INVESTIGATION OF ELEVATION BIAS OF THE SRTM C- AND X-BAND DIGITAL ELEVATION MODELS

Transcription

1 INVESTIGATION OF ELEVATION BIAS OF THE SRTM C- AND X-BAND DIGITAL ELEVATION MODELS K. Becek UBD, Geography Department, Jalan Tungku Link, Gaong, BE141, Brunei Darussalam - kbecek@fass.ub.eu.bn KEY WORDS: Remote Sensing, Vegetation, Retrieval, Multifrequency, DEM/DTM, SAR, Lan Cover ABSTRACT: The paper presents results of a comparative stuy of the vegetation-cause elevation bias of the space shuttle topographic mission ata prouct, both C- an X-ban (SRTM.C/X). The SRTM.C/X bans ata were compare against a high-resolution igital terrain moel. Pixel-base ifferences in SRTM.X minus SRTM.C were correlate with lan cover ( agriculture, house, tree, water ). Finings of the investigations inclue that the SRTM.X oes not represent a canopy top of vegetation an that the X-ban penetrates eeper vegetation cover than the C-ban. As a test site, an area of about 159 km on the Gol Coast, Queenslan, Australia, was selecte. The area of interest is about 57% covere by vegetation varying from grasslan an shrubs to forest. The stuy metho allowe the evelopment of a statistical moel relating the elevation bias to the percentage of the vegetation cover of a given lan parcel. This moel, once verifie on varieties of vegetation types, coul be utilise to estimate an eliminate the elevation bias from the InSAR elevation moel. This moel coul also be utilise for estimating biomass quantities an their variations. It is hope that the results will also stimulate investigations towars eveloping a multi-frequency InSAR system for collecting both terrain elevation ata an attributes of biomass. 1. INTRODUCTION The shuttle raar topography mission elevation ata prouct (SRTM) is one of the most valuable global resources of topographic ata to ate (Rabus, et al., 3). It was evelope for about 8% of the global lanmasses using C- ban (λ = 5.3 cm or f = 5.7 GHz) InSAR (interferometry synthetic aperture raar) technology. The vertical (absolute) accuracy is quote at ±3.3 m 7.3 m (Roríguez, et. al., 5). Pixel size for the U.S. territories is one arc-secon (~3 m), an for the remainer of the globe three arc-secon (~9 m). The secon instrument flown uring the same Eneavour mission (February, ) use the X-ban electromagnetic spectrum (λ = 3.1 cm or f = 9.7 GHz), but without the so-calle scan moe which provie the ata for selecte areas of the globe only. These ata are available at one arc-secon pixel size (~3 m) at a cost of 4 for 15 by 15 tile. Both elevation ata proucts (note neither DTM nor DEM) exhibit elevation bias ue to the partial penetration of vegetation by the electromagnetic waves at those bans (C an X). The effect will be referre to as impenetrability of vegetation cover. The level of impenetrability is the layer of vegetation above the groun which is not penetrable by the C- or X-ban. The magnitue of the impenetrability epens on many factors relate to complex interactions between electromagnetic waves an the 3D object the vegetation cover. The current scientific position is that the C-ban penetrates the vegetation (forest) to about 5% of its thickness, as the X-ban is reflecte from the top of the tree canopy (Carabajal et al., 6; Balzter et al., 7). This position seems to be contraicte by at least a few authors who emonstrate that C/X-ban impenetrability may be very similar (Werner et al., 5; Simar et al., 6). Moreover, it will be shown that the X-ban impenetrability can be smaller than the C-ban. These inconsistencies are most likely cause by the size, shape, an orientation of scatters within the tree canopy, an can theoretically be use for quantitative assessment of vegetation or biomass. Quantitative assessments of vegetation structure using SRTM ata were stuie by (Kellnorfer et. al., 3), who consiere etermination of vegetation height, using for reference the bal-earth elevation an SRTM error mitigation proceure. Walker et al., 7, consiere the quality of the SRTM C- an X-ban elevation ata an their suitability for retrieval of the vegetation canopy height. Balzter et al., 7, experimente with an airborne L- ban an erive an smoothe the bal-earth elevation moel an X-ban canopy height. The reporte accuracy of that experiment is remarkably high probably because of the relatively flat test site. In this paper, the impenetrability of vegetation cover is investigate. The test site, locate in Australia, consists of various types of lan cover, varying between grasslan, urban, an tree cover with various ensities. The main goal of the investigation is to ocument the existence of situations X-ban impenetrability is less than that of C-ban, or in other wors, when X-ban microwaves penetrate the vegetation cover eeper than C-ban waves. An attempt is also mae to relate the ifference in impenetrabilities to the height, ensity, an type of vegetation cover. Answers to those questions can lea to the evelopment of a multifrequency (C/X/L-ban) microwave system for mapping the vertical structure of vegetation cover..1 Test site. MATERIAL AND METHODS The test site comprises the northern part of Gol Coast City, Queenslan, Australia (top left: E, 3.75 S, an bottom right: E, 8 S). All water boies were maske out from further consieration. The area of the consiere terrain was about km. A sun-shaowe view of the test site is shown 15

2 The International Archives of the Photogrammetry, Remote Sensing an Spatial Information Sciences. Vol. XXXVII. Part B1. Beijing 8 very low to none tree cover; an ) water boies in the form of small ams or lakes, an artificial channels connecte to rivers. Lan cover of about 1%, 57%, 19%, an 14% constitute classes a, b, c, an, respectively..5.4 Max = 31º Mean = 3º Meian = º STD = 3.7º.1 Figure 1. Sun-shaowe view of the test site, Gol Coast City, Queenslan, Australia. in Figure 1. The geomorphology of about half of the site is compose of low, flat alluvia; the remainer is forme by eroe hills an valleys of volcanic origin No of points = 46,98 Max = 377m Min = m Mean = 9.43m Meian = 11.8m Elevation (m) Figure. Histogram of elevations of the test site. The highest point is about 377 m a.m.s.l. The mean an meian elevations are about 9 m an 11 m, respectively. Figure shows a histogram of the terrain s elevation, which resembles an exponential istribution. The egree of the terrain s roughness can be seen in Figure 3. The mean slope for AOI is about 3, which is classifie as flat terrain. The AOI lan cover can be ivie into four lan cover classes, e.g., a) agricultural lan (preominantly uner sugar cane an pastoral areas); b) trees an shrubs usually forming ry rainforest an open eucalyptus forests of grey gum (Eucalyptus punctata) open-crowne tree, blue gum (Eucalyptus tereticornis), an stringybark an tallowwoo (Eucalyptus microcorys) trees. Mean tree height is about m, but it can reach 45 m in instances; c) high-ensity housing estates with Slope (eg) Figure 3. Histogram of the terrain s slopes of the test site.. Data SRTM Data The SRTM.C, so-calle finishe ata, version (cell S8E153.hgt.zip) were ownloae from the JPS/NASA site: ftp://esrp1u.ecs.nasa.gov/srtm/version/srtm3/australia/. This is the recommene source of the SRTM.C because its three arc-secon ownsampling has been achieve using the socalle averaging proceure (Becek, 7). A 15 arc-minute SRTM.X one arc-secon cell (starting at E, 8. S bottom left corner) has been purchase from the German Aerospace Center (DLR). All pixels falling within water boies were remove. Every pixel from the SRTM.X ata set was associate with the so-calle height error map value (HEM), a pixel-base accuracy measure provie as a part of the X-ban ata package. The HEM value is statistically etermine from a neighbourhoo of pixels mainly consiering the phase an baseline stability. Thus, it is a relative measure of the precision. The HEM varies in a range from to 55. The C-ban elevations are referre to the sea level means. The X-ban ellipsoial elevation was converte to mean sea level using the AusGeoi98 moel The C-ban pixels were also associate with an accuracy measure erive from the slope of the terrain. In the following section, a proceure facilitating that is escribe. DTM Data As reference terrain elevation ata, a set of spot elevations was use. The accuracy of the photogrammetically/liar erive elevations is better than ±.3 m (1 σ). The mean ensity of the spot elevations was about 48 points /ha. Lan Cover Data 16

3 The International Archives of the Photogrammetry, Remote Sensing an Spatial Information Sciences. Vol. XXXVII. Part B1. Beijing 8 The Digital Caastral Data Base (DCDB), one of the stanar spatial proucts available in Queenslan, Australia, at minimal cost, was use for parcel-base lan cover classification. By means of photointerpretation of highresolution 3 aerial photography (.15-m pixel), about 71,5 lan parcels were classifie as Agriculture, House, Water, an Tree. The Tree parcels were also assigne visually assesse percentages of tree cover. Figure 1 shows DCDB in the backgroun of an aerial photograph. C X CX = C = X = C R, R X, (1) C, X, CX = ifference in elevation, C, X an R = C-, X-ban elevations, an R is the reference elevation, = spatial (buffer) averaging operator. Variation of ifference ( σ a sum of the variations of the C/X-ban ( of the reference elevation ( ): ) was calculate for every buffer as σ R σ C / X ) an variations σ σ + σ = () C / X R σ C / X The pixel-base variation of the C/X-ban ata ( ) was calculate as a sum of the variation of the SRTM instrumental error an error cause by impenetrability in conjunction with C/X - pixel size (Becek, 8): Figure 4. Parcel-base classification of lan cover incluing the percentage of tree cover. A enotes Agriculture, H House, T35 35% of tree cover, an W water..3 Metho In the following, the ata processing proceure will be presente. As a basic unit for calculations an ata aggregations, a buffer with a 45-m raius centre on the centre of every C- ban pixel was use. For every such buffer, the following ata were available: a) Average X-ban elevation (calculate from up to 1 points), b) Average reference elevation (calculate from 13.3 (1-18) - in average - reference spot elevations, c) Type of lan cover, ) Percentage of tree cover, e) Aspect calculate from C-ban ata, f) Slope calculate from C-ban ata, g) HEM value for X-ban pixels, an h) A pixel base accuracy of C-ban elevations. Buffers with missing ata in any fiel or containing SRTM.X pixels with HEM>1 were omitte from further processing. Overall, 53,19 buffers were available for further processing. Data preparation also inclue ientification of horizontal misregistration of both C- an X ban ata in relation to the reference DTM. This was performe by calculating the crosscorrelation plot for two perpenicular transects (N-S an E-W). No shift was etecte at the lag level of.5 m. In the next step, the ifferences in elevations between SRTM an reference DTM for every buffer were calculate: σ = /1* * tan ( ) (3) C / X + s = 3 m or 9 m for X- or C-ban pixel s = slope of terrain within a pixel, an 1.55 m is an experimentally erive stanar eviation of the instrumental errors of the SRTM. In the next step, using a reciprocal of the variance () as the weight, the weighte average ifferences Cw, Xw, CXw, an their stanar eviations were calculate for every parcel (belonging to one of the lan cover classes). The calculations were one using well-known formulas: g w (.) g (.) i = (4) g i σ = (5) 1/ (.)w i = weighte ifference C, X, or CX for i-th parcel = spatial (parcel) averaging operator. The stanar eviation of the average ifference (Equation 4) can be calculate using the following formula: σ = σ g (6) / 17

4 The International Archives of the Photogrammetry, Remote Sensing an Spatial Information Sciences. Vol. XXXVII. Part B1. Beijing 8 Where σ = the stanar eviation of an average ifference with the weight equal to 1, an g = weight (Equation 5). Calculate average ifferences for every parcel were subsequently analyse as a function of the lan cover. 3. RESULTS The histograms in Figures 5 an 6 o not follow the Gaussianfitting curve. This is because they represent a compoun probability istribution function of two stochastic processes: one is the bal-earth ifference between SRTM an reference DTM, which follows the Laplace istribution; the secon one is create as the same ifference but consiere over vegetate areas it follows the Gaussian istribution. The Gaussian probability ensity function is given by the well-known formula: The vegetation impenetrability an anthropogenic obstructions foun above the surface of the Earth introuce asymmetry into the histogram of elevation ifferences (SRTM minus bal- Earth reference elevations) (Heipke, et al., ). Histograms in Figure 5, 6, an 7 were evelope for vegetation impenetrabilities (Equation ). The mean ifferences for SRTM.C/X minus the reference elevation are 6.6 m an.53 m, respectively. Hence, the mean ifference for SRTM.C minus SRTM.X is about 4 m. x m.5 σ 1 f ( x m, σ ) = e, (7) σ π m = mean value, an σ = stanar eviation C - <R> Mean = 6.6m Meian = 4.1m STD = 11.1m The Laplace probability ensity function is given by (Norton, 1984): x μ b 1 f ( x μ, b) = e, (8) b μ = location parameter, b = scale parameter..6.3 For N inepenent an ientically istribute ifferences 1,,..., N, estimator of μ - ~ μ is the meian of ifferences, an the estimator of b - b ~ can be calculate using the maximal likelihoo estimator from: Difference (m) ~ 1 b = N N i i= 1 ~ μ, (9) Figure 5. Histogram of buffer-base elevation ifferences C- ban minus reference elevation X - <R> Mean =.53m Meian =.4m STD = 6.74m..15 Buffers = 53,19 Mean = 4.m Meian = 3.9m STD = +/- 7.8m C - X Laplace Gauss Data Difference (m) Figure 6. Histogram of buffer-base elevation ifferences X- ban minus reference elevation Difference (m) Figure 7. Histogram of ifferences C-ban minus X-ban. Laplace fitting curve was rawn for μ = 3.9 m an b = 4.96 m. Gaussian fitting curve was rawn for m = 4. m an σ = ±7.8 m. 18

5 The International Archives of the Photogrammetry, Remote Sensing an Spatial Information Sciences. Vol. XXXVII. Part B1. Beijing 8 The ifference CX for the whole AOI shown in Figure 7 follows the Laplace istribution. The mean ifference is 4. m, which means that the X-ban vegetation impenetrability is less than the C-ban one. 1 1 Agriculture an Trees. The stanar eviation varie between ±.79 m for Agriculture an ±6.88 m for Trees. 6 5 C - X Exponential fit Impenetrability (m) y =.6x y =.79x +.35 C - <R> X - <R> Tree Cover (%) Figure 8. Impenetrability of the C/X-ban versus percentage of the parcel-base tree cover. A potentially far-reaching consequence for vegetation cover investigations is the relationship between SRTM bias an the percentage of vegetation cover of a given area. This effect is illustrate in Figure 8. For example, any future changes to vegetation cover in terms of spatial extensions (horizontal an vertical) can be easily ientifie by comparing multi-temporal C- or X-ban impenetrability of a given area. However, it is necessary to note that the ata for the C-ban vegetation impenetrability shown in Figure 8 inicate about 4.8 m positive bias (SRTM is above the groun) for the vegetation-free parcels. This issue will be further investigate in the near future. Differences C an X, or elevation bias, are shown in Table 9. Lan Cover Class Difference (m) C ± 1σ X ± 1σ Agriculture.96 ± ± 1.49 House 4.4 ± ± 4.18 Tree (-1%) 8.9 ± ± 6.7 Water 4.34 ± ± 4.54 Table 9. SRTM C/X elevation bias for lan cover classes Closer consieration of the results in Table 9, in particular for Agriculture, can lea to a conclusion that perhaps both C- an X-ban SRTM atasets contain certain reference biases, e.g., C- ban elevations are about 3 m too high, an X-ban elevations are about 1.5 m too low. This coul explain the remarks regaring the 4.8-m bias mae in the previous paragraph. The negative X-ban SRTM elevation bias of the orer of about.6 m was reporte by Heipke et al.,. However, Luwig et al., 6, have not reporte such an elevation bias. Weighte average ifference CXw per Equation 4 was calculate for every lan cover type. The results are very similar, varying between 3.95 m for House an 4.43 m for C - X (m) 4 3 y = 5.113*exp(-.4355*x) R = Tree Cover (%) Figure 1. Weighte average ifference SRTM.C minus SRTM.X versus tree cover expresse as a percentage of the area of the parcel. The weighte average ifference CXw for Tree was also calculate for every parcel as a function of the average percentage of tree cover. The results are shown in Figure 1. The ata appear to follow the exponential fitting curve. The ifference is that CXw reaches its lowest level of about 3.3 m for parcels fully covere by trees. The relatively low value of R is mainly cause by inexperience photointerpreters who estimate the percentage of the tree cover. 4. CONCLUSIONS A comparison of both C- an X-ban SRTM elevation proucts an a high-resolution reference DTM over a large test area in the Gol Coast, Queenslan, Australia, focuse on the influence of the vegetation cover, which was in the leave-on state, on elevation bias an provie an insie look into some of the properties of the InSAR C- an X-ban technology of elevation etermination. There is evience that the X-ban SRTM penetrates the vegetation cover eeper than the C-ban SRTM. This effectively means that the vegetation-cause error in the X-ban SRTM is smaller than that in the C-ban SRTM. However, this has to be further investigate ue to possible systematic error in the C-ban SRTM. It was also shown that there is a linear relationship between the percentage of lan cover an the magnitue of the vegetationcause bias. This property of both SRTM atasets can be utilise for quantitative observations of variations of vegetation cover. The level of the vegetation-cause impenetrability, e.g., about 1 m, is responsible for an error exceeing SRTM mission error specification. In aition, this is vali for about 3% of the global lanmasses covere by forests. Further investigations are neee an planne towars ientifying the best ata source of vegetation cover to be use 19

6 The International Archives of the Photogrammetry, Remote Sensing an Spatial Information Sciences. Vol. XXXVII. Part B1. Beijing 8 to correct the SRTM elevation ata prouct an those which will be erive in the future using the InSAR technology. REFERENCES Balzter, H., Rowlan, C.S. & Saichc, P., 7. Forest canopy height an carbon estimation at Monks Woo National Nature Reserve, UK, using ual-wavelength SAR interferometry. Remote Sensing of Environment, 18(3), pp Becek, K., 6. Accuracy Evaluation of the SRTM Topographic Data Prouct over Selecte Sites in Australia an Brunei Darussalam. Reports on Geoesy, 77(), pp Becek, K., 7. Comparison of Decimation an Averaging Methos of DEM s Resampling. Proceeings of the Map Asia 7 conference, Kuala Lumpur, (accesse March 8). Becek, K., 8. Investigating Error Structure of SRTM Elevation Data Prouct. Submitte to the Geophysical Research Letters. Carabajal C.C. & Haring, D.J., 6. SRTM C-ban an ICESat Laser Altimetry Elevation Comparisons as a Function of Tree Cover an Relief. Photogrammetric Engineering & Remote Sensing, 7(3), pp Gesch, D., 5. Vertical Accuracy of SRTM Data of the Unite States: Implications for Unite States: Implications for Topographic Change Detection. SRTM Data Valiation an Applications Workshop June 14, 5, Gesch.pf (accesse - April 8) Heipke, C., Koch, A. & Lohmann, P. : Analysis of SRTM DTM - Methoology an practical results. Proceeings of ISPRS Commission IV Symposium in Ottawa, July. Kellnorfer, J.M., Walker, W.S., Pierce, L.E., Dobson, M.C., Fites, J. Hunsaker, C., Vona, J., Clutter, M, 4. Vegetation Vegetation height erivation from height erivation from Shuttle Raar Topography Mission an National Elevation ata sets. Remote Sensing of Environment, 93(3), pp Luwig, R., & Schneier, P. 6. Valiation of igital elevation moels from SRTM X-SAR for applications in hyrologic moeling. ISPRS Journal of Photogrammetry an Remote Sensing, 6(5), pp Norton, R.M., Double Exponential Distribution: Using Calculus to Fin a Maximum Likelihoo Estimator. The American Statistician, 38(), pp Rabus, B., Eineer, M., Roth, A., & Bamler, R., 3. The shuttle raar topography mission a new class of igital elevation moels acquire by spaceborne raar. ISPRS Journal of Photogrammetry an Remote Sensing, 57(4), pp Roríguez, E., Morris, C.S., Belz, J.E., Chapin, E.C., Martin, J.M., Daffer, W., & Hensley, S., 5. An assessment of the SRTM topographic proucts. Technical Report JPL D-31639, Jet Propulsion Laboratory, Pasaena, California, 143 pp. Schumann, G., Matgen, P., Cutler, M.E.J., Black, A., Hoffmann, L., & Pfister, L., 7. Comparison of remotely sense water stages from LiDAR, topographic contours an SRTM. ISPRS Journal of Photogrammetry an Remote Sensing, (7). Simar, M., Zhang, K., Rivera-Monroy, V.H., Ross, M.S., Ruiz, P.L., Castañea-Moya, E., Twilley, R.R. & Roriguez, E., 6: Mapping Height an Biomass of Mangrove Forests in the Everglaes National Park with SRTM Elevation Data. Photogrammetric Engineering & Remote Sensing, 7(3), pp Walker, W., Kellnorfer, J. & Pierce, L. 7. Quality Assessment of SRTM C-an X-ban Interferometric Data: Implications for the Retrieval of Vegetation Canopy Height. Remote Sensing of Environment, 16(4) pp Werner, M., Roth, A., Marschalk, U., Eineer, M. & Suchant, S. 5. Comparison of DEMs erive from SRTM/X-an C- Ban. Workshop: The Shuttle Raar Topography Mission Data Valiation an Applications, June 14-16, 5, Reston, Virginia, USA. 11