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Journal articles on the topic 'Anomalous collocation'
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1
Gu, Y. T., and P. Zhuang. "Anomalous sub-diffusion equations by the meshless collocation method." Australian Journal of Mechanical Engineering 10, no. 1 (January 2012): 1–8. http://dx.doi.org/10.7158/m10-722.2012.10.1.
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Tang, Zhuochao, Zhuojia Fu, HongGuang Sun, and Xiaoting Liu. "An efficient localized collocation solver for anomalous diffusion on surfaces." Fractional Calculus and Applied Analysis 24, no. 3 (June 1, 2021): 865–94. http://dx.doi.org/10.1515/fca-2021-0037.
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Abstract This paper introduces an efficient collocation solver, the generalized finite difference method (GFDM) combined with the recent-developed scale-dependent time stepping method (SD-TSM), to predict the anomalous diffusion behavior on surfaces governed by surface time-fractional diffusion equations. In the proposed solver, the GFDM is used in spatial discretization and SD-TSM is used in temporal discretization. Based on the moving least square theorem and Taylor series, the GFDM introduces the stencil selection algorithms to choose the stencil support of a certain node from the whole discretization nodes on the surface. It inherits the similar properties from the standard FDM and avoids the mesh generation, which is available particularly for high-dimensional irregular discretization nodes. The SD-TSM is a non-uniform temporal discretization method involving the idea of metric, which links the fractional derivative order with the non-uniform discretization strategy. Compared with the traditional time stepping methods, GFDM combined with SD-TSM deals well with the low accuracy in the early period. Numerical investigations are presented to demonstrate the efficiency and accuracy of the proposed GFDM in conjunction with SD-TSM for solving either single or coupled fractional diffusion equations on surfaces.
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Jiang, Wei, and Zhong Chen. "A collocation method based on reproducing kernel for a modified anomalous subdiffusion equation." Numerical Methods for Partial Differential Equations 30, no. 1 (October 28, 2013): 289–300. http://dx.doi.org/10.1002/num.21809.
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Pisetskaya, Olga, and Alexander Yarmolenko. "Problem of Determining a Geoid." Baltic Surveying 8 (October 31, 2018): 85–92. http://dx.doi.org/10.22616/j.balticsurveying.2018.011.
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The issue of the study of the problem of determining the geoid and quasi-geoid models is considered. Development of methods for constructing an exact geoid model using different dimensions. Analysis of the calculation of normal heights using satellite measurements, construction of geoid and quasi-geoid models by different methods is performed. Based on the results of the analytical review of existing methods for determining the geoid, it was proposed to use various data (geodetic heights, mixed gravity anomalies, anomalous potential) to construct this model, which allows building a model of a geoid with millimetre accuracy. The possibility of using the collocation method is considered. The task is to develop a methodology for constructing a geoid model using a network of low density gravity points and using pure and mixed gravity anomalies, which allows us to solve the problem of finding potential by solving the Laplace equation or using wavelets.
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Gaetani, Carlo Iapige De, Noemi Emanuela Cazzaniga, Riccardo Barzaghi, Mirko Reguzzoni, and Barbara Betti. "COVARIANCE FUNCTION MODELLING IN LOCAL GEODETIC APPLICATIONS USING THE SIMPLEX METHOD." Boletim de Ciências Geodésicas 22, no. 2 (June 2016): 342–57. http://dx.doi.org/10.1590/s1982-21702016000200019.
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Collocation has been widely applied in geodesy for estimating the gravity field of the Earth both locally and globally. Particularly, this is the standard geodetic method used to combine all the available data to get an integrated estimate of any functional of the anomalous potential T. The key point of the method is the definition of proper covariance functions of the data. Covariance function models have been proposed by many authors together with the related software. In this paper a new method for finding suitable covariance models has been devised. The covariance fitting problem is reduced to an optimization problem in Linear Programming and solved by using the Simplex Method. The procedure has been implemented in a FORTRAN95 software and has been tested on simulated and real data sets. These first tests proved that the proposed method is a reliable tool for estimating proper covariance function models to be used in the collocation procedure
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Hashmi, M. S., Zainab Shehzad, Asifa Ashraf, Zhiyue Zhang, Yu-Pei Lv, Abdul Ghaffar, Mustafa Inc, and Ayman A. Aly. "A New Variant of B-Spline for the Solution of Modified Fractional Anomalous Subdiffusion Equation." Journal of Function Spaces 2021 (July 1, 2021): 1–8. http://dx.doi.org/10.1155/2021/8047727.
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The objective of this paper is to present an efficient numerical technique for solving time fractional modified anomalous subdiffusion equation. Anomalous diffusion equation has its role in various branches of biological sciences. B-spline is a piecewise function to draw curves and surfaces, which maintain its degree of smoothness at the connecting points. B-spline provides an active process of approximation to the limit curve. In current attempt, B-spline curve is used to approximate the solution curve of time fractional modified anomalous subdiffusion equation. The process is kept simple involving collocation procedure to the data points. The time fractional derivative is approximated with the discretized form of the Riemann-Liouville derivative. The process results in the form of system of algebraic equations, which is solved using a variant of Thomas algorithm. In order to ensure the convergence of the procedure, a valid method named Von Neumann stability analysis is attempted. The graphical and tabular display of results for the illustrated examples is presented, which stamped the efficiency of the proposed algorithm.
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Alebrahim, Reza, Pawel Packo, Mirco Zaccariotto, and Ugo Galvanetto. "Wave propagation improvement in two-dimensional bond-based peridynamics model." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 235, no. 14 (January 20, 2021): 2542–53. http://dx.doi.org/10.1177/0954406220985551.
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In this study, methods to mitigate anomalous wave propagation in 2-D Bond-Based Peridynamics (PD) are presented. Similarly to what happens in classical non-local models, an irregular wave transmission phenomenon occurs at high frequencies. This feature of the dynamic performance of PD, limits its potential applications. A minimization method based on the weighted residual point collocation is introduced to substantially extend the frequency range of wave motion modeling. The optimization problem, developed through inverse analysis, is set up by comparing exact and numerical dispersion curves and minimizing the error in the frequency-wavenumber domain. A significant improvement in the wave propagation simulation using Bond-Based PD is observed.
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Sayevand, K., A. Yazdani, and F. Arjang. "Cubic B-spline collocation method and its application for anomalous fractional diffusion equations in transport dynamic systems." Journal of Vibration and Control 22, no. 9 (March 9, 2016): 2173–86. http://dx.doi.org/10.1177/1077546316636282.
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Xi, Qiang, Zhuojia Fu, Timon Rabczuk, and Deshun Yin. "A localized collocation scheme with fundamental solutions for long-time anomalous heat conduction analysis in functionally graded materials." International Journal of Heat and Mass Transfer 180 (December 2021): 121778. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2021.121778.
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Shivanian, Elyas, and Ahmad Jafarabadi. "Time fractional modified anomalous sub-diffusion equation with a nonlinear source term through locally applied meshless radial point interpolation." Modern Physics Letters B 32, no. 22 (August 7, 2018): 1850251. http://dx.doi.org/10.1142/s0217984918502512.
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In this paper, an alternative approach of spectral meshless radial point interpolation (SMRPI) is applied to the modified anomalous fractional sub-diffusion equation with a nonlinear source term in one and two dimensions. The time fractional derivative is described in the Riemann–Liouville sense. The applied approach is based on a combination of meshless methods and the spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct the shape functions which act as basis functions in the frame of the SMRPI. It is proved that the scheme is unconditionally stable with respect to the time variable in [Formula: see text] and convergent with the order of convergence [Formula: see text], [Formula: see text]. In this work, the thin plate splines (TPS) are used as the radial basis functions. In order to eliminate the nonlinearity, a simple predictor–corrector (P–C) scheme is used. The results of numerical experiments are compared to the analytical solutions in order to confirm the accuracy and the efficiency of the presented scheme.
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Heydarizadeh Shali, H., D. Sampietro, A. Safari, M. Capponi, and A. Bahroudi. "Fast collocation for Moho estimation from GOCE gravity data: the Iran case study." Geophysical Journal International 221, no. 1 (January 14, 2020): 651–64. http://dx.doi.org/10.1093/gji/ggaa026.
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SUMMARY The study of the discontinuity between crust and mantle beneath Iran is still an open issue in the geophysical community due to its various tectonic features created by the collision between the Iranian and Arabian Plate. For instance in regions such as Zagros, Alborz or Makran, despite the number of studies performed, both by exploiting gravity or seismic data, the depth of the Moho and also interior structure is still highly uncertain. This is due to the complexity of the crust and to the presence of large short wavelength signals in the Moho depth. GOCE observations are capable and useful products to describe the Earth’s crust structure either at the regional or global scale. Furthermore, it is plausible to retrieve important information regarding the structure of the Earth’s crust by combining the GOCE observations with seismic data and considering additional information. In the current study, we used as observation a grid of second radial derivative of the anomalous gravitational potential computed at an altitude of 221 km by means of the space-wise approach, to study the depth of the Moho. The observations have been reduced for the gravitational effects of topography, bathymetry and sediments. The residual gravity has been inverted accordingly to a simple two-layer model. In particular, this guarantees the uniqueness of the solution of the inverse problem which has been regularized by means of a collocation approach in the frequency domain. Although results of this study show a general good agreement with seismically derived depths with a root mean square deviation of 6 km, there are some discrepancies under the Alborz zone and also Oman sea with a root mean square deviation up 10 km for the former and an average difference of 3 km for the latter. Further comparisons with the natural feature of the study area, for instance, active faults, show that the resulting Moho features can be directly associated with geophysical and tectonic blocks.
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Weiss, Michael. "The paradigm of the word for ‘house, home’ in Old Irish and related issues." Indogermanische Forschungen 122, no. 1 (September 26, 2017): 61–82. http://dx.doi.org/10.1515/if-2017-0003.
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Abstract Old Irish inherited the PIE root noun *doms ~ dm̥- ‘home’, which is reflected chiefly in the fixed locution [Verb of motion] dia daim ‘(go) to (one’s) home’. From the remnants of this ablauting, feminine root noun speakers created a somewhat anomalous i-stem, doim, doma. In addition Old Irish probably inherited a thematic masculine *domos continued mainly in the collocation dom/dam liac ‘house of stone, cathedral’, though the possibility of a Latin loan cannot be entirely excluded. A further trace of the root noun *dom- ~ *dm̥- is seen in déis ‘clientele’, which continues *dm̥-sth2i- ‘located in the house’. This proto-form, suggested by de Bernardo Stempel (NWÄI), has a close formal match in Lith. dimstis ‘courtyard’ and is reminiscent of Lat. domesticus ‘of the household’. This Latin form is shown to be of prehistoric origin despite its relatively late date of attestation. The possibility is explored that domesticus may be a remodeled reflex of the same compound inherited by Old Irish and Lithuanian, although domesticus may also be an inner- Latin formation.
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Safargaleev, V., A. Kozlovsky, T. Sergienko, T. K. Yeoman, M. Uspensky, D. M. Wright, H. Nilsson, T. Turunen, and A. Kotikov. "Optical, radar, and magnetic observations of magnetosheath plasma capture during a positive IMF <I>B<sub>z</sub></I> impulse." Annales Geophysicae 26, no. 3 (March 26, 2008): 517–31. http://dx.doi.org/10.5194/angeo-26-517-2008.
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Abstract. We present a multi-instrument study of the ionospheric response to a northward turning of the IMF. The observations were made in the near-noon (11:00 MLT) sector on Svalbard (at 75° MLAT). The data set includes auroral observations, ionospheric flows obtained from the EISCAT and CUTLASS radars, the spectral width of the HF radar backscatter, particle precipitation and plasma flow data from the DMSP F13 satellite, and Pc1 frequency band pulsations observed by induction magnetometers. Careful collocation of all the observations has been made with the HF radar backscatter located by a ray-tracing procedure utilizing the elevation angle of arrival of the signals and an ionospheric plasma density profile. Prior to IMF turning northward, three auroral arcs were observed at the poleward boundary of the closed llbl, inside the llbl, and in the equatorward part of the llbl, respectively. The northward IMF turning was accompanied by enhanced HF radar returns with a broad Doppler spectrum collocated with the arcs. The auroral arcs shifted poleward whereas the backscatter region moved in the opposite direction, which is consistent, respectively, with reconnection beyond the cusp and the capturing of magnetosheath plasma during northward IMF. Locally, magnetic noise enhancement in the Pc1 frequency band occurred simultaneously with the anomalous radar backscatter, and the absence of such signals at more remote magnetic observatories indicates a local generation of the Pc1 turbulence, which is collocated with the radar backscatter. Finally, we discuss possible interpretation errors which may be caused by limited observational data.
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Zhu, Licai. "A Method of Semantic Hidden Reduction Based on Collocation." Computer and Information Science 10, no. 4 (October 31, 2017): 73. http://dx.doi.org/10.5539/cis.v10n4p73.
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Semantic hiding is the technology of using semantic knowledge to embed secret information into text carrier. Among the many methods of semantic hiding, "synonym substitution" is paid more and more attention by semantic hiding. The main idea of this method is to hide the secret information by replacing synonyms in text so as to retain its original meaning as much as possible. In order to effectively restore hidden information, we need to find the synonym replacement location as accurately as possible, so it is very important to recognize the collocation of words. So far, however, there is no effective way to identify and match Natural Language Processing, that is, it is very difficult to tell exactly whether or not the words in the text have been replaced.In this paper, a hidden reduction method based on collocation is proposed. By analyzing the characteristics of synonyms and their collocation, this paper treats their relation as the relation between the pairs of samples in statistical sense. According to the nature of the statistic, we design several decision features to identify the collocations. At the same time, we introduce the form of point mutual information in the information theory as a feature to use the independence of quantifier pairs. In order to recognize word collocation effectively, this paper combines these features, and uses genetic algorithm to get the recognition degree of each feature. Then, a replacement recognition system based on immune abnormality mechanism is designed. Synonyms for collocation are regarded as "normal", while substitutions are regarded as "anomalies"". The experimental samples are generated by semantic hidden software TLEX. To better render the restore process, we rewrote the TLEX to add the key selection module.
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Dung, Tran Tuan, Nguyen Van Sang, Nguyen Ba Dai, Nguyen Kim Dung, Tran Trong Lap, Tran Tuan Duong, and Nguyen Thi Hai Ha. "Improving accuracy of altimeter-derived marine gravity anomalies in the East Vietnam Sea deep-basin and adjacent area." Tạp chí Khoa học và Công nghệ biển 19, no. 3B (October 21, 2019): 43–53. http://dx.doi.org/10.15625/1859-3097/19/3b/14497.
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In recent years, the satellite altimeter technology allows enhancing the marine investigation in many areas. Up to now, many scientific studies have attempted to improve the accuracy and resolution of altimeter-derived gravity anomalies and have produced a gravity grid with interval of 1’×1’ for most oceans all over the world. However, these gravity anomalies are not very highly accurate and have a large difference compared to shipboard gravity anomalies, especially in the coastal and islands areas. The purpose of this article is to improve the accuracy of altimeter-derived marine gravity anomalies for geological structure research in the East Vietnam Sea deep-basin and adjacent areas. The least squares collocation method is used to correct the altimeter-derived marine gravity data based on the shipboard gravity data in order to improve the accuracy of marine gravity anomalies. In this article, the altimeter-derived marine gravity anomalies are taken from Sandwell, D. T., et al., (V24.1) and the shipboard gravity anomalies are from the survey projects between Vietnam, Russia and other countries. The mean-squared error when comparing both data is about 9,358 mGal. After correcting by collocation method, the error was reduced to 3,208 mGal (for the altimeter data coinciding with shipboard track). Also, in this article, the achieved results show the efficiency and actuality of the corrected-altimeter-derived marine gravity anomalies for more detailed researches of geological structures. Especially, it is more meaningful in the remote or sparsely surveyed regions.
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Mysen, E. "On the uncertainty of height anomaly differences predicted by least-squares collocation." Journal of Geodetic Science 10, no. 1 (October 5, 2020): 53–61. http://dx.doi.org/10.1515/jogs-2020-0111.
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AbstractA 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 \sqrt \Delta, where Δ is the spatial separation of the two locations for which the difference is sought.
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Jarmołowski, Wojciech. "A priori noise and regularization in least squares collocation of gravity anomalies." Geodesy and Cartography 62, no. 2 (December 1, 2013): 199–216. http://dx.doi.org/10.2478/geocart-2013-0013.
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Abstract The paper describes the estimation of covariance parameters in least squares collocation (LSC) by the cross-validation (CV) technique called leave-one-out (LOO). Two parameters of Gauss-Markov third order model (GM3) are estimated together with a priori noise standard deviation, which contributes significantly to the covariance matrix composed of the signal and noise. Numerical tests are performed using large set of Bouguer gravity anomalies located in the central part of the U.S. Around 103 000 gravity stations are available in the selected area. This dataset, together with regular grids generated from EGM2008 geopotential model, give an opportunity to work with various spatial resolutions of the data and heterogeneous variances of the signal and noise. This plays a crucial role in the numerical investigations, because the spatial resolution of the gravity data determines the number of gravity details that we may observe and model. This establishes a relation between the spatial resolution of the data and the resolution of the gravity field model. This relation is inspected in the article and compared to the regularization problem occurring frequently in data modeling.
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Idowu, T. O., P. C. Nwilo, F. A. Fajemirokun, and C. U. Ezeigbo. "Determination of optimum residual gravity anomalies for mineral exploration: a least squares collocation approach." Survey Review 40, no. 309 (July 2008): 294–303. http://dx.doi.org/10.1179/003962608x325367.
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Nahavandchi, H. "COMPUTATION OF MEAN FREE-AIR GRAVITY ANOMALIES BY BJERHAMMAR'S DETERMINISTIC AND COLLOCATION METHODS OVER SCANDINAVIA." Survey Review 35, no. 278 (October 2000): 514–23. http://dx.doi.org/10.1179/sre.2000.35.278.514.
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Abulaitijiang, Adili, Ole Baltazar Andersen, Riccardo Barzaghi, and Per Knudsen. "Coastal marine gravity modelling from satellite altimetry – case study in the Mediterranean." Journal of Geodetic Science 11, no. 1 (January 1, 2021): 29–37. http://dx.doi.org/10.1515/jogs-2020-0200.
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Abstract The coastal marine gravity field is not well modelled due to poor data coverage. Recent satellite altimeters provide reliable altimetry observations near the coast, filling the gaps between the open ocean and land. We show the potential of recent satellite altimetry for the coastal marine gravity modelling using the least squares collocation technique. Gravity prediction error near the coast is better than 4 mGal. The modelled gravity anomalies are validated with sparse shipborne gravimetric measurements. We obtained 4.86 mGal precision when using the altimetry data with the best coastal coverage and retracked with narrow primary peak retracker. The predicted gravity field is an enhancement to EGM2008 over the coastal regions. The potential improvement in alti- metric marine gravity will be beneficial for the next generation of EGM development.
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Sajid, M., S. A. Iqbal, N. Ali, and T. Hayat. "A Legendre wavelet spectral collocation technique resolving anomalies associated with velocity in some boundary layer flows of Walter-B liquid." Meccanica 52, no. 4-5 (April 11, 2016): 877–87. http://dx.doi.org/10.1007/s11012-016-0428-9.
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Hagan, Daniel Fiifi Tawia, Robert M. Parinussa, Guojie Wang, and Clara S. Draper. "An Evaluation of Soil Moisture Anomalies from Global Model-Based Datasets over the People’s Republic of China." Water 12, no. 1 (December 30, 2019): 117. http://dx.doi.org/10.3390/w12010117.
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Soil moisture is an important factor in land-atmosphere interactions and other land processes. Improved estimates from climate models have, in the last two decades, become an important alternate source of information. In this study, we extend the evaluation of soil moisture anomalies of different generations of three families of model datasets (the European Center for Medium-Range Weather Forecasts’ (ECMWF) reanalysis, the Modern Era Retrospective Analysis for Research and Applications of NASA, and the Global Land Data Assimilation System of theNational Oceanic and Atmospheric Administration (NOAA)) in recent studies to the People’s Republic of China. Two validation techniques, namely, root-mean-square error (RMSE) from triple collocation analysis (TCA) and correlations (R) with ground observations, were used. The study confirmed the results of previous studies that focused on other regions and showed that the newer generations of each modeling family generally had better skill than the older generations with higher correlations and lower RMSEs. A cross-validation of the results from the two techniques for the newer products showed that the higher correlations and lower RMSEs from the TCA were found over regions with moderate vegetation cover, while regions with less vegetation cover had lower correlations and larger RMSEs (ECMWF (R: −0.93), NASA (R: −0.73), and NOAA (R: −0.61)), indicating that these two techniques complement each other to fairly validate the products.
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Cammalleri, Carmelo, Jürgen V. Vogt, Bernard Bisselink, and Ad de Roo. "Comparing soil moisture anomalies from multiple independent sources over different regions across the globe." Hydrology and Earth System Sciences 21, no. 12 (December 14, 2017): 6329–43. http://dx.doi.org/10.5194/hess-21-6329-2017.
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Abstract. Agricultural drought events can affect large regions across the world, implying the need for a suitable global tool for an accurate monitoring of this phenomenon. Soil moisture anomalies are considered a good metric to capture the occurrence of agricultural drought events, and they have become an important component of several operational drought monitoring systems. In the framework of the JRC Global Drought Observatory (GDO, http://edo.jrc.ec.europa.eu/gdo/), the suitability of three datasets as possible representations of root zone soil moisture anomalies has been evaluated: (1) the soil moisture from the Lisflood distributed hydrological model (namely LIS), (2) the remotely sensed Land Surface Temperature data from the MODIS satellite (namely LST), and (3) the ESA Climate Change Initiative combined passive/active microwave skin soil moisture dataset (namely CCI). Due to the independency of these three datasets, the triple collocation (TC) technique has been applied, aiming at quantifying the likely error associated with each dataset in comparison to the unknown true status of the system. TC analysis was performed on five macro-regions (namely North America, Europe, India, southern Africa and Australia) detected as suitable for the experiment, providing insight into the mutual relationship between these datasets as well as an assessment of the accuracy of each method. Even if no definitive statement on the spatial distribution of errors can be provided, a clear outcome of the TC analysis is the good performance of the remote sensing datasets, especially CCI, over dry regions such as Australia and southern Africa, whereas the outputs of LIS seem to be more reliable over areas that are well monitored through meteorological ground station networks, such as North America and Europe. In a global drought monitoring system, the results of the error analysis are used to design a weighted-average ensemble system that exploits the advantages of each dataset.
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Zhu, Chengcheng, Jinyun Guo, Cheinway Hwang, Jinyao Gao, Jiajia Yuan, and Xin Liu. "How HY-2A/GM altimeter performs in marine gravity derivation: assessment in the South China Sea." Geophysical Journal International 219, no. 2 (July 23, 2019): 1056–64. http://dx.doi.org/10.1093/gji/ggz330.
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SUMMARY HY-2A is China's first satellite altimeter mission, launched in Aug. 2011. Its geodetic mission (GM) started from 2016 March 30 till present, collecting sea surface heights for about five 168-d cycles. To test how the HY-2A altimeter performs in marine gravity derivation, we use the least-squares collocation method to determine marine gravity anomalies on 1′ × 1′ grids around the South China Sea (covering 0°–30°N, 105°E–125°E) from the HY-2A/GM-measured geoid gradients. We assess the qualities of the HY-2A/GM-derived gravity over different depths and areas using the bias and tilt-adjusted ship-borne gravity anomalies from the U.S. National Centers for Environmental Information (NCEI) and the Second Institute of Oceanography, Ministry of Natural Resources (MNR) of P. R. China. The RMS difference between the HY-2A/GM-derived and the NCEI ship-borne gravity is 5.91 mGal, and is 5.33 mGal when replacing the HY-2A value from the Scripps Institution of Oceanography (SIO) V23.1 value. The RMS difference between the HY-2A/GM-derived and the MNR ship-borne gravity is 2.90 mGal, and is 2.76 mGal when replacing the HY-2A value from the SIO V23.1 value. The RMS difference between the HY-2A and SIO V23.1 value is 3.57 mGal in open sea areas at least 20 km far away from the coast. In general, the difference between the HY-2A/GM-derived gravity and ship-borne gravity decreases with decreasing gravity field roughness and increasing depth. HY-2A results in the lowest gravity accuracy in areas with islands or reefs. Our assessment result suggests that HY-2A can compete with other Ku-band altimeter missions in marine gravity derivation.
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Vu, Dinh Toan, Sean Bruinsma, Sylvain Bonvalot, Dominique Remy, and Georgios S. Vergos. "A Quasigeoid-Derived Transformation Model Accounting for Land Subsidence in the Mekong Delta towards Height System Unification in Vietnam." Remote Sensing 12, no. 5 (March 3, 2020): 817. http://dx.doi.org/10.3390/rs12050817.
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A vertical offset model for Vietnam and its surrounding areas was determined based on the differences between height anomalies derived from 779 Global Navigation Satellite System (GNSS)/levelling points and those derived from a dedicated high-resolution gravimetric-only quasigeoid model called GEOID_LSC. First, the deterministic transformation model to effectively fit the differences between the quasigeoid and GNSS/levelling heights was based on a third-order polynomial model. Second, the residual height anomalies have been interpolated to a grid employing Least-Squares Collocation. Finally, the distortions were restored to the residual grid. This model can be used for combination with a gravimetric quasigeoid model in GNSS levelling. The quality of GNSS/levelling data in Vietnam was analyzed and evaluated in this study. The annual subsidence rate from ALOS-1 was also used to analyze the effects of subsidence on the quality of GNSS/levelling data in the Mekong Delta. From this we made corrections to improve the accuracy of GNSS/levelling data in this region. The offset model was evaluated using cross-validation technique by comparing with GNSS/levelling data. Results indicate that the offset model has a standard deviation of 5.9 cm in the absolute sense. Based on this offset model, GNSS levelling can be carried out in most of Vietnam’s territory complying third-order levelling requirements, while the accuracy requirements for fourth-order levelling networks is met for the entire country. This model in combination with the developed gravimetric quasigeoid model should also contribute to the modernization of Vietnam’s height system. We also used high-quality GNSS/levelling data and the determined quasigeoid model to determine the geopotential value W0 for the Vietnam Local Vertical Datum. The gravity potential of the Vietnam Local Vertical Datum is estimated equal to W 0 LVD = 62,636,846.81 ± 0.70 m2s−2 with the global equipotential surface realized by the conventional value W0 = 62,636,853.4 m2s−2.
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Noël, Stefan, Klaus Bramstedt, Alexei Rozanov, Elizaveta Malinina, Heinrich Bovensmann, and John P. Burrows. "Stratospheric aerosol extinction profiles from SCIAMACHY solar occultation." Atmospheric Measurement Techniques 13, no. 10 (October 22, 2020): 5643–66. http://dx.doi.org/10.5194/amt-13-5643-2020.
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Abstract. The Scanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY) instrument on Envisat provided, between August 2002 and April 2012, measurements of solar and Earthshine spectra from the UV to the shortwave infrared spectral region in multiple viewing geometries. We present a new approach to derive stratospheric aerosol extinction profiles from SCIAMACHY solar occultation measurements based on an onion-peeling method similar to the onion-peeling differential optical absorption spectroscopy (DOAS) retrieval, which has already been successfully used for the derivation of greenhouse gas profiles. Since the retrieval of aerosol extinction requires as input measured transmissions in absolute units, an improved radiometric calibration of the SCIAMACHY solar occultation measurements has been developed, which considers various instrumental and atmospheric effects specific to solar occultation. The aerosol extinction retrieval can in principle be applied to all wavelengths measured by SCIAMACHY. As a first application, we show results for 452, 525 and 750 nm. The SCIAMACHY solar occultation time series has been processed, covering a latitudinal range of about 50–70∘ N. Reasonable aerosol extinctions are derived between about 15 and 30 km with typically larger uncertainties at higher altitudes due to decreasing aerosol extinction. Comparisons with collocated Stratospheric Aerosol and Gas Experiment II (SAGE-II) and SCIAMACHY limb aerosol data products revealed good agreement with essentially no mean bias. However, dependent on altitude, differences of up to ±20 %–30% to SAGE-II at 452 and 525 nm are observed. Similar results are obtained from comparisons with SAGE-III. SCIAMACHY solar occultation data at 750 nm have been compared with corresponding SAGE-III, Optical Spectrograph and InfraRed Imager System (OSIRIS) and SCIAMACHY limb results. The agreement with SCIAMACHY limb data at 750 nm is within 5 %–20 % between 17 and 27 km. SAGE-III and OSIRIS show at this wavelength and altitude range on average about 40 % and 25 % smaller values, with some additional 10 %–20 % modulation with altitude. The altitude variations in the differences are mainly caused by systematic vertical oscillations in the SCIAMACHY occultation data of up to 30 % below about 25 km. These oscillations decrease to amplitudes below 10 % with increasing number of collocations and are no longer visible in monthly anomalies. Major volcanic eruptions as well as occurrences of polar stratospheric clouds (PSCs) can be identified in the time series of aerosol extinction data and related anomalies. The influence of the quasi-biennial oscillation (QBO) is visible above 25 km.
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Anderson, W. B., B. F. Zaitchik, C. R. Hain, M. C. Anderson, M. T. Yilmaz, J. Mecikalski, and L. Schultz. "Towards an integrated soil moisture drought monitor for East Africa." Hydrology and Earth System Sciences 16, no. 8 (August 22, 2012): 2893–913. http://dx.doi.org/10.5194/hess-16-2893-2012.
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Abstract. Drought in East Africa is a recurring phenomenon with significant humanitarian impacts. Given the steep climatic gradients, topographic contrasts, general data scarcity, and, in places, political instability that characterize the region, there is a need for spatially distributed, remotely derived monitoring systems to inform national and international drought response. At the same time, the very diversity and data scarcity that necessitate remote monitoring also make it difficult to evaluate the reliability of these systems. Here we apply a suite of remote monitoring techniques to characterize the temporal and spatial evolution of the 2010–2011 Horn of Africa drought. Diverse satellite observations allow for evaluation of meteorological, agricultural, and hydrological aspects of drought, each of which is of interest to different stakeholders. Focusing on soil moisture, we apply triple collocation analysis (TCA) to three independent methods for estimating soil moisture anomalies to characterize relative error between products and to provide a basis for objective data merging. The three soil moisture methods evaluated include microwave remote sensing using the Advanced Microwave Scanning Radiometer – Earth Observing System (AMSR-E) sensor, thermal remote sensing using the Atmosphere-Land Exchange Inverse (ALEXI) surface energy balance algorithm, and physically based land surface modeling using the Noah land surface model. It was found that the three soil moisture monitoring methods yield similar drought anomaly estimates in areas characterized by extremely low or by moderate vegetation cover, particularly during the below-average 2011 long rainy season. Systematic discrepancies were found, however, in regions of moderately low vegetation cover and high vegetation cover, especially during the failed 2010 short rains. The merged, TCA-weighted soil moisture composite product takes advantage of the relative strengths of each method, as judged by the consistency of anomaly estimates across independent methods. This approach holds potential as a remote soil moisture-based drought monitoring system that is robust across the diverse climatic and ecological zones of East Africa.
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Anderson, W. B., B. F. Zaitchik, C. R. Hain, M. C. Anderson, M. T. Yilmaz, J. Mecikalski, and L. Schultz. "Towards an integrated soil moisture drought monitor for East Africa." Hydrology and Earth System Sciences Discussions 9, no. 4 (April 5, 2012): 4587–631. http://dx.doi.org/10.5194/hessd-9-4587-2012.
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Abstract. Drought in East Africa is a recurring phenomenon with significant humanitarian impacts. Given the steep climatic gradients, topographic contrasts, general data scarcity, and, in places, political instability that characterize the region, there is a need for spatially distributed, remotely derived monitoring systems to inform national and international drought response. At the same time, the very diversity and data scarcity that necessitate remote monitoring also make it difficult to evaluate the reliability of these systems. Here we apply a suite of remote monitoring techniques to characterize the temporal and spatial evolution of the 2010–2011 Horn of Africa drought. Diverse satellite observations allow for evaluation of meteorological, agricultural, and hydrological aspects of drought, each of which is of interest to different stakeholders. Focusing on soil moisture, we apply triple collocation analysis (TCA) to three independent methods for estimating soil moisture anomalies to characterize relative error between products and to provide a basis for objective data merging. The three soil moisture methods evaluated include microwave remote sensing using the Advanced Microwave Scanning Radiometer – Earth Observing System (AMSR-E) sensor, thermal remote sensing using the Atmosphere-Land Exchange Inverse (ALEXI) surface energy balance algorithm, and physically-based land surface modeling using the Noah land surface model. It was found that the three soil moisture monitoring methods yield similar drought anomaly estimates in areas characterized by extremely low or by moderate vegetation cover, particularly during the below-average 2011 long rainy season. Systematic discrepancies were found, however, in regions of moderately low vegetation cover and high vegetation cover, especially during the failed 2010 short rains. The merged, TCA-weighted soil moisture composite product takes advantage of the relative strengths of each method, as judged by the consistency of anomaly estimates across independent methods. This approach holds potential as a remote soil moisture-based drought monitoring system that is robust across the diverse climatic and ecological zones of East Africa.
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Li, Xiaohui, Dongkai Yang, Jingsong Yang, Guoqi Han, Gang Zheng, and Weiqiang Li. "Validation of NOAA CyGNSS Wind Speed Product with the CCMP Data." Remote Sensing 13, no. 9 (May 7, 2021): 1832. http://dx.doi.org/10.3390/rs13091832.
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The National Aeronautics and Space Administration (NASA) Cyclone Global Navigation Satellite System (CyGNSS) mission was launched in December 2016, which can remotely sense sea surface wind with a relatively high spatio-temporal resolution for tracking tropical cyclones. In recent years, with the gradual development of the geophysical model function (GMF) for CyGNSS wind retrieval, different versions of CyGNSS Level 2 products have been released and their performance has gradually improved. This paper presents a comprehensive evaluation of CyGNSS wind product v1.1 produced by the National Oceanic and Atmospheric Administration (NOAA). The Cross-Calibrated Multi-Platform (CCMP) analysis wind (v02.0 and v02.1 near real time) products produced by Remote Sensing Systems (RSS) were used as the reference. Data pairs between the NOAA CyGNSS and RSS CCMP products were processed and evaluated by the bias and standard deviation SD. The CyGNSS dataset covers the period between May 2017 and December 2020. The statistical comparisons show that the bias and SD of CyGNSS relative to CCMP-nonzero collocations when the flag of CCMP winds is nonzero are –0.05 m/s and 1.19 m/s, respectively. The probability density function (PDF) of the CyGNSS winds coincides with that of CCMP-nonzero. Furthermore, the average monthly bias and SD show that CyGNSS wind is consistent and reliable generally. We found that negative deviation mainly appears at high latitudes in both hemispheres. Positive deviation appears in the China Sea, the Arabian Sea, and the west of Africa and South America. Spatial–temporal analysis demonstrates the geographical anomalies in the bias and SD of the CyGNSS winds, confirming that the wind speed bias shows a temporal dependency. The verification and comparison show that the remotely sensed wind speed measurements from NOAA CyGNSS wind product v1.1 are in good agreement with CCMP winds.
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Liu, W. Timothy, Xiaosu Xie, and Pearn P. Niiler. "Ocean–Atmosphere Interaction over Agulhas Extension Meanders." Journal of Climate 20, no. 23 (December 1, 2007): 5784–97. http://dx.doi.org/10.1175/2007jcli1732.1.
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Abstract Many years of high-resolution measurements by a number of space-based sensors and from Lagrangian drifters became available recently and are used to examine the persistent atmospheric imprints of the semipermanent meanders of the Agulhas Extension Current (AEC), where strong surface current and temperature gradients are found. The sea surface temperature (SST) measured by the Advanced Microwave Scanning Radiometer-Earth Observing System (AMSR-E) and the chlorophyll concentration measured by the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) support the identification of the meanders and related ocean circulation by the drifters. The collocation of high and low magnitudes of equivalent neutral wind (ENW) measured by Quick Scatterometer (QuikSCAT), which is uniquely related to surface stress by definition, illustrates not only the stability dependence of turbulent mixing but also the unique stress measuring capability of the scatterometer. The observed rotation of ENW in opposition to the rotation of the surface current clearly demonstrates that the scatterometer measures stress rather than winds. The clear differences between the distributions of wind and stress and the possible inadequacy of turbulent parameterization affirm the need of surface stress vector measurements, which were not available before the scatterometers. The opposite sign of the stress vorticity to current vorticity implies that the atmosphere spins down the current rotation through momentum transport. Coincident high SST and ENW over the southern extension of the meander enhance evaporation and latent heat flux, which cools the ocean. The atmosphere is found to provide negative feedback to ocean current and temperature gradients. Distribution of ENW convergence implies ascending motion on the downwind side of local SST maxima and descending air on the upwind side and acceleration of surface wind stress over warm water (deceleration over cool water); the convection may escalate the contrast of ENW over warm and cool water set up by the dependence of turbulent mixing on stability; this relation exerts a positive feedback to the ENW–SST relation. The temperature sounding measured by the Atmospheric Infrared Sounder (AIRS) is consistent with the spatial coherence between the cloud-top temperature provided by the International Satellite Cloud Climatology Project (ISCCP) and SST. Thus ocean mesoscale SST anomalies associated with the persistent meanders may have a long-term effect well above the midlatitude atmospheric boundary layer, an observation not addressed in the past.
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Zhang, Haixiang, Xuehua Yang, and Qiong Tang. "Discrete-time orthogonal spline collocation method for a modified anomalous diffusion equation." International Journal of Computer Mathematics, March 19, 2020, 1–17. http://dx.doi.org/10.1080/00207160.2020.1741556.
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Bhrawy, A. H. "A space-time collocation scheme for modified anomalous subdiffusion and nonlinear superdiffusion equations." European Physical Journal Plus 131, no. 1 (January 2016). http://dx.doi.org/10.1140/epjp/i2016-16012-0.
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Fu, Zhuo-Jia, Li-Wen Yang, Qiang Xi, and Chein-Shan Liu. "A boundary collocation method for anomalous heat conduction analysis in functionally graded materials." Computers & Mathematics with Applications, March 2020. http://dx.doi.org/10.1016/j.camwa.2020.02.023.
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Kharazmi, Ehsan, and Mohsen Zayernouri. "Operator-Based Uncertainty Quantification of Stochastic Fractional Partial Differential Equations." Journal of Verification, Validation and Uncertainty Quantification 4, no. 4 (December 1, 2019). http://dx.doi.org/10.1115/1.4046093.
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Abstract Fractional calculus provides a rigorous mathematical framework to describe anomalous stochastic processes by generalizing the notion of classical differential equations to their fractional-order counterparts. By introducing the fractional orders as uncertain variables, we develop an operator-based uncertainty quantification framework in the context of stochastic fractional partial differential equations (SFPDEs), subject to additive random noise. We characterize different sources of uncertainty and then, propagate their associated randomness to the system response by employing a probabilistic collocation method (PCM). We develop a fast, stable, and convergent Petrov–Galerkin spectral method in the physical domain in order to formulate the forward solver in simulating each realization of random variables in the sampling procedure.
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Zaky, M. A., S. S. Ezz-Eldien, E. H. Doha, J. A. Tenreiro Machado, and A. H. Bhrawy. "An Efficient Operational Matrix Technique for Multidimensional Variable-Order Time Fractional Diffusion Equations." Journal of Computational and Nonlinear Dynamics 11, no. 6 (June 20, 2016). http://dx.doi.org/10.1115/1.4033723.
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This paper derives a new operational matrix of the variable-order (VO) time fractional partial derivative involved in anomalous diffusion for shifted Chebyshev polynomials. We then develop an accurate numerical algorithm to solve the 1 + 1 and 2 + 1 VO and constant-order fractional diffusion equation with Dirichlet conditions. The contraction of the present method is based on shifted Chebyshev collocation procedure in combination with the derived shifted Chebyshev operational matrix. The main advantage of the proposed method is to investigate a global approximation for spatial and temporal discretizations, and it reduces such problems to those of solving a system of algebraic equations, which greatly simplifies the solution process. In addition, we analyze the convergence of the present method graphically. Finally, comparisons between the algorithm derived in this paper and the existing algorithms are given, which show that our numerical schemes exhibit better performances than the existing ones.
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Zhang, Ning, Steven M. Quiring, and Trent W. Ford. "Blending Noah, SMOS and In-Situ Soil Moisture Using Multiple Weighting and Sampling Schemes." Journal of Hydrometeorology, May 18, 2021. http://dx.doi.org/10.1175/jhm-d-20-0119.1.
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AbstractSoil moisture can be obtained from in-situ measurements, satellite observations, and model simulations. This study evaluates the importance of in-situ observations in soil moisture blending, and compares different weighting and sampling methods for combining model, satellite, and in-situ soil moisture data to generate an accurate and spatially-continuous soil moisture product at 4-km resolution. Four different datasets are used: Antecedent Precipitation Index (API), KAPI, which incorporates in-situ soil moisture observations with the API using regression kriging, SMOS L3 soil moisture, and model-simulated soil moisture from the Noah model as part of the North American Land Data Assimilation System (NLDAS). Triple collocation, least square weighting, and equal weighting are used to generate blended soil moisture products. An enumerated weighting scheme is designed to investigate the impact of different weighting schemes. The sensitivity of the blended soil moisture products to sampling schemes, station density and data formats (absolute, anomalies and percentiles) are also investigated. The results reveal KAPI outperforms API. This indicates that incorporating in-situ soil moisture improves the accuracy of the blended soil moisture products. There are no statistically significant (p>0.05) differences between blended soil moisture using triple collocation and equal weighting approaches, and both methods provide sub-optimal weighting. Optimal weighting is achieved by assigning larger weights to KAPI and smaller weights to SMOS. Using multiple sources of soil moisture is helpful for reducing uncertainty and improving accuracy, especially when the sampling density is low, or the sampling stations are less representative. These results are consistent regardless of how soil moisture is represented (absolute, anomalies or percentiles).
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Wei, Zhijie, Jinyun Guo, Chengcheng Zhu, Jiajia Yuan, Xiaotao Chang, and Bing Ji. "Evaluating Accuracy of HY-2A/GM-Derived Gravity Data With the Gravity-Geologic Method to Predict Bathymetry." Frontiers in Earth Science 9 (April 21, 2021). http://dx.doi.org/10.3389/feart.2021.636246.
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For the first time, HY-2A/GM-derived gravity anomalies determined with the least-squares collocation method and ship-borne bathymetry released from the National Centers for Environmental Information (NCEI) are used to predict bathymetry with the gravity-geologic method (GGM) over three test areas located in the South China Sea (105–122°E, 2–26°N). The iterative method is used to determine density contrasts (1.4, 1.5, and 1.6 g/cm3) between seawater and ocean bottom topography, improving the accuracy of GGM bathymetry. The results show that GGM bathymetry is the closest to ship-borne bathymetry at check points, followed by SRTM15+V2.0 model and GEBCO 2020 model. It is found that in a certain range, the relative accuracy of GGM bathymetry tends to improve with the increase of depth. Different geological structures affect the accuracy of GGM bathymetry. In addition, the influences of gravity anomalies and data processing method on GGM bathymetry are analyzed. Our assessment result suggests that GGM can be widely applied to bathymetry prediction and that HY-2A/GM-derived gravity data are feasible with good results in calculating ocean depth.
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Wojciech Jarmołowski. "Estimation of gravity noise variance and signal covariance parameters in least squares collocation with considering data resolution." Annals of Geophysics 59, no. 1 (February 24, 2016). http://dx.doi.org/10.4401/ag-6831.
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<p>The article describes an implementation of the negative log-likelihood function in the determination of uncorrelated noise standard deviation together with the parameters of spherical signal covariance model in least squares collocation (LSC) of gravity anomalies. The correctness and effectiveness of restricted maximum likelihood (REML) estimates are fully validated by leave-one-out validation (LOO). These two complementary methods give an opportunity to inspect the parametrization of the signal and uncorrelated noise in details and can provide some guidance related to the estimation of individual parameters. The study provides the practical proof that noise variance is related with the data resolution, which is often neglected and the information on a priori noise variance is based on the measurement error. The data have been downloaded from U.S. terrestrial gravity database and resampled to enable an analysis with four different horizontal resolutions. These data are intentionally the same, as in the previous study of the same author, with the application of the planar covariance model. The aim is to compare the results from two different covariance models, which have different covariance approximation at larger distances. The most interesting outputs from this study confirm previous observations on the relations of the data resolution, a priori noise variance, signal spectrum and LSC accuracy.</p>