Using ELLS-1/2 radar satellite data, we generated a Digital Elevation Model by Interferometric Synthetic Aperture Radar, and the ERS-1/2 DEM that we generated is obviously superior to both the 1/25 ten thousand-scale ...Using ELLS-1/2 radar satellite data, we generated a Digital Elevation Model by Interferometric Synthetic Aperture Radar, and the ERS-1/2 DEM that we generated is obviously superior to both the 1/25 ten thousand-scale DEM of the National Fundamental Geographic Information System of China and the 90-m spatial resolution's SRTM DEM that America published in 2004 when it showed the characteristics of tiny structure relief. By analyzing the relief characteristics of the Bengcuo fault zone based on ERS-1/2 DEM, we find that the relief on the connection location of the Bengcuo and Pengcuo fault zones has complex characteristics. A structure relief that is similar to the Pengcuo fault zone crosses through the Dazi-Dasha fault on the the Bengcuo fault zone, while the Dazi-Dasha fault crosses through a gully at this place. This indicates that the Dazi-Dasha fault has been active at this place recently. At the same time, the Naka-Naduiduo fault is severed by the gully which was cut through by the Dazi-Dasha fault. Therefore, the Naka-Naduiduo fault was formed earlier than the Dazi-Dasha fault.展开更多
Displacement monitoring in open-pit mines is one of the important tasks for safe management of mining processes.Differential interferometric synthetic aperture radar(DInSAR),mounted on an artificial satellite,has the ...Displacement monitoring in open-pit mines is one of the important tasks for safe management of mining processes.Differential interferometric synthetic aperture radar(DInSAR),mounted on an artificial satellite,has the potential to be a cost-effective method for monitoring surface displacements over extensive areas,such as open-pit mines.DInSAR requires the ground surface elevation data in the process of its analysis as a digital elevation model(DEM).However,since the topography of the ground surface in open-pit mines changes largely due to excavations,measurement errors can occur due to insufficient information on the elevation of mining areas.In this paper,effect of different elevation models on the accuracy of the displacement monitoring results by DInSAR is investigated at a limestone quarry.In addition,validity of the DInSAR results using an appropriate DEM is examined by comparing them with the results obtained by global positioning system(GPS)monitoring conducted for three years at the same limestone quarry.It is found that the uncertainty of DEMs induces large errors in the displacement monitoring results if the baseline length of the satellites between the master and the slave data is longer than a few hundred meters.Comparing the monitoring results of DInSAR and GPS,the root mean square error(RMSE)of the discrepancy between the two sets of results is less than 10 mm if an appropriate DEM,considering the excavation processes,is used.It is proven that DInSAR can be applied for monitoring the displacements of mine slopes with centimeter-level accuracy.展开更多
The cryosphere is the frozen part of the Earth’s system. Snow and ice are the main constituents of the cryosphere and may be found in different states, such as snow, freshwater ice, sea ice, perma-frost, and continen...The cryosphere is the frozen part of the Earth’s system. Snow and ice are the main constituents of the cryosphere and may be found in different states, such as snow, freshwater ice, sea ice, perma-frost, and continental ice masses in the form of glaciers and ice sheets. The present review mainly deals with state-of-the-art applications of synthetic aperture radar (SAR) with a special emphasize on cryospheric information extraction. SAR is the most important active microwave remote sensing (RS) instrument for ice monitoring, which provides high-resolution images of the Earth’s surface. SAR is an ideal sensor in RS technology, which works in all-weather and day and night conditions to provide useful unprecedented information, especially in the cryospheric regions which are almost inaccessible areas on Earth. This paper addresses the technological evolution of SAR and its applications in studying the various components of the cryosphere. The arrival of SAR radically changed the capabilities of information extraction related to ice type, new ice formation, and ice thickness. SAR applications can be divided into two broad classes-polarimetric applications and interferometric applications. Polarimetric SAR has been effectively used for mapping calving fronts, crevasses, surface structures, sea ice, detection of icebergs, etc. The paper also summarizes both the operational and climate change research by using SAR for sea ice parameter detection. Digital elevation model (DEM) generation and glacier velocity mapping are the two most important applications used in cryosphere using SAR interferometry or interferometric SAR (InSAR). Space-borne InSAR techniques for measuring ice flow velocity and topography have developed rapidly over the last decade. InSAR is capable of measuring ice motion that has radically changed the science of glaciers and ice sheets. Measurement of temperate glacier velocities and surface characteristics by using airborne and space-borne interferometric satellite images have been the significant application in glaciology and cryospheric studies. Space-borne InSAR has contributed to major evolution in many research areas of glaciological study by measuring ice-stream flow velocity, improving understanding of ice-shelf processes, yielding velocity for flux-gate based mass-balance assessment, and mapping flow of mountain glaciers. The present review summarizes the salient development of SAR applications in cryosphere and glaciology.展开更多
Conventional synthetic aperture radar(SAR)interferometry(InSAR)has been successfully used to precisely measure surface deformation in the line-of-sight(LOS)direction,while multiple-aperture SAR interferometry(MAI)has ...Conventional synthetic aperture radar(SAR)interferometry(InSAR)has been successfully used to precisely measure surface deformation in the line-of-sight(LOS)direction,while multiple-aperture SAR interferometry(MAI)has provided precise surface deformation in the along-track(AT)direction.Integration of the InSAR and MAI methods enables precise measurement of the two-dimensional(2D)deformation from an interferometric pair;recently,the integration of ascending and descending pairs has allowed the observation of precise three-dimensional(3D)deformation.Precise 3D deformation measurement has been applied to better understand geological events such as earthquakes and volcanic eruptions.The surface deformation related to the 2016 Kumamoto earthquake was large and complex near the fault line;hence,precise 3D deformation retrieval had not yet been attempted.The objectives of this study were to①perform a feasibility test of precise 3D deformation retrieval in large and complex deformation areas through the integration of offset-based unwrapped and improved multiple-aperture SAR interferograms and②observe the 3D deformation field related to the 2016 Kumamoto earthquake,even near the fault lines.Two ascending pairs and one descending the Advanced Land Observing Satellite-2(ALOS-2)Phased Array-type L-band Synthetic Aperture Radar-2(PALSAR-2)pair were used for the 3D deformation retrieval.Eleven in situ Global Positioning System(GPS)measurements were used to validate the 3D deformation measurement accuracy.The achieved accuracy was approximately 2.96,3.75,and 2.86 cm in the east,north,and up directions,respectively.The results show the feasibility of precise 3D deformation measured through the integration of the improved methods,even in a case of large and complex deformation.展开更多
The geosynchronous circular synthetic aperture radar (GEOCSAR) is an innovative SAR system,which can produce high resolution three-dimensional (3D) images and has the potential to provide 3D deformation measurement.Wi...The geosynchronous circular synthetic aperture radar (GEOCSAR) is an innovative SAR system,which can produce high resolution three-dimensional (3D) images and has the potential to provide 3D deformation measurement.With an orbit altitude of approximately 36 000 km,the orbit motion and orbit disturbance effects of GEOCSAR behave differently from those of the conventional spaceborne SAR.In this paper,we analyze the effects of orbit errors on GEOCSAR imaging and interferometric processing.First,we present the GEOCSAR imaging geometry and the orbit errors model based on perturbation analysis.Then,we give the GEOCSAR signal formulation based on imaging geometry,and analyze the effect of the orbit error on the output focused signal.By interferometric processing on the 3D reconstructed images,the relationship between satellite orbit errors and the interferometric phase is deduced.Simulations demonstrate the effects of orbit errors on the GEOCSAR images,interferograms,and the deformations.The conclusions are that the required relative accuracy of orbit estimation should be at centimeter level for GEOCSAR imaging at L-band,and that millimeter-scale accuracy is needed for GEOCSAR interferometric processing.展开更多
以国内某高速铁路钢拱桥为研究对象,选取2017—2018年期间59幅C波段Senti⁃nel-1号雷达卫星影像,利用PS-InSAR技术处理影像获得桥梁的视线向(Line of Sight,LOS)位移,根据SAR成像空间几何关系解算出支座的纵向位移.研究结果表明:支座纵...以国内某高速铁路钢拱桥为研究对象,选取2017—2018年期间59幅C波段Senti⁃nel-1号雷达卫星影像,利用PS-InSAR技术处理影像获得桥梁的视线向(Line of Sight,LOS)位移,根据SAR成像空间几何关系解算出支座的纵向位移.研究结果表明:支座纵向位移的时空特性与实际桥梁结构相符合,验证了PS-InSAR技术观测桥梁结构位移的可行性.建立支座纵向位移与温度的线性相关模型,并与结构健康监测系统的实测结果进行对比.两者吻合良好,相对误差控制在10%以内,验证了PS-InSAR测量桥梁结构位移的可靠性.利用有限元模拟温度作用下桥梁支座的位移变化,并与PS-InSAR位移时间序列进行对比.两者趋势基本一致,LOS向位移误差在[-10,10]mm,验证了PS-InSAR测量桥梁结构位移的准确性.展开更多
LuTan-1(LT-1)is a constellation with two full-polarization L-band radar satellites designed by China,and the first satellite was scheduled to be launched in December 2021 and the second one in January 2022.The LT-1 wi...LuTan-1(LT-1)is a constellation with two full-polarization L-band radar satellites designed by China,and the first satellite was scheduled to be launched in December 2021 and the second one in January 2022.The LT-1 will be operated for deformation monitoring in repeat-pass mode,and for DEM generation in bistatic mode,improving self-sufficiency of SAR data for the field of geology,earthquake,disaster reduction,geomatics,forestry and so on.In this paper,we focused on designing an algorithm for interferometric DEM generation using LT-1 bistatic satellites.The basic principle,main error sources and errors control of the DEM generation algorithm of LT-1 were systematically analyzed.The experiment results demonstrated that:①The implemented algorithm had rigorous resolution with a theoretic accuracy better than 0.03 m for DEM generation.②The errors in satellite velocity and Doppler centroid had no obvious effect on DEM accuracy and they could be neglected.While the errors in position,baseline,slant range and interferometric phase had a significant effect on DEM accuracy.And the DEM error caused by baseline error was dominated,followed by the slant range error,interferometric phase error and satellite position error.③To obtain an expected DEM accuracy of 2 m,the baseline error must be strictly controlled and its accuracy shall be 1.0 mm or better for Cross-Track and Normal-Direction component,respectively.And the slant range error and interferometric phase error shall be reasonably controlled.The research results were of great significance for accurately grasping the accuracy of LT-1 data products and their errors control,and could provide a scientific auxiliary basis for LT-1 in promoting global SAR technology progress and the generation of high-precision basic geographic data.展开更多
In this paper, an algorithm of generating INSAR unwrapped phase image from SAR single-look complex images is presented. Besides the general processing technique, this article focuses on the methods of flat-earth phase...In this paper, an algorithm of generating INSAR unwrapped phase image from SAR single-look complex images is presented. Besides the general processing technique, this article focuses on the methods of flat-earth phase removal, phase noise reduction and phase unwrapping. The availability is tested by the results of processing ERS-1/2 SAR images.展开更多
Interferometric phase filtering is one of the key steps in interferometricsynthetic aperture radar (InSAR/SAR). However, the ideal filtering results are difficult toobtain due to dense fringe and low coherence regions...Interferometric phase filtering is one of the key steps in interferometricsynthetic aperture radar (InSAR/SAR). However, the ideal filtering results are difficult toobtain due to dense fringe and low coherence regions. Moreover, the InSAR/SAR datarange is relatively large, so the efficiency of interferential phase filtering is one of themajor problems. In this letter, we proposed an interferometric phase filtering methodbased on an amended matrix pencil and linear window mean filter. The combination ofthe matrix pencil and the linear mean filter are introduced to the interferometric phasefiltering for the first time. First, the interferometric signal is analyzed, and theinterferometric phase filtering is transformed into a local frequency estimation problem.Then, the local frequency is estimated using an amended matrix pencil at a window. Thelocal frequency can represent terrain changes, thus suggesting that the frequency can beaccurately estimated even in dense fringe regions. Finally, the local frequency is filteredby using a linear window mean filter, and the filtered phase is recovered. The proposedmethod is calculated by some matrices. Therefore, the computational complexity isreduced, and the efficiency of the interferometric phase filtering is improved.Experiments are conducted with simulated and real InSAR data. The proposed methodexhibits a better filtering effect and an ideal efficiency as compared with the traditionalfiltering method.展开更多
An approach based on interferometry technique is proposed for three-dimensional (3D) bistatic inverse synthetic aperture radar (ISAR) imaging. It is converted to a monostatic problem by using the theory that a bis...An approach based on interferometry technique is proposed for three-dimensional (3D) bistatic inverse synthetic aperture radar (ISAR) imaging. It is converted to a monostatic problem by using the theory that a bistatic radar equals a monostatic radar located on the bisector of bistatic an- gle. Then, interferometric phases extracted from a pair of cross shaped antennas are used to esti- mate the height and associated rotational velocity. Finally, numerical simulations are provided to e- valuate this method.展开更多
基金This project was sponsored bythe Special Programof Social Public Welfare Research of the Ministry of Science and Technology of PRC(2002D1A10001)
文摘Using ELLS-1/2 radar satellite data, we generated a Digital Elevation Model by Interferometric Synthetic Aperture Radar, and the ERS-1/2 DEM that we generated is obviously superior to both the 1/25 ten thousand-scale DEM of the National Fundamental Geographic Information System of China and the 90-m spatial resolution's SRTM DEM that America published in 2004 when it showed the characteristics of tiny structure relief. By analyzing the relief characteristics of the Bengcuo fault zone based on ERS-1/2 DEM, we find that the relief on the connection location of the Bengcuo and Pengcuo fault zones has complex characteristics. A structure relief that is similar to the Pengcuo fault zone crosses through the Dazi-Dasha fault on the the Bengcuo fault zone, while the Dazi-Dasha fault crosses through a gully at this place. This indicates that the Dazi-Dasha fault has been active at this place recently. At the same time, the Naka-Naduiduo fault is severed by the gully which was cut through by the Dazi-Dasha fault. Therefore, the Naka-Naduiduo fault was formed earlier than the Dazi-Dasha fault.
基金partially supported by JSPS KAKENHI(Grant No.16H03153)the Limestone Association of Japan。
文摘Displacement monitoring in open-pit mines is one of the important tasks for safe management of mining processes.Differential interferometric synthetic aperture radar(DInSAR),mounted on an artificial satellite,has the potential to be a cost-effective method for monitoring surface displacements over extensive areas,such as open-pit mines.DInSAR requires the ground surface elevation data in the process of its analysis as a digital elevation model(DEM).However,since the topography of the ground surface in open-pit mines changes largely due to excavations,measurement errors can occur due to insufficient information on the elevation of mining areas.In this paper,effect of different elevation models on the accuracy of the displacement monitoring results by DInSAR is investigated at a limestone quarry.In addition,validity of the DInSAR results using an appropriate DEM is examined by comparing them with the results obtained by global positioning system(GPS)monitoring conducted for three years at the same limestone quarry.It is found that the uncertainty of DEMs induces large errors in the displacement monitoring results if the baseline length of the satellites between the master and the slave data is longer than a few hundred meters.Comparing the monitoring results of DInSAR and GPS,the root mean square error(RMSE)of the discrepancy between the two sets of results is less than 10 mm if an appropriate DEM,considering the excavation processes,is used.It is proven that DInSAR can be applied for monitoring the displacements of mine slopes with centimeter-level accuracy.
文摘The cryosphere is the frozen part of the Earth’s system. Snow and ice are the main constituents of the cryosphere and may be found in different states, such as snow, freshwater ice, sea ice, perma-frost, and continental ice masses in the form of glaciers and ice sheets. The present review mainly deals with state-of-the-art applications of synthetic aperture radar (SAR) with a special emphasize on cryospheric information extraction. SAR is the most important active microwave remote sensing (RS) instrument for ice monitoring, which provides high-resolution images of the Earth’s surface. SAR is an ideal sensor in RS technology, which works in all-weather and day and night conditions to provide useful unprecedented information, especially in the cryospheric regions which are almost inaccessible areas on Earth. This paper addresses the technological evolution of SAR and its applications in studying the various components of the cryosphere. The arrival of SAR radically changed the capabilities of information extraction related to ice type, new ice formation, and ice thickness. SAR applications can be divided into two broad classes-polarimetric applications and interferometric applications. Polarimetric SAR has been effectively used for mapping calving fronts, crevasses, surface structures, sea ice, detection of icebergs, etc. The paper also summarizes both the operational and climate change research by using SAR for sea ice parameter detection. Digital elevation model (DEM) generation and glacier velocity mapping are the two most important applications used in cryosphere using SAR interferometry or interferometric SAR (InSAR). Space-borne InSAR techniques for measuring ice flow velocity and topography have developed rapidly over the last decade. InSAR is capable of measuring ice motion that has radically changed the science of glaciers and ice sheets. Measurement of temperate glacier velocities and surface characteristics by using airborne and space-borne interferometric satellite images have been the significant application in glaciology and cryospheric studies. Space-borne InSAR has contributed to major evolution in many research areas of glaciological study by measuring ice-stream flow velocity, improving understanding of ice-shelf processes, yielding velocity for flux-gate based mass-balance assessment, and mapping flow of mountain glaciers. The present review summarizes the salient development of SAR applications in cryosphere and glaciology.
基金This study was funded by the Korea Meteorological Administration Research and Development Program(KMI2017-9060)the National Research Foundation of Korea funded by the Korea government(NRF-2018M1A3A3A02066008)+1 种基金In addition,the ALOS-2 PALSAR-2 data used in this study are owned by the Japan Aerospace Exploration Agency(JAXA)and were provided through the JAXA’s ALOS-2 research program(RA4,PI No.1412)The GPS data were provided by the Geospatial Information Authority of Japan.
文摘Conventional synthetic aperture radar(SAR)interferometry(InSAR)has been successfully used to precisely measure surface deformation in the line-of-sight(LOS)direction,while multiple-aperture SAR interferometry(MAI)has provided precise surface deformation in the along-track(AT)direction.Integration of the InSAR and MAI methods enables precise measurement of the two-dimensional(2D)deformation from an interferometric pair;recently,the integration of ascending and descending pairs has allowed the observation of precise three-dimensional(3D)deformation.Precise 3D deformation measurement has been applied to better understand geological events such as earthquakes and volcanic eruptions.The surface deformation related to the 2016 Kumamoto earthquake was large and complex near the fault line;hence,precise 3D deformation retrieval had not yet been attempted.The objectives of this study were to①perform a feasibility test of precise 3D deformation retrieval in large and complex deformation areas through the integration of offset-based unwrapped and improved multiple-aperture SAR interferograms and②observe the 3D deformation field related to the 2016 Kumamoto earthquake,even near the fault lines.Two ascending pairs and one descending the Advanced Land Observing Satellite-2(ALOS-2)Phased Array-type L-band Synthetic Aperture Radar-2(PALSAR-2)pair were used for the 3D deformation retrieval.Eleven in situ Global Positioning System(GPS)measurements were used to validate the 3D deformation measurement accuracy.The achieved accuracy was approximately 2.96,3.75,and 2.86 cm in the east,north,and up directions,respectively.The results show the feasibility of precise 3D deformation measured through the integration of the improved methods,even in a case of large and complex deformation.
基金Project(No.2009CB724003) supported by the National Basic Re-search Program (973) of China
文摘The geosynchronous circular synthetic aperture radar (GEOCSAR) is an innovative SAR system,which can produce high resolution three-dimensional (3D) images and has the potential to provide 3D deformation measurement.With an orbit altitude of approximately 36 000 km,the orbit motion and orbit disturbance effects of GEOCSAR behave differently from those of the conventional spaceborne SAR.In this paper,we analyze the effects of orbit errors on GEOCSAR imaging and interferometric processing.First,we present the GEOCSAR imaging geometry and the orbit errors model based on perturbation analysis.Then,we give the GEOCSAR signal formulation based on imaging geometry,and analyze the effect of the orbit error on the output focused signal.By interferometric processing on the 3D reconstructed images,the relationship between satellite orbit errors and the interferometric phase is deduced.Simulations demonstrate the effects of orbit errors on the GEOCSAR images,interferograms,and the deformations.The conclusions are that the required relative accuracy of orbit estimation should be at centimeter level for GEOCSAR imaging at L-band,and that millimeter-scale accuracy is needed for GEOCSAR interferometric processing.
文摘以国内某高速铁路钢拱桥为研究对象,选取2017—2018年期间59幅C波段Senti⁃nel-1号雷达卫星影像,利用PS-InSAR技术处理影像获得桥梁的视线向(Line of Sight,LOS)位移,根据SAR成像空间几何关系解算出支座的纵向位移.研究结果表明:支座纵向位移的时空特性与实际桥梁结构相符合,验证了PS-InSAR技术观测桥梁结构位移的可行性.建立支座纵向位移与温度的线性相关模型,并与结构健康监测系统的实测结果进行对比.两者吻合良好,相对误差控制在10%以内,验证了PS-InSAR测量桥梁结构位移的可靠性.利用有限元模拟温度作用下桥梁支座的位移变化,并与PS-InSAR位移时间序列进行对比.两者趋势基本一致,LOS向位移误差在[-10,10]mm,验证了PS-InSAR测量桥梁结构位移的准确性.
基金National Science Fund for Distinguished Young Scholars(No.41925016)National Natural Science Foundation of China(No.41804008)National Key Research and Development Program of China(No.2018YFC1503603)。
文摘LuTan-1(LT-1)is a constellation with two full-polarization L-band radar satellites designed by China,and the first satellite was scheduled to be launched in December 2021 and the second one in January 2022.The LT-1 will be operated for deformation monitoring in repeat-pass mode,and for DEM generation in bistatic mode,improving self-sufficiency of SAR data for the field of geology,earthquake,disaster reduction,geomatics,forestry and so on.In this paper,we focused on designing an algorithm for interferometric DEM generation using LT-1 bistatic satellites.The basic principle,main error sources and errors control of the DEM generation algorithm of LT-1 were systematically analyzed.The experiment results demonstrated that:①The implemented algorithm had rigorous resolution with a theoretic accuracy better than 0.03 m for DEM generation.②The errors in satellite velocity and Doppler centroid had no obvious effect on DEM accuracy and they could be neglected.While the errors in position,baseline,slant range and interferometric phase had a significant effect on DEM accuracy.And the DEM error caused by baseline error was dominated,followed by the slant range error,interferometric phase error and satellite position error.③To obtain an expected DEM accuracy of 2 m,the baseline error must be strictly controlled and its accuracy shall be 1.0 mm or better for Cross-Track and Normal-Direction component,respectively.And the slant range error and interferometric phase error shall be reasonably controlled.The research results were of great significance for accurately grasping the accuracy of LT-1 data products and their errors control,and could provide a scientific auxiliary basis for LT-1 in promoting global SAR technology progress and the generation of high-precision basic geographic data.
文摘In this paper, an algorithm of generating INSAR unwrapped phase image from SAR single-look complex images is presented. Besides the general processing technique, this article focuses on the methods of flat-earth phase removal, phase noise reduction and phase unwrapping. The availability is tested by the results of processing ERS-1/2 SAR images.
基金The authors would like to thank the support by the State Key Program of National Natural Science Foundation of China under Grant[Number 41774026]the Satellite Mapping Technology and Application,National Administration of Surveying,Mapping and Geoinformation Key Laboratory under Grant[Number KLSMTA-201708].
文摘Interferometric phase filtering is one of the key steps in interferometricsynthetic aperture radar (InSAR/SAR). However, the ideal filtering results are difficult toobtain due to dense fringe and low coherence regions. Moreover, the InSAR/SAR datarange is relatively large, so the efficiency of interferential phase filtering is one of themajor problems. In this letter, we proposed an interferometric phase filtering methodbased on an amended matrix pencil and linear window mean filter. The combination ofthe matrix pencil and the linear mean filter are introduced to the interferometric phasefiltering for the first time. First, the interferometric signal is analyzed, and theinterferometric phase filtering is transformed into a local frequency estimation problem.Then, the local frequency is estimated using an amended matrix pencil at a window. Thelocal frequency can represent terrain changes, thus suggesting that the frequency can beaccurately estimated even in dense fringe regions. Finally, the local frequency is filteredby using a linear window mean filter, and the filtered phase is recovered. The proposedmethod is calculated by some matrices. Therefore, the computational complexity isreduced, and the efficiency of the interferometric phase filtering is improved.Experiments are conducted with simulated and real InSAR data. The proposed methodexhibits a better filtering effect and an ideal efficiency as compared with the traditionalfiltering method.
文摘An approach based on interferometry technique is proposed for three-dimensional (3D) bistatic inverse synthetic aperture radar (ISAR) imaging. It is converted to a monostatic problem by using the theory that a bistatic radar equals a monostatic radar located on the bisector of bistatic an- gle. Then, interferometric phases extracted from a pair of cross shaped antennas are used to esti- mate the height and associated rotational velocity. Finally, numerical simulations are provided to e- valuate this method.