A comparative study of ordinary kriging and support vector machine models for the spatial variability of rock depth in Bangalore

In this paper, reduced level of rock at Bangalore, India is arrived from the 652 boreholes data in the area covering 220 sq.km. In the context of prediction of reduced level of rock in the subsurface of Bangalore and to study the spatial variability of the rock depth, ordinary kriging and Support Vector Machine (SVM) models have been developed. In ordinary kriging, the knowledge of the semivariogram of the reduced level of rock from 652 points in Bangalore is used to predict the reduced level of rock at any point in the subsurface of Bangalore, where field measurements are not available. A cross validation (Q1 and Q2) analysis is also done for the developed ordinary kriging model. The SVM is a novel type of learning machine based on statistical learning theory, uses regression technique by introducing e-insensitive loss function has been used to predict the reduced level of rock from a large set of data. A comparison between ordinary kriging and SVM model demonstrates that the SVM is superior to ordinary kriging in predicting rock depth.

The Discontinuous Nature of Kriging Interpolation for Digital Terrain Modeling

Kriging is a widely employed method for interpolating and estimating elevations from digital elevation data. Its place of prominence is due to its elegant theoretical foundation and its convenient practical implementation. From an interpolation point of view, kriging is equivalent to a thin-plate spline and is one species among the many in the genus of weighted inverse distance methods, albeit with attractive properties. However, from a statistical point of view, kriging is a best linear unbiased estimator and, consequently, has a place of distinction among all spatial estimators because any other linear estimator that performs as well as kriging (in the least squares sense) must be equivalent to kriging, assuming that the parameters of the semivariogram are known. Therefore, kriging is often held to be the gold standard of digital terrain model elevation estimation. However, I prove that, when used with local support, kriging creates discontinuous digital terrain models, which is to say, surfaces with “rips” and “tears” throughout them. This result is general; it is true for ordinary kriging, kriging with a trend, and other forms. A U.S. Geological Survey (USGS) digital elevation model was analyzed to characterize the distribution of the discontinuities. I show that the magnitude of the discontinuity does not depend on surface gradient but is strongly dependent on the size of the kriging neighborhood.

Estimating the effects of ambient temperature on mortality : methodological challenges and proposed solutions

The health impacts of exposure to ambient temperature have been drawing increasing attention from the environmental health research community, government, society, industries, and the public. Case-crossover and time series models are most commonly used to examine the effects of ambient temperature on mortality. However, some key methodological issues remain to be addressed. For example, few studies have used spatiotemporal models to assess the effects of spatial temperatures on mortality. Few studies have used a case-crossover design to examine the delayed (distributed lag) and non-linear relationship between temperature and mortality. Also, little evidence is available on the effects of temperature changes on mortality, and on differences in heat-related mortality over time. This thesis aimed to address the following research questions: 1. How to combine case-crossover design and distributed lag non-linear models? 2. Is there any significant difference in effect estimates between time series and spatiotemporal models? 3. How to assess the effects of temperature changes between neighbouring days on mortality? 4. Is there any change in temperature effects on mortality over time? To combine the case-crossover design and distributed lag non-linear model, datasets including deaths, and weather conditions (minimum temperature, mean temperature, maximum temperature, and relative humidity), and air pollution were acquired from Tianjin China, for the years 2005 to 2007. I demonstrated how to combine the case-crossover design with a distributed lag non-linear model. This allows the case-crossover design to estimate the non-linear and delayed effects of temperature whilst controlling for seasonality. There was consistent U-shaped relationship between temperature and mortality. Cold effects were delayed by 3 days, and persisted for 10 days. Hot effects were acute and lasted for three days, and were followed by mortality displacement for non-accidental, cardiopulmonary, and cardiovascular deaths. Mean temperature was a better predictor of mortality (based on model fit) than maximum or minimum temperature. It is still unclear whether spatiotemporal models using spatial temperature exposure produce better estimates of mortality risk compared with time series models that use a single site’s temperature or averaged temperature from a network of sites. Daily mortality data were obtained from 163 locations across Brisbane city, Australia from 2000 to 2004. Ordinary kriging was used to interpolate spatial temperatures across the city based on 19 monitoring sites. A spatiotemporal model was used to examine the impact of spatial temperature on mortality. A time series model was used to assess the effects of single site’s temperature, and averaged temperature from 3 monitoring sites on mortality. Squared Pearson scaled residuals were used to check the model fit. The results of this study show that even though spatiotemporal models gave a better model fit than time series models, spatiotemporal and time series models gave similar effect estimates. Time series analyses using temperature recorded from a single monitoring site or average temperature of multiple sites were equally good at estimating the association between temperature and mortality as compared with a spatiotemporal model. A time series Poisson regression model was used to estimate the association between temperature change and mortality in summer in Brisbane, Australia during 1996–2004 and Los Angeles, United States during 1987–2000. Temperature change was calculated by the current day's mean temperature minus the previous day's mean. In Brisbane, a drop of more than 3 �C in temperature between days was associated with relative risks (RRs) of 1.16 (95% confidence interval (CI): 1.02, 1.31) for non-external mortality (NEM), 1.19 (95% CI: 1.00, 1.41) for NEM in females, and 1.44 (95% CI: 1.10, 1.89) for NEM aged 65.74 years. An increase of more than 3 �C was associated with RRs of 1.35 (95% CI: 1.03, 1.77) for cardiovascular mortality and 1.67 (95% CI: 1.15, 2.43) for people aged < 65 years. In Los Angeles, only a drop of more than 3 �C was significantly associated with RRs of 1.13 (95% CI: 1.05, 1.22) for total NEM, 1.25 (95% CI: 1.13, 1.39) for cardiovascular mortality, and 1.25 (95% CI: 1.14, 1.39) for people aged . 75 years. In both cities, there were joint effects of temperature change and mean temperature on NEM. A change in temperature of more than 3 �C, whether positive or negative, has an adverse impact on mortality even after controlling for mean temperature. I examined the variation in the effects of high temperatures on elderly mortality (age . 75 years) by year, city and region for 83 large US cities between 1987 and 2000. High temperature days were defined as two or more consecutive days with temperatures above the 90th percentile for each city during each warm season (May 1 to September 30). The mortality risk for high temperatures was decomposed into: a "main effect" due to high temperatures using a distributed lag non-linear function, and an "added effect" due to consecutive high temperature days. I pooled yearly effects across regions and overall effects at both regional and national levels. The effects of high temperature (both main and added effects) on elderly mortality varied greatly by year, city and region. The years with higher heat-related mortality were often followed by those with relatively lower mortality. Understanding this variability in the effects of high temperatures is important for the development of heat-warning systems. In conclusion, this thesis makes contribution in several aspects. Case-crossover design was combined with distribute lag non-linear model to assess the effects of temperature on mortality in Tianjin. This makes the case-crossover design flexibly estimate the non-linear and delayed effects of temperature. Both extreme cold and high temperatures increased the risk of mortality in Tianjin. Time series model using single site’s temperature or averaged temperature from some sites can be used to examine the effects of temperature on mortality. Temperature change (no matter significant temperature drop or great temperature increase) increases the risk of mortality. The high temperature effect on mortality is highly variable from year to year.

Spatiotemporal model or time series model for assessing city-wide temperature effects on mortality?

Most studies examining the temperature–mortality association in a city used temperatures from one site or the average from a network of sites. This may cause measurement error as temperature varies across a city due to effects such as urban heat islands. We examined whether spatiotemporal models using spatially resolved temperatures produced different associations between temperature and mortality compared with time series models that used non-spatial temperatures. We obtained daily mortality data in 163 areas across Brisbane city, Australia from 2000 to 2004. We used ordinary kriging to interpolate spatial temperature variation across the city based on 19 monitoring sites. We used a spatiotemporal model to examine the impact of spatially resolved temperatures on mortality. Also, we used a time series model to examine non-spatial temperatures using a single site and the average temperature from three sites. We used squared Pearson scaled residuals to compare model fit. We found that kriged temperatures were consistent with observed temperatures. Spatiotemporal models using kriged temperature data yielded slightly better model fit than time series models using a single site or the average of three sites' data. Despite this better fit, spatiotemporal and time series models produced similar associations between temperature and mortality. In conclusion, time series models using non-spatial temperatures were equally good at estimating the city-wide association between temperature and mortality as spatiotemporal models.

Spatiotemporal patterns of Aedes aegyptipopulations in Cairns, Australia : assessing drivers of dengue transmission

OBJECTIVES To identify the meteorological drivers of dengue vector density and determine high- and low-risk transmission zones for dengue prevention and control in Cairns, Australia. METHODS Weekly adult female Ae. aegypti data were obtained from 79 double sticky ovitraps (SOs) located in Cairns for the period September 2007-May 2012. Maximum temperature, total rainfall and average relative humidity data were obtained from the Australian Bureau of Meteorology for the study period. Time series-distributed lag nonlinear models were used to assess the relationship between meteorological variables and vector density. Spatial autocorrelation was assessed via semivariography, and ordinary kriging was undertaken to predict vector density in Cairns. RESULTS Ae. aegypti density was associated with temperature and rainfall. However, these relationships differed between short (0-6 weeks) and long (0-30 weeks) lag periods. Semivariograms showed that vector distributions were spatially autocorrelated in September 2007-May 2008 and January 2009-May 2009, and vector density maps identified high transmission zones in the most populated parts of Cairns city, as well as Machans Beach. CONCLUSION Spatiotemporal patterns of Ae. aegypti in Cairns are complex, showing spatial autocorrelation and associations with temperature and rainfall. Sticky ovitraps should be placed no more than 1.2 km apart to ensure entomological coverage and efficient use of resources. Vector density maps provide evidence for the targeting of prevention and control activities. Further research is needed to explore the possibility of developing an early warning system of dengue based on meteorological and environmental factors.

Spatially-explicit modelling of grassland classes - an improved method of integrating a climate-based classification model with interpolated climate surfaces

Spatially-explicit modelling of grassland classes is important to site-specific planning for improving grassland and environmental management over large areas. In this study, a climate-based grassland classification model, the Comprehensive and Sequential Classification System (CSCS) was integrated with spatially interpolated climate data to classify grassland in Gansu province, China. The study area is characterized by complex topographic features imposed by plateaus, high mountains, basins and deserts. To improve the quality of the interpolated climate data and the quality of the spatial classification over this complex topography, three linear regression methods, namely an analytic method based on multiple regression and residues (AMMRR), a modification of the AMMRR method through adding the effect of slope and aspect to the interpolation analysis (M-AMMRR) and a method which replaces the IDW approach for residue interpolation in M-AMMRR with an ordinary kriging approach (I-AMMRR), for interpolating climate variables were evaluated. The interpolation outcomes from the best interpolation method were then used in the CSCS model to classify the grassland in the study area. Climate variables interpolated included the annual cumulative temperature and annual total precipitation. The results indicated that the AMMRR and M-AMMRR methods generated acceptable climate surfaces but the best model fit and cross validation result were achieved by the I-AMMRR method. Twenty-six grassland classes were classified for the study area. The four grassland vegetation classes that covered more than half of the total study area were "cool temperate-arid temperate zonal semi-desert", "cool temperate-humid forest steppe and deciduous broad-leaved forest", "temperate-extra-arid temperate zonal desert", and "frigid per-humid rain tundra and alpine meadow". The vegetation classification map generated in this study provides spatial information on the locations and extents of the different grassland classes. This information can be used to facilitate government agencies' decision-making in land-use planning and environmental management, and for vegetation and biodiversity conservation. The information can also be used to assist land managers in the estimation of safe carrying capacities which will help to prevent overgrazing and land degradation.

Characterising the spatial dynamics of sympatric Aedes aegypti and Aedes albopictus populations in the Philippines

Entomological surveillance and control are essential to the management of dengue fever (DF). Hence, understanding the spatial and temporal patterns of DF vectors, Aedes (Stegomyia) aegypti (L.) and Ae. (Stegomyia) albopictus (Skuse), is paramount. In the Philippines, resources are limited and entomological surveillance and control are generally commenced during epidemics, when transmission is difficult to control. Recent improvements in spatial epidemiological tools and methods offer opportunities to explore more efficient DF surveillance and control solutions: however, there are few examples in the literature from resource-poor settings. The objectives of this study were to: (i) explore spatial patterns of Aedes populations and (ii) predict areas of high and low vector density to inform DF control in San Jose village, Muntinlupa city, Philippines. Fortnightly, adult female Aedes mosquitoes were collected from 50 double-sticky ovitraps (SOs) located in San Jose village for the period June-November 2011. Spatial clustering analysis was performed to identify high and low density clusters of Ae. aegypti and Ae. albopictus mosquitoes. Spatial autocorrelation was assessed by examination of semivariograms, and ordinary kriging was undertaken to create a smoothed surface of predicted vector density in the study area. Our results show that both Ae. aegypti and Ae. albopictus were present in San Jose village during the study period. However, one Aedes species was dominant in a given geographic area at a time, suggesting differing habitat preferences and interspecies competition between vectors. Density maps provide information to direct entomological control activities and advocate the development of geographically enhanced surveillance and control systems to improve DF management in the Philippines.

Spatial prediction on a river network

This article develops methods for spatially predicting daily change of dissolved oxygen (Dochange) at both sampled locations (134 freshwater sites in 2002 and 2003) and other locations of interest throughout a river network in South East Queensland, Australia. In order to deal with the relative sparseness of the monitoring locations in comparison to the number of locations where one might want to make predictions, we make a classification of the river and stream locations. We then implement optimal spatial prediction (ordinary and constrained kriging) from geostatistics. Because of their directed-tree structure, rivers and streams offer special challenges. A complete approach to spatial prediction on a river network is given, with special attention paid to environmental exceedances. The methodology is used to produce a map of Dochange predictions for 2003. Dochange is one of the variables measured as part of the Ecosystem Health Monitoring Program conducted within the Moreton Bay Waterways and Catchments Partnership.

黄土高原降水计算插值与插值计算结果的对比分析

　收集黄土高原及周边地区74 个气象站1952 —2001 年降水数据, 用ArcGIS913 普通克里金(ordinary kriging) 插 值法采用计算插值(calculate then interpolate , CI) 和插值计算(interpolate then calculate , IC) 的方法生成黄土高原地区 1952 —2001 年50 a 平均年降水量和年降水量线性趋势系数空间分布表面, 并对其进行统计分析和地形分析。结果 表明: 1) 从插值结果统计值看, CI、IC 法生成的黄土高原地区50 a 平均年降水量和线性趋势系数空间分布表面平 均值分别为421165、421156 mm和- 01541 0、- 01423 1 mm/ a , 相似系数分别为99178 %和95199 % , 二者一致性良好; 2) 从插值结果表面光滑度看, IC 法稍优于CI 法,借用地形分析对生成表面进行坡度、坡向运算, 可作为评价表面 光滑度、空间数量变化特征和空间方向变化特征的直观方法; 3) 黄土高原地区50 a 平均年降水量具有东南多西北 少、南多北少、东多西少的分布规律, 其中服从东南西北、南北和东西方向递减的地带性分布规律区域占黄土高原 地区面积的89134 % , 非地带性分布规律区域占10166 %; 4) CI 和IC 法计算的黄土高原地区1952 —2001 年降水线 性趋势系数平均- 01541 0 和- 01423 1 mm/ a ,黄土高原地区年降水量有明显减少趋势。

土壤稳定入渗速率空间插值不确定性研究

以黄土丘陵沟壑第三副区的藉河流域为研究区,根据65个实测点数据,采用普通克里格法、反距离权重法、样条函数法等插值方法,分析了测点数量变化、栅格像元尺寸变化及插值方法的差异对土壤稳定入渗速率空间插值结果的影响,剖析了空间插值中的不确定性。结果表明:(1)参与插值站点越多,所得插值结果不确定性越小;(2)像元尺寸在25~800 m间变化对土壤稳定入渗速率的插值结果影响微弱;(3)不同插值方法对插值结果的精度影响较大,说明插值方法的差异对插值结果的不确定性有较大影响。

陕西省水蚀土壤因子指标插值方法比较研究

基于地统计学原理和半变异理论,采用地理信息系统技术定量研究了陕西省水蚀土壤因子指标的空间变异特征。分析比较了反距离权重法、样条函数法与普通克吕格法对陕西省土壤因子指标空间插值的精度。结果表明,研究区土壤抗冲系数具有中等强度的空间相关性,块金系数为32.29%,而稳渗速率、崩解速率、抗剪强度均表现为强烈的空间相关性,块金系数分别为13.19%,11.61%和12.98%。综合考虑平均相对误差、均方差及插值效果,认为普通克吕格法最好,更能反映土壤参数的空间特征并符合区域水土流失模型对数据的要求。对于普通克吕格法,稳渗速率的Lag步长为30 000 m,半方差理论模型为指数模型;抗冲系数、崩解速率、抗剪强度的Lag步长为55 000,半方差理论模型均为高斯模型。在空间分布上,各指标随土壤类型由北到南呈现明显的地带性规律。

Spatial distribution of soil heavy metal pollution estimated by different interpolation methods: Accuracy and uncertainty analysis

Mapping the spatial distribution of contaminants in soils is the basis of pollution evaluation and risk control. Interpolation methods are extensively applied in the mapping processes to estimate the heavy metal concentrations at unsampled sites. The performances of interpolation methods (inverse distance weighting, local polynomial, ordinary kriging and radial basis functions) were assessed and compared using the root mean square error for cross validation. The results indicated that all interpolation methods provided a high prediction accuracy of the mean concentration of soil heavy metals. However, the classic method based on percentages of polluted samples, gave a pollution area 23.54-41.92% larger than that estimated by interpolation methods. The difference in contaminated area estimation among the four methods reached 6.14%. According to the interpolation results, the spatial uncertainty of polluted areas was mainly located in three types of region: (a) the local maxima concentration region surrounded by low concentration (clean) sites, (b) the local minima concentration region surrounded with highly polluted samples; and (c) the boundaries of the contaminated areas. (C) 2010 Elsevier Ltd. All rights reserved.

Dynamical instability in surface permeability characteristics of building sandstones in response to salt accumulation over time

This paper explores how the surface permeability of sandstone blocks changes over time in response to repeated salt weathering cycles. Surface permeability controls the amount of moisture and dissolved salt that can penetrate in and facilitate decay. Connected pores permit the movement of moisture (and hence soluble salts) into the stone interior, and where areas are more or less permeable soluble salts may migrate along preferred pathways at differential rates. Previous research has shown that salts can accumulate in the near-surface zone and lead to partial pore blocking which influences subsequent moisture ingress and causes rapid salt accumulation in the near-surface zone.

Two parallel salt weathering simulations were carried out on blocks of Peakmoor Sandstone of different volumes. Blocks were removed from simulations after 2, 5, 10, 20 and 60 cycles. Permeability measurements were taken for these blocks at a resolution of 20 mm, providing a grid of 100 permeability values for each surface. The geostatistical technique of ordinary kriging was applied to the data to produce a smoothed interpolation of permeability for these surfaces, and hence improve understanding of the evolution of permeability over time in response to repeated salt weathering cycles.

Results illustrate the different responses of the sandstone blocks of different volumes to repeated salt weathering cycles. In both cases, after an initial subtle decline in the permeability (reflecting pore blocking), the permeability starts to increase — reflected in a rise in mean, maximum and minimum values. However, between 10 and 20 cycles, there is a jump in the mean and range permeability of the group A block surfaces coinciding with the onset of meaningful debris release. After 60 cycles, the range of permeability in the group A block surface had increased markedly, suggesting the development of a secondary permeability. The concept of dynamic instability and divergent behaviour is applied at the scale of a single block surface, with initial small-scale differences across a surface having larger scale consequences as weathering progresses.

After cycle 10, group B blocks show a much smaller increase in mean permeability, and the range stays relatively steady — this may be explained by the capillary conditions set up by the smaller volume of the stone, allowing salts to migrate to the ‘back’ of the blocks and effectively relieving stress at the ‘front’ face.

Increasing the accuracy of Nitrogen Dioxide (NO2) pollution mapping using geographically weighted regression (GWR) and geostatistics.

Nitrogen Dioxide (NO2) is known to act as an environmental trigger for many respiratory illnesses. As a pollutant it is difficult to map accurately, as concentrations can vary greatly over small distances. In this study three geostatistical techniques were compared, producing maps of NO2 concentrations in the United Kingdom (UK). The primary data source for each technique was NO2 point data, generated from background automatic monitoring and background diffusion tubes, which are analysed by different laboratories on behalf of local councils and authorities in the UK. The techniques used were simple kriging (SK), ordinary kriging (OK) and simple kriging with a locally varying mean (SKlm). SK and OK make use of the primary variable only. SKlm differs in that it utilises additional data to inform prediction, and hence potentially reduces uncertainty. The secondary data source was Oxides of Nitrogen (NOx) derived from dispersion modelling outputs, at 1km x 1km resolution for the UK. These data were used to define the locally varying mean in SKlm, using two regression approaches: (i) global regression (GR) and (ii) geographically weighted regression (GWR). Based upon summary statistics and cross-validation prediction errors, SKlm using GWR derived local means produced the most accurate predictions. Therefore, using GWR to inform SKlm was beneficial in this study.

Patterns of Holocene relative sea level change in the North of Britain and Ireland

Temporal and spatial patterns of relative sea level (RSL) change in the North of Britain and Ireland during the Holocene are examined. Four episodes, each defined by marked changes in the RSL trend, are identified. Each episode is marked by a rise to a culminating shoreline followed by a fall. Episode HRSL-1 dates from the Younger Dryas to early in the Holocene; HRSL-2 to HRSL-4 occurred later in the Holocene. There is extensive evidence for each episode, and on this basis the spatial distribution of the altitude data for three culminating shorelines and a shoreline formed at the time of the Holocene Storegga Slide tsunami (ca 8110 ± 100 cal. BP) is analysed. Ordinary Kriging is used to determine the general pattern, following which Gaussian Trend Surface Analysis is employed. Recognising that empirical measurements of RSL change can be unevenly distributed spatially, a new approach is introduced which enables the developing pattern to be identified. The patterns for the most widely occurring shorelines were analysed and found to be similar and common centre and axis models were developed for all shorelines. The analyses described provide models of the spatial pattern of Holocene RSL change in the area between ca 8100 cal. BP and ca 1000 cal. BP based on 2262 high resolution shoreline altitude measurements. These models fit the data closely, no shoreline altitude measurement lying more than −1.70 m or +1.82 m from the predicted value. The models disclose a similar pattern to a recently published Glacial Isostatic Adjustment model for present RSL change across the area, indicating that the overall spatial pattern of RSL change may not have varied greatly during the last ca 8000 years.