Status of the European Gravimetric Quasigeoid

Status of the European Gravimetric Quasigeoid C. Voigt, H. Denker {voigt,denker}@ife.uni-hannover.de 1 Introduction 2 The European Gravity and Geoid Project (EGGP) 3 Data Sets 4 Quasigeoid Computation 5 Evaluation of the Results by GPS/Levelling 6 Conclusions

1 Introduction Geoid and Quasigeoid Accuracy requirements: (±0.001 m)... ±0.01 m... ±0.1 m... ±1 m for users in geodesy, oceanography, geophysics, and other disciplines Data requirements (rough estimates): gravity: resolution: 2-5 km; accuracy: approx. 1 mgal terrain (DEM): resolution: 100-500 m; accuracy: approx. 10 m 2

Data Requirements 1 Introduction RMS degree variances for height anomalies and gravity anomalies g (Tscherning/Rapp model 1974): 2 resolution RMS Spherical harmonic l degree l g [km] [m] [mgal] 2... 360 10000... 55 ±30.4614 ±34.05 361... 1000 55... 20 ±0.2172 ±18.13 1001... 2000 20... 10 ±0.0632 ±12.95 2001... 4000 10... 5 ±0.0248 ±9.95 4001... 10000 5... 2 ±0.0078 ±6.19 10001... 2... 0 ±0.0008 ±1.40 2... 10000... 0 ±30.4623 ±42.37 wavelength W 40000 km l, resolution A 1 20000 km W 2 l 3

1 Introduction Gravitational effect of a salt dome 4

Recommendations 1 Introduction Gravity surveys should be connected to a high-precision gravity base network (relying on absolute gravity observations) in order to avoid large-scale systematic errors corresponding accuracies should be 0.01 mgal for gravity, 0.03 m for heights and 1.0 m for horizontal coordinates Accuracy requirements for detail surveys can be relaxed to the level of 1 mgal assuming purely random noise 5

2 The European Gravity and Geoid Project (EGGP) European Gravimetric (Quasi)Geoid Models from Institut für Erdmessung, Leibniz Universität Hannover EGG1: Torge, W., G. Weber, H.-G. Wenzel (1982). Computation of a high resolution European gravimetric geoid (EGG1). Proceed. 2nd Internat. Symp. on the Geoid in Europe and Mediterranean Area, 437-460, Rome. EGG1997: Denker, H., W. Torge (1998). The European gravimetric quasigeoid EGG97 An IAG supported continental enterprise. IAG Symposia 119: 249-254, Springer Verlag. EGG2007: Denker et al. (2009). The Development of the European Gravimetric Geoid Model EGG07. IAG Symposia 133: 177-186, Springer Verlag. EGG2008: Denker, H. (2013). Regional gravity field modeling: Theory and practical results. Monographie in Xu G. (ed.), Sciences of Geodesy II (Chapter 5), 185-291, Springer-Verlag. 6

EGG1997 Institut für Erdmessung 2 The European Gravity and Geoid Project (EGGP) from 1990-2003 IfE acted as the computing center of the IAG Subcommission on the European Geoid several high resolution European (quasi)geoid models were developed the European Gravimetric Geoid 1997 (EGG1997) was published on CD-ROM (> 150 installations) EGG1997 is based on 2.7 million gravity data and 700 million terrain data (data coming from 70 institutions in 29 countries) global geopotential model EGM1996 remove-restore technique, integral formulas (1D FFT) computation area: 25 N 77 N, 35 W 67.4 E 1.0' x 1.5' grid 3,120 x 4,096 = 12,779,520 grid points 7

2 The European Gravity and Geoid Project (EGGP) EGG2007 / EGG2008 European Gravity and Geoid Project (EGGP) project of IAG Commission 2 (CP 2.1), reporting to Sub-Comm. 2.4 start in late 2003 (after the IUGG General Assembly in Sapporo), extended in 2007 (IUGG2007, Perugia) until 2011 national delegates (project members, about 50 persons) connections to other IAG bodies and international agencies main objective of the project is the development of improved geoid and quasigeoid models for Europe results presented roughly annually IAG Sub-Commission 2.4a Gravity and Geoid in Europe since 2011 8

3 Data Sets Gravity data Status of the gravity data base 2007: new or revised data sets included for nearly all European countries some older data sets reprocessed ArcGP (Arctic) and KMS2002 altimetric anomalies included (195,840 and 951,251 values, respectively) common reference systems used for positions (ETRS89), heights (EVRS) and gravity (absolute system) gross error checks performed target area: 25 N 85 N, 50 W 70 E 1' x 1' grid Changes of the gravity data base 2007 / 2008: Greek and Turkish data corrected (in absolute level) a few new sources added new 1' altimetric anomalies (DNSC2008 and Sandwell & Smith), edited near coast (< 10 km offshore) marine gravity data editing improved EGM2008 fillins in Africa and the Caucasus region included 9

3 Data Sets Locations of gravity data stored in IfE data base: Status: EGG1997 Status: EGG2008 (2,684,133 pts. *) (5,355,206 pts. *) (* ArcGP & altimetric data excl.) 10

3 Data Sets Terrain Data Generation of a European terrain data base Merging of the terrain models: national terrain models SRTM3 (54 S 60 N) GTOPO30 (global) GLOBE 1.0 (global; used for evaluation only) gross error checks performed EURDTM3 EURDTM3: 3" x 3" grid size 25 N 85 N, 50 W 70 E 6.6 billion elevations EURDTM1: 1" x 1" grid size Germany, Austria, Switzerland 1.7 billion elevations 11

4 Quasigeoid Computation Remove-Compute-Restore Technique g g g g T M g (integral formulas, collocation) T M long wavelength components are computed from a global Earth gravity model (e.g., EGM96/08, CHAMP/GRACE/GOCE models) short wavelength components are computed from high resolution digital terrain models (DEMs) medium wavelength structures are recovered from terrestrial gravity data 12

4 Quasigeoid Computation Computation procedure: 1 Computation of surface free-air gravity anomalies 2 Computation of residual gravity anomalies (remove step) Δ Δ Δ (geopotential model, l max = 360; RTM terrain reductions 15' 20' ) 13

4 Quasigeoid Computation Harz mountains, Germany Surface free-air gravity anomalies (left) and corresponding RTM 15' 20' reduced values (right) 14

Computation procedure (continued): 3 Gridding of irregularly distributed residual gravity anomalies by leastsquares collocation taking into account the standard deviations of the observations 4 Transformation of residual gravity anomaly grid into corresponding residual quasigeoid height grid based on spectral combination using 1D FFT (compute step) R gw ( ) d, 4 2l 1 W( ) wl Pl(cos ) l 1 with spectral weights for gravity components: w l 2 ( ) l ( ) ( ) T M 2 2 l M T l depend on the error degree variances of the global model and the terrestrial gravity data T G 4 Quasigeoid Computation l 2 [mgal 2 ] 4 [] Cov (,,, R ) 1 e g G g G 15

4 Quasigeoid Computation Spectral weights and corresponding integral kernels related to a GRACE based geopotential model (red; used for EGG2007 and EGG2008), a recent CHAMP model (green), and EGM1996 (black; used for EGG1997), along with the classical Stokes kernel (blue) 16

4 Quasigeoid Computation Computation procedure (continued): 5 Computation of final quasigeoid height grid by restoring contributions from the geopotential model and from topography (restore step) (6 Derivation of geoid undulations by introducing a density hypothesis) 17

4 Quasigeoid Computation EGG1997 EGG2007 EGG2008 Project gravity data base 2,684,133 (744 sources) 5,354,653 (709 sources) 5,355,206 (718 sources) Other gravity data sources 195,840 (ArcGP) 195,840 (ArcGP) 335,124 (KMS1996) 951,251 (KMS2002) 13,222,260 (1' x 1' alt.) 120,747 (EGM2008 fillins) 3,019,257 (Total) 6,501,744 (Total) 18,894,053 (Total) Terrain data base 7.5" 5' resol. 1" 30" resol. 1" 30" resol. 700 million elev. 8.3 billion elev. 8.3 billion elev. 15' x 20' RTM 30' x 45' RTM 15' x 20' RTM Global geopotential model EGM1996 (l max =360) EIGEN-GL04C (l max =360) EGM2008 (l max =360) Computation procedure Remove-restore technique, spectral combination (1D FFT) GRS80, zero-tide system, EVRS Computation grid 25 77 N, 35 W 67.4 E 25 85 N, 50 W 70 E 25 85 N, 50 W 70 E 1.0' x 1.5' 1.0' x 1.0' 1.0' x 1.0' 3,120 x 4,096 pts. 3,600 x 7,200 pts. 3,600 x 7,200 pts. 18

4 Quasigeoid Computation EGG2008 quasigeoid model 0.300 19

4 Quasigeoid Computation Accuracy of combined geoid (global model + terrestrial gravity): GRACE + g (1 mgal): 0.025 m (contribution from degrees l = 91-360: 0.023 m!) Degree range EGM2008 EIGEN-GL04S1/C EIGEN-5S/5C 2 50 0.0028 0.0012 0.0007 51 100 0.0213 0.0114 0.0097 101 200 0.0184 0.0184 0.0184 201 360 0.0115 0.0115 0.0115 361 2,000 0.0071 0.0071 0.0071 2,001 0.0006 0.0006 0.0006 2 0.0314 0.0256 0.0248 20

5 Evaluation of the Results by GPS/Levelling Effect of global geopotential model: Comparison of 907 GPS and levelling stations in Germany with different quasigeoid models. A constant bias is subtracted. Units are m. Terrestrial data Geopotential model Mean RMS Minimum Maximum 1997 (EGG1997) EGM1996 +0.431 0.096 0.188 +0.331 1997 EGM2008 +0.302 0.029 0.095 +0.089 2007 (EGG2007) EIGEN-GL04C +0.298 0.036 0.159 +0.075 2008 EGM1996 +0.416 0.074 0.132 +0.300 2008 EIGEN-CHAMP03S +0.288 0.050 0.116 +0.262 2008 EIGEN-GRACE01S +0.290 0.038 0.111 +0.152 2008 EIGEN-GRACE02S +0.295 0.037 0.080 +0.123 2008 EIGEN-GL04S1 +0.299 0.029 0.097 +0.086 2008 EIGEN-GL04C +0.300 0.028 0.093 +0.082 2008 EIGEN-5S +0.300 0.027 0.097 +0.073 2008 EIGEN-5C +0.298 0.028 0.098 +0.073 2008 (EGG2008) EGM2008 +0.297 0.027 0.091 +0.078 EGM2008 (n max = 2190) +0.302 0.031 0.110 +0.148 21

5 Evaluation of the Results by GPS/Levelling FRG (907 stations from BKG): GPS grav. (after bias fit) EGG1997/EGM1996 Rms: 0.096 m; Min: -0.188 m; Max: +0.331 m EGG2008/EGM2008 Rms: 0.027 m; Min: -0.091 m; Max: +0.078 m 22

5 Evaluation of the Results by GPS/Levelling EUVN_DA (1395 stations): GPS grav. (after bias fit) (* IT & GB excl. in statistics) (* IT & GB excl. in statistics) EGG1997/EGM1996 *Rms: 0.161 m; Min: -0.599 m; Max: +0.636 m EGG2008/EGM2008 *Rms: 0.077 m; Min: -0.250 m; Max: +0.430 m 23

5 Evaluation of the Results by GPS/Levelling Statistics of the GPS/lev comparisons: Quasigeoid (Δg / geopotential model) # Mean RMS Minimum Maximum Improvement vs EGG1997 Germany (2005) EGG1997/EGM1996 907 +0.431 0.096 0.188 +0.331 EGG1997/EGM2008 907 +0.302 0.029 0.095 +0.089 70% EGG2008/EGM2008 907 +0.297 0.027 0.091 +0.078 72% EGM2008 (n max = 2,190) 907 +0.302 0.031 0.110 +0.148 The Netherlands EGG1997/EGM1996 84 +0.244 0.034 0.061 +0.118 EGG1997/EGM2008 84 +0.234 0.021 0.047 +0.050 38% EGG2008/EGM2008 84 +0.255 0.010 0.040 +0.027 71% EGM2008 (n max = 2,190) 84 +0.263 0.030 0.135 +0.036 Austria (2008) EGG1997/EGM1996 170 +0.660 0.108 0.202 +0.248 EGG1997/EGM2008 170 +0.356 0.064 0.129 +0.197 41% EGG2008/EGM2008 170 +0.361 0.037 0.098 +0.100 66% EGM2008 (n max = 2,190) 170 +0.338 0.071 0.212 +0.171 Switzerland EGG1997/EGM1996 188 +0.535 0.080 0.129 +0.258 EGG1997/EGM2008 188 +0.117 0.058 0.201 +0.282 28% EGG2008/EGM2008 188 +0.174 0.052 0.157 +0.230 35% EGM2008 (n max = 2,190) 188 +0.141 0.056 0.170 +0.170 24

5 Evaluation of the Results by GPS/Levelling Statistics of the GPS/lev comparisons (continued): Quasigeoid (Δg / geopotential model) # Mean RMS Minimum Maximum Improvement vs EGG1997 France (North-South traverse with new leveling) EGG1997/EGM1996 16 0.027 0.086 0.188 +0.124 EGG1997/EGM2008 16 0.088 0.032 0.051 +0.068 63% EGG2008/EGM2008 16 0.097 0.026 0.024 +0.059 70% EGM2008 (n max = 2,190) 16 0.100 0.038 0.066 +0.082 Russia EGG1997/EGM1996 48 +0.574 0.256 0.776 +0.707 EGG1997/EGM2008 48 +0.560 0.124 0.261 +0.300 52% EGG2008/EGM2008 48 +0.555 0.076 0.134 +0.163 70% EGM2008 (n max = 2,190) 48 +0.555 0.072 0.120 +0.141 EUVN_DA (all) EGG1997/EGM1996 1,395 +0.287 0.243 0.899 +0.708 EGG1997/EGM2008 1,395 +0.253 0.188 0.693 +0.527 23% EGG2008/EGM2008 1,395 +0.250 0.173 0.688 +0.443 29% EGM2008 (n max = 2,190) 1,395 +0.254 0.171 0.643 +0.481 EUVN_DA (excuding Great Britain and Italy) EGG1997/EGM1996 1,139 +0.359 0.161 0.599 +0.636 EGG1997/EGM2008 1,139 +0.300 0.108 0.607 +0.428 33% EGG2008/EGM2008 1,139 +0.302 0.076 0.302 +0.391 53% EGM2008 (n max = 2,190) 1,139 +0.305 0.077 0.250 +0.430 25

Conclusions significant progress was made within the framework of the European gravity and geoid project to develop the completely updated European Gravimetric Quasigeoid EGG2008 evaluation by independent GPS and levelling data shows substantial improvements compared to the previous model EGG1997 (in total by 35-72%) RMS differences range from about 1-5 cm for areas with good data quality and coverage, but exceed 10 cm for countries with less data quality the accuracy potential of EGG2008 is in the order of 1-3 cm on a national basis, and 2-5 cm on continental scales 26