Interpolation Method In Order Research Articles

Combination of Fourier and CRS-Based Reconstruction Algorithms in Land Seismic Data

ABSTRACT. The reconstruction based on the partial CRS stacking operator presents higher signal-to-noise ratio and better continuity of events. However, irregularly sampled land data often introduce errors in the CRS attributes, creating artifacts that contaminate the seismic data. Recently, the combination of Fourier and CRS-based reconstruction algorithms has significantly solved these problems. The approach consists of applying a Fourier-based interpolation method as a regularization operator to the original data and then the CRS attributes are searched in the reconstructed data. The CRS attributes determined in this way are more accurate and they can be applied in two different forms, either in the interpolation and regularization of the original data or in the denoising of the Fourier-based reconstructed data. We propose to compare the combination of the Fourier-based interpolation methods MWNI and MPFI with the CRSbased interpolation method in order to evaluate which is the best preconditioner of the prestack data to search the CRS attributes. We applied the proposed flowcharts combining the interpolation methods mentioned above to the land seismic data from the Tacutu basin, which is vintage data with very low fold and noisy. The reconstructed data obtained by the combinations show significant improvements compared to the data reconstructed using the algorithms separately, in other words, the weaknesses and limitations of each method are overcome when they are applied in combination. The MWNI+CRS combination flow produces the best results, with the stacked section of reconstructed data showing better noise removal, enhancement of coherent events, better definition and continuity of steeply dipping events.

Assessment of Different Spatial Interpolation Techniques for Generating Synthetic Soil Boring Data

Subsurface soil conditions usually involve special site variability that cannot be ignored for design and analysis. Therefore, the effect of site variability on associated soil properties should be assessed using gathered field data, such as soil boring data collected from discrete locations. In this study, six spatial interpolation techniques, the ordinary kriging (OK), simple kriging (SK), universal kriging (UK), inverse distance weight (IDW), spline, and natural neighbor (NaN) were evaluated to assess the best prediction strategy for considering site variability. The efficacy of these methods was tested at four soil boring sites. Boring profiles were generated using the different techniques at specified locations for each site, and the created data were compared with the measured soil boring profiles. For each location, the best-fit line of measured versus predicted undrained shear strength (Su) or standard penetration test (SPT) number, mean bias factor (λ), coefficient of effectiveness (COE), root mean square error (RMSE), and coefficient of variation (COV), were calculated and used to assess the various interpolation methods. The findings of this study demonstrated the ability of these spatial interpolations to produce precise soil boring data. The slope of best-fit line of measured/generated Su and SPT ranged from 0.89 to 0.99. The best-performing interpolation methods (in order) are: IDW, OK/UK, and SK methods. The results show that the COVs between the measured and synthetic soil boring data at the selected points are significantly lower than the COVs between the measured soil boring profiles for the entire site.

Reliability of smart noise pollution map

AbstractThe problem of noise pollution in Baghdad, the capital city of Iraq, is getting worse every day as a result of the increased volume of traffic. This presents a considerable risk, particularly on the main roads that connect densely populated neighborhoods such as the Al-Sadr City district with the central neighborhoods of the capital. In order to inform decision-makers in urban development and environmental policy about the high values of noise pollution that require remediation and regulation, noise maps are produced. However, two fundamental problems are generally faced in creating a more reliable noise map in the shortest possible time: the excessive time requirements for measuring noise and determining the method of map creation. Therefore, the role of geographic information system (GIS) software in producing noise maps is evident due to the difficulty of increasing the spatial density of measurements and integrating them with spatial information. Hence, an appropriate interpolation method is required. In this article, Moran’sIindex was calculated to assess the spatial autocorrelation of measured traffic noise points. A comparison was made between the Smart Map Plugin ordinary kriging (OK) and the inverse distance weighting (IDW) deterministic interpolation method to determine the best method for producing noise maps for the main entrance and exit roads of Al-Sadr City. The noise values were modeled using the best-performing method. Furthermore, the predictive raster data are displayed in the spatial context as a starting point and reference for identifying and understanding the levels of traffic noise in the selected study area. The locations of selected points for measuring traffic noise values were determined in an organized and homogeneous manner, where noise points for the main entrance and exit roads were opposite each other, and the distance between consecutive noise points on each road was 100 m. Traffic noise measurements were carried out at each selected point using the SVAN977 sound and vibration analyzer. At each measurement point, three noise values (LAeq, Max, Min) were obtained during the three peak times, 7–9 AM, 12–2 PM, and 4–6 PM. QGIS software was used to compare the two interpolation methods, with its strength lying in the use of plugins that facilitate spatial analysis, processing tools, and algorithms. The Smart Map Plugin provided facilities to choose the appropriate semi-variogram in the OK interpolation method. The root mean square error was used to compare the two interpolation methods in order to determine the most suitable method for producing traffic noise maps in the study area. The results indicated that the Smart Map Plugin using OK outperformed the IDW method, as spatial distribution pattern and homogeneity affect the accuracy of interpolation. Moreover, based on the analysis of the three noise attributes (LAeq, Max, Min), the performance of the Smart Map Plugin (OK) was found to be better than IDW when the Moran’sIvalue was high.

Critical assessment of wall model numerical implementation in LBM

In this article, a thorough investigation of wall model numerical implementation at high Reynolds numbers is conducted. In the framework of combined Lattice Boltzmann Method (LBM) and Immersed Boundary Method (IBM), this work focuses on two main axes: First, the influence of the wall model data input interpolation is investigated. After a brief review of the common interpolation methods used in the literature, the accuracy of various interpolation strategies ranging from Inverse Distance Weighing (IDW) to Trilinear methods are assessed. Secondly, the sensitivity of the wall model to its numerical implementation is evaluated by comparing a tried-and-tested wall model with a linearization procedure that aims at dealing with challenging configurations. The comparisons are made on two bidimensional benchmark test-cases, namely the turbulent flat plate and the bump-in-channel. It is shown that first order interpolation methods can lead to spurious oscillations in surface coefficients for challenging test-cases. Moreover, it has been found that the numerical implementation of the wall model has a profound influence on its behavior leading to unphysical friction coefficients if the wall model numerical implementation is not designed to handle properly immersed boundary conditions in the case of complex configurations.

Influence of Interpolation Scheme on the Accuracy of Overset Method for Computing Rudder-Propeller Interaction

Abstract The overset method and associated interpolation schemes are usually thoroughly verified only on synthetic or academic test cases for which conclusions might not directly translate to real engineering problems. In the present work, an overset grid method is used to simulate a rudder-propeller flow, for which a comprehensive verification and validation study is performed. Three overset-related interpolation schemes (first order inverse distance, second order nearest cell gradient and third order least squares) are tested to quantify and qualify numerical errors on integral quantities, mass imbalance, flow features and rudder pressure distributions. The performance overhead is also measured to help make accuracy versus performance balance decisions. Rigorous solution verification is performed to estimate time and space Discretization, iterative and statistical uncertainties. Validation of the propeller-rudder flow against experimental data is also done. The results show that, while the choice of interpolation scheme has minimal impact on time-averaged integral quantities (like propeller and rudder forces), they do influence the smoothness of the time signals, with the first order scheme resulting in large intensity high-frequency temporal oscillations. Lower order interpolation methods also produce more interpolation artifacts in fringe cells, which are then convected downstream. Mass imbalance is also affected by the interpolation scheme, with higher order schemes such as the third order least squares approach resulting in an order of magnitude lower flux errors. The limitations of first order schemes do not, however, result in significant lower computational overhead, with the second order nearest cell gradient being even cheaper than the inverse distance scheme in the tested implementation. Lastly, validation shows promising results with rudder forces within 10% of the experiments.

Reducing volume and shape errors in front tracking by divergence-preserving velocity interpolation and parabolic fit vertex positioning

Volume conservation and shape preservation are two well-known issues related to the advection and remeshing in front tracking. To address these issues, this paper proposes a divergence-preserving velocity interpolation method and a parabolic fit vertex positioning method for remeshing operations for three-dimensional front tracking. Errors in preserving the divergence of the velocity field when interpolating the velocity from the fluid mesh to the vertices of the triangles of the front are a primary reason for volume conservation errors when advecting the front. The proposed interpolation method preserves the discrete divergence of the fluid velocity by construction and is compared in this work with other known interpolation methods in divergence-free and non-divergence-free test cases, with respect to volume conservation and shape preservation of the front. The presented interpolation method conserves the volume and shape up to an order of magnitude better than the conventionally used interpolation methods and is within the range of higher order interpolation methods at lower computational cost. Additionally, the parabolic fit vertex positioning method for remeshing operations locally approximates the front with a smooth polynomial surface, improving volume conservation and shape preservation by an order of magnitude compared to conventional remeshing algorithms.

Cavitation modelling using real gas state equation: A conceptual study

The prediction of the onset of cavitation to allow investigations of the flow in off-design conditions during design is unavoidable for a variety of applications. Numerical modeling of the cavitation phenomena is however computationally challenging due to the nature of the phenomena. High density ratios, steep pressure gradients, the presence of multiple phase including phase change and hence to occurrence of real gas thermophysical behavior would cause a computational effort unmanageable during design. Today’s models are therefore greatly simplified representations of the reality. Conservation equations are usually solved using a mixture approach with flow properties being a volume fraction weighted average of two incompressible fluids thus neglecting real gas effects. The source term from the phase exchange however usually poses significant stability problems. In this article we will therefore present an approach for cavitation modeling using high-order polynomial real-gas state equations to accurately predict the properties of water at any state. Computational performance is improved by the use of structured tabulation using high order interpolation methods. The numerical results are then compared against measurement data and conventional cavitation model results.

Generation and evaluation of synthetic cone penetration test (CPT) data using various spatial interpolation techniques

The cone penetration test (CPT) has been widely used in many geotechnical engineering applications, including soil identification and classification, and evaluation of different soil properties. However, the uncertainties associated with site variation are typical characteristics of subsurface soil conditions that cannot be ignored. Therefore, the effect of site variability on the correlated soil properties from collected field data, such as CPT data, obtained from discrete locations across the site needs to be evaluated. In this study, six well-established spatial interpolation techniques — ordinary kriging (OK), simple kriging (SK), universal kriging (UK), inverse distance weight (IDW), spline, and natural neighbor (NaN) — were investigated to evaluate the best interpolation method for incorporating site variability. Six CPT test sites were used to evaluate the performance of these spatial interpretation methods. For each site, CPT profiles at specified locations were generated using the different interpolation techniques, and the generated CPT profiles were compared with the measured CPT profiles. The best-fit line of measured versus predicted cone tip resistance (qc) values, mean bias factor (λ), coefficient of variation (COV), and root mean square error (RMSE) were calculated for each CPT profile and used as a criteria for evaluating the different spatial interpolation methods. The results of this study demonstrated the ability of these spatial interpolation methods for generating CPT profiles with good accuracy. The slope of best-fit line of measured versus predicted qc ranges from 0.93 to 0.95, the mean of λ ranges from 0.90 to 0.98, and the COV ranges from 0.34 to 0.53. The IDW, OK, and SK showed the best spatial interpolation methods (in order) for four out of the six CPT sites. For site 4, OK, IDW, and SK showed the best spatial interpolation methods (in order); while for site 5, the three best spatial interpolation techniques are SK, IDW, and OK (in order).

Testing Different Interpolation Methods Based on Single Beam Echosounder River Surveying. Case Study: Siret River

Bathymetric measurements play an important role in assessing the sedimentation rate, deposition of pollutants, erosion rate, or monitoring of morphological changes in a river, lake, or accumulation basin. In order to create a coherent and continuous digital elevation model (DEM) of a river bed, various data interpolation methods are used, especially when single-beam bathymetric measurements do not cover the entire area and when there are areas which are not measured. Interpolation methods are based on numerical models applied to natural landscapes (e.g., meandering river) by taking into account various morphometric and morphologies and a wide range of scales. Obviously, each interpolation method, used in standard or customised form, yields different results. This study aims at testing four interpolation methods in order to determine the most appropriate method which will give an accurate description of the riverbed, based on single-beam bathymetric measurements. The four interpolation methods selected in the present research are: inverse distance weighting (IDW), radial basis function (RBF) with completely regularized spline (CRS) which uses deterministic interpolation, simple kriging (KRG) which is a geo-statistical method, and Topo to Raster (TopoR), a particular method specifically designed for creating continuous surfaces from various elevation points, contour, or polygon data, suitable for creating surfaces for hydrologic analysis. Digital elevation models (DEM’s) were statistically analyzed and precision and errors were evaluated. The single-beam bathymetric measurements were made on the Siret River, between 0 and 35 km. To check and validate the methods, the experiment was repeated for five randomly selected cross-sections in a 1500 m section of the river. The results were then compared with the data extracted from each elevation model generated with each of the four interpolation methods. Our results show that: 1) TopoR is the most accurate technique, and 2) the two deterministic methods give large errors in bank areas, for the entire river channel and for the particular cross-sections.

Phylin 2.0: Extending the phylogeographical interpolation method to include uncertainty and user-defined distance metrics.

Estimating geographical ranges of intra-specific evolutionary lineages is crucial to the fields of biogeography, evolution, and biodiversity conservation. Models of isolation mechanisms often consider multiple distances in order to explain genetic divergence. Yet, the available methods to estimate the geographical ranges of lineages are based on direct geographical distances, neglecting other distance metrics that can better explain the spatial genetic structure. We extended the phylogeographical interpolation method (phylin) in order to accommodate user-defined distance metrics and to incorporate the uncertainty associated with genetic distance calculation. These new features were tested with simulated and empirical data sets. Multiple distance matrices were generated including geographical, resistance, and environmental distances to derive maps of lineage occurrence. The new additions to this method improved the ability to predict lineage occurrence, even with low sample size. We used a regression framework to quantify the relationship between the genetic divergence and competing distance matrices representing potential isolation processes that are subsequently used in the interpolation process. Including uncertainty in tree topology and the different distance matrices improved the robustness of the variograms, allowing a better fit of the theoretical model of spatial dependence. The improvements to the method increase its potential application in other fields. Accurately mapping genetic divergence can help to locate potential contact zones between lineages as well as barriers to gene flow, which has a broad interest in biogeographical and evolutionary studies. Additionally, conservation efforts could benefit from the integration of genetic variation and landscape features in a spatially explicit framework.

Spatial variability of soil organic matter content in Eastern Croatia assessed using different interpolation methods

Soil organic matter plays a crucial role in soil health and represents one of the key functions for determining soil suitability for crop production. Recently, intensive agricultu- ral production and climatic changes have led to a decline in organic matter level in soils. This paper is to provide the most accurate spatial predictor using different interpolation methods in order to evaluate in detail the status of organic matter in agricultural soils in the Osijek-Baranja County, Croatia. We applied three different interpolation methods, including inverse distance weighting, ordinary kriging and empirical Bayesian kriging. A total number of 9099 soil samples from 0-30 cm layer were compiled and analysed in the laboratory. The average value of soil organic matter in the study area was 2.66% with moderate variability (CV = 30.62%). The best fit variogram model is exponential in the direction of 20 and its spatial variability indicates that soil organic matter varies widely under pedogenetic and soil management practices. Empirical Bayesian kriging method was the most precise (RMSE = 0.457), followed by ordinary kriging (RMSE = 0.466) and inverse distance weighting (RMSE = 0.476). The investigated area shows a heterogeneous spatial pattern of soil organic matter content, with levels below 3% found mostly in western and south-western parts of county.

Comparative Analysis of the Digital Terrain Models Extracted from Airborne LiDAR Point Clouds Using Different Filtering Approaches in Residential Landscapes

Light Detection And Ranging (LiDAR) is a well-established active remote sensing technology that can provide accurate digital elevation measurements for the terrain and non-ground objects such as vegetations and buildings, etc. Non-ground objects need to be removed for creation of a Digital Terrain Model (DTM) which is a continuous surface representing only ground surface points. This study aimed at comparative analysis of three main filtering approaches for stripping off non-ground objects namely; Gaussian low pass filter, focal analysis mean filter and DTM slope-based filter of varying window sizes in creation of a reliable DTM from airborne LiDAR point clouds. A sample of LiDAR data provided by the ISPRS WG III/4 captured at Vaihingen in Germany over a pure residential area has been used in the analysis. Visual analysis has indicated that Gaussian low pass filter has given blurred DTMs of attenuated high-frequency objects and emphasized low-frequency objects while it has achieved improved removal of non-ground object at larger window sizes. Focal analysis mean filter has shown better removal of nonground objects compared to Gaussian low pass filter especially at large window sizes where details of non-ground objects almost have diminished in the DTMs from window sizes of 25 × 25 and greater. DTM slope-based filter has created bare earth models that have been full of gabs at the positions of the non-ground objects where the sizes and numbers of that gabs have increased with increasing the window sizes of filter. Those gaps have been closed through exploitation of the spline interpolation method in order to get continuous surface representing bare earth landscape. Comparative analysis has shown that the minimum elevations of the DTMs increase with increasing the filter widow sizes till 21 × 21 and 31 × 31 for the Gaussian low pass filter and the focal analysis mean filter respectively. On the other hand, the DTM slope-based filter has kept the minimum elevation of the original data, that could be due to noise in the LiDAR data unchanged. Alternatively, the three approaches have produced DTMs of decreasing maximum elevation values and consequently decreasing ranges of elevations due to increases in the filter window sizes. Moreover, the standard deviations of the created DTMs from the three filters have decreased with increasing the filter window sizes however, the decreases have been continuous and steady in the cases of the Gaussian low pass filter and the focal analysis mean filters while in the case of the DTM slope-based filter the standard deviations of the created DTMs have decreased with high rates till window size of 31 × 31 then they have kept unchanged due to more increases in the filter window sizes.

Quasi-3D higher-order shear deformation theory for thermal buckling analysis of FGM plates based on a meshless method

This study introduces a new quasi-3D (three-dimensional) higher-order shear deformation theory (HSDT) capable of accounting for the through-thickness deformations with only four unknowns, which is suited to the numerical method for buckling analysis of functionally graded material (FGM) plates in thermal environments. The refined quasi-3D HSDT is incorporated into the improved meshless radial point interpolation method (RPIM) in order to scrutinize the thermal buckling responses of FGM plates. In the improved RPIM, the radial basis function is presented in a compactly supported form to build the shape functions without any fitting parameters. Parametric studies on the buckling behavior of FGM plates under various types of through-thickness temperature changes are conducted and the effects of temperature distribution on the plate surface are investigated. Results illustrate the accuracy of the proposed meshless method based on the refined quasi-3D HSDT and the improved RPIM for predicting the thermal buckling behavior of FGM plates.

Comparison of different interpolation methods, used for modelling of probe heads errors

Virtual CMMs allow user to estimate the uncertainty of measurement using multiple measurement simulations. Most often the Virtual CMMs consist of several modules responsible for main errors sources modelling. These modules utilizes different interpolation methods in order to model the error values in any point in machine’s measuring volume. Thus the proper functioning of Virtual CMM depends on chosen interpolation method. Experiment described in this paper is aimed to assess which interpolation method would give the best results for newly developed probe head errors model for the articulated probe heads.

A Comparative Study of Three Non-Geostatistical Methods for Optimising Digital Elevation Model Interpolation

It is common to generate digital elevation models (DEMs) from aerial laser scanning (ALS) data. However, cost and lack of knowledge may preclude its use. In contrast, global navigation satellite systems (GNSS) are seldom used to collect and generate DEMs. These receivers have the potential to be considered as data sources for DEM interpolation, as they can be inexpensive, easy to use, and mobile. The data interpolation method and spatial resolution from this method needs to be optimised to create accurate DEMs. Moreover, the density of GNSS data is likely to affect DEM accuracy. This study investigates three different deterministic approaches, in combination with spatial resolution and data thinning, to determine their combined effects on DEM accuracy. Digital elevation models were interpolated, with resolutions ranging from 0.5 m to 10 m using natural neighbour (NaN), topo to raster (ANUDEM), and inverse distance weighted (IDW) methods. The GNSS data were thinned by 25% (0.389 points m−2), 50% (0.259 points m−2), and 75% (0.129 points m−2) and resulting DEMs were contrast against a DEM interpolated from unthinned data (0.519 points m−2). Digital elevation model accuracy was measured by root mean square error (RMSE) and mean absolute error (MAE). It was found that the highest resolution, 0.5 m, produced the lowest errors in resulting DEMs (RMSE = 0.428 m, MAE = 0.274 m). The ANUDEM method yielded the greatest DEM accuracy from a quantitative perspective (RMSE = 0.305 m and MAE = 0.197 m); however, NaN produced a more visually appealing surface. In all the assessments, IDW showed the lowest accuracy. Thinning the input data by 25% and even 50% had relatively little impact on DEM quality; however, accuracy decreased markedly at 75% thinning (0.129 points m−2). This study showed that, in a time where ALS is commonly used to generate DEMs, GNSS-surveyed data can be used to create accurate DEMs. This study confirmed the need for optimization to choose the appropriate interpolation method and spatial resolution in order to produce a reliable DEM.

An updated full-discretization milling stability prediction method based on the higher-order Hermite-Newton interpolation polynomial

Chatter is undesirable self-excited vibrations, which always lead to adverse effects during milling process. Selecting a reasonable combination of cutting parameters is an effective way to avoid chatter. Based on the mathematical model of milling process and the Floquet theory, the stable cutting area can be determined. The stability lobe diagrams (SLD) could be obtained by different interpolation methods. To study the effect of higher order interpolation methods on the accuracy and efficiency of milling stability prediction, the state item, the time-delayed item, and the periodic-coefficient item of the state-space equation are approximated by different higher order interpolation methods, respectively. The calculations show that when the state item is approximated by the third-order Hermite interpolation polynomial, third-order Newton interpolation of the time-delayed item can improve the accuracy of SLD, while higher order interpolation of periodic-coefficient item has negative effect on improving effectiveness and efficiency compared to high-order interpolation of the state item and the time-delayed item. In order to obtain the SLD of milling process more accurately, an updated full-discretization milling stability prediction method which based on the third-order Hermite-Newton interpolation polynomial approximation is proposed in this paper. By dividing the tooth passing period equally into a finite set of time intervals, the third-order Hermite interpolation polynomial and the third-order Newton interpolation polynomial are utilized in each time interval to estimate the state item and the time-delayed item, respectively. The comparison of convergence rate of the critical eigenvalues and the SLD of the proposed method between the existing methods is carried out. The results indicate that the proposed method show a faster convergence rate than that of other methods, and its SLD is more close to the ideal ones with small number of time intervals.

Thermal Simulation of the Fresh Food Compartment in a Domestic Refrigerator

In the field of domestic refrigeration, it is important to look for methods that can be used to simulate, and, thus, improve the thermal behavior of the fresh food compartment. In this sense, this study proposes some methods to model the thermal behavior of this compartment when the shelves’ positions are changed. Temperature measurements at specific locations in this compartment were obtained. Several shelf position combinations were performed to use three 2D interpolation methods in order to simulate the temperature mean and the temperature variance. The methods used were: Lagrange’s interpolation, cubic spline interpolation and bilinear interpolation. Two validation points were chosen to verify the proposed methods. By comparing the experimental results with the computer simulations, it was possible to conclude that the method of Lagrange’s interpolation provided values that were not close to the real measured values. On the other hand, it was observed that the method of bilinear interpolation offered the best results, estimating values which were very close to the actual experimental measurements. These interpolation methods were used to build color thermal graphs that can be used to find some of the most appropriate shelf position combinations in this type of refrigerator. By inspection of these thermal graphs, it can be seen that the lowest average temperature was obtained when one shelf was located at 24.5 cm while the second shelf was located at 29.5 cm measured from the top of the compartment. In the same way, it can be seen that the minimum temperature variance was obtained when only one shelf was inside the compartment and this shelf was located at 29.5 cm.

Transient simulation of an electrical rotating machine achieved through model order reduction

Model order reduction (MOR) methods are more and more applied on many different fields of physics in order to reduce the number of unknowns and thus the computational time of large-scale systems. However, their application is quite recent in the field of computational electromagnetics. In the case of electrical machine, the numerical model has to take into account the nonlinear behaviour of ferromagnetic materials, motion of the rotor, circuit equations and mechanical coupling. In this context, we propose to apply the proper orthogonal decomposition combined with the (Discrete) empirical interpolation method in order to reduce the computation time required to study the start-up of an electrical machine until it reaches the steady state. An empirical offline/online approach based on electrical engineering is proposed in order to build an efficient reduced model accurate on the whole operating range. Finally, a 2D example of a synchronous machine is studied with a reduced model deduced from the proposed approach.

Wind Resource Mapping Using Landscape Roughness and Spatial Interpolation Methods

Energy saving, reduction of greenhouse gasses and increased use of renewables are key policies to achieve the European 2020 targets. In particular, distributed renewable energy sources, integrated with spatial planning, require novel methods to optimise supply and demand. In contrast with large scale wind turbines, small and medium wind turbines (SMWTs) have a less extensive impact on the use of space and the power system, nevertheless, a significant spatial footprint is still present and the need for good spatial planning is a necessity. To optimise the location of SMWTs, detailed knowledge of the spatial distribution of the average wind speed is essential, hence, in this article, wind measurements and roughness maps were used to create a reliable annual mean wind speed map of Flanders at 10 m above the Earth’s surface. Via roughness transformation, the surface wind speed measurements were converted into meso- and macroscale wind data. The data were further processed by using seven different spatial interpolation methods in order to develop regional wind resource maps. Based on statistical analysis, it was found that the transformation into mesoscale wind, in combination with Simple Kriging, was the most adequate method to create reliable maps for decision-making on optimal production sites for SMWTs in Flanders (Belgium).

The use of surface interpolation methods for landslides monitoring

The subject of this study is selection of mathematical description (interpolation method) of landslides surface for the purpose of periodic control of terrain movements. Monitoring of landslides, considered in this work, concerns points of periodic GPS or tacheometric measurements carried out in a relatively regular grid. For economic reasons, the grid usually consists of limited group of about several dozen of points that do not allow for an exact description of the terrain surface, nevertheless a general movement of a landslide can be detected (observed). Replacement of discrete set of points to a continuous surface model allows for a better assessment of the phenomenon especially within the scope of its main directions of activity. The choice of best performing interpolation method in order to construct a reliable numerical terrain model was performed through tests carried out on complex model surfaces. These model surfaces encompassed various configurations of terrain relief. In this study four interpolation methods i.e. splines, kriging triangulation with linear interpolation and IDW are compared. Tests on model surfaces distinguished the method of splines as the best performing one as well as the method of kriging which is suitable in some instances. The selected method of splines was then applied to periodically monitored landslide in Milowka in the south of Poland. Interpolation by means of splines allowed for observing progressive movements of the landslide surface with accuracy up to several millimeters. This confirms the usefulness and reliability of this method in landslides monitoring. Specialized field: Surveying & Geo-Spatial Engineering: Deformation Surveying.