Robust automatic mapping algorithms in a network monitoring scenario

Automatically generating maps of a measured variable of interest can be problematic. In this work we focus on the monitoring network context where observations are collected and reported by a network of sensors, and are then transformed into interpolated maps for use in decision making. Using traditional geostatistical methods, estimating the covariance structure of data collected in an emergency situation can be difficult. Variogram determination, whether by method-of-moment estimators or by maximum likelihood, is very sensitive to extreme values. Even when a monitoring network is in a routine mode of operation, sensors can sporadically malfunction and report extreme values. If this extreme data destabilises the model, causing the covariance structure of the observed data to be incorrectly estimated, the generated maps will be of little value, and the uncertainty estimates in particular will be misleading. Marchant and Lark [2007] propose a REML estimator for the covariance, which is shown to work on small data sets with a manual selection of the damping parameter in the robust likelihood. We show how this can be extended to allow treatment of large data sets together with an automated approach to all parameter estimation. The projected process kriging framework of Ingram et al. [2007] is extended to allow the use of robust likelihood functions, including the two component Gaussian and the Huber function. We show how our algorithm is further refined to reduce the computational complexity while at the same time minimising any loss of information. To show the benefits of this method, we use data collected from radiation monitoring networks across Europe. We compare our results to those obtained from traditional kriging methodologies and include comparisons with Box-Cox transformations of the data. We discuss the issue of whether to treat or ignore extreme values, making the distinction between the robust methods which ignore outliers and transformation methods which treat them as part of the (transformed) process. Using a case study, based on an extreme radiological events over a large area, we show how radiation data collected from monitoring networks can be analysed automatically and then used to generate reliable maps to inform decision making. We show the limitations of the methods and discuss potential extensions to remedy these.

Fast algorithms for automatic mapping with space-limited covariance functions

In this paper we discuss a fast Bayesian extension to kriging algorithms which has been used successfully for fast, automatic mapping in emergency conditions in the Spatial Interpolation Comparison 2004 (SIC2004) exercise. The application of kriging to automatic mapping raises several issues such as robustness, scalability, speed and parameter estimation. Various ad-hoc solutions have been proposed and used extensively but they lack a sound theoretical basis. In this paper we show how observations can be projected onto a representative subset of the data, without losing significant information. This allows the complexity of the algorithm to grow as O(n m 2), where n is the total number of observations and m is the size of the subset of the observations retained for prediction. The main contribution of this paper is to further extend this projective method through the application of space-limited covariance functions, which can be used as an alternative to the commonly used covariance models. In many real world applications the correlation between observations essentially vanishes beyond a certain separation distance. Thus it makes sense to use a covariance model that encompasses this belief since this leads to sparse covariance matrices for which optimised sparse matrix techniques can be used. In the presence of extreme values we show that space-limited covariance functions offer an additional benefit, they maintain the smoothness locally but at the same time lead to a more robust, and compact, global model. We show the performance of this technique coupled with the sparse extension to the kriging algorithm on synthetic data and outline a number of computational benefits such an approach brings. To test the relevance to automatic mapping we apply the method to the data used in a recent comparison of interpolation techniques (SIC2004) to map the levels of background ambient gamma radiation. © Springer-Verlag 2007.

Sequential, Bayesian geostatistics:a principled method for large data sets

The principled statistical application of Gaussian random field models used in geostatistics has historically been limited to data sets of a small size. This limitation is imposed by the requirement to store and invert the covariance matrix of all the samples to obtain a predictive distribution at unsampled locations, or to use likelihood-based covariance estimation. Various ad hoc approaches to solve this problem have been adopted, such as selecting a neighborhood region and/or a small number of observations to use in the kriging process, but these have no sound theoretical basis and it is unclear what information is being lost. In this article, we present a Bayesian method for estimating the posterior mean and covariance structures of a Gaussian random field using a sequential estimation algorithm. By imposing sparsity in a well-defined framework, the algorithm retains a subset of “basis vectors” that best represent the “true” posterior Gaussian random field model in the relative entropy sense. This allows a principled treatment of Gaussian random field models on very large data sets. The method is particularly appropriate when the Gaussian random field model is regarded as a latent variable model, which may be nonlinearly related to the observations. We show the application of the sequential, sparse Bayesian estimation in Gaussian random field models and discuss its merits and drawbacks.

Optimal design for correlated processes with input-dependent noise

Optimal design for parameter estimation in Gaussian process regression models with input-dependent noise is examined. The motivation stems from the area of computer experiments, where computationally demanding simulators are approximated using Gaussian process emulators to act as statistical surrogates. In the case of stochastic simulators, which produce a random output for a given set of model inputs, repeated evaluations are useful, supporting the use of replicate observations in the experimental design. The findings are also applicable to the wider context of experimental design for Gaussian process regression and kriging. Designs are proposed with the aim of minimising the variance of the Gaussian process parameter estimates. A heteroscedastic Gaussian process model is presented which allows for an experimental design technique based on an extension of Fisher information to heteroscedastic models. It is empirically shown that the error of the approximation of the parameter variance by the inverse of the Fisher information is reduced as the number of replicated points is increased. Through a series of simulation experiments on both synthetic data and a systems biology stochastic simulator, optimal designs with replicate observations are shown to outperform space-filling designs both with and without replicate observations. Guidance is provided on best practice for optimal experimental design for stochastic response models. © 2013 Elsevier Inc. All rights reserved.

Surrogate-based analysis and optimization for the design of heat sinks with jet impingement

Heat sinks are widely used for cooling electronic devices and systems. Their thermal performance is usually determined by the material, shape, and size of the heat sink. With the assistance of computational fluid dynamics (CFD) and surrogate-based optimization, heat sinks can be designed and optimized to achieve a high level of performance. In this paper, the design and optimization of a plate-fin-type heat sink cooled by impingement jet is presented. The flow and thermal fields are simulated using the CFD simulation; the thermal resistance of the heat sink is then estimated. A Kriging surrogate model is developed to approximate the objective function (thermal resistance) as a function of design variables. Surrogate-based optimization is implemented by adaptively adding infill points based on an integrated strategy of the minimum value, the maximum mean square error approach, and the expected improvement approaches. The results show the influence of design variables on the thermal resistance and give the optimal heat sink with lowest thermal resistance for given jet impingement conditions.

System-on-a-Chip (SOC) based environmental monitoring platform for the detection of hazardous materials

The purpose of this research is design considerations for environmental monitoring platforms for the detection of hazardous materials using System-on-a-Chip (SoC) design. Design considerations focus on improving key areas such as: (1) sampling methodology; (2) context awareness; and (3) sensor placement. These design considerations for environmental monitoring platforms using wireless sensor networks (WSN) is applied to the detection of methylmercury (MeHg) and environmental parameters affecting its formation (methylation) and deformation (demethylation). ^ The sampling methodology investigates a proof-of-concept for the monitoring of MeHg using three primary components: (1) chemical derivatization; (2) preconcentration using the purge-and-trap (P&T) method; and (3) sensing using Quartz Crystal Microbalance (QCM) sensors. This study focuses on the measurement of inorganic mercury (Hg) (e.g., Hg2+) and applies lessons learned to organic Hg (e.g., MeHg) detection. ^ Context awareness of a WSN and sampling strategies is enhanced by using spatial analysis techniques, namely geostatistical analysis (i.e., classical variography and ordinary point kriging), to help predict the phenomena of interest in unmonitored locations (i.e., locations without sensors). This aids in making more informed decisions on control of the WSN (e.g., communications strategy, power management, resource allocation, sampling rate and strategy, etc.). This methodology improves the precision of controllability by adding potentially significant information of unmonitored locations.^ There are two types of sensors that are investigated in this study for near-optimal placement in a WSN: (1) environmental (e.g., humidity, moisture, temperature, etc.) and (2) visual (e.g., camera) sensors. The near-optimal placement of environmental sensors is found utilizing a strategy which minimizes the variance of spatial analysis based on randomly chosen points representing the sensor locations. Spatial analysis is employed using geostatistical analysis and optimization occurs with Monte Carlo analysis. Visual sensor placement is accomplished for omnidirectional cameras operating in a WSN using an optimal placement metric (OPM) which is calculated for each grid point based on line-of-site (LOS) in a defined number of directions where known obstacles are taken into consideration. Optimal areas of camera placement are determined based on areas generating the largest OPMs. Statistical analysis is examined by using Monte Carlo analysis with varying number of obstacles and cameras in a defined space. ^

Development of methods for spatial modeling of sediments quality in Lake Okeechobee, Florida

The major objectives of this dissertation were to develop optimal spatial techniques to model the spatial-temporal changes of the lake sediments and their nutrients from 1988 to 2006, and evaluate the impacts of the hurricanes occurred during 1998–2006. Mud zone reduced about 10.5% from 1988 to 1998, and increased about 6.2% from 1998 to 2006. Mud areas, volumes and weight were calculated using validated Kriging models. From 1988 to 1998, mud thicknesses increased up to 26 cm in the central lake area. The mud area and volume decreased about 13.78% and 10.26%, respectively. From 1998 to 2006, mud depths declined by up to 41 cm in the central lake area, mud volume reduced about 27%. Mud weight increased up to 29.32% from 1988 to 1998, but reduced over 20% from 1998 to 2006. The reduction of mud sediments is likely due to re-suspension and redistribution by waves and currents produced by large storm events, particularly Hurricanes Frances and Jeanne in 2004 and Wilma in 2005. Regression, kriging, geographically weighted regression (GWR) and regression-kriging models have been calibrated and validated for the spatial analysis of the sediments TP and TN of the lake. GWR models provide the most accurate predictions for TP and TN based on model performance and error analysis. TP values declined from an average of 651 to 593 mg/kg from 1998 to 2006, especially in the lake’s western and southern regions. From 1988 to 1998, TP declined in the northern and southern areas, and increased in the central-western part of the lake. The TP weights increased about 37.99%–43.68% from 1988 to 1998 and decreased about 29.72%–34.42% from 1998 to 2006. From 1988 to 1998, TN decreased in most areas, especially in the northern and southern lake regions; western littoral zone had the biggest increase, up to 40,000 mg/kg. From 1998 to 2006, TN declined from an average of 9,363 to 8,926 mg/kg, especially in the central and southern regions. The biggest increases occurred in the northern lake and southern edge areas. TN weights increased about 15%–16.2% from 1988 to 1998, and decreased about 7%–11% from 1998 to 2006.

Dinâmica das configurações de formação e inibição das chuvas no Rio Grande do Norte: caracterização hidroclimática do estado

This study aimed to evaluate the influence of the main meteorological mechanisms trainers and inhibitors of precipitation, and the interactions between different scales of operation, the spatial and temporal variability of the annual cycle of precipitation in the Rio Grande do Norte. Além disso, considerando as circunstâncias locais e regionais, criando assim uma base científica para apoiar ações futuras na gestão da demanda de água no Estado. Database from monthly precipitation of 45 years, ranging between 1963 and 2007, data provided by EMPARN. The methodology used to achieve the results was initially composed of descriptive statistical analysis of historical data to prove the stability of the series, were applied after, geostatistics tool for plotting maps of the variables, within the geostatistical we opted for by Kriging interpolation method because it was the method that showed the best results and minor errors. Among the results, we highlight the annual cycle of rainfall the State which is influenced by meteorological mechanisms of different spatial and temporal scales, where the main mechanisms cycle modulators are the Conference Intertropical Zone (ITCZ) acting since midFebruary to mid May throughout the state, waves Leste (OL), Lines of instability (LI), breeze systems and orographic rainfall acting mainly in the Coastal strip between February and July. Along with vortice of high levels (VCANs), Complex Mesoscale Convective (CCMs) and orographic rain in any region of the state mainly in spring and summer. In terms of larger scale phenomena stood out El Niño and La Niña, ENSO in the tropical Pacific basin. In La Niña episodes usually occur normal or rainy years, as upon the occurrence of prolonged periods of drought are influenced by EL NIÑO. In the Atlantic Ocean the standard Dipole also affects the intensity of the rainfall cycle in State. The cycle of rains in Rio Grande do Norte is divided into two periods, one comprising the regions West, Central and the Western Portion of the Wasteland Potiguar mesoregions of west Chapada Borborema, causing rains from midFebruary to mid-May and a second period of cycle, between February-July, where rains occur in mesoregions East and of the Wasteland, located upwind of the Chapada Borborema, both interspersed with dry periods without occurrence of significant rainfall and transition periods of rainy - dry and dry-rainy where isolated rainfall occur. Approximately 82% of the rainfall stations of the state which corresponds to 83.4% of the total area of Rio Grande do Norte, do not record annual volumes above 900 mm. Because the water supply of the State be maintained by small reservoirs already are in an advanced state of eutrophication, when the rains occur, act to wash and replace the water in the reservoirs, improving the quality of these, reducing the eutrophication process. When rain they do not significantly occur or after long periods of shortages, the process of eutrophication and deterioration of water in dams increased significantly. Through knowledge of the behavior of the annual cycle of rainfall can have an intimate knowledge of how it may be the tendency of rainy or prone to shortages following period, mainly observing the trends of larger scale phenomena

Sea surface and the sea floor regionalization of the Southern Ocean by multivariate cluster analysis, links to ArcGIS project files

This study subdivides the Weddell Sea, Antarctica, into seafloor regions using multivariate statistical methods. These regions are categories used for comparing, contrasting and quantifying biogeochemical processes and biodiversity between ocean regions geographically but also regions under development within the scope of global change. The division obtained is characterized by the dominating components and interpreted in terms of ruling environmental conditions. The analysis uses 28 environmental variables for the sea surface, 25 variables for the seabed and 9 variables for the analysis between surface and bottom variables. The data were taken during the years 1983-2013. Some data were interpolated. The statistical errors of several interpolation methods (e.g. IDW, Indicator, Ordinary and Co-Kriging) with changing settings have been compared for the identification of the most reasonable method. The multivariate mathematical procedures used are regionalized classification via k means cluster analysis, canonical-correlation analysis and multidimensional scaling. Canonical-correlation analysis identifies the influencing factors in the different parts of the cove. Several methods for the identification of the optimum number of clusters have been tested. For the seabed 8 and 12 clusters were identified as reasonable numbers for clustering the Weddell Sea. For the sea surface the numbers 8 and 13 and for the top/bottom analysis 8 and 3 were identified, respectively. Additionally, the results of 20 clusters are presented for the three alternatives offering the first small scale environmental regionalization of the Weddell Sea. Especially the results of 12 clusters identify marine-influenced regions which can be clearly separated from those determined by the geological catchment area and the ones dominated by river discharge.

Wind Resource Mapping Using Landscape Roughness and Spatial Interpolation Methods

Energy saving, reduction of greenhouse gasses and increased use of renewables are key policies to achieve the European 2020 targets. In particular, distributed renewable energy sources, integrated with spatial planning, require novel methods to optimise supply and demand. In contrast with large scale wind turbines, small and medium wind turbines (SMWTs) have a less extensive impact on the use of space and the power system, nevertheless, a significant spatial footprint is still present and the need for good spatial planning is a necessity. To optimise the location of SMWTs, detailed knowledge of the spatial distribution of the average wind speed is essential, hence, in this article, wind measurements and roughness maps were used to create a reliable annual mean wind speed map of Flanders at 10 m above the Earth’s surface. Via roughness transformation, the surface wind speed measurements were converted into meso- and macroscale wind data. The data were further processed by using seven different spatial interpolation methods in order to develop regional wind resource maps. Based on statistical analysis, it was found that the transformation into mesoscale wind, in combination with Simple Kriging, was the most adequate method to create reliable maps for decision-making on optimal production sites for SMWTs in Flanders (Belgium).

Spatial and temporal interaction between sediment and microphytobenthos in a temperate estuarine macro-intertidal bay

Intertidal flats of the estuarine macro-intertidal Baie des Veys (France) were investigated to identify spatial features of sediment and microphytobenthos (MPB) in April 2003. Gradients occurred within the domain, and patches were identified close to vegetated areas or within the oyster-farming areas where calm physical conditions and biodeposition altered the sediment and MPB landscapes. Spatial patterns of chl a content were explained primarily by the influence of sediment features, while bed elevation and compaction brought only minor insights into MPB distribution regulation. The smaller size of MPB patches compared to silt patches revealed the interplay between physical structure defining the sediment landscape, the biotic patches that they contain, and that median grain-size is the most important parameter in explaining the spatial pattern of MPB. Small-scale temporal dynamics of sediment chl a content and grain-size distribution were surveyed in parallel during 2 periods of 14 d to detect tidal and seasonal variations. Our results showed a weak relationship between mud fraction and MPB biomass in March, and this relationship fully disappeared in July. Tidal exposure was the most important parameter in explaining the summer temporal dynamics of MPB. This study reveals the general importance of bed elevation and tidal exposure in muddy habitats and that silt content was a prime governing physical factor in winter. Biostabilisation processes seemed to behave only as secondary factors that could only amplify the initial silt accumulation in summer rather than primary factors explaining spatial or long-term trends of sediment changes.

Quantification of air quality in space and time and its effects on health

The long-term adverse effects on health associated with air pollution exposure can be estimated using either cohort or spatio-temporal ecological designs. In a cohort study, the health status of a cohort of people are assessed periodically over a number of years, and then related to estimated ambient pollution concentrations in the cities in which they live. However, such cohort studies are expensive and time consuming to implement, due to the long-term follow up required for the cohort. Therefore, spatio-temporal ecological studies are also being used to estimate the long-term health effects of air pollution as they are easy to implement due to the routine availability of the required data. Spatio-temporal ecological studies estimate the health impact of air pollution by utilising geographical and temporal contrasts in air pollution and disease risk across $n$ contiguous small-areas, such as census tracts or electoral wards, for multiple time periods. The disease data are counts of the numbers of disease cases occurring in each areal unit and time period, and thus Poisson log-linear models are typically used for the analysis. The linear predictor includes pollutant concentrations and known confounders such as socio-economic deprivation. However, as the disease data typically contain residual spatial or spatio-temporal autocorrelation after the covariate effects have been accounted for, these known covariates are augmented by a set of random effects. One key problem in these studies is estimating spatially representative pollution concentrations in each areal which are typically estimated by applying Kriging to data from a sparse monitoring network, or by computing averages over modelled concentrations (grid level) from an atmospheric dispersion model. The aim of this thesis is to investigate the health effects of long-term exposure to Nitrogen Dioxide (NO2) and Particular matter (PM10) in mainland Scotland, UK. In order to have an initial impression about the air pollution health effects in mainland Scotland, chapter 3 presents a standard epidemiological study using a benchmark method. The remaining main chapters (4, 5, 6) cover the main methodological focus in this thesis which has been threefold: (i) how to better estimate pollution by developing a multivariate spatio-temporal fusion model that relates monitored and modelled pollution data over space, time and pollutant; (ii) how to simultaneously estimate the joint effects of multiple pollutants; and (iii) how to allow for the uncertainty in the estimated pollution concentrations when estimating their health effects. Specifically, chapters 4 and 5 are developed to achieve (i), while chapter 6 focuses on (ii) and (iii). In chapter 4, I propose an integrated model for estimating the long-term health effects of NO2, that fuses modelled and measured pollution data to provide improved predictions of areal level pollution concentrations and hence health effects. The air pollution fusion model proposed is a Bayesian space-time linear regression model for relating the measured concentrations to the modelled concentrations for a single pollutant, whilst allowing for additional covariate information such as site type (e.g. roadside, rural, etc) and temperature. However, it is known that some pollutants might be correlated because they may be generated by common processes or be driven by similar factors such as meteorology. The correlation between pollutants can help to predict one pollutant by borrowing strength from the others. Therefore, in chapter 5, I propose a multi-pollutant model which is a multivariate spatio-temporal fusion model that extends the single pollutant model in chapter 4, which relates monitored and modelled pollution data over space, time and pollutant to predict pollution across mainland Scotland. Considering that we are exposed to multiple pollutants simultaneously because the air we breathe contains a complex mixture of particle and gas phase pollutants, the health effects of exposure to multiple pollutants have been investigated in chapter 6. Therefore, this is a natural extension to the single pollutant health effects in chapter 4. Given NO2 and PM10 are highly correlated (multicollinearity issue) in my data, I first propose a temporally-varying linear model to regress one pollutant (e.g. NO2) against another (e.g. PM10) and then use the residuals in the disease model as well as PM10, thus investigating the health effects of exposure to both pollutants simultaneously. Another issue considered in chapter 6 is to allow for the uncertainty in the estimated pollution concentrations when estimating their health effects. There are in total four approaches being developed to adjust the exposure uncertainty. Finally, chapter 7 summarises the work contained within this thesis and discusses the implications for future research.

Transfer function-noise modeling and spatial interpolation to evaluate the risk of extreme (shallow) water-table levels in the Brazilian Cerrados

Water regimes in the Brazilian Cerrados are sensitive to climatological disturbances and human intervention. The risk that critical water-table levels are exceeded over long periods of time can be estimated by applying stochastic methods in modeling the dynamic relationship between water levels and driving forces such as precipitation and evapotranspiration. In this study, a transfer function-noise model, the so called PIRFICT-model, is applied to estimate the dynamic relationship between water-table depth and precipitation surplus/deficit in a watershed with a groundwater monitoring scheme in the Brazilian Cerrados. Critical limits were defined for a period in the Cerrados agricultural calendar, the end of the rainy season, when extremely shallow levels (< 0.5-m depth) can pose a risk to plant health and machinery before harvesting. By simulating time-series models, the risk of exceeding critical thresholds during a continuous period of time (e.g. 10 days) is described by probability levels. These simulated probabilities were interpolated spatially using universal kriging, incorporating information related to the drainage basin from a digital elevation model. The resulting map reduced model uncertainty. Three areas were defined as presenting potential risk at the end of the rainy season. These areas deserve attention with respect to water-management and land-use planning.

Mapeamento de áreas de risco à saúde pública por meio de métodos geoestatísticos

Este trabalho tem por objetivo apresentar uma aplicação de métodos geoestatísticos na elaboração de mapas de risco à saúde pública, por meio da identificação de áreas com maior concentração de metais pesados. Foi escolhido o elemento chumbo (Pb), resultante do transporte aéreo ou do carregamento das partículas causado pela lixiviação do solo, em uma região com grande concentração urbana e industrial na Baixada Santista, São Paulo, Brasil. Elaboraram-se mapas das distribuições espaciais desse elemento por intermédio da krigagem ordinária; posteriormente, utilizando-se a krigagem indicativa, identificaram-se as áreas com valores de contaminação do solo superiores aos níveis máximos aceitáveis pelo órgão de controle ambiental do Estado de São Paulo, originando um mapeamento com áreas com maior probabilidade de risco à saúde pública. Os mapas resultantes mostraram-se ferramentas promissoras para auxiliar a tomada de decisão quanto a questões de políticas públicas relacionadas à saúde e ao planejamento ambiental.

Construcción de mapas de combustible forestal para detectar el peligro de incendio en un bosque de pino-encino

Como herramienta para la identificación de áreas con peligro de incendio se pueden generar mapas a partir de variables que influyen en el comportamiento de estos fenómenos. Los combustibles forestales tienen una influencia directa en el desarrollo y establecimiento de los incendios y son el único componente que puede ser modificado por el hombre. Considerando esto, el presente trabajo se enfocó en la generación de un mapa basado en inventarios de combustibles forestales. La realización de estos inventarios se llevó a cabo mediante la técnica conocida como intersecciones planeares, la información recaudada en campo se aplicó el método Kriging para generar un mapa con la carga de combustible total. Los resultados para el inventario de combustibles se estimaron en un promedio de 37.57 Mg/ha-1. El mapa generado permite identificar áreas con mayor peligro de incendio dentro del área de estudio. La generación de este tipo de información ayuda a la toma de decisiones para la prevención y combate de incendios forestales.