# Geodetic SAR for Height System Unification and Sea Level Research—Results in the Baltic Sea Test Network

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{7}

^{8}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Data Processing and Results for Individual Observation Types

#### 2.1. SAR Data Analysis

^{2}is estimated at the DLR calibration site [5]. The only ECR site that turns out to have limitations is Kobben. Because of concerns regarding radio interference with nearby infrastructure, the installation needed to be shielded by a meshed fence to prevent any signal amplification at low elevation angles. This fencing also causes additional interfering sidelobes in certain pass geometries. Therefore, only some of the observations acquired at Kobben can be used in the SAR positioning. In conclusion, the SAR data analysis preparing the ECR observations is performed very reliably, and only a few ECR observations are marked unusable based on the imaging quality parameters.

**Table 2.**Sentinel-1 SLC image samples showing the ECR point responses for ascending and descending IW TOPS data at some of the selected installation sites. Images display the radar backscatter (sigma 0) in units of decibel [7]. Left columns: original Sentinel-1 SLC SAR image samples showing an area of 150 m × 150 m around ECR peak marked in green. Right columns: image areas of 32 × 32 pixels over-sampled by a factor of 32 as generated by point target analysis to extract the ECR peak position. All images are logarithmically scaled for 10 to 45 dB. In each image, the horizontal axis shows the range from 0 to 150 m and the vertical axis the azimuth from 0 to 150 m.

ECR | Ascending Image Sample | Descending Image Sample |
---|---|---|

Loksa | ||

Vergi | ||

Rauma | ||

Władys-ławowo | ||

Kobben | ||

Vinberget |

- The computation of range and azimuth residuals with respect to the surveyed ECR coordinates, applying the corrections for Sentinel-1 systematic effects, tropospheric and ionospheric delays and solid Earth tides. Note that the analysis is performed with the surveyed ECR origin coordinates corrected for the geometric ECR phase center offsets specified in the ECR manual for ascending and descending passes, following the methods proposed in [10]. The ECR origin coordinates are observed during installation with differential GNSS and are considered to be accurate within 5 cm or better depending on the instrumentation and observation time.
- The removal of outliers from the residuals of each individual geometry using the median and a 95% confidence interval, assuming normal distribution.
- The estimation of average ECR offsets from the cleaned residuals of each geometry along with the 95% confidence interval using least-squares methods.
- The computation of the range and azimuth standard deviation for each set of residuals to empirically quantify the single observation precision (1 sigma) of each geometry.

#### 2.2. SAR Positioning

#### 2.3. GNSS Positioning

#### 2.4. Tide Gauge Data Analysis

#### 2.5. GOCE Based Geoid Determination

_{0}), the value obtained in the NKG2015 geoid project is used (W

_{0}= 62,636,858.18 m

^{2}/s

^{2}). The zero permanent tide system is used in all computations. The postglacial land uplift epoch is taken as 2000.0, which is extrapolated for the final geoid values to the mean epoch of the analysis period (2020.5) (see below).

#### 2.6. Reference Frames and Joint Standards

## 3. Absolute Sea Level and Height System Unification

#### 3.1. Absolute Height Experiments

#### 3.2. Baseline (Relative) Height Experiments

## 4. Data and Products, Summary and Conclusions, Future Work

#### 4.1. Data and Products

#### 4.2. Summary and Conclusions

#### 4.3. Future Work

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Gruber, T.; Ågren, J.; Angermann, D.; Ellmann, A.; Engfeldt, A.; Gisinger, C.; Jaworski, L.; Marila, S.; Nastula, J.; Nilfouroushan, F.; et al. Geodetic SAR for Height System Unification and Sea Level Research—Observation Concept and Preliminary Results in the Baltic Sea. Remote Sens.
**2020**, 12, 3747. [Google Scholar] [CrossRef] - Gisinger, C.; Balss, U.; Pail, R.; Zhu, X.X.; Montazeri, S.; Gernhardt, S.; Eineder, M. Precise Three-Dimensional Stereo Localization of Corner Reflectors and Persistent Scatterers with TerraSAR-X. IEEE Trans. Geosci. Remote Sens.
**2015**, 53, 1782–1802. [Google Scholar] [CrossRef] - Bourbigot, M.; Johnsen, H.; Piantanida, R.; Sentinel-1 Product Definition. Technical Note by Sentinel-1 Mission Performance Center (MPC), Doc. S1-RS-MDA-52-7440, Iss. 2, Rev. 6, Date 22 July 2015. Available online: https://sentinels.copernicus.eu/web/sentinel/user-guides/sentinel-1-sar/document-library/-/asset_publisher/1dO7RF5fJMbd/content/sentinel-1-product-definition (accessed on 17 May 2022).
- Potin, P.; Gascon, F.; Stromme, A.; Zehner, C.; Wilson, H.; Figa, J.; Obligis, E.; Lindstrot, R. Sentinel High Level Operations Plan; ESA Technical Note, COPE-S1OP-EOPG-PL-15-0020, iss. 3, rev. 1; ESA: Frascati, Italy, 2021. [Google Scholar]
- Gisinger, C.; Schubert, A.; Breit, H.; Garthwaite, M.; Balss, U.; Willberg, M.; Small, D.; Eineder, M.; Miranda, N. In-Depth Verification of Sentinel-1 and TerraSAR-X Geolocation Accuracy using the Australian Corner Reflector Array. IEEE Trans. Geosci. Remote Sens.
**2021**, 59, 1154–1181. [Google Scholar] [CrossRef] - Cumming, I.G.; Wong, F.H. Digital Processing of Synthetic Aperture Radar Data; Artech House: London, UK, 2005; ISBN 978-1-58053-058-3. [Google Scholar]
- Miranda, N.; Meadows, P.J. Radiometric Calibration of S-1 Level-1 Products Generated by the S-1 IPF; ESA Technical Document, Doc. ESA-EOPG-CSCOP-TN-0002, Iss. 1.0, Date 21 May 2015; ESA: Frascati, Italy, 2015. [Google Scholar]
- Schubert, A.; Miranda, N.; Geudtner, D.; Small, D. Sentinel-1A/B Combined Product Geolocation Accuracy. Remote Sens.
**2017**, 9, 607. [Google Scholar] [CrossRef] [Green Version] - Hajduch, G.; Vincent, P.; Cordier, K.; Grignoux, M.; Husson, R.; Peureux, C.; Piantanida, R.; Recchia, A.; Francheschi, N.; Schmidt, K.; et al. S-1A & S-1B Annual Performance Report 2020; ESA Technical Document, Doc. MPC-0504, Iss. 1.1, Date 16 March 2021; ESA: Frascati, Italy, 2021. [Google Scholar]
- Czikhardt, R.; van der Marel, H.; Papco, J.; Hanssen, R.F. On the Efficacy of Compact Radar Transponders for InSAR Geodesy: Results of Multiyear Field Tests. IEEE Trans. Geosci. Remote Sens.
**2022**, 60, 1–13. [Google Scholar] [CrossRef] - Dach, R.; Lutz, S.; Walser, P.; Fridez, P. (Eds.) Bernese GNSS Software Version 5.2. User Manual; Astronomical Institute, University of Bern, Bern Open Publishing: Bern, Switzerland, 2015; ISBN 978-3-906813-05-9. [Google Scholar] [CrossRef]
- Altamimi, Z.; Rebischung, P.; Metivier, L.; Collilieux, X. ITRF2014: A new release of the International Terrestrial Reference Frame modeling nonlinear station motions. J. Geophys. Res. Solid Earth
**2016**, 121, 6109–6131. [Google Scholar] [CrossRef] [Green Version] - Petit, G.; Luzum, B. (Eds.) IERS Conventions 2010. 20210, Verlag des Bundesamts für Kartographie und Geodaäsie. Available online: https://iers-conventions.obspm.fr/ (accessed on 17 May 2022).
- Varbla, S.; Ågren, J.; Ellmann, A.; Poutanen, M. Treatment of tide gauge time series and marine GNSS measurements for vertical land motion with relevance to the implementation of the Baltic Sea Chart Datum 2000. Remote Sens.
**2022**, 14, 920. [Google Scholar] [CrossRef] - Moritz, H. Advanced Physical Geodesy; Wichmann; Abacus Press: Karlsruhe, Germany; Tunbridge, UK, 1980; ISBN 978-3-87907-106-7. [Google Scholar]
- Tscherning, C.; Rapp, R.H. Closed Covariance Expressions for Gravity Anomalies, Geoid Undulations, and Deflections of the Vertical Implied by Anomaly Degree Variance Models; Report No. 208; Dep. Geod. Sci. Ohio State University: Columbus, OH, USA, 1974. [Google Scholar]
- Tscherning, C.C. Geoid Determination by 3D Least-Squares Collocation. In Geoid Determination: Theory and Methods; Sansò, F., Sideris, M.G., Eds.; Lecture Notes in Earth System Sciences; Springer: Berlin/Heidelberg, Germany, 2013; pp. 311–336. ISBN 978-3-540-74700-0. [Google Scholar]
- Forsberg, R. A Study of Terrain Reduction, Density, Anomalies and Geophysical Inversion Methods in Gravity Field Modeling; Dep. Geod. Sci. Ohio State University: Columbus, OH, USA, 1984. [Google Scholar]
- Sjöberg, L. Refined least squares modification of Stokes’ formula. Manuscr. Geod.
**1991**, 16, 367–375. [Google Scholar] - Sjöberg, L.E.; Bagherbandi, M. (Eds.) Gravity Inversion and Integration—Theory and Applications in Geodesy and Geophysics; Springer International Publishing: Cham, Switzerland, 2017; ISBN 978-3-319-50298-4. [Google Scholar]
- Ågren, J.; Sjöberg, L.E.; Kiamehr, R. The new gravimetric quasigeoid model KTH08 over Sweden. J. Appl. Geod.
**2009**, 3, 143–153. [Google Scholar] [CrossRef] - Ågren, J.; Strykowski, G.; Bilker-Koivula, M.; Omang, O.; Märdla, S.; Forsberg, R.; Ellmann, A.; Oja, T.; Liepins, I.; Parseliunas, E.; et al. The NKG2015 gravimetric geoid model for the Nordic-Baltic region. In Proceedings of the 1st Joint Commission 2 and IGFS Meeting International Symposium on Gravity, Geoid and Height Systems, Thessaloniki, Greece, 19–23 September 2016; Available online: https://www.isgeoid.polimi.it/Geoid/Europe/NordicCountries/GGHS2016_paper_143.pdf (accessed on 17 May 2022).
- Märdla, S.; Ågren, J.; Strykowski, G.; Oja, T.; Ellmann, A.; Forsberg, R.; Bilker-Koivula, M.; Omang, O.; Paršeliūnas, E.; Liepinš, I.; et al. From Discrete Gravity Survey Data to a High-resolution Gravity Field Representation in the Nordic-Baltic Region. Mar. Geod.
**2017**, 40, 416–453. [Google Scholar] [CrossRef] - Förste, C.; Bruinsma, S.L.; Abrykosov, O.; Lemoine, J.-M.; Marty, J.C.; Flechtner, F.; Balmino, G.; Barthelmes, F.; Biancale, R. EIGEN-6C4 the latest combined global gravity field model including GOCE data up to degree and order 2190 of GFZ Potsdam and GRGS Toulouse. GFZ Data Serv.
**2014**. [Google Scholar] [CrossRef] - Moritz, H. Geodetic Reference System 1980. J. Geod.
**2000**, 74, 128–162. [Google Scholar] [CrossRef] - Förste, C.; Abrykosov, O.; Bruinsma, S.; Dahle, C.; König, R.; Lemoine, J.-M. ESA’s Release 6 GOCE gravity field model by means of the direct approach based on improved filtering of the reprocessed gradients of the entire mission. GFZ Data Serv.
**2019**. [Google Scholar] [CrossRef] - Kvas, A.; Mayer-Gürr, T.; Krauss, S.; Brockmann, J.M.; Schubert, T.; Schuh, W.-D.; Pail, R.; Gruber, T.; Jäggi, A.; Meyer, U. The satellite-only gravity field model GOCO06s. GFZ Data Serv.
**2019**. [Google Scholar] [CrossRef] - Forsberg, R.; Tscherning, C.C. An Overview Manual for the GRAVSOFT Geodetic Gravity Field Modelling Programs, 2nd ed.; 2008; Available online: https://www.academia.edu/9206363/An_overview_manual_for_the_GRAVSOFT_Geodetic_Gravity_Field_Modelling_Programs (accessed on 17 May 2022).
- Tscherning, C.C.; Rapp, R.H. Closed Covariance Expressions for Gravity Anomalies, Geoid Undulations, and Deflections of the Vertical Implied by Anomaly Degree Variance Models; Report No. 355; Dep. Geod. Sci. Ohio State University: Columbus, OH, USA, 1974. [Google Scholar]
- Mayer-Gürr, T.; Behzadpur, S.; Ellmer, M.; Kvas, A.; Klinger, B.; Strasser, S.; Zehentner, N. ITSG-Grace2018—Monthly, Daily and Static Gravity Field Solutions from GRACE. GFZ Data Serv.
**2018**. [Google Scholar] [CrossRef] - Vestøl, O.; Ågren, J.; Steffen, H.; Kierulf, H.; Tarasov, L. NKG2016LU—A new land uplift model for Fennoscandia and the Baltic Region. J. Geod.
**2019**, 93, 1759–1779. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Baltic Sea test network showing ECR locations and ties to GNSS and/or tide gauge stations. Exact coordinates are shown in Table 4.

**Figure 2.**ECR offsets for the different pass geometries observed with the ECR network (colors indicate individual stations). Average offsets estimated with least-squares adjustment from residuals of surveyed ECR positions and measured SAR data filtered for outliers. Range offset estimates per geometry (

**left**) and azimuth offset estimates per geometry (

**right**). Black bars show the 95% confidence intervals of the estimation results. Red lines show the angular-dependent ECR delay models, as listed in Table 3.

**Figure 3.**Empirical estimation of ECR SAR observation quality for the different pass geometries observed with the ECR network (colors indicate individual stations) after applying all data corrections. Standard deviation of residuals derived from surveyed ECR positions and measured SAR data filtered for outliers. Standard deviation of range measurements per geometry (

**left**) and standard deviations of azimuth measurements per geometry (

**right**).

**Figure 4.**Confidence ellipsoids (95% confidence level) for all 12 stations using all available observations in the year 2020. The confidence is shown in the local and east/height (

**left image**) and north/east (

**right image**), coordinate frame with respect to the estimated coordinates.

**Figure 5.**Confidence ellipsoids in local east/height (

**top left**), zoomed out local east/height (

**bottom left**), and local north/east (

**right**) coordinates of all ECR stations using all available observations from 2020. The center position of the ellipsoids is given with respect to reference coordinates, previously measured by GNSS campaigns and therefore represent offsets with respect to reference coordinates.

**Figure 6.**Observation residuals at selected stations. Range observations are colored in red; the different symbols indicate different incidence angles. Azimuth observations are shown in blue; symbols indicate the same incidence angles as for the range observations. Top row: Emäsalo, Finland; Mid row: Władysławowo, Poland; Bottom row: Mårtsbo, Sweden.

**Figure 7.**Standard Deviations of absolute positioning of all ECRs and all temporal resolutions (1 M, 2 M, 3 M, 4 M, yearly) per number of data takes (sum of range and azimuth observations).

**Figure 8.**Positioning offset of the ECR located in Emäsalo for the different temporal resolutions derived from SAR data: monthly (1 M), bimonthly (2 M), trimonthly (3 M), and every four months (4 M) in the year 2020. The offsets are displayed in local North (blue), East (green), and Height (red) with respect to given reference coordinates from GNSS campaigns at the mean date of each observation period. For 1 M and 2 M, the Root Mean Square (RMS) values in meters are displayed in the top left corner of the respective graph. “A”: and “R”: beneath each solution indicate the number of radar measurements used in azimuth and range for the particular solution.

**Figure 9.**Map with distribution of all included GNSS stations. Large black squares are the IGS network stations, smaller black squares are the EPN stations, and red squares are the stations belonging to the EUPOS (FinnRef, ESTPOS, SWEPOS and ASG-EUPOS). Only LEBI station belongs to Leica commercial network. Little green diamonds indicate the locations of the ECR transponders.

**Figure 10.**Residual daily coordinate time series with respect to reference coordinates for the year 2020 for Mårtsbo (MAR6, top panel) and Władysławowo (WLAD, bottom panel) permanent GNSS stations. Ellipsoidal latitude is shown in red, longitude in green, and height in blue color. Vertical axis shows coordinate residuals in the range ±25 mm, horizontal axis specifies the day of year 2020 from day 001 to day 365.

**Figure 11.**Hourly TG sea level time series (in millimeters) for Loksa, Estonia (

**1st row**), Emäsalo, Finland (

**2nd row**), Kobben, Sweden (

**3rd row**), and Władysławowo, Poland (

**4th row**) for the year 2020.

**Figure 12.**Gravity data selected to compute the gravimetric quasi-geoid models over the Baltic Sea test area. The data includes the gravity datasets of the NKG2015 project from Sweden, Finland, and Estonia (plus some other open datasets), new FAMOS marine gravity data from the same countries and the Polish gravity data currently in the NKG2015 gravity database. Pseudo-observations (5′ × 5′) generated by EIGEN-6C4 are plotted as triangles. The TG and ECR locations are plotted as black triangles. The locations of north and large quasi-geoid test areas are also illustrated.

**Figure 13.**GNSS/levelling residuals from the 1-parameter fit of the final quasi-geoid model without corrections for specific country offsets (only one shift parameter estimated). Red arrows mean positive residuals, while blue means negative. The scale is given by the red arrow in the middle of the Baltic Sea.

**Figure 14.**Residual position time series of GNSS station Metsähovi in Finland [Source: EPN website at https://www.epncb.oma.be/_productsservices/timeseries/ (accessed on 17 May 2022)].

**Table 1.**Summary on SAR data collected in 2020 within the project’s ECR network. Active periods are the times the ECRs operated successfully. Passes list the number of repeat pass geometries acquired by Sentinel-1 in ascending and descending orientation at a respective site. Sentinel-1 observations refer to the number of SAR images available in the catalogue whereas acquired observations list successful ECR activations with full performance signals in the SAR data. For the station map, refer to Figure 1.

ECR Station | Active mm/dd-mm/dd | Passes [#] (Asc/ Desc) | Sent.-1 Obs. [#] | Acquired Obs. [#] | Success Rate [%] |
---|---|---|---|---|---|

Loksa (LOKS) | 02/14–09/12 12/28–12/31 | 3/2 | 171 | 164 | 95.61 |

Vergi (VERG) | 03/03–08/01 12/28–12/31 | 3/2 | 81 | 81 | 100.00 |

Emäsalo (EMAE) | 01/23–12/31 | 3/2 | 222 | 185 | 83.33 |

Loviisa (LOVI) | 02/01–10/20 | 2/2 | 132 | 106 | 80.30 |

Rauma (RAUM) | 04/21–12/31 | 2/2 | 142 | 76 | 53.52 |

Władysławowo (WLAD) | 03/20–12/31 | 2/2 | 164 | 142 | 85.59 |

Łeba (LEBA) | 05/15–12/31 | 2/2 | 141 | 116 | 82.27 |

Mårtsbo (MART) | 01/07–12/31 | 3/3 | 322 | 218 | 67.70 |

Kobben (KOBB) | 06/01–12/31 | 2/2 | 160 | 154 | 96.25 |

Vinberget (VINB) | 10/01–12/31 | 2/3 | 57 | 57 | 100.00 |

Oberpfaffenhofen (DLR2) | 01/10–02/25 06/17–09/01 | 2/1 | 85 | 85 | 100.00 |

Oberpfaffenhofen (DLR3) | 01/10–12/31 | 2/1 | 177 | 177 | 100.00 |

**Table 3.**ECR range and azimuth time delay model coefficients for ascending and descending measurements as derived from ECR residuals of the installation sites DLR2, Mårtsbo, Vinberget, Vergi and Loksa, see Figure 2. The a

_{0}denotes the mean offset and the a

_{1}denotes the linear component that depends on the incidence angle of the Sentinel-1 swath, i.e., 20 to 45 degrees.

Configuration | a0 [s] | a1 [s/°] |
---|---|---|

ECR Range Delay Ascending | 7.2416 × 10^{−9} | 1.1405 × 10^{−10} |

ECR Range Delay Descending | 1.1243 × 10^{−8} | −4.7810 × 10^{−11} |

ECR Azimuth Delay Ascending | 9.5494 × 10^{−5} | −2.102 × 10^{−6} |

ECR Azimuth Delay Descending | 1.0584 × 10^{−5} | −2.3110 × 10^{−6} |

**Table 4.**Estimated average GRS-80 ellipsoidal coordinates for year 2020 (longitude, latitude, height) for all stations using all available observations in the year 2020. The epoch is defined as the mid of the total observation period (see Table 1). The number of all valid observations is defined as the number of acquired observations (as shown in Table 1) minus outliers (A: Azimuth, R: Range observations).

ECR Station | Latitude [°] | Longitude [°] | Height [m] | Valid DTs [#] A/R | Epoch |
---|---|---|---|---|---|

Loksa | 59.582555692 | 25.705865677 | 20.0761 | 160/163 | 2020.475 |

Vergi | 59.601493430 | 26.100800251 | 28.9661 | 66/77 | 2020.422 |

Emäsalo | 60.203674412 | 25.625661421 | 34.2932 | 181/165 | 2020.586 |

Loviisa | 60.440749584 | 26.284251613 | 46.8399 | 101/99 | 2020.508 |

Rauma | 61.133538554 | 21.425982308 | 24.0824 | 75/72 | 2020.656 |

Władysławowo | 54.796783467 | 18.418754840 | 34.6395 | 133/139 | 2020.639 |

Łeba | 54.753658763 | 17.534876057 | 34.3894 | 116/109 | 2020.681 |

Mårtsbo | 60.595133036 | 17.258527904 | 75.4769 | 206/194 | 2020.581 |

Kobben | 60.409897086 | 18.230323460 | 25.6586 | 81/78 | 2020.586 |

Vinberget | 62.373892667 | 17.427849782 | 149.6544 | 54/54 | 2020.852 |

DLR2 | 48.084935323 | 11.281195447 | 626.6280 | 83/71 | 2020.542 |

DLR3 | 48.087916451 | 11.279137080 | 623.8140 | 174/172 | 2020.517 |

**Table 5.**Root mean square (RMS) values of the once-monthly (1 M) and bimonthly (2 M) solutions of each station. Loviisa and Kobben were computed without bias correction due to computational issues for single observation intervals. DLR2 is excluded in the table, as its performance significantly changed after each repair of the transponder.

ECR Station | 1 M RMS | 2 M RMS | ||||
---|---|---|---|---|---|---|

dN [m] | dE [m] | dH [m] | dN [m] | dE [m] | dH [m] | |

Loksa | 0.1617 | 0.2267 | 0.1724 | 0.0605 | 0.1702 | 0.1832 |

Vergi | 0.1544 | 0.0817 | 0.0911 | 0.0667 | 0.1032 | 0.0920 |

Emäsalo | 0.1570 | 0.1794 | 0.1242 | 0.1373 | 0.1787 | 0.1143 |

Loviisa | 0.1689 | 0.0647 | 0.1139 | 0.0999 | 0.1328 | 0.0620 |

Rauma | 0.0797 | 0.0580 | 0.0359 | 0.0904 | 0.0394 | 0.0497 |

Władysławowo | 0.2069 | 0.1272 | 0.1309 | 0.1482 | 0.2070 | 0.0725 |

Łeba | 0.1300 | 0.1285 | 0.1201 | 0.0806 | 0.0883 | 0.0280 |

Mårtsbo | 0.1470 | 0.0995 | 0.0889 | 0.2389 | 0.0292 | 0.0736 |

Kobben | 0.1011 | 0.2485 | 0.1748 | 0.0840 | 0.2172 | 0.1269 |

Vinberget | 0.0220 | 0.0549 | 0.0407 | - | - | - |

DLR3 | 0.1348 | 0.3525 | 0.1275 | 0.0645 | 0.3165 | 0.1176 |

Mean: | 0.1330 | 0.1474 | 0.1109 | 0.1071 | 0.1483 | 0.0920 |

Min: | 0.0220 | 0.0549 | 0.0359 | 0.0605 | 0.0292 | 0.0280 |

Max: | 0.2069 | 0.3525 | 0.1748 | 0.2389 | 0.3165 | 0.1832 |

Median: | 0.1470 | 0.1272 | 0.1201 | 0.0872 | 0.1515 | 0.0828 |

No Bias Correction applied for Loviisa and Kobben |

**Table 6.**GNSS stations geodetic coordinates (latitude, longitude, and height) in ITRF2014 epoch 2020.50 (from period 1 January 2020 to 31 December 2020) referred to GRS-80 ellipsoid. Solution from DD method. Only GNSS stations coordinates immediately co-located to an ECR stations are shown.

GNSS Station | Latitude [°] | Longitude [°] | Height [m] |
---|---|---|---|

Łeba (LEBI) | 54.753775669 | 17.534799064 | 37.8856 |

Loviisa (LOV3) | 60.440771458 | 26.283844394 | 49.8794 |

Mårtsbo (MAR6) | 60.595145817 | 17.258531528 | 75.5578 |

Vergi (VERG) | 59.601489744 | 26.100798661 | 30.0692 |

Vinberget (VINB) | 62.373816278 | 17.427743125 | 150.2055 |

Władysławowo (WLAD) | 54.796761422 | 18.418757500 | 34.7580 |

**Table 7.**Summary of the TG and ECR levelling results for year 2020, referred to the national realizations of the EVRS vertical datum.

TG Station | ECR Reference Height [m] | TG Average Sea Level Height [m] | STD TG Time Series [m] | Missing Data [%] |
---|---|---|---|---|

Loksa | 2.6385 | +0.343 | 0.245 | 1.2 |

Emäsalo | 17.8155 | +0.338 | 0.238 | 0.6 |

Rauma | 5.0075 | +0.258 | 0.216 | 1.1 |

Kobben | 2.9606 | +0.188 | 0.200 | 0 |

Vinberget | 123.5233 | +0.175 | 0.215 | 0 |

Władysławowo | 5.6382 | +0.253 | 0.186 | 0.2 |

Łeba | 3.0491 | +0.224 | 0.173 | 0.3 |

Country | ECR Station | Quasi-Geoid Height [m] |
---|---|---|

Estonia | Loksa | 16.821 |

Vergi | 16.555 | |

Finland | Emäsalo | 15.509 |

Loviisa | 15.453 | |

Rauma | 19.096 | |

Sweden | Kobben | 22.381 |

Vinberget | 25.065 | |

Mårtsbo | 24.627 | |

Poland | Władysławowo | 28.883 |

Łeba | 30.787 |

**Table 9.**Summary of observed ellipsoidal, geoid and TG heights at Baltic Sea network. All heights represent mean values averaged over the observation period in year 2020 or for epoch 2020.5. ${h}^{ECR}$: ellipsoidal height of ECR reference point; ${N}^{TG},{N}^{ECR}$: quasi-geoid height at location (same for tide gauge and ECR); ${z}^{TG}$: TG sea level height above zero marker; ${h}^{GNSS}$: ellipsoidal height of GNSS reference point.

ECR Station | Local Tie | ${\mathit{h}}^{\mathit{E}\mathit{C}\mathit{R}}$ Ellipsoidal Height [m] | ${\mathit{N}}^{\mathit{T}\mathit{G}}={\mathit{N}}^{\mathit{E}\mathit{C}\mathit{R}}$ Geoid Height [m] | ${\mathit{z}}^{\mathit{T}\mathit{G}}$ Tide Gauge [m] | ${\mathit{h}}^{\mathit{G}\mathit{N}\mathit{S}\mathit{S}}$ Ellipsoidal Height [m] |
---|---|---|---|---|---|

Władysławowo | TG, GNSS | +34.640 | +28.883 | +0.253 | +34.758 |

Łeba | TG, GNSS | +34.389 | +30.787 | +0.224 | +37.886 |

Vergi | GNSS | +28.966 | +16.555 | n/a | +30.069 |

Loksa | TG | +20.076 | +16.821 | +0.343 | n/a |

Emäsalo | TG | +34.293 | +15.509 | +0.338 | n/a |

Loviisa | GNSS | +46.840 | +15.453 | n/a | +49.879 |

Rauma | TG | +24.082 | +19.096 | +0.258 | n/a |

Kobben | TG | +25.659 | +22.381 | +0.188 | n/a |

Mårtsbo | GNSS | +75.477 | +24.627 | n/a | +75.558 |

Vinberget | TG, GNSS | +149.654 | +25.065 | +0.175 | +150.206 |

**Table 10.**Levelled height differences between ECR reference point and the TG or GNSS reference points. $\Delta {h}_{ECR}^{TG}$: ellipsoidal height difference from ECR reference point to TG zero marker; $\Delta {h}_{GNSS}^{ECR}$: ellipsoidal height difference from GNSS reference point to ECR reference point.

ECR Station | Local Tie | $\mathbf{\Delta}{\mathit{h}}_{\mathit{E}\mathit{C}\mathit{R}}^{\mathit{T}\mathit{G}}$ ECR to Tide Gauge [m] | $\mathbf{\Delta}{\mathit{h}}_{\mathit{G}\mathit{N}\mathit{S}\mathit{S}}^{\mathit{E}\mathit{C}\mathit{R}}$ GNSS to ECR [m] |
---|---|---|---|

Władysławowo | TG | −5.638 | n/a |

Władysławowo | GNSS | n/a | −0.135 |

Łeba | TG | −3.049 | n/a |

Łeba | GNSS | n/a | −3.932 |

Vergi | GNSS | n/a | −0.996 |

Loksa | TG | −2.639 | n/a |

Emäsalo | TG | −17.816 | n/a |

Loviisa | GNSS | n/a | −3.574 |

Rauma | TG | −5.007 | n/a |

Kobben | TG | −2.961 | n/a |

Mårtsbo | GNSS | n/a | −0.032 |

Vinberget | TG | −123.523 | n/a |

Vinberget | GNSS | n/a | −0.998 |

**Table 11.**Comparison of SAR positioning heights at ECR stations to co-located permanent GNSS station heights. ${h}_{comp}^{ECR}={h}^{GNSS}+\Delta {h}_{GNSS}^{ECR}$: ellipsoidal height transferred from GNSS to ECR station; $\Delta {h}^{ECR}$: ellipsoidal height difference transferred GNSS versus ECR.

ECR Station | ${\mathit{h}}_{\mathit{c}\mathit{o}\mathit{m}\mathit{p}}^{\mathit{E}\mathit{C}\mathit{R}}$ Computed Ell. Height [m] | ${\mathit{h}}^{\mathit{E}\mathit{C}\mathit{R}}$ Observed Ell. Height [m] | $\mathbf{\Delta}{\mathit{h}}^{\mathit{E}\mathit{C}\mathit{R}}$ Computed-Observed [m] |
---|---|---|---|

Władysławowo | +34.623 | +34.640 | −0.017 |

Łeba | +33.954 | +34.389 | −0.435 |

Vergi | +29.073 | +28.966 | +0.107 |

Loviisa | +46.305 | +46.840 | −0.535 |

Mårtsbo | +75.526 | +75.477 | +0.049 |

Vinberget | +149.208 | +149.654 | −0.446 |

**Table 12.**Physical heights ${H}^{TG}$ of TG stations as computed from the ECR ellipsoidal height, the local tie from the ECR to the TG and the quasi-geoid height. Absolute sea level heights ${S}^{TG}$ from physical heights and tide gauge readings.

ECR Station | ${\mathit{H}}^{\mathit{T}\mathit{G}}$ Physical Height [m] | ${\mathit{S}}^{\mathit{T}\mathit{G}}$ Absolute Sea Level [m] |
---|---|---|

Władysławowo | +0.119 | +0.372 |

Łeba | +0.553 | +0.777 |

Loksa | +0.616 | +0.959 |

Emäsalo | −0.032 | +0.306 |

Rauma | −0.021 | +0.237 |

Kobben | +0.317 | +0.505 |

Vinberget | +1.066 | +1.241 |

**Table 13.**Relative (baseline) height differences between ECR stations A and B and co-located GNSS stations A and B and differences of the baseline height differences. GNSS height differences and ECR height differences transferred to the GNSS reference markers are computed with the equation above.

Station A | Station B | $\mathbf{\Delta}{\mathit{h}}^{\mathit{G}\mathit{N}\mathit{S}\mathit{S}-\mathit{A}/\mathit{B}}$ Ell. Height Difference [m] | $\mathbf{\Delta}{\mathit{h}}^{\mathit{E}\mathit{C}\mathit{R}-\mathit{A}/\mathit{B}}$ Ell. Height Difference [m] | $\mathbf{\Delta}\mathbf{\Delta}{\mathit{h}}^{(\mathit{G}\mathit{N}\mathit{S}\mathit{S}-\mathit{A}/\mathit{B})-(\mathit{E}\mathit{C}\mathit{R}-\mathit{A}/\mathit{B})}$ Double Difference Ell. Height [m] |
---|---|---|---|---|

Władysławowo | Łeba | +3.128 | +3.546 | −0.418 |

Władysławowo | Vergi | −4.689 | −4.813 | +0.124 |

Władysławowo | Loviisa | +15.121 | +15.639 | −0.518 |

Władysławowo | Mårtsbo | +40.800 | +40.734 | +0.066 |

Władysławowo | Vinberget | +115.448 | +115.877 | −0.429 |

Łeba | Vergi | −7.817 | −8.359 | +0.542 |

Łeba | Loviisa | +11.993 | +12.093 | −0.100 |

Łeba | Mårtsbo | +37.672 | +37.188 | +0.484 |

Łeba | Vinberget | +112.320 | +112.331 | −0.011 |

Vergi | Loviisa | +19.810 | +20.452 | −0.642 |

Vergi | Mårtsbo | +45.489 | +45.547 | −0.058 |

Vergi | Vinberget | +120.137 | +120.690 | −0.553 |

Loviisa | Mårtsbo | +25.679 | +25.095 | +0.584 |

Loviisa | Vinberget | +100.327 | +100.238 | +0.089 |

Mårtsbo | Vinberget | +74.648 | +75.143 | −0.495 |

**Table 14.**Relative (baseline) height differences between ECR stations A and B and between co-located TG stations A and B and differences of baseline height differences. TG height differences and ECR height differences transferred to the TG reference markers are computed with the equation above.

Station A | Station B | $\mathbf{\Delta}{\mathit{z}}^{\mathit{T}\mathit{G}-\mathit{A}/\mathit{B}}$ Tide Gauge Height Difference [m] | $\mathbf{\Delta}{\mathit{S}}^{\mathit{T}\mathit{G}-\mathit{A}/\mathit{B}}$ Absolute Sea Level Height Difference [m] | $\mathbf{\Delta}\mathbf{\Delta}{\mathit{S}}^{\mathit{T}\mathit{G}-\mathit{A}/\mathit{B}}$ Double Difference Sea Level [m] |
---|---|---|---|---|

Władysławowo | Łeba | −0.029 | +0.405 | −0.434 |

Władysławowo | Loksa | +0.090 | +0.587 | −0.497 |

Władysławowo | Emäsalo | +0.085 | −0.066 | +0.151 |

Władysławowo | Rauma | +0.005 | −0.135 | +0.140 |

Władysławowo | Kobben | −0.065 | +0.133 | −0.198 |

Władysławowo | Vinberget | −0.078 | +0.869 | −0.947 |

Łeba | Loksa | +0.119 | +0.182 | −0.063 |

Łeba | Emäsalo | +0.114 | −0.471 | +0.585 |

Łeba | Rauma | +0.034 | −0.540 | +0.574 |

Łeba | Kobben | −0.036 | −0.272 | +0.236 |

Łeba | Vinberget | −0.049 | +0.464 | −0.513 |

Loksa | Emäsalo | −0.005 | −0.653 | +0.648 |

Loksa | Rauma | −0.085 | −0.722 | +0.637 |

Loksa | Kobben | −0.155 | −0.454 | +0.299 |

Loksa | Vinberget | −0.168 | +0.282 | −0.450 |

Emäsalo | Rauma | −0.080 | −0.069 | −0.011 |

Emäsalo | Kobben | −0.150 | +0.199 | −0.349 |

Emäsalo | Vinberget | −0.163 | +0.935 | −1.098 |

Rauma | Kobben | −0.070 | +0.268 | −0.338 |

Rauma | Vinberget | −0.083 | +1.004 | −1.087 |

Kobben | Vinberget | −0.013 | +0.736 | −0.749 |

Product Title | Product Description | Section |
---|---|---|

SAR Target Locations (PTA-RES) | Target range and azimuth location(s) from point target analysis. | Section 2.1 |

SAR Raw Measurements (PTA-OBS) | SAR observation file generated from the point target analysis file. Processor specific corrections are applied to range and azimuth. | Section 2.1 |

SAR Tropospheric Delays (COR-TD) | Tropospheric delays stored as one-way path delay in units of meters. | Section 2.1 |

SAR Ionospheric Delay (COR-ID) | Ionospheric delays stored as one-way path delay in units of meters. | Section 2.1 |

Geodynamic Corrections (COR-GC) | Geodynamic corrections to SAR range and azimuth observations due impact of solid Earth tidal deformations, ocean loading, atmospheric pressure loading, rotational deformation due to polar motion, ocean pole tide loading and secular trends. | Section 2.1 |

Sentinel-1 Systematic Effects (COR-SC) | Sensor specific calibration constants and corrections to be applied to raw range and azimuth observations. | Section 2.1 |

ECR Phase Center (COR-EC1) | Phase center shift of the ECR due to orbit geometry to be added as a correction to the observations. | Section 2.1 |

ECR Electronic Delay (COR-EC2) | ECR electronics causes a signal delay to be corrected in the SAR measurements. | Section 2.1 |

SAR Positions (SAR-POS) | Time series of coordinates of the SAR target as X, Y, Z coordinates in the ITRF2014 and uncertainties. | Section 2.2 |

SAR Observation Residuals (SAR-OBS) | Time series of range and azimuth standard deviations and observation residuals. | Section 2.2 |

GNSS Positions (GNSS-POS) | Coordinates of the GNSS stations as X, Y, Z coordinates in the ITRF2014 and uncertainties. | Section 2.3 |

Sea Surface Height at TG (TG-SSH) | Corrected sea surface heights observed at TG with respect to TG benchmark. | Section 2.4 |

Geoid Heights (GEO-HGT) | Geoid heights with mean epoch 2020.5 for the tide gauge stations. | Section 2.5 |

Tide Gauge Heights (TG-HGT) | Average of unified physical heights of tide gauge stations. | Section 3.1 |

Absolute Sea Level Heights (SL-ABS) | Average of absolute sea level heights of tide gauge stations. | Section 3.1 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Gruber, T.; Ågren, J.; Angermann, D.; Ellmann, A.; Engfeldt, A.; Gisinger, C.; Jaworski, L.; Kur, T.; Marila, S.; Nastula, J.;
et al. Geodetic SAR for Height System Unification and Sea Level Research—Results in the Baltic Sea Test Network. *Remote Sens.* **2022**, *14*, 3250.
https://doi.org/10.3390/rs14143250

**AMA Style**

Gruber T, Ågren J, Angermann D, Ellmann A, Engfeldt A, Gisinger C, Jaworski L, Kur T, Marila S, Nastula J,
et al. Geodetic SAR for Height System Unification and Sea Level Research—Results in the Baltic Sea Test Network. *Remote Sensing*. 2022; 14(14):3250.
https://doi.org/10.3390/rs14143250

**Chicago/Turabian Style**

Gruber, Thomas, Jonas Ågren, Detlef Angermann, Artu Ellmann, Andreas Engfeldt, Christoph Gisinger, Leszek Jaworski, Tomasz Kur, Simo Marila, Jolanta Nastula,
and et al. 2022. "Geodetic SAR for Height System Unification and Sea Level Research—Results in the Baltic Sea Test Network" *Remote Sensing* 14, no. 14: 3250.
https://doi.org/10.3390/rs14143250