Prediction of non-methane hydrocarbons in Kuwait using regression and Bayesian kriged Kalman model

This article describes the hierarchical Bayesian approach for predicting average hourly concentrations of ambient non-methane hydrocarbons (NMHC) in Kuwait where records of six monitor stations located in different sites are observed at successive time points. Our objective is to predict the concentration level of NMHC in unmonitored areas. Here an attempt is made for the prediction of unmeasured concentration of NMHC at two additional locations in Kuwait. We will implement a kriged Kalman filter (KKF) hierarchical Bayesian approach assuming a Gaussian random field, a technique that allows the pooling of data from different sites in order to predict the exposure of the NMHC in different regions of Kuwait. In order to increase the accuracy of the KKF we will use other statistical models such as imputation, regression, principal components, and time series analysis in our approach. We considered four different types of imputation techniques to address the missing data. At the primary level, the logarithmic field is modeled as a trend plus Gaussian stochastic residual model. The trend model depends on hourly meteorological predictors which are common to all sites. The residuals are then modeled using KKF, and the prediction equation is derived conditioned on adjoining hours. On this basis we developed a spatial predictive distribution for these residuals at unmonitored sites. By transforming the predicted residuals back to the original data scales, we can impute Kuwait’s hourly non-methane hydrocarbons field.     

Adding rigor to ecological network models by evaluating a set of pre-balance diagnostics: A plea for PREBAL

The widespread use of ecological network models (e.g., Ecopath, Econetwrk, and related energy budget models) has been laudable for several reasons, chief of which is providing an easy-to-use set of modeling tools that can present an ecosystem context for improved understanding and management of living marine resources (LMR). Yet the ease-of-use of these models has led to two challenges. First, the veritable explosion of the use and application of these network models has resulted in recognition that the content and use of such models has spanned a range of quality. Second, as these models and their application have become more widespread, they are increasingly being used in a LMR management context. Thus review panels and other evaluators of these models would benefit from a set of rigorous and standard criteria from which the basis for all network models and related applications for any given system (i.e., the initial, static energy budget) can be evaluated. To this end, as one suggestion for improving network models in general, here I propose a series of pre-balance (PREBAL) diagnostics. These PREBAL diagnostics can be done, now, in simple spreadsheets before any balancing or tuning is executed. Examples of these PREBAL diagnostics include biomasses, biomass ratios, vital rates, vital rate ratios, total production, and total removals (and slopes thereof) across the taxa and trophic levels in any given energy budget. I assert that there are some general ecological and fishery principles that can be used in conjunction with PREBAL diagnostics to identify issues of model structure and data quality before balancing and dynamic applications are executed. I humbly present this PREBAL information as a simple yet general approach that could be easily implemented, could be considered for further incorporation into these model packages, and as such would ultimately result in a straightforward way to evaluate (and perhaps identify areas for improving) initial conditions in food web modeling efforts.     

Explanation of fluctuations in water use time series

This paper presents techniques for studying the influence of the climatic and other variables for the explanation of the water use with an example of time series in Gainesville, Florida. A statistical methodology is described for separating the different time scale components in time series of water use, namely, long term component, seasonal component, and short term component. We analyze each component separately and we prove that the temperature, precipitation, soil temperature, and relative humidity time series are the main climatic factors for the explanation of the long term, seasonal and short term component of the water use time series. Part of the residuals derived from the linear regression of the long term component of the water use can be explained by the unemployment rate. We also show that with the decomposition of the water use time series the explanation of the water use has been improved approximately two times. The explanation of the long term component of water use by the long term regional weather parameters can enable us to the long term regional prediction of the water resources availabilities. This methodology can be applied for studying the water use time series in other locations, as well.     

Sampling variability and estimates of density dependence: a composite-likelihood approach

It is well known that sampling variability, if not properly taken into account, affects various ecologically important analyses. Statistical inference for stochastic population dynamics models is difficult when, in addition to the process error, there is also sampling error. The standard maximum-likelihood approach suffers from large computational burden. In this paper, I discuss an application of the composite-likelihood method for estimation of the parameters of the Gompertz model in the presence of sampling variability. The main advantage of the method of composite likelihood is that it reduces the computational burden substantially with little loss of statistical efficiency. Missing observations are a common problem with many ecological time series. The method of composite likelihood can accommodate missing observations in a straightforward fashion. Environmental conditions also affect the parameters of stochastic population dynamics models. This method is shown to handle such nonstationary population dynamics processes as well. Many ecological time series are short, and statistical inferences based on such short time series tend to be less precise. However, spatial replications of short time series provide an opportunity to increase the effective sample size. Application of likelihood-based methods for spatial time-series data for population dynamics models is computationally prohibitive. The method of composite likelihood is shown to have significantly less computational burden, making it possible to analyze large spatial time-series data. After discussing the methodology in general terms, I illustrate its use by analyzing a time series of counts of American Redstart (Setophaga ruticilla) from the Breeding Bird Survey data, San Joaquin kit fox (Vulpes macrotis mutica) population abundance data, and spatial time series of Bull trout (Salvelinus confluentus) redds count data.     

Spatial residual analysis of six modeling techniques

In recent years alternative modeling techniques have been used to account for spatial autocorrelations among data observations. They include linear mixed model (LMM), generalized additive model (GAM), multi-layer perceptron (MLP) neural network, radial basis function (RBF) neural network, and geographically weighted regression (GWR). Previous studies show these models are robust to the violation of model assumptions and flexible to nonlinear relationships among variables. However, many of them are non-spatial in nature. In this study, we utilize a local spatial analysis method (i.e., local Moran coefficient) to investigate spatial distribution and heterogeneity in model residuals from those modeling techniques with ordinary least-squares (OLS) as the benchmark. The regression model used in this study has tree crown area as the response variable, and tree diameter and the coordinates of tree locations as the predictor variables. The results indicate that LMM, GAM, MLP and RBF may improve model fitting to the data and provide better predictions for the response variable, but they generate spatial patterns for model residuals similar to OLS. The OLS, LMM, GAM, MLP and RBF models yield more residual clusters of similar values, indicating that trees in some sub-areas are either all underestimated or all overestimated for the response variable. In contrast, GWR estimates model coefficients at each location in the study area, and produces more accurate predictions for the response variable. Furthermore, the residuals of the GWR model have more desirable spatial distributions than the ones derived from the OLS, LMM, GAM, MLP and RBF models.     

Hidden Markov models for circular and linear-circular time series

We introduce a new class of circular time series based on hidden Markov models. These are compared with existing models, their properties are outlined and issues relating to parameter estimation are discussed. The new models conveniently describe multi-modal circular time series as dependent mixtures of circular distributions. Two examples from biology and meteorology are used to illustrate the theory. Finally, we introduce a hidden Markov model for bivariate linear-circular time series and use it to describe larval movement of the fly Drosophila. Received: September 2003 / Revised: March 2004     

Uncertainty analyses for calibrating a soil carbon balance model to agricultural field trial data in Sweden and Kenya

How do additional data of the same and/or different type contribute to reducing model parameter and predictive uncertainties? Most modeling applications of soil organic carbon (SOC) time series in agricultural field trial datasets have been conducted without accounting for model parameter uncertainty. There have been recent advances with Monte Carlo-based uncertainty analyses in the field of hydrological modeling that are applicable, relevant and potentially valuable in modeling the dynamics of SOC. Here we employed a Monte Carlo method with threshold screening known as Generalized Likelihood Uncertainty Estimation (GLUE) to calibrate the Introductory Carbon Balance Model (ICBM) to long-term field trail data from Ultuna, Sweden and Machang’a, Kenya. Calibration results are presented in terms of parameter distributions and credibility bands on time series simulations for a number of case studies. Using these methods, we demonstrate that widely uncertain model parameters, as well as strong covariance between inert pool size and rate constant parameters, exist when root mean square simulation errors were within uncertainties in input estimations and data observations. We show that even rough estimates of the inert pool (perhaps from chemical analysis) can be quite valuable to reduce uncertainties in model parameters. In fact, such estimates were more effective at reducing parameter and predictive uncertainty than an additional 16 years time series data at Ultuna. We also demonstrate an effective method to jointly, simultaneously and in principle more robustly calibrate model parameters to multiple datasets across different climatic regions within an uncertainty framework. These methods and approaches should have benefits for use with other SOC models and datasets as well.     

Estimating wildfire growth from noisy and incomplete incident data using a state space model

Wildfire behaviors are complex and are of interest to fire managers and scientists for a variety of reasons. Many of these important behaviors are directly measured from the cumulative burn area time series of individual wildfires; however, estimating cumulative burn area time series is challenging due to the magnitude of measurement errors and missing entries. To resolve this, we introduce two state space models for reconstructing wildfire burn area using repeated observations from multiple data sources that include different levels of measurement error and temporal gaps. The constant growth parameter model uses a few parameters and assumes a burn area time series that follows a logistic growth curve. The non-constant growth parameter model uses a time-varying logistic growth curve to produce detailed estimates of the burn area time series that permit sudden pauses and pulses of growth. We apply both reconstruction models to burn area data from 13 large wildfire incidents to compare the quality of the burn area time series reconstructions and computational requirements. The constant growth parameter model reconstructs burn area time series with minimal computational requirements, but inadequately fits observed data in most cases. The non-constant growth parameter model better describes burn area time series, but can also be highly computationally demanding. Sensitivity analyses suggest that in a typical application, the reconstructed cumulative burn area time series is fairly robust to minor changes in the prior distributions.     

Testing the robustness of primary production models in shallow coastal areas: a case study

In this paper we investigate the robustness of a dynamic model, which describes the dynamic of the seagrass Zostera marina, with respect to the inter-annual variability of the two main forcing functions of primary production models in eutrophicated environments. The model was previously applied to simulate the seasonal evolution of this species in the Lagoon of Venice during a specific year and calibrated against time series of field data. In the this paper, we present and discuss the results which were obtained by forcing the model using time series of site-specific daily values concerning the solar radiation intensity and water temperature. The latter was estimated by means of a regression model, whose input variable was a site-specific time series of the air temperature. The regression model was calibrated using a year-long time series of hourly observations. The Z. marina model was first partially recalibrated against the same data set that was used in the original paper. Subsequently, the model was forced using a 7-year-long time series of the driving functions, in order to check the reliability of its long-term predictions. Even though the calibration gave satisfactory results, the multi-annual trends of the output variables were found to be in contrast with the observed evolution of the seagrass biomasses. Since detailed information about the air temperature and solar radiation are often available, these findings suggest that the testing of the ecological consistency of the evolution of primary production models in the long term would provide additional confidence in their results, particularly in those cases in which the scarcity of field data does not allow one to perform a formal corroboration/validation of these models.     

Evaluation of discrete host–parasitoid models for diamondback moth and Diadegma semiclausum field time population density series

The performance of discrete mathematical models to describe the population dynamics of diamondback moth (DBM) (Plutella xylostella L.) and its parasitoid Diadegma semiclausum was investigated. The parameter values for several well-known models (Nicholson–Bailey, Hassell and Varley, Beddington, Free and Lawton, May, Holling type 2, 3 and Getz and Mills functional responses) were estimated. The models were tested on 20 consecutive sets of time series data collected at 14 days interval for pest and parasitoid populations obtained from a highland cabbage growing area in eastern Kenya. Model parameters were estimated from minimized squared difference between the numerical solution of the model equations and the empirical data using Powell's method. Maximum calculated DBM growth rates varied between 0.02 and 0.07. The carrying capacity determined at 16.5 DBM/plant by the Beddington et al. model was within the range of field data. However, all the estimated parameter values relating to the parasitoid, including the instantaneous searching rate (0.07–0.28), per capita searching efficiency (0.20–0.27), search time (5.20–5.33), handling time (0.77–0.90), and parasitism aggregation index (0.33), were well outside the range encountered empirically. All models evaluated for DBM under Durbin–Watson criteria, except the May model, were not autocorrelated with respect to residuals. In contrast, the criteria applied to the parasitoid residuals showed strong autocorrelations. Thus, these models failed to estimate parasitoid dynamics. We conclude that the interactions of the DBM with its parasitoid cannot be explained by any of the models tested. Two factors may be associated with this failure. First, the parasitoid in this integrated biological control system may not be playing a major role in regulating DBM population. Second, and perhaps more likely, poor correlations reflect gross inadequacies in the theoretical assumptions that underlie the existing models.     

Applying the Patuxent Landscape Unit Model to human dominated ecosystems: the case of agriculture

Non-spatial dynamics are core to landscape simulations. Unit models simulate system interactions aggregated within one space unit of resolution used within a spatial model. For unit models to be applicable to spatial simulations they have to be formulated in a general enough way to simulate all habitat elements within the landscape. Within the Patuxent River watershed, human dominated land uses, such as agriculture and urban land, are already 50% of the current land use, while urban land is replacing forests, agriculture and wetlands at a rapid rate. The Patuxent Landscape Model (PLM) with the Patuxent General Unit Model as core (Pat-GEM) was developed as a predictive policy tool to estimate environmental impacts of such land use changes. The Pat-GEM is based on the General Ecosystem Model (GEM) developed by [Ecol. Modelling 88 1996 263]. Previous calibrations of the Pat-GEM for anthropogenic land uses have not been satisfactory due to the scarcity of appropriate data. This paper shows Pat-GEM simulations of biomass growth and nutrient uptake for crops typical within the Patuxent watershed. The Pat-GEM was expanded to include processes and fluxes that characterize agricultural land use. The most important extension was to include crop rotation into the model. Additionally, we refined the processes for planting, harvesting and fertilization by introducing specific growth parameters. Our revised Pat-GEM was calibrated against the results from Erosion Productivity Impact Calculator (EPIC) a widely used and calibrated agricultural model. We achieved high correlation between results generated with Pat-GEM and EPIC. The correlation coefficients (r²) varied between 0.87 and 0.98, with the simulation results for winter wheat showing the lowest correlation coefficients. Intercalibration using EPIC is a powerful method for calibrating the Pat-GEM model for agricultural land use. EPIC was able (a) to provide about 30% of the input data required for running the Pat-GEM model; and (b) to provide time series output data (with a daily time step) to calibrate the output variables biomass production and nutrient uptake.     

Predictability of marine nematode biodiversity

In this paper, we investigated: (1) the predictability of different aspects of biodiversity, (2) the effect of spatial autocorrelation on the predictability and (3) the environmental variables affecting the biodiversity of free-living marine nematodes on the Belgian Continental Shelf. An extensive historical database of free-living marine nematodes was employed to model different aspects of biodiversity: species richness, evenness, and taxonomic diversity. Artificial neural networks (ANNs), often considered as “black boxes”, were applied as a modeling tool. Three methods were used to reveal these “black boxes” and to identify the contributions of each environmental variable to the diversity indices. Since spatial autocorrelation is known to introduce bias in spatial analyses, Moran's I was used to test the spatial dependency of the diversity indices and the residuals of the model. The best predictions were made for evenness. Although species richness was quite accurately predicted as well, the residuals indicated a lack of performance of the model. Pure taxonomic diversity shows high spatial variability and is difficult to model. The biodiversity indices show a strong spatial dependency, opposed to the residuals of the models, indicating that the environmental variables explain the spatial variability of the diversity indices adequately. The most important environmental variables structuring evenness are clay and sand fraction, and the minimum annual total suspended matter. Species richness is also affected by the intensity of sand extraction and the amount of gravel of the sea bed.     

The implications of model complexity for environmental management

The purpose of this paper is to consider the implicatons of model complexity for the quality of the information provided by models of production activities that account for the processes involved in residuals generation and treatment. Using each of the three primary technologies for iron and steel-making industry and models of varying detail for each, the paper compares the estimated levels of residuals generated and treatment costs for both atmospheric and waterborne effluents. The findings suggest that there are strategic details in model construction which have fundamental implications for the design of environmental policies. Moreover, preliminary estimates of the costs of model construction and operation suggest that policymakers may not be able to afford complexity for its own sake. Rather these costs will require the development of methods to isolate the strategic details in each technology that are potentially important to environmental policies.     

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 linear programming model of residuals management for integrated iron and steel production

This paper briefly describes a linear programming model designed to allow the exploration of questions surrounding the management of the environmental impacts of integrated iron and steel facilities. In particular, the model can show how plant discharges will change in the absence of specific legal restrictions or effluent charges, with such variables as product mix, steel-furnace type, casting technology, and the scrap-ore price ratio. In addition, the costs implied by placing restrictions on discharges of specific residuals (e.g., BOD, oil, suspended solids, particulates) may be estimated, or response to proposed effluent charges may be predicted.     

The effect of species response form on species distribution model prediction and inference

Ecological theory and current evidence support the validity of various species response curves according to a variety of environmental gradients. Various methods have been developed for building species distribution models but it is not well known how these methods perform under various assumptions about the form of the underlying species response. It is also not well known how spatial correlation in species occurrence affects model performance. These effects were investigated by applying an environmental envelope method (BIOCLIM) and three regression-based methods: logistic regression (LR), generalized additive modelling (GAM), and classification and regression tree (CART) to simulated species occurrence data. Each simulated species was constructed as a sum of responses with varying weights. Three basic species response curves were assumed: Gaussian (bell-shaped), Beta (skew) and linear. The two non-linear responses conform to standard ecological niche theory. All three responses were applied in turn to three simulated environmental variables, each with varying degrees of spatial autocorrelation. GAM produced the most consistent model performance over all forms of simulated species response. BIOCLIM and CART were inclined to underrate the performance of variables with a linear response. BIOCLIM was less sensitive to data density. LR was susceptible to model misspecification. The use of a linear function in LR underestimated the performance of variables with non-linear species response and contributed to increased spatial autocorrelation in model residuals. Omission of important environmental variables with non-linear species response also contributed to increased spatial autocorrelation in model residuals. Adding a spatial autocovariate term to the LR model (autologistic model) reduced the spatial autocorrelation and improved model performance, but did not correct the misidentification of the dominant environmental determinant. This is to be expected since the autologistic approach was designed primarily for prediction and not for inference. Given that various forms of species response to environmental determinants arise commonly in nature: (1) higher order functions should always be tested when applying LR in modelling species distribution; (2) spatial autocorrelation in species distribution model residuals can indicate that environmental determinants with non-linear response are missing from the model; and (3) deficiencies in LR model performance due to model misspecification can be addressed by adding a spatial autocovariate to the model, but care should be taken when interpreting the coefficients of the model parameters.     

Model selection in demographic time series using VC-bounds

The problem of distinguishing density-independent (DI) from density-dependent (DD) demographic time series is important for understanding the mechanisms that regulate populations of animals and plants. We address this problem in a novel way by means of Statistical Learning Theory (SLT); SLT is built around the idea of VC-dimension, a complexity index for classes of parameterized functions. Though VC-dimensions of nonlinear models are generally unknown, in the linear case VC-dimension actually corresponds to the number of free parameters; this allows one to straightforwardly apply the model selection framework developed within SLT, and called Structural Risk Minimization (SRM). We generate noisy artificial time series, both DI and DD, and use SRM to recognize the model underlying the data, choosing among a suite of both density-dependent and independent demographies. We show that SRM significantly outperforms traditional model selection approaches, such as the Schwartz Information Criterion and Final Prediction Error in recognizing both density-dependence and independence.     

Concentration fluctuations in a downtown urban area. Part II: analysis of Joint Urban 2003 wind-tunnel measurements

An analysis of concentration time series measured in a boundary-layer wind tunnel at the University of Hamburg is presented. The measurements were conducted with a detailed aerodynamic model of the Oklahoma City (OKC) central business district (CBD) at the scale of 1:300 and were part of the Joint Urban 2003 (JU2003) project. Concentration statistics, as well as concentration probability density (PDF) and exceedance probability (EDF) functions were computed for street- and roof-level sites for three different wind directions. Taking into account the different length scales and wind speeds in the wind-tunnel (WT) and full-scale experiments, dimensionless concentrations and a dimensionless time scale are computed for the comparison with data from the JU2003 full-scale tracer experiments, conducted in OKC in 2003. Using such dimensionless time, the WT time series cover a ~20 times longer time span than the JU2003 full-scale time series, which are analysed in detail in an accompanying, first part of this paper. The WT time series are thus divided into 20 consecutive blocks of equal length and the statistical significance of parameters based on relatively short records is assessed by studying the variability of the concentration statistics and probability functions for the different blocks. In particular at sites closer to the plume edge, the results for the individual blocks vary significantly and at such sites statistics from short records are not very representative. While the location of three sampling sites in the WT closely matched the sites during the full-scale experiments, the prevailing wind directions during the JU2003 releases were not exactly matched. The comparison between full-scale and WT concentration parameters should thus primarily be interpreted in a qualitative rather than direct quantitative sense. Given the differences in mean wind directions and concerns about the representativeness of full-scale concentration statistics, the WT and full-scale results compared well. The 98 percentile concentrations for almost all full-scale releases analyzed are within the scatter of the percentiles observed in the block analysis of the WT time series. Furthermore, the concentration percentiles appear linearly correlated with the fluctuation intensities and the linear relationships determined in the wind tunnel agree well with full-scale results.     

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.