Nonlinear black-box approaches and data fusion for ocean bathymetry modeling in south Iran

The delimitation of maritime boundaries plays a significant role in preserving the country’s sovereignty and jurisdiction. The maritime baseline was established based on the combination of maritime basepoints, which represents the Lowest Astronomical Tide (LAT) along the coast. However, the current approach still relies on the limited and sparsely distributed tide gauge stations for the determination of LAT. Therefore, this study aims to develop the Peninsular Malaysia Near-Seamless Tidal Datum (PMNSTD) by integrating tide gauge, satellite altimetry, and Tide Model Driver (TMD) data. PMNSTD was further integrated with Digital Elevation Models (DEM) for the delimitation of maritime boundaries. This study methodology includes data acquisitions of 12 tide gauge stations along the coast of Peninsular Malaysia, satellite altimetry data for TOPEX, Jason-1, Jason-2, and GEOSAT Follow-On (GFO) from Radar Altimeter Database System (RADS), TMD, and TerraSAR-X add on for Digital Elevation Measurement 30 m (TanDEM-X) data. The tide gauge, satellite altimetry, and TMD data encompass 23 years of tidal observation data from 1993 to 2015. For the derivation of the tidal datum, the tide gauge and satellite altimetry data were analysed using harmonic analysis in UTide, whereas, for the TMD data, the tidal datum was determined based on tidal prediction. For compatibility in data integration, the derived Lowest and Highest Astronomical Tide (LAT and HAT) from tide gauge, satellite altimetry, and TMD data were referenced to the Mean Sea Level (MSL), denoted as LA T msl and HA T msl respectively. Next, the LA T msl and HA T msl was interpolated using Inverse Distance Weighting (IDW) to develop the PMNSTD ( LA T msl and HA T msl ) using ArcGIS. The statistical assessment indicates that the PMNSTD ( LA T msl and HA T msl ) established from the integration of tide gauge, satellite altimetry, and TMD has a better agreement with the Department of Survey and Mapping Malaysia (DSMM) tide gauges with a Root Mean Square Error (RMSE) and Standard Deviation (STD) of 0.228 m and 0.175 m for LA T msl , as well as 0.159 m and 0.079 m for HA T msl . Next, the PMNSTD ( LA T msl ) was integrated with TanDEM-X using ArcGIS and SURFER for the delimitation of maritime boundaries. The reliability assessment illustrated a significant improvement in the continuation of 201 maritime basepoints in comparison to the 95 maritime basepoints by the DSMM. In conclusion, the proposed approach has shown a continuous, consistent, and wider establishment of the country’s maritime baseline for the Peninsular Malaysia region.

Conventionally, information from the tide gauge stations was used to establish the localized tidal datum. However, limitations in coverage, due to the sparse station distribution along the coast, have caused insufficient tidal datum information in some areas. Therefore, this study aims to develop the Peninsular Malaysia Quasi-Continuous Tidal Datum (PMQCTD) by integrating tide gauges, satellite altimetry, and Tide Model Driver (TMD) data. The research methodology includes data acquisition from 12 Departments of Survey and Mapping Malaysia (DSMMs) tide gauge stations along the coast of Peninsular Malaysia, satellite altimetry data of TOPEX, Jason-1, Jason-2, and GEOSAT Follow-On (GFO) from Radar Altimeter Database System (RADS), and the global hydrodynamic model from TMD. The tide gauge, satellite altimetry, and TMD data encompass 23 years of tidal observation data from 1993 to 2015. For the derivation of the tidal datum, tide gauge, and satellite altimetry data were analyzed following a harmonic analysis approach in the Unified Tidal Analysis and Prediction (UTide) software. Meanwhile, for the TMD data, the tidal datum was determined based on the tidal prediction from the 11 extracted major tidal constituents. For compatibility in data integration, the derived Lowest and Highest Astronomical Tide (LAT and HAT) from tide gauge, satellite altimetry, and TMD data were referenced to the Mean Sea Level (MSL), denoted as LATMSL and HATMSL, respectively. Next, the LATMSL and HATMSL were interpolated employing Inverse Distance Weighting (IDW) to develop the PMQCTD (LATMSL and HATMSL) with the ArcGIS software. The statistical assessment indicated that the established PMQCTD (LATMSL and HATMSL) has a better agreement with the DSMM tide gauges with a Root Mean Square Error (RMSE) of ± 0.228 m for LATMSL and ± 0.159 m for HATMSL In conclusion, the establishment of PMQCTD (LATMSL and HATMSL) has led to the availability of the tidal datum at any location along the coast of Peninsular Malaysia.

Earth gravitational model 2008

The purpose of this paper is to analyze the influence of satellite altimetry data accuracy on the marine gravity anomaly accuracy. The data of 12 altimetry satellites in the research area (5°N–23°N, 105°E–118°E) were selected. These data were classified into three groups: A, B, and C, according to the track density, the accuracy of the altimetry satellites, and the differences of self-crossover. Group A contains CryoSat-2, group B includes Geosat, ERS-1, ERS-2, and Envisat, and group C comprises T/P, Jason-1/2/3, HY-2A, SARAL, and Sentinel-3A. In Experiment I, the 5′×5′ marine gravity anomalies were obtained based on the data of groups A, B, and C, respectively. Compared with the shipborne gravity data, the root mean square error (RMSE) of groups A, B, and C was 4.59 mGal, 4.61 mGal, and 4.51 mGal, respectively. The results show that high-precision satellite altimetry data can improve the calculation accuracy of gravity anomaly, and the single satellite CryoSat-2 enables achieving the same effect of multi-satellite joint processing. In Experiment II, the 2′×2′ marine gravity anomalies were acquired based on the data of groups A, A + B, and A + C, respectively. The root mean square error of the above three groups was, respectively, 4.29 mGal, 4.30 mGal, and 4.21 mGal, and the outcomes show that when the spatial resolution is satisfied, adding redundant low-precision altimetry data will add pressure to the calculation of marine gravity anomalies and will not improve the accuracy. An effective combination of multi-satellite data can improve the accuracy and spatial resolution of the marine gravity anomaly inversion.

Preprocessing of Coastal Satellite Altimetry, Tide Gauges, and GNSS Data: Towards the Possibility of Detected Vertical Deformation of South Java Island

ABSTRACTThe determination of high-resolution geoid for marine regions requires the integration of gravity data provided by different sources, e.g. global geopotential models, satellite altimetry, and shipborne gravimetric observations. Shipborne gravity data, acquired over a long time, comprises the short-wavelengths gravitation signal. This paper aims to produce a consistent gravity field over the Red Sea region to be used for geoid modelling. Both, the leave-one-out cross-validation and Kriging prediction techniques were chosen to ensure that the observed shipborne gravity data are consistent as well as free of gross-errors. A confidence level equivalent to 95.4% was decided to filter the observed shipborne data, while the cross-validation algorithm was repeatedly applied until the standard deviation of the residuals between the observed and estimated values are less than 1.5 mGal, which led to the elimination of about 17.7% of the shipborne gravity dataset. A comparison between the shipborne gravity data with DTU13 and SSv23.1 satellite altimetry-derived gravity models is done and reported. The corresponding results revealed that altimetry models almost have identical data content when compared one another, where the DTU13 gave better results with a mean and standard deviation of −2.40 and 8.71 mGal, respectively. A statistical comparison has been made between different global geopotential models (GGMs) and shipborne gravity data. The Spectral Enhancement Method was applied to overcome the existing spectral gap between the GGMs and shipborne gravity data. EGM2008 manifested the best results with differences characterised with a mean of 1.35 mGal and a standard deviation of 11.11 mGal. Finally, the least-squares collocation (LSC) was implemented to combine the shipborne gravity data with DTU13 in order to create a unique and consistent gravity field over the Red Sea with no data voids. The combined data were independently tested using a total number of 95 randomly chosen shipborne gravity stations. The comparison between the extracted shipborne gravity data and DTU13 altimetry anomalies before and after applying the LSC revealed that a significant improvement is procurable from the combined dataset, in which the mean and standard deviation of the differences dropped from −3.60 and 9.31 mGal to −0.39 and 2.04 mGal, respectively.

The advancement of multi-mission satellite altimeters has greatly enhanced the conventional approach of using a tide gauge station to establish a localised hydrographic datum. However, there are still several limitations in continually depending on a small number of sparsely distributed tide gauge stations and wide satellite altimeter track missions, even with its continuous monitoring of ocean data at local and worldwide coverage. Such limitation has left a region farther away from the satellite altimeter track and tide gauge stations without any hydrographic data. Hence, this study aims to develop Malaysia’s Continuous Hydrographic Datum (MyCHD) by combining the satellite altimeter, tide gauge station, and global hydrodynamic model (GHM). In addition, the reliability of MyCHD was also assessed to determine the rate of improvement by incorporating GHM as additional hydrographic data. The research methodology involves collecting data from the Department of Survey and Mapping Malaysia (DSMM) tide gauge stations along Malaysia’s coastline, as well as satellite altimetry data from TOPEX, Jason-1, Jason-2, and GEOSAT Follow-On (GFO) via the Radar Altimeter Database System (RADS). Additionally, Indian Ocean GHM data from Oregon State University (OSU) was also utilised. The tide gauge, satellite altimetry, and GHM datasets encompass 26 years of tidal observations, spanning from 1993 to 2018. All hydrographic data were processed using harmonic analysis in Unified Tidal Analysis and Prediction (UTide) within MATLAB to establish the hydrographic datum. The derived Lowest and Highest Astronomical Tide (LAT and HAT) from tide gauge, satellite altimetry, and GHM data were referred to the Mean Sea Level (MSL) for compatibility in data integration; these were designated as LATMSL and HATMSL, respectively. Then, using ArcGIS software, the LATMSL and HATMSL were interpolated using Inverse Distance Weighting (IDW). In contrast to the integration of tide gauge and satellite altimeter, the statistical assessment showed that the integration of tide gauge, satellite altimeter, and GHM has a better agreement with the DSMM tide gauges, with a Root Mean Square Error (RMSE) of ± 0.671 m for LATMSL and ± 0.370 m for HATMSL. In percentage terms, incorporating GHM data with tide gauge and satellite altimeter in establishing MyCHD has significantly improved its reliability by 17 % for LATMSL and 30 % for HATMSL respectively. In conclusion, the hydrographic datum is now available at any coordinate along Malaysia’s coast with the establishment of MyCHD (LATMSLand HATMSL).

An improved altimeter-derived gravity anomaly from shipborne gravity based on the mean sea surface height constraint factors method

Rosetta is a port city of the Nile Delta, 65 km east of Alexandria. The village is distinguished by its geographical location as the estuary of the Nile River and on the shore of the Mediterranean Sea. It is also historically distinguished as the original site for the discovery of one of the greatest heritage pieces in the world, the Rosetta stone at the village of Burj Rashid, which is currently in the British Museum. The construction of the High Dam reduces the natural mud deposits cause of the sinking and erosion of the crust there and the city experience variable high rates of erosion with accelerated coastal area lost on the last two decades.  This makes this city is very sensitive to any sea level rise.    Thus, Rashid is one of the most vulnerable coastal cities to the effects of climate change.  The present study provides the contribution of the modernized geodetic and satellite techniques to take part into determination the effect of Mediterranean Sea level rise and land subsidence on the city of Rosetta. To reach the proposed objective the study utilizes   Global Navigation Satellite System (GNSS), tide gauges and satellite altimetry and gravity data. GNSS data has been used to determine the rates of the horizontal and vertical movements of the studied region   and linking the rates of vertical movement of the Delta to the temporal change of the sea level variation of the Mediterranean Sea by tying GPS measurements to tide gauge data. On the other hand, determination of temporal local and regional sea level variation of the southern part of the Mediterranean Sea using tide gauge and satellite altimetry data. Finally, total mass variation and the tectonic settings of the shore line features has been figured out using recent satellite gravity data.   Permanent GNSS network along the Nile Delta shows variable rates of land subsidence, with the subsidence rate of the studied area of about 6mm/y. Satellite altimeter data together with tide gauge data confirm the Sea level rise acceleration on this region with an acceleration of about 7mm/y.  On the other hand, the selected region shows complicated pattern of mass variation, land subsidence and Sea Level Rise. Therefore, impact of climate change may be the biggest challenge in this region. On this context, accurate monitoring on the land subsidence and the sea level rise is of great importance to the climate change mitigation and the protection of this city.

Gravity data were obtained along two transects on the southern coast of Ungava Bay, which provide continuous gravity coverage between Leaf Bay and George River. The transects and the derived gravity profiles extend from the Superior craton to the Rae Province across the New Quebec Orogen (NQO). Interpretation of the transect along the southwestern coast of Ungava Bay suggests crustal thickening beneath the NQO and crustal thinning beneath the Kuujjuaq Terrane, east of the NQO. Two alternative interpretations are proposed for the transect along the southeastern coast of the bay. The first model shows crustal thickening beneath the George River Shear Zone (GRSZ) and two shallow bodies correlated with the northern extensions of the GRSZ and the De Pas batholith. The second model shows constant crustal thickness and bodies more deeply rooted than in the first model. The gravity models are consistent with the easterly dipping reflections imaged along a Lithoprobe seismic line crossing Ungava Bay and suggest westward thrusting of the Rae Province over the NQO. Because no gravity data have been collected in Ungava Bay, satellite altimetry data have been used as a means to fill the gap in data collected at sea. The satellite-derived gravity data and standard Bouguer gravity data were combined in a composite map for the Ungava Bay region. The new land-based gravity measurements were used to verify and calibrate the satellite data and to ensure that offshore gravity anomalies merge with those determined by the land surveys in a reasonable fashion. Three parallel east-west gravity profiles were extracted: across Ungava Bay (59.9°N), on the southern shore of the bay (58.5°N), and onshore ~200 km south of Ungava Bay (57.1°N). The gravity signature of some major structures, such as the GRSZ, can be identified on each profile.

در این تحقیق مدل جدید توپوگرافی متوسط دینامیک با نام انتخابی MDT_IAU_TN_2014 ارائه می‌شود. همچنین بردارهای سرعت جریان‌های دائمی سطحی درشبکه‌ای با ابعاد 2 دقیقه در منطقه خلیج فارس، دریای عمان و شمال اقیانوس هند محاسبه گردیده است. این مدل با استفاده از سطح متوسط دریا‌های به دست آمده از 6 ماهواره ارتفاع سنجی (توپکس پوزیدن، جیسون 1و2، ای.ار.اس 1و2 و ادامه ماموریت ژئوست) و داده‌های ثقل سنجی ماهواره گوس به ترتیب در بازه‌های زمانی مشخص 21 و 4 سال محاسبه شده است. نتایج این مدل با مدل سطح متوسط دریاهای MSS_CNES_CLS11 مقایسه شده که خطای جذر میانگین مربع‌ها (RMS ) 1/0 متر دارد. برای یکسان سازی مدل ژئوئید گوس و سطح متوسط دریاها از نظر طیفی، از فیلتر کوتاه شده گوس با شعاع 386/1 درجه در راستای طول و عرض جغرافیایی استفاده شده است. نتایج مدل توپوگرافی متوسط دینامیک محاسباتی مذکور با مدل جهانی توپوگرافی متوسط دینامیکی که با استفاده از داده‌های ارتفاع سنجی و داده‌های دوماهه گوس به دست آمده، ترمیم گردید. با مقایسه مدل توپوگرافی متوسط دینامیک محاسباتی با دو مدل جهانی، خطای جذر میانگین مربع‌ها به ترتیب 033/0 و 051/0 متر به دست آمد. بردار‌های جریان ژئوستروفیک با بردارهای جریان اکمن حاصل از 22 سال داده‌های بادهای سطحی جمع شده و جریان‌های دائمی سطحی محاسبه گردیدند. مقایسه جریان‌های کلی مدل ارائه شده در این تحقیق با جریان‌های سطحی به دست آمده از داده‌های OSCAR به عمل آمد، و خطای جذر میانگین مربع‌ها در مؤلفه‌های شمالی-جنوبی و شرقی-غربی جریان آب دریا به ترتیب 047/0 و 031/0 متر بر ثانیه محاسبه شد. بردار سرعت جریان‌های حاصل از مدل MDT_IAU_TN_2014 ، در منطقه شمال اقیانوس هند بین 0 تا 61/0 متر برثانیه تغییر می‌نماید.

With the development of satellite altimetry technology and the application of new altimetry satellites, the accuracy and resolution of altimeter-derived gravity field models have improved over the last decades. Nowadays, they are close enough to shipborne gravimetry. In this paper, multi-source shipborne gravity data in the South China Sea were taken to evaluate the accuracies of two high-precision altimeter-derived marine gravity field models (SS V30.1, DTU17). In these shipborne gravity data, there are dozens of routes’ ship gravimetry data, obtained from the National Geophysical Data Center (NGDC); data were tracked from a marine survey with a commercial marine gravimeter (type KSS31M), and data were tracked from a marine gravimetry campaign that was conducted with a newly developed platform gravimeter (type JMG) in the South China Sea in September 2020. After various data filtering, processing, and calibrations, the shipborne gravity data were validated with crossover points analysis. Then, the processed shipborne data were employed to evaluate the accuracy of the altimeter-derived marine gravity field models. During this procedure, the quality of JMG shipborne gravity data was compared with the results of KSS31M and NGDC data. Analysis and evaluation results show that the crossover points verification accuracies of KSS31M and JMG are 0.70 mGal and 1.61 mGal, which are much better than the accuracy of NGDC, which is larger than 8.0 mGal. In the area where the bathymetry changes slowly, the root mean square error values between altimetry gravity models and KSS31M data are respectively 3.28 mGal and 4.54 mGal, and those of the JMG data are respectively 2.94 mGal and 2.60 mGal. According to the above results, we can conclude that the JMG has the same 1–2 mGal accuracy level as KSS31M and can meet the measurement requirements of marine gravity.

Chapter 5 - Satellite altimetry in Indonesian waters: accuracy assessment and its applications

Sea level variations (SLVs) can be divided into two major components: the steric SLV and the mass-induced SLV. These two components of SLV in the South China Sea (SCS) are studied by using satellite altimetry, GRACE (Gravity Recovery and Climate Experiment) satellite gravity, and oceanographic data on annual and inter-annual timescales. On the annual timescale, the geographic distribution of mass-induced SLV’s amplitude jointly estimated from altimetry and the ECCO (Estimation of the Circulation and Climate of the Ocean) model agrees very well with that from GRACE. GRACE observes obvious seasonal mass-induced SLV in the SCS with annual amplitude of 2.7±0.4 cm, which is consistent with the annual amplitude of 2.7±0.3 cm estimated from the steric-corrected altimetry. On the inter-annual timescales, the mean SLV in the SCS shows a large oscillation, which is mainly caused by the steric effect. The trend of mean SLV inferred from altimetry in the SCS is 5.5±0.7 mm/yr for the period of 1993–2009, which is significantly higher than the global sea level rise rate of 3.3±0.4 mm/yr in the same period. There is no obvious trend signal in the mass-induced SLV detected from GRACE that indicates the water exchange between the SCS and its adjacent seas and land is in balance within the study period.

<p>The relationship between satellite-derived absolute sea level change rates, tide gauge (TG) observations of relative sea level change and global positioning system (GPS) measurements of vertical land motion (VLM) at local scale has been investigated in previous studies [eg. Vignudelli et al., 2018]. The paucity of collocated TG-GPS data and the lack of a well-established mathematical frame in which simultaneous and optimal solutions can be derived, have emphasized the difficulty of deriving spatially-consistent information on the sea level rates. Other studies have claimed the possibility to set locally isolated information into a coherent regional framework using a constrained linear inverse problem approach [Kuo et al., 2004; Wöppelmann and Marcos, 2012].</p><p>The approach cited in the above papers has been recently improved in De Biasio et al. [2020]. A step in advance is now to develop an effective synergistic use of global positioning system (GPS) data, tide gauge measurements and satellite altimetry observations. In this study GPS data are used as a real source of information on the relative Vertical Land Motion (VLM) between pairs of tide gauges, and not as mere term of comparison of the results obtained by differencing relative and absolute sea level observations time series.</p><p>Long, consistent and collocated tide gauge and GPS observations time series are extracted for a handful of suitable coastal locations, and used in the original formulation of the constrained linear inverse problem, together with satellite altimetry data. Some experiments are conducted without GPS observations (traditional setup), and with GPS observations (the new proposed approach) Results are compared in order to assess the impact of GPS observations directly into the formulation of the constrained linear inverse problem.</p><p>The satellite altimetry data-set used in this study is that offered by the European Copernicus Climate Change Service (C3S) through its Climate Data Store archive. It covers the global ocean since 1993 to present, with spatial resolution of 0.25 x 0.25 degrees. This data set is constantly updated and relies only on a couple of simultaneous altimetry missions at a time to provide stable long-term variability estimates of sea level. Tide gauge data are extracted from the Permanent Service for Mean Sea Level archive and from other local sea level monitoring services. GPS vertical position time series and/or VLM rates are taken from the Nevada Geodetic Laboratory and other public GPS repositories.</p><p>REFERENCES</p><p>Vignudelli, S.; De Biasio, F.; Scozzari, A.; Zecchetto, S.; Papa, A. In Proceedings of the International Association of Geodesy Symposia; Mertikas, S.P., Pail, R., Eds.; Springer: Cham, Switzerland, 2020; Volume 150, pp. 65–74. DOI: 10.1007/1345_2018_51</p><p>Kuo, C.Y.; Shum, C.K.; Braun, A.; Mitrovica, J.X. Geophys. Res. Lett. 2004, 31. DOI: 10.1029/2003GL019106</p><p>Wöppelmann, G.; Marcos, M. J. Geophys. Res. Ocean. 2012, 117. DOI: 10.1029/2011JC007469</p><p>De Biasio, F.; Baldin, G.; Vignudelli, S. J. Mar. Sci. Eng. 2020, 8, 949. DOI: 10.3390/jmse8110949</p>