Final composite report

Transcription

1 Conduct aerial gravity survey countrywide for height component of the geodetic network Final composite report Part 1: Final gravity acquisition and processing report Part 2: Geoid model for Tanzania from airborne and surface gravity submitted to Ministry of Lands Housing and Human Settlements Development Kivukoni Waterfront Dar es Salaam CVR-nr. DK Kgs Lyngby December 2013 Arne Vestergaard Olesen & Rene Forsberg Technical University of Denmark DTU Space National Space Institute Elektrovej Kgs Lyngby Denmark Ph Dir Fax

2 - 1 - Final gravity acquisition and processing report Content: 1. Introduction p 2 2. Operational overview p 3 3. Instruments p 4 4. GPS processing and reference station coordinates. P 5 5. Gravity ties p 6 6. Airborne gravity processing p 6 7. Data validation p 8 8. Summary p 10 Appendix A: Flight summary p 11 CVR-nr. DK Technical University of Denmark DTU Space National Space Institute Elektrovej Kgs Lyngby Denmark Ph Dir Fax avo@space.dtu.dk

3 Introduction We started out with some delays. First an intentional delay in order to wait for better weather conditions. A prolonged wet season over most parts of Tanzania this year forced us to make some changes to the scheduling of the airborne survey operations. The survey was initially planned to commence by mid May but was postponed to early June. After this planned delay came some unforeseen delays. Clearances from TCAA and from the military were not in place by early June. We did a test flight on June 21 and got a good to go from the Technical Supervisor. But we had to wait until June 25 before the military released the security officer and we could commence survey operations out of Dodoma. Figure 1. Survey blocks and airports of operation: DO=Dodoma, KJ=Kilimanjaro, TG=Tanga, MT=Mtwara. Technical University of Denmark DTU Space National Space Institute Elektrovej Kgs Lyngby Denmark Ph Dir Fax avo@space.dtu.dk

4 -3- Coastal Aviation ( provided aircraft and crew for the survey. We used Coastal s newest Cessna Grand Caravan, 5H BEE, which is equipped with the most modern avionics. This air craft was also used for the 2012 airborne gravity survey and with very satisfying results. 2. Operational overview The general survey layout is detailed in Figure 1. We started with operations out of Dodoma (DO) on June 25 to cover the southern part of Block 4 and then proceeded to Kilimanjaro (KJ) on July 2 to fin ish the northern part of Block 4 from there. Block 4 was completed on July 10. Block 3 was flown from Kilimanjaro as well. The completion of Block 3 and transfer to Tanga (TG) on July 16 marked the halfway point for the survey. Block 2 was flown from Tanga. We moved to Mtwara on July 20 and fin ished operations in block 1 on July 26. Figure 2. Ground track pattern Technical University of Denmark Elektrovej 328 Ph avo@space.dtu.dk DTU Space 2800 Kgs Lyngby Dir National Space Institute Denmark Fax

5 - 4 - Figure 2 shows ground track pattern for the whole survey. All survey lines have been flown at constant altitude. The quality of airborne gravity measurement is very dependent on turbulence which means it should preferable be flown when the atmosphere is more settled. All survey lines have therefore been flown at night and in the early morning hours. Details for individual flights are listed in Appendix A. 3. Instruments Figure 3. Cabin layout in 5H BEE. To the right the LCR gravimeter and behind it the Chekan meter. The following survey equipment was installed in the aircraft: LaCoste & Romberg Air/Sea gravimeter S 38 Chekan AM gravimeter #24 Honeywell INS Javad Lexon GPS receivers (aircraft) Javad Delta GPS receivers (aircraft) Technical University of Denmark DTU Space National Space Institute Elektrovej Kgs Lyngby Denmark Ph Dir Fax avo@space.dtu.dk

6 GPS processing and reference station coordinates. GPS reference stations were operated in all airports. These stations together with reference stations operated by SMD were used for differential trajectory determination of the aircraft. Table 1. Coordinates for airport GPS reference stations (ITRF 2008) Airport Designation Lattitude Longitude Height ell. (m) Dodoma DO Kilimanjaro KL Tanga TG Mtwara MT Coordinates for the GPS reference stations were obtained from the AUSPOS GPS service provided by Geoscience Australia. Coordinates are given in the ITRF2008 frame, see The AUSPOS service also provides estimates of the accuracy with which the coordinates are determined. These estimates in general amounted to 0.5 to 2 cm for the height component for individual sessions. Variations in the results from different sessions, typical 5 to 8 hours, were consistent with the noise estimates. Mean values for several sessions were used as final coordinates for the reference receivers, see table 1. Aircraft trajectories were computed with the WayPoint software package from NovAtel (Calgary, Canada) using precise ephemerides from International GNSS Service ( More combinations of rover and base receiver were computed for each flight and the best performing solution chosen for the final iteration of the gravity processing. Figure 4. Airport GPS reference receiver. Technical University of Denmark DTU Space National Space Institute Elektrovej Kgs Lyngby Denmark Ph Dir Fax avo@space.dtu.dk

7 Gravity ties Three absolute gravity stations were established in Tanzania in The main airports were subsequently tied to these three absolute stations, see Morgan and Francis Apron reference gravity was tied to the newly established SMD gravity points in or near Dodoma, Moshi, Tanga and Mtwara airports. The gravity ties were done with LaCoste&Romberg G 466 land gravimeter. Table3. Airport gravity values (P. Morgan personal comm.) Airport G value Sigma Dodoma Moshi Tanga Mtwara Table 4. Derived apron gravity values Airport G value Sigma Dodoma Kilimanjaro Tanga Mtwara Airborne gravity processing Free air gravity anomalies at aircraft level are obtained from Δg γ h 2 f f h δg δg g γ ( h N h N ) (1) z z0 eotvos tilt h γ 2 Technical University of Denmark DTU Space National Space Institute Elektrovej Kgs Lyngby Denmark Ph Dir Fax avo@space.dtu.dk

8 - 7 - where f z is the gravimeter observation, f z0 the apron base reading, h the GPS vertical acceleration, g eotvos the Eötvös correction computed by the formulas of Harlan (1968), g 0 the apron gravity value, γ 0 normal gravity, h the GPS ellipsoidal height and N the geoid undulation (EGM08 used throughout). γ 0 and the second order height correction in equation (1) is based on GRS80 definitions (Moritz, 1980). An altitude dependent atmospheric correction has been applied, see eg Hintze et al EGM08 values are derived from the pre computed geoid undulations grid Und_min2.5x2.5_egm2008_isw=82_WGS84_TideFree_SE provided by N. Pavlis, see The platform off level correction g tilt is based on a platform modeling approach as described in Olesen (2003). All data were filtered with a symmetric second order Butterworth filter with a half power point at 170 seconds, corresponding to a resolution of 6 km (half wavelength). The impulse response and spectral behavior of the filter are shown in Figure 5. See Olesen 2003 for further details regarding the airborne gravity data reduction. Apron base readings were performed each day before and after the flight in order to monitor drift of the airborne gravimeter and make a proper connection of airborne readings to the national gravity network. normalized weight transmission seconds 1E-3 1E-2 frequency, Hz Figure 5. Impulse response (normalized) and spectral representation of the filter Technical University of Denmark DTU Space National Space Institute Elektrovej Kgs Lyngby Denmark Ph Dir Fax avo@space.dtu.dk

9 Data validation Weather conditions and thereby data quality has in general been good. We only encountered a few situations with more severe turbulence. The affected parts have been re flown. Figure 6 shows the acquired free air anomalies at flight altitude. The figure shows nice color agreement where lines intersect indicating consistent and healthy data. A closer examination of the misfit where lines intersect show a 3.2 mgal RMS error indicating 2.3 mgal average noise for the whole data set. This is very satisfying results and in line with other surveys flown under similar conditions. Figure 6. Free air anomalies at flight altitude Technical University of Denmark DTU Space National Space Institute Elektrovej Kgs Lyngby Denmark Ph Dir Fax avo@space.dtu.dk

10 - 9 - Figure 7 shows the countrywide airborne gravity coverage. The plot shows that the June/July data blends seamlessly with the two other surveys, the 2012 and the September/October 2013 survey underscoring the good and even quality of the three surveys. This combined data set forms the basis for the computation of the Tanzanian geoid. The geoid computations are described in part 2 of the composite report. Figure 7. Gridded free air anomalies for the three surveys; the 2012 survey, the June/July 2013 survey and the September/October 2013 survey. Technical University of Denmark DTU Space National Space Institute Elektrovej Kgs Lyngby Denmark Ph Dir Fax avo@space.dtu.dk

11 Summary The survey was successfully completed and with very satisfying results. Cross over error estimates indicate a 2.3 mgal average noise on the data. The good data quality was achieved due to proper planning and preparations. The fact that we were able to fly at night contributed significantly to data quality. The successful completion was in large parts thanks to the preparations and support from SMD. References Harlan, R. B.: Eotvos corrections for airborne gravimetry, J. Geophys. Res., 3, , Morgan P. and O. Francis, Implementing an absolute gravity network in Tanzania. Report, 20 pages, 2010 Moritz H.: Geodetic Reference System Journal of Geodesy, 54, Olesen, A. V.: Improved airborne scalar gravimetry for regional gravity field mapping and geoid determination, Kort og Matrikelstyrelsen Technical Report no. 24, 55 pp, 2003 Technical University of Denmark DTU Space National Space Institute Elektrovej Kgs Lyngby Denmark Ph Dir Fax avo@space.dtu.dk

12 Appendix A: Flight summary MLHHSD-DTU flights Tanzania 2013 (5H-BEE) Date/JD* Flight from to Airborne Landed Airborne time 21 June/172 Test Dar-Dar Ferry Dar-Dod h37 25 June/176 F01 Dod-Dod h35 26 June/177 F02 Dod-Dod h34 27 June/178 F03 Dod-Dod h41 28 June/179 F04 Dod-Dod h03 29 June/180 F05 Dod-Dod h30 30 June/181 None 01 July/182 F06 Dod-Dod h55 02 July/183 F07 Dod-Kmj h21 03 July/184 F08 Kmj-Kmj h56 04 July/185 F09 Kmj-Kmj h47 05 July/186 F10 Kmj-Kmj h21 06 July/187 None 07 July/188 F11 Kmj-Kmj h55 08 July/189 F12 Kmj-Kmj h10 09 July/190 F14 Kmj-Kmj h35 10 July/191 F15 Kmj-Kmj h08 11 July/192 F16 Kmj-Kmj h58 12 July/193 F17 Kmj-Kmj h25 13 July/194 F18 Kmj-Kmj h41 14 July/195 None 15 July/196 F19 Kmj-Kmj h15 16 July/197 F20 Kmj-Zan h Ferry Zan-Tng h32 17 July/198 F21 Tng-Zan h Ferry Zan-Tng h35 18 July/199 F22 Tng-Dar h08 19 July/200 F23 Dar-Mtw h06 20 July/201 F25 Mtw-Mtw h07 22 July/203 F26 Mtw-Mtw h25 23 July/204 F27 Mtw-Mtw h11 24 July/205 F28 Mtw-Mtw h30 25 July/206 F29 Mtw-Mtw h47 26 July/207 F24 Mtw-Mtw h Ferry Mtw-Dar h32 Technical University of Denmark DTU Space National Space Institute Elektrovej Kgs Lyngby Denmark Ph Dir Fax avo@space.dtu.dk

13 Background Geoid model for Tanzania from airborne and surface gravity Rene Forsberg, Arne V. Olesen National Space Institute, Technical University of Denmark (DTU-Space) James Mtamakaya, Cresensia Tarimo Survey and Mapping Division Ministry of Lands, Housing and Human Settlements Development Dar Es Salaam, Tanzania Prosper Ulotu Ardhi University, Dar Es Salaam, Tanzania A new preliminary geoid model for the area of Tanzania has been computed from gravity data measured during the 2013 DTU-Space and the Tanzania-SMD airborne gravity survey, supplemented with marine gravity data (shipborne measurements and satellite altimetry altimetry), from GRACE satellite data as implemented in the global gravity field model EGM08, and from new high-resolution satellite gravity data from the GOCE mission. Digital terrain models used in the computation process was based on 15 SRTM data. A geoid model is a surface (N) which describes the theoretical height of the ocean and the zerolevel surface on land. The geoid is required to obtain orthometric height H ( height above sea level ) from GPS by H = h GPS N (1) where h GPS is the GPS ellipsoidal height, and H the levelled (orthometric) height. This equation is the classic equation for height determination with GPS. However, it only holds in a global system of reference, so to be consistent with local heights, the geoid need to be fitted to local heights, based on local sea level. This is in practice done by making apparent local geoid heights at points with both precise GPS and levelling heights and then fitting an empirical surface to the differences N GPS = h GPS H (2) = N grav - N GPS (3) and modelling this difference across a larger area, giving a GPS geoid. It should be noted that a GPS geoid is not a geoid in the classical definition (geoid is defined as an equipotential surface in the earth s gravity field), but rather a surface which is a composite of the geoid, the mean sea surface topography variations, as well as errors in GPS and levelling heights.

14 For Tanzania this fitting has been done in the simplest possible way, just adding a constant to the new gravimetric geoid model, giving the final Tanzanian GPS geoid TZG013. The constant of m for fit to the Tanzanian height datum has been determined from a set of 20 GPS Benchmark GPS-levelling point data, provided by SMD and Ardhi University. Gravimetric geoid computation - principles The Tanzania gravimetric geoid is computed by the GRAVSOFT system, a set of Fortran routines developed through many years of research and project work at DTU-Space and Niels Bohr Institute, University of Copenhagen [1]. It forms the base of major recent geoid computation projects, such as the joint Nordic NKG geoid models, undertaken as joint geoid model computations of the Nordic and Baltic countries [2] under the auspices of the Nordic Commission for Geodesy (NKG), as well as the OSGM02 geoid model of the UK and Ireland [3], and several national geoid models done from airborne surveys in recent years (Malaysia, Mongolia, Indonesia and others). The Tanzania geoid has been computed by a remove-restore technique, where a spherical harmonic earth geopotential model (EGM) is used as a base, and the geoid is computed from the global contribution N EGM, a local gravity derived component N 2, and a terrain part N 3. N grav = N EGM + N 2 + N 3 (4) The spherical harmonic expression as a function of latitude, longitude and height is of form n N n GM R N(,, r) C nm cos m S nm sin m P nm sin R n 2 r (5) m 0 where GM, R and are earth parameters. For the EGM08/GOCE models used here, this involves more than 4 mio coefficients C nm and S nm derived from a very large set of global satellite data and regional (average) gravity data from all available sources, both open-file and classified, for details see The EGM08 model is incorporating GRACE satellite data, which determines the error spectrum of the EGM08 up to spherical harmonic degree 80 or so. New satellite data from the GOCE mission have recently been made available by the European Space Agency, for details see We have for the Tanzania geoid used the latest GOCE spherical harmonic model ( Direct Release 4 model), complete to degree and order 260. The EGM08 field has been updated with the GOCE data in the following way: - EGM08 used unchanged in spherical harmonic orders 2-80, and from 200 up - GOCE R4 direct model used in band A linear blending of the two models done in bands and The blending has been done with GRAVSOFT program POTCOMB, and is a relative simple way of improving the EGM08 in the medium wavelength band, before a future EGM201? incorporating GOCE is available. The mixed spherical harmonic model (termed EGM08GOCE) has here been used to spherical harmonic degree N = 720, corresponding to a resolution of 15 or approximately 28 km. This choice of resolution is based on experience from recent DTU geoid projects in France (Auvergne), Malaysia, and Nepal, and appears to be a good trade off between the full resolution of EGM08 2

15 (degree 2160) and the local gravity data. Because the full-resolution gravity data used in the construction EGM08 is classified, there is no good information on the quality of the errors in EGM08 at the high wavelengths, and only 15 mean gravity data are assumed to be underlying EGM08 in Africa. All spherical harmonic computations were done in a grid using the geocol17 program in grid mode. The terrain part of the computations were based on the RTM method, where topography is referred to a mean elevation level, and only residuals relative to this level is taken into account. The mean elevation surface were derived from the SRTM 15 detailed model through a moving average filter with a resolution of approximately 45 km (slightly longer than the 15 data resolution implied by spherical harmonic degree 720, in order to have a more smooth residual gravity signal g 2 ). The difference in resolution between reference field and RTM is not a theoretical issue, as the removerestore method takes any double accounted topography into account fully. The method for the gravimetric geoid determination is spherical FFT with optimized kernels. This is a variant of the classical geoid integral ( Stokes integral ), in which there is a proper weighting of the long wavelengths from EGM08 and the shorter wavelengths from the local gravity data. Mathematically it involves evaluating convolution expressions of form N 2 = S ref (, ) [ g 2 (, )sin ] = F -1 [F(S ref )F( gsin )] (6) Here S ref is a modified Stokes kernel, g 2 = g - g EGM is the EGM08GOCE-reduced free-air gravity anomalies, and F is the 2-dimensional Fourier transform operator. For details see references [2]-[4] and further references therein. The Tanzania geoid is computed on a grid of 0.02 x 0.02 resolution (corresponding to roughly 2 x 2 km grid). The area of computation is 13 S-1 N and E, covering a major part of the Indian Ocean offshore Tanzania as well. The computations have been based on least squares collocation and Fast Fourier Transformation methods. The FFT transformations at the 2 km resolution involve 1400 x 1500 grid points, corresponding to 100% zero padding. The data are gridded and downward continued by least squares collocation using the planar logarithmic model. A number of GRAVSOFT programs are involved in this process (gpcol1, spfour, gcomb, geoip), and jobs for the processing have been set up in a directory structure, outlined in Appendix 2. Several geoid models were computed, either by simple set ups based on surface data only, or more elaborate setups incorporating full three-dimensional handling of airborne and surface gravity data. The selected final gravimetric geoid solution was computed by following steps: - Subtraction of EGM08GOCE spatial reference field (in a 3-D sandwich mode ) - RTM terrain reduction of surface gravimetry, after editing for outliers - Reduction of DTU-10 satellite altimetry in ocean areas away from airborne data - Downward continuation to the terrain level and gridding of all data by least-squares collocation using a 1 x 1 moving-block scheme with 0.6 overlap borders - Spherical Fourier Transformation from gravity to geoid - Restore of RTM and EGM08GOCE effects on the geoid 3

16 The above scheme technically results in a quasigeoid, and a correction based on 2 km-resolution height and Bouguer anomaly grids was added in the end to obtain the classical geoid. An alternative setup, producing directly the classical geoid using the Helmert condensation method, was also implemented and tested, and gave similar results. No evaluation of different geoid results by precise GPS-levelling was possible, due to the limited accuracy of the available GPS levelling data. However, it is believed from experience in other regions that the general accuracy of the geoid is around 10 cm, with 2-5 cm relative accuracy in the more flat regions of additional gravity data coverage (such as the Dar Es Salaam region), and larger errors in the border regions, where data in neighbouring countries are sparse or absent. Fig. 1. The Tanzanian geoid Contour interval 2 m. Note the Rift Valley feature (a geoid low). Data used and QC for the geoid computation The November 2013 Tanzania gravimetric geoid is based on the following data: - Airborne gravity data, final results (file: tz-airborna.faa). Data are free-air anomalies at the aircraft altitude, with atmospheric correction. - Land gravity and marine gravity data from various sources, compiled by Ardhi University and SMD (version Nov 28, 2013) - DTU10 global gravity anomalies from multi-mission satellite altimetry. These data were selected only in the ocean area, and further selected only at least 15 km away from the airborne data points, as comparisons showed very large errors in excess of 20 mgal close to the coast (as expected, the inversion of satellite altimetry is not reliable in such regions) - SRTM 15 DEM data for the East Africa region - EGM08 and GOCE RL4 satellite data Some plots of the used data are shown in the Figs. 2-5 below. 4

17 Fig 2. SRTM DEM data (upper); low-pass filtered mean elevation surface (lower), used as reference in RTM terrain reductions. Elevations in meters. Ocean depths are not used in the Tanzanian geoid computations. 5

18 Fig 3. Tanzanian land gravity data used for the geoid determination, before(top) and after(bottom) removing a major problematic surface gravity area in the SW region (data here did not fit well with the airborne data) 6

19 Fig. 4. Airborne gravity data (top: free-air anomalies at altitude, mgal; lower: flight elevations, lower). Flight line spacing 10 nm. The changing survey heights are taken fully into account in the post-processing. 7

20 Fig. 5. Satellite altimetry gravity from DTU10 solution. Data deleted in airborne coverage areas. The available data from the airborne and surface sources were quality controlled through plotting of the EGM08GOCE and terrain reduction residuals, and through prediction of surface gravity anomalies from the airborne data. A direct comparison of the surface free-air gravity data to the airborne by a simple collocation prediction (geogrid) is shown in Fig. 6. It is seen that there are some problems with a major dense gravity source in SW-Tanzania. Inspection of the data indicated the heights to be erroneous, and the data in this region have therefore been deleted by a eliminating data in a number of square blocks (as detailed source information was not available). The deleted data were in the following blocks: [8-6 S, E], [10-8 S, E], [9-8 S, E], [8.5-8 S, E] In addition to this, a few obvious outliers were deleted in the final geoid processing (cutting residual gravity anomalies greater than +/-100 mgal). The edited surface data are shown in Fig. 7. The figure also shows the large misfit of the airborne data and the altimetry in the inshore areas. The airborne gravity data was checked for internal consistency by cross-over analysis, and comparison to GOCE. The cross-over errors were 3.3 mgal, indicating an r.m.s. accuracy of the airborne survey of 1.8 mgal. The comparison to the GOCE RL4 field showed the following fits: Difference to GOCE (max degree 200): mean = 1.4, std.dev. = 27.4 mgal Difference to GOCE (max degree 260): mean = 1.3, std.dev. = 24.5 mgal With no cross-over adjustment applied, the high airborne gravity quality is therefore confirmed. 8

21 Fig. 6. Difference between surface data and interpolated airborne data, when distance < 5 km. Fig. 7. The complete set of edited surface and altimetry gravity, shown here as reduced data. 9

22 Geoid processing results The plots in the sequel shows the intermediate results of the final remove-restore geoid processing ( geoid3 ), computed with full 3-dimensional modelling, going via the quasigeoid to the classical, final geoid for Tanzania. The final geoid covers the region 13 S-1 N, E, and has a resolution of 0.02, with restore digital terrain models used at this resolution as well. The internal reduced gravity grid has a resolution of 0.05, as the data density does not warrant a more detailed gridding. The airborne and surface gravity data were gridded by spatial least squares collocation (gpcol1, using covariance parameters C 0 = 15 mgal, D = 5 km, T = 25 km). A priori errors assumed were 2 mgal for the airborne data, and 1 mgal for surface data (averaged in 0.02 blocks). The collocation downward continuation was done in 1 x 1 blocks, with 0.6 overlaps. Table 1 shows the statistics of the remove steps. It is seen that the residual surface and airborne data has only a small bias. Fig 8 shows the downward continued, merged gravity grid used for the geoid. Table 1. Statistics of remove steps in the Tanzanian gravimetric geoid computation Unit: mgal Mean Std.dev. Min. Max. Land gravity data Land gravity minus EGM08GOCE and RTM Airborne gravity data Airborne minus EGM08GOCE and RTM All gravity data minus EGM08GOCE and RTM Fig. 8. Downward continued reduced gravity data from the least squares blocked computation. 10

23 For the spherical FFT transformation of gravity to geoid, 3 reference bands were used. Grid dimensions of 560 x 600 points for gravity, and 1400 x 1500 points for the terrain, corresponding to 100% zero padding. Fig. 9 shows the reduced geoid (i.e., the geoid determined from the grid in Fig. 8), Fig. 10 the RTM-contribution to the geoid, and Fig the geoid-quasigeoid correction data. Fig. 9. Reduced geoid (after spherical FFT transformation) Fig. 10. RTM restore terrain effect on the geoid. 11

24 Fig. 11. Correction applied to obtain classical geoid (classical geoid minus quasigeoid separation) Fig. 12. Bouguer anomaly grid, derived from the reduced data. Used for the geoid-quasigeoid estimation.. 12

25 Table 2. Statistics of the restore quantities on the geoid Unit: m Mean Std.dev. Min. Max. Reduced geoid (after spherical FFT) RTM restore effects (computed by FFT) Final gravimetric geoid statistics GPS data comparison and final geoid A set of 21 GPS data on levelling benchmarks was available from a recent campaign (TGZ2008), and provided by Ardhi University. Data cover the northern-central part of Tanzania, and was used to approximately transform the final gravimetric geoid (in a world height system) to the Tanzanian height datum. The fit of the GPS-levelling data to various gravimetric geoids is shown in Table 3, and the location of the points in Fig. 13. Table 3. Comparison of GPS-levelling data to the gravimetric geoids Unit: m Mean Std.dev. Min. Max. EGM08 to degree Geoid from surface data only (geoid1) Geoid from airborne data only (geoid2) Classical geoid from all data (geoid3) Classical geoid, Helmert condensation method with terrain reduction (geoid4) Fig. 13. Location of GPS-levelling data. Colours show difference to EGM2008. Unfortunately the GPS-levelling data appears to have relatively large errors, and it is therefore difficult to use these data for error assessment of the geoids. Based on the experience and 13

26 collocation error estimates from other regions with similar data quality and coverage, the geoid error is estimated to be on the order of 10 cm for most of the region. However, systematic errors exist, especially related to the methodology of downward continuation and use of terrain reductions, including the quasigeoid to geoid conversion and indirect effects. These errors are at the 10 cm r.m.s. level as well, as indicated in Fig. 14. Since the Tanzanian levelling network has been adjusted without use of actual gravity observations as normal orthometric heights, there would be theoretical inconsistencies relative to the classical geoid. A comparison to the full EGM08 model (without GOCE) is shown in Fig. 15. Here is seen that the new geoid has improved the EGM08 considerably, especially in the southwestern parts of the country. Fig. 14. Difference between two classical geoid models (geoid4-geoid3), derived either using the quasigeoid as intermediate step (downward continuation to the surface of terrain plus N- correction), or the Helmert condensation method (downward continuation to sea level plus indirect geoid effect term). For the selected final bias-fitted geoid of Tanzania TCG013 the GPS-levelling was used to estimate an overall offset, to make the geoid roughly consistent with the existing Tanzania height datum. For this purpose 20 GPS benchmark stations were used (the southernmost point, an apparent outlier, was omitted, cf. Fig. 13). The offset applied to the geoid3 to obtain the final geoid was m This offset represents both the mean ocean dynamic topography at the defining tide gauge of the Tanzanian height system, as well as reference system computation datum biases in the geocol17 software used for the reference fields. It should be noted that a similar bias was found in Ref

27 The final geoid is given as a GRAVSOFT grid, and can be interpolated by the GUI program gridint (or the command line program geoid ), provided to DSM as part of the computations (Fig. 16). The final geoid is shown as a contour plot in Fig. 17. An application example for the new geoid (height of Mt. Kilimanjaro) is given in Appendix 1, and Appendix 2 lists the main jobs and file names for the geoid computations. Fig 15. Difference between new geoid model and EGM2008 to degree 2160 (global datum). Fig. 16. Interpolation program grid_int user interface. 15

28 Fig. 17. Geoid of Tanzania in national datum (tz_geoid2013) from satellite, airborne and surface gravity References [1] Forsberg, R and C C Tscherning: Overview manual for the GRAVSOFT Geodetic Gravity Field Modelling Programs, 2 nd Ed. Technical report, DTU-Space, August [2] Forsberg, R., D. Solheim and J. Kaminskis: Geoid of the Nordic and Baltic area from gravimetry and satellite altimetry. Proc. Int. Symposium on Gravity, Geoid and Marine Geodesy, Tokyo, Sept. 1996, pp , Springer Verlag IAG Series, [3] Forsberg, R., G. Strykowski, J.C. Illife, M. Ziebart, P.A.Cross, C.C. Tscherning, P. Cruddace, K. Stewart, C. Bray and O. Finch: OSGM02: A new geoid model of the British Isles. Proceedings of the 3rd meeting of the International Gravity and Geoid Comission, GG2002, Aug , 2002, Thessaloniki, I. Tziavos (ed.), Editions Ziti, pp , [4] Forsberg, R. and A. Olesen: Forsberg, Airborne gravity field determination. In: G. Xu (ed): Sciences of Geodesy I, Advances and Future Directions, pp , Springer Verlag, 2010, ISBN [5] Fernandes, R., J. Msemwa, J. Saburi and others: Precise Determination of the Orthometric Height of Mt. Kilimanjaro. FIG Working Week,

29 [6] N. Angelakis: Mt Kilimanjaro Expedition 1999 GPS Data Processing and Evaluation of the ITRF-Position and Height of Mt Kilimanjaro, First Workshop on GPS and Mathematical Geodesy in Tanzania (Kilimanjaro Expedition 1999). Fachhochschule Karlsruhe, October Appendix 1. Application of the new geoid for the height of Mt Kilimanjaro A international team of Portuguese, Tanzanian and Kenyan geodesists have determined the precise ellipsoidal height of the summit of Kilimanjaro (Uhuru Peak), the highest mountain in Africa, based on a 2008 GPS field campaign, involving also gravity observations. The ITRF-2005 coordinates of the summit was determined from a combination of different GPS software or services (AUSPOS, Bernese, SCOUT, GIPSY) to be m (±5 cm). The following values of the orthometric height from the new geoids are obtained: Orthometric heights of the Kilimanjaro Summit ( S, E) Official value (1952 British Ordnance Survey triangulation) Rui et al. [ref 5], EGM08+local gravity survey, Tanzanian datum Rui et al., as above, global datum Angelakis, 1999, using EGM96 [ref 6] New value from tz_geoid2013, Tanzanian height datum New value, Helmert condensation geoid (geoid4), Tanzanian datum 5895 m m m m m m Unfortunately this gave a lower value of the height. The new value is probably correct to ±20 cm, but error could be larger due to lack of data close to the border of Kenya. Appendix 2. Directory structures of the software. For the future recomputation of the Tanzanian geoid, a detailed set of GRAVSOFT jobs were given to SMD. To repeat the geoid computation with new gravity data, it is essential to keep the existing directory structure. Directory structure and primary files EGM08GOCE Jobs for making grids of from spherical harmonics FITGEOID Job for fitting geoid to GPS levelling (important to plot fitgeoid_dif.gri misfit grid) GEOID1 Directory for simple geoid from surface data (geoid1.job) GEOID1\RD-TC EGM and terrain reduction of surface gravimetry (rd.job) Restore geoid correction (n_rtm.gri) for all geoids in this dir GEOID2 Directory for geoid from airborne (gpcol1.job and geoid2.job) GEOID2\RD-TC EGM and terrain reduction for airborne (including filtering) GEOID3 Directory for final geoid (gpcol1.job and geoid3.job)) GEOID3\RD-TC Terrain and EGM reduction (rd_surface.job and rd_air.job) GEOID4 Helmert condensation method (not provided, experimental software) TZ-FINAL Final airborne data tz-airborne.faa ULOTU\GRAVITY Surface land and marine gravimetry (comp_surface.job compares to airborne data; edit_surface.job removes SW data blocks) ULOTU\DEMS SRTM 15 DEM data and averaged grids (2km_tdem.gri) Reference topography (ref_tdem.gri) made with tcgrid.job dtu10mss.dat DTU-10 mean sea surface height above Topex ellipsoid geoip.job Simple comparison job (gps geoid values minus geoid grid) gps_lev.n GPS levelling data from Ardhi University kimanjaro.job Job for getting Kilimanjaro height by interpolation tz_geoid2013.gri Final geoid Steps for final geoid computation (GEOID3): 17

30 rd_air.job rd_surface.job bouguer.job gpcol1.job geoid3.job Reduce airborne data (filter.out defines along-track filtering) Reduce edited surface data (land, marine, altimetry) Bouguer grid estimation(needed for geoid-quasigeoid separation) Downward continuation by block collocation Spherical FFT, restore RTM and EGM08GOCE, quasigeoid correction (the 1.05 m for final geoid is added by a gcomb call) It should be noted that to update the geoid by new GPS-levelling data, only fitgeoid.job is needed. Correlation length and a priori standard error of the GPS levelling of the geoid correction surface must be defined empirically, and especially the output file fitgeoid_dif.gri should be carefully inspected for interpolation artefacts before adopting a new fitted GPS geoid model for Tanzania. Copenhagen, Dec 3,