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In order to provide a theoretical basis for the precise finite element method (FEM) analysis of the long-range operation structural behavior of concrete faced rockfill dams (CFRDs), an improved creep model and the parameter spatial estimation method under digital construction were proposed. Creep characteristics of rockfill materials were studied by large-scale indoor triaxial creep test. The precision of traditional creep model was analyzed, and an improved model was proposed. The average fitting accuracy of the test results improved by 32.9% compared to the traditional model, which greatly improves the accuracy of creep characterization. Then, two models were applied for the FEM calculations of the dam under different porosities. The maximum relative difference of dam settlement brought by the two models was 60.6%. On this basis, the abnormal early warning curves of dam deformation and face deflection were proposed. Furthermore, the regression models between porosity and improved model parameters were established. Finally, the parameter spatial estimation of the improved model was achieved relying on the digital construction technology. This method takes into account the spatial variations of the mechanical parameters of dam materials, thus aligning more closely with the actual conditions. [ABSTRACT FROM AUTHOR]

Accurate spatial estimation of extremes is an increasingly important topic in environmental research and risk assessment. Conditional bias (CB)-penalized kriging (CBPK) improves such estimation by minimizing linearly weighted sum of error variance and variance of Type-II error. However, CBPK requires skillful prescription of the weight for the CB penalty which is a significant challenge in practice. In this paper, we describe an extension of CBPK, referred to herein as adaptive conditional bias-penalized kriging (ACBPK), which objectively prescribes the weight for improved estimation of extremes without deteriorating performance in the unconditional mean squared error sense. For comparative evaluation in the real world, cross validation experiments were carried out for precipitation estimation using hourly rain gauge data in the Arkansas-Red River Basin (AB), central Texas (TX) and southeastern US (SE) areas. The results show that CB is detected for about 26, 24 and 25% of all data points in the AB, TX and SE cases, respectively, and that, given detection of CB, ACBPK reduces root mean square error of hourly precipitation exceeding 12.7 mm by 15, 21 and 9% and hourly precipitation exceeding 25.4 mm by 14, 26 and 10% relative to ordinary kriging (OK) for the AB, TX and SE cases, respectively. The overall findings indicate that, if accurate spatial estimation in the tails of the distribution is important or accurate modeling of spatiotemporally-varying correlation structure is a challenge, ACBPK should be favored over OK. [ABSTRACT FROM AUTHOR]

In this study, we have developed a comprehensive machine learning (ML) framework for long-term groundwater contamination monitoring as the Python package PyLEnM (Python for Long-term Environmental Monitoring). PyLEnM aims to establish the seamless data-to-ML pipeline with various utility functions, such as quality assurance and quality control (QA/QC), coincident/colocated data identification, the automated ingestion and processing of publicly available spatial data layers, and novel data summarization/visualization. The key ML innovations include (1) time series/multianalyte clustering to find the well groups that have similar groundwater dynamics and to inform spatial interpolation and well optimization, (2) the automated model selection and parameter tuning, comparing multiple regression models for spatial interpolation, (3) the proxy-based spatial interpolation method by including spatial data layers or in situ measurable variables as predictors for contaminant concentrations and groundwater levels, and (4) the new well optimization algorithm to identify the most effective subset of wells for maintaining the spatial interpolation ability for long-term monitoring. We demonstrate our methodology using the monitoring data at the Savannah River Site F-Area. Through this open-source PyLEnM package, we aim to improve the transparency of data analytics at contaminated sites, empowering concerned citizens as well as improving public relations.

Air pollutants harm human health and the environment. Nowadays, deploying an air pollution monitoring network in many urban areas could provide real-time air quality assessment. However, these networks are usually sparsely distributed and the sensor calibration problems that may appear over time lead to missing and wrong measurements. There is an increasing interest in developing air quality modelling methods to minimize measurement errors, predict spatial and temporal air quality, and support more spatially-resolved health effect analysis. This research aims to evaluate the ability of three feed-forward neural network architectures for the spatial prediction of air pollutant concentrations using the measures of an air quality monitoring network. In addition to these architectures, Support Vector Machines and geostatistical methods (Inverse Distance Weighting and Ordinary Kriging) were also implemented to compare the performance of neural network models. The evaluation of the methods was performed using the historical values of seven air pollutants (Nitrogen monoxide, Nitrogen dioxide, Sulphur dioxide, Carbon monoxide, Ozone, and particulate matters with size less than or equal to 2.5 μ m and to 10 μ m) from an urban air quality monitoring network located at the metropolitan area of Madrid (Spain). To assess and compare the predictive ability of the models, three estimation accuracy indicators were calculated: the Root Mean Squared Error, the Mean Absolute Error, and the coefficient of determination. FFNN-based models are superior to geostatistical methods and slightly better than Support Vector Machines for fitting the spatial correlation of air pollutant measurements. [ABSTRACT FROM AUTHOR]

Dissolved oxygen is essential for all marine life, especially for benthic organisms that live on the seafloor and are unable to escape if oxygen concentrations fall below critical thresholds. Therefore, near-bottom oxygen concentrations are a key component of environmental assessments and are measured widely. To gain the full picture of hypoxic areas, spatial gaps between monitoring stations must be closed. Therefore, we applied two spatial interpolation methods, where estimated near-bottom oxygen concentrations were solely based on measurements. Furthermore, two variants of the machine learning algorithm Quantile Regression Forest were applied, and any uncertainties in the results were evaluated. All geostatistical methods were evaluated for one year and over a longer period, showing that Quantile Regression Forest methods achieved better results for both. Afterward, all geostatistical methods were applied to estimate the areas below different critical oxygen thresholds from 1950 to 2019 to compute oxygen-deficient areas and how they changed when faced with anthropogenic pressures, especially in terms of increased nutrient inputs. [ABSTRACT FROM AUTHOR]

We present a scheme aimed at estimating daily spatial snow water equivalent (SWE) maps in real time and at high spatial resolution from scarce in-situ SWE measurements from Internet of Things (IoT) devices at actual sensor locations and historical SWE maps. The method consists of finding a background SWE field, followed by an update step using ensemble optimal interpolation to estimate the residuals. This novel approach allowed for areas with parsimonious sensors to have accurate estimates of spatial SWE without explicitly discovering and specifying the spatial-interpolation features. The scheme is evaluated across the Tuolumne River basin on a 50 m grid using an existing LiDAR-based product as the historical dataset. Results show a minimum RMSE of 30% at 50 m resolutions. Compared with the operational SNODAS product, reduction in error is up to 80% with historical LiDAR-measured snow depth as input data.

Precipitation patterns are vital to water resource management and hydrological research, especially in the upper reaches of inland rivers in arid and semiarid areas. However, estimating spatiotemporal precipitation patterns at a basin scale is challenging due to limited observations. In this study, spatiotemporal patterns of precipitation amount, frequency, duration, and intensity at different time scales from 2014 to 2019 are estimated using the Bayesian maximum entropy method in the Tianlaochi catchment of the Heihe River watershed, northwest China. The study's results show that the annual average precipitation amount was 535.9 mm from 2014 to 2019, with precipitation amount between May and September accounting for 85.9% of the annual precipitation amount. For daily precipitation, the average frequency rate of light precipitation is highest at 59.55%, however, the average contribution rate of moderate precipitation is highest at 50.33%. The spatial distribution of precipitation is characterized by high-value areas concentrated in the central valley and low-value areas located at the catchment's outlet. The most important driving factors of precipitation patterns are elevation, relative humidity, and wind direction. These outcomes can be used to establish accurate hydrological models in the catchment and provide support for water resource management in the Heihe River watershed.

Accurate mapping of farmland soil organic carbon (SOC) provides valuable information for evaluating soil quality and guiding agricultural management. The integration of natural factors, agricultural activities, and landscape patterns may well fit the high spatial variation of SOC in low-relief farmlands. However, commonly used prediction methods are global models, ignoring the stratified heterogeneous relationship between SOC and environmental variables and failing to reveal the determinants of SOC in different subregions. Using 242 topsoil samples collected from Jianghan Plain, China, this study explored the stratified heterogeneous relationship between SOC and natural factors, agricultural activities, and landscape metrics, determined the dominant factors of SOC in each stratum, and predicted the spatial distribution of SOC using the Cubist model. Ordinary kriging, stepwise linear regression (SLR), and random forest (RF) were used as references. SLR and RF results showed that land use types, multiple cropping index, straw return, and percentage of water bodies are global dominant factors of SOC. Cubist results exhibited that the dominant factors of SOC vary in different cropping systems. Compared with the SOC of paddy fields, the SOC of irrigated land was more affected by irrigation-related factors. The effect of straw return on SOC was diverse under different cropping intensities. The Cubist model outperformed the other models in explaining SOC variation and SOC mapping (fitting R2 = 0.370 and predicted R2 = 0.474). These results highlight the importance of exploring the stratified heterogeneous relationship between SOC and covariates, and this knowledge provides a scientific basis for farmland zoning management. The Cubist model, integrating natural factors, agricultural activities, and landscape metrics, is effective in explaining SOC variation and mapping SOC in low-relief farmlands. [ABSTRACT FROM AUTHOR]

Geostatistical estimation methods rely on experimental variograms that are mostly erratic, leading to subjective model fitting and assuming normal distribution during conditional simulations. In contrast, Machine Learning Algorithms (MLA) are (1) free of such limitations, (2) can incorporate information from multiple sources and therefore emerge with increasing interest in real-time resource estimation and automation. However, MLAs need to be explored for robust learning of phenomena, better accuracy, and computational efficiency. This paper compares MLAs, i.e., Multiple Linear Regression (MLR) and Random Forest (RF), with Ordinary Kriging (OK). The techniques were applied to the publicly available Walkerlake dataset, while the exhaustive Walker Lake dataset was validated. The results of MLR were significant (p < 10 × 10−5), with correlation coefficients of 0.81 (R-square = 0.65) compared to 0.79 (R-square = 0.62) from the RF and OK methods. Additionally, MLR was automated (free from an intermediary step of variogram modelling as in OK), produced unbiased estimates, identified key samples representing different zones, and had higher computational efficiency. [ABSTRACT FROM AUTHOR]

Data on human brain function obtained with direct electrical stimulation (DES) in neurosurgical patients have been recently integrated and combined with modern neuroimaging techniques, allowing a connectome-based approach fed by intraoperative DES data. Within this framework is crucial to develop reliable methods for spatial localization of DES-derived information to be integrated within the neuroimaging workflow. To this aim, we applied the Kernel Density Estimation for modelling the distribution of DES sites from different patients into the MNI space. The algorithm has been embedded in a MATLAB-based User Interface, Peaglet. It allows an accurate probabilistic weighted and unweighted estimation of DES sites location both at cortical level, by using shortest path calculation along the brain 3D geometric topology, and subcortical level, by using a volume-based approach. We applied Peaglet to investigate spatial estimation of cortical and subcortical stimulation sites provided by recent brain tumour studies. The resulting NIfTI maps have been anatomically investigated with neuroimaging open-source tools. Peaglet processes differently cortical and subcortical data following their distinguishing geometrical features, increasing anatomical specificity of DES-related results and their reliability within neuroimaging environments. Peaglet provides a robust probabilistic estimation of the cortical and subcortical distribution of DES sites going beyond a region of interest approach, respecting cortical and subcortical intrinsic geometrical features. Results can be easily integrated within the neuroimaging workflow to drive connectomic analysis. • Peaglet is a matlab software allowing a spatial estimation of stimulation sites in the MNI space. • Dedicated cortical and subcortical analysis can be applied for spatial estimation. • Peaglet results can be visualised and inspected with common open-source software. • Peaglet results can be used to build ROIs to drive neuroimaging analysis. [ABSTRACT FROM AUTHOR]

Mineral resource estimation is an integral part of making informed decisions while evaluating a mining operation's feasibility. Geostatistical tools estimate geological features with the assumptions of first and second-order stationarity. Kriging is considered the best linear unbiased estimation technique for modelling geological features; however, in domains where data is non-Gaussian, and features are complex, the assumption of stationarity and the linearity of kriging can lead to suboptimal estimates. This manuscript presents a hybrid machine learning and geostatistical algorithm to improve estimation in complex domains. Elliptical radial basis function neural networks (ERBFN) take advantage of non-stationary functions to generate geological estimates. An ERBFN does not require the assumption of stationarity, and the only input features required are the spatial coordinates of the known data. The proposed hybrid estimation considers the machine learning estimate as exhaustive secondary data in ordinary intrinsic collocated cokriging, taking advantage of kriging's exactitude while including the non-stationary features modelled in the ERBFN. The principle results of integrating geostatistics and machine learning indicate an improved estimation technique in domains with complex features, poorly defined domains, or non-Gaussian data. The major conclusion from this paper is that using the proposed hybrid algorithm can improve mineral resource estimations. [ABSTRACT FROM AUTHOR]

A growing number of studies in the spatial estimation of geological features use machine learning (ML) models, as these models promise to provide efficient solutions for estimation especially in non-Gaussian, non-stationary and complex cases. However, these models have two major limitations: (1) the data are considered to be independent and identically distributed (or spatially uncorrelated), and (2) the data are not reproduced at their locations. Kriging, on the other hand, has a long history of generating unbiased estimates with minimum error variance at unsampled locations. Kriging assumes stationarity and linearity. This study proposes a methodology that combines kriging and ML models to mitigate the disadvantages of each method and obtain more accurate estimates. In the proposed methodology, a stacked ensemble model, which is also referred to as the super learner (SL) model, is applied for ML modeling. We have shown how the estimates generated by the SL model and estimates obtained from kriging can be combined through a weighting function based on a kriging variance. The weights are optimized using the sequential quadratic programming. The proposed methodology is demonstrated in two synthetic case studies containing data with non-stationarity and non-Gaussian features; a real case study using a dataset from an oilsands deposit is also presented. The performance of the combined model is compared with the SL model and kriging using the coefficient of determination (R-squared), root mean squared error, and mean absolute error criteria. The combined model appears to yield more accurate estimates than the ones generated by SL model and kriging in all cases. [ABSTRACT FROM AUTHOR]

Precipitation patterns are vital to water resource management and hydrological research, especially in the upper reaches of inland rivers in arid and semiarid areas. However, estimating spatiotemporal precipitation patterns at a basin scale is challenging due to limited observations. In this study, spatiotemporal patterns of precipitation amount, frequency, duration, and intensity at different time scales from 2014 to 2019 are estimated using the Bayesian maximum entropy method in the Tianlaochi catchment of the Heihe River watershed, northwest China. The study's results show that the annual average precipitation amount was 535.9 mm from 2014 to 2019, with precipitation amount between May and September accounting for 85.9% of the annual precipitation amount. For daily precipitation, the average frequency rate of light precipitation is highest at 59.55%, however, the average contribution rate of moderate precipitation is highest at 50.33%. The spatial distribution of precipitation is characterized by high-value areas concentrated in the central valley and low-value areas located at the catchment's outlet. The most important driving factors of precipitation patterns are elevation, relative humidity, and wind direction. These outcomes can be used to establish accurate hydrological models in the catchment and provide support for water resource management in the Heihe River watershed. [ABSTRACT FROM AUTHOR]

ABSTRACT Spatial variability description of soil chemical properties by thematic maps depends substantially on suitable geostatistical models. One of the parameters composing a geostatistical model is nugget effect. This study aimed to evaluate the simultaneous influence of nugget effect and sampling design on geostatistical model estimation and estimation of soil chemical properties at unsampled sites, considering simulated data. Our results will be used as scientific basis for spatial variability analyses of soil chemical properties in agricultural areas. Given the simulation results and agricultural data, we concluded that the high nugget effect values obtained here reduced spatial estimation efficiency. Moreover, a systematic sampling design promoted the least accurate estimates of geostatistical model and at non-sampled sites. Despite that, these nugget effect estimates should be kept in the analysis. However, further studies will be needed to investigate which factors are responsible for such high nugget effect values.

Multiple groups of triaxial shear tests and creep tests were performed on rockfill materials, stress–strain, volume-strain, volumetric creep-time and axial creep-time curves were obtained under different porosity levels. Based on the analysis of the test results, the improved Shen Zhujiang double yield surface elastic–plastic model and the improved creep model were proposed for deformation prediction with higher accuracy, and they were incorporated into the calculation program for concrete face rockfill dams (CFRDs) by program development. Afterward, the regression models were established between the porosity and the parameters of the improved models, which offer quick derivation of the model parameters by porosity under the condition that lithology and gradation are basically the same. Furthermore, relying on digital construction technology, the spatial distributions of model parameters within the entire dam were estimated. Finally, a set of improved model parameters reflecting actual construction quality was assigned to an element, and the refined finite element method (FEM) numerical simulation of the long-term deformation of the CFRD considering the actual construction quality was realized. The engineering example shows that the proposed method can greatly improve the simulation accuracy of the long-term service behavior of the CFRDs. [ABSTRACT FROM AUTHOR]

Most studies on how people perceive a given quantity of items were conducted with visual cues exclusively and only offered spatial area based explanations, such as spatial estimation and perceptual grouping theories. This article establishes how people perceive a given quantity when only a written description is provided without any visual cues. Across two studies we show that variety decreases perceived quantity when a variety cue is given, while variety increases perceived quantity when a visual cue is not given. This is because people tend to rely heavily on spatial areas when a visual cue is present and because people are prone to confirmation bias when they are provided with no visual cues but only written descriptions. Furthermore, we highlight that quantity perception has a mediation effect on consumers’ attitude―the intention to participate in sales promotional events. Lastly, we summarize the article and discuss its contributions, implications, limitations, and suggestions for future research.

Geostatistical estimation methods rely on experimental variograms that are mostly erratic, leading to subjective model fitting and assuming normal distribution during conditional simulations. In contrast, Machine Learning Algorithms (MLA) are (1) free of such limitations, (2) can incorporate information from multiple sources and therefore emerge with increasing interest in real-time resource estimation and automation. However, MLAs need to be explored for robust learning of phenomena, better accuracy, and computational efficiency. This paper compares MLAs, i.e., Multiple Linear Regression (MLR) and Random Forest (RF), with Ordinary Kriging (OK). The techniques were applied to the publicly available Walkerlake dataset, while the exhaustive Walker Lake dataset was validated. The results of MLR were significant (p < 10 × 10−5), with correlation coefficients of 0.81 (R-square = 0.65) compared to 0.79 (R-square = 0.62) from the RF and OK methods. Additionally, MLR was automated (free from an intermediary step of variogram modelling as in OK), produced unbiased estimates, identified key samples representing different zones, and had higher computational efficiency.

Accurate mapping of farmland soil organic carbon (SOC) provides valuable information for evaluating soil quality and guiding agricultural management. The integration of natural factors, agricultural activities, and landscape patterns may well fit the high spatial variation of SOC in low-relief farmlands. However, commonly used prediction methods are global models, ignoring the stratified heterogeneous relationship between SOC and environmental variables and failing to reveal the determinants of SOC in different subregions. Using 242 topsoil samples collected from Jianghan Plain, China, this study explored the stratified heterogeneous relationship between SOC and natural factors, agricultural activities, and landscape metrics, determined the dominant factors of SOC in each stratum, and predicted the spatial distribution of SOC using the Cubist model. Ordinary kriging, stepwise linear regression (SLR), and random forest (RF) were used as references. SLR and RF results showed that land use types, multiple cropping index, straw return, and percentage of water bodies are global dominant factors of SOC. Cubist results exhibited that the dominant factors of SOC vary in different cropping systems. Compared with the SOC of paddy fields, the SOC of irrigated land was more affected by irrigation-related factors. The effect of straw return on SOC was diverse under different cropping intensities. The Cubist model outperformed the other models in explaining SOC variation and SOC mapping (fitting R2 = 0.370 and predicted R2 = 0.474). These results highlight the importance of exploring the stratified heterogeneous relationship between SOC and covariates, and this knowledge provides a scientific basis for farmland zoning management. The Cubist model, integrating natural factors, agricultural activities, and landscape metrics, is effective in explaining SOC variation and mapping SOC in low-relief farmlands.

Machine learning (ML) models provide useful tools to generate spatial estimations of geological features, but they do not consider the spatial dependence among the observations and they primarily use coordinates as predictors. Thus, many ML models produce visible artifacts in the resulting estimates along the coordinate directions. To overcome this significant problem, this paper presents an ensemble super learner (ESL) model which uses the super learner (SL) model as the ML model. In the ESL model, numerous training sets are created from the original dataset by a coordinate rotation strategy and then the estimates obtained from the fitted SL models are ensembled to produce a final estimate. A dataset from a high-grade gold deposit demonstrates the approach and compares the results to kriging and the SL model. The results demonstrate that the ESL model manages artifacts in ML spatial estimation. It also provides better results than the kriging and SL model in terms of estimation accuracy. [ABSTRACT FROM AUTHOR]

Spatial predictions of forest variables are required for supporting modern national and sub-national forest planning strategies, especially in the framework of a climate change scenario. Nowadays methods for constructing wall-to-wall maps and calculating small-area estimates of forest parameters are becoming essential components of most advanced National Forest Inventory (NFI) programs. Such methods are based on the assumption of a relationship between the forest variables and predictor variables that are available for the entire forest area. Many commonly used predictors are based on data obtained from active or passive remote sensing technologies. Italy has almost 40% of its land area covered by forests. Because of the great diversity of Italian forests with respect to composition, structure and management and underlying climatic, morphological and soil conditions, a relevant question is whether methods successfully used in less complex temperate and boreal forests may be applied successfully at country level in Italy.For a study area of more than 48,657 km2 in central Italy of which 43% is covered by forest, the study presents the results of a test regarding wall-to-wall, spatially explicit estimation of forest growing stock volume (GSV) based on field measurement of 1350 plots during the last Italian NFI. For the same area, we used potential predictor variables that are available across the whole of Italy: cloud-free mosaics of multispectral optical satellite imagery (Landsat 5 TM), microwave sensor data (JAXA PALSAR), a canopy height model (CHM) from satellite LiDAR, and auxiliary variables from climate, temperature and precipitation maps, soil maps, and a digital terrain model.Two non-parametric (random forests and k-NN) and two parametric (multiple linear regression and geographically weighted regression) prediction methods were tested to produce wall-to-wall map of growing stock volume at 23-m resolution. Pixel level predictions were used to produce small-area, province-level model-assisted estimates. The performances of all the methods were compared in terms of percent root mean-square error using a leave-one-out procedure and an independent dataset was used for validation. Results were comparable to those available for other ecological regions using similar predictors, but random forests produced the most accurate results with a pixel level R2 = 0.69 and RMSE% = 37.2% against the independent validation dataset. Model-assisted estimates were more precise than the original design-based estimates provided by the NFI.

Performance of artificial neural network modeling and Kriging interpolation in PM2.5 concentration estimation varies with sample sizes and predictor variables change. This paper analyzes the performance of ordinary Kriging (OK), radical basis function (RBF) networks based on geographic coordinates, CoKriging and RBF with the key factor(s) (CK and CoRBF) selected by correlation analysis and RBF network, using different training sets with various sizes. The spatial distribution of PM2.5 concentration is then estimated by the best performed method. Results show that RBF, CoRBF, OK, and CK can all be used to estimate PM2.5 concentration efficiently, and their accuracies improved unstably as the number of training sites increase. CoRBF with the key factor of population illustrates the largest variation of PM2.5 concentration, while CK has the highest coefficient of determination (R² ) and index of agreement (IOA) and the lowest mean square error (MSE), mean absolute error (MAE), and relative error (RE). Correspondingly, the spatial pattern of CK estimated PM2.5 concentration is smoother than CoRBF estimated PM2.5 concentration, while they both are very similar to site measurements and reveal detailed information. [ABSTRACT FROM AUTHOR]

Finding accurate methods for estimating and mapping land prices at the macro-scale based on publicly accessible and low-cost spatial data is an essential step in producing a meaningful reference for regional planners. This asset would assist them in making economically justified decisions in favor of key investors for development projects and post-disaster recovery efforts. Since 2005, the Ministry of Land, Infrastructure, and Transport of Japan has made land price data open to the public in the form of observations at dispersed locations. Although this data is useful, it does not provide complete information at every site for all market participants. Therefore, estimating and mapping land prices based on sound statistical theories is required. This paper presents a comparative study of spatial prediction of land prices in 2015 in Fukushima prefecture based on geostatistical methods and machine learning algorithms. Land use, elevation, and socioeconomic factors, including population density and distance to railway stations, were used for modeling. Results show the superiority of the random forest algorithm. Overall, land prices are distributed unevenly across the prefecture with the most expensive land located in the western region characterized by flat topography and the availability of well-connected and highly dense economic hotspots. [ABSTRACT FROM AUTHOR]

Spatial variable estimation is a basic application of geostatistics. In general, this task is performed based on observations of limited points. For some cases, intensive observed data obtained from other sources are also available as the auxiliary variables. To utilize the auxiliary information in these data, methods such as regression kriging (RK) or cokriging are proposed. However, these methods all assume that the auxiliary variables keep linear correlation with the target variable implicitly, which is not satisfied in most cases. In this letter, through the combination of nonlinear machine learning mapping (MLM), we propose a novel hybrid method to relax the linear assumption of RK. The proposed method is applied to a real-world subsurface shale volume estimation task for demonstration. Compared with existing methods such as ordinary kriging, RK, and MLM, the relative estimation error reduction of the proposed method is larger than 10%. Meanwhile, the estimation resolution is also improved. This indicates that the proposed method provides an alternative way for further spatial variable estimation practices. [ABSTRACT FROM AUTHOR]

Dissolved oxygen (DO) is a direct indicator of water pollution and an important water quality parameter that affects aquatic life. Based on the fundamental theorem of surfaces in differential geometry, the present study proposes a new modeling approach to estimate DO concentrations with high accuracy by assessing the spatial correlation and heterogeneity of DO with respect to explanatory variables. Specifically, a regularization penalty term is integrated into the high-accuracy surface modeling (HASM) method by applying geographically weighted regression (GWR) with some covariates. A modified version of HASM, namely HASM_MOD, is illustrated through a case study of Poyang Lake, China, by comparing the results of HASM, a support vector machine (SVM), and cokriging. The results indicate that HASM_MOD yields the best performance, with a mean absolute error (MAE) that is 38%, 45%, and 42% lower than those of HASM, the SVM, and cokriging, respectively, by using the cross-validation method. The introduction of a regularization penalty term by using GWR with respect to covariates can effectively improve the quality of the DO estimates. The results also suggest that HASM_MOD is able to effectively estimate nonlinear and nonstationary time series and outperforms three other methods using cross-validation, with a root-mean-square error (RMSE) of 0.20 mg/L and R2 of 0.93 for the two study sites (Sanshan and Outlet_A stations). The proposed method, HASM_MOD, provides a new way to estimate the DO concentration with high accuracy.

Highlights • A hybrid predictive model was designed to model soil electrical conductivity. • The proposed model integrated the multilayer perceptron with Firefly Algorithm. • The MLP-FFA model performance was compared with the MLP and ordinary kriging models. • The hybrid model estimated EC more accurately than the MLP and OK models. • There was no significant difference between the results of standalone MLP and OK. Abstract Expert systems adopted to support modern and rapidly advancing proximal soil sensing technologies can help generate accurately modelled electrical conductivity, as a decision-support parameter defining soil health in terms of the salinity, clay and bulk density compositions, among the other primal soil properties. Electrical conductivity (EC) is expected to correlate with the pertinent factors that regulate the crop yield (i.e., soil texture, cation exchange, drainage conditions, organic matter level, salinity, and the subsoil characteristics), which in turn, can also acts to control the overall health of the crop. Utilizing a fast and efficient artificial intelligence approach, this study designs a hybrid predictive model integrating multilayer perceptron with the Firefly Algorithm (MLP-FFA), and then evaluates its performance in respect to the standalone MLP and the ordinary kriging (OK) model applied in agricultural locality of the Soofiyan, plains in Tabriz, northwest of Iran. To develop a spatial modelling framework, 126 distinct measurements of EC were obtained through a grid sampled at 1000 m × 1000 m spacing, partitioned in training (88) and testing (38) sets. Applying a ratio of nugget to sill to determine the spatial dependence, a spatial modelling strategy was utilized where the spherical, exponential, Gaussian and linear semi-variograms depicting the autocorrelation of the sampled points (latitude × longitude) over the study area were analyzed in ArcGIS to deduce the optimal data characteristics and the respective statistical model. Spherical semi-variogram was the optimal representor for EC, relative to its latitude and longitude, in agreement with the lowest Residual Sums of Squares (RSS) and the highest coefficient of determination (R 2). Hybrid MLP-FFA and standalone MLP models were thus developed with latitude, longitude and measured electrical conductivity in the training set and evaluated in respect to the OK method by means of statistical scores: root mean square error (RMSE), mean absolute error (MAE) including the normalized metrics represented by Willmott's Index (WI), Nash Sutcliffe's coefficient (E NS) and Legates & McCabe's Index (E LM). Verified by diagnostic plots and grid-averaged metrics, the results revealed that the hybrid MLP-FFA model performed significantly better than both comparative models, with WI = 0.780 relative to 0.637 (MLP) and 0.714 (OK) models and E NS = 0.725 (vs. 0.511 & 0.589) and E LM = 0.552 (vs. 0.402 & 0.413), respectively. Expanded uncertainty, t -statistic and global performance indicators combining the R 2, RMSE and mean bias error and a Taylor plot also confirmed the efficacy of the hybrid MLP-FFA over the standalone MLP and OK model. There was no significant difference between the results of standalone MLP and OK when evaluated through spatial trend maps, while the hybrid MLP-FFA model exhibited a better ability to establishing nonlinear relationships with electrical conductivity data, resulting in a better representation of the spatially modelled EC. Our results ascertain the prodigious performance of a hybrid MLP-FFA over a standalone MLP and ordinary kriging approaches, attributable to a better utility of the Firefly algorithm in improved spatial estimation of electrical conductivity. This study concludes that the hybrid MLP-FFA model should be explored to solve practical problems in soil physics, particularly in designing decision-support systems to attain agricultural precision. [ABSTRACT FROM AUTHOR]

Abstract In this study, data collected from an urban air quality monitoring network are being used for the purpose of evaluating various methodologies used for spatial interpolation in the context of proposing an effective yet simple to apply scheme for PM spatial point estimations. The examined methods are the Inverse Distance Weighting, two linear regression models, the Multiple Linear Regression and the Linear Mixed Model, along with a Feed Forward Neural Network (FFNN) model. These schemes utilize daily PM 10 and PM 2.5 concentrations collected from five and three air quality monitoring sites respectively. In order to obtain the resulted estimations, the leave-one-out cross-validation methodology is used for all methods. The evaluation of their predictive ability is performed by using a combination of difference and correlation statistical measures, scatter plots and statistical tests. The results indicate the usefulness of FFNNs as they are found to be statistically significantly superior for modelling the particulate matter spatial variability. The model performance statistics show that in most cases the error values are considerably lower for the FFNN model. Additionally, the rank and Wilcoxon rank tests reveal that the null hypothesis for equal predictive accuracy is rejected for the majority of monitoring sites and schemes (values lower than the critical t-value). According to the comparison results, the FFNN model is selected for forecasting air quality limit exceedances set by the European Union and World Health Organization air quality standards. For two monitoring sites in which the largest number of exceedances occurred, the probability of detection is high while the probability of false detection is very low, further establishing the neural networks' predictive ability. Graphical abstract Image 1 Highlights • The modeling of PM spatial variability requires advanced nonlinear approaches. • FFNN are significantly statistical superior compared to LMEM, IDW and MLR models. • FFNNs can predict accurately the PM concentration limit exceedances. • FFNNs can be used operationally for data imputation problems. Feed Forward Neural Network models can be used effectively in spatial forecasting of particulate matter concentrations and their limit exceedances, thus providing valuable information for human health protection measures. [ABSTRACT FROM AUTHOR]

Information about forest cover and its characteristics are essential in national and international forest inventories, monitoring programs, and reporting activities. Two of the most common forest variables needed to support sustainable forest management practices are forest cover area and growing stock volume (GSV m3 ha−1). Nowadays, national forest inventories (NFI) are complemented by wall-to-wall maps of forest variables which rely on models and auxiliary data. The spatially explicit prediction of GSV is useful for small-scale estimation by aggregating individual pixel predictions in a model-assisted framework. Spatial knowledge of the area of forest land is an essential prerequisite. This information is contained in a forest mask (FM). The number of FMs is increasing exponentially thanks to the wide availability of free auxiliary data, creating doubts about which is best-suited for specific purposes such as forest area and GSV estimation. We compared five FMs available for the entire area of Italy to examine their effects on the estimation of GSV and to clarify which product is best-suited for this purpose. The FMs considered were a mosaic of local forest maps produced by the Italian regional forest authorities; the FM produced from the Copernicus Land Monitoring System; the JAXA global FM; the hybrid global FM produced by Schepaschencko et al., and the FM estimated from the Corine Land Cover 2006. We used the five FMs to mask out non-forest pixels from a national wall-to-wall GSV map constructed using inventory and remotely sensed data. The accuracies of the FMs were first evaluated against an independent dataset of 1,202,818 NFI plots using four accuracy metrics. For each of the five masked GSV maps, the pixel-level predictions for the masked GSV map were used to calculate national and regional-level model-assisted estimates. The masked GSV maps were compared with respect to the coefficient of correlation (ρ) between the estimates of GSV they produced (both in terms of mean and total of GSV predictions within the national and regional boundaries) and the official NFI estimates. At the national and regional levels, the model-assisted GSV estimates based on the GSV map masked by the FM constructed as a mosaic of local forest maps were closest to the official NFI estimates with ρ = 0.986 and ρ = 0.972, for total and mean GSV, respectively. We found a negative correlation between the accuracies of the FMs and the differences between the model-assisted GSV estimates and the NFI estimate, demonstrating that the choice of the FM plays an important role in GSV estimation when using the model-assisted estimator.

With the development of machine learning technology, research cases for spatial estimation through machine learning approach (MLA) in addition to the traditional geostatistical techniques are increasing. MLA has the advantage that spatial estimation is possible without stationary hypotheses of data, but it is possible for the prediction results to ignore spatial autocorrelation. In recent studies, it was considered by using a distance matrix instead of raw coordinates. Although, the performance of spatial estimation could be improved through this approach, the computational complexity of MLA increased rapidly as the number of sample points increased. In this study, we developed a method to reduce the computational complexity of MLA while considering spatial autocorrelation. Principal component analysis is applied to it for extracting spatial features and reducing dimension of inputs. To verify the proposed approach, indicator Kriging was used as a benchmark model, and each performance of MLA was compared when using raw coordinates, distance vector, and spatial features extracted from distance vector as inputs. The proposed approach improved the performance compared to previous MLA and showed similar performance compared with Kriging. We confirmed that extracted features have characteristics of rigid classification in spatial estimation; on this basis, we conclude that the model could improve performance.

We present a scheme aimed at estimating daily spatial snow water equivalent (SWE) maps in real time and at high spatial resolution from scarce in-situ SWE measurements from Internet of Things (IoT) devices at actual sensor locations and historical SWE maps. The method consists of finding a background SWE field, followed by an update step using ensemble optimal interpolation to estimate the residuals. This novel approach allowed for areas with parsimonious sensors to have accurate estimates of spatial SWE without explicitly discovering and specifying the spatial-interpolation features. The scheme is evaluated across the Tuolumne River basin on a 50 m grid using an existing LiDAR-based product as the historical dataset. Results show a minimum RMSE of 30% at 50 m resolutions. Compared with the operational SNODAS product, reduction in error is up to 80% with historical LiDAR-measured snow depth as input data.

Quality levels for rockfill dam compaction (herein, porosity is an important index for assessing dam-material compaction quality) in any location can be estimated based on construction digitization technologies. According to the results of large-scale laboratory triaxial tests, the quantitative relationship between dam-material compaction quality and Duncan-Chang constitutive model parameters is established. In turn, the spatial estimation of model parameters of any location of a rockfill dam can be achieved. These parameters, which can reflect the actual conditions of dam-material compaction quality, can be assigned to each finite element by customizing Abaqus software. The refined three-dimensional (3D) rockfill dam model is then built for considering the influence of the actual foundation terrain on dam deformation. On this basis, the actual load process is determined from construction progress and practical dam appearances, and in turn, the refined finite-element modeling and analysis of structural behaviors (deformation and stress) occurring during rockfill dam construction is achieved. The proposed method considers spatial differences in constitutive model parameters resulting from the spatial differences in actual dam construction quality, thus representing an improvement in accuracy from the conventional method, which typically assigns the same parameters to elements of the same dam zone. A case study shows that the calculation results of the proposed method are more consistent with the measured values and can reflect structural behaviors more objectively. The method can serve as a new tool for simulating the regularity of the structural behaviors of rockfill dams. [ABSTRACT FROM AUTHOR]