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Effect of the SRTM global DEM on the determination of a high-resolution geoid model: a case study in IranAbstract Any errors in digital elevation models (DEMs) will introduce errors directly in gravity anomalies and geoid models when used in interpolating Bouguer gravity anomalies.Errors are also propagated into the geoid model by the topographic and downward continuation (DWC) corrections in the application of Stokess formula.The effects of these errors are assessed by the evaluation of the absolute accuracy of nine independent DEMs for the Iran region. It is shown that the improvement in using the high-resolution Shuttle Radar Topography Mission (SRTM) data versus previously available DEMs in gridding of gravity anomalies, terrain correction sand DWC effects for the geoid model are significant.Based on the Iranian GPS/levelling network data, we estimate the absolute vertical accuracy of the SRTM in Iran to be 6.5 m, which is much better than the estimated global accuracy of the SRTM (say 16 m). Hence, this DEM has a comparable accuracy to a current photogrammetric high-resolution DEM of Iran under development. We also found very large differences between the GLOBE and SRTM models on the range of750 to 550 m. This difference causes an error in the range of 160 to 140 mGal in interpolating surface gravity anomalies and 60 to 60 mGal in simple Bouguer anomaly correction terms. In the view of geoid heights, we found large differences between the use of GLOBE and SRTM DEMs, in the range of 1.1 to 1m for the study area. The terrain correction of the geoid model at selected GPS/levelling points only differs by 3 cm for these two DEMs.Keywords Digital elevation model (DEM) Geoid Iran Shuttle Radar Topography Mission (SRTM)1 IntroductionAdigital elevation model(DEM)is a computer representation of the Earths surface; it provides a base dataset from which topographic parameters can be digitally generated. DEMs are used, e.g., to determine the terrain correction and downward continuation (DWC) corrections in geoid modelling, geo-morphological simulation and classification and hydrological run-off modelling.However, a DEM is only a model of the elevation surface,and like other models, it is subject to errors (e.g., Hiltonet al. 2003). Like any other source of data in geoid determination(e.g., global geopotential models and gravity data), it is important to evaluate the accuracy of the DEM in the area of interest before using it. The accuracy of DEMs usually is not uniform because they use various data sources in their construction. To make such an assessment, users must first be aware of the impact of errors of the DEM (e.g., Merry 2003).The error can be directly estimated by comparing the heights extracted from a DEM and their values interpolated from GPS/levelling data (where GPS is used for the horizontal control). However, because of the presence of datum problems among different types of heights, in particular in the determination of heights by levelling, this effect must be eliminated before any detailed discussion.There have been a few studies on DEM-error effects in geoid modelling. Merry (2003) compared the effect of some regional and global DEMs according to Molodenskys theory for computing the G1 term and the influence of the grid size of DEMs on quasi-geoid in a small part of South Africa.Based on his work, an error in height of 120m introduces a RMS error in the height anomaly ( ) and G1 term in the order of 7 and 2 cm, respectively. After the release of the high-resolution Shuttle Radar Topography Mission (SRTM) DEM,it is of interest to investigate the quality and effect of thisnew data source versus regional and global DEMs in geoidmodelling.The test area that we have chosen for this purpose is inIran, bounded by N N and 44E E(where 1 is latitude and is longitude), that has one ofthe most complicated and rough topographies in the world.The topography and geoid heights vary in the range of 26 to 5595m and 40 to +30 m, respectively. Also, instead ofusing the height anomaly (cf. Merry 2003), this research is concerned with the comparison of geoid height differences between DEMs. In the first step, we evaluate the absolute accuracy of nine different DEMs in the area. Then, we estimate the effect of using the new SRTM DEM versus GLOBE version 1 (Hastings and Dunbar 1999) in creating a gravity anomaly database and a geoid model.2 Global elevation modelsThere are numerous elevation datasets with global or nearglobal coverage. In this section, we give a brief outline of some of these. 2.1 GTOPO30 DEM GTOPO30 (US Geological Survey 1997) is a global DEM with a horizontal grid spacing of 30_ (1 km). Detailed information on the characteristics of GTOPO30 including the data distribution format, the data sources, production methods, accuracy, and hints for users, can be found at http:/edcdaac. usgs. gov/gtopo30/README.asp. Recently, SRTM data (see below) were used to update the older USGS GTOPO30 global DEM, by averaging them to 30_ resolution and replacing GTOPO30 data between the latitudes of 60N and 56S.2.2 NOAA GLOBE DEMGLOBE (Hastings and Dunbar 1999) is a global 30_ DEM referenced to WGS84 and mean sea level. Eleven previous DEMs and cartographic sources were evaluated and compared in selecting the best available data for GLOBE. The vertical accuracy of GLOBE ranges from 1015m for some of its best sources, to 150500mfor poor sources. This model is newer than the original GTOPO30, and it also includes bathymetry data.2.3 Shuttle Radar Topography MissionThe SRTM data products result from a collaborative mission by the National Aeronautics and Space Administration (NASA), the National Imagery and MappingAgency (NIMA),the German space agency (DLR) and Italian space agency(ASI), to generate a near-global DEM of the Earth usingsatellite radar interferometry.The SRTM flight occurred during February 1122, 2000,and successfully fulfilled all mission objectives. The mission collected 3-D measurements of the Earths land surface using radar interferometry, which compares two radar images taken at slightly different locations (stereo effect) to obtain elevation information. The collected radar images were converted to DEMs spanning the globe between 60N and 58S. The “virtual Earth” is reconstructed as a mesh of 30m spacing, and it is accompanied for each point by a measure of the reflected energy of the radar signal, the intensity image.The memorandum of understanding between NASA and NIMA for SRTM specifies that data will be processed at 3_(90 m) for any point on Earth and made available unrestricted, as will the 1_(30 m) data for the United States and its territories. Distribution of 1_data for outside the United States is approved by NIMA on a case-by-case basis for NASA investigators, for their use only. The overall estimation for the absolute horizontal and vertical accuracy is 20 and 16 m, respectively in a90%confidence interval. (Detailed documentation with technical specification of the SRTMdata can be found at /srtm/ Documentation/).The data are available from the USGS server:/pub/data/srtm/.There are also a very large number of holes or gaps inthe data, especially in mountainous areas. There are several versions of freely available software for patching the gaps in SRTM files (e.g. SRTMFILL (/srtmfill.html), BlackArt (/) and VTBuilder (/Doc/VTBuilder/ overview.html). However, there are not yet any tools for using shoreline vectors to fix the noise in SRTM DEM water areas. Finally, the SRTM DEM does not include any bathymetric data.2.4 ComputaMaps DEMThis model is extracted from SRTMdata and has a 500mhorizontal resolution. It is published in the UTM map projection system. Detailed documentation with technical specification of the model can be found /freedata. php/pub/data/srtm/. .SRTM Topo.txt.2.5 ETOPOETOPO5 is another global DEM that was published by US National Geophysical Data Centre (NOAA) in 1988, and it has 5_ resolution (approximately 9 km). The 2_ (3.6 km) version of this model was published in 2001. The five major data sources were assembled into the single ETOPO22_ data base: data derived from GLOBE DEM, Sandwell and Smith (1997) bathymetric data and Digital BathymetricData Base (DBDB), International Bathymetric Chart ofthe Arctic Ocean (IBCAO) and the Digital Bathymetric Data Base 5_ (DBDB5) filling any gaps. For more information, see:www.ngdc.noaa. gov/mgg/fliers/01mgg04.html.2.6 SandwellSmithDEM Sandwell and Smith (1997) published another global bathymetric DEM with 310 km resolution that is claimed to have higher accuracy compared to the ETOPO models. The information in land areas is extracted directly from the GTOPO DEM. For more information, see: /WWW html/mar topo.html. 2.7 Summary of DEMsTable 1 presents a summary of currently available DEMsin the world. In order to compare the differences betweenDEMs in Iran, we extracted heights over an area bounded by25N 40N, 44E 64E from each DEM.Table 2 shows a summary of a statistical analysis for theDEMs under consideration in this region.3 Review of current Iranian DEM modelsHere we briefly reviewthe currentDEMsof the Iranian region and their accuracies. Two different local DEMs have been computed for Iran since 1997. The computation of the first DEM was conducted jointly by the Institut fur Angewandte Geodasie (IfAG), Germany, the Institute of Geophysics, Tehran University (IGTU) and the National Cartographic Centre of Iran (NCC) (Hamesh and Zomorrodian 1992). The DEM height was extracted directly from the old 1/250000 photogrammetric-based maps (paper versions) at a 1 kmresolution. Based on NCC technical standards issue for Iranian maps,the vertical and horizontal accuracies of interpolated heights from paper maps are in the best case estimated to be 1/3 of the contour interval and 0.5mm in paper map scale, respectively. That means that this DEM has vertical and horizontalaccuracies near 80 and 125 m, respectively. The IfAG groupused it to compute the first gravimetric geoid model of Iran(Hamesh and Zomorrodian 1992).Because of the presence of outliers and the low accuracy of the abovementioned DEM, an old version of GTOPO was used in the computation of more recent geoid models of Iran e.g., TUG (Ardalan and Grafarend 2004) and KNTUG(Najafi 2004).In 2001, NCC decided to produce a national DEM from the 1/25000 base map series with 10mresolution. At present, 80% of the country is covered by theDEM(http:/ .ir/index1e.htm).As mentioned before, the SRTM DEM originally has some gaps that must be filled before its application in any practical geoid computation. In this research, a new IranianDEM, denoted IRD04 (limited to 23 42, 42 67), was created with 3_resolution based on the original 100m resolution SRTM DEM data. The small gaps were patched and filled by interpolation using SRTMFILL software. The large gaps in land and marine areas were filled using information from the ComputaMaps DEM. The minimum, maximum, mean and standard deviation of the IRD04 model are 26, 5595, 1059 and 734 m, respectively.4 DEMs versus GPS/levelling DataA total of 260 precise levelling benchmarks (occupied with GPS) are available within the test region (Fig. 1). The data are reasonably well distributed in different topographical areas. The minimum, maximum, mean and standard deviationof these levelled heights are 21.45, 2551.55, 1083.68 and651.99 m, respectively. They originate from the first- and second-order national levelling networks.The spirit levelled heights are believed to be accurate at the 0.7mlevel, limited by the neglect of the sea surface topography (Abbolgasem 1994) and the presence of the significant systematic errors (e.g., refraction, staff settlement, etc), neglecting the correction of gravity to orthometric heights (Hamesh 1991) in the determination and adjustment of leveling network, and some uncertainty about the definition and establishment of an improper height reference system in the adjustment of the network (Hamesh 1991).The horizontal positions of the points are derived from the first- and second-order Iranian GPS networks based on the WGS84 ellipsoid. Most of these points are common with the Iranian first-order levelling network. The observations of the GPS network started in August 1988 and continued through 2004.Acknowledgements The land surveying and gravity anomalies data used for this research were provided by National Cartographic Centre of Iran. Constructive comments of Prof. W.E. Featherstone, Prof. C. Merry and two unknown reviewers are gratefully acknowledged.ReferencesAbbolgasemA(1994) Iranian sea surface topography.MScThesis, K.N.Toosi University, TehranAgren J (2004) Regional geoid determination methods for the era ofsatellite gravimetry, PhD Thesis, Royal Institute of Technology,Stockholm, SwedenArdalan AA, Grafarend EW (2004) High resolution geoid computation without applying Stokess formula case study: high resolution geoidof Iran. J Geod 78:138156Forsberg R (1985) Gravity field terrain effect computations by FFT.Bull Geod 59:342360Fotopoulos G, Kotsakis C, Sideris MG (2003) How accurately can wedetermine orthometric height differences from GPS and geoid data?Simulated case studies inWestern Canada. J Surv Eng 129(1):110Hamesh M (1991) Technical report about adjustment of Iranian first order levelling network, National Cartographic Centre of Iran. J Surveying 1:920Hamesh M, Zomorrodian H (1992) Iranian gravimetric geoid determination second step, National Cartographic Centre of Iran. J Surv6:1724, 5263Hastings DA, Dunbar PK (1999) Global land one-kilometer base elevation(GLOBE): NGDC key to geophysical records documentation No. 34. National Geophysical Data Center, Boulder, Colorado, p 138HeiskanenWA, Moritz H (1967) Physical geodesy. Freeman, San FranciscoHilton RD, Featherstone WE, Berry PAM, Johnson CPD, Kirby JF(2003) Comparison of digital elevation models over Australia andexternal validation using ERS-1 satellite radar altimetry. Aust J EarthSci 50:157168Kiamehr R, Sjoberg LE (2005) The qualities of Iranian gravimetricgeoid models versus recent gravity field missions. Studia Geophysicaet Geodaetica 49:289304Kiamehr R (2005) Qualification and refinement of the Iranian gravitydatabase. In: Proceedings of the National Cartographic Center ofIran Geomatics 84 Conferences, TehranKotsakis C, Sideris MG (1999) On the adjustment of combined GPS/levelling/geoid networks. J Geod 73(8):412421Lemoine FG, Kenyon SC, Factor JK, Trimmer RG, Pavlis NK, ChinnDS, Cox CM, Klosko SM, Luthcke SB, Torrence MH, Wang YM,Williamson RG, Pavlis EC, Rapp RH, Olson TR (1998) The developmentof the joint NASA GSFC and the National Imagery andMapping Agency (NIMA) Geopotential Model EGM96, NASA/TP-1998206861. Goddard Space Flight Center, GreenbeltMerry CL (2003) DEM-induced errors in developing a quasi-geoidmodel for Africa. J Geod 77:537542Najafi M (2004) New Iranian geoid model using Stokes-Helmert approach.Tech report. National Cartographic Centre of Iran, TehranTscherning CC, Knudsen P, Forsberg R (1994) Description of the GRAVSOFT package. Geophysical Institute, University of Copenhagen,Technical report, 1991, 2nd edn, 1992, 3rd edn, 1993, 4thednSandwell DT, SmithWHF (1997) Marine gravity anomaly from Geosat and ERS 1 satellite altimetry. J Geophys Res 102(B5):1003910054 Sjoberg LE (1991) Refined least squares modification of Stokess formula.Manuscr Geod 16:367375Sjoberg LE (2003) A computational scheme to model the geoid by themodified Stokes formula without gravity reductions. J Geod 77:423432US Geological Survey (1997) GTOPO30 digital elevation model. USGeological Survey航天飞机雷达地形测绘全球数字高程模型对测定一个高分辨率大地水准面模型的作用：在伊朗一个案例研究摘要：数字高程模型（DEM）的任何错误会在重力异常和大地水准面模型内插布格重力时引入误差。误差通过地形向下继续传播到大地水准面模型，应用斯托克斯公式改正。这些误差由伊朗的9个独立DEM分析评估后得到的。结果表明在使用中的重力异常，地形校正对DWC的影响，为大地水准面模型网格高分辨率航天飞机雷达地形测绘使命（到SRTM）提供的数据与以前的DEM有显著的改善. 基于/伊朗的GPS水准网的数据，我们估计在伊朗的地区SRTM绝对垂直精度为6.5米，比预计的到SRTM（全球16米）精度更好。因此，这个数字高程模型已发展到一个根据伊朗目前的摄影高分辨率数字高程模型比较准确。我们还发现在范围为750至550米之间GLOBE 和 SRTM的差距非常大。在大地水准面的高度来看，我们发现水准点的选择对GPS大地水准面模型地形对这两个DEM还说仅相差3厘米。关键词：数字高程模型 航天飞机雷达地形测绘引言数字高程模型是地球表面形态的数字化延伸：它提供了一个从该数字地形参数可生成的基础数据集。DEM信息的使用，例如，在大地水准面模型，地理形态和分类，水文模拟径流模型中确定地形改正和向下延续（DW）的更正。然而，数字高程模型知识高程模型的表面，像其他模型一样，它也有误差（例如，Hiltonet人。2003年）。像任何其他大地水准面的数字资源一样（例如，全球重力场模型和重力数据），数字高程模型在应用它之前先确定他的精度是很重要的。DEM的精度不是不一样的，因为他们用各种不同的数据建立数据库。为了做这样的评估，用户必须认识到误差对DEM的重要影响（例如，2003年快乐的错误造成的影响）。该错误可以直接通过比较高，估计从提取DEM和他们的价值观的GPS插/水准数据（如全球定位系统是为平面控制使用）。但是，由于不同类型之间的高度数据存在的问题，特别是在平整的高度测定，必须在这方面的详细discussion.There淘汰已在大地水准面模型DEM的错误影响少数研究。风流（2003）比较了一些区域和全球DEM的效果为依据计算的G1学期及关于似大地水准面DEM信息网格大小的小南对他的工作，一个错误Africa.Based部分影响，广义Molodensky的理论在120m高的高度提出了一种在高度均方根误差在7日和2厘米秩序异常（）和G1条款。后高分辨率航天飞机雷达地形测绘使命（到SRTM）数字高程模型，它感兴趣的是，调查数据质量和thisnew在geoidmodelling与区域和全球DEM信息源的影响释放。该试验区，我们为此选择在伊朗，由N N and 44E E（其中1是经度和纬度是），即在一个ofthe的world.The地形最复杂，粗糙地形和大地水准面的高度变化范围在-26和-40至5595米三十米分别。此外，而不是ofusing高度距平（见风流2003年），本研究关注的是大地水准面的高度之间DEM的差异比较。在第一步，我们评估该地区的9个不同DEM的绝对准确性。然后，我们估计，使用新的SRTM DEM的版本1与全球方案，创造一个重力异常数据库和大地水准面模型（黑斯廷斯和邓巴1999年）起生效。2全球高程模型 这个高程数据库包括了全球或几乎全球所有的高程，在本节中，我们给出了其中的一些简要概述。2.1 GTOPO30数字高程模型水平网格间距GTOPO30（美国地质调查局1997年）是一个有_水平网格间距的全球数字高程模型。详细资料，包括数据分布格式，数据来源，生产方法，准确性GTOPO30的特点，可在 http:/edcdaac. usgs. gov/gtopo30/README.asp.网站查找。最近，SRTM数据（见下文）被用来更新旧的美国地质勘探局GTOPO30全球平均数字高程模型的分辨率。他们用30取代北纬至的 GTOPO30数据。2.2 NOAA全球数字高程模型地球仪（黑斯廷斯和邓巴1999年）是一个全球性30_参照德国马克的WGS84和平均海平面。前11个DEM与制图来源进行了评价和比较，选择地球上最好的数据。以全球范围的垂直精度由最好的10-15米到最差的150-500m。该模型是原来GTOPO30的更新，也包括水深数据。2.3航天飞机雷达地形测绘SRTM数据的产品美国国家航空和航天局（NASA）合作任务的结果，国家影像制图局（