Abstract The GRACE mission has demonstrated a tremendous potential for observing mass changes in the Earth system from space for climate research and the observation of climate change. Future mission should on the one hand extend the already existing time series and also provide higher spatial and temporal resolution that is required to fulfil all needs placed on a future mission. To analyse the applicability of such a Next Generation Gravity Mission (NGGM) concept regarding hydrological applications, two GRACE-FO-type pairs in Bender formation are analysed. The numerical closed loop simulations with a realistic noise assumption are based on the short arc approach and make use of the Wiese approach, enabling a self-de-aliasing of high-frequency atmospheric and oceanic signals, and a NRT approach for a short latency. Numerical simulations for future gravity mission concepts are based on geophysical models, representing the time-variable gravity field. First tests regarding the usability of the hydrology component contained in the Earth System Model (ESM) by the European Space Agency (ESA) for the analysis regarding a possible flood monitoring and detection showed a clear signal in a third of the analysed flood cases. Our analysis of selected cases found that detection of floods was clearly possible with the reconstructed AOHIS/HIS signal in 20% of the tested examples, while in 40% of the cases a peak was visible but not clearly recognisable.
{"title":"Applicability of NGGM near-real time simulations in flood detection","authors":"A. Purkhauser, J. Koch, R. Pail","doi":"10.1515/jogs-2019-0011","DOIUrl":"https://doi.org/10.1515/jogs-2019-0011","url":null,"abstract":"Abstract The GRACE mission has demonstrated a tremendous potential for observing mass changes in the Earth system from space for climate research and the observation of climate change. Future mission should on the one hand extend the already existing time series and also provide higher spatial and temporal resolution that is required to fulfil all needs placed on a future mission. To analyse the applicability of such a Next Generation Gravity Mission (NGGM) concept regarding hydrological applications, two GRACE-FO-type pairs in Bender formation are analysed. The numerical closed loop simulations with a realistic noise assumption are based on the short arc approach and make use of the Wiese approach, enabling a self-de-aliasing of high-frequency atmospheric and oceanic signals, and a NRT approach for a short latency. Numerical simulations for future gravity mission concepts are based on geophysical models, representing the time-variable gravity field. First tests regarding the usability of the hydrology component contained in the Earth System Model (ESM) by the European Space Agency (ESA) for the analysis regarding a possible flood monitoring and detection showed a clear signal in a third of the analysed flood cases. Our analysis of selected cases found that detection of floods was clearly possible with the reconstructed AOHIS/HIS signal in 20% of the tested examples, while in 40% of the cases a peak was visible but not clearly recognisable.","PeriodicalId":44569,"journal":{"name":"Journal of Geodetic Science","volume":"36 1","pages":"111 - 126"},"PeriodicalIF":1.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80007095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Knowledge of vertical crustal movement is fundamental to quantify absolute sea level changes at tide gauge locations as well as for satellite altimetry calibration validations. While GPS measurements at collocated tide gauge stations fulfill this need, currently only few hundred tide gauge stations are equipped with GPS, and their measurements do not span a long period of time. In the past, several studies addressed this problem by calculating relative and geocentric trends from the tide gauge and satellite altimetry measurements respectively, and then difference the two trends to calculate the rate of changes at the tide gauge stations. However, this approach is suboptimal. This study offers an optimal statistical protocol based on the method of condition equations with unknown parameters. An example solution demonstrates the proposed mathematical and statistical models’ optimality in estimating vertical crustal movement and its standard error by comparing them with the results of current methods. The proposed model accounts for the effect of autocorrelations in observed tide gauge and satellite altimetry sea level time series, adjusts observed corrections such as inverted barometer effects, and constraints tide gauge and satellite altimeter measurement to close. The new model can accommodate estimating other systematic effects such as pole tides that are not eliminated by differencing.
{"title":"Optimal mathematical and statistical models to estimate vertical crustal movements using satellite altimetry and tide gauge data","authors":"H. Iz, T. Y. Yang, C. Shum, C. Kuo","doi":"10.1515/jogs-2019-0014","DOIUrl":"https://doi.org/10.1515/jogs-2019-0014","url":null,"abstract":"Abstract Knowledge of vertical crustal movement is fundamental to quantify absolute sea level changes at tide gauge locations as well as for satellite altimetry calibration validations. While GPS measurements at collocated tide gauge stations fulfill this need, currently only few hundred tide gauge stations are equipped with GPS, and their measurements do not span a long period of time. In the past, several studies addressed this problem by calculating relative and geocentric trends from the tide gauge and satellite altimetry measurements respectively, and then difference the two trends to calculate the rate of changes at the tide gauge stations. However, this approach is suboptimal. This study offers an optimal statistical protocol based on the method of condition equations with unknown parameters. An example solution demonstrates the proposed mathematical and statistical models’ optimality in estimating vertical crustal movement and its standard error by comparing them with the results of current methods. The proposed model accounts for the effect of autocorrelations in observed tide gauge and satellite altimetry sea level time series, adjusts observed corrections such as inverted barometer effects, and constraints tide gauge and satellite altimeter measurement to close. The new model can accommodate estimating other systematic effects such as pole tides that are not eliminated by differencing.","PeriodicalId":44569,"journal":{"name":"Journal of Geodetic Science","volume":"IA-23 1","pages":"144 - 153"},"PeriodicalIF":1.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84611530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The NKG2015 geoid model covers the Nordic and Baltic countries and has been computed based on the least-squares modification of Stokes’ formula with additive corrections method. New and precise terrestrial, airborne and shipborne gravimetric measurements, the recent global gravity model of the gravity field and steady-state ocean circulation explorer (GOCE) and detailed digital terrain models over each territory have been used for computing this new geoid model. Some estimates for the error of this model have been roughly presented by comparing it with the global navigation satellite system (GNSS) data over each country. In this paper, our goal is to have a closer look at the relative error of this model by performing some statistical tests and finding the proper corrective surface for absorbing the systematic errors over each country. Our main assumption is realisticity of the errors of GNSS/levelling data and we will investigate its consequences in estimating the error of the geoid model. Our results show that the 4-parameter corrective surface is suitable for modelling the systematic trends of the differences between the gravimetric and GNSS geoid heights in Sweden, Denmark and Finland, but a filtered discrepancies by a confidence interval of 95% should be used for Sweden. A 7-aparameter model is suitable for the filtered discrepancies with the confidence interval of 95% in Norway. Based on the selected corrective surface and our newly developed regional iterative variance estimator, the confidence interval for the error of NKG2015 geoid model in Sweden, Denmark and Norway yielded 0-6.5 mm, 1.8-5.2 mm, 14.8-17.7 mm, respectively with a confidence level of 95%. We could not estimate the geoid error in Finland because the given error of the GNSS/levelling heights is significantly larger than the size of residuals. Based on the selected corrective surfaces and our presented local variance estimator, the average error of geoid becomes 3.6, 2.4, 8.8 and 5.8 mm with a confidence interval of 68%, respectively, over Sweden, Denmark, Norway and Finland.
{"title":"On quality of NKG2015 geoid model over the Nordic countries","authors":"M. Eshagh, Jenny Berntsson","doi":"10.1515/jogs-2019-0010","DOIUrl":"https://doi.org/10.1515/jogs-2019-0010","url":null,"abstract":"Abstract The NKG2015 geoid model covers the Nordic and Baltic countries and has been computed based on the least-squares modification of Stokes’ formula with additive corrections method. New and precise terrestrial, airborne and shipborne gravimetric measurements, the recent global gravity model of the gravity field and steady-state ocean circulation explorer (GOCE) and detailed digital terrain models over each territory have been used for computing this new geoid model. Some estimates for the error of this model have been roughly presented by comparing it with the global navigation satellite system (GNSS) data over each country. In this paper, our goal is to have a closer look at the relative error of this model by performing some statistical tests and finding the proper corrective surface for absorbing the systematic errors over each country. Our main assumption is realisticity of the errors of GNSS/levelling data and we will investigate its consequences in estimating the error of the geoid model. Our results show that the 4-parameter corrective surface is suitable for modelling the systematic trends of the differences between the gravimetric and GNSS geoid heights in Sweden, Denmark and Finland, but a filtered discrepancies by a confidence interval of 95% should be used for Sweden. A 7-aparameter model is suitable for the filtered discrepancies with the confidence interval of 95% in Norway. Based on the selected corrective surface and our newly developed regional iterative variance estimator, the confidence interval for the error of NKG2015 geoid model in Sweden, Denmark and Norway yielded 0-6.5 mm, 1.8-5.2 mm, 14.8-17.7 mm, respectively with a confidence level of 95%. We could not estimate the geoid error in Finland because the given error of the GNSS/levelling heights is significantly larger than the size of residuals. Based on the selected corrective surfaces and our presented local variance estimator, the average error of geoid becomes 3.6, 2.4, 8.8 and 5.8 mm with a confidence interval of 68%, respectively, over Sweden, Denmark, Norway and Finland.","PeriodicalId":44569,"journal":{"name":"Journal of Geodetic Science","volume":"116 1","pages":"110 - 97"},"PeriodicalIF":1.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89329031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Spherical harmonic expansion is a commonly applied mathematical representation of the earth’s gravity field. This representation is implied by the potential coeffcients determined by using elements/parameters of the field observed on the surface of the earth and/or in space outside the earth in the spherical harmonic expansion of the field. International Centre for Gravity Earth Models (ICGEM) publishes, from time to time, Global Gravity Field Models (GGMs) that have been developed. These GGMs need evaluation with terrestrial data of different locations to ascertain their accuracy for application in those locations. In this study, Bouguer gravity anomalies derived from a total of eleven (11) recent GGMs, using sixty sample points, were evaluated by means of Root-Mean-Square difference and correlation coeficient. The Root-Mean-Square differences of the computed Bouguer anomalies from ICGEMwebsite compared to their positionally corresponding terrestrial Bouguer anomalies range from 9.530mgal to 37.113mgal. Additionally, the correlation coe_cients of the structure of the signal of the terrestrial and GGM-derived Bouguer anomalies range from 0.480 to 0.879. It was observed that GECO derived Bouguer gravity anomalies have the best signal structure relationship with the terrestrial data than the other ten GGMs. We also discovered that EIGEN-6C4 and GECO derived Bouguer anomalies have enormous potential to be used as supplements to the terrestrial Bouguer anomalies for Enugu State, Nigeria.
{"title":"Evaluation of Gravity Data Derived from Global Gravity Field Models Using Terrestrial Gravity Data in Enugu State, Nigeria","authors":"O. I. Apeh, E. C. Moka, V. Uzodinma","doi":"10.1515/jogs-2018-0015","DOIUrl":"https://doi.org/10.1515/jogs-2018-0015","url":null,"abstract":"Abstract Spherical harmonic expansion is a commonly applied mathematical representation of the earth’s gravity field. This representation is implied by the potential coeffcients determined by using elements/parameters of the field observed on the surface of the earth and/or in space outside the earth in the spherical harmonic expansion of the field. International Centre for Gravity Earth Models (ICGEM) publishes, from time to time, Global Gravity Field Models (GGMs) that have been developed. These GGMs need evaluation with terrestrial data of different locations to ascertain their accuracy for application in those locations. In this study, Bouguer gravity anomalies derived from a total of eleven (11) recent GGMs, using sixty sample points, were evaluated by means of Root-Mean-Square difference and correlation coeficient. The Root-Mean-Square differences of the computed Bouguer anomalies from ICGEMwebsite compared to their positionally corresponding terrestrial Bouguer anomalies range from 9.530mgal to 37.113mgal. Additionally, the correlation coe_cients of the structure of the signal of the terrestrial and GGM-derived Bouguer anomalies range from 0.480 to 0.879. It was observed that GECO derived Bouguer gravity anomalies have the best signal structure relationship with the terrestrial data than the other ten GGMs. We also discovered that EIGEN-6C4 and GECO derived Bouguer anomalies have enormous potential to be used as supplements to the terrestrial Bouguer anomalies for Enugu State, Nigeria.","PeriodicalId":44569,"journal":{"name":"Journal of Geodetic Science","volume":"11 1","pages":"145 - 153"},"PeriodicalIF":1.3,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85148800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This article studies the Optimal Biased Kriging (OBK) approach which is an alternative geostatistical method that gives up the unbiasedness condition of Ordinary Kriging (OK) to gain an improved Mean Squared Prediction Error (MSPE). The system of equations for the optimal linear biased Kriging predictor is derived and itsMSPE is compared with that of Ordinary Kriging. A major impediment in implementing this system of equations and performing Kriging interpolation with massive datasets is the inversion of the spatial coherency matrix. This problem is investigated and a novel method, called “homeogram tapering”, which exploits spatial sorting techniques to create sparse matrices for efficient matrix inversion, is described. Finally, as an application, results from experiments performed on a geoid undulation dataset from Korea are presented. A precise geoid is usually the indispensable basis for meaningful hydrological studies over wide areas. These experiments use the theory presented here along with a relatively new spatial coherency measure, called the homeogram, also known as the non-centered covariance function.
{"title":"Optimal biased Kriging: Homeogram tapering and applications to geoid undulations in Korea","authors":"B. Schaffrin, T. Bae, Y. Felus","doi":"10.1515/jogs-2018-0016","DOIUrl":"https://doi.org/10.1515/jogs-2018-0016","url":null,"abstract":"Abstract This article studies the Optimal Biased Kriging (OBK) approach which is an alternative geostatistical method that gives up the unbiasedness condition of Ordinary Kriging (OK) to gain an improved Mean Squared Prediction Error (MSPE). The system of equations for the optimal linear biased Kriging predictor is derived and itsMSPE is compared with that of Ordinary Kriging. A major impediment in implementing this system of equations and performing Kriging interpolation with massive datasets is the inversion of the spatial coherency matrix. This problem is investigated and a novel method, called “homeogram tapering”, which exploits spatial sorting techniques to create sparse matrices for efficient matrix inversion, is described. Finally, as an application, results from experiments performed on a geoid undulation dataset from Korea are presented. A precise geoid is usually the indispensable basis for meaningful hydrological studies over wide areas. These experiments use the theory presented here along with a relatively new spatial coherency measure, called the homeogram, also known as the non-centered covariance function.","PeriodicalId":44569,"journal":{"name":"Journal of Geodetic Science","volume":"111 1","pages":"154 - 161"},"PeriodicalIF":1.3,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85697120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Predicting sea level rise is essential for current climate discussions. Empirical models put in use to monitor and analyze sea level variations observed at globally distributed tide gauge stations during the last decade can provide reliable predictions with high resolution. Meanwhile, prediction intervals, an alternative to confidence intervals, are to be recognized and deployed in sea level studies. Predictions together with their prediction intervals, as demonstrated in this study, can quantify the uncertainty of a single future observation from a population, instead of the uncertainty of a conceivable average sea level namely a confidence interval, and it is thereby, better suited for coastal risk assessment to guide policy development for mitigation and adaptation responses.
{"title":"Why and how to predict sea level changes at a tide gauge station with prediction intervals","authors":"H. Iz","doi":"10.1515/jogs-2018-0012","DOIUrl":"https://doi.org/10.1515/jogs-2018-0012","url":null,"abstract":"Abstract Predicting sea level rise is essential for current climate discussions. Empirical models put in use to monitor and analyze sea level variations observed at globally distributed tide gauge stations during the last decade can provide reliable predictions with high resolution. Meanwhile, prediction intervals, an alternative to confidence intervals, are to be recognized and deployed in sea level studies. Predictions together with their prediction intervals, as demonstrated in this study, can quantify the uncertainty of a single future observation from a population, instead of the uncertainty of a conceivable average sea level namely a confidence interval, and it is thereby, better suited for coastal risk assessment to guide policy development for mitigation and adaptation responses.","PeriodicalId":44569,"journal":{"name":"Journal of Geodetic Science","volume":"10 1","pages":"121 - 129"},"PeriodicalIF":1.3,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82241679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The geoid, but not the quasigeoid, is an equipotential surface in the Earth’s gravity field that can serve both as a geodetic datum and a reference surface in geophysics. It is also a natural zero-level surface, as it agrees with the undisturbed mean sea level. Orthometric heights are physical heights above the geoid,while normal heights are geometric heights (of the telluroid) above the reference ellipsoid. Normal heights and the quasigeoid can be determined without any information on the Earth’s topographic density distribution, which is not the case for orthometric heights and geoid. We show from various derivations that the difference between the geoid and the quasigeoid heights, being of the order of 5 m, can be expressed by the simple Bouguer gravity anomaly as the only term that includes the topographic density distribution. This implies that recent formulas, including the refined Bouguer anomaly and a difference between topographic gravity potentials, do not necessarily improve the result. Intuitively one may assume that the quasigeoid, closely related with the Earth’s surface, is rougher than the geoid. For numerical studies the topography is usually divided into blocks of mean elevations, excluding the problem with a non-star shaped Earth. In this case the smoothness of both types of geoid models are affected by the slope of the terrain,which shows that even at high resolutions with ultra-small blocks the geoid model is likely as rough as the quasigeoid model. In case of the real Earth there are areas where the quasigeoid, but not the geoid, is ambiguous, and this problem increases with the numerical resolution of the requested solution. These ambiguities affect also normal and orthometric heights. However, this problem can be solved by using the mean quasigeoid model defined by using average topographic heights at any requested resolution. An exact solution of the ambiguity for the normal height/quasigeoid can be provided by GNSS-levelling.
{"title":"On the geoid and orthometric height vs. quasigeoid and normal height","authors":"L. Sjöberg","doi":"10.1515/jogs-2018-0011","DOIUrl":"https://doi.org/10.1515/jogs-2018-0011","url":null,"abstract":"Abstract The geoid, but not the quasigeoid, is an equipotential surface in the Earth’s gravity field that can serve both as a geodetic datum and a reference surface in geophysics. It is also a natural zero-level surface, as it agrees with the undisturbed mean sea level. Orthometric heights are physical heights above the geoid,while normal heights are geometric heights (of the telluroid) above the reference ellipsoid. Normal heights and the quasigeoid can be determined without any information on the Earth’s topographic density distribution, which is not the case for orthometric heights and geoid. We show from various derivations that the difference between the geoid and the quasigeoid heights, being of the order of 5 m, can be expressed by the simple Bouguer gravity anomaly as the only term that includes the topographic density distribution. This implies that recent formulas, including the refined Bouguer anomaly and a difference between topographic gravity potentials, do not necessarily improve the result. Intuitively one may assume that the quasigeoid, closely related with the Earth’s surface, is rougher than the geoid. For numerical studies the topography is usually divided into blocks of mean elevations, excluding the problem with a non-star shaped Earth. In this case the smoothness of both types of geoid models are affected by the slope of the terrain,which shows that even at high resolutions with ultra-small blocks the geoid model is likely as rough as the quasigeoid model. In case of the real Earth there are areas where the quasigeoid, but not the geoid, is ambiguous, and this problem increases with the numerical resolution of the requested solution. These ambiguities affect also normal and orthometric heights. However, this problem can be solved by using the mean quasigeoid model defined by using average topographic heights at any requested resolution. An exact solution of the ambiguity for the normal height/quasigeoid can be provided by GNSS-levelling.","PeriodicalId":44569,"journal":{"name":"Journal of Geodetic Science","volume":"58 1","pages":"115 - 120"},"PeriodicalIF":1.3,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90977748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
H. Koivula, J. Kuokkanen, Simo Marila, S. Lahtinen, Tuukka Mattila
Abstract We tested the accuracy and usability of a sparse GNSS reference station network for network RTK (NRTK) using the Finnish permanent GNSS network FinnRef. We modified the configuration of the FinnRef network stations used in NRTK computation. This allowed us to perform the test both inside and outside of the network area using different NRTK methods and two different RTK receivers. In the test area the average distance between the FinnRef stationswas 160 km. As a comparison,we tested also with the commercial Trimnet and HxGN SmartNet positioning services operated by Geotrim Oy and Leica Geosystems Finland, respectively. Tests showed that the horizontal and vertical rms of Trimnet servicewas 16mmand 40 mm, and of HxGN SmartNet service 23mmand 48 mm. The best rms for the sparse NLS (National Land Survey of Finland) Service was 22 mm and 56 mm. These results indicate that a good NRTK solution can be achieved with a sparser network than typically used. This study also indicates, that the methods for NRTK processing can also affect the quality of the solution.
{"title":"Assessment of sparse GNSS network for network RTK","authors":"H. Koivula, J. Kuokkanen, Simo Marila, S. Lahtinen, Tuukka Mattila","doi":"10.1515/jogs-2018-0014","DOIUrl":"https://doi.org/10.1515/jogs-2018-0014","url":null,"abstract":"Abstract We tested the accuracy and usability of a sparse GNSS reference station network for network RTK (NRTK) using the Finnish permanent GNSS network FinnRef. We modified the configuration of the FinnRef network stations used in NRTK computation. This allowed us to perform the test both inside and outside of the network area using different NRTK methods and two different RTK receivers. In the test area the average distance between the FinnRef stationswas 160 km. As a comparison,we tested also with the commercial Trimnet and HxGN SmartNet positioning services operated by Geotrim Oy and Leica Geosystems Finland, respectively. Tests showed that the horizontal and vertical rms of Trimnet servicewas 16mmand 40 mm, and of HxGN SmartNet service 23mmand 48 mm. The best rms for the sparse NLS (National Land Survey of Finland) Service was 22 mm and 56 mm. These results indicate that a good NRTK solution can be achieved with a sparser network than typically used. This study also indicates, that the methods for NRTK processing can also affect the quality of the solution.","PeriodicalId":44569,"journal":{"name":"Journal of Geodetic Science","volume":"41 1","pages":"136 - 144"},"PeriodicalIF":1.3,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77262213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This observational study reports that several globally distributed tide gauge stations exhibit a propensity of statistically significant sea level accelerations during the satellite altimetry era. However, the magnitudes of the estimated tide gauge accelerations during this period are systematically and noticeably smaller than the global mean sea level acceleration reported by recent analyses of satellite altimetry. The differences are likely to be caused by the interannual, decadal and interdecadal sea level variations, which are modeled using a broken trend model with overlapping harmonics in the analyses of tide gauge data but omitted in the analysis of satellite altimetry.
{"title":"Sea level accelerations at globally distributed tide gauge stations during the satellite altimetry era","authors":"H. Iz, C. Shum, C. Kuo","doi":"10.1515/jogs-2018-0013","DOIUrl":"https://doi.org/10.1515/jogs-2018-0013","url":null,"abstract":"Abstract This observational study reports that several globally distributed tide gauge stations exhibit a propensity of statistically significant sea level accelerations during the satellite altimetry era. However, the magnitudes of the estimated tide gauge accelerations during this period are systematically and noticeably smaller than the global mean sea level acceleration reported by recent analyses of satellite altimetry. The differences are likely to be caused by the interannual, decadal and interdecadal sea level variations, which are modeled using a broken trend model with overlapping harmonics in the analyses of tide gauge data but omitted in the analysis of satellite altimetry.","PeriodicalId":44569,"journal":{"name":"Journal of Geodetic Science","volume":"117 1","pages":"130 - 135"},"PeriodicalIF":1.3,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78383815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In order to accelerate the spherical/spheroidal harmonic synthesis of any function, we developed a new recursive method to compute the sine/cosine series coefficient of the 4π fully- and Schmidt quasi-normalized associated Legendre functions. The key of the method is a set of increasing-degree/order mixed-wavenumber two to four-term recurrence formulas to compute the diagonal terms. They are used in preparing the seed values of the decreasing-order fixed-degree, and fixed-wavenumber two- and three-term recurrence formulas, which are obtained by modifying the classic relations. The new method is accurate and capable to deal with an arbitrary high degree/ order/wavenumber. Also, it runs significantly faster than the previous method of ours utilizing the Wigner d function, say around 20 times more when the maximum degree exceeds 1,000.
{"title":"Fast computation of sine/cosine series coefficients of associated Legendre function of arbitrary high degree and order","authors":"T. Fukushima","doi":"10.1515/jogs-2018-0017","DOIUrl":"https://doi.org/10.1515/jogs-2018-0017","url":null,"abstract":"Abstract In order to accelerate the spherical/spheroidal harmonic synthesis of any function, we developed a new recursive method to compute the sine/cosine series coefficient of the 4π fully- and Schmidt quasi-normalized associated Legendre functions. The key of the method is a set of increasing-degree/order mixed-wavenumber two to four-term recurrence formulas to compute the diagonal terms. They are used in preparing the seed values of the decreasing-order fixed-degree, and fixed-wavenumber two- and three-term recurrence formulas, which are obtained by modifying the classic relations. The new method is accurate and capable to deal with an arbitrary high degree/ order/wavenumber. Also, it runs significantly faster than the previous method of ours utilizing the Wigner d function, say around 20 times more when the maximum degree exceeds 1,000.","PeriodicalId":44569,"journal":{"name":"Journal of Geodetic Science","volume":"37 1","pages":"162 - 173"},"PeriodicalIF":1.3,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73550615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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