Spatial Distribution Of Errors Research Articles

ASSESSMENT OF THREE-DIMENSIONAL MODELS DERIVED FROM LIDAR AND TLS DATA

Abstract. This paper suggests the use of specific methods for assessing the geometry of 3D building models, by considering models extracted automatically from terrestrial laser scanning (TLS) data and aerial laser scanning (ALS) data. Well known quality factors have been applied for assessing roofs and façades separately. A projection into 2D makes sense in this case, because currently, 3D models or point clouds of façades are often projected into 2D for generating 2D façade maps, as required in the building trades. For assessing roofs in 3D, error maps have been suggested especially for analysing the spatial distribution of plane adjustment errors which might affect the final reconstructed 3D model. For assessing 3D building vector models as one object, first experiments based on volumetric quality factors are presented. This approach is based on ratios inspired from quality factors that have already proven themselves in the literature for comparing surface areas. The volumes considered here are computed on vector models (faceted solids) and not voxels. Further investigations are necessary on the one hand, for testing the sensitivity of these factors. On the other hand, the approach must be completed by criteria allowing the detection of shape differences, independently of the building volume.

Systematic and random error components in satellite precipitation data sets

This study contributes to characterization of satellite precipitation error which is fundamental to develop uncertainty models and bias reduction algorithms. Systematic and random error components of several satellite precipitation products are investigated over different seasons, thresholds and temporal accumulations. The analyses show that the spatial distribution of systematic error has similar patterns for all precipitation products. However, the systematic (random) error of daily accumulations is significantly less (more) than that of high resolution 3‐hr data. One should note that the systematic biases of satellite precipitation are distinctively different in the summer and winter. The systematic (random) error is remarkably higher (lower) during the winter. Furthermore, the systematic error seems to be proportional to the rain rate magnitude. The findings of this study highlight that bias removal methods should take into account the spatiotemporal characteristics of error as well as the proportionality of error to the magnitude of rain rate.

2-매개변수 지반분류 방법 및 지반 증폭계수의 검증 (I) - 국외 내진설계기준 및 부지응답특성과의 비교

최근 제안된 2-매개변수 지반분류 방법 및 지반 증폭계수가 국내 지반조건 및 지반증폭특성에 적합함을 검증하기 위하여 내진설계기준연구II, Eurocode-8, 현재 개정중인 미국 동부지역 NYC DOT 내진설계기준과 비교를 수행하였다. 유사한 조건의 지반 조건에 대하여 각 기준의 설계응답스펙트럼을 비교한 결과, 2-매개변수 지반분류, Eurocode-8, NYC DOT 내진설계기준은 일반적인 국내 지반특성인 단주기 영역의 증폭을 크게 고려하고 있는 반면, 내진설계기준 연구II는 장주기 영역의 증폭을 크게 평하는 것으로 나타났다. 추가적으로 경주시 <TEX>$10km{\times}10km$</TEX> 지역내 50개 부지에 대한 지반응답해석 결과를 확보하고, 이를 내진설계기준연구II 및 2-매개변수 지반분류 방법에서 제안하는 지반 증폭계수와 2차원 공간적인 비교를 수행하였다. 단주기 및 장주기 증폭계수 모두에 대하여 내진설계기준연구II가 2-매개변수 지반분류 방법에 비하여 부지응답해석 결과와의 오차값이 월등히 큰 것으로 평가되어, 2-매개변수 지반분류 방법에서 제안하는 지반 증폭계수의 타당성을 확인하였다. In order to verify that the recently proposed two-parameters site classification system and the corresponding site coefficients are suitable for the local geological conditions in Korea, a comparison was conducted with current Korean seismic code, Eurocode-8, NYC DOT seismic code. The design spectrum of the current Korean seismic code is significantly amplified in the long-period range, whereas the other response spectra, including the proposed two-parameters approach, are significantly amplified in the short-period range, which is a typical geological condition in Korea. In addition, based on the results of site response analyses in the specific <TEX>$10km{\times}10km$</TEX> area of Gyeongju, spatial distributions of site coefficients from site-specific seismic response analyses were compared with the proposed site coefficients, as well as those specified in the current Korean seismic code. The site coefficients (<TEX>$F_a$</TEX> and <TEX>$F_v$</TEX>) from the current Korean seismic codes show significantly high spatial error distributions compared with those specified by the two-parameters site classification system. Therefore, the proposed system is suitable for regions of shallow bedrock including the Korean peninsula.

Research on optimal measurement area of flexible coordinate measuring machines

When we measure a workpiece in the optimal measurement area of the flexible coordinate measuring machines (FCMMs), the measuring precision can be improved. The flexible CMM’s measuring space is given. Then its spatial error distribution model is build by using support vector machine theory. Finally, the two solutions of the optimal measurement area are discussed and solved through experiments. The high precision measurement results can be realized by using a low-precision measuring machine without any increase in hardware manufacturing cost. This is of great theoretical value and practical significance for the flexible CMM’s further development.

Performance Analysis of a Synchronized-Router-Based Flat-Passband Filter Using Multiple-Input Arrayed Waveguide Grating With Phase Errors

The filtering performance of a synchronized-router-based flat-passband filter with random phase errors is analyzed. For this purpose, an analytical model of a synchronized-router-based flat-passband filter using a multiple-input arrayed waveguide grating (AWG) with phase errors is derived without the assumption of the independence of random errors so that the model can treat general types of phase errors. For average transmittance, we proposed the analytical model for the variance of transmittance for a multiple-input AWG to predict the deviation of the transmittance. By using the proposed analytical model, device performance can be estimated once the spectral information of phase errors is given. The analysis clarifies that the frequency dependence of crosstalk reflects the spatial spectral distribution of phase errors. We also compared the transmittance characteristics of the synchronized-router-based flat-passband filter with conventional Gaussian and flat-type AWGs. We found that the crosstalk in the synchronized-router type has a different behavior from those in the conventional types, i.e., the crosstalk in the synchronized-router type has a periodic behavior according to the function of the input router. The probability distribution of the transmittance of the flat-passband filter is also calculated by random simulation and compared with the result from the analytical model. The agreement between the model and the random simulation confirms that the proposed model is effective for analytically estimating the performance of a synchronized-router-based flat-passband filter with phase errors.

Properties of the target registration error for surface matching in neuronavigation

Objective: Surface matching is a relatively new method of spatial registration in neuronavigation. Compared to the traditional point matching method, surface matching does not use fiducial markers that must be fixed to the surface of the head before image scanning, and therefore does not require an image acquisition specifically dedicated for navigation purposes. However, surface matching is not widely used clinically, mainly because there is still insufficient knowledge about its application accuracy. This study aimed to explore the properties of the Target Registration Error (TRE) of surface matching in neuronavigation.Materials and Methods: The surface matching process was simulated in the image space of a neuronavigation system so that the TRE could be calculated at any point in that space. For each registration, two point clouds were generated to represent the surface extracted from preoperative images (PCimage) and the surface obtained intraoperatively by laser scanning (PClaser). The properties of the TRE were studied by performing multiple registrations with PClaser point clouds at different positions and generated by adding different types of error.Results: For each registration, the TRE had a minimal value at a point in the image space, and the iso-valued surface of the TRE was approximately ellipsoid with smaller TRE on the inner surfaces. The position of the point with minimal TRE and the shape of the iso-valued surface were highly random across different registrations, and the surface registration error between the two point clouds was irrelevant to the TRE at a specific point. The overall TRE tended to increase with the increase in errors in PClaser, and a larger PClaser made it less sensitive to these errors. With the introduction of errors in PClaser, the points with minimal TRE tended to be concentrated in the anterior and inferior part of the head.Conclusion: The results indicate that the alignment between the two surfaces could not provide reliable information about the registration accuracy at an arbitrary target point. However, according to the spatial distribution of the target registration error of a single registration, enough application accuracy could be guaranteed by proper visual verification after registration. In addition, surface matching tends to achieve high accuracy in the inferior and anterior part of the head, and a relatively large scanning area is preferable.

Spatial Distribution and Evolution of Extratropical Cyclone Errors over North America and its Adjacent Oceans in the NCEP Global Forecast System Model

Abstract Short- to medium-range (1–5 day) forecasts of extratropical cyclones around North America and its adjacent oceans are verified within the Global Forecast System (GFS) model at the National Centers for Environmental Prediction (NCEP) during the 2002–07 cool seasons (October–March). Cyclones in the immediate lee of the Rockies and U.S. Great Plains have 25%–50% smaller pressure errors than other regions after hour 36. The central pressure and displacement errors are largest over the central and eastern Pacific for the 42–72-h forecast, while the western and central Atlantic pressure errors for 96–120 h are similar to the central and eastern Pacific. For relatively strong cyclones, the western Atlantic and central/eastern Canada pressure errors are larger than those for the Pacific by 108–120 h. There are large spatial variations in the central pressure biases at 72–120 h, with overdeepened GFS cyclones (negative errors) extending from the northern Pacific and Bering Strait eastward to western Canada, while underdeepened GFS cyclones (positive errors) occur across northeast Canada and just east of the U.S. east coast. GFS cyclone tracks and spatial composites using the daily NCEP reanalysis are used to illustrate flow patterns and source regions for some of the large GFS cyclone errors and biases. Relatively large central pressure errors over the central Pacific early in the forecast (30 h) spread eastward over Canada by 66 h and the eastern United States by 84 h. The underdeepened GFS cyclone errors (&amp;gt;1.5 standard deviations) at day 4 over the western Atlantic are associated with an anomalous ridge over the western United States and trough over the eastern United States, and most of the underdeepening occurs with cyclones tracking east-northeastward across the Gulf Stream. Many of the overdeepened cyclones have tracks more parallel to the U.S. east coast. The underdeepened cyclones over the central and eastern Pacific tend to occur farther south (35°–45°N) than the overdeepened events.

Research on the Spatial Error Distribution Model of Flexible Coordinate Measuring Machines Based on Support Vector Regression

One of the main reasons on Flexible Coordinate Measuring Machines’ (FCMM) less application is that its accuracy can’t meet the practical requirements. The spatial error distribution model of FCMM is build using Support Vector Regression (SVR) method. The test shows the data from the model can effectively fit the samples, and arguably the model based on SVR is feasible. The novel method gives an idea of studying the spatial error distribution model of FCMM. Futhermore, the model can provide reasearch foundations for definiting optimal measurement area and thus help to improve the measurement accuracy in the next work.

The spatial distributions of the errors in determination of the earthquake coordinates at the Garm test site

In this work, the spatial distribution of errors in the localization of the earthquake epicenters at the Garm geophysical test site is analyzed. For this purpose, the coordinates of earthquakes over the period of 1955–1991 were calculated using three different methods and compared. It is shown that the residual errors of intrinsic convergence of the data presented in the catalogs as a characteristic of the accuracy in the determination of the earthquake hypocenter cannot serve as true estimates of errors of the epicenter location and should be supplemented by other characteristics, such as maximum errors of estimates. It is proposed to use the maps of difference between the corresponding coordinates of earthquakes in addition to the error estimates obtained using some other methods.

APPLICATION OF ERROR-ENSEMBLE METHOD TO A SHORT-TERM RAINFALL PREDICTION WITH TRANSRATION MODEL CONSIDERING OROGRAPHIC RAINFALL

To improve short term prediction accuracy of rainfall, especially for orographic rainfall over mountain areas, a physical approach and a stochastic approach were introduced into a radar image extrapolation method with translation model. In the physical approach, radar observed rain field is separated into orographic and non-orographic rain fields by solving physically-based equations. In the stochastic approach, a bias-modified prediction field was calculated from a lot of spatial error distributions of the pre-predicted rain fields. In order to improve the separation accuracy of the physically-based orographic model, vertical wind velocity W is updated so that the physically-based procedure could re-predict the rain filed which meets to the bias-modified deterministic prediction field. As a result, one-hour prediction accuracy especially over mountain areas were much improved. In the future, more accurate predictions can be expected by improving the W-updating procedure.

Effects of large-scale nonstationarity on parametric maps. A study of rest perfusion CASL data

This study investigates the emergence of characteristic patterns in clusters thresholded at uncorrected significance levels, using as a case study rest perfusion images obtained with the continuous arterial spin labelling technique (CASL). The origin of these patterns is traced back to the existence of large-scale spatial covariance, a violation of the stationarity assumption on the spatial distribution of residual errors. It is shown that in the presence of large-scale covariance, several principles or intuitions common among experimenters when evaluating the inferential strength of their analyses are not applicable. Thresholded maps and clusters are confounded by the spatial patterns of large-scale covariance, irrespective of the existence of a true effect, as shown in t maps constructed by resampling groups at random from a large pool of volumes. Filtering clusters according to their size made the problem worse, and corrections on cluster size based on random field theory models of smoothness had only a minor impact on their tendency to appear in characteristic locations. A formal analysis shows that the large-scale covariance at the origin of these problems is retained in the parametric map irrespective of sample size. Therefore, neither sample independence nor sample size protect from replications of effects being confounded by replications of the spatial covariance of residual errors. In contrast, cluster peaks were not affected by large-scale covariance but only by local differences in smoothness levels, as predicted by random field theory for the distribution of maxima, highlighting the different inferential robustness of cluster-based and maxima-based statistics. A framework is provided to generalize these results to mixed effects models with nested random effects, applicable also to activation studies. Large-scale nonstationarity is most problematic when the variance source at the origin of the characteristic patterns is not specific to a function or variable involved in the inferential process, as typically in observational studies of individual differences. These results raise the question of the existence and impact of large-scale nonstationarity in studies with data obtained with other techniques.

A method to map errors in the deformable registration of 4DCT images.

To present a new approach to the problem of estimating errors in deformable image registration (DIR) applied to sequential phases of a 4DCT data set. A set of displacement vector fields (DVFs) are made by registering a sequence of 4DCT phases. The DVFs are assumed to display anatomical movement, with the addition of errors due to the imaging and registration processes. The positions of physical landmarks in each CT phase are measured as ground truth for the physical movement in the DVF. Principal component analysis of the DVFs and the landmarks is used to identify and separate the eigenmodes of physical movement from the error eigenmodes. By subtracting the physical modes from the principal components of the DVFs, the registration errors are exposed and reconstructed as DIR error maps. The method is demonstrated via a simple numerical model of 4DCT DVFs that combines breathing movement with simulated maps of spatially correlated DIR errors. The principal components of the simulated DVFs were observed to share the basic properties of principal components for actual 4DCT data. The simulated error maps were accurately recovered by the estimation method. Deformable image registration errors can have complex spatial distributions. Consequently, point-by-point landmark validation can give unrepresentative results that do not accurately reflect the registration uncertainties away from the landmarks. The authors are developing a method for mapping the complete spatial distribution of DIR errors using only a small number of ground truth validation landmarks.

Error analysis in the digital elevation model of Kuwait desert derived from repeat pass synthetic aperture radar interferometry

The aim of this paper is to analyze the errors in the Digital Elevation Models (DEMs) derived through repeat pass SAR interferometry (InSAR). Out of 29 ASAR images available to us, 8 are selected for this study which has unique data set forming 7 InSAR pairs with single master image. The perpendicular component of baseline (B) varies between 200 to 400 m to generate good quality DEMs. The Temporal baseline (T) varies from 35 days to 525 days to see the effect of temporal decorrelation. It is expected that all the DEMs be similar to each other spatially with in the noise limits. However, they differ very much with one another. The 7 DEMs are compared with the DEM of SRTM for the estimation of errors. The spatial and temporal distribution of errors in the DEM is analyzed by considering several case studies. Spatial and temporal variability of precipitable water vapour is analysed. Precipitable water vapour (PWV) corrections to the DEMs are implemented and found to have no significant effect. The reasons are explained. Temporal decorrelation of phases and soil moisture variations seem to have influence on the accuracy of the derived DEM. It is suggested that installing a number of corner reflectors (CRs) and the use of Permanent Scatter approach may improve the accuracy of the results in desert test sites.

An oscillating sweeping gap test for VMAT quality assurance

The objective of this study was to develop an oscillating sweeping gap test for volumetric modulated arc therapy (VMAT) quality assurance (QA). A novel test was designed and used to simultaneously determine uncertainties associated with linac performance, dose calculation and dosimetric MLC parameters during VMAT delivery. Delivered doses were measured with Matrixx™, ionization chamber A12 and EDR2™ films, and compared to calculations from the treatment planning system (TPS) Eclipse™. A new gantry and MLC motion pattern, called here ‘oscillating sweeping gap’, is developed as an extension of the standard sweeping gap MLC pattern developed for IMRT QA. Specifically, in the oscillating sweeping gap test, a uniform MLC gap is moving repeatedly back and forth across the field at a constant speed during a full rotation of the gantry. The dose distribution generated by the combined gantry and MLC motion pattern is designed to be quasi-uniform within a cylindrical target volume with a sharp penumbra. The test design allows for an easy detection of dose errors as deviations from the uniform background. MLC gap sizes, gantry and MLC speeds and monitor units (MU) are selected according to a formula determining the magnitude of dose delivered to the target. Both measured and calculated dose distributions were analyzed as a function of the number of control points in the TPS, MLC gap size and magnitude of the gantry angle error. Dose calculation errors due to the insufficient number of control points in the gantry and MLC motion pattern appear as streak artifacts. The magnitude of these artifacts is increasing with the decreased number of control points, and with the decreased MLC gap size. The spatial distribution of dose errors due to the gantry angle errors (unsteady rocking motion) appears as high-frequency noise for higher wobble frequencies and as large hot/cold spots for lower wobble frequencies. The actual MLC leaf position as a function of time (or the gantry angle), determined from the Matrixx snaps (dose images measured per time interval) of the moving gap and compared to the ideal leaf positions, reveal discrepancies in agreement with theoretical calculations. The MLC parameters determined for VMAT with the oscillating sweeping gap test, their uncertainties and the associated dose errors are similar to those determined for IMRT with the standard sweeping gap test. The oscillating sweeping gap test has been developed for the gantry and MLC QA. Applications include commissioning of the planning system for VMAT and performing routine linac QA. The test is sensitive to several errors in dose calculation and delivery.

Full Positional Accuracy Analysis of Spatial Data by Means of Circular Statistics

AbstractThe positional error in spatial data is defined as a vector by comparing the coordinates between the true position and the measured position. The standard tests to assess the positional accuracy use only the magnitude of the vector and omit the azimuth. This article suggests that the use of both values allows a much more complete analysis of the positional error. A set of tests is proposed that are relevant for this purpose and demonstrate that some important features are not identified by the common procedures. The test samples come from two datasets. The first is obtained from the comparison of 100 homologous points in two conventional maps, and the second one comes from the geometric calibration of a photogrammetric scanner. The results are analyzed and discussed, showing that important issues such as error anisotropy are detected only by means of the circular statistics tests and density maps of distribution. Therefore, tests that assess the goodness of fit for uniform distribution in azimuths, such as Rayleigh and Rao tests, give low probabilities (P = 0 and P &gt; 0.01). Moreover, density maps working with both magnitude and angle can locate the outlier candidate and offer more information about the spatial distribution of error.

On the reliability of HELIOSAT method: A comparison with experimental data

This study deals with comparison of Cameroonian ground based measurements with estimations done using satellite images, by applying the second version of the HELIOSAT method, as computed by the web tool HELIOCLIM of the SoDa project. Measurements and satellite resources were chosen for the same period of the year 1985, on ten Cameroonian locations, distributed with mean spatial resolution of 200 km between two neighbouring stations. Correlations curves are constructed between daily irradiation estimates from satellite data and from measurements. The consequent regression equations are established, using the least square method. Finally, a brief discussion is carried out on the spatial distribution of errors observed on results. Similarly to previous studies this study confirmed the capability of the method to produce good results for the Garoua location, and established its extension on other sahelian sites, comparatively to the poor agreement observed on southern sites. Furthermore, even if the study was not done on a long period, it brought out the necessity to correct the HELIOSAT results for many Cameroonian locations, to march the experimental results.

Dual-scale validation of a medium-resolution coastal DEM with terrestrial LiDAR DSM and GPS

The use of medium-resolution photogrammetric-derived Digital Elevation Models (DEMs) to model coastal inundation risk is commonplace in the geosciences. However, these datasets are often characterised by relatively large and loosely defined elevation errors, which can seriously limit their reliability. Post-processed and static RTK dual-frequency GPS data and very high-resolution Terrestrial Laser Scanning DSM data are used here to quantify the magnitude and spatial distribution of elevation error on a 10 km coastal section of a medium-resolution photogrammetric DEM. The validation data are captured at two scales and spatial-resolutions to minimise the risk of spatial bias in the validation results. The strengths and shortcomings of each validation dataset are assessed, and the complimentary value of GPS and Terrestrial Laser Scanning for external validation is demonstrated. Elevation errors highlighted in the photogrammetric DEM are found to be significantly larger than suggested by the data suppliers, with a tendency for the larger errors to occur with increasing proximity to the coastline. The results confirm the unsuitability of the DEM tested for the local spatial modelling of coastal inundation risk, highlighting difficulties that may be prone to occur when similar DEM datasets are used in coastal studies elsewhere.

Modelling the spatial distribution of DEM error with geographically weighted regression: An experimental study

Digital elevation models are digital representations of topography and are the principal digital data source for many disciplines. The accuracy of a digital elevation model is particularly important with its intended use. The assessment of accuracy is usually undertaken by deriving some measures of indices. These indices are usually global indices and summarise the accuracy. In this study, a more detailed accuracy is discussed by examining the magnitudes and spatial patterning of elevation errors. Many researches have demonstrated the effects of interpolation methods and the nature of errors in digital elevation models for small-scale areas. On the contrary, this study investigated the size and spatial patterning of errors in a large-scale area, by comparing three different interpolation algorithms. This research also examined the accuracy related with data density and surface characteristics at the field scale. Finally, ordinary least squares and geographically weighted regression models were used to model the relationship between error and surface characteristics. Geographically weighted regression modelling gave better results than ordinary least-squares regression modelling.

Efficient data assimilation method based on chaos theory and Kalman filter with an application in Singapore Regional Model

Data assimilation is a methodology that utilizes information from observations, and assimilates it into numerical models, with the intention of improving the quality and accuracy of the model outputs. This paper introduces a hybrid data assimilation scheme, which combines a temporal error prediction algorithm based on local model (LM) inspired by chaos theory and a spatial error distribution scheme through the propagation of error covariances derived from the Kalman filter (KF). Local model is only capable of predicting the model errors at the stations where the observations are available, while the effect of traditional Kalman filter is limited to a time horizon where the improved initial conditions are washed out. The hybrid scheme outlined in this paper is performed in two steps: (i) predicting the model errors at the measurement stations using the local model approach and (ii) distributing the predicted errors over the computational domain using the Kalman filter. Incorporating error distribution with error prediction assimilates limited information from the observed data into non-measurement stations. Therefore all stations of interest are able to be benefited. The proposed hybrid scheme has been implemented in the Singapore Regional Model (SRM) constructed by Delft3D modelling system, with the improvements in the assimilated characteristics discussed in detail.

Adjoint-based h– p adaptive discontinuous Galerkin methods for the 2D compressible Euler equations

In this paper, we investigate and present an adaptive Discontinuous Galerkin algorithm driven by an adjoint-based error estimation technique for the inviscid compressible Euler equations. This approach requires the numerical approximations for the flow (i.e. primal) problem and the adjoint (i.e. dual) problem which corresponds to a particular simulation objective output of interest. The convergence of these two problems is accelerated by an hp-multigrid solver which makes use of an element Gauss–Seidel smoother on each level of the multigrid sequence. The error estimation of the output functional results in a spatial error distribution, which is used to drive an adaptive refinement strategy, which may include local mesh subdivision ( h-refinement), local modification of discretization orders ( p-enrichment) and the combination of both approaches known as hp-refinement. The selection between h- and p-refinement in the hp-adaptation approach is made based on a smoothness indicator applied to the most recently available flow solution values. Numerical results for the inviscid compressible flow over an idealized four-element airfoil geometry demonstrate that both pure h-refinement and pure p-enrichment algorithms achieve equivalent error reductions at each adaptation cycle compared to a uniform refinement approach, but requiring fewer degrees of freedom. The proposed hp-adaptive refinement strategy is capable of obtaining exponential error convergence in terms of degrees of freedom, and results in significant savings in computational cost. A high-speed flow test case is used to demonstrate the ability of the hp-refinement approach for capturing strong shocks or discontinuities while improving functional accuracy.