Ioannis Dimopoulos

Review and comparison of methods to study the contribution of variables in artificial neural network models

Abstract Convinced by the predictive quality of artificial neural network (ANN) models in ecology, we have turned our interests to their explanatory capacities. Seven methods which can give the relative contribution and/or the contribution profile of the input factors were compared: (i) the ‘PaD’ (for Partial Derivatives) method consists in a calculation of the partial derivatives of the output according to the input variables; (ii) the ‘Weights’ method is a computation using the connection weights; (iii) the ‘Perturb’ method corresponds to a perturbation of the input variables; (iv) the ‘Profile’ method is a successive variation of one input variable while the others are kept constant at a fixed value; (v) the ‘classical stepwise’ method is an observation of the change in the error value when an adding (forward) or an elimination (backward) step of the input variables is operated; (vi) ‘Improved stepwise a’ uses the same principle as the classical stepwise, but the elimination of the input occurs when the network is trained, the connection weights corresponding to the input variable studied is also eliminated; (vii) ‘Improved stepwise b’ involves the network being trained and fixed step by step, one input variable at its mean value to note the consequences on the error. The data tested in this study concerns the prediction of the density of brown trout spawning redds using habitat characteristics. The PaD method was found to be the most useful as it gave the most complete results, followed by the Profile method that gave the contribution profile of the input variables. The Perturb method allowed a good classification of the input parameters as well as the Weights method that has been simplified but these two methods lack stability. Next came the two improved stepwise methods (a and b) that both gave exactly the same result but the contributions were not sufficiently expressed. Finally, the classical stepwise methods gave the poorest results.

Application of neural networks to modelling nonlinear relationships in ecology

Abstract Two predictive modelling principles are discussed: multiple regression (MR) and neural networks (NN). The MR principle of linear modelling often gives low performance when relationships between variables are nonlinear; this is often the case in ecology; some variables must therefore be transformed. Despite these manipulations, the results often remain disappointing: poor prediction, dependence of residuals on the variable to predict. On the other hand NN are nonlinear type models. They do not necessitate transformation of variables and can give better results. The application of these two techniques to a set of ecological data (study of the relationship between density of brown trout spawning sites (redds) and habitat characteristics), shows that NN are clearly more performant than MR (R2 = 0.96 vs R2 = 0.47 or R2 = 0.72 in raw variables or nonlinear transformed variables). With the calculation power now currently available, NN are easy to implement and can thus be recommended for modelling of a number ecological processes.

Neural network models to study relationships between lead concentration in grasses and permanent urban descriptors in Athens city (Greece)

The aim of the present work is to propose a model for the estimation of lead concentration in grasses using urban descriptors easily accessible and to study the specific effect of each descriptor on lead concentration. Six descriptors were considered: the density of vegetation, the vegetation height, wind velocity, height of building, distance of adjacent street, traffic volume. Lead concentrations were determined in one grass species, Cynodon dactylon (L.) Pers, (Bermuda grass), collected from 30 different locations in Athens city. The proposed model is a multilayer perceptron (MLP) trained by backpropagation. The predictive quality of the model was judged by two cross-validation methods. The generalization ability of the model is confirmed by a determination coefficient higher than 0.91. The study of the first partial derivatives of the output of the MLP with respect to each input is used to identify of the factors influencing the lead concentration and the mode of action of each factor. Results allow to classify the environmental descriptors by their decreasing influence on lead concentration: distance of adjacent street, traffic volume, density of vegetation, wind velocity, height of building and vegetation height.

Artificial neural networks as a classification method in the behavioural sciences

The classification and recognition of individual characteristics and behaviours constitute a preliminary step and is an important objective in the behavioural sciences. Current statistical methods do not always give satisfactory results. To improve performance in this area, we present a methodology based on one of the principles of artificial neural networks: the backpropagation gradient. After summarizing the theoretical construction of the model, we describe how to parameterize a neural network using the example of the individual recognition of vocalizations of four fallow deer (Dama dama). With 100% recognition and 90% prediction success, the results are very promising.

An application of artificial neural network models to estimate air temperature data in areas with sparse network of meteorological stations

In this work artificial neural network (ANN) models are developed to estimate meteorological data values in areas with sparse meteorological stations. A more traditional interpolation model (multiple regression model, MLR) is also used to compare model results and performance. The application site is a canyon in a National Forest located in southern Greece. Four meteorological stations were established in the canyon; the models were then applied to estimate air temperature values as a function of the corresponding values of one or more reference stations. The evaluation of the ANN model results showed that fair to very good air temperature estimations may be achieved depending on the number of the meteorological stations used as reference stations. In addition, the ANN model was found to have better performance than the MLR model: mean absolute error values were found to be in the range 0.82–1.72°C and 0.90–1.81°C, for the ANN and the MLR models, respectively. These results indicate that ANN models may provide advantages over more traditional models or methods for temperature and other data estimations in areas where meteorological stations are sparse; they may be adopted, therefore, as an important component in various environmental modeling and management studies.

A Preliminary Study of the Application of Some Predictive Modeling Techniques to Assess Atmospheric Mercury Emissions from Terrestrial Surfaces

Abstract Predictive modeling techniques are applied to investigate their potential usefulness in providing first order estimates on atmospheric emission flux of gaseous soil mercury and in identifying those parameters most critical in controlling such emissions. Predicted data by simulation and statistical techniques are compared to previously published observational data. Results showed that simulation techniques using air/soil coupling may provide a plausible description of mercury flux trends with a RMSE of 24.4 ng m−2 h−1 and a mean absolute error of 10.2 ng m−2 h−1 or 11.9%. From the statistical models, two linear models showed the lowest predictive abilities (R2 = 0.76 and 0.84, respectively) while the Generalized Additive model showed the closest agreement between estimated and observational data (R2 = 0.93). Predicted values from a Neural Network model and the Locally Weighted Smoother model showed also very good agreement to measured values of mercury flux (R2 = 0.92). A Regression Tree model demonstrated also a satisfactory predictability with a value of R2 = 0.90. Sensitivities and statistical analyses showed that surface soil mercury concentrations, solar radiation and, to a lesser degree, temperature are important parameters in predicting airborne Hg flux from terrestrial soils. These findings are compatible with results from recent experimental studies. Considering the uncertainties associated with mercury cycling and natural emissions, it is concluded, that predictions based on simple modeling techniques seem quite appropriate at present; they can be useful tools in evaluating the role of terrestrial emission sources as part of mercury modeling in local and regional airsheds.

Combining Neural Network Models to Predict Spatial Patterns of Airborne Pollutant Accumulation in Soils around an Industrial Point Emission Source

Abstract Neural networks (NNs) have the ability to model a wide range of complex nonlinearities. A major disadvantage of NNs, however, is their instability, especially under conditions of sparse, noisy, and limited data sets. In this paper, different combining network methods are used to benefit from the existence of local minima and from the instabilities of NNs. A nonlinear k-fold cross-validation method is used to test the performance of the various networks and also to develop and select a set of networks that exhibits a low correlation of errors. The various NN models are applied to estimate the spatial patterns of atmospherically transported and deposited lead (Pb) in soils around an historical industrial air emission point source. It is shown that the resulting ensemble networks consistently give superior predictions compared with the individual networks because, for the ensemble networks, R2 values were found to be higher than 0.9 while, for the contributing individual networks, values for R2 ranged between 0.35 and 0.85. It is concluded that combining networks can be adopted as an important component in the application of artificial NN techniques in applied air quality studies.

Estimating airborne pollutant concentrations in vegetated urban sites using statistical models with microclimate and urban geometry parameters as predictor variables: A case study in the city of Athens Greece

The present study demonstrates the efficiency of applying statistical models to estimate airborne pollutant concentrations in urban vegetation by using as predictor variables readily available or easily accessible data. Results revealed that airborne cadmium concentrations in vegetation showed a predictable response to wind conditions and to various urban landscape features such as the distance between the vegetation and the adjacent street, the mean height of the adjacent buildings, the mean density of vegetation between vegetation and the adjacent street and the mean height of vegetation. An artificial neural network (ANN) model was found to have superiority in terms of accuracy with an R2 value on the order of 0.9. The lowest R2 value (on the order of 0.7) was associated with the linear model (SMLR model). The linear model with interactions (SMLRI model) and the tree regression (RTM) model gave similar results in terms of accuracy with R2 values on the order of 0.8. The improvement of the results with the use of the non-linear models (RTM and ANN) and the inclusion of interaction terms in the SMLRI model implied the nonlinear relationships of pollutant concentrations to the selected predictors and showed the importance of the interactions between the various predictor variables. Despite the limitations of the models, some of them appear to be promising alternatives to multimedia-based simulation modeling approaches in urban areas with vegetation, where the application of typical deposition models is sometimes limited.

An evaluation of the performance of the soil temperature simulation algorithms used in the PRZM model.

Soil temperature simulation is an important component in environmental modeling since it is involved in several aspects of pollutant transport and fate. This paper deals with the performance of the soil temperature simulation algorithms of the well-known environmental model PRZM. Model results are compared and evaluated based on the basis of its ability to predict in situ measured soil temperature profiles in an experimental plot during a 3-year monitoring study. The evaluation of the performance is based on linear regression statistics and typical model statistical errors such as the root mean square error (RMSE) and the normalized objective function (NOF). Results show that the model required minimal calibration to match the observed response of the system. Values of the determination coefficient R2 were found to be in all cases around the value of 0.98 indicating a very good agreement between measured and simulated data. Values of the RMSE were found to be in the range of 1.2 to 1.4°C, 1.1 to 1.4°C, 0.9 to 1.1°C, and 0.8 to 1.1°C, for the examined 2, 5, 10 and 20 cm soil depths, respectively. Sensitivity analyses were also performed to investigate the influence of various factors involved in the energy balance equation at the ground surface on the soil temperature profiles. The results showed that the model was able to represent important processes affecting the soil temperature regime such as the combined effect of the heat transfer by convection between the ground surface and the atmosphere and the latent heat flux due to soil water evaporation.

An Application of Parametric and Nonparametric Models to the Assessment of Fluoride Levels in Vegetation Exposed to Stack Emissions of an Aluminum Reduction Plant in Greece

Abstract Various statistical models were developed for assessing airborne fluoride (F) levels in natural vegetation near an aluminum reduction plant using as predictor variables the distance from the emission source, the predominating wind, and characteristic topography-geomorphology parameters. Results revealed that F concentrations in vegetation showed a predictable response to both wind conditions and landscape features. The linear model was found to give good estimations, taking advantage of the relatively strong linear correlation between concentration and distance. A nonlinear relationship between the F concentration in vegetation and the other variables was also found, while interactions between the variables were found to be non-first-order. The nonlinear relationship hypothesis was supported by the improved results of various nonlinear models that also indicated the importance of the area’s topography-geomorphology and meteorology in model predictions. The application of an artificial neural network (ANN) model showed the closest agreement between predicted and observed values with a correlation coefficient of 0.92. The improved reliability of the ANN and a regression tree model (RTM) also were indicated by the normal distribution of their residuals. The RTM and the ANN were further investigated and found to be capable of identifying the importance of the variables in vegetation exposure to air emissions.