Comparison of Spatial Methods for the Assessment of Planktonic Patches

Planktonic patches are defined as areas where the abundance of plankters is above a threshold value τ. The estimation of patch size and shape can be approached using spatial statistical tools, using truncated random fields or indicator random fields as classifiers. In all cases there is the risk of false positive and false negative errors. In this paper we present the results of a comparative study on the performance of four commonly used methods: conditional simulation and kriging, both in the original measurement units of the data and under an indicator transform. We used a misclassification cost function to compare the four methods. Our results show that conditional simulation in the original measurement units attains the lowest misclassification cost. We also illustrate how the point at which this minimum is attained can be used to chose an optimal cut-off value for binary classification. Received: December 2003 / Revised: June 2005     

Estimating the area affected by phosphorus runoff in an Everglades wetland: a comparison of universal kriging and Bayesian kriging

Phosphorus-enriched agriculture runoff is believed to be the leading cause of ecosystem changes of Everglades wetlands. To study this effect, it is necessary to estimate the area of the affected region. In this study, Bayesian kriging and universal kriging were used to estimate the area by analysing the data collected by Reddy et al. (1991). The background level of the soil's total phosphorus concentration is usedto determine whether the region is affected by the agriculture runoff, through an indicator function. The area of the affected region was represented by the integration of the indicator function over the entire wetland. The expected value of the affected area was calculated using the results derived from Bayesian and universal kriging. The outcome indicates that universal kriging is sensitive to specification of thecovariance model. It was observed that universal kriging and Bayesian kriging yield comparable results, if the specified covariance structures are of similar nature.     

Monitoring and estimating the flow conditions and fish presence probability under various flow conditions at reach scale using genetic algorithms and kriging methods

The combination of current velocity and water depth influences stream flow conditions, and fish activities prefer particular flow conditions. This study develops a novel optimal flow classification method for identifying types of stream flow based on the current velocity and the water depth using a genetic algorithm. It is applied to the Datuan stream in northern Taiwan. Fish were sampled and their habitat investigated at the study site during the spring, summer, fall and winter of 2008-2009. The current velocity, water depth and maps of the presence probability of fish were estimated by ordinary and indicator kriging. The optimal classification results were compared with the classification results obtained using the Froude number and empirical methods. The flow classification results demonstrate that the proposed optimal flow classification method that considers depth-velocity and optimally identified criteria for classifying flow types, yields a current velocity and water depth of 0.32 (m/s) and 0.29 (m), respectively, and classifies the flow conditions in the study area as pool, run, riffle and slack. The variography results of the current velocity and the water depth data reveal that seasonal flows are not spatially stationary among seasons in the study area. Kriging methods and a two-dimensional hydrodynamic model (River 2D) with empirical and optimal flow classification methods are more effective than the Froude number method in classifying flow conditions in the study area. The flow condition classifications and probability maps were generated by River 2D, ordinary kriging and indicator kriging, to quantify the flow conditions preferred by Sicyopterus japonicus in the study area. However, the proposed optimal classification method with kriging and River 2D is an effective alternative method for mapping flow conditions and determining the relationship between flow and the presence probability of target fish in support of stream restoration.     

Ordinary kriging for function-valued spatial data

In various scientific fields properties are represented by functions varying over space. In this paper, we present a methodology to make spatial predictions at non-data locations when the data values are functions. In particular, we propose both an estimator of the spatial correlation and a functional kriging predictor. We adapt an optimization criterion used in multivariable spatial prediction in order to estimate the kriging parameters. The curves are pre-processed by a non-parametric fitting, where the smoothing parameters are chosen by cross-validation. The approach is illustrated by analyzing real data based on soil penetration resistances.     

Cost analysis of composite sampling for classification

When an environmental sampling objective is to classify all the sample units as contaminated or not, composite sampling with selective retesting can substantially reduce costs by reducing the number of units that require direct analysis. The tradeoff, however, is increased complexity that has its own hidden costs. For this reason, we propose a model for assessing the relative cost, expressed as the ratio of total expected cost with compositing to total expected cost without compositing (initial exhaustive testing). Expressions are derived for the following retesting protocols: (i) exhaustive, (ii) sequential and (iii) binary split. The effects of both false positive and false negative rates are also derived and incorporated. The derived expressions of relative cost are illustrated for a range of values for various cost components that reflect typical costs incurred with hazardous waste site monitoring. Results allow those who are designing sampling plans to evaluate if any of these compositing/retesting protocols will be cost effective for particular applications.     

Multiscale advanced raster map analysis system: Definition, design and development

This paper brings together a multidisciplinary initiative to develop advanced statistical and computational techniques for analyzing, assessing, and extracting information from raster maps. This information will provide a rigorous foundation to address a wide range of applications including disease mapping, emerging infectious diseases, landscape ecological assessment, land cover trends and change detection, watershed assessment, and map accuracy assessment. It will develop an advanced map analysis system that integrates these techniques with an advanced visualization toolbox, and use the system to conduct large case studies using rich sets of raster data, primarily from remotely sensed imagery. As a result, it will be possible to study and evaluate raster maps of societal, ecological, and environmental variables to facilitate quantitative characterization and comparative analysis of geospatial trends, patterns, and phenomena. In addition to environmental and ecological studies, these techniques and tools can be used for policy decisions at national, state, and local levels, crisis management, and protection of infrastructure. Geospatial data form the foundation of an information-based society. Remote sensing has been a vastly under-utilized resource involving a multi-million dollar investment at the national levels. Even when utilized, the credibility has been at stake, largely because of lack of tools that can assess, visualize, and communicate accuracy and reliability in timely manner and at desired confidence levels. Consider an imminent 21st century scenario: What message does a multi-categorical map have about the large landscape it represents? And at what scale, and at what level of detail? Does the spatial pattern of the map reveal any societal, ecological, environmental condition of the landscape? And therefore can it be an indicator of change? How do you automate the assessment of the spatial structure and behavior of change to discover critical areas, hot spots, and their corridors? Is the map accurate? How accurate is it? How do you assess the accuracy of the map? How do we evaluate a temporal change map for change detection? What are the implications of the kind and amount of change and accuracy on what matters, whether climate change, carbon emission, water resources, urban sprawl, biodiversity, indicator species, human health, or early warning? And with what confidence? The proposed research initiative is expected to find answers to these questions and a few more that involve multi-categorical raster maps based on remote sensing and other geospatial data. It includes the development of techniques for map modeling and analysis using Markov Random Fields, geospatial statistics, accuracy assessment and change detection, upper echelons of surfaces, advanced computational techniques for geospatial data mining, and advanced visualization techniques.     

禹城地区土壤铅含量空间分布的指示克里格估值

以鲁西北禹城地区土壤重金属Pb含量为例,针对其存在特异值与偏态分布的特点,利用指示克里格法研究了土壤Pb含量小于特定阈值的条件概率分布,分析了该地区土壤Pb含量的空间分布特征,并对普通克里格和指示克里格的估值效果进行交叉验证。结果表明：研究区土壤Pb含量总体较低,未超过国家标准的限值,但不同部位土壤Pb含量差异较大;普通克里格法和指示克里格法形成的土壤Pb含量空间分布格局相似,但普通克里格法的平滑效果强于指示克里格法;研究区域土壤环境质量总体良好,Pb含量高值区主要集中在各乡镇驻地附近的农田;指示克里格对土壤Pb含量空间估值的精度优于普通克里格,指示克里格法更适用于原始数据呈非正态分布且特异值对估值结果有较大影响的土壤属性。本研究结果为该地区土壤环境质量评价和重金属污染防控提供科学依据。     

Estimating the spatial covariance structure using the geoadditive model

In geostatistics, both kriging and smoothing splines are commonly used to generate an interpolated map of a quantity of interest. The geoadditive model proposed by Kammann and Wand (J R Stat Soc: Ser C (Appl Stat) 52(1):1–18, 2003) represents a fusion of kriging and penalized spline additive models. Complex data issues, including non-linear covariate trends, multiple measurements at a location and clustered observations are easily handled using the geoadditive model. We propose a likelihood based estimation procedure that enables the estimation of the range (spatial decay) parameter associated with the penalized splines of the spatial component in the geoadditive model. We present how the spatial covariance structure (covariogram) can be derived from the geoadditive model. In a simulation study, we show that the underlying spatial process and prediction of the spatial map are estimated well using the proposed likelihood based estimation procedure. We present several applications of the proposed methods on real-life data examples.     

Spatially stratified sampling using auxiliary information for geostatistical mapping

This paper presents a method of spatial sampling based on stratification by Local Moran’s I _i calculated using auxiliary information. The sampling technique is compared to other design-based approaches including simple random sampling, systematic sampling on a regular grid, conditional Latin Hypercube sampling and stratified sampling based on auxiliary information, and is illustrated using two different spatial data sets. Each of the samples for the two data sets is interpolated using regression kriging to form a geostatistical map for their respective areas. The proposed technique is shown to be competitive in reproducing specific areas of interest with high accuracy.     

A GIS-based approach to spatio-temporal analysis of environmental pollution in urban areas: A case study of Prague's environment extended by LIDAR data

Environmental pollution of urban areas is one of key factors that state authorities and local agencies have to consider in the decision-making process. To find a compromise among many criteria, spatial analysis extended by geostatistical methods and dynamic models has to be carried out. In this case, spatial analysis includes processing of a wide range of air, water and soil pollution data and possibly noise assessment and waste management data. Other spatial inputs consist of data from remote sensing and GPS field measurements. Integration and spatial data management are carried out within the framework of a geographic information system (GIS). From a modeling point of view, GIS is used mainly for the preprocessing and postprocessing of data to be displayed in digital map layers and visualized in 3D scenes. Moreover, for preprocessing and postprocessing, deterministic and geostatistical methods (IDW, ordinary kriging) are used for spatial interpolation; geoprocessing and raster algebra are used in multi-criteria evaluation and risk assessment methods. GIS is also used as a platform for spatio-temporal analyses or for building relationships between the GIS database and stand-alone modeling tools. A case study is presented illustrating the application of spatial analysis to the urban areas of Prague. This involved incorporating environmental data from monitoring networks and field measurements into digital map layers. Extra data inputs were used to represent the 3D concentration fields of air pollutants (ozone, NO₂) measured by differential absorption LIDAR. ArcGIS was used to provide spatial data management and analysis, extended by modeling tools developed internally in the ArcObjects environment and external modules developed with MapObjects. Ordinary kriging methods were employed to predict ozone concentrations in selected 3D locations together with estimates of variability. Higher ozone concentrations were found above crossroads with their heavy traffic than above the surrounding areas. Ozone concentrations also varied with height above the digital elevation model. Processed data, spatial analysis and models are integrated within the framework of the GIS project, providing an approach that state and local authorities can use to address environmental protection issues.     

Spatial interpolation of air temperature using environmental context: Application to a crop model

The air temperature is one of the main input data in models for water balance monitoring or crop models for yield prediction. The different phenological stages of plant growth are generally defined according to cumulated air temperature from the sowing date. When these crop models are used at the regional scale, the meteorological stations providing input climatic data are not spatially dense enough or in a similar environment to reflect the crop local climate. Hence spatial interpolation methods must be used. Climatic data, particularly air temperature, are influenced by local environment. Measurements show that the air above dry surfaces is warmer than above wet areas. We propose a method taking into account the environment of the meteorological stations in order to improve spatial interpolation of air temperature. The aim of this study is to assess the impact of these corrected climatic data in crop models. The proposed method is an external drift kriging where the Kriging system is modified to correct local environment effects. The environment of the meteorological stations was characterized using a land use map summarized in a small number of classes considered as a factor influencing local temperature. This method was applied to a region in south-east France (150×250 km) where daily temperatures were measured on 150 weather stations for two years. Environment classes were extracted from the CORINE Landcover map obtained from remote sensing data. Categorical external drift kriging was compared to ordinary kriging by a cross validation study. The gain in precision was assessed for different environment classes and for summer days. We then performed a sensitivity study of air temperature with the crop model STICS. The influence of interpolation corrections on the main outputs as yield or harvest date is discussed. We showed that the method works well for air temperature in summer and can lead to significant correction for yield prediction. For example, we observed by cross validation a bias reduction of 0.5 to 1.0°C (exceptionally 2.5°C for some class), which corresponds to differences in yield prediction from 0.6 to 1.5 t/ha.     

Pigeon homing: new airbag experiments to assess the role of olfactory information for pigeon navigation

Summary In three series of experiments we assessed the effects of olfactory and non-olfactory information collected en route or at the release site on the initial orientation of homing pigeons. In the first experiment, pigeons were transported in open crates to two sites located in opposite directions from the home loft. They were left at the site for 1 h, then put into airtight containers filled with air from that site and brought back to the loft. From there, controls were transported back to the original site. Experimentals were transported to the opposite site. Upon arrival at the site, the olfactory mucosae of both groups were anesthetized with Gingicain. Thus in this experiment, control and experimental pigeons were exposed to different olfactory as well as to different non-olfactory information during displacement and at the site. In the second series, controls and experimentals were treated as in the first experiment, except that they were enclosed in the airtight containers at the very beginning of the experiment and were ventilated with synthetic air until arrival at the final release site. This treatment excluded the possibility to perceive olfactory information en route or at the site. In this series, the two groups differed only with respect to non-olfactory information perceived during displacement and/or at the release site. In the third series, we exposed pigeons at the loft to air collected either at the later release site (controls) or to air collected at a site located in opposite direction of the home loft (experimentals). Here the two groups differed only with respect to their exposure to air of different origin. In all three series, the pooled controls showed a directional preference that was statistically indistinguishable from the home direction. All three experimental groups were disoriented. In the first two series, the differences in the initial orientation of control and experimental pigeons were highly significant. In the third experiment, there was only very weak statistical evidence for a difference between controls and experimentals. These results suggest that more than one factor is involved in the pigeons' navigation system. According to the present experiment with synthetic air, pigeons probably gather and process non-olfactory information during the first part of their transport from the home loft to the release site. Thus, some kind of, in this case non-olfactory, route reversal seems to be involved in the homing process. In addition, the experiment involving only manipulations of airborne information indicated some olfactory component. Previous experiments at our loft did not result in disorientation of the pigeons if either only the access to airborne information had been removed or when otherwise unmanipulated pigeons had been transported in detours to the final release site. Therefore, we assume that our pigeons' navigation system relies on several cues. Deletion of one cue can be compensated by other information. Often the initial orientation of our pigeons is disturbed only when at least one cue is removed and another one provides false information.     

A multiscale hierarchical Markov transition matrix model for generating and analyzing thematic raster maps

A model is described for generating hierarchically scaled spatial pattern as represented in a thematic raster map. The model involves a series of Markov transition matrices, one for each level in the scaling hierarchy. In full generality, the model allows the transition matrices to be different at each level, potentially making available a large number of parameters for landscape characterization. The model is self-similar when the transition matrices are all equal. A method is presented for fitting the model to data that take the form of a single-resolution thematic raster map. Explicit analytic solutions are obtained for the fitted parameters. The fitting method is based on a relationship between the hierarchical transitions in the model and spatial transitions at varying distance scales in the data map, a categorical analogy of the geostatistical variogram.     

Application of geostatistical methods to arsenic data from soil samples of the Cova dos Mouros mine (Vila Verde-Portugal)

A total of 286 soil samples were collected in the Cova dos Mouros area. All samples were dry sieved into the <200 mesh size fraction and analysed for Fe, Cu, Zn, Pb, Co, Ni, Bi and Mn by atomic absorption spectrometry (AAS) and for As, Se, Sb and Te by atomic absorption spectrometry-hydrid generation (AAS-HG). Only the results of arsenic are discussed in this paper although the survey was extended to all analysed chemical elements. The purpose of this study was to make a risk probability mapping for arsenic that would allow better knowledge about the vulnerability of the soil to arsenic contamination. To achieve this purpose, the initial variable was transformed into an indicator variable using as thresholds the risk-based standards (intervention values) for soils, as proposed by [Swartjes 1999. Risk based assessment of soil and groundwater quality in the Netherlands: Standards and remediation. J. Geochem. Explor.73 1–10]. To account for spatial structure, sample variograms were computed for the main directions of the sampling grid and a spherical model was fitted to each sample variogram (arsenic variable and indicator variables). The parameters of the spherical model fitted to the arsenic variable were used to predict arsenic concentrations at unsampled locations. A risk probability mapping was also done to assess the vulnerability of the soil towards the mining works. The parameters of the spherical model fitted to each indicator variable were used to estimate probabilities of exceeding the corresponding threshold. The use of indicator kriging as an alternative to ordinary kriging for the soil data of Cova dos Mouros produced unbiased probability maps that allowed assessment of the quality of the soil.     

Mapping water chemical variables with spatially correlated errors

One of the most important considerations in many environmental studies is need to allow for correlations among the variables. Monitoring and analyzing relationships between chemical environmental parameters using spatial correlation based regression modelling is the main motivation of this applied study. For this purpose, some noticeable environmental parameters of data sets obtained from two lakes have been considered and the concentrations of chemical variables such as cadmium and nitrate have been appraised by a regression-based geostatistical methodology. The modelling procedure consists of two stages. In the first stage, spatial variables are analyzed via multi-linear regression and some relationships are provided. Next, by using the spatial auto-correlations of the residuals, a type of regression-based kriging procedure is applied. The capacity of the model for appraising the water chemical variables is also tested and performance comparisons with ordinary kriging are conducted. Finally, the applications showed that analyzing water chemical variables with spatially correlated errors is a convenient and applicable approach for assessing the environmental systems.     

Application of partial order to stream channel assessment at bridge infrastructure for mitigation management

Many environmental systems and infrastructure systems are monitored using a set of indicator values that assess several aspects of site condition. The values of different indicators often convey different comparative messages for the study sites. The comparability between sites is analyzed within the theory of partially-ordered sets and visualized with Hasse diagrams. This paper demonstrates that properties of partially-ordered sets and the conversion of indicator scores into a rank matrix provide a manager or decision-maker with valuable information that would be lost if the monitored indicator data were aggregated only into a single index. Stream stability assessment data from 49 bridge crossing sites in the United States are used to demonstrate these techniques in prioritization and identification of restoration and maintenance needs of stream channels at bridge crossings.     

Prediction of potential areas of species distributions based on presence-only data

We introduce a methodology to infer zones of high potential for the habitat of a species, useful for management of biodiversity, conservation, biogeography, ecology, or sustainable use. Inference is based on a set of sites where the presence of the species has been reported. Each site is associated with covariate values, measured on discrete scales. We compute the predictive probability that the species is present at each node of a regular grid. Possible spatial bias for sites of presence is accounted for. Since the resulting posterior distribution does not have a closed form, a Markov chain Monte Carlo (MCMC) algorithm is implemented. However, we also describe an approximation to the posterior distribution, which avoids MCMC. Relevant features of the approach are that specific notions of data acquisition such as sampling intensity and detectability are accounted for, and that available a priori information regarding areas of distribution of the species is incorporated in a clear-cut way. These concepts, arising in the presence-only context, are not addressed in alternative methods. We also consider an uncertainty map, which measures the variability for the predictive probability at each node on the grid. A simulation study is carried out to test and compare our approach with other standard methods. Two case studies are also presented.     

Generalized site occupancy models allowing for false positive and false negative errors

Site occupancy models have been developed that allow for imperfect species detection or "false negative" observations. Such models have become widely adopted in surveys of many taxa. The most fundamental assumption underlying these models is that "false positive" errors are not possible. That is, one cannot detect a species where it does not occur. However, such errors are possible in many sampling situations for a number of reasons, and even low false positive error rates can induce extreme bias in estimates of site occupancy when they are not accounted for. In this paper, we develop a model for site occupancy that allows for both false negative and false positive error rates. This model can be represented as a two-component finite mixture model and can be easily fitted using freely available software. We provide an analysis of avian survey data using the proposed model and present results of a brief simulation study evaluating the performance of the maximum-likelihood estimator and the naive estimator in the presence of false positive errors.     

Regional assessment of plant growth problems for colliery spoil reclamation

The data on plant growth conditions collected for 34 sites in the Barnsley and South Yorkshire Areas of the National Coal Board are analysed using methods of ordination and numerical classification in order to display the regional variations of plant growth characteristics. The potential value of such regional analyses and the manner in which such information could be used by reclamation agencies is discussed and a detailed example is presented for one site. The complete methodology and its limitations are reviewed and the implications for planning of reclamation projects discussed.     

Assessing the risk of soil contamination in the Swiss Jura using indicator geostatistics

The probability that the concentrations of toxic substances in soil or other medium exceed tolerablemaxima at any unsampled place can be estimated by indicator geostatistics. The method is developed and used to estimate and map the risk of contamination by cadmium, copper and lead in the topsoil of a 14.5 km 2 region in the Swiss Jura. It combines both direct measurements of metal concentrations and thecalibration of a geological map, and it shows that the risk of toxicity is least on Argovian rocks. Two approaches are proposed to divide a region into safe' and 'hazardous' zones on the basis of probability maps. The first declares as contaminated all places where the risk of contamination exceeds a given threshold. The second approach first evaluates the financial costs that might result from a wrongdeclaration, after which the site is allocated to a class so as to minimize that cost. The risk of exposure for humans and animals is generally greater for contaminated agricultural land than for forest soil, and so land use is taken into account in both procedures.