannot be gven. A possble explanaton can be derved from the calbraton of the ITED-2 data used for the nvestgaton. An error n the heghts selected for the calbraton drectly nfluences the results of our study. Whle n many cases IfSAR orbts are processed and calbrated from coast to coast and thus the ocean serves as absolute reference, the orbt contanng the data of the test ste was shorter and had to be handled n a dfferent way. If any buldngs and vegetaton exsted n the areas selected for calbraton and were not properly accounted for, the absolute ITED-2 heghts would ndeed come out too low, explanng the obtaned results. It should be ponted out, however, that ths hypothess could not be further tested, because no addtonal nformaton about the calbraton stes and procedure was avalable. 5. QUALITY ASSESSMENT BY USING THE DIGITAL TERRAIN MODEL ATKIS DGM5 Fgure 2 shows the nfluence of terran nose on the sgn of local vertcal systematc errors. The fgure represents a postve vertcal systematc error n open terran. The heght level of ITED-2 s lower than the heght level of the reference data. Addtonally, t can be seen that terran nose (vegetaton and buldngs) ncreases the heght level of the SRTM ITED-2 data and thus decreases the systematc vertcal shft. The value Z0 can thus become negatve. Fgure 2. Heght dfferences between DGM5 and ITED-2 The relatve frequency dstrbuton n fgure 3 confrms the obtaned results. The non-symmetrc dstrbuton s caused by objects lyng above the terran. Obvously the left negatve part of the hstogram represents these objects. Addtonally n contrast to the calculated mean value Z0 (see table 2) the maxmum of the hstogram s n the postve part. Ths means that the vertcal systematc error seems to be agan postve. Ths result confrms those of chapter 4. In a frst step the heght dfferences between correspondng values were calculated neglectng the nfluence of any knd of terran nose (buldngs, trees). In a second step only the heght dfferences outsde urban and forest regons were used. The algorthm descrbed n chapter 2 was utlsed ntroducng one and seven unknown transformaton parameters. 5.1 Investgatons wth all DGM5 heght values About 1,2 mllon reference DTM ponts were avalable nsde the test ste. In contrast to the nvestgatons before, the planmetrc postons of the ITED-2 data were used to obtan the correspondng heght values of the DGM5 usng a blnear nterpolaton. Then the heght dfferences were calculated and the qualty measures were derved (see equaton 7). The followng table 2 shows the results: Values Z0 [m] -2,63 s [m] ±9,08 s Z0 [m] ±8,68 n Table 2. Qualty measures usng all DGM5 ponts The sgn of the mean value of the heght dfferences Z0 s negatve. It means that the heght level of the ITED-2 data s hgher than the level of the DGM5. Ths result s n contradcton to the obtaned value of the nvestgatons usng the Trgonometrc Ponts (see table 1). A possble reason s the nfluence of vegetaton and buldngs. Whereas n chapter 4 only ponts whch are not nfluenced by terran nose were used, here the heght values are dstrbuted over the complete test area, also across forests and urban regons. Fgure 3. Relatve frequency dstrbuton of the heght dfferences between DGM5 and ITED Investgatons wth DGM5 heght values n open landscape Agan the ATKIS-Bass DLM of LGN was used for the classfcaton of the DGM5 heght values. Because the msson was flown n February, the SRTM data also represent the terran n agrcultural felds. The vegetaton heghts are completely neglgble. Values n forest and urban regons were excluded amountng to approxmately ponts or 40 % of the avalable DGM5 heght values. The results (see table 3) confrm the nvestgatons before. The sgn of the mean value Z0 s postve. The nfluence of large negatve dfferences caused by terran nose thus s sgnfcant. As was to be expected the value Z0 does not correspond exactly to the value usng the TPs (see chapter 4). There remans a dfference caused by borders of forest and urban regons and other secondary effects. The standard devatons are nearly the same. The results show hgh qualty of the SRTM data set.

5 Values Z0 [m] + 2,62 s [m] ± 4,32 s Z0 [m] ±3,44 n Table 3. Qualty measures usng DGM5 ponts n "open landscape" 5.3 Investgatons usng seven unknown transformaton parameters In ths paragraph the results obtaned wth the algorthm based on a spatal smlarty transformaton are presented (see chapter 2). As n secton 5.2. only heght values n open terran were used. The results are shown n table 4. Value X0 [m] +0,60 Y0 [m] -2,32 Z0 [m] +2,28 ω [grad] -0,003 ϕ [grad] +0,002 κ [grad] -0,007 m [ ] +0, Table 4. Transformaton parameters The value Z0 s comparable to the mean value n table 3. The horzontal shfts X0 and Y0 descrbe systematc dfferences between the data sets. The values amount to only a fracton of the spacng between neghbourng heght values. Accordngly the horzontal accuracy of the SRTM data seems to be qute good. The rotaton angles ω and ϕ cause maxmum vertcal shfts of ±1,22 m and ±0,98 m at the border of the test ste. The scale factor causes maxmum horzontal shfts of ±0,76 m n both drectons. Altogether the seven parameters lead to maxmum planmetrc shfts of 4 m n north-south and 6 m n east-west drecton. The maxmum vertcal shft s 4,5 m at the borders of the test ste observatons were used n the nvestgaton. The standard devaton of the SRTM heghts, comparable to s Z0 above, amounts to ±3,3 m, the vertcal shft and the standard devaton of the heghts reported n ths secton are rather close to those presented n secton 5.2. (see table 3). Thus, the SRTM ITED-2 s free of systematc errors whch can be modelled by the spatal smlarty transformaton. 6. FURTHER INVESTIGATIONS As mentoned before the qualty of the SRTM ITED-2 data,.e. the order of magntude of random and systematc errors, s nfluenced by terran nose: The larger the percentage of regons contanng vegetaton and buldngs the larger s the systematc vertcal shft and the larger s the standard devaton of the remanng resduals. In order to properly assess the SRTM data not only n open landscape but also n urban and forest areas, two sample stes wth a sze of 2x2 km² were analysed by obtanng a Dgtal Surface Model by usng analytcal photogrammetry. The photogrammetrc measurements have a heght accuracy of about 0,4 m. The frst sample ste s stuated n Hldeshem. The area s charactersed by sngle and complex houses wth gardens. The second test area s manly charactersed by decduous forest. Addtonally, agrcultural felds and a freeway are n the centre of the area. It s a regon n the south of Hannover. urban regon forest regon DGM5 Z0 [m] -5,13-13,19 - s [m] ±8,46 ±15,18 ITED-2 n DSM Z0 [m] +1,05 +1,84 - s [m] ±5,09 ±4,57 ITED-2 n Table 5. Qualty measures n urban and forest regons, upper part: comparson between DGM5 and ITED-2, lower part: comparson between measured DSM and ITED-2 Table 5 shows the results of comparng the ITED-2 data wth the reference DGM5 and the photogrammetrcally obtaned DSM. The spatal smlarty transformaton usng the seven parameters of table 4 was appled before calculatng the heght dfferences. Thus, the expected value for Z0 under deal condtons (DSM from SRTM and photogrammetry represent the same surface) s zero, and the standard devaton s should be close to the results obtaned n chapter 4 and 5. The three upper rows represent the results from the comparson of DGM5 and ITED-2, the lower part shows the results of comparng the DSM of SRTM wth the photogrammetrcally measured DSM. Consderng the DGM5 both regons are charactersed by a negatve vertcal shft Z0,.e. the values are nfluenced by terran nose. Addtonally the standard devatons are very large. Usng the measured DSM the shft becomes postve. That means, that the ITED-2 les sgnfcantly below the DSM (the values of table 4 and 5 must be added to obtan the complete shft). For the urban area ths result can be explaned wth nterpolaton effects: there are probably some ponts on the ground nfluencng the result. In the forest area, an addtonal explanaton may be the fact that the X-band sgnals somewhat penetrate nto the canopy (remember that the msson was flown n February, thus the trees dd not cover leaves). Also the standard devatons are larger than n the open landscape. As an overall result, t can be stated that n urban and forested areas, the qualty of the ITED-2, whle stll meetng the predcted values, s somewhat poorer than n open landscape. 7. CONCLUSIONS Ths paper contans the results of assessng the qualty of the SRTM ITED-2 data. The algorthm used s based on a spatal smlarty transformaton wthout usng any knd of control pont nformaton. The SRTM data was matched to a reference data set of better accuracy, the obtaned seven transformaton parameters descrbe potentally exstng systematc errors of ITED-2. Frst nvestgatons were carred out by ntroducng just a vertcal systematc shft. Ths procedure corresponds to the

6 calculaton of a dfference DTM and yelds the mean value and standard devaton of the heght dfferences. Investgatons usng only regons wthout vegetaton and buldngs lead to a postve vertcal shft of about 2,6 metres. Thus, the heght level of the SRTM data seems to be too low. A possble explanaton for ths result s the fact that the ITED-2 DSM was calbrated over land rather than coastal waters. The standard devaton of the SRTM ITED-2 was found to be ±3,3 m n open landscape, after applyng the spatal smlarty transformaton. Maxmum systematc shfts of 4-6 m were detected, representng only % of the ITED-2 grd sze. In summary, t can be stated that the results are much better than predcted before the start of the msson. Thus, the qualty of the SRTM ITED-2 s ndeed remarkable. REFERENCES Bamler, R., The SRTM Msson A World-Wde 30 m Resoluton DEM from SAR Interferometry n 11 Days. In. D. Frtsch, R. Spller (Eds.), Photogrammetrc Week 99, Wchmann Verlag, Hedelberg, Germany, pp Kleusberg, A., Klaedtke, H.-G., Accuracy assessment of a dgtal heght model derved from arborne synthetc aperture radar measurements. In: D. Frtsch, R. Spller (Eds.), Photogrammetrc Week 99, Wchmann Verlag, Hedelberg, Germany, pp Koch, A., Hepke, C., Qualty Assessment of Dgtal Surface Models derved from the Shuttle Radar Topography Msson (SRTM). Proceedngs of IGARSS, Sydney, Australa, Supplement CD. Rosen, P., Eneder, M., Rabus, B., Gurrola, E., Hensley, S., Knöpfle, W., Bret, H., Roth, A., Werner, M., 2001a. SRTM- Msson Cross Comparson of X and C Band Data Propertes. Proceedngs of IGARSS, Sydney, Australa, CD. Rosen, P. A., Hensley, S., Gurrola, E., Rogez, F., Chan, S., Martn, J., Rodrguez, E., 2001b. SRTM C-Band Topographc Data: Qualty Assessments and Calbraton Actvtes. Proceedngs of IGARSS, Sydney, Australa, CD. Werner, Status of the SRTM data processng: when wll the world-wde 30m DTM data be avalable? Geo- Informatonssysteme 12/2001. Herbert Wchmann Verlag, Hüthg GmbH & Co. KG. Hedelberg, pp ACKNOWLEDGEMENT Ths research has been partly supported by the German Mnstry for Research and Educaton BMBF through the German Aerospace Research Center DLR under contract no. 50EE9927. We are also thankful to LGN for provdng the reference data.