Ordinary Kriging Approach Research Articles

Large-scale rain gauge network optimization using a kriging emulator

Rain gauge networks deliver crucial observations for many water-related applications but can be expensive to purchase and operate, which makes optimization of the number and locations of gauges an important task. Traditional optimization approaches often focus on kriging-based methods that are computationally expensive, which limits the scale of the optimization to small areas or a very limited number of gauges. This study presents a novel workflow with high computational efficiency that is able to handle optimization problems on large rain gauge networks. This is accomplished by developing a fast parametric emulator of the commonly used ordinary kriging approach. The results show that the developed emulator is able to accurately reproduce the original kriging uncertainty estimates with a computational speed up of a factor of 3000. In order to determine the best locations for new gauges, a greedy optimization heuristic that relies on sequential placement of gauges is developed. The sequential optimization can lead to sub-optimal solutions by itself, so a resubstitution mechanism is introduced to correct for this. The workflow is applied to the national gauging network of Denmark with 291 gauges, where it is able to optimally place 175 new gauges within 1 h of running time. A similar optimization with a traditional kriging approach would have taken approximately 125 days to complete highlighting the value the workflow.

Assessing the Spatial Variability of Soil Physical Properties of the Lesser Himalayas in India

Understanding the spatial variability of soil properties is crucial for assessing the impact of measures taken to address land surface processes such as soil erosion and water pollution. It is also vital for recommending effective land management strategies. The present study was conducted to assess the spatial variations in soil textural fractions (sand, silt, and clay), bulk density and porosity. Soil samples were collected from 115 randomly selected locations using the Global Positioning System (GPS). The samples were taken at an average depth of 0-20 cm. A thorough examination was carried out in the laboratory to assess the physical properties of the soil. Afterwards, there was an analysis conducted to characterise the physical properties of soil and understand how they vary across different locations. The measured soil properties showed low to very high variability (6.26- 37.2%) for the Coefficient of variation (CV). The spatial dependence of soil properties was observed through the weak to strong nugget-to-sill ratios. Mapping the spatial variability of soil parameters involved using the Ordinary Kriging (OK) approach of Geostatistical analysis. This method helped identify the best-fit models for different soil parameters, such as Spherical for Silt, bulk density and porosity. Exponential for clay; and Gaussian for sand these spatial interpolation maps can be a valuable tool for pinpointing areas of land degradation in the study region and recommending specific land management strategies.

Multiband 2D InSAR deformation models with error estimates from natural neighbour interpolation: Case study in the Latrobe Valley, Australia

A long term objective for Australia is to develop a continent-wide 2D deformation model based on satellite interferometric synthetic aperture radar (InSAR). Nation-wide InSAR processing has been demonstrated in European countries and Japan. However, there are some key differences to the Australian situation for a 2D model (i.e., vertical and east–west surface movement rates) where SAR data from ascending and descending satellite orbits are needed. The primary difference is that while ESA’s Sentinel-1 ascending and descending satellite observations underpin 2D models in other parts of the world, the Australian continent is only covered by descending Sentinel-1 SAR data in most areas. Combined with Australia’s large size of 7.63 million km2, this means a different approach is needed to realise 2D deformation models. In this article, we propose the novel approach of (1) combining supplementary multiband SAR (ascending X-band and L-band) with the descending C-band Sentinel-1 data, and (2) using natural neighbour (NN) interpolation as a computationally efficient interpolation method for combining the multiband InSAR data on common grids prior to 2D model computation. This is an alternative to the computationally intensive Ordinary Kriging (OK) approach. A disadvantage of NN compared to OK is that it does not compute an error estimate, which we address by deriving an error estimate for the NN interpolation so that errors are provided for each 2D rate to aid with their correct interpretation. To demonstrate our new approach, we compute experimental 2D deformation models that propagate the full error budget from InSAR, a GNSS connection to ITRF2014 and NN interpolation into an error grid in the Latrobe Valley in southeast Australia. The significance of our approach is that it provides a suitable combination of methods that may be used to develop 2D continental deformation models for Australia’s unique circumstances. Our results demonstrate the accuracy of NN and OK interpolation are at the same level (within error), and the error estimates from both interpolation techniques are also comparable: X band (TerraSAR-X) ∼ 1 mm/yr; C band (Sentinel-1) ∼ 2.5 mm/yr, and L band (ALOS PALSAR1) 4 mm/yr. For the first time, we reveal 2D deformation in the Latrobe Valley region showing horizontal east–west deformation in the area surrounding an above-ground mine and reaching 20 mm/yr, with vertical subsidence rates reaching −40 mm/yr.

Prediction of Rainfall Classification of Java Island with ANN-Feature Expansion and Ordinary Kriging

Precipitation is one of the most important climatic variables in many aspects of our daily lives. High rainfall intensity can cause floods, landslides, and other natural disasters. Therefore, rainfall prediction is important for predicting natural disasters, assisting farmers in production decisions, and crop harvesting. In this research, a system is built to create a rainfall prediction map using a machine learning approach and spatial interpolation algorithms in Java, Indonesia. In the field of weather prediction, the artificial neural network approach is a popular machine learning method. The artificial neural network (ANN) method is a method that has the advantage of studying connections in the previously unknown hidden layer between input data and output data through training procedures. By using the ANN method, historical weather and climate data can be applied to create a classification model and predict rainfall classes. The classification of data is determined based on the attributes of historical weather and climate data, namely temperature, humidity, air pressure, evaporation, sunlight, and the level of rainfall in the time range per day and month. From the results of the ANN modeling, it was found that the 5C month model with an accuracy value of 89% as the best monthly ANN model, and the 6C day model with an accuracy value of 81% as the best daily ANN model. After going through ANN modeling, there is a spatial interpolation algorithm that is often used to estimate rainfall, namely Ordinary Kriging. The Ordinary Kriging approach is used to reduce the estimated variance and estimate the rainfall value in the case study area. After going through Ordinary Kriging modeling, a rainfall prediction map for the next six months and seven days is made based on the coordinates as a result of the research. The results of this research are rainfall prediction maps for the next six months and the next seven days on Java Island.

Evaluating sample sizes and design for monitoring and characterizing the spatial variations of potentially toxic elements in the soil

Cost-effective, representative and spatial coverage sampling designs are required to monitor the effects of potentially toxic elements (PTEs) in the soil. This study aims to evaluate the minimum sample sizes and placement of soil sampling designs to monitor and characterize the spatial variation of the PTEs (Cu, Zn, Cd, Cr, Pb, and Ni) in the soils. However, there is no standardized approach for evaluating the optimum soil sample size and monitoring location because of the spatial heterogeneity of PTEs in the soil. As a result, three broad techniques were applied. The first step was to use Global Moran's I and q-statistic values to describe the variability of soil PTEs and select appropriate evaluation methods. Second, using simple random sampling (SRS), ordinary kriging (OK), and Mean of Surface with Non-homogeneity (MSN), we estimated and evaluated soil PTEs in the current soil sampling schemes. Finally, MSN and spatial simulated annealing (SSA) optimization techniques were used to assess the required sample sizes and placements in the existing designs. Method performance was evaluated using a standard error (SE) and a relative standard error of the mean (RSE). Except for Zn and Cd, all PTEs tested showed heterogeneous distributions over the area. The MSN lowered the predicted SE by 79–86 % compared with SRS. The OK approach also outperformed the SRS method regarding mean estimated values of soil PTEs by 42–57 %. After SSA refined the initial design, the predicted SE by MSN of Cr and Zn was lowered by 13 % and 39 %, respectively. The MSN was effective with small sample sizes, reducing sample sizes and surveying costs by 39 % after SSA optimized the existing sample numbers. Thus, integrating various sampling strategies may be efficient for building optimal sample designs to monitor PTEs in the soil.

Spatially variable soils affecting geotechnical strip foundation design

Natural soil variability is a well-known issue in geotechnical design, although not frequently managed in practice. When subsoil must be characterized in terms of mechanical properties for infrastructure design, random finite element method (RFEM) can be effectively adopted for shallow foundation design to gain a twofold purpose: (1) understanding how much the bearing capacity is affected by the spatial variability structure of soils, and (2) optimisation of the foundation dimension (i.e. width B ). The present study focuses on calculating the bearing capacity of shallow foundations by RFEM in terms of undrained and drained conditions. The spatial variability structure of soil is characterized by the autocorrelation function and the scale of fluctuation ( δ ). The latter has been derived by geostatistical tools such as the ordinary Kriging (OK) approach based on 182 cone penetration tests (CPTs) performed in the alluvial plain in Bologna Province, Italy. Results show that the increase of the B / δ ratio not only reduces the bearing capacity uncertainty but also increases its mean value under drained conditions. Conversely, under the undrained condition, the autocorrelation function strongly affects the mean values of bearing capacity. Therefore, the authors advise caution when selecting the autocorrelation function model for describing the soil spatial variability structure and point out that undrained conditions are more affected by soil variability compared to the drained ones. • RFEM is able to consider the soil variability structure in strip foundation design. • Bearing capacity mean value is affected by soil spatial variability. • Bearing capacity is affected by autocorrelation function model. • Coefficient of variation COV reduces as the foundation size increases. • Both drained and undrained soil conditions show similar COV reduction.

The SAFER geodatabase for the Kathmandu valley: Bayesian kriging for data-scarce regions

Geostatistical methods are valuable to better understand the spatial distribution of geotechnical parameters at regional scale and to optimize the locations of future ground investigations. This article investigates the use of the kriging interpolation method to extend the knowledge of a specific geotechnical property from a few sites to a broader geographical area with a focus on the Kathmandu valley (Nepal). A Bayesian form of kriging is proposed in this article. The estimation of the shear wave velocity in the uppermost 30 m of soil ( VS30) in the Kathmandu valley is examined. Slope-based VS30 estimates from the United States Geological Survey are used as prior information, and 15 VS30 measurements are used as more precise data. Considering the limited number of high-quality VS30 measurements available in the valley, it is shown that the Bayesian scheme can lead to a more robust estimation of VS30 than that obtained with the ordinary kriging approach. A methodology for conditioning prior low-precision data to the measurements is also presented.

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

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

A multiobjective stochastic simulation optimization algorithm

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

Estimation of Rainfall Curve by using Functional Data Analysis and Ordinary Kriging Approach

Rainfall is an interesting phenomenon to investigate since it is directly related to all aspects of life on earth. One of the important studies is to investigate and understand the rainfall patterns that occur throughout the year. To identify the pattern, it requires a rainfall curve to represent daily observation of rainfall received during the year. Functional data analysis methods are capable to convert discrete data intoa function that can represent the rainfall curve and as a result, try to describe the hidden patterns of the rainfall. This study focused on the distribution of daily rainfall amount using functional data analysis. Fourier basis functions are used for periodic rainfall data. Generalized cross-validation showed 123 basis functions were sufficient to describe the pattern of daily rainfall amount. North and west areas of the peninsula show a significant bimodal pattern with the curve decline between two peaks at the mid-year. Meanwhile,the east shows uni-modal patterns that reached a peak in the last three months. Southern areas show more uniform trends throughout the year. Finally, the functional spatial method is introduced to overcome the problem of estimating the rainfall curve in the locations with no data recorded. We use a leave one out cross-validation as a verification method to compare between the real curve and the predicted curve. We used coefficient of basis functions to get the predicted curve. It was foundthatthe methods ofspatial prediction can match up with the existing spatial prediction methods in terms of accuracy,but it is better as the new approach provides a simpler calculation.

Spatial analysis of the risk to human health from exposure to arsenic contaminated groundwater: A kriging approach

A long-term groundwater quality survey in northeastern Taiwan's Lanyang Plain has revealed obvious contamination of the groundwater in some areas, with measured As concentrations in excess of the acceptable level of 10μg/L. Efforts for assessing the health risk associated with the intake of As through the drinking of contaminated groundwater are a necessary part of the important work of health risk management. However, the standard approach to assessing risks to human health does not adequately account for spatial heterogeneity in the measured As concentrations. Thus, this study applies two different kriging approaches to carry out a spatial analysis of the health risk associated with ingesting As through the drinking of groundwater in the Lanyang Plain. It is found that the indicator kriging (IK) approach, with occurrence probability threshold values of 0.4, 0.5 and 0.6 yields correct classification percentages of 75%, 68% and 61%, respectively, of unacceptable HQ zones. An HQ map prepared with the ordinary kriging (OK) approach shows a correct classification of unacceptable HQ zones of 80%. Considering that the OK approach does not require subjective selection of an occurrence probability threshold value as is the case with the IK approach and can yield a higher percentage of correct classification for unacceptable HQ zones, it is recommended as a more direct and reliable method for spatial analysis of human health risk due to arsenic exposure through the drinking of groundwater. The results show that the geographical distribution of unacceptable HQ zones is concentrated in the eastern part of the study area, which includes the high-population density townships. In other words, 34% of the people had access to groundwater where the HQ was >1. The results of this type of spatial health risk assessment can provide a basis for improving the decision-making process for health risk management.

Performance of Optimally Merged Multisatellite Precipitation Products Using the Dynamic Bayesian Model Averaging Scheme Over the Tibetan Plateau

AbstractAccurate estimation of precipitation from satellites at high spatiotemporal scales over the Tibetan Plateau (TP) remains a challenge. In this study, we proposed a general framework for blending multiple satellite precipitation data using the dynamic Bayesian model averaging (BMA) algorithm. The blended experiment was performed at a daily 0.25° grid scale for 2007–2012 among Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis (TMPA) 3B42RT and 3B42V7, Climate Prediction Center MORPHing technique (CMORPH), and Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks‐Climate Data Record (PERSIANN‐CDR). First, the BMA weights were optimized using the expectation‐maximization (EM) method for each member on each day at 200 calibrated sites and then interpolated to the entire plateau using the ordinary kriging (OK) approach. Thus, the merging data were produced by weighted sums of the individuals over the plateau. The dynamic BMA approach showed better performance with a smaller root‐mean‐square error (RMSE) of 6.77 mm/day, higher correlation coefficient of 0.592, and closer Euclid value of 0.833, compared to the individuals at 15 validated sites. Moreover, BMA has proven to be more robust in terms of seasonality, topography, and other parameters than traditional ensemble methods including simple model averaging (SMA) and one‐outlier removed (OOR). Error analysis between BMA and the state‐of‐the‐art IMERG in the summer of 2014 further proved that the performance of BMA was superior with respect to multisatellite precipitation data merging. This study demonstrates that BMA provides a new solution for blending multiple satellite data in regions with limited gauges.

Soil C quantities of mangrove forests, their competing land uses, and their spatial distribution in the coast of Honda Bay, Philippines

Mangrove forests provide many ecosystem goods and services and they contain large amount of carbon (C) especially in their soil. Yet, their global area is still declining owing to conversion to non-forest land uses. While studies have been conducted on mangrove soil C stocks, our knowledge on how C stocks of mangrove forests compare with those of non-forest land uses that replaced them is still limited. This knowledge is crucial in land use planning and decision-making in the coastal zone. Site-scale mapping and assessments of mangrove soil C stocks and the land uses that replaced them are also limited. The aim of this study was to quantify and compare the soil C stocks in mangrove forests and their competing non-forest land uses (represented by aquaculture pond, coconut plantation, salt pond and cleared mangrove), estimate soil C loss arising from conversion, and model the soil C stock distribution in the entire study site. On the average, the soil C stock of mangrove forests was 851.9±87MgC ha−1 while that of their non-forest competing land uses was less than half at 365.1±31MgC ha−1. Closed canopy mangrove was highest at 1040±104MgC ha−1, followed by open canopy mangrove (640±131MgC ha−1) while aquaculture, salt pond and cleared mangrove had comparable C stocks (454±32, 401±9, 413±25MgC ha−1, respectively) and coconut plantation had the least (42±0.7MgC ha−1). Overall, the reduction in soil C stock (soil C loss) due to land use conversion in mangrove ranged from 398 to 809MgCha−1 (mean: 486.8MgCha−1) or a decline of 57% in soil C stock, on the average. It was possible to model the site-scale spatial distribution of soil C stocks and predict their values with 85% overall certainty using the Ordinary Kriging approach. Results from this study could help inform current discussions on Blue Carbon and REDD+ as well as policy and program development that advance research on soil C conservation and ecosystem services in coastal forested wetlands.

Data‐driven model based design and analysis of antenna structures

Data-driven models, or metamodels, offer an efficient way to mimic the behaviour of computation-intensive simulators. Subsequently, the usage of such computationally cheap metamodels is indispensable in the design of contemporary antenna structures where computation-intensive simulations are often performed in a large scale. Although metamodels offer sufficient flexibility and speed, they often suffer from an exponential growth of required training samples as the dimensionality of the problem increases. In order to alleviate this issue, a Gaussian process based approach, known as Gradient-Enhanced Kriging (GEK), is proposed in this work to achieve cost-efficient modelling of antenna structures. The GEK approach incorporates adjoint-based sensitivity data in addition to function data obtained from electromagnetic simulations. The approach is illustrated using a dielectric resonator and an ultra-wideband antenna structures. The method demonstrates significant accuracy improvement with the less number of training samples over the Ordinary Kriging (OK) approach which utilises function data only. The discussed technique has been favourably compared with OK in terms of computational cost.

Spatial assessment of soil organic carbon and physicochemical properties in a horticultural orchard at arid zone of India using geostatistical approaches.

Soil organic carbon (SOC) is a major indicator of long-term sustenance of agricultural production system. Apart from sustaining productivity, SOC plays a crucial role in context of climate change. Keeping in mind these potentials, spatial variation of SOC contents of a fruit orchard comprising several arid fruit plantations located at arid region of India is assessed in this study through geostatistical approaches. For this purpose, surface and subsurface soil samples from 175 locations from a fruit orchard spreading over 14.33ha area were collected along with geographical coordinates. SOC content and soil physicochemical properties of collected soil samples were determined followed by geostatistical analysis for mapping purposes. Average SOC stock density of the orchard was 14.48Mgha(-1) for 0- to 30-cm soil layer ranging from 9.01Mgha(-1) in Carissa carandas to 19.52Mgha(-1) in Prosopis cineraria block. Range of spatial variation of SOC content was found about 100m, while two other soil physicochemical properties, e.g., pH and electrical conductivity (EC) also showed similar spatial trend. This indicated that minimum sampling distance for future SOC mapping programme may be kept lower than 100m for better accuracy. Ordinary kriging technique satisfactorily predicted SOC contents (in percent) at unsampled locations with root-mean-squared residual (RMSR) of 0.35-0.37. Co-kriging approach was found slightly superior (RMSR=0.26-0.28) than ordinary kriging for spatial prediction of SOC contents because of significant correlations of SOC contents with pH and EC. Uncertainty of SOC estimation was also presented in terms of 90% confidence interval. Spatial estimates of SOC stock through ordinary kriging or co-kriging approach were also found with low uncertainty of estimation than non-spatial estimates, e.g., arithmetic averaging approach. Among different fruit block plantations of the orchard, the block with Prosopis cineraria ('khejri') has higher SOC stock density than others.

Ordinary kriging as a tool to estimate historical daily streamflow records

Abstract. Efficient and responsible management of water resources relies on accurate streamflow records. However, many watersheds are ungaged, limiting the ability to assess and understand local hydrology. Several tools have been developed to alleviate this data scarcity, but few provide continuous daily streamflow records at individual streamgages within an entire region. Building on the history of hydrologic mapping, ordinary kriging was extended to predict daily streamflow time series on a regional basis. Pooling parameters to estimate a single, time-invariant characterization of spatial semivariance structure is shown to produce accurate reproduction of streamflow. This approach is contrasted with a time-varying series of variograms, representing the temporal evolution and behavior of the spatial semivariance structure. Furthermore, the ordinary kriging approach is shown to produce more accurate time series than more common, single-index hydrologic transfers. A comparison between topological kriging and ordinary kriging is less definitive, showing the ordinary kriging approach to be significantly inferior in terms of Nash–Sutcliffe model efficiencies while maintaining significantly superior performance measured by root mean squared errors. Given the similarity of performance and the computational efficiency of ordinary kriging, it is concluded that ordinary kriging is useful for first-order approximation of daily streamflow time series in ungaged watersheds.

Spatial variability estimation and risk assessment of the aquifer level at sparsely gauged basins using geostatistical methodologies

The spatial variability evaluation of the water table level of an aquifer provides useful information in water resources management plans. Three different approaches are applied to estimate the spatial variability of the water table in the study basin. All of them are based on the Kriging methodology. The first is the classical Ordinary Kriging approach, while the second involves information from a secondary variable (surface elevation) and the application of Residual Kriging. The third calculates the probability to lie below a certain groundwater level limit that could cause significant problems in groundwater resources availability. The latter is achieved by means of Indicator Kriging. A recently developed non-linear normalization method is used to transform both data and residuals closer to normal distribution for improved prediction results. In addition, the recently developed Spartan variogram model is applied to determine the spatial dependence of the measurements. The latter proves to be the optimal model, compared to a series of models tested, which provides in combination with the Kriging methodologies the most accurate cross validation estimations. The variogram form is explained with respect to the radius of influence of the pumping wells representing the spatial impact of the pumping activity. Groundwater level and probability maps are developed providing the ability to assess the spatial variability of the groundwater level in the basin and the risk that certain locations have in terms of a safe groundwater level limit that has been set for the sustainability of the groundwater resources of the basin.

Assessing biomass based on canopy height profiles using airborne laser scanning data in eucalypt plantations

This study aimed to map the stem biomass of an even-aged eucalyptus plantation in southeastern Brazil based on canopy height profile (CHPs) statistics using wall-to-wall discrete return airborne laser scanning (ALS), and compare the results with alternative maps generated by ordinary kriging interpolation from field-derived measurements. The assessment of stem biomass with ALS data was carried out using regression analysis methods. Initially, CHPs were determined to express the distribution of laser point heights in the ALS cloud for each sample plot. The probability density function (pdf) used was the Weibull distribution, with two parameters that in a secondary task, were used as explanatory variables to model stem biomass. ALS metrics such as height percentiles, dispersion of heights, and proportion of points were also investigated. A simple linear regression model of stem biomass as a function of the Weibull scale parameter showed high correlation (adj.R2 = 0.89). The alternative model considering the 30th percentile and the Weibull shape parameter slightly improved the quality of the estimation (adj.R2 = 0.93). Stem biomass maps based on the Weibull scale parameter doubled the accuracy of the ordinary kriging approach (relative root mean square error = 6 % and 13 %, respectively).

A modeling framework for characterizing near-road air pollutant concentration at community scales

In this study, we combine information from transportation network, traffic emissions, and dispersion model to develop a framework to inform exposure estimates for traffic-related air pollutants (TRAPs) with a high spatial resolution. A Research LINE source dispersion model (R-LINE) is used to model multiple TRAPs from roadways at Census-block level for two U.S. regions. We used a novel Space/Time Ordinary Kriging (STOK) approach that uses data from monitoring networks to provide urban background concentrations. To reduce the computational burden, we developed and applied the METeorologically-weighted Averaging for Risk and Exposure (METARE) approach with R-LINE, where a set of selected meteorological data and annual average daily traffic (AADT) are used to obtain annual averages. Compared with explicit modeling, using METARE reduces CPU-time by 88-fold (46.8h versus 32min), while still retaining accuracy of exposure estimates. We show two examples in the Piedmont region in North Carolina (~105,000 receptors) and Portland, Maine (~7000 receptors) to characterize near-road air quality. Concentrations for NOx, PM2.5, and benzene in Portland drop by over 40% within 200m away from the roadway. The concentration drop in North Carolina is less than that in Portland, as previously shown in an observation-based study, showing the robustness of our approach. Heavy-duty diesel vehicles (HDDV) contribute over 55% of NOx and PM2.5 near interstate highways, while light-duty gasoline vehicles (LDGV) contribute over 50% of benzene to urban areas where multiple roadways intersect. Normalized mean error (NME) between explicit modeling and METARE in Portland ranges from 12.6 to 14.5% and normalized mean bias (NMB) ranges from −12.9 to −11.2%. When considering a static emission rate (i.e. the emission does not have temporal variability), both NME and NMB improved (10.5% and −9.5%). Modeled concentrations in Detroit, Michigan at an array of near-road monitors are within a factor of 2 of observed values for CO but not NOx.

Ordinary kriging approach to predicting long-term particulate matter concentrations in seven major Korean cities

Objectives Cohort studies of associations between air pollution and health have used exposure prediction approaches to estimate individual-level concentrations. A common prediction method used in Korean cohort studies is ordinary kriging. In this study, performance of ordinary kriging models for long-term particulate matter less than or equal to 10 μm in diameter (PM10) concentrations in seven major Korean cities was investigated with a focus on spatial prediction ability. Methods We obtained hourly PM10 data for 2010 at 226 urban-ambient monitoring sites in South Korea and computed annual average PM10 concentrations at each site. Given the annual averages, we developed ordinary kriging prediction models for each of the seven major cities and for the entire country by using an exponential covariance reference model and a maximum likelihood estimation method. For model evaluation, cross-validation was performed and mean square error and R-squared (R2) statistics were computed. Results Mean annual average PM10 concentrations in the seven major cities ranged between 45.5 and 66.0 μg/m3 (standard deviation=2.40 and 9.51 μg/m3, respectively). Cross-validated R2 values in Seoul and Busan were 0.31 and 0.23, respectively, whereas the other five cities had R2 values of zero. The national model produced a higher crossvalidated R2 (0.36) than those for the city-specific models. Conclusions In general, the ordinary kriging models performed poorly for the seven major cities and the entire country of South Korea, but the model performance was better in the national model. To improve model performance, future studies should examine different prediction approaches that incorporate PM10 source characteristics. Keywords: Exposure prediction, Health effect, Kriging, Long-term exposure, Particulate matter