Multi-scale support vector algorithms for hot spot detection and modelling

The algorithmic approach to data modelling has developed rapidly these last years, in particular methods based on data mining and machine learning have been used in a growing number of applications. These methods follow a data-driven methodology, aiming at providing the best possible generalization and predictive abilities instead of concentrating on the properties of the data model. One of the most successful groups of such methods is known as Support Vector algorithms. Following the fruitful developments in applying Support Vector algorithms to spatial data, this paper introduces a new extension of the traditional support vector regression (SVR) algorithm. This extension allows for the simultaneous modelling of environmental data at several spatial scales. The joint influence of environmental processes presenting different patterns at different scales is here learned automatically from data, providing the optimum mixture of short and large-scale models. The method is adaptive to the spatial scale of the data. With this advantage, it can provide efficient means to model local anomalies that may typically arise in situations at an early phase of an environmental emergency. However, the proposed approach still requires some prior knowledge on the possible existence of such short-scale patterns. This is a possible limitation of the method for its implementation in early warning systems. The purpose of this paper is to present the multi-scale SVR model and to illustrate its use with an application to the mapping of Cs¹³⁷ activity given the measurements taken in the region of Briansk following the Chernobyl accident.     

Point process-based modeling of multiple debris flow landslides using INLA: an application to the 2009 Messina disaster

We develop a stochastic modeling approach based on spatial point processes of log-Gaussian Cox type for a collection of around 5000 landslide events provoked by a precipitation trigger in Sicily, Italy. Through the embedding into a hierarchical Bayesian estimation framework, we can use the integrated nested Laplace approximation methodology to make inference and obtain the posterior estimates of spatially distributed covariate and random effects. Several mapping units are useful to partition a given study area in landslide prediction studies. These units hierarchically subdivide the geographic space from the highest grid-based resolution to the stronger morphodynamic-oriented slope units. Here we integrate both mapping units into a single hierarchical model, by treating the landslide triggering locations as a random point pattern. This approach diverges fundamentally from the unanimously used presence–absence structure for areal units since we focus on modeling the expected landslide count jointly within the two mapping units. Predicting this landslide intensity provides more detailed and complete information as compared to the classically used susceptibility mapping approach based on relative probabilities. To illustrate the model’s versatility, we compute absolute probability maps of landslide occurrences and check their predictive power over space. While the landslide community typically produces spatial predictive models for landslides only in the sense that covariates are spatially distributed, no actual spatial dependence has been explicitly integrated so far. Our novel approach features a spatial latent effect defined at the slope unit level, allowing us to assess the spatial influence that remains unexplained by the covariates in the model. For rainfall-induced landslides in regions where the raingauge network is not sufficient to capture the spatial distribution of the triggering precipitation event, this latent effect provides valuable imaging support on the unobserved rainfall pattern.     

Simulation-based risk assessment of contaminated sites under remediation scenarios, planning periods, and land-use patterns—a Canadian case study

Risk assessment of contaminated sites is crucial for quantifying adverse impacts on human health and the environment. It also provides effective decision support for remediation and management of such sites. This study presents an integrated approach for environmental and health risk assessment of subsurface contamination through the incorporation of a multiphase multicomponent modeling system within a general risk assessment framework. The method is applied to a petroleum-contaminated site in western Canada. Three remediation scenarios with different efficiencies (0, 60, and 90%) and planning periods (10, 20, 40, 60, and 80 years later) are examined for each of the five potential land-use plans of the study site. Then three risky zones with different temporal and spatial distributions are identified based on the local environmental guidelines and the excess lifetime cancer risk criteria. The obtained results are useful for assessing potential human health effects when the groundwater is used for drinking water supply. They are also critical for evaluating environmental impacts when the groundwater is used for irrigation, stockbreeding, fish culture, or when the site remains the status quo. Moreover, the results indicate that the proposed method can effectively identify risky zones with different risk levels under various remediation actions, planning periods, and land-use patterns.     

Stochastic simulation of regionalized ground motions using wavelet packets and cokriging analysis

Performance‐based earthquake engineering often requires ground‐motion time‐history analyses to be performed, but very often, ground motions are not recorded at the location being analyzed. The present study is among the first attempt to stochastically simulate spatially distributed ground motions over a region using wavelet packets and cokriging analysis. First, we characterize the time and frequency properties of ground motions using the wavelet packet analysis. The spatial cross‐correlations of wavelet packet parameters are determined through geostatistical analysis of regionalized ground‐motion data from the Northridge and Chi‐Chi earthquakes. It is observed that the spatial cross‐correlations of wavelet packet parameters are closely related to regional site conditions. Furthermore, using the developed spatial cross‐correlation model and the cokriging technique, wavelet packet parameters at unmeasured locations can be best estimated, and regionalized ground‐motion time histories can be synthesized. Case studies and blind tests using data from the Northridge and Chi‐Chi earthquakes demonstrate that the simulated ground motions generally agree well with the actual recorded data. The proposed method can be used to stochastically simulate regionalized ground motions for time‐history analyses of distributed infrastructure and has important applications in regional‐scale hazard analysis and loss estimation. Copyright © 2014 John Wiley & Sons, Ltd.     

Analysis of the influence of parameter and scale uncertainties on a local multi-criteria land use evaluation model

Land use evaluation involves careful consideration of several environmental factors and their relative importance quantified by factor weights. Local multi-criteria evaluation provides a mechanism for computing factor (criteria) weights within local neighborhoods that capture spatial heterogeneity and contribute to more accurate evaluation results. The accuracy of results, however, is tempered by the potential uncertainty of criteria weights. The paper presents a spatially explicit approach to uncertainty and sensitivity analysis of local criteria weights and modeling scale on the variability of model output. The efficacy of the approach is presented on the example of Environmental Benefit Index (EBI) model used by the U.S. Department of Agriculture Conservation Reserve Program (CRP) to select environmentally sensitive agricultural areas for conservation. The uncertainty analysis resulted in identifying robust areas for CRP selection characterized by high suitability and low uncertainty. The sensitivity analysis focused on the next-best group of candidates characterized by high suitability and high uncertainty. The results show that there is a relationship between spatial heterogeneity, data representation scale, and the level of uncertainty in the results of EBI model. The sensitivity of model output can be attributed to both the uncertainty of criteria weights and the modeling scale. A potential practical value of this approach is the improved analytical support for land suitability evaluation requiring a consideration of sub-optimal land units (high suitability/high uncertainty). Also, this approach can guide modelling effort by allowing the analyst to visualize spatial distribution and patterns of model output uncertainty and focus data collection on influential model input factors.     

An information-fusion method to identify pattern of spatial heterogeneity for improving the accuracy of estimation

While spatial autocorrelation is used in spatial sampling survey to improve the precision of the feature’s estimate of a certain population at area units, spatial heterogeneity as the stratification frame in survey also often have a considerable effect upon the precision. Under the context of increasingly enriched spatiotemporal data, this paper suggests an information-fusion method to identify pattern of spatial heterogeneity, which can be used as an informative stratification for improving the estimation accuracy. Data mining is major analysis components in our method: multivariate statistics, association analysis, decision tree and rough set are used in data filter, identification of contributing factors, and examination of relationship; classification and clustering are used to identify pattern of spatial heterogeneity using the auxiliary variables relevant to the goal and thus to stratify the samples. These methods are illustrated and examined in the case study of the cultivable land survey in Shandong Province in China. Different from many stratification schemes which just uses the goal variable to stratify which is too simplified, information from multiple sources can be fused to identify pattern of spatial heterogeneity, thus stratifying samples at geographical units as an informative polygon map, and thereby to increase the precision of estimates in sampling survey, as demonstrated in our case research.     

Spatial prediction of river channel topography by kriging

Topographic information is fundamental to geomorphic inquiry, and spatial prediction of bed elevation from irregular survey data is an important component of many reach‐scale studies. Kriging is a geostatistical technique for obtaining these predictions along with measures of their reliability, and this paper outlines a specialized framework intended for application to river channels. Our modular approach includes an algorithm for transforming the coordinates of data and prediction locations to a channel‐centered coordinate system, several different methods of representing the trend component of topographic variation and search strategies that incorporate geomorphic information to determine which survey data are used to make a prediction at a specific location. For example, a relationship between curvature and the lateral position of maximum depth can be used to include cross‐sectional asymmetry in a two‐dimensional trend surface model, and topographic breaklines can be used to restrict which data are retained in a local neighborhood around each prediction location. Using survey data from a restored gravel‐bed river, we demonstrate how transformation to the channel‐centered coordinate system facilitates interpretation of the variogram, a statistical model of reach‐scale spatial structure used in kriging, and how the choice of a trend model affects the variogram of the residuals from that trend. Similarly, we show how decomposing kriging predictions into their trend and residual components can yield useful information on channel morphology. Cross‐validation analyses involving different data configurations and kriging variants indicate that kriging is quite robust and that survey density is the primary control on the accuracy of bed elevation predictions. The root mean‐square error of these predictions is directly proportional to the spacing between surveyed cross‐sections, even in a reconfigured channel with a relatively simple morphology; sophisticated methods of spatial prediction are no substitute for field data. Copyright © 2007 John Wiley & Sons, Ltd.     

逸度模型在湖泊流域农药多介质归趋研究中的应用与展望

农药的施用在促进农业经济发展的同时,也带来了诸多环境问题.农药由农业活动排放进入到环境后会通过不同的途径在各介质之间进行迁移和转化,最后由径流作用汇聚于湖泊中,破坏生态环境,影响人类健康.因此,研究湖泊流域生态系统中农药的多介质归趋具有重要意义.使用基于逸度的多介质模型模拟农药在环境中的行为是一个十分有效的方法.逸度模型利用"逸度"的概念描述污染物在各个环境介质之间的迁移和转化过程趋势,其结果建立在化学物质自身物化性质和环境系统性质之上,不仅适用于预测农药在环境各介质中的残留水平,还可以揭示区域内污染的空间分布特征,是湖泊流域生态系统管理中一个重要的工具.本文综述了逸度模型的理论基础,对近年来国内外逸度模型的发展现状、相关环境模型及其在农药归趋研究和湖泊流域生态系统管理中的运用进行了总结,并展望了逸度模型在农药多介质研究中的应用前景,以期对我国农药的管理、合理施用方面提供科学与技术支持.     

A UK perspective on the development of marine ecosystem indicators

This paper reviews the suite of marine ecosystem indicators currently in use or under development in the UK to support the major national and international biodiversity and ecosystem policies. Indicators apply to a range of different ecosystem components, and range from those that can only be used for high level environmental health monitoring, to those which actively support management. Assessment of indicators against a management framework of driving force, pressure, state, impact and response, has shown that there are many indicators of state for ecosystem components, but relatively few for pressure of human activities on the environment, or of the socio-economic response to those pressures. This outcome, a result of unplanned sectorally driven indicator development, is not a co-ordinated contribution to marine environmental management and must be addressed if we are to avoid high monitoring costs and duplication of effort.     

The implementation of Bayesian structural additive regression models in multi-city time series air pollution and human health studies

In this study, a novel Bayesian semiparametric structural additive regression (STAR) model is introduced in multi-city time series air pollution and human health studies. This modeling approach can simultaneously take into account the fixed effects, random effects, nonlinear smoothing functions and spatial functions in an integrated model framework. This study focuses on examining the powerful functionalities of this approach in modeling air pollution and mortality data of 100 U.S. cities from 1987 to 2000. Compared with previous studies, the modeling approach used in this study yields consistent findings of nation-level and city-level PM₁₀ (particulate matter less than 10?μm) effects on mortality. Notably, cities with significantly elevated mortality rates were concentrated in the Northeastern U.S. This modeling approach also emphasizes the important functionality of the spatial function in visualizing disease mapping. Model diagnostics were performed to confirm the availability of the STAR model. We also found consistent findings by using different hyperparameters in the sensitivity analysis. To sum up, the implementation of this modeling approach has achieved the goals of applying a spatial function and obtaining robust results in the multi-city time series air pollution and human health study.     

Application of multivariate analyses in studies of the organization and structure of fish and invertebrate communities

Ecological studies often attempt to link observed effects to multiple causal factors which may be operating simultaneously. Although in situ randomized experiments in which factor levels are controlled may be a powerful means for disentangling causal relationships, an experimental approach is not always feasible or even a desirable first step in the analysis, particularly when there is insufficient background knowledge of the system. In such cases, analysis of survey data, reflecting natural (co)variation in the putative causal factors and their direct and indirect effects, can be a practical and useful alternative to experiments. When set in the proper statistical framework, survey data can be used to assess whether a given factor has a detectable effect once the effect of other factors has been accounted for statistically (by partialling), and to estimate what proportion of the effect can be attributed to each factor (by variance decomposition). This analysis can help establish whether a particular causal model is consistent with the data at hand, and should be viewed as preliminary to a mechanistic approach, providing support and guidance for the investigation of more realistic variables. Here, we use three examples based on survey data from fish and invertebrate lacustrine communities to illustrate the application of partialling and variance decomposition in a multivariate setting. The first example shows that variation in the abundance and size structure of cladoceran taxa is still associated with fish species composition when potentially confounding effects of abiotic variables are accounted for by partialling. In the second and third examples, variance decomposition is used to determine the relative contribution of the environmental and spatial components to variation in the community structure of littoral zoobenthos and in the diet of a freshwater fish species.Contribution of the Group for Interuniversitary Research in Limnology (G.R.I.L.).     

Estimating the provincial environmental Kuznets curve in China: a geographically weighted regression approach

This study estimates the environmental Kuznets curve (EKC) relationship at the province level in China. We apply empirical methods to test three industrial pollutants—SO₂ emission, wastewater discharge, and solid waste production—in 29 Chinese provinces in 1994–2010. We use the geographically weighted regression (GWR) approach, wherein the model can be fitted at each spatial location in the data, weighting all observations by a function of distance from the regression point. Hence, considering spatial heterogeneity, the EKC relationship can be analyzed region-specifically through this approach, rather than describing the average relationship over the entire area examined. We also investigate the spatial stratified heterogeneity to verify and compare risk factors that affect regional pollution with statistical models. This study finds that the GWR model, aimed at considering spatial heterogeneity, outperforms the OLS model; it is more effective at explaining the relationships between environmental performance and economic growth in China. The results indicate a significant variation in the existence of the EKC relationship. Such spatial patterns suggest province-specific policymaking to achieve balanced growth in those provinces.     

Spatial variability of infiltration and related properties of tropical soils

The levels of variance associated with measuring the infiltration process and modelling it by means of a regression model are compared to see which approach yields the best results in terms of effort and accuracy. A nested sampling scheme has been used in the three major physiographic units of central Guyana, South America: ‘White Sands’; (Haplic and Ferralic Arenosols), ‘Brown Sands’ (Haplic Ferrasols) and ‘Laterite’ (Xanthic and Dystric Leptosols). Cluster analysis yields three sample groups that reflect the sharp landscape boundaries between the units. Multiple regression analysis shows that each unit has a different combination of soil properties that explains the variance in final infiltration rate and sorptivity satisfactorily. Nested analysis of variance indicates that clear spatial patterns with distances of variation of several hundred metres exist for final infiltration rate in White Sands and Laterite. Infiltration rate in Brown Sands and sorptivity in all units have large short-distance variabilities and high ‘noise’ levels. The correlated independent variables behave accordingly. For the majority of the soil properties, sampling at distances of 100 to 200 m results in variance levels of more than 80 per cent of the total variance, which indicates that only a detailed investigation can assess spatial variation in soil hydrological behaviour. The use of simple soil properties to predict infiltration is only possible in a very general sense and with the acceptance of high variance levels.     

Using geographically weighted regression to explore the spatially heterogeneous spread of bovine tuberculosis in England and Wales

An understanding of the factors that affect the spread of endemic bovine tuberculosis (bTB) is critical for the development of measures to stop and reverse this spread. Analyses of spatial data need to account for the inherent spatial heterogeneity within the data, or else spatial autocorrelation can lead to an overestimate of the significance of variables. This study used three methods of analysis—least-squares linear regression with a spatial autocorrelation term, geographically weighted regression (GWR) and boosted regression tree (BRT) analysis—to identify the factors that influence the spread of endemic bTB at a local level in England and Wales. The linear regression and GWR methods demonstrated the importance of accounting for spatial differences in risk factors for bTB, and showed some consistency in the identification of certain factors related to flooding, disease history and the presence of multiple genotypes of bTB. This is the first attempt to explore the factors associated with the spread of endemic bTB in England and Wales using GWR. This technique improves on least-squares linear regression approaches by identifying regional differences in the factors associated with bTB spread. However, interpretation of these complex regional differences is difficult and the approach does not lend itself to predictive models which are likely to be of more value to policy makers. Methods such as BRT may be more suited to such a task. Here we have demonstrated that GWR and BRT can produce comparable outputs.     

Predicting quantiles of water quality from catchment characteristics

Water quality is often highly variable both in space and time, which poses challenges for modelling the more extreme concentrations. This study developed an alternative approach to predicting water quality quantiles at individual locations. We focused on river water quality data that were collected over 25 years, at 102 catchments across the State of Victoria, Australia. We analysed and modelled spatial patterns of the 10th, 25th, 50th, 75th and 90th percentiles of the concentrations of sediments, nutrients and salt, with six common constituents: total suspended solids (TSS), total phosphorus (TP), filterable reactive phosphorus (FRP), total Kjeldahl nitrogen (TKN), nitrate-nitrite (NO_x), and electrical conductivity (EC). To predict the spatial variation of each quantile for each constituent, we developed statistical regression models and exhaustively searched through 50 catchment characteristics to identify the best set of predictors for that quantile. The models predict the spatial variation in individual quantiles of TSS, TKN and EC well (66%–96% spatial variation explained), while those for TP, FRP and NO_x have lower performance (37%–73% spatial variation explained). The most common factors that influence the spatial variations of the different constituents and quantiles are: annual temperature, percentage of cropping land area in catchment and channel slope. The statistical models developed can be used to predict how low- and high-concentration quantiles change with landscape characteristics, and thus provide a useful tool for catchment managers to inform planning and policy making with changing climate and land use conditions.     

Direct forecasting of subsurface flow response from non-linear dynamic data by linear least-squares in canonical functional principal component space

Inverse modeling is widely used to assist with forecasting problems in the subsurface. However, full inverse modeling can be time-consuming requiring iteration over a high dimensional parameter space with computationally expensive forward models and complex spatial priors. In this paper, we investigate a prediction-focused approach (PFA) that aims at building a statistical relationship between data variables and forecast variables, avoiding the inversion of model parameters altogether. The statistical relationship is built by first applying the forward model related to the data variables and the forward model related to the prediction variables on a limited set of spatial prior models realizations, typically generated through geostatistical methods. The relationship observed between data and prediction is highly non-linear for many forecasting problems in the subsurface. In this paper we propose a Canonical Functional Component Analysis (CFCA) to map the data and forecast variables into a low-dimensional space where, if successful, the relationship is linear. CFCA consists of (1) functional principal component analysis (FPCA) for dimension reduction of time-series data and (2) canonical correlation analysis (CCA); the latter aiming to establish a linear relationship between data and forecast components. If such mapping is successful, then we illustrate with several cases that (1) simple regression techniques with a multi-Gaussian framework can be used to directly quantify uncertainty on the forecast without any model inversion and that (2) such uncertainty is a good approximation of uncertainty obtained from full posterior sampling with rejection sampling.     

LASSO as a tool for downscaling summer rainfall over the Yangtze River Valley

Building statistical downscaling models often faces a large number of potential predictors from atmospheric circulation fields. The least absolute shrinkage and selection operator (LASSO) has been used to downscale monthly rainfall in summer over the Yangtze River Valley. Based on the shrinkage of coefficients of the model, LASSO can provide sparse models with many coefficients being zero. Geopotential height at 500-hPa was used as the predictor set. The results show that LASSO can reproduce the spatial pattern of anomalies of rainfall in most years. Furthermore, LASSO can reproduce the shift of the rainfall over the Yangtze River Valley in the late 1970s. The performance of the elastic net was also tested, and its grouping effect should be noted. It was also found that LASSO performs better than principal component regression.     

Regionalization of precipitation characteristics in the Canadian Prairie Provinces using large-scale atmospheric covariates and geophysical attributes

Observed data at most stations are often inadequate to obtain reliable estimates of many hydro-meteorological variables that not only define water availability across a region but also the vulnerability of social infrastructure to climatic extremes. To overcome this, data from neighboring sites with similar statistical characteristics are often pooled. The pooling process is based on partitioning of a larger region into smaller sub-regions with homogeneous features of interest. The established approaches rely heavily on statistics computed from observed precipitation data rather than the covariates that play a significant role in modulating the regional and local climate patterns at various temporal and spatial scales. In this study, a new approach for identifying homogeneous regions for regionalization of precipitation characteristics is proposed for the Canadian Prairie Provinces. This approach incorporates information about large-scale atmospheric covariates, teleconnection indices and geographical site attributes that impact spatial patterns of precipitation in order to delineate homogeneous precipitation regions through combined use of multivariate approaches—principal component analysis, canonical correlation analysis and fuzzy C-means clustering. Results of the analyses suggest that the study area can be partitioned into five homogeneous regions. These partitions are validated independently for homogeneity using statistics computed from monthly and seasonal precipitation totals, and seasonal extremes from a network of observation stations. Furthermore, based on the identified regions, precipitation magnitude-frequency relationships of warm and cold season single- and multi-day precipitation extremes, developed through regional frequency analysis, are mapped spatially. Such estimates are important for numerous water resources related activities.     

Approximate copula-based estimation and prediction of discrete spatial data

The present paper reports on the use of copula functions to describe the distribution of discrete spatial data, e.g. count data from environmental mapping or areal data analysis. In particular, we consider approaches to parameter point estimation and propose a fast method to perform approximate spatial prediction in copula-based spatial models with discrete marginal distributions. We assess the goodness of the resulting parameter estimates and predictors under different spatial settings and guide the analyst on which approach to apply for the data at hand. Finally, we illustrate the methodology by analyzing the well-known Lansing Woods data set. Software that implements the methods proposed in this paper is freely available in Matlab language on the author’s website.     

Where are the limits of model predictive capabilities?

Distributed hydrological models can make predictions with much finer spatial resolution than the supporting field data. They will, however, usually not have a predictive capability at model grid scale due to limitations of data availability and uncertainty of model conceptualizations. In previous publications, we have introduced the Representative Elementary Scale (RES) concept as the theoretically minimum scale at which a model with a given conceptualization has a potential for obtaining a predictive accuracy corresponding to a given acceptable accuracy. The new RES concept has similarities to the 25‐year‐old Representative Elementary Area concept, but it differs in the sense that while Representative Elementary Area addresses similarity between subcatchments by sampling within the catchment, RES focuses on effects of data or conceptualization uncertainty by Monte Carlo simulations followed by a scale analysis. In the present paper, we extend and generalize the RES concept to a framework for assessing the minimum scale of potential predictability of a distributed model applicable also for analyses of different model structures and data availabilities. We present three examples with RES analyses and discuss our findings in relation to Beven's alternative blueprint and environmental modeling philosophy from 2002. While Beven here addresses model structural and parameter uncertainties, he does not provide a thorough methodology for assessing to which extent model predictions for variables that are not measured possess opportunities to have meaningful predictive accuracies, or whether this is impossible due to limitations in data and models. This shortcoming is addressed by the RES framework through its analysis of the relationship between aggregation scale of model results and prediction uncertainties and for considering how alternative model structures and alternative data availability affects the results. We suggest that RES analysis should be applied in all modeling studies that aim to use simulation results at spatial scales smaller than the support scale of the calibration data.