Open Access Published by De Gruyter Open Access

Volume 10 Issue 1

January 2020

Issue of Journal of Geodetic Science

Contents
Journal Overview

Open Access March 31, 2020

A statistical protocol for a holistic adjustment of global sea level budget

H. Bâki Iz, C. K. Shum

Page range: 1-6

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Abstract

Current studies in global mean sea level, GMSL, studies assess the closure/misclosure of the GMSL budget components and their uncertainties. Because Earth’s hydrosphere conserves water, a closed global mean sea level budget with a consistent set of estimates and their statistics is necessary. An unclosed budget means that there are problems to be addressed such as biases in the budget components, unreliable error statistics about the estimates, unknown or known but unmodeled budget components. In a misclosed global mean sea level budget, as practiced in recent studies, the trend estimates for the budget components and their errors account only for the anomalies of each budget component in isolation. On the other hand, the trend of each series must consider the trends of the other series in tandem such that the global mean sea level budget is closed for a holistic assessment, which can only be achieved by adjusting global mean sea level budget components simultaneously. In this study, we demonstrate a statistical protocol to ameliorate this deficiency, which potentially have implications for future sea level science studies, including the future Intergovernmental Panel on Climate Change (IPCC) Assessment Reports, and the US Climate Assessment Reports.

Open Access May 4, 2020

Testing normality of chosen R-estimates used in deformation analysis

R. Duchnowski, P. Wyszkowska

Page range: 7-13

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Abstract

The normal distribution is one of the most important distribution in statistics. In the context of geodetic observation analyses, such importance follows Hagen’s hypothesis of elementary errors; however, some papers point to some leptokurtic tendencies in geodetic observation sets. In the case of linear estimators, the normality is guaranteed by normality of the independent observations. The situation is more complex if estimates and/or the functional model are not linear. Then the normality of such estimates can be tested theoretically or empirically by applying one of goodness-of-fit tests. This paper focuses on testing normality of selected variants of the Hodges-Lehmann estimators (HLE). Under some general assumptions the simplest HLEs have asymptotical normality. However, this does not apply to the Hodges-Lehmann weighted estimators (HLWE), which are more applicable in deformation analysis. Thus, the paper presents tests for normality of HLEs and HLWEs. The analyses, which are based on Monte Carlo method and the Jarque–Bera test, prove normality of HLEs. HLWEs do not follow the normal distribution when the functional model is not linear, and the accuracy of observation is relatively low. However, this fact seems not important from the practical point of view.

Open Access May 4, 2020

Classification of poplar trees with object-based ensemble learning algorithms using Sentinel-2A imagery

H. Tonbul, I. Colkesen, T. Kavzoglu

Page range: 14-22

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Abstract

The poplar species in the forest ecosystems are one of the most valuable and beneficial species for the society and environment. Conventional methods require high cost, time and labor need, and the results obtained vary and are insu˚cient in terms of achieved accuracy level. Determination of poplar cultivated fields and mapping of their spatial sites play a vital role for decision-makers and planners to enhance the economic and ecological value of poplar trees. The study aims to map Poplar (P. deltoides ) cultivated areas in Akyazi district of Sakarya, Turkey province using various combinations of the Sentinel-2A image bands. For this purpose, object-based classification based on multi-resolution segmentation algorithm was utilized to produce image objects and ensemble learning algorithms, namely, Adaboost (AdaB), Random Forest (RF), Rotation Forest (RotFor) and Canonical correlation forest (CCF) were applied to produce thematic maps. In order to analyze the effects of the spectral bands of the Sentinel-2A image on the object-based classification performance, three datasets consisting of different spectral band combinations (i.e. four 10 m bands, six 20 m bands and ten 10m pan-sharpened bands) were used. The results showed that the RotFor and CCF classifiers produced superior classification performances compared to the AdaB and RF classifiers for the band combinations regarded in this study. Moreover, it was found that determination of poplar tree class level accuracy reached to ~94% in terms of F-score. It was also observed that the inclusion of the six spectral bands at 20 m resolution resulted in a noteworthy increase in classification accuracy (up to 6%) compared to single 10m band combination.

Open Access May 4, 2020

Improved indoor positioning based on range-free RSSI fingerprint method

Marcin Uradzinski, Hang Guo, Min Yu

Page range: 23-28

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Abstract

As the development of modern science and technology, LBS and location-aware computing are increasingly important in the practical applications. Currently, GPS positioning system is a mature positioning technology used widely, but signals are easily absorbed, reflected by buildings, and attenuate seriously. In such situation, GPS positioning is not suitable for using in the indoor environment. Wireless sensor networks, such as ZigBee technology, can provide RSSI (received signal strength indicator) which can be used for positioning, especially indoor positioning, and therefore for location based services (LBS).The authors are focused on the fingerprint database method which is suitable for calculating the coordinates of a pedestrian location. This positioning method can use the signal strength indication between the reference nodes and positioning nodes, and design algorithms for positioning. In the wireless sensor networks, according to whether measuring the distance between the nodes in the positioning process, the positioning modes are divided into two categories which are range-based and range-free positioning modes. This paper describes newly improved indoor positioning method based on RSSI fingerprint database, which is range-free. Presented fingerprint database positioning can provide more accurate positioning results, and the accuracy of establishing fingerprint database will affect the accuracy of indoor positioning. In this paper, we propose a new method about the average threshold and the effective data domain filtering method to optimize the fingerprint database of ZigBee technology. Indoor experiment, which was conducted at the University of Warmia and Mazury, proved that the distance achieved by this system has been extended over 30 meters without decreasing the positioning accuracy. The weighted nearest algorithm was chosen and used to calculate user’s location, and then the results were compared and analyzed. As a result, the positioning accuracy was improved and error did not exceed 0.69 m. Therefore, such system can be easily applied in a bigger space inside the buildings, underground mines or in the other location based services.

Open Access May 29, 2020

The certitude of a global sea level acceleration during the satellite altimeter era

H. Bâki İz, C.K. Shum

Page range: 29-40

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Abstract

Recent studies reported a uniform global sea level acceleration during the satellite altimetry era (1993–2017) by analyzing globally averaged satellite altimetry measurements. Here, we discuss potential omission errors that were not thoroughly addressed in detecting and estimating the reported global sea level acceleration in these studies. Our analyses results demonstrate that the declared acceleration in recent studies can also be explained equally well by alternative kinematic models based on previously well-established multi-decadal global mean sea level variations of various origins, which suggests prudence before declaring the presence of an accelerating global mean sea level with confidence during the satellite altimetry era.

Open Access June 2, 2020

Systematic bias of selected estimates applied in vertical displacement analysis

P. Wyszkowska, R. Duchnowski

Page range: 41-47

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Abstract

In surveying problems we almost always use unbiased estimators; however, even unbiased estimator might yield biased assessments, which is due to data. In statistics one distinguishes several types of such biases, for example, sampling, systemic or response biases. Considering surveying observation sets, bias from data might result from systematic or gross errors of measurements. If nonrandom errors in an observation set are known, then bias can easily be determined for linear estimates (e.g., least squares estimates). In the case of non-linear estimators, it is not so simple. In this paper we are focused on a vertical displacement analysis and we consider traditional least squares estimate, two M split estimates and two basic robust estimates, namely M-estimate, R-estimate. The main aim of the paper is to assess estimate biases empirically by applying Monte Carlo method. The smallest biases are obtained for M- and R-estimates, especially for a high magnitude of a gross error. On the other hand, there are several cases when M split estimates are the best. Such results are acquired when the magnitude of a gross error is moderate or small. The outcomes confirm that bias of M split estimates might vary for different point displacements.

Open Access June 24, 2020

On the application of nature-inspired grey wolf optimizer algorithm in geodesy

M. Yetkin, O. Bilginer

Page range: 48-52

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Abstract

Nowadays, solving hard optimization problems using metaheuristic algorithms has attracted bountiful attention. Generally, these algorithms are inspired by natural metaphors. A novel metaheuristic algorithm, namely Grey Wolf Optimization (GWO), might be applied in the solution of geodetic optimization problems. The GWO algorithm is based on the intelligent behaviors of grey wolves and a population based stochastic optimization method. One great advantage of GWO is that there are fewer control parameters to adjust. The algorithm mimics the leadership hierarchy and hunting mechanism of grey wolves in nature. In the present paper, the GWO algorithm is applied in the calibration of an Electronic Distance Measurement (EDM) instrument using the Least Squares (LS) principle for the first time. Furthermore, a robust parameter estimator called the Least Trimmed Absolute Value (LTAV) is applied to a leveling network for the first time. The GWO algorithm is used as a computing tool in the implementation of robust estimation. The results obtained by GWO are compared with the results of the ordinary LS method. The results reveal that the use of GWO may provide efficient results compared to the classical approach.

Open Access October 5, 2020

On the uncertainty of height anomaly differences predicted by least-squares collocation

E. Mysen

Page range: 53-61

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Abstract

A network of pointwise available height anomalies, derived from levelling and GPS observations, can be densified by adjusting a gravimetric quasigeoid using least-squares collocation. The resulting type of Corrector Surface Model (CSM) is applied by Norwegian surveyors to convert ellipsoidal heights to normal heights expressed in the official height system NN2000. In this work, the uncertainty related to the use of a CSM to predict differences in height anomaly was sought. As previously, the application of variograms to determine the local statistical properties of the adopted collocation model led to predictions that were consistent with their computed uncertainties. For the purpose of predicting height anomaly differences, the effect of collocation was seen to be moderate in general for the small spatial separations considered (< 10 km). However, the relative impact of collocation could be appreciable, and increasing with distance, near the network. At last, it was argued that conservative uncertainties of height anomaly differences may be obtained by rescaling output of a grid interpolation by Δ\sqrt \Delta, where Δ is the spatial separation of the two locations for which the difference is sought.

Open Access October 27, 2020

Conflation of satellite altimetry and tide gauge records at coast

H. Bâki Iz, C. K. Shum, T. Y. Yang

Page range: 62-68

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Abstract

This study demonstrates that absolute (geocentric) and relative sea level trends, sea level acceleration, low frequency sea level variations and linear trends in vertical crustal movements experienced at a tide gauge station can be estimated simultaneously using conflated satellite altimetry and tide gauge measurements without the aid of GPS measurements. The formulation is the first of its kind in sea level studies and its effectiveness is exemplified using tide gauge, and satellite altimetry measurements carried out in the vicinity of a tide gauge station.

Open Access October 27, 2020

Fitting a triaxial ellipsoid to a geoid model

G. Panou, R. Korakitis, G. Pantazis

Page range: 69-82

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Abstract

The aim of this work is the determination of the parameters of Earth’s triaxiality through a geometric fitting of a triaxial ellipsoid to a set of given points in space, as they are derived from a geoid model. Starting from a Cartesian equation of an ellipsoid in an arbitrary reference system, we develop a transformation of its coefficients into the coordinates of the ellipsoid center, of the three rotation angles and the three ellipsoid semi-axes. Furthermore, we present different mathematical models for some special and degenerate cases of the triaxial ellipsoid. We also present the required mathematical background of the theory of least-squares, under the condition of minimization of the sum of squares of geoid heights. Also, we describe a method for the determination of the foot points of the set of given space points. Then, we prepare suitable data sets and we derive results for various geoid models, which were proposed in the last fifty years. Among the results, we report the semi-axes of the triaxial ellipsoid of geometric fitting with four unknowns to be 6378171.92 m, 6378102.06 m and 6356752.17 m and the equatorial longitude of the major semi-axis –14.9367 degrees. Also, the parameters of Earth’s triaxiality are directly estimated from the spherical harmonic coefficients of degree and order two. Finally, the results indicate that the geoid heights with reference to the triaxial ellipsoid are smaller than those with reference to the oblate spheroid and the improvement in the corresponding rms value is about 20 per cent.

Open Access December 17, 2020

Year by year closure adjustment of global mean sea level budget, inclusive of lumped snow, water vapor, and permafrost mass components

H. Bâki Iz, C. K. Shum

Page range: 83-90

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Abstract

Global mean sea level budget is rigorously adjusted during the period 2005–2015 with an emphasis on closing the budget on a year by year basis as opposed to using linear trends of global mean sea level components. The adjustment also accounts for the effect of snow, water vapor, and permafrost mass components as a lump sum. The approach provides better resolution for evaluating individual contribution of each budget component year by year in tandem with the other components. Year by year budget misclosures and the confidence intervals of the year by year adjusted budget components are suggestive of an increasing non-linearity in satellite altimetry derived global mean sea level measurements starting in 2012, which are not present in the other components. The solution also generates time series iteratively for the lumped snow, water vapor, and permafrost mass components as well as an estimate for its linear trend, 0.06±0.59 mm/yr. Nonetheless, its standard error is markedly large because of the un-modeled variability in satellite altimetry observed yearly averaged global mean sea level anomalies.

Open Access December 31, 2020

Semi-kinematic geodetic reference frame based on the ITRF2014 for Malaysia

M. Azhari, Z. Altamimi, G. Azman, M. Kadir, W.J.F Simons, R. Sohaime, M.Y. Yunus, M.J. Irwan, C.A. Asyran, N. Soeb, A. Fahmi, A. Saiful

Page range: 91-109

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Abstract

Malaysia is located at the stable part of the tec-tonic Sundaland platelet in SE Asia. The platelet is surrounded in almost every direction by tectonically active convergent boundaries, at which the Philippine Sea, the Australian and the Indian Plates are subducting respectively from the East, South and West.The current Malaysia geodetic reference frame called MGRF2000 is a static reference frame and hence did not incorporate the effects of plate motion and the ensuing deformation from (megath-rust) earthquakes. To prevent degradation of Continuously Operating Reference Station (CORS) coordinates, a new time-dependent national reference frame was developed. Taking advantage of the availability of the GNSS data of the CORS network in Malaysia, notably the Malaysia Active GPS System (MASS) and Malaysia Real-Time Kinematic GNSS Network (MyRTKnet), a more accurate and robust Malaysian geodetic reference frame was determined, fully aligned and compatible with ITRF2014. The cumulative solution obtained from stacking Malaysian CORS position time series formed the basis of the new MGRF2020 realization. It consists of 100+ station positions at epoch 2020.0, station velocities and Post-Seismic Deformation (PSD) parametric models for stations subjected to major earthquakes. The (1999-2018) position time series exhibit Weighted Mean Root Square (WRMS) values of 3.0, 3.2 and 7.6 mm in respectively the East, North and Vertical components. A new semi-kinematic geodetic datum (GDM2020) for Malaysia, useable for GIS, mapping and cadastre applications is proposed to replace the existing static datum (GDM2000). A transformation suite to convert the spatial databases from GDM2000 to GDM2020 was also developed.

Open Access December 31, 2020

On the BIC for determining the number of control points in B-spline surface approximation in case of correlated observations

Gaël Kermarrec, Hamza Alkhatib

Page range: 110-123

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Abstract

B-spline curves are a linear combination of control points (CP) and B-spline basis functions. They satisfy the strong convex hull property and have a fine and local shape control as changing one CP affects the curve locally, whereas the total number of CP has a more general effect on the control polygon of the spline. Information criteria (IC), such as Akaike IC (AIC) and Bayesian IC (BIC), provide a way to determine an optimal number of CP so that the B-spline approximation fits optimally in a least-squares (LS) sense with scattered and noisy observations. These criteria are based on the log-likelihood of the models and assume often that the error term is independent and identically distributed. This assumption is strong and accounts neither for heteroscedasticity nor for correlations. Thus, such effects have to be considered to avoid under-or overfitting of the observations in the LS adjustment, i.e. bad approximation or noise approximation, respectively. In this contribution, we introduce generalized versions of the BIC derived using the concept of quasi- likelihood estimator (QLE). Our own extensions of the generalized BIC criteria account (i) explicitly for model misspecifications and complexity (ii) and additionally for the correlations of the residuals. To that aim, the correlation model of the residuals is assumed to correspond to a first order autoregressive process AR(1). We apply our general derivations to the specific case of B-spline approximations of curves and surfaces, and couple the information given by the different IC together. Consecutively, a didactical yet simple procedure to interpret the results given by the IC is provided in order to identify an optimal number of parameters to estimate in case of correlated observations. A concrete case study using observations from a bridge scanned with a Terrestrial Laser Scanner (TLS) highlights the proposed procedure.

Open Access December 31, 2020

Spherical approximating and interpolating moving least squares in geodesy and geophysics: a case study for deriving gravity acceleration at sea surface in the Persian Gulf

M. Kiani

Page range: 124-135

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Abstract

This paper is aimed at introducing the concept of Spherical Interpolating Moving Least Squares to the problems in geodesy and geophysics. Based on two previously known methods, namely Spherical Moving Least Squares and Interpolating Moving Least Squares, a simple theory is formulated for using Spherical Moving Least Squares as an interpolant. As an application, a case study is presented in which gravity accelerations at sea surface in the Persian Gulf are derived, using both the approximation and interpolation mode of the Spherical Moving Least Squares. The roles of the various elements in the methods-weight function, scaling parameter, and the degree of spherical harmonics as the basis functions-are investigated. Then, the results of approximation and interpolation are compared with the field data at sea surface, collected by shipborne gravimetry approach. Finally, the results are compared with another independent interpolation method-spline interpolation. It is shown that in this particular problem, SMLS approximation and SIMLS interpolation present a better accuracy than spherical splines.

Open Access December 28, 2020

GPS measurements on pre-, co- and post-seismic surface deformation at first multi-parametric geophysical observatory, Ghuttu in Garhwal Himalaya, India

P.K. Gautam, S. Rajesh, N. Kumar, C.P. Dabral

Page range: 136-144

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Abstract

We investigate the surface deformation pattern of GPS station at MPGO Ghuttu (GHUT) to find out the cause of anomalous behavior in the continuous GPS time series. Seven years (2007-2013) of GPS data has been analyzed using GAMIT/GLOBK software and generated the daily position time series. The horizontal translational motion at GHUT is 43.7 ± 1 mm/yr at an angle of 41°± 3° towards NE, while for the IGS station at LHAZ, the motion is 49.4 ±1 mm/yr at 18 ± 2.5° towards NEE. The estimated velocity at GHUT station with respect to IISC is 12 ± 1 mm/yr towards SW. Besides, we have also examined anomalous changes in the time series of GHUT before, after and during the occurrences of local earthquakes by considering the empirical strain radius; such that, a possible relationship between the strain radius and the occurrences of earthquakes have been explored. We considered seven local earthquakes on the basis of Dobrovolsky strain radius condition having magnitude from 4.5 to 5.7, which occurred from 2007 to 2011. Results show irrespective of the station strain radius, pre-seismic surface deformational anomalies are observed roughly 70 to 80 days before the occurrence of a Moderate or higher magnitude events. This has been observed for the cases of those events originated from the Uttarakashi and the Chamoli seismic zones in the Garhwal and Kumaun Himalaya. Occurrences of short (< 100 days) and long (two years) inter-seismic events in the Garhwal region plausibly regulating and diffusing the regional strain accumulation.

Open Access December 31, 2020

Recent and future manifestations of a contingent global mean sea level acceleration

H. Bâki İz, C.K. Shum

Page range: 153-162

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Abstract

We analyzed globally averaged satellite altimetry mean sea level time series during 1993 – 2018 and their future manifestations for the following 25 years using a kinematic model, which consists of a trend, a contingent uniform acceleration, and a random error model. The analysis of variance results shows that the model explains 71.7% of the total variation in global mean sea level for which 70.6% is by the secular trend, and 1.07% is due to a contingent uniform acceleration. The remaining 28.3% unexplained variation is due to the random errors, which are dominated by a first order autoregressive process driven mostly by oceanic and atmospheric variations over time. These numbers indicate more bumps and jumps for the future manifestations of the global mean sea level anomalies as illustrated using a one-step ahead predictor in this study. Our findings suggest preponderant random errors are poised to further confound and negatively impact the certitude of published estimates of the uniform global sea level acceleration as well as its prediction under an increasingly warmer Earth.

About this journal

Journal of Geodetic Science is a peer-reviewed, electronic-only journal that publishes original, high-quality research on topics broadly related to Geodesy. The journal focuses on theoretical and application papers. The aim of the Journal is to become a premier source of knowledge and a worldwide-recognized platform of exchange for scientists of different disciplinary origins and backgrounds (e.g., Surveyors, Geodesists and Geophysicists). The journal publishes geodetic research from a broad range of topics and approaches including Geodetic Networks, Deformation analysis, Adjustment theory and application of mathematical statistics, Satellite Geodesy, Physical Geodesy, Geodynamics, Geometric Geodesy, (see the scope listed below for more). However, we will accept both theoretical and empirical contributions in all subfields of Geodesy as long as they contribute in a broad sense to the core theme.

The scope includes, but is not restricted to:

Surveying Engineering
Geodetic Networks
Deformation Analysis
Adjustment Theory and Mathematical Geodesy
Global Navigation Satellite Systems (GNSS)
Inertial Geodesy
Geoid determination and height systems
Marine Geodesy and Satellite Altimetry
Satellite Gravimetry
Geometric Geodesy
Numerical methods and software developments in Geodesy
Geodynamics
Geophysical Geodesy

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