Functional regression on remote sensing data in oceanography

The aim of this study is to propose the use of a functional data analysis approach as an alternative to the classical statistical methods most commonly used in oceanography and water quality management. In particular we consider the prediction of total suspended solids (TSS) based on remote sensing (RS) data. For this purpose several functional linear regression models and classical non-functional regression models are applied to 10 years of RS data obtained from medium resolution imaging spectrometer sensor to predict the TSS concentration in the coastal zone of the Guadalquivir estuary. The results of functional and classical approaches are compared in terms of their mean square prediction error values and the superiority of the functional models is established. A simulation study has been designed in order to support these findings and to determine the best prediction model for the TSS parameter in more general contexts.     

Testing the robustness of management decisions to uncertainty: Everglades restoration scenarios.

To effectively manage large natural reserves, resource managers must prepare for future contingencies while balancing the often conflicting priorities of different stakeholders. To deal with these issues, managers routinely employ models to project the response of ecosystems to different scenarios that represent alternative management plans or environmental forecasts. Scenario analysis is often used to rank such alternatives to aid the decision making process. However, model projections are subject to uncertainty in assumptions about model structure, parameter values, environmental inputs, and subcomponent interactions. We introduce an approach for testing the robustness of model-based management decisions to the uncertainty inherent in complex ecological models and their inputs. We use relative assessment to quantify the relative impacts of uncertainty on scenario ranking. To illustrate our approach we consider uncertainty in parameter values and uncertainty in input data, with specific examples drawn from the Florida Everglades restoration project. Our examples focus on two alternative 30-year hydrologic management plans that were ranked according to their overall impacts on wildlife habitat potential. We tested the assumption that varying the parameter settings and inputs of habitat index models does not change the rank order of the hydrologic plans. We compared the average projected index of habitat potential for four endemic species and two wading-bird guilds to rank the plans, accounting for variations in parameter settings and water level inputs associated with hypothetical future climates. Indices of habitat potential were based on projections from spatially explicit models that are closely tied to hydrology. For the American alligator, the rank order of the hydrologic plans was unaffected by substantial variation in model parameters. By contrast, simulated major shifts in water levels led to reversals in the ranks of the hydrologic plans in 24.1-30.6% of the projections for the wading bird guilds and several individual species. By exposing the differential effects of uncertainty, relative assessment can help resource managers assess the robustness of scenario choice in model-based policy decisions.     

Predictive modelling of eelgrass (Zostera marina) depth limits

Empirical models relating secchi depths to maximum depth limits of eelgrass (Zostera marina L.) can describe basic differences in depth limits between areas or time periods exhibiting large differences in secchi depth. However, these models cannot predict the precise depth limit at a particular site at any specific time. In this study we aim to improve the ability of regression models to predict maximum depth limits by: (1) assuming that eelgrass depth limits respond to changes in secchi depth with a temporal delay of 1–2 years, (2) including other water-quality variables in addition to secchi depth, and (3) taking into account that factors regulating depth limits may vary between years and between sites. We were not able to improve the models by introducing a systematic delay in the response of depth limits to changes in secchi depths. The reason for this failure is likely to have been the systematic nature of our approach, since some sites responded with a delay, while others did not. The explanatory power of the models increased when additional water-quality variables were added in a multiple regression model. Where secchi depth alone explained 58% of the variations in depth limits, addition of winter [NH₄⁺] and maximum water depth as independent variables increased the explanatory power to 71%. These models applied to data from one specific year, but when data from several years (1989–1998) were included, only 35% of the variation in depth limits could be explained by the three factors. More detailed analyses showed that the regulation of eelgrass depth limits varied considerably between years and between sites, and the models were further improved by taking this information into account. Our results confirmed previous studies by showing light to be the most important parameter in the regulation of eelgrass depth limits, but also revealed a complexity in the regulation of depth limits not expressed in earlier studies. Limited colonisation potentials may delay the response to improved light conditions, and hypoxia/anoxia and indirect effects of nutrients may prevent eelgrass from attaining the depth limit that light levels would allow. The power to predict depth limits on the basis of secchi depths can therefore be improved by taking site-specific information on eelgrass growth conditions into account.Communicated by M. Kühl, Helsingør     

Composite likelihood approach to the regression analysis of spatial multivariate ordinal data and spatial compositional data with exact zero values

In many environmental and ecological studies, it is of interest to model compositional data. One approach is to consider positive random vectors that are subject to a unit-sum constraint. In landscape ecological studies, it is common that compositional data are also sampled in space with some elements of the composition absent at certain sampling sites. In this paper, we first propose a practical spatial multivariate ordered probit model for multivariate ordinal data, where the response variables can be viewed as the discretized non-negative compositions without the unit-sum constraint. We then propose a novel two-stage spatial mixture Dirichlet regression model. The first stage models the spatial dependence and the presence of exact zero values, and the second stage models all the non-zero compositional data. A maximum composite likelihood approach is developed for parameter estimation and inference in both the spatial multivariate ordered probit model and the two-stage spatial mixture Dirichlet regression model. The standard errors of the parameter estimates are computed by an estimate of the Godambe information matrix. A simulation study is conducted to evaluate the performance of the proposed models and methods. A land cover data example in landscape ecology further illustrates that accounting for spatial dependence can improve the accuracy in the prediction of presence/absence of different land covers as well as the magnitude of land cover compositions.     

Geographic mosaic of mutually exclusive dominance of obligate commensals in symbiotic communities associated with a burrowing echiuran worm

Species richness and community composition of symbionts associated with the burrowing echiuran worm, Ochetostoma erythrogrammon Leuckart & Rüppell, 1828, were quantitatively surveyed on subtropical intertidal flats in the Ryukyu Archipelago, Japan. Overall, we recorded seven species of burrow associates, including at least six obligate commensals. According to symbiont community composition, the study sites were largely divided into two groups; one was characterized by the dominance of a snapping shrimp, Alpheus barbatus Coutière, 1897, and the other by the dominance of a scale worm, Lepidonotus sp. Furthermore, a granulometric analysis showed that the sediment characteristics differed significantly between shrimp- and scale worm-dominant sites in terms of median diameter and inclusive graphic standard deviation. These results suggest that these symbionts have different habitat requirements, resulting in the mutually exclusive dominance pattern. Our findings indicate that habitat heterogeneity is important to the evaluation and conservation of the symbiotic diversity in intertidal flats.     

Bayesian Ecological Regression with Latent Factors: Atmospheric Pollutants Emissions and Mortality for Lung Cancer

In this work we propose a Bayesian ecological analysis in which a latent variable summarizes data on emissions of atmospheric pollutants. We specified a hierarchical Bayesian model with spatially structured and unstructured random terms with a nested latent factor model. This can be considered a combination of the convolution spatial model of Besag et al. (1991) and an ecological regression analysis in which a latent variable plays the role of the covariate. The unified approach allows to proper account for the uncertainty in the latent score estimation in the regression analysis. The Bayesian Latent Factor model is used to summarize the information on environmental pressure derived from three stressors: Carbon Monoxide, Nitrogen Oxides and Inhalable Particles. We found evidence of positive correlation between Lung cancer mortality and environmental pressure indicators, in males, Tuscany (Italy), 1995–1999. Environmental pressure seems to be restricted to fourteen municipalities (top 5% of the Latent Factor distribution). The model identified two areas with high point source emissions.     

Multiple-pattern parameter identification and uncertainty analysis approach for water quality modeling

This paper presents a multiple-pattern parameter identification and uncertainty analysis approach for robust water quality modeling using a neural network (NN) embedded genetic algorithm (GA). The modeling approach uses an adaptive NN–GA framework to inversely solve the governing equations in a water quality model for multiple parameter patterns, along with an alternating fitness method to maintain solution diversity. The procedure was demonstrated through a coupled 2D hydrodynamic and eutrophication model for Loch Raven Reservoir in Maryland. The inverse problem was formulated as a nonlinear optimization problem minimizing the degree of misfit (DOM) between model results and observed data. A set of NN models was developed to approximate the input-output response relationship of the Loch Raven Reservoir model and was incorporated into a GA framework in an adaptive fashion to search for near-optimal solutions minimizing the DOM. The numerical example showed that the adaptive NN–GA approach is capable of identifying multiple parameter patterns that reproduce the observed data equally well. The resulting parameter patterns were incorporated into the numerical model, and a multiple-pattern robust water quality modeling analysis, along with a compound margin of safety (CMOS) method, was proposed and applied to analyze the parameter pattern uncertainty.     

Simulation of water quality in a flood detention area using models of different spatial discretization

Detention areas provide a means to lower peak discharges in rivers by temporarily storing excess water. In the case of extreme flood events, the storage effect reduces the risk of dike failures or extensive inundations for downstream reaches and near the site of abstraction. Due to the large amount of organic matter contained in the river water and the inundation of terrestrial vegetation in the detention area, a deterioration of water quality may occur. In particular, decay processes can cause a severe depletion of dissolved oxygen (DO) in the temporary water body. In this paper, we studied the potential of a water quality model to simulate the DO dynamics in a large but shallow detention area to be built at the Elbe River (Germany). Our focus was on examining the impact of spatial discretization on the model’s performance and usability. Therefore, we used a zero-dimensional (0D) and a two-dimensional (2D) modeling approach in parallel. The two approaches solely differ in their spatial discretization, while conversion processes, parameters, and boundary conditions were kept identical. The dynamics of DO simulated by the two models are similar in the initial flooding period but diverge when the system starts to drain. The deviation can be attributed to the different spatial discretization of the two models, leading to different estimates of flow velocities and water depths. Only the 2D model can account for the impact of spatial variability on the evolution of state variables. However, its application requires high efforts for pre- and post-processing and significantly longer computation times. The 2D model is, therefore, not suitable for investigating various flood scenarios or for analyzing the impact of parameter uncertainty. For practical applications, we recommend to firstly set up a fast-running model of reduced spatial discretization, e.g. a 0D model. Using this tool, the reliability of the simulation results should be checked by analyzing the parameter uncertainty of the water quality model. A particular focus may be on those parameters that are spatially variable and, therefore, believed to be better represented in a 2D approach. The benefit from the application of the more costly 2D model should be assessed, based on the analyses carried out with the 0D model. A 2D model appears to be preferable only if the simulated detention area has a complex topography, flow velocities are highly variable in space, and the parameters of the water quality model are well known.     

Studying crop sequences with CarrotAge,a HMM-based data mining software

We have developed a knowledge discovery system based on high-order hidden Markov models for analyzing spatio-temporal data bases. This system, named CarrotAge , takes as input an array of discrete data – the rows represent the spatial sites and the columns the time slots – and builds a partition together with its a posteriori probability. CarrotAge has been developed for studying the cropping patterns of a territory. It uses therefore an agricultural drench database, named Ter-Uti , which records every year the land-use category of a set of sites regularly spaced. The results of CarrotAge are interpreted by agronomists and used in research works linking agricultural land use and water management. Moreover, CarrotAge can be used to find out and study crop sequences in large territories, that is a main question for agricultural and environmental research, as discussed in this paper.     

Artificial neural network modeling of the river water quality—A case study

The paper describes the training, validation and application of artificial neural network (ANN) models for computing the dissolved oxygen (DO) and biochemical oxygen demand (BOD) levels in the Gomti river (India). Two ANN models were identified, validated and tested for the computation of DO and BOD concentrations in the Gomti river water. Both the models employed eleven input water quality variables measured in river water over a period of 10 years each month at eight different sites. The performance of the ANN models was assessed through the coefficient of determination (R²) (square of the correlation coefficient), root mean square error (RMSE) and bias computed from the measured and model computed values of the dependent variables. Goodness of the model fit to the data was also evaluated through the relationship between the residuals and model computed values of DO and BOD. The model computed values of DO and BOD by both the ANN models were in close agreement with their respective measured values in the river water. Relative importance and contribution of the input variables to the model output was evaluated through the partitioning approach. The identified ANN models can be used as tools for the computation of water quality parameters.     

Predicting water quality data in an unfilled reservoir using microcosm sediment-water simulation

The technique of microcosm sediment-water simulation was used to obtain predictive water quality data for the proposed Jordanelle Reservoir, Heber City, Utah. Sediment-water microcosms were prepared for four sites located in the north arm of the reservoir basin, including two sites located in an abandoned acid mine tailings pond. Data obtained from the tailings pond microcosms indicated that low pH water and high trace metal concentrations may exist in this area of the reservoir. These data suggested that the tailings material should be contained or removed prior to reservoir filling. Other sites in the reservoir basin exhibited water quality considered normal for reservoirs of similar elevation and basin geology. Near the proposed dam, anaerobic conditions could develop rapidly due to available concentrations of organic carbon, and the subsequent release of Zn, Fe, and Mn may pose a water quality problem. At the sampling site near Keetley, simulation data indicated that anaerobic conditions will not develop as quickly or be as severe as conditions expected near the dam. Overall, the availability of nitrogen and phosphorus in the Provo River and Jordanelle sediments indicated that problems with algal blooms may exist in the reservoir. Also presented is a brief discussion of the advantages and disadvantages associated with microcosm sediment-water simulation.     

Male residence and the patterning of serum testosterone in vervet monkeys (<Emphasis Type="Italic">Cercopithecus aethiops</Emphasis>)

This study investigated hormonal and demographic processes underlying unimale and multimale mating systems in primates. Reproductive skew and challenge models of male competition provide conflicting predictions of the relationship of male residence to group composition and androgen regulation. These predictions were tested using endocrine and socioecological data from Kenyan vervet monkeys (Cercopithecus aethiops). Serum samples from 57 adult male monkeys, drawn from 19 separate groups and 4 populations, were assayed for testosterone by radioimmunoassay. Male ability to respond to conspecific challenge was assessed by their testosterone response to the capture protocol.Analyses showed that reproductive skew models were useful predictors of intergroup and interpopulation variation in male residence and T profiles. The Limited Control model of male residence was supported by positive correlations of the number of males per group with the number of females without dependent offspring, demonstrating that monopolization potential was a key determinant of male residence. Testosterone concentrations under conditions that elevated serum levels were positively correlated with infanticide risk, supporting the Concession model. Population comparisons provided evidence for increased T responsiveness where groups were predominantly unimale. Unimale populations were from sites with higher rainfall, suggesting that ecological factors contributed to population differences in male residence and T regulation.For species name, we follow the 2000 taxonomy of the IUCN/SSC Primate Specialist Groups workshop (Grubb et al. 2003)     

Predicting abundance of desert riparian birds: validation and calibration of the Effective Area Model.

Reliable prediction of the effects of landscape change on species abundance is critical to land managers who must make frequent, rapid decisions with long-term consequences. However, due to inherent temporal and spatial variability in ecological systems, previous attempts to predict species abundance in novel locations and/or time frames have been largely unsuccessful. The Effective Area Model (EAM) uses change in habitat composition and geometry coupled with response of animals to habitat edges to predict change in species abundance at a landscape scale. Our research goals were to validate EAM abundance predictions in new locations and to develop a calibration framework that enables absolute abundance predictions in novel regions or time frames. For model validation, we compared the EAM to a null model excluding edge effects in terms of accurate prediction of species abundance. The EAM outperformed the null model for 83.3% of species (N=12) for which it was possible to discern a difference when considering 50 validation sites. Likewise, the EAM outperformed the null model when considering subsets of validation sites categorized on the basis of four variables (isolation, presence of water, region, and focal habitat). Additionally, we explored a framework for producing calibrated models to decrease prediction error given inherent temporal and spatial variability in abundance. We calibrated the EAM to new locations using linear regression between observed and predicted abundance with and without additional habitat covariates. We found that model adjustments for unexplained variability in time and space, as well as variability that can be explained by incorporating additional covariates, improved EAM predictions. Calibrated EAM abundance estimates with additional site-level variables explained a significant amount of variability (P < 0.05) in observed abundance for 17 of 20 species, with R2 values >25% for 12 species, >48% for six species, and >60% for four species when considering all predictive models. The calibration framework described in this paper can be used to predict absolute abundance in sites different from those in which data were collected if the target population of sites to which one would like to statistically infer is sampled in a probabilistic way.     

Impacts of cyclone Hamish at One Tree Reef: integrating environmental and benthic habitat data

The southern Great Barrier Reef (GBR), a region that rarely experiences cyclones, was impacted by tropical cyclone (TC) Hamish in March 2009. We documented on-reef physical and habitat conditions before, during and after the cyclone at One Tree Reef (OTR) using data from environmental sensor instrumentation and benthic surveys. Over 5 years of monitoring, ocean mooring data revealed that OTR experienced large swells (4–8 m) of short duration (10–20 min) not associated with a cyclone in the area. These swells may have contributed to the physical disturbance of benthic biota and decline in coral cover recorded prior to and after TC Hamish. During the cyclone, OTR sustained southeasterly gale force winds (>61.2 km h⁻¹) for 18.5 h and swells >6 m in height for 4 h. Benthic surveys of exposed sites documented a 20% drop in live coral cover, 30% increase in filamentous algae cover and the presence of dislodged corals and rubble after the storm. Leeward sites were largely unaffected by the cyclone. Benthic cover did not change in the lagoon sites. Significant rubble movement and infill of the lagoon occurred. Two years after the cyclone, algal cover remained high and laminar corals had not recovered. Total coral cover at impacted sites had continued to decline. Environmental conditions and habitat surveys supported Puotinen’s (Int J Geogr Inf Sci 21:97–120, 2007) model for cyclone conditions that cause reef destruction. While TC Hamish had a major impact on the reef, change in benthic cover over several years was due to multiple stressors. This on-reef scale integration of physical and biological data provided a rare opportunity to assess impacts of a major storm and other disturbances, showing the importance of considering multiple stressors (short-lived and sustained) in assessing change to reef habitats.     

Updating coarse-scale species distribution models using small fine-scale samples

Large, fine-grained samples are ideal for predictive species distribution models used for management purposes, but such datasets are not available for most species and conducting such surveys is costly. We attempted to overcome this obstacle by updating previously available coarse-grained logistic regression models with small fine-grained samples using a recalibration approach. Recalibration involves re-estimation of the intercept or slope of the linear predictor and may improve calibration (level of agreement between predicted and actual probabilities). If reliable estimates of occurrence likelihood are required (e.g., for species selection in ecological restoration) calibration should be preferred to other model performance measures. This updating approach is not expected to improve discrimination (the ability of the model to rank sites according to species suitability), because the rank order of predictions is not altered. We tested different updating methods and sample sizes with tree distribution data from Spain. Updated models were compared to models fitted using only fine-grained data (refitted models). Updated models performed reasonably well at fine scales and outperformed refitted models with small samples (10-100 occurrences). If a coarse-grained model is available (or could be easily developed) and fine-grained predictions are to be generated from a limited sample size, updating previous models may be a more accurate option than fitting a new model. Our results encourage further studies on model updating in other situations where species distribution models are used under different conditions from their training (e.g., different time periods, different regions).     

Modelling species distributions with penalised logistic regressions: A comparison with maximum entropy models

An important aspect of species distribution modelling is the choice of the modelling method because a suboptimal method may have poor predictive performance. Previous comparisons have found that novel methods, such as Maxent models, outperform well-established modelling methods, such as the standard logistic regression. These comparisons used training samples with small numbers of occurrences per estimated model parameter, and this limited sample size may have caused poorer predictive performance due to overfitting. Our hypothesis is that Maxent models would outperform a standard logistic regression because Maxent models avoid overfitting by using regularisation techniques and a standard logistic regression does not. Regularisation can be applied to logistic regression models using penalised maximum likelihood estimation. This estimation procedure shrinks the regression coefficients towards zero, causing biased predictions if applied to the training sample but improving the accuracy of new predictions. We used Maxent and logistic regression (standard and penalised) to analyse presence/pseudo-absence data for 13 tree species and evaluated the predictive performance (discrimination) using presence-absence data. The penalised logistic regression outperformed standard logistic regression and equalled the performance of Maxent. The penalised logistic regression may be considered one of the best methods to develop species distribution models trained with presence/pseudo-absence data, as it is comparable to Maxent. Our results encourage further use of the penalised logistic regression for species distribution modelling, especially in those cases in which a complex model must be fitted to a sample with a limited size.     

Compositional analysis of overdispersed counts using generalized estimating equations

Multivariate abundance data are commonly collected in ecology, and used to explore questions of “community composition”—how relative abundance of different taxa changes with environmental conditions. In this paper, we propose a log-linear marginal modeling approach for analyzing such compositional count data, via generalized estimating equations. This method exploits the multiplicative nature of log-linear models for counts, by reparameterizing models that describe marginal effects on mean abundance. This allows partitioning into “main effects” and compositional effects, which is appealing for interpretation. We apply the proposed approach to reanalyze compositional counts of benthic invertebrates from Delaware Bay, and data of invertebrate communities inhabiting Acacia plants in eastern Australia. In both cases we resort to a resampling approach to make inferences about regression parameters, because the number of clusters was not large compared to cluster size.     

Evolving social influence in large populations

Darwinian studies of collective human behaviour, which deal fluently with change and are grounded in the details of social influence among individuals, have much to offer “social” models from the physical sciences which have elegant statistical regularities. Although Darwinian evolution is often associated with selection and adaptation, “neutral” models of drift are equally relevant. Building on established neutral models, we present a general, yet highly parsimonious, stochastic model, which generates an entire family of real-world, right-skew socio-economic distributions, including exponential, winner-take-all, power law tails of varying exponents, and power laws across the whole data. The widely used Barabási and Albert (1999) Science 286: 509-512 “B-A” model of preferential attachment is a special case of this general model. In addition, the model produces the continuous turnover observed empirically within these distributions. Previous preferential attachment models have generated specific distributions with turnover using arbitrary add-on rules, but turnover is an inherent feature of our model. The model also replicates an intriguing new relationship, observed across a range of empirical studies, between the power law exponent and the proportion of data represented in the distribution.     

An integrated modeling framework for performing environmental assessments: Application to ecosystem services in the Albemarle-Pamlico basins (NC and VA, USA)

The U.S. Environmental Protection Agency uses environmental models to inform rulemaking and policy decisions at multiple spatial and temporal scales. As decision-making has moved towards integrated thinking and assessment (e.g. media, site, region, services), the increasing complexity and interdisciplinary nature of modern environmental problems has necessitated a new generation of integrated modeling technologies. Environmental modelers are now faced with the challenge of determining how data from manifold sources, types of process-based and empirical models, and hardware/software computing infrastructure can be reliably integrated and applied to protect human health and the environment.In this study, we demonstrate an Integrated Modeling Framework that allows us to predict the state of freshwater ecosystem services within and across the Albemarle-Pamlico Watershed, North Carolina and Virginia (USA). The Framework consists of three facilitating technologies: Data for Environmental Modeling automates the collection and standardization of input data; the Framework for Risk Assessment of Multimedia Environmental Systems manages the flow of information between linked models; and the Supercomputer for Model Uncertainty and Sensitivity Evaluation is a hardware and software parallel-computing interface with pre/post-processing analysis tools, including parameter estimation, uncertainty and sensitivity analysis. In this application, five environmental models are linked within the Framework to provide multimedia simulation capabilities: the Soil Water Assessment Tool predicts watershed runoff; the Watershed Mercury Model simulates mercury runoff and loading to streams; the Water quality Analysis and Simulation Program predicts water quality within the stream channel; the Habitat Suitability Index model predicts physicochemical habitat quality for individual fish species; and the Bioaccumulation and Aquatic System Simulator predicts fish growth and production, as well as exposure and bioaccumulation of toxic substances (e.g., mercury).Using this Framework, we present a baseline assessment of two freshwater ecosystem services-water quality and fisheries resources-in headwater streams throughout the Albemarle-Pamlico. A stratified random sample of 50 headwater streams is used to draw inferences about the target population of headwater streams across the region. Input data is developed for a twenty-year baseline simulation in each sampled stream using current land use and climate conditions. Monte Carlo sampling (n = 100 iterations per stream) is also used to demonstrate some of the Framework's experimental design and data analysis features. To evaluate model performance and accuracy, we compare initial (i.e., uncalibrated) model predictions (water temperature, dissolved oxygen, fish density, and methylmercury concentration within fish tissue) against empirical field data. Finally, we ‘roll-up’ the results from individual streams, to assess freshwater ecosystem services at the regional scale.     

Interpolation performance of a spatio-temporal model with spatially varying coefficients: application to PM<Subscript>10</Subscript> concentrations in Rio de Janeiro

In this work we present a Bayesian analysis in linear regression models with spatially varying coefficients for modeling and inference in spatio-temporal processes. This kind of model is particularly appealing in situations where the effect of one or more explanatory processes on the response present substantial spatial heterogeneity. We describe for this model how to make inference about the regression coefficients and response processes under two scenarios: when the explanatory processes are known throughout the study region, and when they are known only at the sampling locations. Using a simulation experiment we investigate how parameter inference and interpolation performance are affected by some features of the data and prior distribution that is used. The proposed methodology is used to model the dataset on PM₁₀ levels in the metropolitan region of Rio de Janeiro presented in Paez and Gamerman (2003).