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All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

Regression methods for spatial data

The kriging approach, a parametric regression method used by hydrologists and mining engineers, among others also provides an error estimate the integral of the regression function. The kriging method is explored and some of its statistical characteristics are described. The Watson method and theory are extended so that the kriging features are displayed. Theoretical and computational comparisons of the kriging and Watson approaches are offered.

Yakowitz, S. J.↗
NASA NTRS2005

Using IKONOS Imagery to Estimate Surface Soil Property Variability in Two Alabama Physiographies

Knowledge of surface soil properties is used to assess past erosion and predict erodibility, determine nutrient requirements, and assess surface texture for soil survey applications. This study was designed to evaluate high resolution IKONOS multispectral data as a soil- mapping tool. Imagery was acquired over conventionally tilled fields in the Coastal Plain and Tennessee Valley physiographic regions of Alabama. Acquisitions were designed to assess the impact of surface crusting, roughness and tillage on our ability to depict soil property variability. Soils consisted mostly of fine-loamy, kaolinitic, thermic Plinthic Kandiudults at the Coastal Plain site and fine, kaolinitic, thermic Rhodic Paleudults at the Tennessee Valley site. Soils were sampled in 0.20 ha grids to a depth of 15 cm and analyzed for % sand (0.05 - 2 mm), silt (0.002 -0.05 mm), clay (less than 0.002 mm), citrate dithionite extractable iron (Fe(sub d)) and soil organic carbon (SOC). Four methods of evaluating variability in soil attributes were evaluated: 1) kriging of soil attributes, 2) co-kriging with soil attributes and reflectance data, 3) multivariate regression based on the relationship between reflectance and soil properties, and 4) fuzzy c-means clustering of reflectance data. Results indicate that co-kriging with remotely sensed data improved field scale estimates of surface SOC and clay content compared to kriging and regression methods. Fuzzy c-means worked best using RS data acquired over freshly tilled fields, reducing soil property variability within soil zones compared to field scale soil property variability.

Sullivan, Dana↗
NASA NTRS2013

Mapping the Daily Progression of Large Wildland Fires Using MODIS Active Fire Data

High temporal resolution information on burned area is a prerequisite for incorporating bottom-up estimates of wildland fire emissions in regional air transport models and for improving models of fire behavior. We used the Moderate Resolution Imaging Spectroradiometer (MODIS) active fire product (MO(Y)D14) as input to a kriging interpolation to derive continuous maps of the evolution of nine large wildland fires. For each fire, local input parameters for the kriging model were defined using variogram analysis. The accuracy of the kriging model was assessed using high resolution daily fire perimeter data available from the U.S. Forest Service. We also assessed the temporal reporting accuracy of the MODIS burned area products (MCD45A1 and MCD64A1). Averaged over the nine fires, the kriging method correctly mapped 73% of the pixels within the accuracy of a single day, compared to 33% for MCD45A1 and 53% for MCD64A1.

Aqua↗
DOE OSTI2019

Linear Regression Based Multi-fidelity Surrogate for Disturbance Amplification in Multi-phase Explosion

When simulations are very expensive and many are required, as for optimization or uncertainty quantification, a way to reduce cost is using surrogates. With multiple simulations to predict the quantity of interest, some being very expensive and accurate (high-fidelity simulations) and others cheaper but less accurate (low-fidelity simulations), it may be worthwhile to use multifidelity surrogates (MFSs). Moreover, if we can afford just a few high-fidelity simulations or experiments, MFS becomes necessary. Co-Kriging, which is probably the most popular MFS, replaces both low-fidelity and high-fidelity simulations by a single MFS. A recently proposed linear regression–based MFS (LR-MFS) offers the option to correct the LF simulations instead of correcting the LF surrogate in the MFS. When the low-fidelity simulation is cheap enough for use in an application, such as optimization, this may be an attractive option. Here, we explore the performance of LR-MFS using exact and surrogate-replaced low-fidelity simulations. The concern studied is a cylindrical dispersal of 100-μ m-diameter solid particles after detonation and the quantity of interest is a measure of the amplification of the departure from axisymmetry. We find very substantial accuracy improvements for this problem using the LR-MFS with exact low-fidelity simulations. Inspired by these results, we also compare the performance of co-Kriging to the use of Kriging to correct exact low-fidelity simulations and find a similar accuracy improvement when simulations are directly used. For this problem, further improvements in accuracy are achievable by taking advantage of inherent parametric symmetries. These findings may alert users of MFSs to the possible advantages of using exact low-fidelity simulations when this is affordable.

42 ENGINEERING↗
DOE OSTI2018

Assessment and uncertainty analysis of groundwater risk

Highlights: • Two different sets of index evaluation systems for shallow and deep groundwater were built respectively. • Ordinary kriging was adopted to execute the interpolation estimation. • The synthetic weights were adopted merging the AHP method and PCA method. • The uncertainty of groundwater risk was analyzed by indicator kriging. Groundwater with relatively stable quantity and quality is commonly used by human being. However, as the over-mining of groundwater, problems such as groundwater funnel, land subsidence and salt water intrusion have emerged. In order to avoid further deterioration of hydrogeological problems in over-mining regions, it is necessary to conduct the assessment of groundwater risk. In this paper, risks of shallow and deep groundwater in the water intake area of the South-to-North Water Transfer Project in Tianjin, China, were evaluated. Firstly, two sets of four-level evaluation index system were constructed based on the different characteristics of shallow and deep groundwater. Secondly, based on the normalized factor values and the synthetic weights, the risk values of shallow and deep groundwater were calculated. Lastly, the uncertainty of groundwater risk assessment was analyzed by indicator kriging method. The results meet the decision maker's demand for risk information, and overcome previous risk assessment results expressed in the form of deterministic point estimations, which ignore the uncertainty of risk assessment.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

The geostatistical approach for structural and stratigraphic framework analysis of offshore NW Bonaparte Basin, Australia

Geostatistics or statistical approach is based on the studies of temporal and spatial trend, which depend upon spatial relationships to model known information of variable(s) at unsampled locations. The statistical technique known as kriging was used for petrophycial and facies analysis, which help to assume spatial relationship to model the geological continuity between the known data and the unknown to produce a single best guess of the unknown. Kriging is also known as optimal interpolation technique, which facilitate to generate best linear unbiased estimation of each horizon. The idea is to construct a numerical model of the lithofacies and rock properties that honor available data and further integrate with interpreting seismic sections, techtonostratigraphy chart with sea level curve (short term) and regional tectonics of the study area to find the structural and stratigraphic growth history of the NW Bonaparte Basin. By using kriging technique the models were built which help to estimate different parameters like horizons, facies, and porosities in the study area. The variograms were used to determine for identification of spatial relationship between data which help to find the depositional history of the North West (NW) Bonaparte Basin.

58 GEOSCIENCES↗
DOE OSTI2021

Estimating basis functions in massive fields under the spatial mixed effects model

Abstract Spatial prediction is commonly achieved under the assumption of a Gaussian random field by obtaining maximum likelihood estimates of parameters, and then using the kriging equations to arrive at predicted values. For massive datasets, fixed rank kriging using the expectation–maximization algorithm for estimation has been proposed as an alternative to the usual but computationally prohibitive kriging method. The method reduces computation cost of estimation by redefining the spatial process as a linear combination of basis functions and spatial random effects. A disadvantage of this method is that it imposes constraints on the relationship between the observed locations and the knots. We develop an alternative method that utilizes the spatial mixed effects model, but allows for additional flexibility by estimating the range of the spatial dependence between the observations and the knots via an alternating expectation conditional maximization algorithm. Experiments show that our methodology improves estimation without sacrificing prediction accuracy while also minimizing the additional computational burden of extra parameter estimation. The methodology is applied to a temperature dataset archived by the United States National Climate Data Center, with improved results over previous methodology.

Pazdernik, Karl↗
DOE OSTI2017

Geometry Optimization with Machine Trained Topological Atoms

The geometry optimization of a water molecule with a novel type of energy function called FFLUX is presented, which bypasses the traditional bonded potentials. Instead, topologically-partitioned atomic energies are trained by the machine learning method kriging to predict their IQA atomic energies for a previously unseen molecular geometry. Proof-of-concept that FFLUX’s architecture is suitable for geometry optimization is rigorously demonstrated. It is found that accurate kriging models can optimize 2000 distorted geometries to within 0.28kJmol-1 of the corresponding ab initio energy, and 50% of those to within 0.05kJmol-1. Kriging models are robust enough to optimize the molecular geometry to sub-noise accuracy, when two thirds of the geometric inputs are outside the training range of that model. Finally, the individual components of the potential energy are analyzed, and chemical intuition is reflected in the independent behavior of the three energy terms Eintra A (intra-atomic),' Vcl AA (electrostatic) an' Vx AA (exchange), in contrast to standard force fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

General-Surrogate Adaptive Sampling Using Interquartile Range for Design Space Exploration

Abstract A surrogate model is a common tool to approximate system response at untested points for design space exploration. Adaptive sampling has been studied for improving the accuracy of surrogates iteratively by introducing additional samples (simulations and experiments). New samples are often selected based on the estimated uncertainty in the design space. While some surrogates such as kriging have readily available uncertainty models for their predictions, other surrogates do not. Consequently, there have been studies of using the process of leaving-samples-out (LSO) used in cross-validation tools to estimate prediction uncertainty, such as the universal prediction distribution (UPD). In this paper, an adaptive sampling scheme for general surrogates is proposed based on LSO, similar to cross-validation and interquartile range (IQR). Multiple submodels are first developed from LSO. The uncertainty is then estimated from the IQR of these surrogates at a given point. New samples are added iteratively at the point with maximum IQR for design space exploration. The proposed scheme is illustrated using kriging, radial basis function, and neural network surrogates. The proposed scheme is evaluated using four algebraic test functions. Multiple sets of initial samples were produced to account for randomness. For these test functions, the proposed scheme was found to be more accurate and robust than kriging with its own uncertainty model. The proposed scheme was more accurate than the UPD for three out of the four test functions. For a fixed number of samples, the IQR-based adaptive sampling also proved to be more accurate than all-at-once sampling in most cases even when the estimated uncertainty was only mildly correlated with prediction errors.

Engineering↗
DOE OSTI2015

Snake River Plain Geothermal Play Fairway Analysis Heat, Permeability, and Seal CRS Map Raster Files

Snake River Plain Play Fairway Analysis - Phase 1 CRS Raster Files. This dataset contains raster files created in ArcGIS. These raster images depict Common Risk Segment (CRS) maps for HEAT, PERMEABILITY, AND SEAL, as well as selected maps of Evidence Layers. These evidence layers consist of either Bayesian krige functions or kernel density functions, and include: (1) HEAT: Heat flow (Bayesian krige map), Heat flow standard error on the krige function (data confidence), volcanic vent distribution as function of age and size, groundwater temperature (equivalue interval and natural breaks bins), and groundwater T standard error. (2) PERMEABILTY: Fault and lineament maps, both as mapped and as kernel density functions, processed for both dilational tendency (TD) and slip tendency (ST), along with data confidence maps for each data type. Data types include mapped surface faults from USGS and Idaho Geological Survey data bases, as well as unpublished mapping; lineations derived from maximum gradients in magnetic, deep gravity, and intermediate depth gravity anomalies. (3) SEAL: Seal maps based on presence and thickness of lacustrine sediments and base of SRP aquifer. Raster size is 2 km. All files generated in ArcGIS.

15 GEOTHERMAL ENERGY↗
NASA NTRS2013

Eliminating Obliquity Error from the Estimation of Ionospheric Delay in a Satellite-Based Augmentation System

Current satellite-based augmentation systems estimate ionospheric delay using algorithms that assume the electron density of the ionosphere is non-negligible only in a thin shell located near the peak of the actual profile. In its initial operating capability, for example, the Wide Area Augmentation System incorporated the thin shell model into an estimation algorithm that calculates vertical delay using a planar fit. Under disturbed conditions or at low latitude where ionospheric structure is complex, however, the thin shell approximation can serve as a significant source of estimation error. A recent upgrade of the system replaced the planar fit algorithm with an algorithm based upon kriging. The upgrade owes its success, in part, to the ability of kriging to mitigate the error due to this approximation. Previously, alternative delay estimation algorithms have been proposed that eliminate the need for invoking the thin shell model altogether. Prior analyses have compared the accuracy achieved by these methods to the accuracy achieved by the planar fit algorithm. This paper extends these analyses to include a comparison with the accuracy achieved by kriging. It concludes by examining how a satellite-based augmentation system might be implemented without recourse to the thin shell approximation.

delay estimation↗
DOE OSTI2018

Spatiotemporal interpolation of air pollutants in the Greater Cairo and the Delta, Egypt

Highlights: • Data from network of monitoring stations in Egypt are used for studying SO{sub 2}, NO{sub 2}, and PM{sub 10.} • Trans-Gaussian Spatiotemporal kriging is used as a spatiotemporal interpolation method. • The whole area under study is suffering from high values of PM{sub 10} throughout 2015. • For NO{sub 2} and SO{sub 2}, the highest value is noticed in February. • Concerns must be given to the monitoring network to improve the prediction precision. This paper analyses the spatiotemporal variability of air pollutants in Egypt using monthly averages from the air quality monitoring network from 2011 to 2015. Particulate Matters (PM{sub 10}) Nitrogen Dioxide (NO{sub 2}) and Sulfur Dioxide (SO{sub 2}), measured by the monitoring stations network are studied. A log transformation is applied for the three pollutants to achieve normality. The sum-metric function is utilized for modelling the spatiotemporal variogram as it gave the smallest Mean Squared Error (MSE) compared to other forms namely separable, metric, and product sum models. Therefore, employing the gstat package in R together with the trans-Gaussian spatiotemporal kriging, the maps are generated for the interpolated surfaces for the monthly averages of 2015 and the corresponding standard error values. These maps will help the decision maker to understand and visualize the spatial and temporal variability of the measured pollutants and hence undertake the necessary policies and decisions. The results show that the down town area has the highest pollutants levels. As concerns the temporal dimension, the highest values are depicted during the month of February as compared to the rest of the year. Furthermore, Egypt is suffering from a serious PM{sub 10} problem for the area and period under study that extremely exceed the WHO and Egyptian guidelines.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Spatial modeling of daily concentrations of ground-level ozone in Montreal, Canada: A comparison of geostatistical approaches

Highlights: • The KED model with road and vegetation density as covariates showed good performance for all six synoptic classes. • The model using KED demonstrated the best results (R{sup 2} = 0.92; RMSE = 3.14 ppb). • The model using OK demonstrated a R{sup 2} = 0.85 and RMSE = 4 ppb. • Our results showed that errors appear to be substantially reduced with the KED model. • When measurements at numerous monitoring stations in a region are available, it may be better to use KED. • The BME may be more useful for prediction when data is not available. Ground-level ozone (O{sub 3}) is a powerful oxidizing agent and a harmful pollutant affecting human health, forests and crops. Estimating O{sub 3} exposure is a challenge because it exhibits complex spatiotemporal patterns. The aim in this study was to provide high-resolution maps (100 × 100 m) of O{sub 3} for the metropolitan area of Montreal, Canada. We assessed the kriging with external drift (KED) model to estimate O{sub 3} concentration by synoptic weather classes for 2010. We compared these results with ordinary kriging (OK), and a simple average of 12 monitoring stations. We also compared the estimates obtained for the 2010 summer with those from a Bayesian maximum entropy (BME) model reported in the literature (Adam-Poupart et al., 2014). The KED model with road and vegetation density as covariates showed good performance for all six synoptic classes (daily R{sup 2} estimates ranging from 0.77 to 0.92 and RMSE from 2.79 to 3.37 ppb). For the summer of 2010, the model using KED demonstrated the best results (R{sup 2} = 0.92; RMSE = 3.14 ppb), followed by the OK model (R{sup 2} = 0.85, RMSE = 4 ppb). Our results showed that errors appear to be substantially reduced with the KED model. This may increase our capacity of linking O{sub 3} levels to health problems by means of improved assessments of ambient exposures. However, future work integrating the temporal dependency in the data is needed to not overstate the performance of the KED model.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Spatial distribution of soil carbon stocks in a semi-arid region of India

We predicted total carbon (TC) stocks in the 0–30 cm soil depth of two southern states in India using field observations, environmental covariates and geospatial approaches. We compared the Geographically Weighted Regression Kriging (GWRK) with Linear Regression Kriging (LRK) approach to predict the TC stocks. Greater spatial heterogeneity in TC stocks (2–15 kg m –2 ) were predicted with lower estimation errors (RMSE = 2 kg m –2 R 2 = 0.63) in GWRK in comparison to the LRK approach (RMSE = 3 kg m –2 , R 2 = 0.55). The average decrease in the prediction error was 39% in GWRK in comparison to the LRK approach. The total TC stock in the 0–30 cm depth of the study area was estimated at 1.5 Pg C with upper and lower prediction intervals of 1 and 2 Pg C, respectively. The cropland stored largest (65%, 1 Pg C) amount of TC stocks followed by forest (21%, 0.31 Pg C) and plantation (8%, 0.12 Pg C) land cover types. Among soil types the Alfisols stored largest (33%, 0.49 Pg C) amount of TC stocks followed by Inceptisols (23%; 0.35 Pg C) and Entisols (18%, 0.27 Pg C). The uncertainty in TC stock predictions ranged from 41 to 75% and 69 to 91% under various land covers and soil types, respectively. Highest uncertainties in predicted TC stocks were associated with the forest land cover type and Mollisols soil order. Similarly, lowest uncertainties were found in the built up areas and Aridisols soil order. Our results suggest that GWRK is a useful approach to spatially predict the TC stocks at regional scales.

58 GEOSCIENCES↗
DOE OSTI2015

Evaluation of convergence behavior of metamodeling techniques for bridging scales in multi-scale multimaterial simulation

The effectiveness of several metamodeling techniques, viz. the Polynomial Stochastic Collocation method, Adaptive Stochastic Collocation method, a Radial Basis Function Neural Network, a Kriging Method and a Dynamic Kriging Method is evaluated. This is done with the express purpose of using metamodels to bridge scales between micro- and macro-scale models in a multi-scale multimaterial simulation. The rate of convergence of the error when used to reconstruct hypersurfaces of known functions is studied. For sufficiently large number of training points, Stochastic Collocation methods generally converge faster than the other metamodeling techniques, while the DKG method converges faster when the number of input points is less than 100 in a two-dimensional parameter space. Because the input points correspond to computationally expensive micro/meso-scale computations, the DKG is favored for bridging scales in a multi-scale solver.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Statistical Interpolation for Surface Reconstruction of PDV and BLR Data

Data collection is becoming more and more dense in dynamic experiments, requiring a variety of diagnostics. Data are detected through such means as holography, Mie scattering / extinction, assay foils, surface imaging, and high-speed photography. The data are measured by radiography, velocimetry, ranging, Fiber Bragg, and pyrometry. The question is how can we unify information from multiple diagnostics and incorporate uncertainties to tell a coherent story about an experiment in a meaningful way? This presentation provides an overview of statistical interpolation by means of Kriging. Kriging involves three basic steps: (1) compute and model covariance spatial structure; (2) compute weights by minimizing mean squared prediction error; and (3) predict at the desired prediction sites.

dynamic experiments, holography, Mie scattering/ex↗
DOE OSTI2020

GIS-Based Modeling of Contaminated Soil Volumes at Multiple Sites in the Formerly Utilized Sites Remedial Action Program - 20149

The remediation of hazardous, toxic, and radioactive waste (HTRW) sites produces cost-related risks associated with the estimation of contaminated soil or debris volumes. Historical risk-management techniques include cost contingencies to cover volume uncertainties that affect project budgeting and decision-making. The Buffalo District teamed with project partners to lessen volume uncertainty and reduce project risks at multiple HTRW sites managed under the Formerly Utilized Sites Remedial Action Program (FUSRAP). Historical remedial investigations under FUSRAP commonly identified the presence of radiological material in site media, the associated human health risk, and then areas of remediation. To manage remedial execution and reduce risk, pre-design or remediation-phase sampling essentially 'chased' contamination, which was not conducive to efficient predictive budgeting derived from Feasibility Study (FS) cost analyses. The Buffalo District first optimized their approach to better understand volume uncertainty by utilizing the Argonne National Laboratory's Bayesian Approaches for Adaptive Spatial Sampling (BAASS) software [1]. BAASS processed soft data (e.g., gamma walk-over data) and spatial sampling data to estimate the lateral extent of contaminated soil irrespective of depth (i.e., gross contamination extent) and define areas of contaminant uncertainty. The software performed a binary transformation of contaminant concentrations at all sampling points based upon remedial action goals or a sum of ratios approach (i.e., clean, impacted, or range of impacts in soil). The model produced two-dimensional (horizontal) contaminant probability contours and statistical uncertainty in the sampling coverage and resulting contaminant extents. This method was translated vertically by partitioning the sampling data into depth brackets that produced a stacked representation of contaminant extents and uncertainty in the subsurface (i.e., similar to construction lifts). The results commonly led to a better understanding of project uncertainty and the need for sampling strategies that produce high-confidence soil volumes, which control costs. The BAASS-based delineations were eventually replaced by Empirical Bayesian Kriging (EBK) methods available in ArcGIS Spatial or 3D Analysts [2]. The EBK method calculates contaminant probability zones derived from user-controlled semivariograms of the spatial datasets. The resulting probability zones (e.g., 50% or 80% of contaminant probability) represent the two-dimensional surface delineation of the overall horizontal remedial area, similarly to BAASS. However, unlike BAASS, the vertical sampling data within these probability zones became vertical control points to contour a subterranean surface that connects subsurface points to the land-surface delineations of contamination. The resulting representation of horizontal and vertical impacts within an enclosed envelop (volume) of soil included uncertainty distributions that are used to plan uncertainty-reduction sampling. These data-driven and math-based models of three-dimensional sampling results produced well-bounded remedial volumes for project planning and better uncertainty predictions during project budgeting. The EBK method was applied to several FUSRAP sites managed by the Buffalo District and compared to less rigorously modeled sites previously remediated by the District. The comparison of modeled to actual remediated volumes provide a basis for validating the volume-estimation method. This comparison is important to ensure modeled volumes match physical boundaries of site remediation. FUSRAP sites with denser investigative sampling and lesser volume uncertainty proved useful in remedial planning and contracting. The Buffalo District noted that historical sites with sparser sampling arrays had greater disparity between estimated volumes and final remedial volumes. The benefit achieved over the cost of detailed soil sampling appears positive for FUSRAP projects, especially where impacts vary widely and appear unbounded by investigation-phase sampling. The subsequent Empirical Bayesian Kriging of contamination coupled with vertical contouring for soil estimations reduces uncertainty in soil volumes or indicates where sampling is required to reduce uncertainty, which together optimize remedial planning and budgeting. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2017

Evaluation of a data fusion approach to estimate daily PM{sub 2.5} levels in North China

PM{sub 2.5} air pollution has been a growing concern worldwide. Previous studies have conducted several techniques to estimate PM{sub 2.5} exposure spatiotemporally in China, but all these have limitations. This study was to develop a data fusion approach and compare it with kriging and Chemistry Module. Two techniques were applied to create daily spatial cover of PM{sub 2.5} in grid cells with a resolution of 10 km in North China in 2013, respectively, which was kriging with an external drift (KED) and Weather Research and Forecast Model with Chemistry Module (WRF-Chem). A data fusion technique was developed by fusing PM{sub 2.5} concentration predicted by KED and WRF-Chem, accounting for the distance from the central of grid cell to the nearest ground observations and daily spatial correlations between WRF-Chem and observations. Model performances were evaluated by comparing them with ground observations and the spatial prediction errors. KED and data fusion performed better at monitoring sites with a daily model R{sup 2} of 0.95 and 0.94, respectively and PM{sub 2.5} was overestimated by WRF-Chem (R{sup 2}=0.51). KED and data fusion performed better around the ground monitors, WRF-Chem performed relative worse with high prediction errors in the central of study domain. In our study, both KED and data fusion technique provided highly accurate PM{sub 2.5}. Current monitoring network in North China was dense enough to provide a reliable PM{sub 2.5} prediction by interpolation technique. - Highlights: • KED and data fusion model predicted daily PM{sub 2.5} with high accuracy. • WRF-Chem performed worse in PM{sub 2.5} prediction compared with KED and data fusion. • The PM{sub 2.5} monitoring network in North China was able to support reliable PM{sub 2.5} interpolation.

54 ENVIRONMENTAL SCIENCES↗