Urban total ecological footprint forecasting by using radial basis function neural network: A case study of Wuhan city, China

Ecological Indicators 10 (2010) 241–248

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Urban total ecological footprint forecasting by using radial basis function neural network: A case study of Wuhan city, China X.M. Li a,b, R.B. Xiao b, S.H. Yuan a, J.An. Chen c, J.X. Zhou a,* a

School of Environmental Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, PR China Institute of Systems Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, PR China c School of Economics and Management, Wuhan University, Wuhan, Hubei, 430072, PR China b

A R T I C L E I N F O

A B S T R A C T

Article history: Received 24 September 2008 Received in revised form 27 March 2009 Accepted 19 May 2009

Ecological footprint (EF) forecasting is essential for dynamically evaluating human impact on earth as well as for planning for a sustainable future. In this paper, a radial basis function neural network (RBFNN) model was developed to forecast the total ecological footprint (TEF) from 2006 to 2015. For a case study of Wuhan city, Hubei province in central China, per capita ecological footprint (EF) and biological capacity (BC) were calculated from 1988 to 2005. Partial least square (PLS) was used to select the important impact factors. We put the selected socio-economic factors as input and the TEF as output together to build RBFNN model and predict the development trends of the TEF in the following 10 years. Five-fold cross-validation was conducted to validate the model in the process of input selection and RBFNN model training. From the results, continuous increase of per capita EF (1988–2005) indicated stronger and stronger human effect on the district and Wuhan’s ecological state is in the ecological deficit. Up to 2015, the district would have been bearing accumulative TEF of 24.782 million gha, which is near 2.5 times of that in 1988. Although the increase rate of gross domestic product (GDP) would be restricted in a lower level from 2006 to 2015, the urban ecological environmental burden could only respond to the socio-economic circumstances moderately. ß 2009 Elsevier Ltd. All rights reserved.

Keywords: Total ecological footprint (TEF) Biological capacity (BC) Radial basis function neural network (RBFNN) Partial least square (PLS) Development trends analysis

1. Introduction The human economy depends on the planet’s natural capital that provides all ecological services and natural resources. Humans have posed a considerable impact on the earth, associated with population increase and economic development. The natural capital accounts are essential for the overall assessments of human impact as well as for planning specific steps towards a sustainable future (Wackernagel and Yount, 2000). Ecological footprint (abbreviated as EF hereafter) methodology introduced in the early-1990s (Rees, 1992; Rees and Wackernagel, 2004; Wackernagel and Rees, 1996; Wackernagel et al., 2005) can serve such a purpose. Ecological footprints ‘translate’ a variety of relevant resources used by a nation, a community, a production process, or an individual into a common unit, namely bioproductive area. They track the amount of natural resources a population uses and compare it to the amount the ecosystems of a region, or the world as a whole, can regenerate (Wackernagel et al., 2004a).

* Corresponding author. Tel.: +86 27 87792240; fax: +86 27 87792240. E-mail addresses: [email protected] (X.M. Li), [email protected] (J.X. Zhou). 1470-160X/$ – see front matter ß 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ecolind.2009.05.003

Recent work indicates that global overshoot is raising, and that takes the biosphere currently 1.2 years to regenerate what humans use in 1 year (Wackernagel et al., 2004b). We seem to be getting further and further away from sustainability. To help decision-makers track ecological overshoot over time and identify sustainability policies, many researchers have been working on EF time series on different spatial levels (Hanley et al., 1999; Van Vuuren and Smeets, 2000; Haberl et al., 2001; Senbel et al., 2003; Erb, 2004; Wackernagel et al., 2004b), to provide effective support for sustainability science. To analyze development trends of EF in the future, Medved (2006) predicted the future EF of Slovenia for the year 2020 by analyzing the documents promoting energy conservation and renewable energy sources, without the use of a simulation model. Yue et al. (2006) introduced two indices of ‘change rate’ and ‘scissors difference’ by a polynomial regression analysis to quantitatively describe the development trends of EF time series. In addition, Wu et al. (2006) used Autoregressive Integrated Moving Average (ARIMA) model to predict temporal variation of water EF in Guangzhou, China. However, none of them had provided us an effective tool for predicting the development trends of EF in the future. Some critics argued that EF analysis could not provide a dynamic window on the future, but rather a snapshot in time (Costanza, 2000; van den

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Bergh and Verbruggen, 1999; Kitzes and Wackernagel, 2007; Rees, 2006; Turner et al., 2007). That is, EF analysis produces static estimates, whereas both nature and economy are dynamic system. Moreover, one important goal of the EF is to document overshoot and link it to socio-economic variables such as development trends, economic prosperity or lifestyle (Wackernagel et al., 2004b). Therefore, socio-economic factors should be used to forecast the development trends of ecological sustainability in a long-time series. Discussion in the context indicated that further work is needed to develop new approaches for simulating the development trends of EF in the future and to give us valid, plausible results and sound advice for policy-making. Because the total ecological footprint (abbreviated as TEF hereafter), which is the summed footprint of a defined population of an area, can represent the total human impact on a given area, our purpose is to predict the TEF of Wuhan, Hubei province, by applying new approaches. In this paper, a radial basis function neural network (RBFNN) model was developed to forecast the TEF. Among assorted artificial neural networks (ANNs), RBFNN, developed by Broomhead and Lowe (1988), have been widely applied in many research fields, such as function approximation, nonlinear control and pattern recognition (Yao et al., 2006; Haddadnia et al., 2003; Celikoghu, 2006; Ng et al., 2007). The increasing popularity of RBFNN is partly due to the easier initialization, faster training procedure, and more stable performance compared to other multilayer feed forward neural networks. The objectives of the present study are: (1) to calculate time serial per capita ecological footprint (EF) and biological capacity (BC) from 1988 to 2005; (2) to select the important socio-economic impact factors of TEF by using partial least square (PLS); (3) to develop a RBFNN dynamic model by using selected socio-economic factors as input and TEF as output; (4) to analyze the development trends of the TEF of Wuhan, Hubei province from 2006 to 2015. 2. Materials and methods 2.1. The studied area Wuhan city, as a central hinterland megapolis of China, and significant fulcrum of central China economic booming strategy designated by the Chinese government, is located in Hubei province, between 1138410 -1158050 E and 298580 -318220 N. The city consists of 13 counties and its topography has relatively gentle changes, including even plains, slightly rolling plains, foothills and mounds. It has a vast expanse of territory, covering an overall area of 8,494 km2, with built-up area taking up 2.61% of the whole area. It is rich in biological and mineral resources. Yangtze River and Hanjiang River flow across Wuhan and a great deal of lakes are distributed on the district. Furthermore, the total water area in Wuhan reaches 2,187 km2, accounting for 25.7% of total land area of the district. From the statistical figures in 2005, the population of Wuhan was 8,013,600 and the average annual population growth rate was 1.242% from 1988 to 2005. With growth of population and economy in recent years, human impact on land resources has been increasing and pollution contributed by socio-economic growth is critically serious, and conspicuous conflict appeared between huge number of population and insufficient natural resources. 2.2. The ecological footprint and its impact factors The EF methodology uses a common measurement unit to express EF and BC in terms of a biological productive area with the global average productivity, introducing the ‘equivalence factor’ and ‘yield factor’. So the areas are expressed in standardized hectares called ‘global hectares (gha)’ (Wackernagel et al., 2002).

In this study, the basic calculation procedure follows the quantitative method for ecological footprints (Wackernagel and Rees, 1996; Wackernagel et al., 1999a,b). The methodology for EF calculation includes mainly three basic formulae as following,

EF ¼

6 X j¼1

BC ¼

Qj

35  X i¼1

Ci N  EQ i j

 6  X Q j  Y j  Aj j¼1

ED ¼ BC  EF

N

!

 ð100  12Þ%

(1)

(2)

(3)

where EF, BC, ED is the per capita ecological footprint, biological capacity, ecological deficit (ED  0) or surplus (ED  0), respectively; j (=1–6 in the present study) is the type of land being considered, which included arable land, pasture area, forest area, water area, fossil energy land and built-up area; Qj is an equivalence factor for the jth type of land, and represents the ratio of the biological productivity of the jth type of land to the global average biological productivity for all types of bioproductive land, which equals the average bioproductivity for the six types of global land included in the present study (Wackernagel and Rees, 1996; Wackernagel et al., 1999a,b); i (=1–35 in the present study) is the number of products being analyzed; Ci is the total demand for the ith product by humans (kg year1); N is the total population; and EQij is the global biological yield for the ith product provided by the jth type of land (kg/ha); Yj is a yield factor for the jth type of land and represents the ratio of local biological yield of that type of land to the global average biological yield for the jth type of land (Wackernagel et al., 1999a,b, 2002). Aj is the total available supply in a given year for the jth type of land (ha). Moreover, it is assumed that the yield-adjusted equivalent area is decreased by 12% to allow for the creation of biodiversity reserves (Wackernagel et al., 1999a,b, 2002). In the study, the ‘equivalency factors’ and the ‘yield factors’ were both calculated by means of the average yield of Wuhan and the global average yield changing with years (WWF, 2006). The conversion factor of fossil–energy footprints published by Wackernagel et al. (1999a,b) was used as the constant over time. In the paper, the EF methodology is used to calculate the natural capital of Wuhan city for 1988–2005. The EF represents the critical natural capital requirements of a defined economy or population in terms of the corresponding bioproductive areas. Evidently, the area of the footprint depends on the population size, material living standards, used technology and ecological productivity (Wackernagel et al., 1999b). Some researchers suggested that the EF is simply one indicator of human’s ‘engagement’ and EF analysis should be used in conjunction with economic, social or any other indicators that bear on the issues at hand (Rees, 2006). Therefore, after qualitatively analyzing the concept and the model of the EF, we confined ten effect factors correlated with the TEF as follows, gross domestic product (GDP, 109, Z1), annual increase rate of GDP (%, Z2), population (106 person, Z3), proportion of tertiary industry (%, Z4), level of urbanization (%, Z5), total retail sales of consumer goods ( 109, Z6), total amount of energy consume (104 t SCE, Z7), expenditures by city residents ( year1, Z8), contributing rate of scientific and technical progress (%, Z9) and total amount of imports and exports ( 109, Z10). In other words, the ten factors were served as drivers of the TEF by the qualitative analysis. To further select the vital drivers, PLS and cross-validation was applied to select the impact factors (see Section 3.2).

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2.3. Radial basis function neural network RBFNN can be described as a three-layer feedforward structure with multi-inputs, multi-outputs, and linear output mapping between the hidden nodes and the output nodes (Bianchini et al., 1995). Normally, a RBFNN is comprised of three different layers: an input layer, a hidden layer and an output layer. In this study, the neurons of the input layer are comprised of socio-economic factors of the TEF and the number of neurons is obtained by using partial least square (PLS). The output layer contains one neuron, namely the prediction value of the TEF. The input layer does not process the information and only distributes the input vectors to the hidden layer. Here, inputs x1 ; x2 ; . . . ; xm , composing an input vector x, are applied to all neurons in the hidden layer. The hidden layer is composed of number n radial basis functions (RBFs) that are connected directly to all the elements in the output layer. Each hidden layer unit represents a single radial basis function, with associated center position and width. A node in the hidden layer will produce a greater output when the input pattern presented is close to its center. The basis function for the hidden nodes is often defined by a Gaussian function shown as follows: Gðkxð jÞ  T i kÞ ¼ exp½ðkxð jÞ  T i kb1 ;

i ¼ 1; 2; . . . ; n

(4)

where x(j) is the input vector of the jth input node, xð jÞ ¼ ðx1 ; x2 ; . . . ; xm Þ; Ti is the center of the ith RBF unit, T i ¼ ðt 1 ; t 2 ; . . . ; t n Þ; b1 is the bias in the hidden layer; kxð jÞ  T i k represents the vector distance between x(j) and Ti. The network output yk is formed by a linearly weighted sum of the number of basis function in the hidden layer. The values for the output nodes can be calculated as: yk ¼

n X wik Gðkxð jÞ  T i kÞ þ b2

(5)

i¼1

where yk is the output of the kth node in the output layer, wik is the weight from the ith hidden layer neuron to the kth output neuron, and b2 is the bias in the output layer. The RBFNN structure is depicted in Fig. 1. The bias neurons, controlled by a specific value, called ‘‘spread’’ number, are applied to adjust the sensitivity of the network. Each bias is set as sqrt(log(0.5))/spread (Demuth and Beale, 2003). The selected ‘‘spread’’ value should be large enough for neurons in the hidden layer to include the whole range of the input data. To improve the generalizability of RBFNN model, the number of hidden nodes

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should be minimized. To limit the maximum number of hidden nodes, the criterion N hid  Nin p Nout was applied, where the number of nodes in the input, hidden, and output layers are Ninp, Nhid and Nout, respectively (Masters, 1993). Furthermore, five-fold crossvalidation was conducted to confirm the appropriate number of hidden nodes while avoiding over-fitting. Each of the five folds was used, in turn, for validation while the remainder was used for model training. The procedure was repeated five times, each time with a new set of randomly selected folds. The solutions of the five networks were then averaged to obtain representative model performance for the test data (i.e., a cross-validation R2 value), which indicated the model’s generalizability (Basheer and Hajmeer, 2000). For comparison of the model’s simulation performance, several RBFNN model candidates that differed in terms of the number of hidden nodes (from two to six) were developed. The overall performance of RBFNN model was compared with that of PLS. Two indices for the model’s performance were examined: root mean squared error (RMSE) and the crossvalidated R2 obtained by the five-fold cross-validation. When RBFNN is used to establish the TEF forecasting model, the Neural Network Toolbox available in MATLAB 7.0 (Demuth and Beale, 2003) is implemented in this study to design, train and validate the RBFNN. 2.4. Partial least squares PLS, as a major regression technique for multivariate data, was introduced by Wold et al. (1983). The function of the PLS included multiple linear regression analysis, canonical correlation analysis and principal component analysis. PLS has been applied to many fields in science with great success since its use in chemistry initially. It is aimed at finding relationships between a group of explanatory variables (the Z matrix including the ‘‘impact factors’’) and a set of dependent variables (the Y matrix including the ‘‘response’’). It is important to determine how many significant PLS components are necessary using the cross-validation technique (Wold, 1978). To achieve this goal, the data is divided into a training set and a validation set. The model is established using the training set, the validation set is then used to validate the predicted values. In this paper, PLS employs five-fold cross-validation (iterative recalculation of the model omitting a different fold each time to test for sensitivity of the model toward a particular fold). The statistical results obtained by the PLS method are able to detect the relative importance of impact factors with respect to response variables by means of the VIP values. VIP is used to determine the significance of PLS components. Furthermore, the predictive performance of the PLS was evaluated by the use of the RMSE and cross-validated R2. In this paper, Matlab (version 7.0, Mathworks 2004) software was used to build a PLS model for impact selection of the TEF and for TEF prediction. 2.5. Data sources and their reliability

Fig. 1. A standard RBFNN structure.

The calculation of ecological footprint requires large amounts of data on human consumption, population, and land use. In this study, the primary consumption and population data were obtained from the 1989 to 2006 Wuhan Statistical Yearbooks (Wuhan Statistical Bureau, 1989–2006), as well as from the results of annual surveys of 1% of the households in urban and rural areas within the city’s administrative boundaries, provided by the Wuhan Statistical Bureau. The data for land use was obtained from the Wuhan Statistical Yearbook (1989–2006), which compiled data obtained from annual surveys of changes in Wuhan’s land use by the Wuhan Land Administration. Other related coefficients used

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Table 1 The per capita EF, BC, ecological budget and TEF for Wuhan, 1988–2005. Time (year)

Total population (person)

EF (gha per cap)

BC (gha per cap)

Ecological budget (gha per cap)

TEF (gha)

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

6,417,300 6,532,600 6,697,500 6,770,400 6,844,700 6,917,000 7,000,100 7,100,100 7,159,500 7,239,100 7,317,900 7,402,000 7,492,000 7,582,300 7,681,000 7,811,900 7,859,100 8,013,610

1.556 1.590 1.671 1.652 1.683 1.752 1.757 1.859 1.951 1.958 1.925 1.952 2.010 2.091 2.150 2.180 2.234 2.290

0.439 0.445 0.446 0.442 0.443 0.459 0.487 0.527 0.533 0.551 0.537 0.562 0.532 0.527 0.545 0.536 0.552 0.547

1.117 1.145 1.225 1.210 1.240 1.293 1.270 1.332 1.418 1.407 1.388 1.390 1.478 1.564 1.605 1.644 1.686 1.743

9,985,319 10,386,834 11,191,523 11,184,700 11,519,630 12,118,584 12,299,178 13,199,086 13,968,185 14,174,158 14,086,958 14,448,704 15,058,920 15,854,589 16,514,150 17,029,942 17,557,300 18,351,167

in EF calculation were taken from the FAO Yearbook (1989–2006) published by the Food and Agriculture Organization of the United Nations. In addition, the factors selection of TEF involves large amounts of statistic data. All data sources from 1988 to 2005 were taken from Wuhan Statistical Year Book (1989–2006) published by China Statistics Press. There were inadequate data sources for the emissions of wastes and for some consumption categories such as freshwater for the city, so the calculation of ecological footprints in this study did not include the assimilation of wastes. And the amount of freshwater only covered part of the industrial, agricultural, and domestic usages. This limitation of data availability typically leads to underestimate of the TEF. For the data analysis in this study, the calculation results are expressed to a maximum of three decimal places (where possible) and all percentages were rounded to a maximum of one decimal place. 3. Results 3.1. Calculation of the TEF of Wuhan for 1988–2005 In this paper, Wuhan’s EF, BC and ED were assessed for 1988– 2005 by Eqs. (1)–(3) (Table 1). According to Table 1, the per capita EF in Wuhan increased from 1.556 gha in 1988 to 2.290 gha in 2005, the per capita BC from 0.439 gha to 0.547 gha correspondingly. The per capita ED was negative all along during the studied period, indicating that Wuhan’s ecological state is in the ecological deficit. For only 18 years, the per capita ‘overshoot’ (as per capita EF minus per capita BC) increased quickly from 1.117 gha as in 1988 to 1.743 gha as in 2005. The above results of EF were aggregated according to the customary EF classification into the following land-use classes: arable land, pasture area, forest area, water area and fossil energy land (including fossil energy land and built-up area). Fig. 2 shows the development trend of the per capita EF of the five main categories of bioproductive area and the corresponding contributions to the TEF in Wuhan from 1988 to 2005. It is found that the per capita EF of all kinds of bioproductive area increases gradually for the whole period. The per capita EF of pasture area, water area and fossil energy increases more markedly than that of arable land and forest area, suggesting the fact that not only the consumption of fossil energy, but also people’s demand for meat food and fishery products increase steadily. The diet structure of citizen is changing gradually from a heavy reliance on grains to more on meat. People’s living standards have been continuously improved in

Wuhan city recently. Though Wuhan’s biocapacity has steadily increased during this period with the application of fertilizers and other land improvements, the ecological deficit is continuously increasing all along. Seeing that the ‘overshoot’ is correlated to a larger consumption of natural resources, it is of great importance to forecast the TEF in order to acquaint policymakers and researchers with the future status of the natural resources utilization in advance and allow them to make choices for regional sustainable development. 3.2. Important impact factors selection of the TEF To decrease the complexity of the model and eliminate noise, the selection of impact factors has been done by the use of partial least squares (PLS) and five-fold cross-validation. PLS was established to find relationships between the ten factors (as explanatory variables, forming the Z matrix) and the TEF (as dependent variables, forming the Y matrix). Each of the five folds was used, in turn, for validation while the remainder was used for model building. PLS employed five-fold cross-validation to detect which factors in the Z matrix are relevant to determine the TEF in the Y matrix by means of the VIP values. Finally, six factors: gross domestic product (GDP, 109, Z1), population (106 person, Z3),

Fig. 2. The development trend of per capita EF of five main categories of bioproductive area for Wuhan, 1988–2005.

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X matrix. The only output of the model is the TEF of Wuhan achieved by EF methodology. Generally, the larger the training sample the better the regression performance, although the returns begin to diminish once a certain volume of training data is exceed (Witten and Frank, 2005). In the paper, the data used in training and testing, including the TEF (the Y matrix) and the six factors (the X matrix) from 1988 to 2005 were converted into the 153 samples by Eq. (6) (n = 18). The samples, which consist of temporal sequence increments of the TEF and the six factors, were divided into five folds for RBFNN model development and parameter estimation. Additionally, generalization samples, which as the inputs were presented to the developed RBFNN model for predicting future TEF (2006–2015), could be obtained by transforming the several samples in matrix X0 by Eq. (7). 

Dxi; j ¼ xiþ j  xi Dyi; j ¼ yiþ j  y j i ¼ 1; 2; . . . ; n; j ¼ 1; 3; . . . ; n  i

(6)

Fig. 3. The VIP values of ten impact factors of the TEF.

Dx0i ¼ xiþ1  xi ; level of urbanization (%, Z5), total retail sales of consumer goods ( 109, Z6), total amount of energy consumption (104 t SCE, Z7), expenditures by city residents ( year1, Z8) were selected. Furthermore, the VIP values obtained by the PLS method are able to detect the relative importance of selected impact factors with respect to the TEF (see Fig. 3). Fig. 3 shows the VIP values of GDP and total amount of energy consumption are much more than others, arriving at 1.301 and 1.245, respectively. This implies GDP and total amount of energy consume are the most important impact factors of TEF. The results fit well with the actual situation of urban ecological impact in other areas. The VIP values of the other several factors is 1.169, 1.051, 1.094, 1.138, orderly. The other factors’ VIP values were less than one (VIP < 1). The six factors comprised X matrix were selected eventually to simulate development trend of the TEF from 2006 to 2015 in the next step. Additionally, according to ‘Wuhan General Planning Guideline (2006–2015)’, we could obtain the planned values of six factors in 2010 and 2015. Furthermore, when PLS approach exacted four main components, its perturbation error reached the minimum and related validation parameters was showed in Table 2. Additionally, to expediently determine the annual values of the selected factors, assuming the selected six factors show average increasing tendency from 2006 to 2010 and from 2010 to 2015, we would get the corresponding values of factors from 2006 to 2015 and form matrix X0 using the corresponding factors values. The values would be used to predict the TEF by the built model.

i ¼ 1; 2; . . . ; n  1

(7)

where xi (x0i ) is the ith time serial values of certain impact factor from 1988 to 2005 (2006–2015); yi is the ith time serial values of TEF. xi+j is the (i + j)th time serial values of certain impact factor from 1988 to 2005, the same with yi+j. The RBFNN model analysis with five-fold cross-validation were conducted for five model configurations that differed in the number of hidden nodes (Table 2). In the names of the RBFNN models in Table 2, the first number represents the number of hidden layer nodes, and the second number represents the number of output nodes. In the analysis, minimizing the number of hidden layer nodes led to the use of from two to six hidden nodes. The RBFNN-4-1 model showed the best performance based on having the third-best values of RMSE, R2 and the best values of crossvalidated R2 (CVR2). With the increase of the number of hidden nodes, R2 showed the increase tendency, while CVR2 the decrease tendency. Although the RBFNN-6-1 model showed the best performance values of R2 and RMSE, the CVR2 value decreased markedly compared with the uncorrected R2, which likely suggested over-fitting (Table 2). Apart from RBFNN-6-1, which provided worse overall performance, the PLS model performed less well than the RBFNN-4-1 model (Table 2). The RBFNN-4-1 model was applied to predict the training and testing samples. The relationship between the observed TEF values and the predicted TEF values using the RBFNN-4-1 model was illustrated in Fig. 4. Subsequently, by the generalization samples, the RBFNN model

3.3. Simulation study on the development trend of the TEF To develop the RBFNN model for forecasting the TEF, the inputs to the model include GDP, population, level of urbanization, total retail sales of consumer goods, total amount of energy consumption and expenditures by city residents. These inputs comprise the Table 2 Results of the RBFNN models and PLS. Model

Number of hidden nodes

R2

CVR2

RMSE

PLS RBFNN-2-1 RBFNN-3-1 RBFNN-4-1 RBFNN-5-1 RBFNN-6-1

– 2 3 4 5 6

0.82 0.62 0.79 0.85 0.90 0.97

0.70 0.68 0.69 0.75 0.59 0.39

1.98 2.43 2.25 1.80 1.21 0.95

The number of hidden nodes for the RBFNN models that produced the best results, the proportion of variation explained by the models (R2), the results of the five-fold cross-validation (CVR2) and the root mean squared error (RMSE).

Fig. 4. Relationship between the observed TEF and the values forecasted by the RBFNN-4-1 model.

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Table 4 The increase rate of TEF and GDP within several periods.

1988–2005 2005–2010 2010–2015

The increase rate of TEF

The increase rate of GDP

1.035 1.020 1.041

1.159 1.123 1.078

and that of the TEF during several different periods which summarize the overall development trend of GDP and TEF. Moreover, as is shown in Fig. 5 and Table 4, the growth rate of TEF would increase all along from 2006 to 2015, although that of the planned GDP from 2010 to 2015 almost halved compared with that of the Eleventh Five-year plan period (2006–2010). This fully exhibited the dynamic relationships between economic development and environmental degradation during general planning period. Fig. 5. The trends of total ecological footprint and GDP (2006–2015).

4. Discussion with the best performance (RBFNN4-1) predicted he development tendency of the TEF from 2006 to 2015.

4.1. The overall development trends and impact factors of Wuhan’s ecological footprint

3.4. Future development trend analysis of the TEF for Wuhan 2006–2015

The development trends of Wuhan’s ecological footprint reflected the changes in the same area required for resource use to maintain or enhance the city’s development without compromising its biocapacity. In this study, the dynamic analysis of EF was composed of two parts, i.e. applying conventional EF methodology to provide an estimate of the true ecological demand for natural resource from 1988 to 2005 and adopting RBFNN and PLS approaches to display a dynamic window for humanity’s consumption of natural capital during Wuhan general planning period. The methods used in the paper produced useful results which could reveal the state of ecological sustainability and development trends in the future. The key finding was that across overall studied period, Wuhan’s ecological footprint continuously exceeded its biocapacity (EF > EC) as urban economy developed rapidly, and that more and more of the resources required to support this rapid development were obtain from outside the city. The larger the total number of population, the greater its total ecological footprint became, and the ecological ‘overshoot’ also became higher and higher (see Tables 1 and 3). It was important to pointed out that although the growth rate of the planned GDP from 2006 to 2015 were in a state of descending trend, that of the predicted TEF maintain a still higher trend of growth. It could be inferred that urban eco-environment burden would not be improved immediately due to the slowing speed of economic development. For Wuhan city, the conflict between ecological environment and economic development will exist for a long run. Not surprisingly, the sustainable development of Wuhan city was faced with great challenge in the future. In order to permit future sustainable

The above six factors are assumed to be still the important impact factors of the TEF in the future and the development trend of these factors is assumed to continue according to ‘Wuhan General Planning Guideline (2006–2015)’. By presenting generalization samples to the developed RBFNN model, we may obtain Wuhan’s TEF from 2006 to 2015 (Fig. 5) and then get the Wuhan’s per capita EF. At the same time, we presumed Wuhan’s per capita BC would be increasing gradually and its growth rate is set as 1.012, which is the same as the annual average increase rate of the past 18 years. The TEF, per capita EF, BC and ecological budget (2006–2015) are listed in Table 3. In Table 3 and Fig. 5, the forecast results provide a dynamic window for humanity’s consumption of natural capital of Wuhan in future time series. According to the forecast results, Wuhan would bear an accumulative TEF of 24.782 million gha in 2015, which is nearly 1.35 times that of 2005 and nearly 2.5 times that of 1988; the per capita EF would increase from 2.259 gha in 2006 to 2.788 gha in 2015. If the increase rate of per capita BC was set to 1.012, BC would arise gradually to 0.617 gha in 2015 and the ecological budget would be reduced to 2.171 gha. In 2015, the per capita EF demand will be 4.5 times the per capita BC supply, and correspondingly the per capita ‘overshoot’ would accounts for nearly 80% of the EF demand. Obviously, the conflict between the people and the land will become more and more tense and the city will be in a state of unsustainable development in the next 10 years. Table 4 shows the different values of the increase rate of GDP

Table 3 The forecasting values of TEFs, per capita EF, BC, and ecological budget for Wuhan, 2006–2015. Time (year)

Total population (person)

TEF (gha)

EF (gha per cap)

BC (gha per cap)

Ecological budget (gha per cap)

2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

8,043,900 8,141,200 8,239,600 8,339,200 8,440,000 8,528,700 8,618,400 8,709,000 8,800,500 8,890,000

18,169,000 18,588,000 19,074,000 19,558,000 20,280,000 21,300,000 22,457,000 22,985,000 23,587,000 24,782,000

2.259 2.283 2.315 2.345 2.403 2.498 2.606 2.640 2.680 2.788

0.554 0.561 0.568 0.575 0.582 0.589 0.596 0.603 0.610 0.617

1.705 1.722 1.747 1.770 1.821 1.909 2.010 2.037 2.070 2.171

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development of the city, the local governments in Wuhan can make relevant regional strategic plans for environmental management and development. The analysis suggested four main strategies for the local governments: (1) to confine the population growth moderately; (2) to change the unreasonable human consumption pattern in order to reduce the EF without the reduction of the consumption level; (3) to enhance energy efficiency and develop the high-tech industry; and (4) to increase yield through technological innovations, so as to enhance the per capita BC to narrow the difference between both for the ultimate goal of restoring Wuhan on a sustainable track. According to factors selection of PLS approach, the urban economic development (GDP), total amount of energy consumption and population growth were three main driving factors that affected the dynamics of Wuhan’s total ecological footprint, and the impact factors interacted to determine the sustainability of the city’s development. The phenomenon is particularly significant in light of a rapidly growing consumer class around the world (Myers and Kent, 2003). It may appear unremarkable to some observers that population and affluence are so palpable indication of their importance in generating impacts. For energy consumption, not only Fig. 2, which shows the fossil energy footprint of the city’s total footprint increased much faster than other component footprint, but also it’s VIP value could testified its importance in environmental impacts. However, because of the lack of widely available measures, we have not explored the effects of other potential factors of interest including social equality, public welfare, and technological stock. Future explorations of such factors may further increase our understanding of anthropogenic drivers for the TEF. 4.2. Evaluation of the RBFNN model In this study, a RBFNN model with the best performance was developed to simulate the development tendency of the TEF from 2006 to 2015. It was noted that the developed RBFNN model used just six impact factors as inputs selected by PLS. Furthermore, in order to increase the generalization capability of model or avoid the over-fitting, the cross-validation technique was used to not only select the input variables (impact factors), but also validate the RBFNN model. According to the study above, the RBFNN was superior to the PLS approach. There were two main features explaining why the RBFNN was applied as following. First, RBFNN could flexibly tackle complex nonlinear relationships. It is well known that the TEF is affected by numerous socioeconomic factors and there exist dynamic, nonlinear characteristics among them. Therefore, the RBFNN model based on the ‘‘black-box’’ principle could efficiently grasp the nonlinear relationship between the TEF and the impact factors by the hidden layer with radial basis functions, thereby realizing the simulation of objective issues. Second, as a type of artificial neural networks (ANNs), RBFNN can overcome some of the shortcomings of back-propagation neural network (BPNN) including the very slow convergence speed of learning, susceptibility to converging to a local minimum and the difficult determination of better initial weights. Furthermore, the RBFNN model has superior mapping ability, because the distance between the input and center is employed in its training process instead of the weighted sum of the input vector used in BPNN. Therefore, RBFNN gets the broader application than BPNN. However, like other ANNs, RBFNN is susceptible to over-fitting. In the study, the RBFNN-6-1 that displayed the best performance in terms of its RMSE and R2 values appears to have suffered from over-fitting based on the marked decrease in its cross-validation R2. Even for RBFNN-4-1 model with best performance, over-fitting in the higher TEF values is suggested by the good fit between the

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observed and forecasted values. These results indicated that the ability of the RBFNN model to be generalized decreases at higher TEF values. Nevertheless, this simple model to be a particular tool was expected to predict the consumed natural capital where the TEF will be particular high in the future. Additionally, to achieve the same accuracy with BPNN, the RBFNN model needed larger number of hidden neurons (Demuth and Beale, 2003). This make the RBFNN need more costs and time than BPNN do. 5. Conclusions In this paper, a RBFNN model was set up to forecast the TEF in Wuhan, Hubei Province, China from 2006 to 2015. It is worthwhile to bring forward that the five-fold cross-validation was used to not only select the input variables, but also validate the RBFNN model, in order to avoid the over-fitting. Furthermore, the RBFNN model, which includes four hidden layer nodes, has the best performance compared with other several models including PLS, and was used to predict the development trends of the TEF. The predicting results would offer vital information on the future trend of regional human consumption of natural capital in a long time series. With the proposed approaches in this study, ecological sustainability could be analyzed in advance of the following years. Hence, the policymakers would be aided in setting goals for ecological sustainability and monitoring sustainable progress in order to defend the eco-environmental crisis in the future. Acknowledgements We gratefully acknowledge the helpful suggestions from two anonymous reviewers. This work was supported by the National Natural Science Foundation of China (No. 60474077). References Basheer, I.A., Hajmeer, M., 2000. Artificial neural networks: fundamentals, computing, design, and application [J]. Journal of Microbiological Methods 43, 3–31. Bianchini, M., Frasconi, P., Gori, M., 1995. Learning without local minima in radial basis function networks [J]. IEEE Transaction on Neural Networks 6 (1), 749– 756. Broomhead, D.S., Lowe, D., 1988. Multi-variable functional interpolation and adaptive networks [J]. Complex Systems 20 (1), 321–355. Celikoghu, H.B., 2006. Application of radial basis function and generalized regression neural networks in non-linear utility function specification for travel mode choice modeling [J]. Mathematical and Computer Modelling 44 (7–8), 640–658. Costanza, R., 2000. Forum: the ecological footprint. The dynamics of the ecological footprint concept [J] Ecological Economics 32 (2), 341–345. Demuth, H., Beale, M., 2003. Neural Network Toolbox: For Use with Matlab [M]. Mathworks, Inc., Natick, MA. Erb, K.H., 2004. Actual land demand of Austria 1926–2000: a variation on ecological footprint assessment [J]. Land Use Policy 21 (3), 247–259. FAO, Food and Agriculture Organization of the United Nations, 1989–2006. FAO Yearbook [M]. FAO, Rome. Haberl, H., Erb, K.H., Krausmanm, F., 2001. How to calculate and interpret ecological footprints for long periods of time: the case of Austria 1926–1995 [J]. Ecological Economics 38 (1), 25–45. Haddadnia, J., Faez, K., Ahmadi, M., 2003. A fuzzy hybrid learning algorithm for radial basis function neural network with application in human face recognition [J]. Pattern Recognition 36 (5), 1187–1202. Hanley, N., Moffatt, I., Faichney, R., Wilson, M., 1999. Measuring sustainability: a time series of alternative indicators for Scotland [J]. Ecological Economics 28 (1), 55–73. Kitzes, J., Wackernagel, M., 2007. A research agenda for ecological footprint accounting. International Ecological Footprint Conference (Stepping up the Pace: New Developments in Ecological Footprint Methodology, Policy & Practice). Masters, T., 1993. Practical Neural Network Recipes in C++. Academic Press, Boston, MA. Myers, N., Kent, J., 2003. New consumers: the influence of affluence on the environment. Proceedings of the National Academy of Sciences 1000, 4963– 4968. Medved, S., 2006. Present and future ecological footprint of Slovenia—the influence of energy demand scenarios [J]. Ecological Modelling 192 (1–2), 25–36. Ng, W.W.Y., Dorado, A., Yeung, D.S., Pedrycz, W., Izquierdo, E., 2007. Image classification with the use of radial basis function neural networks and the mini-

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