Traditional Spatial Interpolation Research Articles

Boosting house price estimations with Multi-Head Gated Attention

Evaluating house prices is crucial for various stakeholders, including homeowners, investors, and policymakers. However, traditional spatial interpolation methods have limitations in capturing the complex spatial relationships that affect property values. To address these challenges, we have developed a new method called Multi-Head Gated Attention for spatial interpolation. Our approach builds upon attention-based interpolation models and incorporates multiple attention heads and gating mechanisms to better capture spatial dependencies and contextual information. Importantly, our model produces embeddings that reduce the dimensionality of the data, enabling simpler models like linear regression to outperform complex ensembling models. We conducted extensive experiments to compare our model with baseline methods and the original attention based interpolation model. The results show a significant improvement in the accuracy of house price predictions, validating the effectiveness of our approach. This research advances the field of spatial interpolation and provides a robust tool for more precise house price evaluation. Our GitHub repository.11Final_file/tree/main/ASI-main. contains the data and code for all datasets, which are available for researchers and practitioners interested in replicating or building upon our work.

Electromagnetic Radiation Space Field Construction Collected along the Road Based on Layered Radial Basis Function

The electromagnetic radiation (EMR) data collected along a road have a largely empty region overall, while they have a linear distribution locally. Moreover, the traditional spatial interpolation method is not suitable for the electromagnetic radiation space field (EMR-SF) construction collected along the road. In this paper, a layered radial basis function (LRBF) method is proposed to generate the EMR-SF, which interpolates from outside to inside in a layered strategy. First, the regular grid points are constructed based on RBF within the range of sampling data and then are layered based on Ripley’s K function. Second, on the basis of layering, the EMR of grid points is generated layer by layer using the LRBF method. Finally, EMR-SF is constructed by using the sampling data and grid points. The LRBF method is applied to EMR data from an area of Yunnan Normal University in Kunming, China. The results show that the LRBF accuracy is higher than that of the ordinary kriging (OK) and inverse-distance-weighted (IDW) interpolation methods. The LRBF interpolation accuracy can be improved through the strategy of regular grid point construction and layering, and the EMR-SF constructed by LRBF is more realistic than OK and IDW.

Improved three‐dimensional mapping of soil chromium pollution with sparse borehole data: Incorporating multisource auxiliary data into IDW‐based interpolation

AbstractDeriving an accurate three‐dimensional (3D) spatial distribution of heterogeneous soil pollutants at contaminated sites using traditional spatial interpolation methods, such as inverse distance weighting (IDW), is challenging; especially when only limited borehole data are available. This study presents a novel IDW‐COV method, where weighting is determined by optimizing relative importance between feature distances of covariates and spatial distances to soil sample locations. The method was tested by mapping the 3D distributions of Cr (VI) and total Cr at a Cr salt production workshop (Site A) and a legacy Cr slag stacking site (Site B). The results were compared with those of IDW, the soil land inference model (SoLIM), and the SoLIM combined with IDW method (SoLIM‐IDW). The proposed IDW‐COV method returned the highest accuracy, with R2 values of 0.83 for Cr (VI) in Site A and 0.75 for total Cr in Site B, compared with 0.65 and 0.57 for IDW, 0.16 and 0.58 for SoLIM, and 0.73 and 0.61 for SoLIM‐IDW. This study highlights the importance of considering differences in explanatory power between multidimensional covariate and geographical spatial distance when incorporating multisource auxiliary data into weighted average estimators and provides guidance for mapping 3D distributions of heterogeneous pollutants from sparse soil borehole data.

Hyperspectral imagery reveals large spatial variations of heavy metal content in agricultural soil - A case study of remote-sensing inversion based on Orbita Hyperspectral Satellites (OHS) imagery

The widespread heavy metal contamination in soil induced by extensive human disturbance has been a global significant issue because of its chronic toxic effects on human health. However, the establishment of effective monitoring and assessing methods for heavy metal content in the soil remain a long-term challenge due to the intrinsic limitation of the current multi-band remote sensing technology and field measurement methods. Prompted by this significant technique gap, we represent an implementation of remote-sensing inversion models based on hyperspectral imagery to reconstruct soil heavy metal contents within an experimental farmland located in Mianzhu city, Sichuan, China. We collected soil samples at the pre-defined sites, and measured soil heavy metal contents and soil spectrum in the laboratory condition. Meanwhile, we obtained Orbita Hyperspectral Satellites (OHS) imagery and quantified the associated vegetation indexes. The measured soil spectrum, bands of OHS, and the generated vegetation indexes were mathematically transformed to better represent their relations with soil heavy metal contents. Consequently, the most sensitive variables were selected as potent predictors of soil heavy metal contents in the inversion models. After evaluating the optimal inversion models for each heavy metal element, we implemented them to reconstruct the spatial patterns of soil heavy metal contents over the study landscape. We found obvious benefits of the remote sensing inversion model in predicting the spatial heterogeneity of heavy metal content within this small landscape patch. Specifically, the inversion model unraveled a normal distribution of heavy metal contents within the landscape, while the traditional spatial interpolation based on field measurements may suggest a largely skewed distribution. Compared with airborne-based studies, this study represents an application of spaceborne satellite data, which can be easily applied to a large spatial scale and long-term monitoring.

Terrain feature-aware deep learning network for digital elevation model superresolution

Neural networks (NNs) have demonstrated the potential to recover finer textural details from lower-resolution images by superresolution (SR). Given similar grid-based data structures, some researchers have transferred image SR methods to digital elevation models (DEMs). These efforts have yielded better results than traditional spatial interpolation methods. However, terrain data present inherently different characteristics and practical meanings compared with natural images. This makes it unsuitable for existing SR methods on perceptually visual features of images to be directly adopted for extracting terrain features. In this paper, we argue that the problem lies in the lack of explicit terrain feature modeling and thus propose a terrain feature-aware superresolution model (TfaSR) to guide DEM SR towards the extraction and optimization of terrain features. Specifically, a deep residual module and a deformable convolution module are integrated to extract deep and adaptive terrain features, respectively. In addition, explicit terrain feature-aware optimization is proposed to focus on local terrain feature refinement during training. Extensive experiments show that TfaSR achieves state-of-the-art performance in terrain feature preservation during DEM SR. Specifically, compared with the traditional bicubic interpolation method and existing neural network methods (SRGAN, SRResNet, and SRCNN), the RMSE of our results is improved by 1.1% to 23.8% when recovering the DEM from 120 m to 30 m, by 4.9% to 22.7% when recovering the DEM from 60 m to 30 m, and by 7.8% to 53.7% when recovering the DEM from 30 m to 10 m. The source code that has been developed is shared on Figshare (https://doi.org/10.6084/m9.figshare.19597201).

Real-time prediction of indoor humidity with limited sensors using cross-sample learning

Indoor Environment Monitoring Systems (IEMSs) are equipped in buildings to improve building energy efficiency, ensure good human health and safety, and promote digital buildings. Because only a few sensors can be installed in a building, an IEMS only senses labeled positions where sensors are installed. Real-time prediction of the indoor environmental quality (IEQ) such as the humidity at unlabeled positions is still challenging. Previous approaches usually utilized a spatial interpolation algorithm, which predicts the IEQ of an unlabeled position using fixed coefficients from labeled positions assigned by experts. Noticing that labeled positions suggest different cues to infer an unlabeled position in different scenarios, the performance of traditional spatial interpolation algorithms can be improved by introducing dynamic coefficients for labeled positions. Inspired by this assumption, a novel machine-learning-based real-time prediction of indoor humidity status scheme, termed ML-PIS, is proposed. First, a spatial graph model is proposed to represent the correlation between any two spatial positions. Second, a cross-sample training algorithm is designed to learn the coefficients of labeled positions within the spatial graph model, which further predicts the status of any unlabeled position. Finally, the performance of ML-PIS is systematically evaluated using humidity in a real-world environment. The experimental results showed that the mean absolute error of ML-PIS is less than 54.3% of that obtained with the inverse-distance-weighted-based spatial interpolation algorithm (IDW); the root mean square error of ML-PIS is less than 50.4%; the relative error is less than 6.05%; and the accuracy is higher than 6.05%. The proposed ML-PIS is a generalized version of spatial interpolation algorithms. The proposed ML-PIS is able to provide accurate information for digital buildings, thereby allowing better decisions to be made in indoor environments.

Predicting and mapping soil magnetic susceptibility in an agro-pastoral transitional zone: Influencing factors and implications

Soil magnetic susceptibility (MS) is a basic soil physical property that is influenced by environmental factors and processes. Mapping MS is fundamental to exploring its spatial pattern, influencing factors and practical applications. However, the traditional spatial interpolation method is difficult to implement in detailed large-scale mapping. Digital soil mapping (DSM) based on environmental factors provides a more effective method. It has been widely adopted in the prediction of soil physiochemical characteristics, but not yet in MS mapping. This study aimed to explore the spatial pattern of soil MS in an agro-pastoral transitional zone (APTZ) of north China, reveal influencing factors of MS, and extract the significance of DSM of MS and its possible applications. Soil samples were collected from two layers (0–5 and 35–40 cm) in an APTZ. For each sample, χlf and χfd were measured. The quantile regression forest (QRF) model was used to predict MS and assess uncertainties. The results indicated substantial spatial variation of MS in APTZ. QRF predicted MS with satisfying accuracy (adjusted R2 = 0.37–0.64). Influencing factors of MS included parent material, topography, and vegetation. The predominant factors varied with MS attributes, depth, and environment. Soil redistribution further complicated the MS spatial pattern. Water erosion resulted in declining topsoil χfd at steep slopes. Topsoil χfd of grassland transect showed higher covariate of variation (8.23%) compared with forest (4.83%). Wind brought exogenous particles with low MS and led to a weaker correlation between topsoil χlf and χfd (p > 0.1) compared with subsoil (p < 0.05). DSM of MS based on environmental factors reveals the undetected influencing factors at a small scale and helps to identify dominant factors in different environments, which provides the possibility of adopting MS in practical works at a large scale.

A Spatial Interpolation of Meteorological Parameters considering Geographic Semantics

Spatial interpolation of meteorological parameters, closely related to the earth surface, plays important roles in climatological study. However, most of traditional spatial interpolation methods ignore the geographic semantics of interpolation sample points in practical application. This paper attempts to propose an improved inverse-distance weighting interpolation algorithm considering geographic semantics (S-IDW), which adds geographic semantic similarity to the traditional IDW formula and adjusts weight coefficient. In the interpolation process, the geographic semantic differences between sample points and estimation points are considered comprehensively. In this study, 3 groups of land surface temperature data from 2 different areas were selected for experiments, and several commonly used spatial interpolation methods were compared. Experimental results indicated that S-IDW outperformed IDW and several existing spatial interpolation methods, but there were also some abnormal value and interpolation outliers. This method provides a new insight toward the estimation accuracy, data missing, and error correction of spatial attributes related to meteorological parameters.

Towards mapping large scale soil erodibility by using pedological knowledge

ABSTRACT Soil erodibility is a key parameter to measure soil susceptibility to water erosion and thus to soil erosion modelling, introduced as K factor in the Universal Soil Loss Equation (USLE) and the Revised Universal Soil Loss Equation (RUSLE). However, subject to soil spatial heterogeneity and data availability, large-scale K value acquisition has not been properly addressed. In this study, authors aimed to construct a new large-scale soil erodibility mapping technique to provide methodological support for regional soil erosion surveys. Taking the mountainous Yunnan province as a case, 743 soil samples from 252 typical soil series were collected. A ‘GIS-based pedological method’ was developed to construct a large-scale soil erodibility database by linking a soil map with soil properties. K value in Yunnan varied between 0.0004 and 0.0169 t ha h ha−1 MJ−1 mm−1, with an average of 0.0065 t ha h ha−1 MJ−1 mm−1. Significantly different K values were found among different types of soils and land use (p < 0.05). Redundancy analysis indicated that annual average temperature and latitude were the dominant control factors. The study showed that regional K value estimated by ‘GIS-based pedological method’ manifested an improvement compared to the traditional spatial interpolation method.

Rainfall Spatial Estimations: A Review from Spatial Interpolation to Multi-Source Data Merging

Rainfall is one of the most basic meteorological and hydrological elements. Quantitative rainfall estimation has always been a common concern in many fields of research and practice, such as meteorology, hydrology, and environment, as well as being one of the most important research hotspots in various fields nowadays. Due to the development of space observation technology and statistics, progress has been made in rainfall quantitative spatial estimation, which has continuously deepened our understanding of the water cycle across different space-time scales. In light of the information sources used in rainfall spatial estimation, this paper summarized the research progress in traditional spatial interpolation, remote sensing retrieval, atmospheric reanalysis rainfall, and multi-source rainfall merging since 2000. However, because of the extremely complex spatiotemporal variability and physical mechanism of rainfall, it is still quite challenging to obtain rainfall spatial distribution with high quality and resolution. Therefore, we present existing problems that require further exploration, including the improvement of interpolation and merging methods, the comprehensive evaluation of remote sensing, and the reanalysis of rainfall data and in-depth application of non-gauge based rainfall data.

Fusion of sensor geometry into additive strain fields measured with sensing skin

Recently, numerous studies have been conducted on flexible skin-like membranes for the cost effective monitoring of large-scale structures. The authors have proposed a large-area electronic consisting of a soft elastomeric capacitor (SEC) that transduces a structure’s strain into a measurable change in capacitance. Arranged in a network configuration, SECs deployed onto the surface of a structure could be used to reconstruct strain maps. Several regression methods have been recently developed with the purpose of reconstructing such maps, but all these algorithms assumed that each SEC-measured strain located at its geometric center. This assumption may not be realistic since an SEC measures the average strain value of the whole area covered by the sensor. One solution is to reduce the size of each SEC, but this would also increase the number of required sensors needed to cover the large-scale structure, therefore increasing the need for the power and data acquisition capabilities. Instead, this study proposes an algorithm that accounts for the sensor’s strain averaging feature by adjusting the strain measurements and constructing a full-field strain map using the kriging interpolation method. The proposed algorithm fuses the geometry of an SEC sensor into the strain map reconstruction in order to adaptively adjust the average kriging-estimated strain of the area monitored by the sensor to the signal. Results show that by considering the sensor geometry, in addition to the sensor signal and location, the proposed strain map adjustment algorithm is capable of producing more accurate full-field strain maps than the traditional spatial interpolation method that considered only signal and location.

Measuring Spatial Distribution Characteristics of Heavy Metal Contaminations in a Network-Constrained Environment: A Case Study in River Network of Daye, China

Measuring the spatial distribution of heavy metal contaminants is the basis of pollution evaluation and risk control. Considering the cost of soil sampling and analysis, spatial interpolation methods have been widely applied to estimate the heavy metal concentrations at unsampled locations. However, traditional spatial interpolation methods assume the sample sites can be located stochastically on a plane and the spatial association between sample locations is analyzed using Euclidean distances, which may lead to biased conclusions in some circumstances. This study aims to analyze the spatial distribution characteristics of copper and lead contamination in river sediments of Daye using network spatial analysis methods. The results demonstrate that network inverse distance weighted interpolation methods are more accurate than planar interpolation methods. Furthermore, the method named local indicators of network-constrained clusters based on local Moran’ I statistic (ILINCS) is applied to explore the local spatial patterns of copper and lead pollution in river sediments, which is helpful for identifying the contaminated areas and assessing heavy metal pollution of Daye.

A neural network approach to efficient valuation of large portfolios of variable annuities

Managing and hedging the risks associated with Variable Annuity (VA) products require intraday valuation of key risk metrics for these products. The complex structure of VA products and computational complexity of their accurate evaluation have compelled insurance companies to adopt Monte Carlo (MC) simulations to value their large portfolios of VA products. Because the MC simulations are computationally demanding, especially for intraday valuations, insurance companies need more efficient valuation techniques. Recently, a framework based on traditional spatial interpolation techniques has been proposed that can significantly decrease the computational complexity of MC simulation (Gan and Lin, 2015). However, traditional interpolation techniques require the definition of a distance function that can significantly impact their accuracy. Moreover, none of the traditional spatial interpolation techniques provide all of the key properties of accuracy, efficiency, and granularity (Hejazi et al., 2015). In this paper, we present a neural network approach for the spatial interpolation framework that affords an efficient way to find an effective distance function. The proposed approach is accurate, efficient, and provides an accurate granular view of the input portfolio. Our numerical experiments illustrate the superiority of the performance of the proposed neural network approach compared to the traditional spatial interpolation schemes.

HASM-AD algorithm based on the sequential least squares

The HASM (high accuracy surface modeling) technique is based on the fundamental theory of surfaces, which has been proved to improve the interpolation accuracy in surface fitting. However, the integral iterative solution in previous studies resulted in high temporal complexity in computation and huge memory usage so that it became difficult to put the technique into application, especially for large-scale datasets. In the study, an innovative model (HASM-AD) is developed according to the sequential least squares on the basis of data adjustment theory. Sequential division is adopted in the technique, so that linear equations can be divided into groups to be processed in sequence with the temporal complexity reduced greatly in computation. The experiment indicates that the HASM-AD technique surpasses the traditional spatial interpolation methods in accuracy. Also, the cross-validation result proves the same conclusion for the spatial interpolation of soil PH property with the data sampled in Jiangxi province. Moreover, it is demonstrated in the study that the HASM-AD technique significantly reduces the computational complexity and lessens memory usage in computation.

Comparison of temporal and unresolved spatial variability in multiyear time-averages of air temperature

When compiling climatological means of air temperature, station data usually are selected on the basis of whether they exist within a fixed base period (e.g. 1961 to 1990). Within such analyses, station records that do not contain sufficient data during the base period or only contain data from other base periods are excluded. If between-station variability is of interest (e.g. a map or gridded field is needed), then removing such stations assumes that spatial interpolation to the location of culled stations is more reliable than using a temporal mean from a shorter or different averaging period — the latter is a process that we call 'temporal substitution.' Data from the United States Historical Climate Network (HCN) are used to examine whether spatial interpolation or temporal substitution is more reliable for multiyear averages of monthly and annual mean air temperature. After exhaustively sam- pling all possible 5-, 10-, and 30-yr averaging periods from 1921 to 1994, spatially averaged inter- polation and substitution errors are estimated for all months and for annual averages. For all months, temporal substitution produces lower overall error than traditional spatial interpolation for both 10- and 30-yr averages. Maps of mean absolute error (for all averaging periods) show that spatial interpolation errors are largest in mountainous regions while temporal substitution errors are largest in the north- central and eastern USA, especially in winter. A spatial interpolation algorithm (topographically aided interpolation, TAI) that incorporates elevation data reduces interpolation error, but also produces larger errors than temporal substitution for all months when using 30-yr averages and for all months except January, February, and March when using 10-yr averages. For 5-yr averages, however, TAI produces lower errors than temporal substitution, especially in winter. For the USA, therefore, it is suggested that for averaging periods less than 10 yr in length, elevation-aided spatial interpolation is preferable to temporal substitution. Conversely, for averaging periods longer than 10 yr in length, temporal substitu- tion is preferable to spatial interpolation. Analysis of the 1961 to 1990 period using a wide range of network densities demonstrates that temporal substitution generally is more reliable than spatial inter- polation of 30-yr averages, regardless of network density.