Constructed wetland modelling for watershed ecosystem protection under a certain economic load: A case study at the Chaohu Lake watershed, China

Ecological Modelling 368 (2018) 180–190

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Ecological Modelling journal homepage: www.elsevier.com/locate/ecolmodel

Constructed wetland modelling for watershed ecosystem protection under a certain economic load: A case study at the Chaohu Lake watershed, China Jingneng Ni a,c , Jiuping Xu a,b,∗ , Mengxiang Zhang a a

Uncertainty Decision-Making Laboratory, Sichuan Univ., Chengdu, 610064, PR China State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan Univ., Chengdu, 610064, PR China c Department of Mathematics and Physics, Hefei Univ., Hefei, 230601, PR China b

a r t i c l e

i n f o

Article history: Received 16 April 2017 Received in revised form 7 October 2017 Accepted 18 November 2017 Keywords: Constructed wetland Ecosystem protection FRS-based NSAA Fuzzy random variable Optimization model

a b s t r a c t The two major aims of watershed management are regional economic development and watershed ecosystem protection. In this paper, constructed wetland (CW) technology is employed to examine watershed ecosystem protection under a certain regional economic load. The Chaohu Lake watershed in China was chosen as the target study area and fuzzy random variables used to describe the uncertainties. Then, a bi-level optimization model for watershed-scale CW planning was developed and applied to the Chaohu Lake watershed with the aim of protecting ecosystem health. To solve the model, a fuzzy random simulation-based nested simulated annealing algorithm was designed. The results showed that there was a “finite sum game” relationship between economic development and ecosystem health within the Chaohu Lake watershed. Under a probability and possibility of 0.9, to achieve the ecological goal F1 = 70, it was estimated that a 348.19 (ha) CW needed to be constructed. The impacts of environmental policies and economic development on the watershed ecosystem were found to be significant. One of the key practical results indicated that: in the Chaohu Lake watershed, the water environmental treatment of rivers should take precedence over that of lakes; a result which could be of assistance to local government policy making. © 2017 Elsevier B.V. All rights reserved.

1. Introduction The conflict between ecosystem protection and economic development has become a global watershed management issue (Patterson et al., 2004; Dong et al., 2012; Koundouri et al., 2015). Ecological mismanagement in the past decades has meant that in many parts of the world, watershed ecosystem health has been seriously damaged because of rapid and uncontrolled economic development and urbanization (Moxnes, 1998). With the ideology of “development first, environmental protection later”, this ecological mismanagement has been especially true in China (Liu, 2010), where three decades of rapid economic growth has caused and then exacerbated water body problems (Wang et al., 2008; Liu and Yang, 2012), seriously damaging local ecosystems (Takungpao, 2013). The Chaohu Lake watershed, one of the most seriously polluted areas

∗ Corresponding author at: Uncertainty Decision-Making Laboratory, Sichuan Univ., Chengdu, 610064, PR China. E-mail address: [email protected] (J. Xu). https://doi.org/10.1016/j.ecolmodel.2017.11.019 0304-3800/© 2017 Elsevier B.V. All rights reserved.

in China, is a prime example (Xinhua News Agency, 2014). Given its current economic development load, it has now become critical to restore and protect the health of the Chaohu Lake watershed ecosystems. To develop regional economies, watershed managers (usually local governments) need to expand industrial production; however, these decisions inevitably lead to increased industrial waste such as waste water, waste gas, and solid waste. The contamination carrying capacity of the natural watershed environment, however, is limited; when pollution emissions exceed the carrying capacity upper bound, the watershed ecosystem can be seriously damaged or destroyed. These watershed carrying capacity limitations, therefore, mean that there is an inherent conflict between ecosystem protection and economic development (Chen and Chen, 2006; Dong et al., 2012). The two sustainable development aims for a watershed, however, are healthy ecosystems and developed economies (Liu et al., 2008; Parkes et al., 2010). As CWs have multiple service functions; for example, purifying water quality, increasing biodiversity, providing wildlife habitats, and maintaining the stability and integrity of the ecosystem; they can be implemented to resolve

J. Ni et al. / Ecological Modelling 368 (2018) 180–190

Notations Indices i j k

river, i ∈ {1, 2, . . ., I}; industrial product, j ∈ {1, 2, . . ., J}; and pollutant, k ∈ {1, 2, . . ., K}.

Fuzzy random parameters P˜ ijk pollutant k emissions per unit of product j in river basin i (kg); ˜ annual degradation of pollutant k per unit area of De ik

constructed wetland in river basin i (kg/ha); e˜ ij

the economic benefits per unit of product j in river basin i (104 CNY);

˜ N i

annual estimated visitor numbers in river basin i (person/ha · yr); and

C˜ i

CW construction costs per unit area in river basin i (104 CNY/ha).

Crisp parameters Raij the production tax rate of industrial product j in river basin i (%); Wij wages for per unit industrial product j in river basin i (104 CNY/yr); Rpik the Pigovian tax rate for pollutant k in river basin i (104 CNY/t); the pollutant k emissions allowances in river basin Alik i (t/yr); Capik maximum capacity of pollutant k in river i (t); river ik policy control valve for pollutant k in river basin i; maximum production capacity of product j in river YijU basin i; Ti CW eco-tourism scenic spot ticket price in river basin i (CNY/person); Pi a Pigovian tax function for pollution emissions in river basin i; gi annual management fee for per unit constructed wetland i (CNY/ha · yr); i Vriver the annual average flow of the river i (m3 /yr); XiL , XiU lower and upper limits of available land (ha); k policy control valve for pollutant k in lake; Capklake the maximum capacity of lake for pollutant k (t); k Cwetlandin concentration of pollutant k in the constructed wetland inflow (mg/L); Qrain the annual precipitation (mm); ˛1 , ˛2 , ϑi probability level; ˇ1 , ˇ2 ,  i possibility level; F1 , fi values for the upper and lower level budget objectives; F2 economic load (108 CNY); W1 , W2 benchmark adjustment coefficients; ABio , AWE normalization coefficient for biological abundance and water environment; w1 , w2 , w3 weighted coefficients; and A1 , A2 , A3 , A the area of river, lake, wetland, watershed (km2 ). Decision variables xi planned constructed wetland area in river basin i (ha), the upper level decision variables; and amount of product j in river basin i (t), the lower yij level decision variables.

181

these conflicts (Martín et al., 2013; Jiang et al., 2015). Therefore, in our research, a CW is employed as a technical ecosystem protection tool. Constructed wetland as an artificial ecological engineering has been widely used for watershed management around the world. Xu et al. (2015) studied the requirements for a new CW planning project, and developed CW construction schemes based on the different demands of the regional economy, social employment, and water quality protection; however, the CW contributions to watershed ecosystem protection were not investigated. Seeking dynamic equilibrium, Ni et al. studied the use of a CW to balance the needs of the watershed ecosystem and economic development (Ni et al., 2016). However, in watershed management, the regional economic development budget is generally a constant value. Therefore, to address these previous oversights, in this paper, CW-based ecosystem protection is examined under a specific regional economic load, for which new mathematical models, algorithms, and case validations are developed. The identification of accurate quantitative expressions for the ecology, the economy, the pollutants, and the environmental policies are essential in watershed management research. As mathematical modelling techniques have been proven to be effective quantitative description tools, they have been widely applied in many research disciplines, including watershed management (Pahl-Wostl, 2007; Zhang and Huang, 2011). Nonetheless, as there are also many ecological, economic, and environmental uncertainties in watershed systems (Clark, 1985; Guillaume et al., 2012), watershed management modelling is significantly more complex than traditional mathematical modelling methods (Xu et al., 2013). To deal with the random and fuzzy uncertainty in previous modelling attempts, stochastic, fuzzy, and interval approaches have been proposed (Huang and Loucks, 2000; Saadatpour and Afshar, 2007; Ni et al., 2013; Li et al., 2014; Zhang et al., 2014; Xie et al., 2014), in which the fuzziness and randomness were separated. However, there are other uncertainties which have elements of both randomness and fuzziness, such as pollutant degradation degree; therefore, to deal with this situation, in this paper, a fuzzy random variable (Kwakernaak, 1978, 1979) is employed to describe these kinds of uncertainties, and a bi-level optimization model is established to mimic the bi-level watershed management structure. Based on the new large-scale CW planning project at the Chaohu Lake watershed, this paper focuses on ecosystem protection under a certain regional economic load. The specific research objectives were: (1) to embed the CW as a watershed management system component; (2) to clarify the Chaohu Lake watershed bi-level management structure; (3) to establish a bi-level optimization model for watershed ecosystem protection; (4) to quantitatively describe the environmental policies in the model in accordance with the local environmental management status; and (5) to investigate the practical results so as to give guidance to watershed management.

2. Methodology 2.1. Conceptual model Different from sewage treatment plants, CW can not only treat various water pollutants, but can also repair watershed ecosystems. Therefore, watershed management departments (usually local governments) have begun to plan for watershed-scale CW systems. Depending on the pollution treatments required in the CW, local governments assign pollution emissions allowances to industrial enterprises in each river basin, after which the industrial enterprises organize production based on the emissions allowances to maximize profits. Therefore, watershed management has a bi-level

182

J. Ni et al. / Ecological Modelling 368 (2018) 180–190

Fig. 1. Conceptual model framework for CW-based watershed management.

management structure, in which the local government as the upper level decision maker has the authoritative position, and the industrial enterprises in each watershed river basin as the lower level decision makers have a subordinate position. These complex relationships can be shown in a conceptual model framework, as shown in Fig. 1. 2.2. Uncertainty processing

Fig. 2. Uncertainty processing method.

Watershed management systems have many inherent uncertainties (Clark, 1985; Beck, 1987; Guillaume et al., 2012). As an example, here, the CW pollutant degradation ability for a certain pollutant (denoted De) is taken to illustrate the uncertainty processing method used in this paper. Based on historical data, the current situation, and expert professional knowledge, the degradation ability of the pollutant per CW unit area De can be determined by an expert group En (n = 1, 2, . . ., N) and expressed in linguistic terms as an interval (i.e., [an , cn ]) with a most possible value (i.e., bn ), where N and En denote N different experts and the nth expert. Therefore, minn {an } and maxn {cn } are the lower and upper bounds of De. By comparing the bn obtained from N different experts, it can be found that bn is a random variable (denoted b) that approximately follows a normal distribution (i.e., b∼N(,  2 )), which can be estimated using a maximum likelihood method and justified using a chi-square goodness-of-fit test. From these procedures, it can be deduced that De has the fuzzy random variable characteristics proposed by Kwakernaak (1978, 1979). Therefore, ˜ and De ˜ = (a, b, c), where a = min {a }, De can be described as De, n

n

c = maxn {cn }, b∼N(,  2 ). The entire process is shown in Fig. 2. Other uncertainties in this paper are similarly handled.

Evaluation Criteria, – the Technical Criterion for Eco-environmental Status Evaluation (HJ/T192-2006) (MEP, 2006). EI = W1 Bio + W2 WE

where W1 and W2 are the dimension adjustment coefficients; Bio 3 denotes the biological abundance indicator, Bio = A1 ABio l=1 wl Al , wl is the weight; A1 , A2 , A3 and A respectively denote the river, lake, wetland and watershed areas; WE denotes the environmental K J I ˜ (100 − A (P y − water indicator, and WE = 1 K

The CW-based bi-level optimization model for watershed ecosystem protection under a certain economic load is established in line with the conceptual model framework (Fig. 1) and on the basis of the bi-level optimization method proposed by Bracken and McGill (1973). In China, all ecological indicators are quantitatively described as the weighted sum of the biological abundance index, the vegetation cover index, the water network density index, the land degradation index, and the environmental quality index. In this study, as only the watershed ecosystem is investigated, the ecological sustainability was calculated from the Chinese Ecological Environmental

k=1

WE

j=1

i=1

ijk ij

˜ x )/Q ), x is the planned CW area in river basin i (ha) and is De i ik i rain the upper level decision variable; yij is the amount of product j in the river basin i (103 kg/yr) and are the lower level decision variables; P˜ denotes the pollutant k emissions per unit of product j in ijk

˜ denotes the annual degradation of polthe river basin i (kg); De ik lutant k per unit area of the CW i (kg/ha); Qrain denotes the annual precipitation (mm); ABio and AWE are normalization coefficients. Therefore, Formula (1) can be rewritten as, EI =

2.3. Model formulation

(1)

⎛

  1 1 W1 ABio wl Al + W2 A 3 3

K

l=1

k=1

⎝100 − AWE

J I  

⎞

˜ x )/Q ⎠ (P˜ ijk yij − De ik i rain

(2)

j=1 i=1

Normally, the local government has a target ecological budget ˜ are fuzzy random F1 (a crisp number). In Formula (2), P˜ ijk and De ij variables; therefore, as the Formula (2) result is also a fuzzy random number, it cannot be compared with a crisp number. To deal with this situation, a chance measure (Xu and Yao, 2011) is used to describe the possibility that the Formula (2) result is not less than the target budget F1 under a probability level ˛1 , as shown in

J. Ni et al. / Ecological Modelling 368 (2018) 180–190

Formula (3),

 

Pos

Pr

variable cannot be directly compared with an exact variable. Therefore, an expected value operator (EV) is employed for the fuzzy random variable (Xu and Zhou, 2011), and the environmental policy constraint for the lake can be written as

  1 1 wl Al + W2 W1 ABio A 3

⎛ ⎝100 − AWE

3

K

l=1

k=1

J I  

⎞

˜ x )/Q ⎠  F (P˜ ijk yij − De 1 ik i rain

j=1 i=1

⎫ ⎬ ⎭

 ˛1

⎛

⎫ ⎬ ⎭

EV ⎝ (3)

where Pr{ · } denotes the probability of a random event { · }, Pr{ · } ≥ ˛1 denotes that the probability of a random event { · } is not less than ˛1 ,  denotes “not less than”, and Pos{ · } denotes the possibility of a fuzzy event { · }. Formula (3) denotes that under probability level ˛1 , the local government seeks a maximum possibility (ˇ1 ) that the watershed ecological situation is no lower than the target budget F1 . Therefore, Formula (3) can be converted into a dependent chance objective and its constraint (Xu and Zhou, 2011), as follows, max ˇ1



s.t. Ch

J



I

˜ x )/Q 100 − AWE   (P˜ ijk yij − De ik i rain

(4)

  F1

(˛1 ) ≥ ˇ1

j=1 i=1

Developing the watershed economy is an important management task for the local government. Under a probability ˛2 and a possibility ˇ2 , the local government seeks to ensure that the total watershed economy is no less than a target budget F2 . In this research, the watershed economy is considered to have three ˜ x ), parts: industrial taxes (Ra e˜ y ), CW eco-tourism income (T N ij ij ij

i

and C˜ i respectively denote in river basin i, the production tax rate of industrial product j (%), the economic benefits per unit for product j (104 CNY), CW eco-tourism scenic spot ticket price (CNY/person), annual estimated visitor numbers (person/ha · yr) and CW construction costs per unit area (104 CNY/ha). Therefore, the watershed economic development is described as a chance constraint (Xu and Ding, 2011).

Ch

⎩

Raij e˜ ij yij +

j=1 i=1

I 

˜ x − Ti N i i

i=1

I 

C˜ i xi  F2

i=1

⎫ ⎬ ⎭

(5)

Land area for the CW is limited in each river basin; that is, xi ≤ XiU , XiU is the maximum usable area. At the same time, as a large-scale project, there are minimum construction area constraints (XiL ), i.e., 0 < XiL ≤ xi . Therefore, the CW area constraints for the upper level model are, 0 < XiL ≤ xi ≤ XiU ,

∀i

(6)

To protect watershed ecosystem health, the total amount of pollutant k discharged into the lake should not exceed k times the maximum capacity of the lake under natural conditions (Capklake ), k ∈ (0, 1]. k is the local government policy that regulates pollutant k emissions and specifies the local government administrative strictures to be applied to protect the lake water environment; the smaller the value of k , the more stringent the pollution control policy. The total amount of pollutants discharged into the lake can J I ˜ ˜ x ). As P˜ and De ˜ are fuzzy (P y − De be written as j=1

i=1

ijk ij

ik i

ijk

ik

random variables, k Capklake is an exact variable, the fuzzy random

˜ x )⎠ ≤  Capk , (P˜ ijk yij − De ik i k lake

k ∈ (0, 1],

∀k (7)

The maximum capacity Capklake is calculated using the Vollenweider model (Vollenweider, 1975, 1976). The industrial enterprises’ decision goal is profit maximization, which is determined from industrial production revenue (e˜ ij yij ) minus the fines/penalties for excessive pollution emissions

Pi

J ˜ P y j=1 ijk ij

wages (Wij yij ). J 

e˜ ij yij −

K 



, the CW daily management fee (gi xi ), and

⎛ Pi ⎝

J 

k=1

⎞ P˜ ijk yij ⎠ − gi xi −

j=1

J 

Wij yij ,

∀i

(8)

j=1

where e˜ ij , Pi , gi and Wij respectively denote the economic benefits per unit of product j in river basin i (104 CNY), a Pigovian tax function, the annual management fee per unit area of CW i (CNY/ha · yr), and the wages per unit of industrial product j in river basin i (104 CNY/yr). Under a probability ϑi and possibility  i , the industrial enterprises located in river basin i seek to maximize profit fi . Formula (8) can, therefore, be rewritten as a chance objective (Xu and Yao, 2011; Xu and Zhou, 2011), as follows. max fi s.t. Ch



 e˜ ij yij −  Pi

J

J ˜  P ijk yij

j=1

j=1

K

k=1



J

−gi xi −  Wij yij  fi



(9) (ϑi )≥i

j=1

River pollution protection is similar to lake pollution protection; that is, the total quantity of pollutant k discharged into river i should not exceed ik times the maximum capacity of river i (Capik river );

J ˜ that is, the P y is not more than ik Capik river . ik , ik ∈ (0, 1] j=1 ijk ij is another local government policy regulation. Using the expected value operator, this can be written as ⎛

EV ⎝ (˛2 ) ≥ ˇ2

⎞

j=1 i=1

i i

and the CW construction costs (C˜ i xi ), which can be written as J I I ˜ ˜ x − I C˜ x , where Ra , e˜ , T , N Raij e˜ ij yij + TN ij i ij i j=1 i=1 i=1 i i i i=1 i i

⎧ J I ⎨ 

J I  

j=1

3 K 1 1 W1 ABio  wl Al + W2  A 3 l=1 k=1

183

J 

⎞

P˜ ijk yij ⎠ ≤ ik Capik river ,

ik ∈ (0, 1],

∀i, k

(10)

j=1

The value of Capik river is calculated using the Thomas model. The Pigovian tax is a commonly used method for regulating pollution emissions. Each industrial enterprise is allocated certain pollutant k emissions allowances (Alik ); however, if the pollutant k emissions exceed the given allowances, a Pigou tax is imposed, which is mathematically expressed as, Pi (P˜ ijk yij ) =

K  k=1

⎛ +EV ⎝

J 

⎛

⎛

J 

Rpik ⎝EV ⎝|

⎞

P˜ ijk yij − Alik |⎠

j=1

⎞⎞ P˜ ijk yij − Alik ⎠⎠ /2

(11)

j=1

where Rpik denotes the Pigovian tax rate for pollutant k in river basin i (104 CNY/t). As the CW is to be built in the river mouth, the river outflow is the CW inflow. According to the Technical Specification for Constructed Wetlands for Wastewater Treatment Engineering (HJ

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J. Ni et al. / Ecological Modelling 368 (2018) 180–190

2005–2010), the pollutant k concentration in the river outflow (i.e., J ˜ P y /V i , V i denotes the flow of the river i) must not j=1 ijk ij

river

river

exceed the CW input concentration standard; that is,

⎛

EV ⎝

J 

⎞

i k ⎠ ≤ Cwetlandin , P˜ ijk yij /Vriver

∀k

(12)

j=1

The industrial enterprises’ production capacities are considered nonnegative and finite; that is, 0 ≤ yij ≤ yijU ,

∀i, j

(13)

2.4. Global model From the integration of Formulas (4)–(7) and (9)–(13), a CWbased bi-level optimization model under uncertainty for ecosystem protection under a certain economic load is obtained, as follows: max ˇ1

⎧  3 K 1 1 ⎪  wl Al + W2  ⎪ ⎪ Ch A W1 ABio l=1 3 k=1 ⎪ ⎪

  ⎪ ⎪ J I ⎪ ˜ ˜ ⎪ 100 − A ( y − x )/Q  F1 (˛1 ) ≥ ˇ1 P De ⎪   WE ijk ij ik i rain ⎪ ⎪ j=1 i=1 ⎪  ⎪ ⎪ ⎪ J I I I ⎪ ˜ ˜ ⎪ Ch   Raij e˜ ij yij +  Ti N i xi −  C i xi  F2 (˛2 ) ≥ ˇ2 ⎪ ⎪ i=1 i=1 j=1 i=1 ⎪ ⎪  ⎪ J I  ⎪ ⎪ ˜ ˜ ⎪ EV P y − De x ≤ k Capklake   ijk ij ik i ⎪ ⎪ j=1 i=1 ⎪ ⎪ ⎪ 0 < X L ≤ xi ≤ X U ⎪ i i ⎪ ⎪ ⎪ ⎪ max fi ⎪ ⎪ ⎪ ⎧

 ⎪ ⎪ ⎨ ⎪ J J K ˜ ˜ ⎪ Ch e y − P P y  i  ij ij  ijk ij − gi xi ⎪ s.t. ⎪ j=1 k=1 j=1 ⎪  ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ J ⎪ ⎪ ⎪ ⎪ −  Wij yij  fi (ϑi ) ≥ i ⎪ ⎪ ⎪ ⎪ j=1 ⎪ ⎪

 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ J ⎪ ⎪ ˜ ⎪ ⎪ EV ≤ ik Capik P y  ijk ij ⎪ river ⎪ ⎪ ⎨ j=1 ⎪ ⎪  ⎪ ⎪ ⎪ J s.t. ⎪ ˜ i k ⎪ EV ≤ Cwetlandin  P ijk yij /Vriver ⎪ ⎪ ⎪ ⎪ j=1 ⎪ ⎪ ⎪   ⎪ ⎪ ⎪ ⎪ P P˜ y = K Rp ⎪ ⎪ ⎪  ik i ijk ij ⎪ ⎪ ⎪ ⎪ k=1 ⎪ ⎪ ⎪ ⎪



 ⎪ ⎪ ⎪ ⎪ J J ⎪ ⎪ ˜ ˜ ⎪ ⎪ EV |  P ijk yij − Alik | + EV P ijk yij − Alik /2 ⎪  ⎪ ⎪ ⎪ ⎪ j=1 j=1 ⎪ ⎪ ⎪ ⎪ ⎪ U ⎩ ⎩ 0 ≤ yij ≤ Yij

Another difficulty in model (14) is the calculations for the 119 fuzzy random variables. There are two common ways to deal with fuzzy random variables: (1) converting them into exact numbers using a mathematical operator (Li et al., 2006; Xu et al., 2013), and (2) using fuzzy random simulation (FRS) (Xu et al., 2015; Ni et al., 2016). As FRS has less information loss, it is employed to deal with the fuzzy random parameters in model (14). Based on the above and the bi-level structure of model (14), a new algorithm, the fuzzy random simulation-based nested simulated annealing algorithm (FRS-based NSAA) is designed to solve the model. The FRS-based NSAA algorithmic flow chart is shown in Fig. 3. Fuzzy random simulation fitness value procedure Step 1. Generate independently random numbers ω1 , ω2 from

1 , 2 according to the probability measure Pr; ˜ ik (ω2 ) based on Step 2. Produce fuzzy variables P˜ ijk (ω1 ) and De ˜ , respecthe structure of the fuzzy random variables P˜ ijk and De ik tively; Step 3. Let ˇ1 = ε, ε is a sufficiently small positive number; Step 4. Randomly generate crisp numbers Pijk and Deik from the ˜ ik (ω2 ), respectively; ε-level set of the fuzzy variables P˜ ijk (ω1 ) and De Step 1 W2 3

K

5.

k=1



Compute 100 − AWE

Step 6. Let  = 

the

J I

value

P˜ ijk

j=1

i=1

(Pijk ) ∧ 

v = A1 W1 ABio

3  l=1 wl Al +

(Pijk yij − Deik xi )/Qrain ;

˜ ik De

(Deik );

Step 7. If v ≥ F1 and  > ˇ1 replace ˇ1 with ; Step 8. Repeat Step 4 to Step 7 M times, return ˇ1 ; (1)

(2)

(N)

Step 9. Repeat Step 1 to Step 8 N times, return ˇ1 , ˇ1 , . . ., ˇ1 ; Step 10. Let N be the integer part of ˛1 N; (14)

In model (14), as all model parameters are written as undetermined parameters, the model can be easily applied to other watersheds. For example, the environmental policy parameters k and ik , and the possibility  i and probability ϑi levels in model (14) can be calibrated according to local environmental policies when the model is applied to other watersheds. Other parameters can be similarly calibrated. 2.5. Algorithm design Even in the simplest case, solving a bi-level programming problem is NP-hard (Bard, 1991). Therefore, it is difficult to solve multi-objective bi-level programming in model (14) because it contains fuzzy random variables. The simulated annealing technique (SAT) proposed by Kirkpatrick (Kirkpatrick et al., 1983), however, has been proven to be suitable for calculating the numerical solution to complex optimization problems in various fields (Liu et al., 2017; Haghi et al., 2017; Mahmoodpour and Masihi, 2016). Therefore, because of the SATs good convergence, it is used as the basic framework for the design of the new algorithm to solve model (14).

(1)

(2)

(N)

Step 11. Return the N th largest element in {ˇ1 , ˇ1 , . . ., ˇ1 }. 3. Case study 3.1. Study area Chaohu Lake is situated in central Anhui Province in eastern China and is one of the five largest freshwater lakes in China. The Chaohu Lake watershed has an area of 13,486 km2 , a catchment population of 10.2 million, an average annual temperature of 15–16 ◦ C and a mean annual precipitation of 1000–1100 mm. Thirty-three rivers, including seven main rivers, are radially distributed in the watershed, all of which finally flow into Chaohu Lake, as shown in Fig. 4. 3.2. Data collection For this research, seven major rivers, three major pollutants, and three industrial product categories at the Chaohu Lake watershed were included. Therefore, the river, pollutant, and industrial product indices were set at: I = 7, K = 3, and J = 3; that is, i = 1, 2, . . ., 7, k = 1, 2, 3, and j = 1, 2, 3. To solve the model, the data for the model parameters were collected and collated from the Anhui Province Hydrology Bureau and Environmental Protection Office, the Anhui Provincial Statistics Bureau, the Chaohu Lake Administration Bureau, the Anhui Province Inland Revenue Bureau, and the Technical Criterion for Ecoenvironmental Status Evaluation (HJ/T192-2006) (MEP, 2006). Due to the local geography and Chaohu Lake management policies, price levels across the entire Chaohu Lake watershed were very similar; therefore, the following parameters were considered to be the same throughout the Chaohu Lake watershed, for all i = 1, 2, . . ., 7: gi = 1.5 (104 CNY/ha · yr), Ti = 30 (CNY/person), Wi1 = 13 (104 CNY/person · yr), Wi2 = Wi3 = 11.5 (104 CNY/person · yr), Rai1 = Rai3 = 5 (%),

J. Ni et al. / Ecological Modelling 368 (2018) 180–190

185

Fig. 3. FRS-based NSAA algorithmic flow chart.

Fig. 4. Schematic diagram for the Chaohu Lake watershed water system.

Rpi1 = Rpi2 = Rpi2 = 20 (%), C˜ i = (135, c i , 167), c i ∼N(151, 11) ˜ 4 N ∼N(11, 000, 200) (10 CNY/ha), N = (9000, N , 12, 000), i

i

i

(person/ha · yr). The other parameters are shown in Tables 1–4.

The basic Chaohu Lake watershed situation data are listed in Table 1. The basic Chaohu Lake watershed data for ecosystem status are listed in Table 2. The other fuzzy random parameters are listed in Tables 3 and 4.

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J. Ni et al. / Ecological Modelling 368 (2018) 180–190

Table 1 Chaohu Lake watershed – basic data. Indicators

Chaohu lake

River basin 1

River basin 2

River basin 3

River basin 4

River basin 5

River basin 6

River basin 7

769 17.9 Nil Nil Nil Nil

70 6.70 4031.0 1305.2 70.7 10/170

60 5.64 1166.6 326.8 18.4 10/130

117 11.00 2332.7 548.1 49.6 10/190

146 13.73 650.5 136.4 12.5 10/95

34 3.72 954.1 223.8 16.4 10/110

27 2.21 767.6 157.5 11.6 10/70

48 4.51 143.2 62.8 0.7 10/31

Area (km2 )/length (km) Volume/flow (108 m3 ) Ali1 (t/yr) Ali2 (t/yr) Ali3 (t/yr) XiL /XiU (ha)

Table 2 Chaohu Lake watershed ecosystem status parameters. Benchmark adjustment coefficients W1 = 0.625 W2 = 0.375 Normalization coefficients ABio = 676 AWE = 0.058

River, lake, wetland area (km2 ) Alake = 764 Weight coefficients w2 = 0.3

Ariver=9082 w1 = 0.1

Rainfall (mm) Qrain = 1050 Watershed area (km2 ) 13,486

Awetland = 153 w3 = 0.6

Table 3 ˜ Degradation of pollutant k per unit area of CW (Deij ) and economic benefits per unit of product j (e˜ ij ). For all river basin i, i = 1, 2, . . ., 7. j

1

˜ Deij (kg/ha) e˜ ij (CNY/t)

2

3

(330, Dei1 , 390), Dei1 ∼N(360, 23)

(11, Dei2 , 27), Dei2 ∼N(19, 1.7)

(5.5, Dei3 , 11.5) Dei3 ∼N(8.5, 1.15)

(5000, ei1 , 6000), ei1 ∼N(5500, 210),

(500, ei2 , 700), ei2 ∼N(600, 70)

(3000, ei3 , 3800), ei3 ∼N(3400, 110)

Table 4 ˜ Pollutant k emissions per unit of product j in river basin i (P ijk ) (kg). i

j

˜ P ij1

1

1 2 3

(15, P 111 , 29), P 111 ∼N(22, 1.9) (10, P 121 , 18), P 121 ∼N(14, 1.7) (13, P 131 , 25), P 131 ∼N(19, 2.1)

(3, P 112 , 7), P 112 ∼N(5, 0.3)) (1, P 122 , 5), P 122 ∼N(3, 0.15)) Nil

(1.15, P 113 , 5.25), P 113 ∼N(3.2, 0.17) Nil (1.2, P 133 , 3.6), P 133 ∼N(2.4, 0.11)

2

1 2 3

(17, P 211 , 33), P 211 ∼N(25, 2.1) (12, P 221 , 18), P 221 ∼N(15, 2.3) (15, P 231 , 25), P 231 ∼N(20, 1.9)

(3, P 212 , 7), P 212 ∼N(5, 0.4)) (1.3, P 222 , 5.5), P 222 ∼N(3.4, 0.16)) Nil

(1.5, P 213 , 6.5), P 213 ∼N(4.0, 0.23) Nil (1.3, P 233 , 3.7), P 233 ∼N(2.5, 0.11)

3

1 2 3

(15, P 311 , 27), P 311 ∼N(21, 2.3) (11, P 321 , 19), P 321 ∼N(15, 2.5) (13, P 331 , 27), P 331 ∼N(20, 2.1)

(3, P 312 , 9), P 312 ∼N(6, 0.5)) (1.5, P 322 , 4.5), P 322 ∼N(3, 0.15)) Nil

(1.3, P 313 , 5.5), P 313 ∼N(3.4, 0.17) Nil (1.2, P 333 , 3.6), P 333 ∼N(2.4, 0.11)

4

1 2 3

(14, P 411 , 30), P 411 ∼N(22, 1.9) (11, P 421 , 23), P 421 ∼N(17, 2.3) (11, P 431 , 27), P 431 ∼N(19, 2.7)

(3, P 412 , 7), P 412 ∼N(5, 0.3)) (0.9, P 422 , 4.7), P 422 ∼N(2.8, 0.13)) Nil

(1.3, P 413 , 5.7), P 413 ∼N(3.5, 0.15) Nil (1.1, P 433 , 3.7), P 433 ∼N(2.4, 0.11)

5

1 2 3

(15, P 511 , 31), P 511 ∼N(23, 2.1) (9, P 521 , 19), P 521 ∼N(14, 2.3) (11, P 531 , 25), P 531 ∼N(18, 2.9)

(3, P 512 , 7.4), P 512 ∼N(5.2, 0.3)) (1, P 522 , 5), P 522 ∼N(3, 0.11)) Nil

(1.25, P 513 , 5.15), P 513 ∼N(3.2, 0.15) Nil (1.1, P 533 , 3.9), P 533 ∼N(2.5, 0.11)

6

1 2 3

(15, P 611 , 31), P 611 ∼N(23, 2.5) (10, P 621 , 18), P 621 ∼N(14, 2.1) (13, P 631 , 25), P 631 ∼N(19, 2.5)

(3, P 612 , 7), P 612 ∼N(5, 0.3)) (1, P 622 , 5), P 622 ∼N(3, 0.15)) Nil

(1.15, P 613 , 5.25), P 613 ∼N(3.2, 0.17) Nil (1.2, P 633 , 3.6), P 633 ∼N(2.4, 0.11)

7

1 2 3

(16, P 711 , 30), P 711 ∼N(23, 2.5) (11, P 721 , 21), P 721 ∼N(16, 2.7) (13, P 731 , 25), P 731 ∼N(19, 2.7)

(2, P 712 , 8), P 712 ∼N(5, 0.3)) (1.3, P 722 , 5.3), P 722 ∼N(3.3, 0.15)) Nil

(1.1, P 713 , 5.1), P 713 ∼N(3.1, 0.13) Nil (1.2, P 733 , 3.6), P 733 ∼N(2.4, 0.13)

˜ P ij2

˜ P ij3

Table 5 Optimal objective values and schemes. i The optimal objective values The optimal schemes

1 ˇ1∗ fi∗ (×109 CNY) xi∗ (ha) ∗ yi1 (×105 t/yr) ∗ yi2 (×105 t/yr) ∗ yi3 (×105 t/yr)

6.41 75.08 1.78 1.35 1.80

2 7.16 85.34 2.19 2.42 0.23

3 7.50 88.05 3.85 4.90 1.82

4 3.98 42.61 0.35 1.66 0.60

5 0.879 4.24 46.45 1.83 1.43 0.12

6

7

Total

3.01 27.97 0.37 0.88 1.03

3.99 22.69 1.94 0.01 1.99

36.29 388.19 12.31 12.65 7.59

J. Ni et al. / Ecological Modelling 368 (2018) 180–190

187

Table 6 Impact of environmental policies on the watershed ecosystem.

ik ˇ1∗

0.2 0.922

0.25 0.921

0.3 0.921

0.35 0.922

k ˇ1∗

0.2 0.968

0.25 0.967

0.3 0.963

0.35 0.953

Set k = 0.5, k = 1, 2, 3, ik changed from 0.2 to 0.95, k = 1, 2, 3, i = 1, 2, . . ., 7 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.915 0.902 0.879 0.862 0.831 0.775 0.694 0.643 Set ik = 0.5, k = 1, 2, 3, i = 1, 2, . . ., 7, k changed from 0.2 to 0.95, k = 1, 2, 3 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.927 0.909 0.879 0.845 0.811 0.779 0.748 0.723

0.8 0.611

0.85 0.593

0.9 0.585

0.95 0.583

0.8 0.705

0.85 0.687

0.9 0.686

0.95 0.685

Table 7 Impact of economic development level on the watershed ecosystem. F2 (×108 CNY) ˇ1∗

2.0 0.956

2.5 0.945

3.0 0.928

3.5 0.907

4.0 0.879

4.5 0.847

5.0 0.811

5.5 0.778

6.0 0.751

6.5 0.728

7.0 0.711

7.5 0.697

8.0 0.685

Table 8 Constructed wetland for watershed ecosystem compensation F2 (×108 CNY) The area of CW (ha)

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

8.0

0

56.0

176.35

345.84

408.19

687.73

972.96

1294.53

1691.68

2104.45

2519.98

2935.21

3351.36

3.3. Model results

fore, the results in Table 6 reveal that environmental management policies play a key role in protecting watershed ecosystem health.

Based on the flow of the FRS-based NSAA algorithm (Fig. 3), a computer program was developed to run model (14) using MATLAB software. By comparing the results of the preliminary experiments, which observed the behavior of FRS-based NSAA at different parameter settings, the most reasonable parameters were set as follows: initial temperatures for the outer and inner layers T1 = 300, T2 = 200; sampling times for the outer and inner layers l1 = 500, l2 = 300; and the outer and inner layer cooling rates 1 = 2 = 0.95. The program was run on a Pentium 4, 2.40 GHz clock pulse with a 1024 MB memory personal computer, and the model calculation results were obtained. When the decision makers’ control parameters were set at F1 = 70, F2 = 4 ×108 , ˛1 = ˛2 = 0.9, ˇ2 = 0.9, k = 0.5, ik = 0.5 and ϑi =  i = 0.85, k = 1, 2, 3, i = 1, 2, . . ., 7, the optimal objective values and optimal schemes were derived, as shown in Table 5. The results showed that under a regional economic load of F2 = 4 ×108 CNY/yr, if the watershed ecological health index F1 = 70 was obtained at a possibility level of 0.879, then 338 hectares of constructed wetlands would need to be built in the different river basins.

4. Discussion 4.1. Impact of environmental policy on ecosystem health The decision makers’ control parameters were set at F1 = 70, F2 = 4 ×108 , ˛1 = ˛2 = 0.9, ˇ2 = 0.9, and ϑi =  i = 0.85, i = 1, 2, . . ., 7, and the policy control valves k and ik , k = 1, 2, 3, i = 1, 2, . . ., 7 were individually adjusted from 0.2 to 0.95 with a step-size of 0.05. Under a probability of 0.9, with the change in ik /k , the possibility of achieving the ecological target F1 = 70 was calculated, as shown in Table 6. It can be seen from Table 6 that the smaller the value for ik /k , the greater the possibility of achieving the target F1 = 70 and the better the ecosystem.

 In model (14), in the constraints EV

and EV

J I j=1



˜ x) (P˜ y − De ik i i=1 ijk ij

J ˜ P y j=1 ijk ij

≤ ik Capik river

≤ k Capklake , the variables ik

and k describe the intensity of the local government environmental policies. As ik , k ∈ [0, 1], for all k = 1, 2, 3, i = 1, 2, . . ., 7, the smaller the value of ik /k , the less the river/lake capacity to discharge pollutants, and the greater the intensity of the environmental protection policies, the better the watershed ecosystem. There-

4.2. Insights from the model into the necessity for public resource management When all the environmental policy conditions in model (14) are removed and the watershed ecosystem protection objective is also removed, then, under the constraint   J I Raij e˜ ij yij  F2 (˛2 ) ≥ ˇ2 , model (14) degenerCh j=1

i=1

ates to a single-level optimization model, the formula for which is as follows, max fi s.t.

⎧ ⎨ Ch

J

J

j=1

j=1



 e˜ ij yij −  Wij yij  fi

⎩ 0 ≤ y ≤ YU ij ij

(ϑi ) ≥ i

(15)

Formula (15) indicates that the local government has an annual economic development budget F2 and that the industrial enterprises located in each river basin are pursuing maximum profit under the premise that the economic development budget must be maintained; therefore, this could be seen to be an exact expression for the economic development pattern in initial economic development stage in developing countries. Under this development pattern, the ecosystems  damage is the most serious.  J I If constraint Ch Raij e˜ ij yij  F2 (˛2 ) ≥ ˇ2 is j=1

i=1

removed, Formula (15) then implies that individual production is free. Driven by the profit maximization objective, environmental resources are totally consumed by the industrial enterprises to expand production, resulting in what is known as “the tragedy of the commons” (Hardin, 1968). The above two ecosystem damage scenarios are a result of poor resource management (Moxnes, 1998). Therefore, as environmental resource management needs to be strengthened (Ostrom, 1990), model (14) is ideal for investigating the relationship between economic development, ecosystem protection, and environmental management policy. 4.3. Practical management insights in the Chaohu Lake watershed Based on the results shown in Table 6, the impact relationships between the river and lake environmental policies on the watershed ecosystem were identified, as shown in Fig. 5.

188

J. Ni et al. / Ecological Modelling 368 (2018) 180–190

Fig. 5. Impact of river and lake environmental policies on the watershed ecosystem. Fig. 6. Impact of economic development level on the watershed ecosystem.

Fig. 5 shows that the watershed ecosystem is more sensitive to policies related to the environmental control of the river (i.e., ik ) than to policies related to the environmental control of the lake (i.e., k ). The impact on the watershed ecosystem of both river and lake environmental policies was found to be the most significant between 0.4 and 0.8; that is, when pollution emissions reach 40% to 80% of the river/lake carrying capacities, policy intervention is necessary. From above analyses, two conclusions about the Chaohu Lake watershed management can be made: (1) in the Chaohu Lake watershed, the environmental treatment of the water in the river should take precedence over the environmental treatment of the water in the lake; (2) environmental management policies should be strengthened when pollutant emissions reach 40% of the river/lake carrying capacity; if pollutant emissions exceeds 80% of the river/lake carrying capacity, the water environment will be damaged and the environmental policies will no longer be effective. 4.4. The “finite sum game” relationship between economic development and ecosystem health To simulate the impact of economic development on the watershed ecosystem, the decision makers’ control parameters were set at F1 = 70, ˛1 = ˛2 = 0.9, ˇ2 = 0.9, k = 0.5, ik = 0.5 and ϑi =  i = 0.85, k = 1, 2, 3, i = 1, 2, . . ., 7, and the economic budget F2 (×108 CNY) was adjusted from 2 to 8 with a step-size of 0.5 (×108 CNY). In this way, the impact of economic development on the watershed ecosystem was simulated. The simulation results are shown in Table 7. The results showed that the impact of the regional economy on the watershed ecosystem was significant. Under a probability of 0.9, the possibility of achieving ecological goal F1 = 70 was as high as 0.956, when the total regional economy was F2 = 2 ×108 CNY. However, when F2 was increased to 8 × 108 CNY, the possibility fell to 0.685. To interpret the economic development impact on the watershed ecosystem, the relationship between economic development level and the watershed ecosystem figures in Table 7 were visualized in Fig. 6. Table 7 and Fig. 6 show that due to the limited carrying capacity of the environment, there is a “finite sum game” relationship between economic development and ecosystem health in the watershed, indicating that ecosystem protection and economic development are conflicted in watershed management. Necessary measures such as the construction of CW are required to develop the regional economy while protecting the watershed ecosystem.

Fig. 7. Simulation results for the watershed ecosystem compensation.

4.5. Effectiveness of the constructed wetland to protect the watershed ecosystem The parameters of the model remained set at F1 = 70, ˛1 = ˛2 = 0.9, ˇ2 = 0.9, k = 0.5, ik = 0.5, ϑi =  i = 0.85, k = 1, 2, 3, i = 1, 2, . . ., 7 and the economic budget F2 (×108 CNY) was adjusted from 2 to 8 by a step-size of 0.5 (×108 CNY). The effect of the CW on watershed ecosystem compensation was thus simulated, the results for which were listed in Table 8. The results showed that to ensure watershed ecosystem health, the index cannot fall below 70 (F1 ≥ 70) and the regional economy cannot exceed 2.0 × 108 CNY. If these were maintained at these levels, there would be no need to construct wetlands to compensate for the loss of ecosystem health. If this were not the case, however, a certain area must be allocated to constructed wetlands. When the economy reaches 8.0 × 108 CNY, an area of 3351.36 ha CW would be needed to compensate for the losses in watershed ecosystem health caused by the economic development. The effect of the CW on watershed ecosystem compensation in Table 8 was visualized in Fig. 7. From Fig. 7, it can be seen that a CW is effective in repairing watershed ecologies. In the Chaohu Lake watershed, when the

J. Ni et al. / Ecological Modelling 368 (2018) 180–190

size of the watershed economy is small (i.e., F2 ≤ 2 ×108 CNY) and the total pollution generated by the economic development is not beyond the carrying capacity of the watershed environment, there is no need for constructed wetlands. As the economy grows, however, there is a commensurate rise in pollutant emissions, which eventually exceed the environmental carrying capacity and cause ecosystem damage; therefore, an increasingly large CW would be needed to repair the watershed ecosystem. When the size of the economy is larger than 6.0 × 108 CNY, the relationship between economic growth and the CW area is nearly linear, which indicates that the degradation caused by the pollutants generated by the economic development is almost entirely dependent on an increase in the CW area, and also reveals the effectiveness of the CW in ecosystem maintenance and restoration.

5. Conclusions A watershed management framework and an inexact bi-level programming model were established to investigate ecosystem protection under a certain economic load. In modelling, a CW system was used as a technological tool, and a new algorithm, the FRS-based NSAA, was designed to solve the model. Chaohu Lake watershed in China was chosen as a case study area to verify the model. Some management insights were gained from the results of the model. (1) There is a “finite sum game” relationship between ecosystem health and economic development in a watershed. The underlying cause of this relationship is the limited environmental carrying capacity. When economic development reaches a certain level, the environmental carrying capacity is insufficient to simultaneously support an increased economic load and maintain ecosystem health, at which point a conflict between economic development and the ecosystem emerges. (2) Environmental management policies play a key role in protecting watershed ecosystem health. When pollution emissions reach around 40% to 80% of the environmental carrying capacity, policy intervention is necessary. For the Chaohu Lake watershed, the environmental treatment of river water should take precedence over that of lake water. The serious ecosystem damage in developing countries and the occurrence of “the tragedy of the commons” phenomenon have mainly been because of poor or no management of public resources. (3) As a type of artificial ecological engineering, CW systems are effective in maintaining and restoring ecosystems. However, this “effectiveness” is conditional, as the land available to construct the CW is limited in most watersheds. Nonetheless, the insights gained from this study could be helpful in guiding watershed management practices. Constructed wetland modelling for watershed ecosystem protection can be combined with other watershed management measures such as pollution emissions permit trading. This would require the development of new mathematical models and algorithms, and the uncertainties in the systems would need to be reinvestigated and processed, all of which we plan to examine further in future work.

Acknowledgements This research is supported by the Key Program of National Natural Science Foundation of China (Grant No. 70831005), and also supported by the Research Foundation of Ministry of Education for the Doctoral Program of Higher Education of China (Grant No. 20130181110063), the Social Science Foundation of Anhui Province (Grant No. AHSKY2017D83), and the Quality Engineering Project of Hefei University (Grant No. 2017jyxm016).

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