Time-varying models for extreme values

We propose a new approach for modeling extreme values that are measured in time and space. First we assume that the observations follow a Generalized Extreme Value (GEV) distribution for which the location, scale or shape parameters define the space–time structure. The temporal component is defined through a Dynamic Linear Model (DLM) or state space representation that allows to estimate the trend or seasonality of the data in time. The spatial element is imposed through the evolution matrix of the DLM where we adopt a process convolution form. We show how to produce temporal and spatial estimates of our model via customized Markov Chain Monte Carlo (MCMC) simulation. We illustrate our methodology with extreme values of ozone levels produced daily in the metropolitan area of Mexico City and with rainfall extremes measured at the Caribbean coast of Venezuela.     

Bayesian entropy for spatial sampling design of environmental data

We develop a spatial statistical methodology to design national air pollution monitoring networks with good predictive capabilities while minimizing the cost of monitoring. The underlying complexity of atmospheric processes and the urgent need to give credible assessments of environmental risk create problems requiring new statistical methodologies to meet these challenges. In this work, we present a new method of ranking various subnetworks taking both the environmental cost and the statistical information into account. A Bayesian algorithm is introduced to obtain an optimal subnetwork using an entropy framework. The final network and accuracy of the spatial predictions is heavily dependent on the underlying model of spatial correlation. Usually the simplifying assumption of stationarity, in the sense that the spatial dependency structure does not change location, is made for spatial prediction. However, it is not uncommon to find spatial data that show strong signs of nonstationary behavior. We build upon an existing approach that creates a nonstationary covariance by a mixture of a family of stationary processes, and we propose a Bayesian method of estimating the associated parameters using the technique of Reversible Jump Markov Chain Monte Carlo. We apply these methods for spatial prediction and network design to ambient ozone data from a monitoring network in the eastern US.     

Parameterization of Albedo over Heterogeneous Surfaces in Coupled Land-Atmosphere Schemes for Environmental Modeling. Part I: Theoretical Background

In grid-based environmental models, the underlying surface consists of patches of solid and liquid parts and different plant communities, creating a very heterogeneous picture in the grid cell. In these cases, numerical modelers usually use a simple arithmetic average to determine the grid-cell albedo, a key variable in the parameterization of the land-surface radiative transfer over the grid cell. The object of this paper is to consider the assumptions for aggregating the albedo over a very heterogeneous surface where various surfaces occur at different heights, and, then propose a method for deriving a general expression for it. The suggested expression for the albedo is compared with the conventional approach, for the two-patches grid-cell with a simple geometrical distribution and different heights of its components. A numerical test is performed to compare the two approaches by numerical simulation of the evolution of the surface temperature over the particular grid-cell. Specifically, a one-dimensional land-surface model was applied to an isolated rocky grid-cell with a hole in the center; the model was forced with meteorological observations taken on July 17, 1999 in Philadelphia, PA.     

Multimethod,multistate Bayesian hierarchical modeling approach for use in regional monitoring of wolves

In many cases, the first step in large‐carnivore management is to obtain objective, reliable, and cost‐effective estimates of population parameters through procedures that are reproducible over time. However, monitoring predators over large areas is difficult, and the data have a high level of uncertainty. We devised a practical multimethod and multistate modeling approach based on Bayesian hierarchical‐site‐occupancy models that combined multiple survey methods to estimate different population states for use in monitoring large predators at a regional scale. We used wolves (Canis lupus) as our model species and generated reliable estimates of the number of sites with wolf reproduction (presence of pups). We used 2 wolf data sets from Spain (Western Galicia in 2013 and Asturias in 2004) to test the approach. Based on howling surveys, the naïve estimation (i.e., estimate based only on observations) of the number of sites with reproduction was 9 and 25 sites in Western Galicia and Asturias, respectively. Our model showed 33.4 (SD 9.6) and 34.4 (3.9) sites with wolf reproduction, respectively. The number of occupied sites with wolf reproduction was 0.67 (SD 0.19) and 0.76 (0.11), respectively. This approach can be used to design more cost‐effective monitoring programs (i.e., to define the sampling effort needed per site). Our approach should inspire well‐coordinated surveys across multiple administrative borders and populations and lead to improved decision making for management of large carnivores on a landscape level. The use of this Bayesian framework provides a simple way to visualize the degree of uncertainty around population‐parameter estimates and thus provides managers and stakeholders an intuitive approach to interpreting monitoring results. Our approach can be widely applied to large spatial scales in wildlife monitoring where detection probabilities differ between population states and where several methods are being used to estimate different population parameters.     

Multivariate Bayesian analysis of atmosphere–ocean general circulation models

Numerical experiments based on atmosphere–ocean general circulation models (AOGCMs) are one of the primary tools in deriving projections for future climate change. Although each AOGCM has the same underlying partial differential equations modeling large scale effects, they have different small scale parameterizations and different discretizations to solve the equations, resulting in different climate projections. This motivates climate projections synthesized from results of several AOGCMs’ output. We combine present day observations, present day and future climate projections in a single highdimensional hierarchical Bayes model. The challenging aspect is the modeling of the spatial processes on the sphere, the number of parameters and the amount of data involved. We pursue a Bayesian hierarchical model that separates the spatial response into a large scale climate change signal and an isotropic process representing small scale variability among AOGCMs. Samples from the posterior distributions are obtained with computer-intensive MCMC simulations. The novelty of our approach is that we use gridded, high resolution data covering the entire sphere within a spatial hierarchical framework. The primary data source is provided by the Coupled Model Intercomparison Project (CMIP) and consists of 9 AOGCMs on a 2.8 by 2.8 degree grid under several different emission scenarios. In this article we consider mean seasonal surface temperature and precipitation as climate variables. Extensions to our model are also discussed.     

Spatial scale affects community concordance among fishes, benthic macroinvertebrates, and bryophytes in streams.

Owing to the lack of information about the distribution patterns of many taxonomic groups, biodiversity conservation strategies commonly rely on a surrogate taxa approach for identifying areas of maximum conservation potential. Macroinvertebrates or fish are the most likely candidates for such a role in many freshwater systems. The usefulness of the surrogate taxa depends largely on community concordance, i.e., the degree of similarity in community patterns among taxonomic groups across a set of sites. We examined the effect of the spatial scale of a. study on the strength of community concordance among macroinvertebrates, bryophytes, and fish by comparing the concordance between ordinations of these groups in 101 boreal stream sites. We specifically asked if communities spanning several drainages are more concordant than those originating from a single drainage system. Our results indicate that community concordance is affected by spatial extent, being variable and generally weak at the scale of individual drainages, but strong across multiple drainage systems and ecoregions. We attribute this finding to different taxonomic groups responding to similar environmental factors and sharing a similar latitudinal gradient of community structure when viewed across large spatial scales. We also identified a "gradient of concordance," with sites contributing disproportionately to community concordance being in relatively large streams with high microhabitat variability. Overall, our results suggest that the degree of community concordance among freshwater organism groups depends critically on the spatial extent of the study, and surrogate groups at the scale of single river systems should be used with caution.     

Improving inverse model fitting in trees—Anisotropy,multiplicative effects,and Bayes estimation

Model fitting for individual-based effects in forests has some problems. Because samples measuring the separate influence of each individual are rarely available, the measured value in the sample represents the influence of all surrounding individual trees. Therefore, it is helpful to build inverse models that use the spatial pattern of the variable as well as that of the source trees. For example, since seed dispersal is influenced by wind effects, a model is discussed describing anisotropic effects to ensure an unbiased estimate of the total fruit number. Further, we present a model describing the absorption of radiation by trees. In this case a multiplicative combination of individual effects yields the total effect. Our approach uses logarithmic transformations of the original data to model multiplicative combinations as sum of transformed single effects. For fitting model parameters we propose an approach based on Bayesian statistics, to ensure ecologically interpretable parameters.     

Spatial location dominates over host plant genotype in structuring an herbivore community

Recent work has shown a potential role for both host plant genotype and spatial context in structuring insect communities. In this study, we use three separate data sets on herbivorous insects on oak (Quercus robur) to estimate the relative effects of host plant genotype (G), location (E), and the G x E interaction on herbivore community structure: a common garden experiment replicated at the landscape scale (approximately 5 km2); two common gardens separated at the regional scale (approximately 10 000 km2); and survey data on wild trees in various spatial settings. Our experiments and survey reveal that, at the landscape scale, the insect community is strongly affected by the spatial setting, with 32% of the variation in species richness explained by spatial connectivity. In contrast, G and G x E play minor roles in structuring the insect community. Results remained similar when extending the spatial scale of the study from the more local (landscape) level to the regional level. We conclude that in our study system, spatial processes play a major role in structuring these insect communities at both the landscape and regional scales, whereas host plant genotype seems of secondary importance.     

Dose-response modeling for developmental neurotoxicity data

The fact that maternal exposures to some chemicals during pregnancy can adversely affect the structure and function of the nervous system in the offspring is well established. Government agencies have for a long time been concerned with regulation of developmental neurotoxicants and safe perinatal exposures. However, despite this concern, current guidelines provide only broad and nonspecific recommendations and lack clear directions for a model based approach to risk estimation. In this paper we propose a dose-response model for the nonquantal data obtained from developmental neurotoxicological experiments. To account for the critical issue of the correlation among responses from pups in the same litter, the so called intralitter correlation, a hierarchical distributional structure is used to derive the underlying unconditional distribution of responses. The maximum likelihood method is used to estimate model parameters and the covariance matrix of the estimates is derived. An example is used to illustrate the results.     

Spatial variogram estimation from temporally aggregated seabird count data

Seabird abundance is an important indicator for assessing impact of human activities on the marine environment. However, data collection at sea is time consuming and surveys are carried out over several consecutive days for efficiency reasons. This study investigates the validity of aggregating those data over time to estimate a spatial variogram that is representative for spatial correlation in species abundance. For this purpose we simulate four-day surveys of seabird count data that contain spatial and temporal correlation arising from temporal changes in the spatial pattern of environmental conditions. Estimates of the aggregated spatial variogram are compared to a variogram that would arise when data were collected over a single day. The study reveals that, under changing environmental conditions over surveys days, aggregating data over a four-day survey increases both the non-spatial variation in the data and the scale of spatial correlation in seabird data. Next, the effect of using an aggregated variogram on the statistical power to test the significance of an impact is investigated. The impact concerns a case of establishing an offshore wind farm resulting in seabird displacement. The study shows that both overestimation and underestimation of statistical power occurs, with power estimates differing up to a factor of two. We conclude that the spatial variation in seabird abundance can be misrepresented by using temporally aggregated data. In impact studies, such misrepresentation can lead to erroneous assessments of the ability to detect impact.     

Toward accurate and precise estimates of lion density

Reliable estimates of animal density are fundamental to understanding ecological processes and population dynamics. Furthermore, their accuracy is vital to conservation because wildlife authorities rely on estimates to make decisions. However, it is notoriously difficult to accurately estimate density for wide‐ranging carnivores that occur at low densities. In recent years, significant progress has been made in density estimation of Asian carnivores, but the methods have not been widely adapted to African carnivores, such as lions (Panthera leo). Although abundance indices for lions may produce poor inferences, they continue to be used to estimate density and inform management and policy. We used sighting data from a 3‐month survey and adapted a Bayesian spatially explicit capture‐recapture (SECR) model to estimate spatial lion density in the Maasai Mara National Reserve and surrounding conservancies in Kenya. Our unstructured spatial capture‐recapture sampling design incorporated search effort to explicitly estimate detection probability and density on a fine spatial scale, making our approach robust in the context of varying detection probabilities. Overall posterior mean lion density was estimated to be 17.08 (posterior SD 1.310) lions >1 year old/100 km², and the sex ratio was estimated at 2.2 females to 1 male. Our modeling framework and narrow posterior SD demonstrate that SECR methods can produce statistically rigorous and precise estimates of population parameters, and we argue that they should be favored over less reliable abundance indices. Furthermore, our approach is flexible enough to incorporate different data types, which enables robust population estimates over relatively short survey periods in a variety of systems. Trend analyses are essential to guide conservation decisions but are frequently based on surveys of differing reliability. We therefore call for a unified framework to assess lion numbers in key populations to improve management and policy decisions.     

The impact of chemical lateral boundary conditions on CMAQ predictions of tropospheric ozone over the continental United States

A sensitivity study is performed to examine the impact of lateral boundary conditions (LBCs) on the NOAA-EPA operational Air Quality Forecast Guidance over continental USA. We examined six LBCS: the fixed profile LBC, three global LBCs, and two ozonesonde LBCs for summer 2006. The simulated results from these six runs are compared to IONS ozonesonde and surface ozone measurements from August 1 to 5, 2006. The choice of LBCs can affect the ozone prediction throughout the domain, and mainly influence the predictions in upper altitude or near inflow boundaries, such as the US west coast and the northern border. Statistical results shows that the use of global model predictions for LBCs could improve the correlation coefficients of surface ozone prediction over the US west coast, but could also increase the ozone mean bias in most regions of the domain depending on global models. In this study, the use of the MOZART (Model for Ozone And Related chemical Tracers) prediction for CMAQ (Community Multiscale Air Quality) LBC shows a better surface ozone prediction than that with fixed LBC, especially over the US west coast. The LBCs derived from ozonesonde measurements yielded better O₃ correlations in the upper troposphere.     

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.     

Integrating Landscape and Metapopulation Modeling Approaches: Viability of the Sharp-Tailed Grouse in a Dynamic Landscape

Abstract:  The lack of management experience at the landscape scale and the limited feasibility of experiments at this scale have increased the use of scenario modeling to analyze the effects of different management actions on focal species. However, current modeling approaches are poorly suited for the analysis of viability in dynamic landscapes. Demographic (e.g., metapopulation) models of species living in these landscapes do not incorporate the variability in spatial patterns of early successional habitats, and landscape models have not been linked to population viability models. We link a landscape model to a metapopulation model and demonstrate the use of this model by analyzing the effect of forest management options on the viability of the Sharp-tailed Grouse (  Tympanuchus phasianellus ) in the Pine Barrens region of northwestern Wisconsin (U.S.A.). This approach allows viability analysis based on landscape dynamics brought about by processes such as succession, disturbances, and silviculture. The landscape component of the model (LANDIS) predicts forest landscape dynamics in the form of a time series of raster maps. We combined these maps into a time series of patch structures, which formed the dynamic spatial structure of the metapopulation component (RAMAS). Our results showed that the viability of Sharp-tailed Grouse was sensitive to landscape dynamics and demographic variables such as fecundity and mortality. Ignoring the landscape dynamics gave overly optimistic results, and results based only on landscape dynamics (ignoring demography) lead to a different ranking of the management options than the ranking based on the more realistic model incorporating both landscape and demographic dynamics. Thus, models of species in dynamic landscapes must consider habitat and population dynamics simultaneously.     

Hierarchical spatial modeling for estimation of population size

Estimation of population size has traditionally been viewed from a finite population sampling perspective. Typically, the objective is to obtain an estimate of the total population count of individuals within some region. Often, some stratification scheme is used to estimate counts on subregions, whereby the total count is obtained by aggregation with weights, say, proportional to the areas of the subregions. We offer an alternative to the finite population sampling approach for estimating population size. The method does not require that the subregions on which counts are available form a complete partition of the region of interest. In fact, we envision counts coming from areal units that are small relative to the entire study region and that the total area sampled is a very small proportion of the total study area. In extrapolating to the entire region, we might benefit from assuming that there is spatial structure to the counts. We implement this by modeling the intensity surface as a realization from a spatially correlated random process. In the case of multiple population or species counts, we use the linear model of coregionalization to specify a multivariate process which provides associated intensity surfaces hence association between counts within and across areal units. We illustrate the method of population size estimation with simulated data and with tree counts from a Southwestern pinyon-juniper woodland data set.     

The scale transition: scaling up population dynamics with field data

Applying the recent developments of scale transition theory, we demonstrate a systematic approach to the problem of scaling up local scale interactions to regional scale dynamics with field data. Dynamics on larger spatial scales differ from the predictions of local dynamics alone because of an interaction between nonlinearity in population dynamics at the local scale and spatial variation in density and environmental factors over the regional population. Our systematic approach to scaling up involves the following five steps. First, define a model for dynamics on the local spatial scale. Second, apply scale transition theory to identify key interactions between nonlinearity and spatial variation that translate local dynamics to the regional scale. Third, measure local-scale model parameters to determine nonlinearities at local scales. Fourth, measure spatial variation. Finally, combine nonlinearity and variation measures to obtain the scale transition. Using field data for the dynamics of grazers and periphyton in a freshwater stream, we show that scale transition terms greatly reduce the growth and equilibrium density of the periphyton population at the stream scale compared to rock scale populations, confirming the importance of spatial mechanisms to stream-scale dynamics.     

Modeling and forecasting daily maximum hourly ozone concentrations using the RegAR model with skewed and heavy-tailed innovations

This paper considers the modeling and forecasting of daily maximum hourly ozone concentrations in Laranjeiras, Serra, Brazil, through dynamic regression models. In order to take into account the natural skewness and heavy-tailness of the data, a linear regression model with autoregressive errors and innovations following a member of the family of scale mixture of skew-normal distributions was considered. Pollutants and meteorological variables were considered as predictors, along with some deterministic factors, namely week-days and seasons. The Oceanic Niño Index was also considered as a predictor. The estimated model was able to explain satisfactorily well the correlation structure of the ozone time series. An out-of-sample forecast study was also performed. The skew-normal and skew-t models displayed quite competitive point forecasts compared to the similar model with gaussian innovations. On the other hand, in terms of forecast intervals, the skewed models presented much better performance with more accurate prediction intervals. These findings were empirically corroborated by a forecast Monte Carlo experiment.     

A regional forest ecosystem carbon budget model: impacts of forest age structure and landuse history

This study investigated the impacts of landuse history and forest age structure on regional carbon fluxes for the forests in the Pacific Northwest of the United States based on a two-stage modeling strategy. In the first stage, an individual-based forest ecosystem carbon flux model (IntCarb) at stand scale is developed. IntCarb combines components from the ZELIG and CENTURY models to simulate forest development and heterotrophic respiration, respectively. Stand scale carbon fluxes simulated by IntCarb strongly depend on stand age. A forest stand can be a carbon sink for up to 200 years old with a peak at 30–40 years old. Old-growth stands are carbon neutral to the atmosphere in the long term. For any particular year, an old-growth stand can be either a carbon sink or source. The interannual variation of Net Ecosystem Productivity (NEP) for an old-growth stand is primarily determined by heterotrophic respiration. Due to the high spatial variability of stand ages, forest age structure needs to be taken into account to improve estimation of carbon budgets of forest ecosystems over large areas. In the stand stage, a regional carbon budget model (RegCarb) is developed to estimate regional carbon fluxes over large areas based on forest age structure, adjusting for the nonrespiratory carbon losses (timber harvesting). Our initial estimate with RegCarb for the Pacific Northwest of the United States indicates that this region was a tremendous carbon source to the atmosphere from 1890 to 1990 due to extensive logging of old-growth forest. Projection for the role of forests in this region in global carbon cycle in the future strongly depend on the amount of timber to be harvested, i.e. how the age structure of forests in this region is to be altered.