Kriging Approach Research Articles

Augmenting Geostatistics with Matrix Factorization: A Case Study for House Price Estimation

Singular value decomposition (SVD) is ubiquitously used in recommendation systems to estimate and predict values based on latent features obtained through matrix factorization. But, oblivious of location information, SVD has limitations in predicting variables that have strong spatial autocorrelation, such as housing prices which strongly depend on spatial properties such as the neighborhood and school districts. In this work, we build an algorithm that integrates the latent feature learning capabilities of truncated SVD with kriging, which is called SVD-Regression Kriging (SVD-RK). In doing so, we address the problem of modeling and predicting spatially autocorrelated data for recommender engines using real estate housing prices by integrating spatial statistics. We also show that SVD-RK outperforms purely latent features based solutions as well as purely spatial approaches like Geographically Weighted Regression (GWR). Our proposed algorithm, SVD-RK, integrates the results of truncated SVD as an independent variable into a regression kriging approach. We show experimentally, that latent house price patterns learned using SVD are able to improve house price predictions of ordinary kriging in areas where house prices fluctuate locally. For areas where house prices are strongly spatially autocorrelated, evident by a house pricing variogram showing that the data can be mostly explained by spatial information only, we propose to feed the results of SVD into a geographically weighted regression model to outperform the orginary kriging approach.

Guided patchwork kriging to develop highly transferable thermal conductivity prediction models

The machine learning models developed on a dataset comprising particular class of materials show poor transferability across different classes. The problem can be partially solved by increasing the variability in the dataset at the cost of prediction accuracy. To develop a model on a highly variable database, we propose a localized regression based patchwork kriging approach for capturing most of the complex details in the data. In this approach, the data is partitioned into smaller regions with shared patches of few datapoints across the neighboring boundaries. Local regression functions are developed in each partition with a constrain to give similar performance at the boundary. Out of 17 different properties tried for partitioning the data, the decomposition with respect to target output κl gave local models with unprecedented accuracies. The partitioning with respect to κl, however, requires its estimate for any unknown compound beforehand. To address this, we developed a global model for the entire database. The global model accurately predicts the order of magnitude of κl for the compounds in the dataset and hence, directs them towards a particular partition for more accurate prediction. We define this stepwise approach as guided patchwork kriging, which can be applied to develop highly accurate transferable prediction models.

Probability-Adaptive Kriging in n-Ball (PAK-Bn) for reliability analysis

Complexity of today’s engineering systems inevitably makes the computational simulation of their performance challenging and time-consuming. Since structural reliability analysis methods generally repeat such computational simulations, it is essential to reduce the number of function evaluations required to achieve reliable estimates. In research efforts to fulfill this aim, adaptive Kriging methods have gained significant interest because of desirable properties and accuracy of the surrogate model. A new adaptive Kriging approach proposed in this paper improves the efficiency of reliability analysis by incorporating the probabilistic density of the random variable space into the adaptive procedure of identifying the surrogate limit-state surface. In addition, samples distributed uniformly inside the n-ball domain are used as the candidate points to enrich the experimental design, and the best candidate for simulation is determined in terms of influence on the failure probability estimation. The efficiency and accuracy of the proposed Probability-Adaptive Kriging in n-Ball (PAK-Bn) method are demonstrated by several reliability examples characterized by highly non-linear limit-state functions, small failure probability and multiple design points. The results confirm that the method facilitates convergence to the failure probability with a smaller number of function evaluations. The supporting source codes are available for download at https://github.com/Jungh0Kim/PAK-Bn.

Mapping occupational health risk factors in the primary sector—A novel supervised machine learning and Area-to-Point Poisson kriging approach

Workers around the world spend nearly a quarter of their time at work Occupational health is gaining great importance due to the profound impact on people long term health. The health status of the primary sector workforce is a great unknown for medical geography where health maps and spatial patterns have not been able to explain years of changing disease rates. This article proposes a new approach based on a solid characterization of the health status, which is the target node of an information theory-based Bayesian network machine-learnt from 13,000 medical examinations undertook to rural workers in Spain between 2012 and 2016. From the main health risks identified, a supervised binary logistic regression is used to produce a classification of adverse medical conditions giving rise to not healthy workers. Finally, Area-to-Point Poisson kriging is computed to provide a spatial analysis representing the incidence rate and spatial patterns of the main adverse medical conditions over the Spanish territory. The study illustrates how to overcome the challenges of working with discrete occupational data. Conceptually, high cholesterol and high glucose can be pinpointed with accuracy as the two main health risks for the working population in the primary sector.

Quantification of Spatial Variability of Soil Physical Properties in a Lesser Himalayan Sub-Basin of India

The quantification of spatial variability of soil properties is indispensable for evaluating the effectiveness of provisions undertaken to tackle various land surface processes like soil erosion, diffuse water pollution, etc. and is also essential for suggesting precise land management strategies. The present study was carried out in an urban sub-basin of lesser Himalayas, India, to appraise the spatial variability of soil textural fractions (sand, silt, and clay), bulk density (ρb), porosity (η) and saturated hydraulic conductivity (Ks). Using the Global positioning system (GPS) soil samples from 100 randomly selected locations were collected at an average depth of 25 cm under different land covers. Laboratory analysis was conducted to determine the soil physical properties. This was followed by statistical and geostatistical analysis for characterizing physical properties of soil and their spatial variability. The Coefficient of variation (CV) displayed moderate variability (0.14–0.36) for measured soil properties except for ρb which has low variability (CV = 0.08). The variability of soil physical properties under distinct land covers was determined by creating Box plots, and it was revealed that in general, shrubland has significantly lower Ks, ρb and sand content and higher η, silt and clay content than farmland and built-up land covers (P < 0.05) mainly due to lesser anthropogenic activities and continuous vegetal cover in shrub lands. The nugget to sill ratios for all the soil properties showed moderate to strong degree of spatial dependence. For mapping spatial variability of soil parameters, Ordinary Kriging (OK) approach of Geostatistical analysis was utilized revealing Spherical (Sand, ρb and η); Exponential (clay and Ks) and Gaussian (sand and silt) as the best fit models. Analysis by Moran’s I signified that about 1850 m sampling interval would be sufficient to detect spatial structure of soil physical properties. The generated spatial interpolation maps could serve as efficient tool for identifying land degradation spots in the study region and suggesting precise land management strategies.

Hydrological impacts of climate change on a data-scarce Greek catchment

This paper demonstrates a climate change impact study on the hydrological process of a data-scarce Greek watershed. The Soil and Water Assessment Tool (SWAT) and, particularly, the ArcSWAT interface was used for the watershed simulation. The ERA-Interim reanalysis climate data regarding the period from 1981 to 2000 were used for the historical simulation of the watershed. The ArcSWAT simulated data were evaluated against the observed discharge data for the periods with the available data. The statistical evaluation confirmed the ArcSWAT model’s capability in simulating the hydrological process of the research area. The climate change consequences on the hydrological components of the research area until the end of the twenty-first century were estimated by driving the ArcSWAT model with the Regional Climate Model Version 4 (RegCM4) forcing data under the extreme RCP 8.5 scenario, namely the simulations of the MPI and HadGEM2 general circulation models (GCMs), resulted from the spatio-temporal kriging approach. Based on the results, the increase in the minimum and the maximum temperature contributed to an increase in the actual evapotranspiration and the surface runoff. In contrast, the temperature increase caused a reduction in the infiltration. An increase (reduction) in the precipitation led to an increase (reduction) in the hydrological components. The climate change impact analysis of the Greek watershed showed that not only the precipitation changes but the temperature changes as well directly influence the water balance components of the research area and particularly the infiltration.

Gaussian process approach for dose mapping in radiation fields

In this work, a Gaussian Process (Kriging) approach is proposed to provide efficient dose mapping for complex radiation fields using limited number of responses. Given a few response measurements (or simulation data points), the proposed approach can help the analyst in completing a map of the radiation dose field with a 95% confidence interval, efficiently. Two case studies are used to validate the proposed approach. The First case study is based on experimental dose measurements to build the dose map in a radiation field induced by a D-D neutron generator. The second, is a simulation case study where the proposed approach is used to mimic Monte Carlo dose predictions in the radiation field using a limited number of MCNP simulations. Given the low computational cost of constructing Gaussian Process (GP) models, results indicate that the GP model can reasonably map the dose in the radiation field given a limited number of data measurements. Both case studies are performed on the nuclear engineering radiation laboratories at the University of Sharjah.

Spatio‐temporal prediction of land surface temperature using semantic kriging

AbstractSpatio‐temporal prediction and forecasting of land surface temperature (LST) are relevant. However, several factors limit their usage, such as missing pixels, line drops, and cloud cover in satellite images. Being measured close to the Earth's surface, LST is mainly influenced by the land use/land cover (LULC) distribution of the terrain. This article presents a spatio‐temporal interpolation method which semantically models LULC information for the analysis of LST. The proposed spatio‐temporal semantic kriging (ST‐SemK) approach is presented in two variants: non‐separable ST‐SemK (ST‐SemKNSep) and separable ST‐SemK (ST‐SemKSep). Empirical studies have been carried out with derived Landsat 7 ETM+ satellite images of LST for two spatial regions: Kolkata, India and Dallas, Texas, U.S. It has been observed that semantically enhanced spatio‐temporal modeling by ST‐SemK yields more accurate prediction results than spatio‐temporal ordinary kriging and other existing methods.

Modelling the spatial variability of Standard Penetration Test data for Chennai City using kriging and product-sum model

ABSTRACT Modelling the spatial variability of soil properties is very much essential in establishing the engineering parameters for the design and construction of geotechnical structures and facilities. The Standard Penetration Test (SPT) ‘N’ value of a location is widely used to determine the engineering properties of the soils through empirical correlations. In this study, a 3D site characterisation model is developed using ordinary and simple kriging with an objective of evaluating the spatial variability of corrected SPT ‘N’ (N corrected ) values in the subsurface of Chennai City. The alternative kriging approach using product-sum covariance model is implemented to model the SPT N corrected values in an anisotropic environment. The estimated SPT N corrected values are compared with the actual borehole data at selected locations. It is noted that the ordinary kriging has given more accurate estimates closer to the actual SPT N corrected values than the simple kriging. The estimated SPT N corrected values in the 3D subsurface environment will help in better interpretation of the subsurface information, making informed decisions with regard to future developmental activities and effective management of the urban centres of the Chennai City.

Nonlinear modelling of the dynamic response of pipe conveying fluid coated with FRP under seismic load: comparison of RSM and kriging approach

Nonlinear modelling of the dynamic response of pipe conveying fluid coated with FRP under seismic load: comparison of RSM and kriging approach

Spatial distribution and risk area assessment of Aphelenchoides besseyi using geostatistical approaches inGiridih district of Jharkhand, India.

Distributed widely across the rice growing regions of India, the rice leaf and bud nematode (Aphelenchoides besseyi Christie 1942) can cause substantial yield loss in rice. Whitening of leaf tips is the characteristics damage symptom of this nematode and therefore it is popularly referred to as the rice white tip nematode (RWTN). While information on the damage severity of RWTN is available from others parts of the country, to date, no information is available from the state of Jharkhand. In order to generate a detailed information on spatial distribution of this nematode and to identify infestation hotspots, extensive field sampling was conducted across the Giridih district of Jharkhand. In total, 163 samples with each sample consisting of 30 randomly chosen panicles from three nearby rice fields were collected across the district. Moran’s I spatial autocorrelation test confirmed the presence of significant spatial clustering among the sampling locations. Optimized hotspot analysis found the presence of one significant hotspot in Dumri block and cold spots in adjoining areas of Gawan, Tisri, and Dhanwar blocks. Spatial interpolation techniques like inverse distance weighting (IDW) and ordinary kriging (OK) were employed to predict the population density at unsampled locations. Both IDW and OK resulted into generation of similar kind of maps where population density was found to be higher in Dumri, Giridih, Bengabad and some other pockets of the district. Finally, indicator kriging approach was employed which resulted into identifying both risk and nematode free areas. In risk areas, where the probability of the population density exceeding the economic threshold limit is high, immediate quarantine measures should be taken to prevent further dissemination of contaminated seeds. Our study provided a scientifically based decision method to devise preventive and curative protection measures against A. besseyi, a neglected pest of quarantine significance of rice in India.

SPATIAL REPRESENTATION OF SURFACE WATER MONITORING AND ITS ASSESSMENT USING GEOSTATISTICAL AND NON-GEOSTATISTICAL TECHNIQUES IN GIS

Continuous monitoring of surface water is essential in terms of heavy metals investigation. Therefore, surface water quality is an environmental aspect which should be analyzed and monitored depending on its spatial distribution. The aim of this study is to provide an overview for evaluation of surface water pollution in the Mitrovica area by applying spatial distribution using Geographic Information System (GIS), geostatistical and non-geostatistical techniques. Nowadays, GIS with the geostatistics and non-geostatistics are very frequently used techniques in environmental monitoring studies. By providing the spatial distribution, there is possibility to place the pollution values in space. The surface water pollution caused by heavy metals (As, Cr, Cu, Ni, Pb, Zn and Cd) were sampled and analyzed from six monitoring stations in Sitnica river on different time series within three months countineously. The monitoring stations (samples) in Sitnica river were been distributed randomly. Pollution maps were produced using geostatistical and non-geostatistical (Spline and Kriging) approach. There were produced different pollution values in Sitnica river during the period of monitoring. Mainly the north part of Sitnica river has been poluted mostly with Heavy Metal Pollution Index (HPI) from 50 to 85 in the month of May, from 125 to 265 in the month of June and from 320 to 535 in the month of July. As well as the Metal Index (MI) from 0.60 to 2.05 in the month of May, June and July. The different statistical models were tested for geostatistical and non-geostatistical techniques in order to identify the best fitted technique for the pollution indices and the best interpolation techniques were selected on the basis of Mean Square Error (MSE), Mean Absolute Deviation (MAD), Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE). These statistical tested model have shown that the best fitted interpolation technique is Kriging because of the lowest values of MSE, MAD, RMSE, MAE and MAPE. In the study were involved statistical models such as correlation and regression, for showing the relation between time series datasets and interpolated pollution indices as well. The cartographic output derived from the study were raster maps (15m spatial resolution) which represent the spatial distribution of surface water pollution as a result of monitoring process on time series. It is our believe that the present study will be used as a reference study for further environmental investigation and monitoring in Mitrovica since.

Increment-averaged kriging: a comparison with depth-harmonized mapping of soil exchangeable sodium percentage in a cropping region of eastern Australia

Soil sodicity, generally measured through the exchangeable sodium percentage (ESP), is the most prevalent edaphic stress in Australia, particularly in the northern grains-growing region (NGR) of Australia. Farmers, scientists and policy-makers need accurate maps of sodicity for environmental modelling, and to make rational decisions for management. A common approach to mapping soil properties for multiple target depths is to first harmonize soil profile data to the target depth intervals, usually through equal-area spline functions, then undertake a two-dimensional spatial analysis (often regression kriging) for each interval; we refer to this as a ‘spline-then-krige’ (STK) approach. An alternative is to calibrate a single three-dimensional model that describes soil variation both horizontally and vertically, as is done in the increment-averaged kriging (IAK) approach. This study compares IAK and STK for mapping ESP in the NGR. A machine-learning algorithm was used to model trends based on environmental covariates in both approaches. Both IAK and STK captured the ESP variation reasonably well (concordance correlation coefficient values for IAK around 0.5 for all depths), with IAK giving slightly better predictive accuracies for all depths, most evidently in the topsoil. IAK allows the natural use of all available data, explicitly accounts for the sample support of the soil data and the horizontal and vertical auto-correlation between and within soil profiles, and enables the propagation of uncertainty from the original data through to the final predictions and prediction uncertainties. We conclude that IAK can provide a competitive alternative to STK approaches for mapping soil properties in three dimensions.

Modeling mesoscale energy localization in shocked HMX, Part II: training machine-learned surrogate models for void shape and void–void interaction effects

Surrogate models for hotspot ignition and growth rates were presented in Part I, where the hotspots were formed by the collapse of single cylindrical voids. Such isolated cylindrical voids are idealizations of the void morphology in real meso-structures. This paper therefore investigates the effect of non-cylindrical void shapes and void-void interactions on hotspot ignition and growth. Surrogate models capturing these effects are constructed using a Bayesian Kriging approach. The training data for machine learning the surrogates are derived from reactive void collapse simulations spanning the parameter space of void aspect ratio (AR), void orientation ($\theta$), and void fraction ($\phi$). The resulting surrogate models portray strong dependence of the ignition and growth rates on void aspect ratio and orientation, particularly when they are oriented at acute angles with respect to the imposed shock. The surrogate models for void interaction effects show significant changes in hotspot ignition and growth rates as the void fraction increases. The paper elucidates the physics of hotspot evolution in void fields due to the creation and interaction of multiple hotspots. The results from this work will be useful not only for constructing meso-informed macro-scale models of HMX, but also for understanding the physics of void-void interactions and sensitivity due to void shape and orientation.

A multiobjective stochastic simulation optimization algorithm

The use of kriging metamodels in simulation optimization has become increasingly popular during recent years. The majority of the algorithms so far uses the ordinary (deterministic) kriging approach for constructing the metamodel, assuming that solutions have been sampled with infinite precision. This is a major issue when the simulation problem is stochastic: ignoring the noise in the outcomes may not only lead to an inaccurate metamodel, but also to potential errors in identifying the optimal points among those sampled. Moreover, most algorithms so far have focused on single-objective problems. In this article, we test the performance of a multiobjective simulation optimization algorithm that contains two crucial elements: the search phase implements stochastic kriging to account for the inherent noise in the outputs when constructing the metamodel, and the accuracy phase uses a well-known multiobjective ranking and selection procedure in view of maximizing the probability of selecting the true Pareto-optimal points by allocating extra replications on competitive designs. We evaluate the impact of these elements on the search and identification effectiveness, for a set of test functions with different Pareto front geometries, and varying levels of heterogeneous noise. Our results show that the use of stochastic kriging is essential in improving the search efficiency; yet, the allocation procedure appears to lose effectiveness in settings with high noise. This emphasizes the need for further research on multiobjective ranking and selection methods.

A VS30 Map for New Zealand Based on Geologic and Terrain Proxy Variables and Field Measurements

A time-averaged 30-m-depth shear wave velocity ( V S30) map is developed for New Zealand as a weighted combination of a geology-based and a terrain-based model. A Bayesian updating process allows local V S30 measurements to control model estimates where data exist and uses model estimates developed for other parts of the world where local data are sparse or nonexistent. Geostatistical interpolation is performed on the geology-based and terrain-based models using local V S30 measurements to constrain the model in the vicinity of data. Conventional regression kriging is compared with a flexible multivariate normal (MVN) approach that allows for arbitrary assumptions regarding measurement uncertainty at each data location. A modification to the covariance structure in the MVN application allows for more realistic estimates by reducing undesirable extrapolation across geologic boundaries. The results of kriging and MVN approaches are compared. The geology-based and terrain-based MVN models are combined to produce a final model suitable for engineering applications. The 100-m resolution map outputs are publicly available.

A method to assess the impact of soil available water capacity uncertainty on crop models with a tipping‐bucket approach

AbstractMost agronomic crop models use a reservoir tipping‐bucket approach to model the water budget in the soil. Soil available water capacity (AWC) is the main soil property considered in this approach. Because AWC is difficult to measure, uncertainty in AWC may be high. We developed a method using a specific kriging technique to determine the effects of uncertainty in AWC on crop model predictions. The AqYield crop model was used as an example to assess the effects of uncertainty in AWC on two agronomic output variables (grain yield and drainage). The factors considered were the climatic region, crop type and soil depth. We assessed the results using the coefficient of variation (CV) and sets of critical values for which CV exceeded 5, 10 and 15%. The experiment provided insight into the criticality of AWC uncertainty over a wide range of agropedoclimatic situations according to crop, model and output of interest. The method revealed the greater effect of AWC uncertainty on both outputs for the spring crop than for the winter crop and identified cases where AWC uncertainty was critical. There was a stronger effect of AWC uncertainty on yield for shallow soil and climatic water deficit conditions. For each situation, the AWC uncertainty levels were determined above or below which the impact becomes significant on a given output because the sensitivity was very dependent on climate–crop–soil combinations. It was also observed that uncertainty in AWC had little effect in AqYield for a wide range of situations. The method developed uses a small number of model simulations to produce accurate results to better understand the impact of this major soil input data according to the target model and specific objectives. It could help to determine the level of accuracy needed in AWC measurement, depending on the objectives.Highlights The method quantifies the effects of AWC uncertainty on crop models with a tipping‐bucket approach. This method can assess the impact of uncertainty with only a few runs using a kriging approach. The method identifies critical situations for a wide range of agropedoclimatic conditions. Critical region graphs give critical thresholds for accuracy needed in AWC.

Spatio-temporal regression kriging for modelling urban NO2 concentrations

ABSTRACT Recently developed urban air quality sensor networks are used to monitor air pollutant concentrations at a fine spatial and temporal resolution. The measurements are however limited to point support. To obtain areal coverage in space and time, interpolation is required. A spatio-temporal regression kriging approach was applied to predict nitrogen dioxide (NO2) concentrations at unobserved space-time locations in the city of Eindhoven, the Netherlands. Prediction maps were created at 25 m spatial resolution and hourly temporal resolution. In regression kriging, the trend is separately modelled from autocorrelation in the residuals. The trend part of the model, consisting of a set of spatial and temporal covariates, was able to explain 49.2% of the spatio-temporal variability in NO2 concentrations in Eindhoven in November 2016. Spatio-temporal autocorrelation in the residuals was modelled by fitting a sum-metric spatio-temporal variogram model, adding smoothness to the prediction maps. The accuracy of the predictions was assessed using leave-one-out cross-validation, resulting in a Root Mean Square Error of 9.91 μg m−3, a Mean Error of −0.03 μg m−3 and a Mean Absolute Error of 7.29 μg m−3. The method allows for easy prediction and visualization of air pollutant concentrations and can be extended to a near real-time procedure.

Regional modeling of daily precipitation fields across the Great Lakes region (Canada) using the CFSR reanalysis

High densities of local-scale daily precipitation series across relatively large domains are of special interest for a wide range of applications (e.g., hydrological modeling, agriculture). The focus of the present study is to post-process gridded precipitation from a single reanalysis to correct bias and scale mismatch with observations, and to extend the same post-processing at sites without historical data. A Stochastic Model Output Statistical approach combined with meta-Gaussian spatiotemporal random fields, calibrated at sites, is employed to post-process the Climate Forecast System Reanalysis (CFSR) precipitation. The post-processed data, characterized by local parameters, is then mapped across the Great Lakes region (Canada) using two different approaches: (1) kriging, and (2) Vector Generalized Additive Model (VGAM) with spatial covariates. The kriging enables the interpolation of these parameters, while the spatial VGAM helps to spatially post-process CFSR precipitation using a single model. The k-fold cross-validation procedure is employed to assess the ability of the two approaches to predict selected characteristics and climate indices. The kriging and spatial VGAM approaches modeled effectively the distribution of the precipitation process to similar extents (e.g., mean daily precipitation, variability and the number of wet days). The kriging approach produces slightly better estimates of climate indices than the spatial VGAM models. Both approaches demonstrate significant improvement of the metric estimation compared to those of CFSR without post-processing.

Prediction of spatial functional random processes: comparing functional and spatio-temporal kriging approaches

We present and compare functional and spatio-temporal (Sp.T.) kriging approaches to predict spatial functional random processes (which can also be viewed as Sp.T. random processes). Comparisons with respect to computational time and prediction performance via functional cross-validation is evaluated, mainly through a simulation study but also on a real data set. We restrict comparisons to Sp.T. kriging versus ordinary kriging for functional data (OKFD), since the more flexible functional kriging approaches pointwise functional kriging (PWFK) and the functional kriging total model coincide with OKFD in several situations. Here we formulate conditions under which we show that OKFD and PWFK coincide. From the simulation study, it is concluded that the prediction performance of the two kriging approaches in general is rather equal for stationary Sp.T. processes. However, functional kriging tends to perform better for small sample sizes, while Sp.T. kriging works better for large sizes. For non-stationary Sp.T. processes, with a common deterministic time trend and/or time varying variances and dependence structure, OKFD performs better than Sp.T. kriging irrespective of the sample size. For all simulated cases, the computational time for OKFD was considerably lower compared to those for the Sp.T. kriging methods.