A Bi-level optimization approach to reduce the pollution burden of lake water with ecological compensation

Ecological Indica o s 151 (2023) 110334 A ailable online 12 May 2023 1470-160X/© 2023 The Au ho s. Published by Else ie L d. This is an open access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by- nc-nd/4.0/). A Bi-le el op imiza ion app oach o educe he pollu ion bu den o lake wa e wi h ecological compensa ion Linhuan He a , b , Liming Yao a , * , Pe a Sabe Va bano b a Business School, Sichuan Uni e si y, Chengdu 610065, China b Sus ainable P ocess In eg a ion Labo a o y –SPIL, NETME Cen e, Facul y o Mechanical Enginee ing, B no Uni e si y o Technology - VUT B no, Technick´ a 2896/2, 616 69 B no, Czech Republic ARTICLE INFO Keywo ds: Wa e en i onmen al ecosys em Lake ecological compensa ion Bi-le el op imiza ion Equi abili y Cos -e iciency ABSTRACT Lake Ecological Compensa ion (LEC) mechanism is a localized app oach o paymen o ecosys em se ices o add ess he con lic be ween economic de elopmen and ecological conse a ion. Howe e , how o mo i a e egional s akeholde s o pa icipa e in wa e quali y p o ec ion is a challenge. Based on he adi ional Coase Theo em, e ical eco-compensa ion mechanism has been p oposed o sol e pollu ion o lake basin. The quan- i ica ion o LEC is cha ac e ized by key wa e quali y indica o s (NH 3 -N and COD) in his pape . In eg a ing LEC mechanism wi h he ecological-economic model, his pape p oposes a bi-le el op imiza ion amewo k o he conse a ion o he lake wa e en i onmen . Re e ing o Coase’s heo y, he leade ’s goal is o dis ibu e was e load pe mi s equally o sub- egions while ollowe s aim o minimize en i onmen al cos s. The app op ia e applica ion o his me hod o Taihu Basin demons a es i s e iciency and p ac icali y. The LEC mechanism wi h di e en scena ios is analyzed and sugges ions o lake wa e quali y a e made. The esul s show ha : (1) Conside ing equi able p inciple, he new COD alloca ion scheme has educed he o al amoun o emissions by 17% compa ed o he da a in 2020, and he o al amoun o NH 3 -N has dec eased by 16%. (2) Wi h he coop- e a ion o lake basin ins i u ions, he LEC mechanism is p o ed o be an e ec i e measu e in p omo ing he conse a ion o he lake wa e en i onmen . (3) The spillo e e ec o en i onmen al and ecological policies in lake wa e indica es he need o upg ade indus ial s uc u e. This pape p oposes o p o ide a mo e eliable he conse a ion o he lake wa e en i onmen pa adigm. 1. In oduc ion Paymen o Ecosys em Se ices (PES) has been p oposed and ope a ed as economic incen i es o ecological conse a ion ac oss di e en egions and coun ies o abou wo decades (Engel e al., 2008; Ouyang e al., 2016; Zhang e al., 2022; Wunde e al., 2008). Ecological conse a ion is a gene al beha io a ge ing he na u al en i onmen . The di e si ica ion o PES p ac ice is an ine i able esul o a ious en i onmen al and ins i u ional se ings (Zeng e al., 2021). Fo es Res o a ion P og ams in he wes e n US (Bela enu i e al., 2022), he Oka ango Ri e Basin in Sou h A ica (Wang and Nuppenau, 2021), and he Lake E ie Wa e shed (Xu e al., 2018) a e all success ul applica ions o PES. How he PES mechanism adop ed, comp ehended and imple- men ed by he Chinese local go e nmen s is no ewo hy o ecological conse a ion. Fo he localiza ion o PES in o he Chinese ecological conse a ion, eco-compensa ion is concep ualized as a na ional en i onmen al p o ec ion policy in China (Feng e al., 2018). Wa e shed PES (US$24.7 billion in 62 coun ies in 2015) (Salzman e al., 2018), also known as wa e shed ecological compensa ion, mainly es ic s he beha io o pollu e s h ough he design o a ewa d and punishmen mechanism. The ecological compensa ion mechanism, as an e ec i e en i onmen al policy, ha uses economic ins umen s o co- o dina e he in e es s o s akeholde s has been he ocus o many schola s (Conno e al., 2022; Jiang e al., 2019). Howe e , ew o hem syne gize he ins i u ional s uc u e o lake basins wi h ecological compensa ion mechanisms. Exis ing s udies ha e paid li le a en ion o lake ecological compensa ion (LEC) o he conse a ion o he lake wa e en i onmen , which means speci ic beha io a ge ing wa e quali y. Lake basin, as in eg a ed place o accommoda e wa e bodies, plays i al ecological oles such as lood egula ion and s o age, wa e di e - sion o i iga ion, d inking wa e sou ces, aquacul u e, and ou ism * Co esponding au ho . E-mail add ess: [email p o ec ed] (L. Yao). Con en s lis s a ailable a ScienceDi ec Ecological Indica o s jou nal homepage: www.else ie .com/loca e/ecolind h ps://doi.o g/10.1016/j.ecolind.2023.110334 Recei ed 15 Ma ch 2023; Recei ed in e ised o m 28 Ap il 2023; Accep ed 4 May 2023 Ecological Indica o s 151 (2023) 110334 2 (Wa son e al., 2016; Woolway e al., 2021). Howe e , he con inuous de e io a ion o lake ecological en i onmen has become an impedimen o he sus ainable de elopmen o social economy. The inc easing nu- ien s in lakes has pu wa e quali y a isk wo ldwide. Va ying deg ees o wa e eu ophica ion and wa e quali y deg ada ion ha e been disco e ed in he No h Ame ican G ea Lakes (Riccia di and MacIsaac, 2000), Lake Biwa in Japan (Ma e al., 2022), Lake Bolsena and Lake Chiusi in cen al I aly (Fische e al., 2016), and Lake E hai in China (Lin e al., 2021). Acco ding o he Uni ed Na ions’ Sus ainable De elopmen Goals (SDGs) (Pe ei a and Ma ques, 2021; Wang e al., 2022), clean wa e o SDGs 6 and 4 is u gen ly needed o he whole wo ld. Based on wa e quali y moni o ing and combined wi h modelling s udies (V¨ o ¨ osma y e al., 2010), e iews o global wa e pollu ion indica e e ec i e measu es need o be aken o con ol he ecosys em pollu ion o lake wa e s. LEC mechanism is one o he sensible economic means o wa e pollu ion con ol and ecological conse a ion (Shen e al. 2021). I seeks o in e nalize he ex e nali ies ela ed o human beha io s and c ea es incen i es o sub- egions o ensu e ecological se ice p o ision. To cla i y ha , he dominan pape s o PES esea ches a e summa ized in Table 1. The quan i ica ion o compensa ion is a key link in he imple- men a ion o ecological compensa ion o wa e quali y pollu ion. Nash equilib ium model (Nimubona and Pe eau), op imal model (Zhao e al., 2013), S ackelbe g game (Fe nandez, 2013), and he e olu iona y game (Gao e al., 2019) a e ypical me hodologies used in p e ious esea ch. Wa e quali y equi emen s o he lake and discha ge s anda ds a e he aim o pollu ion planning and he key indica o s o decision-making. To he bes o he au ho s’ knowledge, exis ing li e a u e lacks comp ehensi e s udies ha combine ma hema ical models o lake wa e en i onmen al ecology and was e load alloca ion o quan i y he lake ecological compensa ion mechanism. Wha ’s mo e, in he ins i u- ional s uc u e sys em, wo le els o decision-make s a e included which a e he Lake En i onmen Commi ee and sub- egional au ho - i ies. The Lake En i onmen Commi ee is he p io i y decision-make ha makes i necessa y o alloca e he was e load pe mi s e ec i ely. The sub- egional au ho i ies, as he lowe -le el decision make s, y o minimize he en i onmen al cos s unde he LEC mechanism. This pape makes signi ican con ibu ions in h ee aspec s. Fi s ly, i e ines an analy ical amewo k o quan i y lake ecological compensa- ion, which helps o esol e he con lic be ween economic de elopmen and he conse a ion o he lake wa e en i onmen . Secondly, a bi-le el op imiza ion model is p oposed based on he Coase Theo em, which enables equi able was e load alloca ion and easonable annual planning o wa e quali y con ol. Thi dly, a ious scena ios o join go e nance o he lake wa e ecosys em in Taihu Basin a e discussed, p o iding suppo o i s sus ainable de elopmen . 2. Key p oblem s a emen The o e -exploi a ion o wa e esou ces in lakes has agg a a ed he de e io a ion o wa e quali y. The e o e, how o coo dina e egional economic de elopmen wi h wa e en i onmen al p o ec ion has a ac ed widesp ead a en ion. In his pape , wo pe spec i es a e conside ed which a e was e load amoun con ol and wa e pollu ion concen a ion con ol based on he go e nance sys em. Each pe spec i e has mul iple conside a ions. This esea ch is conduc ed o shed ligh on he s a egy o main aining sus ainable de elopmen o he lake wa e ecosys em. 2.1. Mul i-s akeholde go e nance sys em The o ma ion and e olu ion o lakes a e no only a ec ed by he changes o na u al ac o s in he basin bu also in luenced by human ac i i ies. Hence, lakes p esen di e en egional e olu iona y cha ac- e is ics and ecological p oblems. Coase Theo em (Hahn, 2013), p oposed by a Nobel P ize winne , is well-known in ecological conse a ion. Based on Coase Theo em, en i- onmen al ex e nali ies a e u ned in o p ope y igh p oblems, as i uses a ma ke mechanism o maximize he en i onmen al and economic bene i s based on clea p ope y igh s. Coase’s heo y also suppo s he quan i ica ion and equi able alloca ion o was e load pe mi s. The con- se a ion o he lake wa e en i onmen is mainly mani es ed mainly in h ee aspec s. 1. The apid economic de elopmen o he lake a eas, as he ocus o local go e nmen s, will ine i ably cause wa e quali y deg ada ion, o he pollu an -holding capaci y o lakes is limi ed. The equi able alloca ion o limi ed was e load pe mi s (WLP) is a easible me hod o he conse a ion o he lake wa e en i onmen . 2. The lack o an e ec i e beha io al egula o y mechanism a ec s he sus ainable de elopmen o lakes. I he local go e nmen conduc s li le in e en ion in local sewage discha ge, he pollu ion o lakes will be disas ous. 3. The sus ainabili y o he wa e ecosys em in he basin needs mul i- index and mul i-dimensional measu es ins ead o simple e alua- ion. Mul i-sec o al in ol emen , co e ing Lake En i onmen Com- mi ee and sub- egional au ho i ies, is equally i al. Fo he ins i u ional s uc u e o lake managemen , he Lake En i- onmen Commi ee wo ks as he uppe -le el decision make (Leade ) and sub- egional au ho i ies o lakes a e he lowe -le el decision make s (Followe s). As he supe iso o he o e all wa e quali y in he lake basin, he Lake En i onmen Commi ee ocuses on how o a ionally alloca e he o al amoun o WLP as i is limi ed. Fu he mo e, he Lake En i onmen Commi ee o mula es he LEC mechanism and egula es egional beha io s by moni o ing sec ion da a. Regional go e nmen s mainly wo k on he annual a e age concen a ion o pollu an s wi hin Table 1 P ac ice and applica ion o paymen o ecosys em se ices. A icles Resea ch objec Key p oblem and inno a ion Eco-compensa ion Mechanism Me hods Nimubona and pe eau, 2022 We land To analyze he economic e iciency be ween he bene icia ies and p o ide s hough no el paymen schemes. √ A Nash equilib ium model wi h h ee ypes o agen s Zhao e al., 2013 Lake To compu e he cos o minimized ans e ax a e along wi h he educ ion quan i ies o indi idual egions. A bi-le el p og amming amewo k Fe nandez, 2009; 2013 T ansna ional i e To help s akeholde s bea pollu ion aba emen cos s and sha e wa e moni o ing esponsibili y. A S ackelbe g game and Nash Equilib ium Gao e al., 2019 T ansbounda y i e To explo e how ecological bene i s a e dis ibu ed be ween di e en go e nmen s. √ An e olu iona y game o mul i- go e nmen s Lu e al., 2020 T ansbounda y i e To build an econome ic model o economic loss and calcula e he amoun o compensa ion o economic loss due o wa e pollu ion. An econome ic model o calcula e he economic loss Smi h e al., 2019 Land To design a land paymen o ecosys em se ices mechanism and examine spa ial coo dina ion on he demand side o he ma ke . √ Spa ial simula ion modelling L. He e al. Ecological Indica o s 151 (2023) 110334 3 he mechanism. The decision a iables ep esen he ac ual discha ge amoun in he egion om he leade pa and he annual a e age wa e quali y concen a ion o he moni o ing sec ion om he lowe pa . The goal is o ind he balance be ween economic bene i s and he sus ain- abili y o he wa e ecosys em. 2.2. S uc u ing incen i e mechanism A g owing amoun o esea ch sugges s ha using he LEC mecha- nism as economic incen i es o main ain wa e sus ainabili y is a mo e di ec app oach o achie ing he goal (Guan e al., 2021; Li e al., 2022). Howe e , he exis ing quan i a i e analysis o lake eco-compensa ion is no su icien ly sys ema ic and is somewha de ec i e. To ill hese gaps, we explo e he es ablishmen o LEC mechanism based on wa e quali y and he quan i y o discha ged con aminan s. A adeo occu s when was ewa e emission inc eases because o economy p oduc ion and ecology alue educes acco dingly . Howe e , a syne gy wo ks when all sub- egions ake he sus ainabili y o lake wa e en i onmen as hei own mission. The LEC mechanism is an embodimen o PES which e e s o ewa d and punishmen . Beha io s ha p o ec he wa e en i onmen a e ewa ded, while beha io s ha cause damages a e punished (Wu e al. 2018). In essence, he LEC is an en i onmen al and economic incen i e policy and i akes he o m o iscal unding be ween he Lake En i- onmen Commi ee and indi idual sub- egions. Fu he mo e, as he e is no s ic di ision be ween ups eam and downs eam in he lake, how o judge he impac o sewage among di e en egions is also ega ded as a ough assignmen . The con ol o pollu an concen a ion is he main indica o o he LEC mechanism. Th ough he da a analysis o he moni o ing sec ion, he ewa d and punishmen o sub- egions can be judged. The lake eco- compensa ion mechanism is exp essed as he ollowing unc ion g(yij): g(yij) = {− α pi,0<pi⩽1 βpi,pi>1 α ,β>0(1) Pi= μ 0∑ n j=1 kj yij Cijo (2) whe e p is he compensa ion index o he moni o ing sec ion, i is he sub- egion loca ed a he same lake, and j p esen s di e en con aminan s. μ 0 is he lake wa e quali y s abili y coe icien which mainly conside s he in luence o na u al condi ions such as ain all and uno ；kj is he indica o weigh coe icien ；yij is he annual mean concen a ion alue o he indica o ；Cij0 is he basic limi o he indica o , whe e he lowe limi o he III class o wa e quali y is used as he s anda d. The decision amewo k o lake wa e en i onmen managemen is illus a ed in Fig. 1. Fig. 1. Decision amewo k o lake wa e en i onmen managemen in his pape . L. He e al. Ecological Indica o s 151 (2023) 110334 4 3. Me hod A bi-le el op imiza ion model has been de eloped o he lake eco- compensa ion mechanism o he wa e shed by analyzing he s uc u e o he lake wa e en i onmen managemen . The o mula ion p ocess placed a s ong emphasis on he model’s easibili y and p ac icali y, aking in o accoun he eal-wo ld con ex o he p oblem. 3.1. F amewo k o he model 3.1.1. Assump ion The comple e he conse a ion o he lake wa e en i onmen e- qui es he Lake En i onmen Commi ee o alloca e was e load pe mi s equally o sub- egional au ho i ies. On he o he hand, sub- egional au ho i ies should con ol he a e age annual concen a ion o wa e con aminan s wi hin he LEC egula ion amewo k. The implemen a- ion o he LEC mechanism has s imula ed he p o ec ion o wa e quali y in he egion. Be o e es ablishing he basic model, ou hy- po heses a e made as ollows. Assump ion 1.The e is no ob ious ups eam o downs eam ela ionship in he lake. Regional au ho i ies sha e equal powe in lake managemen , and he Lake En i onmen Commi ee has he p io i y igh o supe ise all o hem. Assump ion 2.Each sub- egion o he lake is willing o implemen he lake ecological compensa ion mechanism. Assump ion 3.The planned in e al is one yea . The concen a ion o wa e con aminan as an indica o is based on he a e age alue o he moni o ing sec ion in sub- egions. Assump ion 4.Regional au ho i ies a e esponsible o wa e pollu ion aba emen cos s and ake cos minimiza ion as he objec i e unc ion o de- cision-making. 3.1.2. Uppe -le el op imiza ion model Equi able alloca ion o WLP is conside ed o be he main goal o he Lake En i onmen Commi ee based on he Coase Theo em. As he leade decision-make , Lake En i onmen Commi ee concen a es on a ionally alloca ing he annual amoun o he sewage o sub- egion. Gini (Dal on, 1920) p oposed he Gini coe icien o measu e income inequali y, and i also has been used o measu e land inequali y and wa e alloca ion inequali y in ecen yea s. The h eshold o he Gini coe icien is 0 o 1, and he lowe he alue, he mo e equi y i is. Speci ically, he Gini coe icien can be cons uc ed o was e load alloca ion in he wa e shed sys em (Hou e al., 2021). Equi y is speci - ically exp essed as he di e ence o in was e load pe mi s pe uni o economic bene i wi hin sub- egions. This pape p oposes ha he smalle he di e ence, he mo e easonable i is. The speci ic model is exp essed in e ms o he Gini coe icien . The i s op imiza ion objec- i e can be w i en as: MinG =∑ n j=1 1 2m∑m i=1 xij EBi∑ m l=1∑ m h=1 xlj EBl −xhj EBh (3) whe e xij is he decision a iable, which means he amoun o WLP alloca ed o suba ea i o con aminan j. m is he egion ela ed o he same lake. EB i is he annual a e age o economic bene i s as an indica o o egional economic de elopmen . The cons ain s a e o mula ed as ollows. (1) Limi ed was ewa e load capaci y cons ain . The o al en i onmen al ca ying capaci y o he whole lake basin is limi ed. Tj is he o al amoun o WLP ha can be alloca ed by he Lake En i onmen Commi ee unde he condi ion o ensu ing he sus ainable de elopmen o he wa e shed. ∑ m i=1 xij⩽Tj(4) (2) Sa is ac ion o basic de elopmen cons ain . When making decisions, he uppe le el needs o conside ha he ac ual emission igh s o he egion a e g ea e han he ac ual amoun o pollu ion emi ed. The ac ual discha ge o egional wa e pollu an s should be lowe han he alloca ed amoun . ϕi p esen s he educ ion a e o con aminan . Qi ep esen s he a e age annual was ewa e low. yij is he annual concen a ion o he moni o ing sec ion con olled by he sub- egion au ho i ies unde he LEC mechanism. ∑ n i=1 h1+ϕi)xij⩾∑ n i=1 Qiyij (5) 3.1.3. Lowe -le el op imiza ion model Sub- egional au ho i ies implemen he ac ic o achie e i s op imal a e age annual concen a ion a he lowes en i onmen al cos unde he lake eco-compensa ion mechanism. Fo lake sub- egions, he To al En i onmen al Cos (TEC) con ains wo pa s, co e ing pollu ion educ ion cos and eco-compensa ion ee. MinTECi=∑ n j=1 η ijϕixij +g(yij)(6) whe e η ij is he uni educ ion cos o con aminan . g(yij)is he exp es- sion o he lake eco-compensa ion mechanism which is shown as Eq.(1). yij is he decision a iable. The ecological compensa ion alue can be posi i e o nega i e. A posi i e numbe ep esen s an inc ease in he o al en i onmen al cos o penal ies due o he high concen a ion o wa e discha ged. Nega i e alue is he opposi e. The cons ain s a e o mula ed as ollows. (1) Limi ed was ewa e load capaci y cons ain . Fo a sub- egion o he lake, ac ual annual discha ge amoun should no exceed he allowable emission pe mi s. The educ ion o con aminan s can inc ease he o al amoun o emission pollu ion. Qi ep esen s he a e age annual was ewa e low. Qiyij⩽h1+ϕi)xij (7) (2) Sa is ac ion o minimum equi emen cons ain . As pollu- ion emission and economic de elopmen a e closely ela ed in some way. The igh o pollu ion emission can be seen as he igh o economic de elopmen . In o de o ensu e he basic de elopmen o economy, he o al amoun o pollu an s has a minimum alue. Qiyij⩾Mmin ij (8) whe e Mmin ij is he basic emission equi emen o egional economic de elopmen . (3) Wa e quali y index cons ain . Pollu an concen a ion is a signi ican indica o in lake wa e en i onmen managemen . The main unc ion o he wa e quali y moni o ing sec ion o he lake is o de ec he pollu ion concen a ion. yij⩽Cmax j0(9) whe e Cmax j0 is he uppe limi o he concen a ion s anda d. 3.2. Global model In e ac i e decision-making managemen be ween Lake En i on- men Commi ee and mul iple sub- egional au ho i ies in he lake is p oposed in ou model. Hie a chical decision p ocess is conside ed as a S ackelbe g game model (Fische i e al., 2017). The objec i e unc ion o he uppe le el is o maximize he equi y o alloca ion, and he lowe le el is mainly o minimize he en i onmen al cos s. L. He e al. Ecological Indica o s 151 (2023) 110334 5 MinG =∑ n j=1 1 2m∑m i=1 xij EBi∑ m l=1∑ m h=1 xlj EBl −xhj EBh s. ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ∑ m i=1 xij⩽Tj ∑ n i=1 h1+ϕi)xij⩾∑ n i=1 Qiyij xij⩾0 MinTECi=∑ n j=1 η ijϕixij +g(yij) s. ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ g(yij) = ⎧ ⎨ ⎩ − α pi,0<pi⩽1 βpi,pi>1 Pi= μ 0∑ n j=1 kj yij Cij0 Qiyij⩽h1+ϕi)xij Qiyij⩾Mmin ij yij⩽Cmax j0 yij⩾0 μ 0>0 α ,β>0 (10) 4. Case s udy and esul s 4.1. S udy a ea Taihu Basin, spanning Jiangsu, Zhejiang and Shanghai, co e s a o al a ea o 31,800 km 2 . As a majo pa o he Yang ze Ri e Del a, he a ea wi nesses a la ge popula ion densi y, de eloped indus ial and ag icul- u al p oduc ion, as -g owing GDP and high pe capi a income. In his case, Taihu Basin includes 4 ci ies in Jiangsu P o ince (Suzhou, Wuxi, Changzhou and Zhenjiang), 3 ci ies in Zhejiang P o ince (Huzhou, Jiaxing and Hangzhou), and 3 owns in Shanghai (Lian ang, Jinze and Zhujiajiao). Fig. 2 displays he loca ion o Taihu Basin and demons a es he poo wa e quali y in he basin. Acco ding o he change in he nu ien index in he Taihu Lake Heal h S a us Repo (2012–2018), he wa e body o Taihu Lake is in a mode a ely eu ophic s a e. The e o e, e ec i e measu es o he conse a ion o he lake wa e en i onmen a e necessa y o he sus ainable de elopmen o he lake. 4.2. Da a collec ion The da a collec ed in his case is om he O e all Plan o Comp e- hensi e Wa e En i onmen Managemen in Taihu Basin in 2013 and 2022 om he Na ional Bu eau o S a is ics in China and he Depa men o Ecology and En i onmen o he h ee a eas. Acco ding o he la es documen , he main pollu ion indica o s o he basin a e COD and NH 3 - N. Basic da a o Taihu Basin in 2020 a e shown in Table 2. As shown in he able, Jiangsu has he la ges a ea in he basin while Shanghai has he smalles . I can be seen om Table 2 ha Jiangsu P o ince in Taihu Basin has he wides a ea and he la ges amoun o sewage. Only a small pa o Shanghai is loca ed in he Taihu Basin, so he index alue is he smalles acco dingly. As i s pollu ion load in o he lake is ela i ely la ge, Jiangsu is conside ed as a key a ea o he p e en ion and con ol o pollu ion loads. Fo mo e de ailed da a, o calcula e he op imal model, he ini ial assignmen based on his o ical da a is summa ized in Table 3. In e ms o loca ion, Jiangsu and Zhejiang ha e mo e es ua ies ela ed o he lake, while Shanghai is close o he lowe each o Taihu. The e o e, Shanghai poses a ela i ely smalle impac on he lake. In he calcula ion alue o he P i , 15 mg/L was used as he basic limi o COD and 0.5 mg/L o NH 3 -N. 4.3. Op imal esul s A e assigning he pa ame e alues, he so wa e is u ilized o calcula e he op imiza ion model in his sec ion. In addi ion, he cha - ac e is ics o egional decision-making beha io in di e en scena ios a e also discussed. Fu he mo e, i p o ides da a suppo o he p o- ec ion and sus ainable de elopmen o he lake ecological en i onmen . Acco ding o he abo e model cons uc ion, his is a linea bi-le el op imiza ion p oblem ega ded as NP-ha d. Bi-le el p og amming is mo i a ed by S ackelbe g o sol e he unbalanced economic ma ke p oblems (Colson e al. 2005). Gene ally, Ka ush-Kuhn-Tucke (KKT) (Lu e al., 2006; Shi e al., 2005; Sinha and Sinha, 2002) ans o ma ion app oach has been applied o mul i-le el decen alized op imiza ion model. This pape ega ds P i >1 as he base scena io. Th ee egions a e chosen as he paye s o ecological compensa ion o economic de el- opmen . En i onmen Commi ee o Taihu Lake as he leade pu sues he equi able alloca ion o WLP, and ini ial esul s a e shown in Fig. 3. The alue o he uppe objec i e unc ion is 0.58. Zhejiang has been alloca ed he la ges amoun , Jiangsu he second and Shanghai he leas . Al hough Jiangsu has a la ge a ea han Zhejiang, he decision make gi es Zhejiang mo e WLP. Fo he eason, economic de elopmen is one ac o , and on he o he hand, Zhejiang is willing o pay mo e compensa ion. The annual a e age pollu an concen a ion o moni- o ing poin s is used as he main indica o o ewa d and punishmen , and is supe ised by he uppe le el. The new COD alloca ion scheme has educed he o al amoun o emissions by 17% compa ed o he 2020 da a, and he o al amoun o NH 3 -N has dec eased by 16%. The ed moni o ing poin s in Fig. 3 a e no ac ual moni o ing poin s, bu only ep esen he phenomenon o wa e quali y de ec ion, which is no mal in eali y. The e a e many ac ual moni o ing poin s o na ional and p o incial le els. Wi h hese wa e quali y da a, manage s can p e en excessi e wa e pollu ion, and local go e nmen can adjus policy di ec i es h ough he concen a ion da a. The ini ial calcula ion esul s o lowe le el a e shown in Table 4, which con ain he annual a e age concen a ion o pollu an s, o al en i onmen al cos s and ecological compensa ion alues. The eco- compensa ion alues a e all posi i e, meaning ha all h ee egions ha e op ed o pay pollu ion ines. Zhejiang has he la ges ecological compensa ion alue. I is demons a ed ha in his case, in o de o de elop he economy, Zhejiang would like o pay o wa e pollu ion. 5. Discussion 5.1. Scena io analysis Unde he ecological compensa ion mechanism, each egion has wo L. He e al. Ecological Indica o s 151 (2023) 110334 6 op ions: ei he be penalized o a la ge amoun o pollu an discha ge o be ewa ded o educing emissions. As he di e en choices o sub- egions will a ec he alloca ion made by uppe -le el decision-make s. The Taihu Basin is di ided in o h ee egions, esul ing in a o al o eigh scena ios. Fig. 4 p esen s a scena io analysis, which mainly e lec s he egional go e nmen s’ p io i ies ega ding en i onmen al p o ec ion. P i ep esen s he willingness o local go e nmen o pa icipa e in en i onmen al p o ec ion. P i >1 means ha he egion chooses o pay he compensa ion alue, he eby expanding he amoun o sewage. 0 < P i ≤1 means o be ewa ded wi h ecological compensa ion o con- olling pollu an discha ge. P1 ep esen s Jiangsu, P2 p esen s Zhejiang and P3 p esen s Shanghai. As can be seen in Fig. 4, h ee egions choose o be punished in scena io 1. Jiangsu chooses o be ewa ded and Zhe- jiang and Shanghai choose o be punished in scena io 2. Zhejiang chooses o be ewa ded and Jiangsu and Shanghai choose o be punished in scena io 3. Shanghai chooses o be ewa ded and Jiangsu and Zhe- jiang choose o be punished in scena io 4. Shanghai chooses o be punished and Jiangsu and Zhejiang chooses o be ewa ded in scena io 5. Zhejiang choose o be punished and Jiangsu and Shanghai chooses o be ewa ded in scena io 6. Jiangsu chooses o be punished and Zhejiang and Shanghai chooses o be ewa ded in scena io 7. Th ee egions choose o be ewa ded in scena io 8. As can be seen in Fig. 4, when a egion chooses o ecei e ecological compensa ion incen i es, he annual a e age concen a ion o pollu - an s will dec ease. The main objec i e o he lowe le el is o minimize he en i onmen al cos s ha a e a ec ed by he go e nance cos and ecological compensa ion alue. The index ha a ec s LEC alue is he concen a ion o pollu an s. Regional go e nmen s can con ol he o al en i onmen al cos s h ough he annual concen a ion o pollu an s. As shown in Fig. 3, he e a e many wa e quali y moni o ing poin s, and his pape uses he annual a e age concen a ion o wa e quali y moni o ing poin s o ep esen he alue. Acco ding o Eq. (1), di e en concen a ion alues will a ec he ecological compensa ion alue. The Table 2 Basic da a o Taihu Basin in 2020. Sub egion A eas loca ed a he basin A ea da a GDP (10 9 yuan) Main wa e quali y indica o s ( ) Basin a ea (km 2 ) P opo ion COD NH 3 -N Jiangsu 4 ci ies 16,854 53.0% 4366 327,690 22,000 Zhejiang 3 ci ies 10,621 33.4% 2482 156,897 11,894 Shanghai 3 owns 4325 13.6% 277 5257 538 Taihu Basin — 31,800 100% 7125 489,844 34,432 Fig. 2. Loca ion map and wa e quali y si ua ion o Taihu Basin. L. He e al. Ecological Indica o s 151 (2023) 110334 7 op imal concen a ion is in scena io 8, whe e each egion chooses o con ol wa e pollu ion discha ge, and hus ecei es a ewa d. As can be seen in Fig. 4, he willingness o local go e nmen s o pa icipa e in wa e ecological en i onmen p o ec ion will di ec ly a ec he local wa e quali y concen a ion. When local go e nmen s a e willing o make e o s o p o ec wa e quali y, he concen a ion o pollu an s will be lowe . Economic incen i e policies ha e a ce ain deg ee o in luence on ecological and en i onmen al p o ec ion, bu he a i ude o local go e nmen s is also e y impo an . On he one hand, local go e nmen s should ollow he cen al en i onmen al policy. On he o he hand, i should adjus he en i onmen al p o ec ion s a egy acco ding o local eali ies. 5.2. LEC sensi i i y analysis How do changes o he ewa d and punishmen se ings o he LEC mechanism impac he concen a ions o pollu an s? The es ablishmen and implemen a ion o a c edible scien i ic LEC mechanism has become an e ec i e go e nance measu e o coo dina e he ela ionship be ween p o i and loss wi hin a i e basin, and also an impo an gua an ee o p omo e equi able de elopmen among egions. This pa discusses he sensi i i y o LEC in eigh scena ios om 1 o 8. Posi i e numbe s o eo- compensa ion mean being punished, and nega i e numbe s mean being ewa ded. En i onmen al policy is an impo an measu e o p omo e he sus- ainable and coo dina ed de elopmen o bo h he economy and he en i onmen . The en i onmen al policy could be di ided in o h ee ypes: command-con ol en i onmen al policy, ma ke -based en i on- men al policy and public pa icipa ion en i onmen al policy. En i on- men al policy is mainly h ough he design o en i onmen al mechanisms o educe pollu ion emissions. Ma ke -based en i onmen al policy is ega ded as an incen i e-based egula ion app oach which e- lies on ma ke incen i es o educe pollu ion and minimize pollu ion con ol cos s. Acco ding o Fig. 5, when he punishmen is inc eased, he concen- a ion will dec ease. The maximum punishmen o LEC can each 180.90 million yuan and he maximum ewa d can each 89.4 million yuan. High paymen cos s d i e egions o con ol he concen a ion o pollu an s. Fo Jiangsu, he LEC alues o scena ios 2, 5, 6, and 8 a e posi i e, which means ha Jiangsu chose o pay he penal y ee. In scena ios 1, 3, 4, and 7, Jiangsu chose o be ewa ded. Zhejiang is punished in scena ios 1, 2, 4, and 6, and ewa ded in scena ios 3, 5, 7, and 8. Shanghai chose o be punished in scena ios 1, 2, 3, and 5, and ewa ded in scena ios 4, 6, 7, and 8. Di e en egions ha e di e en sensi i i ies o en i onmen al policies. Jiangsu is he mos sensi i e one o policies, indica ing ha i s egional de elopmen is closely ela ed o policies. Shanghai is less a ec ed by policies due o i s smalle a ea. Table 3 Ini ial assignmen o main pa ame e s o model calcula ion. Sub egion Quan i y o was ewa e (Qi, 10 6 m 3 ) Reduc ion a e (ϕi,%) Demand limi (Mij, ) Adjus men coe icien ( μ 0) Concen a ion uppe limi (Cmax j0, mg/L) Compensa ion coe icien (yuan) COD NH 3 -N COD NH 3 -N α β Jiangsu 3120 85 158,978 16,800 0.75 30 1.5 10 6 10 7 Zhejiang 1575 80 139,259 8490 0.8 30 1.5 10 6 10 7 Shanghai 840 70 5157 416 0.85 30 1.5 10 6 10 7 Fig. 3. The calcula ion esul s o uppe le el a ini ial pa ame e alue. Table 4 The ini ial esul s o lowe decision a iables and objec i e unc ion. Sub egion Decision a iables o he lowe le el (mg/L) Objec i e unc ion alue o he lowe le el (TECi,10 8 yuan) Lake ecological compensa ion alue (g (y), 10 8 yuan) Yi1 Yi2 Jiangsu 12.82 0.85 2.3 3.4 Zhejiang 16.93 0.95 2.8 4.2 Shanghai 9.52 0.74 1.4 2.7 L. He e al. Ecological Indica o s 151 (2023) 110334 8 Fig. 4. Op imal concen a ion o COD and NH 3 -N unde eigh scena ios. L. He e al. Ecological Indica o s 151 (2023) 110334 9 F om he esul s o he en i onmen al Gini coe icien in Fig. 5, i can be ound ha local beha io will a ec he decision o uppe -le el decision- make s. When all h ee egions choose o p o ec he en i onmen , he Gini coe icien is a i s lowes a 0.46, indica ing ha he uppe -le el decision-make s a e making he mos equi able alloca ion. 5.3. Policy ecommenda ions Th ee policies o wa e quali y managemen in he Taihu Basin a e p oposed om he pe spec i es o s akeholde s, incen i e mechanism, and ex ensibili y, based on he compu a ional esul s and analysis p e- sen ed abo e. 5.3.1. In e ac i e hie a chical ins i u ional s uc u e is equi ed F om he pe spec i e o pa icipa ing s akeholde s, he in e ac i e communica ion be ween di e en le els is o g ea help o wa e en i onmen managemen wi hin he basin. Collabo a i e go e nance o ansbounda y wa e sheds e e s o he o ma ion o a join go e - nance mechanism o ansbounda y en i onmen al pollu ion manage- men in acco dance wi h he idea o di ision o labo , cos sha ing, and bene i sha ing. I highligh s he join p o ec ion o he ecological en i onmen in Taihu Basin. The go e nance o Taihu Basin equi es no only he managemen commi ee om he uppe le el, bu also he ac i e pa icipa ion o local go e nmen s om he lowe le el. The uppe -le el go e nmen needs o decide he e ec i e alloca ion o WLP acco ding o he o e all si ua ion o he wa e shed and local beha io s. Meanwhile, Fig. 5 illus a es ha local go e nmen s need o adjus hei de elopmen s a egies acco ding o he uppe policies. As shown in Fig. 1, he coupling managemen be ween mul iple subjec s makes he go e nance o he en i e wa e shed e en mo e e ec i e. 5.3.2. LEC mechanism is an e ec i e economic incen i e policy F om he pe spec i e o incen i e mechanism, eco-compensa ion o lake can e ec i ely mo i a e egional au ho i ies o con ol pollu ion emissions, and i he punishmen is inc eased, he e ec will be mo e ob ious as demons a ed in Fig. 4 and Fig. 5. LEC is an economic incen i e means o e ec i ely balance he ela ionship be ween wa e shed economic de elopmen and wa e quali y p o ec ion. The es ablishmen and implemen a ion o a scien i ic and easonable ecological compensa ion mechanism has become an e ec i e go e - nance measu e o coo dina e he ela ionship be ween p o i and loss wi hin lake basins. Based on he abo e analysis, a sound basin LEC mechanism should co e he ollowing basic con en s: basin manage- men mechanism, compensa ion s anda ds, compensa ion mode, and compensa ion subjec and objec . These in e ela ed con en s wo k oge he o o m he amewo k o LEC mechanism wi h an aim o achie e he goals o ecological g een de elopmen , coo dina ed eco- nomic g ow h, and common social p og ess in he lake basin. 5.3.3. Spillo e e ec o lake en i onmen al conse a ion policy dese es a en ion F om he pe spec i e o ex ensibili y, he spillo e e ec o lake wa e en i onmen al policy dese es a en ion (B¨ o ne e al., 2017). The spillo e e ec o lake en i onmen al policy means ha when he go - e nmen implemen s an en i onmen managemen policy o he lake, i will no only p omp he adjus men o he emission o he o al pollu ion as expec ed, bu also has an impac on local indus ial ins i u ions (Feng e al., 2021). The adjus men o pollu an amoun s o ces he ans- o ma ion o indus ial s uc u e. Taihu Basin, loca ed in he Yang ze Ri e Del a as shown in Fig. 2, is one o he egions wi h he mos ac i e economic de elopmen , he highes deg ee o openness and he s on- ges inno a ion capabili y in China. The go e nance o Taihu Basin wa e en i onmen will ine i ably p omo e he change o indus ial s uc u e in he Yang ze Ri e Del a. Al hough his pape does no analyze he beha io s o en e p ises, he managemen o he lake en i- onmen canno be sepa a ed om he pa icipa ion o local en e p ises. The upg ada ion o indus ial s uc u e is su ely conduci e o i s en i onmen - iendly de elopmen . 6. Conclusion and u u e wo ks An analy ical amewo k is e ined o localize he PES o add ess he con lic be ween economy and he conse a ion o he lake wa e en i onmen . Acco ding o Coase Theo em, a bi-le el op imal model is Fig. 5. The alue o LEC and Gini coe icien unde di e en scena ios. L. He e al.