Multi-watershed nonpoint source pollution management through coupling Bayesian-based simulation and mechanism-based effluent trading optimization

Abstract

Multiple rivers flowing into the same bay can be correlated in water quality management and together determine the environmental status of the bay. Nonpoint source pollution management for multi-watershed aiming to alleviate environmental contamination as well as yield considerable economic and environmental benefits can be under additional challenges. In this study, a Bayesian simulation-based multi-watershed effluent trading designing model (BS-METM) is established for multi-watershed nonpoint source pollution management through incorporating techniques of water quality simulation, uncertainty analysis with Bayesian inference, optimal design for effluent trading, as well as mechanism analysis. BS-METM is capable of reflecting parameter uncertainties in nutrient simulation, disclosing the detailed optimal trading schemes under the impact of uncertainties and vital factors, and identifying optimal effluent trading mechanisms through revealing interaction among trading processes of multiple watersheds. BS-METM is applied to a real case of adjacent coastal watersheds (i.e. Daguhe and Moshuihe watersheds), which are identified as major sources of total phosphorus and ammonia nitrogen loadings to Jiaozhou Bay, China. Effluent trading optimization under multiple mechanisms, including intra-watershed trading, cross-watershed trading and non-trading, are conducted. The optimized industry scales and trading processes are obtained. The effects of vital factors on the trading process (i.e. environmental allowance-violation risk level and water availability level) are investigated. The interactions between water availability level and trading mechanism are also analyzed. It is proved that non-trading mechanism would be recommended under low water availability level and cross-watershed trading mechanism would be recommended under medium and high water availability level. The results provide a solid scientific basis for nonpoint source pollution management as well as effective sustainable development for multi-watershed region.

Graphical abstract

Appendices

Appendix A

The assessment of SWAT model parameters contains uncertainties originating from errors and spatiotemporal heterogeneity, which may encounter difficulties in accurately depicting nutrient fate with an unrealistic estimation of parameter uncertainty. MCMC will provide a valid way that would account for parameter uncertainty in a Bayesian inference. The Bayesian theorem can be showed as follows (Zhang et al. 2019a, b):

$$ f_{post} (\theta \left| {y_{obs} )} \right. = \frac{{f_{pri} (\theta ) \cdot f_{M} (y_{obs} \left| {\theta )} \right.}}{{\int {f_{pri} (\theta ) \cdot f_{M} (y_{obs} \left| {\theta )d\theta } \right.} }} $$

(A1)

where $f_{post} (\theta \left| {y_{obs} } \right.)$ represents the posterior distribution of parameter set $\theta$ that is dated from the prior distribution $f_{pri} (\theta )$ conditioned on observed data $y_{obs}$; $f_{M} (y_{obs} \left| \theta \right.)$ is the likelihood function. In the study, the simulation errors are assumed to be independent and identically normally distributed, which determines the construction of the likelihood function and is the basis of the entire Bayesian calibration process. The likelihood function is (Raje and Krishnan 2012):

$$ f_{M} (y_{obs} \left| \theta \right._{M} ) = \prod\limits_{t} {\frac{1}{{\sqrt {2\Pi } \sigma_{e} }}{\kern 1pt} } \exp \left[ { - \frac{{(y_{t} - y_{obs,t} )^{2} }}{{2\sigma_{e}^{2} }}} \right] $$

(A2)

where $y_{t}$ is the simulated nutrient loading with SWAT at time step $t$; $y_{obs,t}$ is the observed data at time step $t$; $\sigma_{e}^{2}$ is the variance of the simulation errors.

Phosphorous (P) and Nitrogen (N) are transported by attaching to eroded soil or being dissolved in surface runoff, which is simulated based on spatial information on climate, topography, soil properties, land use and management practices. The process simulation of nitrogen (N) in soil can be divided into two main parts, including nitrate transport and organic nitrogen N loss. Nitrate is transported by dissolving in surface runoff, lateral flow, or percolation. The nitrate concentration in mobile water can be calculated by the following equation:

$$ w_{{3{\kern 1pt} surf}} = Q_{surf} + Q_{lat,ly} + w_{perc,ly} $$

(A9)

$$ NO_{{3{\kern 1pt} surf}} = \frac{{\beta_{{NO_{3} }} Q_{surf} NO_{{3{\kern 1pt}_{ly} }} \left\{ {1 - \exp \left[ {{{ - w_{mobile} } \mathord{\left/ {\vphantom {{ - w_{mobile} } {\left( {1 - \theta_{e} } \right)SAT_{ly} }}} \right. \kern-\nulldelimiterspace} {\left( {1 - \theta_{e} } \right)SAT_{ly} }}} \right]} \right\}}}{{w_{mobile} }} $$

(A10)

where $NO_{{3{\kern 1pt} surf}}$ is the nitrate removed in surface runoff (kg/ha); $\beta_{{NO_{3} }}$ represents the nitrate percolation coefficient; $NO_{{3{\kern 1pt}_{ly} }}$ is the amount of nitrate in the soil layer (kg/ha); $w_{mobile}$ represents the amount of mobile water in the layer (mm H₂O); $\theta_{e}$ is the fraction of porosity from which anions are excluded; $SAT_{ly}$ is the water content of the soil layer; $Q_{lat,ly}$ represents the water discharged from the layer by lat-eral flow (mm H₂O); and $w_{perc,ly}$ denotes the amount of water percolating to the underlying soil layer (mm H₂O). The organic N runoff loss based on the organic N concentration in the top soil layer and the sediment yield can be calculated by using the following equation:

$$ orgN_{surf} = \frac{{0.001conc_{orgN} \varepsilon_{sedN} sed}}{{area_{hru} }} $$

(A11)

where $orgN_{surf}$ is the amount of organic N transported to the chief channel in surface runoff (kg/ha); $conc_{orgN}$ denotes the organic N concentration in the top 10 mm (g/kg); $area_{hru}$ is the HRU area (ha); and $\varepsilon_{sedN}$ represents the N enrichment ratio. SWAT simulates the dynamics of three forms of phosphorous (P), including organic P which exists in humus, insoluble mineral P and soluble P. The amount of organic P transported with sediment to the stream is simulated with a loading function as depicted in organic N as follows:

$$ orgP_{surf} = {{0.001conc_{orgP} \varepsilon_{sedP} sed} \mathord{\left/ {\vphantom {{0.001conc_{orgP} \varepsilon_{sedP} sed} {area_{hru} }}} \right. \kern-\nulldelimiterspace} {area_{hru} }} $$

(A12)

where $orgP_{surf}$ is the amount of organic P transported to the main channel in surface runoff (kg/ha); $conc_{orgP}$ denotes the organic P concentration in the top 10 mm (g/kg); and $\varepsilon_{sedP}$ represents the P enrichment ratio. Because of the low mobility of soluble P, SWAT only considers the loss of the soluble P with surface runoff based on labile P concentration in the top soil layer. The migration of soluble P in surface runoff is:

$$ P_{surf} = \frac{{10P_{soluble,surf} Q_{surf} }}{{\rho_{b} k_{d,surf} }} $$

(A13)

where $P_{surf}$ represents the amount of soluble P lost in surface runoff (kg/ha); $P_{soluble,surf}$ is the amount of soluble P in the top 10 mm (kg/ha); $\rho_{b}$ denotes the bulk density of the top 10 mm (Mg/m³); and $k_{d,surf}$ the P soil partitioning coefficient (m³ /Mg).

Appendix B

1. Intra-watershed trading case:

$$ \begin{gathered} M{\text{a}}xf = \sum\limits_{i = 1}^{5} {\sum\limits_{j = 1}^{11} {\sum\limits_{w = 1}^{3} {AB_{{_{j} }}^{ \pm } \cdot (X_{ij}^{ - } + \Delta X_{ij} \cdot o_{ijw} )} } } + \sum\limits_{n = 1}^{3} {\sum\limits_{r = 1}^{4} {\sum\limits_{w = 1}^{3} {W_{{_{r} }}^{ \pm } \cdot (N_{nr}^{ - } { + }\Delta N_{nr} \cdot r_{nrw} )} } } \hfill \\ { + }\sum\limits_{p = 1}^{3} {\sum\limits_{w = 1}^{3} {SB_{{_{p} }}^{ \pm } \cdot (Z_{p}^{ - } + \Delta Z_{p} \cdot s_{pw} )} } { + }\sum\limits_{m = 1}^{7} {\sum\limits_{w = 1}^{3} {CB_{{_{m} }}^{ \pm } \cdot (Y_{m}^{ - } + \Delta Y_{m} \cdot e_{mw} )} } \hfill \\ \, - \sum\limits_{i = 1}^{5} {\sum\limits_{k = 1}^{3} {\sum\limits_{w = 1}^{3} {h_{k} \cdot EDPA_{{_{ikw} }}^{ \pm } \cdot PF^{ \pm } } } } - {\kern 1pt} {\kern 1pt} \sum\limits_{n = 1}^{3} {\sum\limits_{w = 1}^{3} {EDPR_{{_{nw} }}^{ \pm } \cdot PF^{ \pm } } } \hfill \\ \, - {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \sum\limits_{p = 1}^{3} {\sum\limits_{w = 1}^{3} {EDPP_{pw}^{ \pm } \cdot PF^{ \pm } } } - {\kern 1pt} \sum\limits_{m = 1}^{7} {\sum\limits_{w = 1}^{3} {EDPC_{{_{mw} }}^{ \pm } \cdot PF^{ \pm } } } {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \hfill \\ \, - \sum\limits_{i = 1}^{5} {\sum\limits_{s = 1}^{3} {\sum\limits_{w = 1}^{3} {k_{s} \cdot EDNA_{{_{isw} }}^{ \pm } \cdot NF^{ \pm } } } } - {\kern 1pt} {\kern 1pt} \sum\limits_{n = 1}^{3} {\sum\limits_{w = 1}^{3} {EDNR_{{_{nw} }}^{ \pm } \cdot NF^{ \pm } } } \hfill \\ \, - {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \sum\limits_{p = 1}^{3} {\sum\limits_{w = 1}^{3} {EDNP_{pw}^{ \pm } \cdot NF^{ \pm } } } - {\kern 1pt} \sum\limits_{m = 1}^{7} {\sum\limits_{w = 1}^{3} {EDNC_{{_{mw} }}^{ \pm } \cdot NF^{ \pm } } } {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \hfill \\ \end{gathered} $$

(B1)

The objective is to maximize the ultimate net system benefit, which is calculated with the total environmental penalty and the total initial net system benefit which removes the cost. The ultimate system net benefit considers the total initial system net benefits and the environmental penalties of agriculture, livestock and poultry industry, fishery and company. The constraints to be complied with can be divided into the following groups:

(a) Constraints for TP permit reallocation

$$ \sum\limits_{j = 1}^{11} {(X_{ij}^{ - } + \Delta X_{ij} \cdot o_{ijw} ) \cdot CWPA_{k}^{ \pm } } - EDPA_{ikw}^{ \pm } \le ACEP_{iw} $$

(B2)

$$ \sum\limits_{r = 1}^{4} {(N_{nr}^{ - } + \Delta N_{nr} \cdot r_{nrw} ) \cdot CWPR_{r}^{ \pm } - EDPR_{nw}^{ \pm } } \le LCEP_{nw} $$

(B3)

$$ (Z_{p}^{ - } + \Delta Z_{p} \cdot s_{pw} ) \cdot DWP^{ \pm } \cdot CWPP^{ \pm } - EDPP_{pw}^{ \pm } \le SCEP_{pw} {\kern 1pt} $$

(B4)

$$ (Y_{m}^{ - } + \Delta Y_{m} \cdot e_{mw} ) \cdot DWM_{m}^{ \pm } \cdot CWPM_{m}^{ \pm } - EDPC_{mw}^{ \pm } \le CCEP_{mw} $$

(B5)

(b) Constraints for NH₃-N permit reallocation

$$ \sum\limits_{j = 1}^{11} {(X_{ij}^{ - } + \Delta X_{ij} \cdot o_{ijw} ) \cdot CWNA_{s}^{ \pm } } - EDNA_{isw}^{ \pm } \le ACEN_{iw} $$

(B6)

$$ \sum\limits_{r = 1}^{4} {(N_{nr}^{ - } + \Delta N_{nr} \cdot r_{nrw} ) \cdot CWNR_{r}^{ \pm } } - EDNR_{nw}^{ \pm } \le LCEN_{nw} {\kern 1pt} $$

(B7)

$$ (Z_{p}^{ - } + \Delta Z_{p} \cdot s_{pw} ) \cdot DWP^{ \pm } \cdot CWNP^{ \pm } - EDNP_{pw}^{ \pm } \le SCEN_{pw} $$

(B8)

$$ (Y_{m}^{ - } + \Delta Y_{m} \cdot e_{mw} ) \cdot DWM_{m}^{ \pm } \cdot CWNM_{m}^{ \pm } - EDNC_{mw}^{ \pm } \le CCEN_{mw} $$

(B9)

Constraints (B2)–(B5) and (B6)–(B9) represent the trading process of TP and NH₃-N discharge permits for 18 pollution sources, respectively. Through the trading, the reallocation of discharge permits can be optimized to obtain the maximum net benefits and minimum environmental penalties. In addition, the reallocated TP and NH₃-N discharge permits for each pollution source in Daguhe watershed and Moshuihe watershed respectively are equal to that the initial discharge permits plus the purchasing permits, and minus the selling permits.

(c) Constraints for TP trading rules

$$ \begin{gathered} \sum\limits_{i^{\prime} = 1}^{4} {TP_{ii^{\prime}w} } + \sum\limits_{n = 1}^{3} {TPs_{inw} } + \sum\limits_{p = 1}^{3} {TPs_{ipw} } \hfill \\ \le TPI_{iw} + \sum\limits_{i^{\prime} = 1}^{4} {TP_{i^{\prime}iw} /tp_{i^{\prime}i} } + \sum\limits_{n = 1}^{3} {TPb_{niw} /tp_{ni} } + \sum\limits_{p = 1}^{3} {TPb_{piw} /tp_{pi} } {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} i \ne 5 \hfill \\ \end{gathered} $$

(B10)

$$ \begin{gathered} \sum\limits_{n^{\prime} = 1}^{3} {TP_{nn^{\prime}w} } + \sum\limits_{i = 1}^{4} {TPs_{niw} } + \sum\limits_{p = 1}^{3} {TPs_{npw} } \hfill \\ \le TPN_{nw} + \sum\limits_{n^{\prime} = 1}^{3} {TP_{n^{\prime}nw} /tp_{n^{\prime}n} } + \sum\limits_{i = 1}^{4} {TPb_{inw} /tp_{in} } + \sum\limits_{p = 1}^{3} {TPb_{pnw} /tp_{pn} } \hfill \\ \end{gathered} $$

(B11)

$$ \begin{gathered} \sum\limits_{p^{\prime} = 1}^{3} {TP_{pp^{\prime}w} } + \sum\limits_{i = 1}^{4} {TPs_{piw} } + \sum\limits_{n = 1}^{3} {TPs_{pnw} } \hfill \\ \le TPP_{pw} + \sum\limits_{p^{\prime} = 1}^{3} {TP_{p^{\prime}pw} /tp_{p^{\prime}p} } + \sum\limits_{{{\text{n}} = 1}}^{3} {TPb_{npw} /tp_{np} } + \sum\limits_{i = 1}^{4} {TPb_{ipw} /tp_{ip} } \hfill \\ \end{gathered} $$

(B12)

$$ \sum\limits_{m = 1}^{7} {TPs_{imw} } \le TPI_{iw} + \sum\limits_{m = 1}^{7} {TPb_{miw} /tp_{mi} } {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} i = 5 $$

(B13)

$$ \sum\limits_{m^{\prime} = 1}^{7} {TP_{mm^{\prime}w} } + TPs_{miw} \le TPM_{mw} + \sum\limits_{m^{\prime} = 1}^{7} {TP_{m^{\prime}mw} /tp_{m^{\prime}m} } + TPb_{imw} /tp_{im} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} i = 5 $$

(B14)

(d) Constraints for NH₃-N trading rules

$$ \begin{gathered} \sum\limits_{i^{\prime} = 1}^{4} {TN_{ii^{\prime}w} } + \sum\limits_{n = 1}^{3} {TNs_{inw} } + \sum\limits_{p = 1}^{3} {TNs_{ipw} } { + } \hfill \\ \le TNI_{iw} + \sum\limits_{i^{\prime} = 1}^{4} {TN_{i^{\prime}iw} /t{\text{n}}_{i^{\prime}i} } + \sum\limits_{n = 1}^{3} {TNb_{niw} /tn_{ni} } + \sum\limits_{p = 1}^{3} {TNb_{piw} /tn_{pi} } {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} i \ne 5 \hfill \\ \end{gathered} $$

(B15)

$$ \begin{gathered} \sum\limits_{n^{\prime} = 1}^{3} {TN_{nn^{\prime}w} } + \sum\limits_{i = 1}^{4} {TNs_{niw} } + \sum\limits_{p = 1}^{3} {TNs_{npw} } \hfill \\ \le TNN_{nw} + \sum\limits_{n^{\prime} = 1}^{3} {TN_{n^{\prime}nw} /t{\text{n}}_{n^{\prime}n} } + \sum\limits_{i = 1}^{4} {TNb_{inw} /tn_{in} } + \sum\limits_{p = 1}^{3} {TNb_{pnw} /tn_{pn} } \hfill \\ \end{gathered} $$

(B16)

$$ \begin{gathered} \sum\limits_{p^{\prime} = 1}^{3} {TN_{pp^{\prime}w} } + \sum\limits_{i = 1}^{4} {TNs_{piw} } + \sum\limits_{n = 1}^{3} {TNs_{pnw} } \hfill \\ \le TNP_{pw} + \sum\limits_{p^{\prime} = 1}^{3} {TN_{p^{\prime}pw} /t{\text{n}}_{p^{\prime}p} } + \sum\limits_{n = 1}^{3} {TNb_{npw} /tn_{np} } + \sum\limits_{i = 1}^{4} {TNb_{ipw} /tn_{ip} } \hfill \\ \end{gathered} $$

(B17)

$$ \sum\limits_{m = 1}^{7} {TNs_{imw} } \le TNI_{iw} + \sum\limits_{m = 1}^{7} {TNb_{miw} /tn_{mi} } {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} i = 5 $$

(B18)

$$ \sum\limits_{m^{\prime} = 1}^{7} {TN_{mm^{\prime}w} } + TNs_{miw} \le TNM_{mw} + \sum\limits_{m^{\prime} = 1}^{7} {TN_{m^{\prime}mw} /tn_{m^{\prime}m} } + TNb_{imw} /tn_{im} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} i = 5 $$

(B19)

Constraints (B10)–(B14) and (B15)–(B19) can contribute to the trading of TP and NH3-N discharge permits for pollution sources in Daguhe watershed and Moshuihe watershed, respectively. And following the trading rules that the discharge permits sold by the pollution sources should be larger than the sum of the discharge permits they purchase and possess.

(e) Constraints for TP environmental limit.

$$ACEP_{iw} \le TPA_{iw},\,LCEP_{nw} \le TPL_{nw}$$

(B20)

$$SCEP_{pw} \le TPS_{pw},\,CCEP_{mw} \le TPC_{mw}$$

(B21)

$$ ACEP_{iw} + LCEP_{nw} + SCEP_{pw} \le TPGF_{qw} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \forall i = n = p,{\kern 1pt} {\kern 1pt} i = 1,2,3,{\kern 1pt} {\kern 1pt} q \ne 4 $$

(B22)

$$ ACEP_{iw} \le TPGF_{qw} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} i = 4,{\kern 1pt} {\kern 1pt} q = 4 $$

(B23)

$$ ACEP_{5w} + CCEP_{3w} + CCEP_{4w} + CCEP_{5w} + CCEP_{6w} \le TPWF_{1w} $$

(B24)

$$ CCEP_{1w} + CCEP_{2w} + CCEP_{7w} \le TPWF_{2w} $$

(B25)

$$ \sum\limits_{i = 1}^{4} {ACEP_{iw} } + \sum\limits_{n = 1}^{3} {LCEP_{nw} + \sum\limits_{p = 1}^{3} {SCEP_{pw} } } \le TPG_{w}^{{1 - p_{h} }} $$

(B26)

$$ ACEP_{iw} + \sum\limits_{m = 1}^{7} {CCEP_{mw} } \le TPW_{w} \, i = 5 $$

(B27)

(f) Constraints for NH₃-N environmental limit.

$$ ACEN_{iw} \le TNA_{iw},\, LCEN_{nw} \le TNL_{nw}$$

(B28)

$$SCEN_{pw} \le TNS_{pw},\,CCEN_{mw} \le TNC_{mw}$$

(B29)

$$ ACEN_{iw} + LCEN_{nw} + SCEN_{pw} \le TNGF_{qw} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \forall i = n = p,{\kern 1pt} {\kern 1pt} i = 1,2,3,{\kern 1pt} {\kern 1pt} q \ne 4 $$

(B30)

$$ ACEN_{iw} \le TNGF_{qw} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} i = 4,{\kern 1pt} {\kern 1pt} q = 4 $$

(B31)

$$ ACEN_{5w} + CCEN_{3w} + CCEN_{4w} + CCEN_{5w} + CCEN_{6w} \le TNWF_{1w} $$

(B32)

$$ CCEN_{1w} + CCEN_{2w} + CCEN_{7w} \le TNWF_{2w} $$

(B33)

$$ \sum\limits_{i = 1}^{4} {ACEN_{iw} } + \sum\limits_{n = 1}^{3} {LCEN_{nw} + \sum\limits_{p = 1}^{3} {SCEN_{pw} } } \le TNG_{w}^{{1 - p_{h} }} $$

(B34)

$$ ACEN_{iw} + \sum\limits_{m = 1}^{7} {CCEN_{mw} } \le TNW_{w} \, i = 5 $$

(B35)

The environmental limits for TP and NH₃-N are set for the four industries, the four reaches in Daguhe watershed, the two reaches in Moshuihe watershed, the whole Daguhe watershed and the whole Moshuihe watershed in constraints (B20)–(B27) and (B28)–(B35).

(g) Energy and protein requirements constraints

$$ \begin{gathered} \sum\limits_{i = 1}^{4} {\sum\limits_{j = 1}^{11} {AP_{{_{ij} }}^{ \pm } } \cdot (X_{ij}^{ - } + \Delta X_{ij} \cdot o_{ijw} ) \cdot PE_{j} } - \sum\limits_{n = 1}^{3} {\sum\limits_{r = 1}^{4} {LE_{r} \cdot (N_{nr}^{ - } + \Delta N_{nr} \cdot r_{nrw} )} } \hfill \\ - DP \cdot NE \ge 0{\kern 1pt} \hfill \\ \end{gathered} $$

(B36)

$$ \begin{gathered} \sum\limits_{i = 1}^{4} {\sum\limits_{j = 1}^{11} {AP_{{_{ij} }}^{ \pm } } \cdot (X_{ij}^{ - } + \Delta X_{ij} \cdot o_{ijw} ) \cdot CE_{{_{j} }}^{ \pm } } - \sum\limits_{n = 1}^{3} {\sum\limits_{r = 1}^{4} {LP_{r} \cdot (N_{nr}^{ - } + \Delta N_{nr} \cdot r_{nrw} )} } \hfill \\ - {\text{DP}} \cdot NP \ge 0 \hfill \\ \end{gathered} $$

(B37)

$$ \sum\limits_{j = 1}^{11} {AP_{{_{ij} }}^{ \pm } } \cdot (X_{ij}^{ - } + \Delta X_{ij} \cdot o_{ijw} ) \cdot PE_{j} - MP \cdot NE \ge 0 \, {\kern 1pt} i = 5 $$

(B38)

$$ \sum\limits_{j = 1}^{11} {AP_{{_{ij} }}^{ \pm } } \cdot (X_{ij}^{ - } + \Delta X_{ij} \cdot o_{ijw} ) \cdot CE_{j} - MP \cdot NP \ge 0 \, i = 5 $$

(B39)

Constraints (B36) and (B37) represent that the energy and digestible protein content from crops in Daguhe watershed should be larger than the demand of humans and livestocks, respectively. Constraints (B38) and (B39) represent that the energy and digestible protein content from crops in Moshuihe watershed should be larger than the demand of humans, respectively.

(h) Technical and non-negativity constraint

$$ 0 \le o_{ijw} \le 1,{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} 0 \le r_{nrw} \le {1,}{\kern 1pt} {\kern 1pt} {\kern 1pt} 0 \le s_{pw} \le 1,{\kern 1pt} {\kern 1pt} {\kern 1pt} 0 \le e_{mw} \le 1{\kern 1pt} {\kern 1pt} $$

(B40)

Besides, the technology and non-negative constraints comprise other decision variables in the model, including the excess TP and NH₃-N emission of each pollution source and the trading amount between two pollution sources from the same watershed. In addition, the excess TP and NH₃-N emission of each pollution source are lower than the total TP and NH₃-N emission from the pollution source, respectively; the pollution sources’ reallocated TP and NH₃-N emission permits should be higher than the minimum reallocated emission permits, which are set as 25% of the initial emission permits in this study; within the same watershed the TP and NH₃-N emission permits sold from source A to source B should be equal to the emission permits purchased from source A by source B, such as $TPb_{niw} { = }TPs_{niw}$, and the TP and NH₃-N trading amount should be lower than the initial pollutant discharge permit of the source.

2. Non-trading case:

$$ \begin{gathered} M{\text{a}}xf = \sum\limits_{i = 1}^{5} {\sum\limits_{j = 1}^{11} {\sum\limits_{w = 1}^{3} {AB_{{_{j} }}^{ \pm } \cdot (X_{ij}^{ - } + \Delta X_{ij} \cdot o_{ijw} )} } } + \sum\limits_{n = 1}^{3} {\sum\limits_{r = 1}^{4} {\sum\limits_{w = 1}^{3} {W_{r}^{ \pm } \cdot (N_{nr}^{ - } { + }\Delta N_{nr} \cdot r_{nrw} )} } } \hfill \\ { + }\sum\limits_{p = 1}^{3} {\sum\limits_{w = 1}^{3} {SB_{p}^{ \pm } \cdot (Z_{p}^{ - } + \Delta Z_{p} \cdot s_{pw} )} } { + }\sum\limits_{m = 1}^{7} {\sum\limits_{w = 1}^{3} {CB_{m}^{ \pm } \cdot (Y_{m}^{ - } + \Delta Y_{m} \cdot e_{mw} )} } \hfill \\ - \sum\limits_{i = 1}^{5} {\sum\limits_{k = 1}^{3} {\sum\limits_{w = 1}^{3} {h_{k} \cdot EDPA_{ikw}^{ \pm } \cdot PF^{ \pm } } } } - {\kern 1pt} {\kern 1pt} \sum\limits_{n = 1}^{3} {\sum\limits_{w = 1}^{3} {EDPR_{nw}^{ \pm } \cdot PF^{ \pm } } } \hfill \\ - {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \sum\limits_{p = 1}^{3} {\sum\limits_{w = 1}^{3} {EDPP_{pw}^{ \pm } \cdot PF^{ \pm } } } - {\kern 1pt} \sum\limits_{m = 1}^{7} {\sum\limits_{w = 1}^{3} {EDPC_{mw}^{ \pm } \cdot PF^{ \pm } } } {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \hfill \\ - \sum\limits_{i = 1}^{5} {\sum\limits_{s = 1}^{3} {\sum\limits_{w = 1}^{3} {k_{s} \cdot EDNA_{isw} \cdot NF^{ \pm } } } } - {\kern 1pt} {\kern 1pt} \sum\limits_{n = 1}^{3} {\sum\limits_{w = 1}^{3} {EDNR_{nt}^{ \pm } \cdot NF^{ \pm } } } \hfill \\ - {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \sum\limits_{p = 1}^{3} {\sum\limits_{w = 1}^{3} {EDNP_{pw}^{ \pm } \cdot NF^{ \pm } } } - {\kern 1pt} \sum\limits_{m = 1}^{7} {\sum\limits_{w = 1}^{3} {EDNC_{mw}^{ \pm } \cdot NF^{ \pm } } } {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \hfill \\ \end{gathered} $$

(B41)

(a) Constraints for TP environmental limit

$$ \sum\limits_{j = 1}^{11} {(X_{ij}^{ - } + \Delta X_{ij} \cdot o_{ijw} ) \cdot CWPA_{k}^{ \pm } } {\text{ - EDPA}}_{ikw}^{ \pm } \le TPI_{iw} $$

(B42)

$$ \sum\limits_{r = 1}^{4} {(N_{nr}^{ - } { + }\Delta N_{nr} \cdot r_{nrw} ) \cdot CWPR_{r}^{ \pm } } - EDPR_{nw}^{ \pm } \le TPN_{nw} $$

(B43)

$$ (Z_{p}^{ - } + \Delta Z_{p} \cdot s_{pw} ) \cdot DWP^{ \pm } \cdot CWPP^{ \pm } - EDPP_{pw}^{ \pm } \le TPP_{pw} $$

(B44)

$$ (Y_{m}^{ - } + \Delta Y_{m} \cdot e_{mw} ) \cdot DWM_{m}^{ \pm } \cdot CWPM_{m}^{ \pm } - EDPC_{mw}^{ \pm } \le TPM_{mw} $$

(B45)

$$ \begin{gathered} \sum\limits_{j = 1}^{11} {(X_{1j}^{ - } + \Delta X_{1j} \cdot o_{1jw} ) \cdot CWPA_{k}^{ \pm } } {\text{ - EDPA}}_{1kw}^{ \pm } { + }\sum\limits_{r = 1}^{4} {(N_{1r}^{ - } { + }\Delta N_{1r} \cdot r_{1rw} ) \cdot CWPR_{r}^{ \pm } } \hfill \\ - EDPR_{1w}^{ \pm } { + }(Z_{1}^{ - } + \Delta Z_{1} \cdot s_{1w} ) \cdot DWP^{ \pm } \cdot CWPP^{ \pm } - EDPP_{1w}^{ \pm } \le TPGF_{1w} \hfill \\ \end{gathered} $$

(B46)

$$ \begin{gathered} \sum\limits_{j = 1}^{11} {(X_{2j}^{ - } + \Delta X_{2j} \cdot o_{2jw} ) \cdot CWPA_{k}^{ \pm } } {\text{ - EDPA}}_{2kw}^{ \pm } { + }\sum\limits_{r = 1}^{4} {(N_{2r}^{ - } { + }\Delta N_{2r} \cdot r_{2rw} ) \cdot CWPR_{r}^{ \pm } } \hfill \\ - EDPR_{2w}^{ \pm } { + }(Z_{2}^{ - } + \Delta Z_{2} \cdot s_{2w} ) \cdot DWP^{ \pm } \cdot CWPP^{ \pm } - EDPP_{2w}^{ \pm } \le TPGF_{2w} \hfill \\ \end{gathered} $$

(B47)

$$ \begin{gathered} \sum\limits_{j = 1}^{11} {(X_{3j}^{ - } + \Delta X_{3j} \cdot o_{3jw} ) \cdot CWPA_{k}^{ \pm } } {\text{ - EDPA}}_{3kw}^{ \pm } { + }\sum\limits_{r = 1}^{4} {(N_{3r}^{ - } { + }\Delta N_{3r} \cdot r_{3r} ) \cdot CWPR_{r}^{ \pm } } \hfill \\ - EDPR_{3w}^{ \pm } { + }(Z_{3}^{ - } + \Delta Z_{3} \cdot s_{3w} ) \cdot DWP^{ \pm } \cdot CWPP^{ \pm } - EDPP_{3w}^{ \pm } \le TPGF_{3w} \hfill \\ \end{gathered} $$

(B48)

$$ \sum\limits_{j = 1}^{11} {(X_{4j}^{ - } + \Delta X_{4j} \cdot o_{4jw} ) \cdot CWPA_{k}^{ \pm } } {\text{ - EDPA}}_{4kw}^{ \pm } \le TPGF_{4w} $$

(B49)

$$ \begin{gathered} \sum\limits_{j = 1}^{11} {(X_{5j}^{ - } + \Delta X_{5j} \cdot o_{5jw} ) \cdot CWPA_{k}^{ \pm } } - EDPA_{5kw}^{ \pm } \hfill \\ { + }(Y_{3}^{ - } + \Delta Y_{3} \cdot e_{3w} ) \cdot DWM_{3}^{ \pm } \cdot CWPM_{3}^{ \pm } - EDPC_{3w}^{ \pm } \hfill \\ { + }(Y_{4}^{ - } + \Delta Y_{4} \cdot e_{4w} ) \cdot DWM_{4}^{ \pm } \cdot CWPM_{4}^{ \pm } - EDPC_{4w}^{ \pm } \hfill \\ { + }(Y_{5}^{ - } + \Delta Y_{5} \cdot e_{5w} ) \cdot DWM_{5}^{ \pm } \cdot CWPM_{5}^{ \pm } - EDPC_{5w}^{ \pm } \hfill \\ { + }(Y_{6}^{ - } + \Delta Y_{6} \cdot e_{6w} ) \cdot DWM_{6}^{ \pm } \cdot CWPM_{6}^{ \pm } - EDPC_{6w}^{ \pm } \le TPWF_{1w} \hfill \\ \end{gathered} $$

(B50)

$$ \begin{gathered} (Y_{1}^{ - } + \Delta Y_{1} \cdot e_{1w} ) \cdot DWM_{1}^{ \pm } \cdot CWPM_{1}^{ \pm } - EDPC_{1w}^{ \pm } \hfill \\ { + }(Y_{2}^{ - } + \Delta Y_{2} \cdot e_{2w} ) \cdot DWM_{2}^{ \pm } \cdot CWPM_{2}^{ \pm } - EDPC_{2w}^{ \pm } \hfill \\ { + }(Y_{7}^{ - } + \Delta Y_{7} \cdot e_{7w} ) \cdot DWM_{7}^{ \pm } \cdot CWPM_{7}^{ \pm } - EDPC_{7w}^{ \pm } \le TPWF_{2w} \hfill \\ \end{gathered} $$

(B51)

$$ \begin{gathered} \sum\limits_{i = 1}^{4} {\sum\limits_{j = 1}^{11} {(X_{ij}^{ - } + \Delta X_{ij} \cdot o_{ijw} ) \cdot CWPA_{k}^{ \pm } } } - EDPA_{ikw}^{ \pm } \hfill \\ + \sum\limits_{n = 1}^{3} {\sum\limits_{r = 1}^{4} {(N_{nr}^{ - } { + }\Delta N_{nr} \cdot r_{nrw} ) \cdot CWPR_{r}^{ \pm } } - EDPR_{nw}^{ \pm } } \hfill \\ + \sum\limits_{p = 1}^{3} {(Z_{p}^{ - } + \Delta Z_{p} \cdot s_{pw} ) \cdot DWP^{ \pm } \cdot CWPP^{ \pm } - EDPP_{pw}^{ \pm } } \le TPG_{w}^{{1 - p_{h} }} \hfill \\ \end{gathered} $$

(B52)

$$ \begin{gathered} \sum\limits_{j = 1}^{11} {(X_{ij}^{ - } + \Delta X_{ij} \cdot o_{ijw} ) \cdot CWPA_{k}^{ \pm } } - EDPA_{ikw}^{ \pm } \hfill \\ + \sum\limits_{m = 1}^{7} {(Y_{m}^{ - } + \Delta Y_{m} \cdot e_{mw} ) \cdot DWM_{m}^{ \pm } \cdot CWPM_{m}^{ \pm } - EDPC_{mw}^{ \pm } } \le TPW_{w} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} i{ = }5 \hfill \\ \end{gathered} $$

(B53)

$$ \begin{gathered} \sum\limits_{i = 1}^{5} {\sum\limits_{j = 1}^{11} {(X_{ij}^{ - } + \Delta X_{ij} \cdot o_{ijw} ) \cdot CWPA_{k}^{ \pm } } } - EDPA_{ikw}^{ \pm } \hfill \\ + \sum\limits_{n = w}^{3} {\sum\limits_{r = 1}^{4} {(N_{nr}^{ - } { + }\Delta N_{nr} \cdot r_{nrw} ) \cdot CWPR_{r}^{ \pm } } - EDPR_{nw}^{ \pm } } \hfill \\ + \sum\limits_{p = 1}^{3} {(Z_{p}^{ - } + \Delta Z_{p} \cdot s_{pw} ) \cdot DWP^{ \pm } \cdot CWPP^{ \pm } - EDPP_{pw}^{ \pm } } \hfill \\ + \sum\limits_{m = 1}^{7} {(Y_{m}^{ - } + \Delta Y_{m} \cdot e_{mw} ) \cdot DWM_{m}^{ \pm } \cdot CWPM_{m}^{ \pm } - EDPC_{mw}^{ \pm } } \le TPT_{w} \hfill \\ \end{gathered} $$

(B54)

(b) Constraints for NH₃-N environmental limit

$$ \sum\limits_{j = 1}^{11} {(X_{ij}^{ - } + \Delta X_{ij} \cdot o_{ijw} ) \cdot CWNA_{s}^{ \pm } } {\text{ - EDNA}}_{isw}^{ \pm } \le TNI_{iw} $$

(B55)

$$ \sum\limits_{r = 1}^{4} {(N_{nr}^{ - } { + }\Delta N_{nr} \cdot r_{nrw} ) \cdot CWNR_{r}^{ \pm } } - EDNR_{nw}^{ \pm } \le TNN_{nw} $$

(B56)

$$ (Z_{p}^{ - } + \Delta Z_{p} \cdot s_{pw} ) \cdot DWP^{ \pm } \cdot CWNP^{ \pm } - EDNP_{pw}^{ \pm } \le TNP_{pw} $$

(B57)

$$ (Y_{m}^{ - } + \Delta Y_{m} \cdot e_{mw} ) \cdot DWM_{m}^{ \pm } \cdot CWNM_{m}^{ \pm } - EDNC_{mw}^{ \pm } \le TNM_{mw} $$

(B58)

$$ \begin{gathered} \sum\limits_{j = 1}^{11} {(X_{1j}^{ - } + \Delta X_{1j} \cdot o_{1jw} ) \cdot CWNA_{s}^{ \pm } } {\text{ - EDNA}}_{1sw}^{ \pm } { + }\sum\limits_{r = 1}^{4} {(N_{1r}^{ - } { + }\Delta N_{1r} \cdot r_{1rw} ) \cdot CWNR_{r}^{ \pm } } \hfill \\ - EDNR_{1w}^{ \pm } { + }(Z_{1}^{ - } + \Delta Z_{1} \cdot s_{1w} ) \cdot DWP^{ \pm } \cdot CWNP^{ \pm } - EDNP_{1w}^{ \pm } \le TNGF_{1w} \hfill \\ \end{gathered} $$

(B59)

$$ \begin{gathered} \sum\limits_{j = 1}^{11} {(X_{2j}^{ - } + \Delta X_{2j} \cdot o_{2jw} ) \cdot CWNA_{s}^{ \pm } } {\text{ - EDNA}}_{2sw}^{ \pm } { + }\sum\limits_{r = 1}^{4} {(N_{2r}^{ - } { + }\Delta N_{2r} \cdot r_{2rw} ) \cdot CWNR_{r}^{ \pm } } \hfill \\ - EDNR_{2w}^{ \pm } { + }(Z_{2}^{ - } + \Delta Z_{2} \cdot s_{2w} ) \cdot DWP^{ \pm } \cdot CWNP^{ \pm } - EDNP_{2w}^{ \pm } \le TNGF_{2w} \hfill \\ \end{gathered} $$

(B60)

$$ \begin{gathered} \sum\limits_{j = 1}^{11} {(X_{3j}^{ - } + \Delta X_{3j} \cdot o_{3jw} ) \cdot CWNA_{s}^{ \pm } } {\text{ - EDNA}}_{3sw}^{ \pm } { + }\sum\limits_{r = 1}^{4} {(N_{3r}^{ - } { + }\Delta N_{3r} \cdot r_{3rw} ) \cdot CWNR_{r}^{ \pm } } \hfill \\ - EDNR_{3w}^{ \pm } { + }(Z_{3}^{ - } + \Delta Z_{3} \cdot s_{3w} ) \cdot DWP^{ \pm } \cdot CWNP^{ \pm } - EDNP_{3w}^{ \pm } \le TNGF_{3w} \hfill \\ \end{gathered} $$

(B61)

$$ \sum\limits_{j = 1}^{11} {(X_{4j}^{ - } + \Delta X_{4j} \cdot o_{4jw} ) \cdot CWNA_{s}^{ \pm } } - EDNA_{4sw}^{ \pm } \le TNGF_{4w} $$

(B62)

$$ \begin{gathered} \sum\limits_{j = 1}^{11} {(X_{5j}^{ - } + \Delta X_{5j} \cdot o_{5jw} ) \cdot CWNA_{s}^{ \pm } } - EDNA_{5sw}^{ \pm } \hfill \\ { + }(Y_{3}^{ - } + \Delta Y_{3} \cdot e_{3w} ) \cdot DWM_{3}^{ \pm } \cdot CWNM_{3}^{ \pm } - EDNC_{3w}^{ \pm } \hfill \\ { + }(Y_{4}^{ - } + \Delta Y_{4} \cdot e_{4w} ) \cdot DWM_{4}^{ \pm } \cdot CWNM_{4}^{ \pm } - EDNC_{4w}^{ \pm } \hfill \\ { + }(Y_{5}^{ - } + \Delta Y_{5} \cdot e_{5w} ) \cdot DWM_{5}^{ \pm } \cdot CWNM_{5}^{ \pm } - EDNC_{5w}^{ \pm } \hfill \\ { + }(Y_{6}^{ - } + \Delta Y_{6} \cdot e_{6w} ) \cdot DWM_{6}^{ \pm } \cdot CWNM_{6}^{ \pm } - EDNC_{6w}^{ \pm } \le TNWF_{1w} \hfill \\ \end{gathered} $$

(B63)

$$ \begin{gathered} (Y_{1}^{ - } + \Delta Y_{1} \cdot e_{1w} ) \cdot DWM_{1}^{ \pm } \cdot CWNM_{1}^{ \pm } - EDNC_{1w}^{ \pm } \hfill \\ { + }(Y_{2}^{ - } + \Delta Y_{2} \cdot e_{2w} ) \cdot DWM_{2}^{ \pm } \cdot CWNM_{2}^{ \pm } - EDNC_{2w}^{ \pm } \hfill \\ { + }(Y_{7}^{ - } + \Delta Y_{7} \cdot e_{7w} ) \cdot DWM_{7}^{ \pm } \cdot CWNM_{7}^{ \pm } - EDNC_{7w}^{ \pm } \le TNWF_{2w} \hfill \\ \end{gathered} $$

(B64)

$$ \begin{gathered} \sum\limits_{i = 1}^{4} {\sum\limits_{j = 1}^{11} {(X_{ij}^{ - } + \Delta X_{ij} \cdot o_{ijw} ) \cdot CWNA_{s}^{ \pm } } - EDNA_{isw}^{ \pm } } \hfill \\ + \sum\limits_{n = 1}^{3} {\sum\limits_{r = 1}^{4} {(N_{nr}^{ - } { + }\Delta N_{nr} \cdot r_{nrw} ) \cdot CWNR_{r}^{ \pm } } - EDNR_{nw}^{ \pm } } \hfill \\ + \sum\limits_{p = 1}^{3} {(Z_{p}^{ - } + \Delta Z_{p} \cdot s_{pw} ) \cdot DWP^{ \pm } \cdot CWNP^{ \pm } - EDNP_{pw}^{ \pm } } \le TNG_{w}^{{1{ - }p_{h} }} \hfill \\ \end{gathered} $$

(B65)

$$ \begin{gathered} \sum\limits_{j = 1}^{11} {(X_{ij}^{ - } + \Delta X_{ij} \cdot o_{ijw} ) \cdot CWNA_{s}^{ \pm } } - EDNA_{isw}^{ \pm } \hfill \\ + \sum\limits_{m = 1}^{7} {(Y_{m}^{ - } + \Delta Y_{m} \cdot e_{mw} ) \cdot DWM_{m}^{ \pm } \cdot CWNM_{m}^{ \pm } - EDNC_{mw}^{ \pm } } \le TNW_{w} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} i{\kern 1pt} { = }5 \hfill \\ \end{gathered} $$

(B66)

$$ \begin{gathered} \sum\limits_{i = 1}^{5} {\sum\limits_{j = 1}^{11} {(X_{ij}^{ - } + \Delta X_{ij} \cdot o_{ijw} ) \cdot CWNA_{s}^{ \pm } } - EDNA_{isw}^{ \pm } } \hfill \\ + \sum\limits_{n = 1}^{3} {\sum\limits_{r = 1}^{4} {(N_{nr}^{ - } { + }\Delta N_{nr} \cdot r_{nrw} ) \cdot CWNR_{r}^{ \pm } } - EDNR_{nw}^{ \pm } } \hfill \\ + \sum\limits_{p = 1}^{3} {(Z_{p}^{ - } + \Delta Z_{p} \cdot s_{pw} ) \cdot DWP^{ \pm } \cdot CWNP^{ \pm } - EDNP_{pw}^{ \pm } } \hfill \\ + \sum\limits_{m = 1}^{7} {(Y_{m}^{ - } + \Delta Y_{m} \cdot e_{mw} ) \cdot DWM_{m}^{ \pm } \cdot CWNM_{m}^{ \pm } - EDNC_{mw}^{ \pm } } \le TNT_{w} \hfill \\ \end{gathered} $$

(B67)

(c) Energy and protein requirements constraints

$$ \begin{gathered} \sum\limits_{i = 1}^{5} {\sum\limits_{j = 1}^{11} {AP_{{_{ij} }}^{ \pm } } \cdot (X_{ij}^{ - } + \Delta X_{ij} \cdot o_{ijw} ) \cdot PE_{j} } \hfill \\ - \sum\limits_{n = 1}^{3} {\sum\limits_{r = 1}^{4} {LE_{r} \cdot (N_{nr}^{ - } { + }\Delta N_{nr} \cdot r_{nrw} ) - } } DP \cdot NE - MP \cdot NE \ge 0{\kern 1pt} \hfill \\ \end{gathered} $$

(B68)

$$ \begin{gathered} \sum\limits_{i = 1}^{5} {\sum\limits_{j = 1}^{11} {AP_{{_{ij} }}^{ \pm } } \cdot (X_{ij}^{ - } + \Delta X_{ij} \cdot o_{ijw} ) \cdot CE_{j} } \hfill \\ - \sum\limits_{n = 1}^{3} {\sum\limits_{r = 1}^{4} {LP_{r} \cdot (N_{nr}^{ - } { + }\Delta N_{nr} \cdot r_{nrw} ) - } DP \cdot NP} - MP \cdot NP \ge 0 \hfill \\ \end{gathered} $$

(B69)

(d) Technical and non-negativity constraints

$$ 0 \le o_{ijw} \le 1,{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} 0 \le r_{nrw} \le {1,}{\kern 1pt} {\kern 1pt} {\kern 1pt} 0 \le s_{pw} \le 1,{\kern 1pt} {\kern 1pt} {\kern 1pt} 0 \le e_{mw} \le 1{\kern 1pt} $$

(B70)

Besides, the technology and non-negative constraints comprise the excess TP and NH₃-N emission of each pollution source. And the excess TP and NH₃-N emission of each pollution source are lower than the total TP and NH₃-N emission from the source, respectively.

Appendix C

See Tables 5, 6, 7, 8,

Table 5 The detailed trading process for TP under Case 1 when p = 0.01 and w = 1

Table 6 The detailed trading process for NH₃-N under Case 1 when p = 0.01 and w = 1

Table 7 The detailed trading process for TP under Case 2 when p = 0.01 and w = 1

Table 8 The detailed trading process for NH₃-N under Case 2 when p = 0.01 and w = 1

Table 9 The detailed trading process for TP under Case 1 and p = 0.01 in medium level of water availability (w = 3)

9,

Table 10 The detailed trading process for NH₃-N under Case 1 and p = 0.01 in medium level of water availability (w = 3)

10,

Table 11 The detailed trading process for TP under Case 2 and p = 0.01 in medium level of water availability (w = 3)

11, and

Table 12 The detailed trading process for NH₃-N under Case 2 and p = 0.01 in medium level of water availability (w = 3)

12.

Appendix D

$i$	Agricultural zone, $i = 1, \, 2, \, 3, \, 4, \, 5$; $i = 1$ for Laixi zone, $i = 2$ for Pingdu zone, $i = 3$ for Jiaozhou zone, $i = 4$ for Daguhe Jimo zone, $i = 5$ for Moshuihe Jimo zone
$j$	Species of crops, $j = 1, \, 2, \, 3, \, 4, \ldots ,11$; $j = 1$ for wheat, $j = 2$ for corn, $j = 3$ for peanut, $j = 4$ for chinese cabbage, $j = 5$ for celery, $j = 6$ for carrot, $j = 7$ for potato, $j = 8$ for apple, $j = 9$ for pear, $j = 10$ for peach, $j = 11$ for grape
$n$	Livestock and poultry industry zone, $n = 1, \, 2, \, 3$; $n = 1$ for Laixi zone,$n = 2$ for Pingdu zone, $n = 3$ for Jiaozhou zone
$r$	Species of livestocks, $r = 1, \, 2, \, 3, \, 4$; $r = 1$ for chicken, $r = 2$ for pig, $r = 3$ for cattle, $r = 4$ for cow
$p$	Fishery zone, $p = 1, \, 2, \, 3$; $p = 1$ for Laixi zone, $p = 2$ for Pingdu zone, $p = 3$ for Jiaozhou zone
$m$	company, $m = 1, \, 2, \, 3, \, 4, \, 5, \, 6, \, 7$; $m = 1$ for Qingdao Zhengyuan Iron and Steel Co., Ltd $m = 2$ for Qingdao Tongyuanchang Steel Co., Ltd $m = 3$ for Qingdao Hehe Chemical Co., Ltd $m = 4$ for Qingdao Zeyukaisheng Machinery Manufacturing Co., Ltd $m = 5$ for Qingdao Huataida Machinery Manufacturing Co., Ltd $m = 6$ for Qingdao Jingrui Machinery Manufacturing Co., Ltd $m = 7$ for Qingdao Jinguangxin Textile Co., Ltd
$i^{\prime}$	Other agricultural zone except zone $i$
$n^{\prime}$	Other livestock and poultry industry zone except zone $n$
$r^{\prime}$	Other species of livestocks except $r$
$p^{\prime}$	Other fishery zone except zone $p$
$m^{\prime}$	Other company except company $m$
$w$	The level of water availability, $w = 1, \, 2, \, 3$; $w = 1$ for high level, $w = 2$ for low level, $w = 3$ for medium level
$q$	Reaches in Daguhe watershed, $q = 1, \, 2, \, 3, \, 4$;$q = 1$ for Laixi reach,$q = 2$ for Pingdu reach,$q = 3$ for Jiaozhou reach,$q = 4$ for Jimo reach
$o$	Reaches in Moshuihe watershed,$o = 1, \, 2$
$k$	TP-generation level of agriculture
$s$	NH3-N-generation level of agriculture
$h$	A prescribed level of probability for each constraint
$AB_{j}^{ \pm }$	Net benefit of crop $j$ (RMB¥/ha)
$AP_{ij}^{ \pm }$	Production level of crop $j$ in agricultural zone $i$ (kg/ha)
$X_{ij}^{ - } ,\Delta X_{ij}$	Lower bound and range of area target for crop j in zone $i$ (ha)
$o_{ijw} , \, r_{nrw} , \, s_{pw} , \, e_{mw}$	Decision variables which are used for identifying the optimized targets of cropped area, the scale of livestock and poultry industry, the scale of fishery and the production level of company
$SB_{p}^{ \pm }$	Net benefit of zone $p$ (RMB¥/ha)
$Z_{p}^{ - } ,\Delta Z_{p}$	Lower bound and range of the scale of fishery zone $p$
$CB_{m}^{ \pm }$	Net benefit of per unit product of company $m$ (RMB¥)
$Y_{m}^{ - } ,\Delta Y_{m}$	Lower bound and range of the production level of company $m$
$h_{k}$	Probability of TP generation rate in agriculture
$k_{s}$	Probability of NH3-N generation rate in agriculture
$PF$	Penalties per ton excess TP effluents exceeding to discharge permits from pollution source (RMB¥/ton)
$NF$	Penalties per ton excess NH3-N effluents exceeding to discharge permits from pollution source (RMB¥/ton)
$EDPA_{ikw}^{ \pm } ,{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} EDPR_{nw}^{ \pm } EDPP_{pw}^{ \pm } EDPC_{mw}^{ \pm }$	Excess annual TP loading for agricultural zone $i$, livestock and poultry industry zone $n$, fishery zone $p$ and company $m$ (ton)
$EDNA_{isw}^{ \pm } , \, EDNR_{nw}^{ \pm } , \, EDNP_{pw}^{ \pm } , \, EDNC_{mw}^{ \pm }$	Excess annual NH3-N loading for agricultural zone i, livestock and poultry industry zone $n$, fishery zone $p$ and company $m$ (ton)
$DWP^{ \pm } , \, DWM_{{_{m} }}^{ \pm }$	Effluent generation rate of fishery zone and company $m$ (m3/ha; m3/ton, item)
$CWPA_{{_{k} }}^{ \pm } , \, CWPR_{{_{r} }}^{ \pm } , \, CWPP^{ \pm } , \, CWPM_{{_{m} }}^{ \pm }$	TP generation rate of agricultural zone $i$, livestock $r$, fishery zone $p$ and company $m$ (ton/ha; ton/item; ton/m3; ton/m3)
$CWNA_{{_{s} }}^{ \pm } ,{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} CWNR_{{_{r} }}^{ \pm } , \, CWNP^{ \pm } , \, CWNM_{{_{m} }}^{ \pm }$	NH3-N generation rate of agricultural zone $i$, livestock $r$, fishery zone $p$ and company $m$ (ton/ha; ton/item; ton/m3; ton/m3)
$TPI_{iw} , \, TPN_{nw} , \, TPP_{pw} , \, TPM_{mw}$	TP discharge permit allocated to agricultural zone $i$, livestock and poultry industry $n$, fishery zone $p$ and company $m$ in level $w$, respectively (ton)
$TNI_{iw} TNN_{nw} TNP_{pw} TNM_{mw}$	NH3-N discharge permit allocated to agricultural zone $i$, livestock and poultry industry $n$, fishery zone $p$ and company $m$ in level $w$, respectively (ton)
$ACEP_{iw} ,{\kern 1pt} \, LCEP_{nw} , \, SCEP_{pw} , \, CCEP_{mw}$	TP discharge permit that agricultural $i$, livestock and poultry industry zone $n$, fishery zone $p$ and company $m$ possess after trading program in level $w$ (ton)
$ACEN_{iw} , \, LCEN_{nw} , \, SCEN_{pw} , \, CCEN_{mw}$	NH3-N discharge permit that agricultural $i$, livestock and poultry industry zone $n$, fishery zone $p$ and company $m$ possess after trading program in level $w$ (ton)
$TP_{i^{\prime}iw} {, }TPs_{niw} , \, TPs_{piw} , \, TPs_{miw}$	TP discharge permit sold to agricultural zone $i$ from agricultural zone $i^{\prime}$, livestock and poultry industry zone $n$, fishery zone $p$ and company $m$, respectively (ton)
$TP_{n^{\prime}nw} , \, TPs_{inw} , \, TPs_{pnw} , \, TPs_{mnw}$	TP discharge permit sold to livestock and poultry industry zone $n$ from livestock and poultry industry zone $n^{\prime}$, agricultural zone $i$, fishery zone $p$ and company $m$, respectively (ton)
$TP_{p^{\prime}pw} , \, TPs_{ipw} , \, TPs_{npw} , \, TPs_{mpw}$	TP discharge permit sold to fishery zone $p$ from fishery zone $p^{\prime}$, agricultural zone $i$, livestock and poultry industry zone $n$ and company $m$, respectively (ton)
$TP_{m^{\prime}mw} , \, TPs_{imw} , \, TPs_{nmw} , \, TPs_{pmw}$	TP discharge permit sold to company $m$ from company $m^{\prime}$, agricultural zone $i$, livestock and poultry industry zone $n$ and fishery zone $p$, respectively (ton)
$TPb_{niw} , \, TPb_{piw} , \, TPb_{miw}$	TP discharge permit in agricultural zone $i$ purchased from livestock and poultry industry zone $n$, fishery zone $p$ and company $m$, respectively (ton)
$TPb_{inw} , \, TPb_{pnw} , \, TPb_{mnw}$	TP discharge permit in livestock and poultry industry zone $n$ purchased from agricultural zone $i$, fishery zone $p$ and company $m$, respectively (ton)
$TPb_{ipw} , \, TPb_{npw} , \, TPb_{mpw}$	TP discharge permit in fishery zone $p$ purchased from agricultural zone $i$, livestock and poultry industry zone $n$ and company $m$, respectively (ton)
$TPb_{imw} , \, TPb_{nmw} , \, TPb_{pmw}$	TP discharge permit in company $m$ purchased from agricultural zone $i$, livestock and poultry industry zone $n$ and fishery zone $p$, respectively (ton)
$TP_{ii^{\prime}w} , \, TP_{nn^{\prime}w} , \, TP_{pp^{\prime}w} , \, TP_{mm^{\prime}w}$	TP discharge permit agricultural zone $i$ sold to $i^{\prime}$, livestock and poultry industry zone $n$ sold to $n^{\prime}$, fishery zone $p$ sold to $p^{\prime}$ and company $m$ sold to $m^{\prime}$,respectively (ton)
$TN_{i^{\prime}iw} , \, TNs_{niw} , \, TNs_{piw} , \, TNs_{miw}$	NH3-N discharge permit sold to agricultural zone $i$ from agricultural zone $i^{\prime}$, livestock and poultry industry zone $n$, fishery zone $p$ and company $m$, respectively (ton)
$TN_{n^{\prime}nw} , \, TNs_{inw} , \, TNs_{pnw} , \, TNs_{mnw}$	NH3-N discharge permit sold to livestock and poultry industry zone $n$ from livestock and poultry industry zone $n^{\prime}$, agricultural zone $i$, fishery zone $p$ and company $m$, respectively (ton)
$TN_{p^{\prime}pw} , \, TNs_{ipw} , \, TNs_{npw} , \, TNs_{mpw}$	NH3-N discharge permit sold to fishery zone $p$ from fishery zone $p^{\prime}$, agricultural zone $i$, livestock and poultry industry zone $n$ and company $m$, respectively (ton)
$TN_{m^{\prime}mw} , \, TNs_{imw} , \, TNs_{nmw} , \, TNs_{pmw}$	NH3-N discharge permit sold to company $m$ from company $m^{\prime}$, agricultural zone $i$, livestock and poultry industry zone $n$ and fishery zone $p$, respectively (ton)
$TNb_{niw} , \, TNb_{piw} , \, TNb_{miw}$	NH3-N discharge permit in agricultural zone $i$ purchased from livestock and poultry industry zone $n$, fishery zone $p$ and company $m$, respectively (ton)
$TNb_{inw} , \, TNb_{pnw} , \, TNb_{mnw}$	NH3-N discharge permit in livestock and poultry industry zone $n$ purchased from agricultural zone $i$, fishery zone $p$ and company $m$, respectively (ton)
$TNb_{ipw} , \, TNb_{npw} , \, TNb_{mpw}$	NH3-N discharge permit in fishery zone $p$ purchased from agricultural zone $i$, livestock and poultry industry zone $n$ and company $m$, respectively (ton)
$TNb_{imw} TNb_{nmw} TNb_{pmw}$	NH3-N discharge permit in company $m$ purchased from agricultural zone $i$, livestock and poultry industry zone $n$ and fishery zone $p$, respectively (ton)
$TN_{ii^{\prime}w} , \, TN_{nn^{\prime}w} , \, TN_{pp^{\prime}w} , \, TN_{mm^{\prime}w}$	NH3-N discharge permit agricultural zone $i$ sold to $i^{\prime}$, livestock and poultry industry zone $n$ sold to $n^{\prime}$, fishery zone $p$ sold to $p^{\prime}$ and company $m$ sold to $m^{\prime}$,respectively (ton)
$tp_{i^{\prime}i} , \, tp_{ni} , \, tp_{pi} , \, tp_{mi}$	TP trading ratio of transaction from agricultural zone $i^{\prime}$, livestock and poultry industry zone $n$, fishery zone $p$ and company $m$ to agricultural zone $i$, respectively
$tp_{n^{\prime}n} , \, tp_{in} , \, tp_{pn} , \, tp_{mn}$	TP trading ratio of transaction from livestock and poultry industry zone $n^{\prime}$, agricultural zone $i$, fishery zone $p$ and company $m$ to livestock and poultry industry zone $n$, respectively
$tp_{p^{\prime}p} , \, tp_{ip} , \, tp_{np} , \, tp_{mp}$	TP trading ratio of transaction from fishery zone $p^{\prime}$, agricultural zone $i$, livestock and poultry industry zone $n$ and company $m$ to fishery zone $p$, respectively
$tp_{m^{\prime}m} , \, tp_{im} , \, tp_{nm} , \, tp_{pm}$	TP trading ratio of transaction from company $m^{\prime}$, agricultural zone $i$, livestock and poultry industry zone $n$ and fishery zone $p$ to company $m$, respectively
$tp_{ii^{\prime}} , \, tp_{nn^{\prime}} , \, tp_{pp^{\prime}} , \, tp_{mm^{\prime}}$	TP trading ratio of transaction from agricultural zone $i$ to $i^{\prime}$, from livestock and poultry industry zone $n$ to $n^{\prime}$, from fishery zone $p$ to $p^{\prime}$ and from company $m$ to $m^{\prime}$, respectively
$tn_{i\prime,i} , \, tn_{ni} , \, tn_{pi} , \, tn_{mi}$	NH3-N trading ratio of transaction from agricultural zone $i^{\prime}$, livestock and poultry industry zone $n$, fishery zone $p$ and company $m$ to agricultural zone $i$, respectively
$tn_{n^{\prime}n} , \, tn_{in} , \, tn_{pn} , \, tn_{mn}$	NH3-N trading ratio of transaction from livestock and poultry industry zone $n^{\prime}$, agricultural zone $i$, fishery zone $p$ and company $m$ to livestock and poultry industry zone $n$, respectively
$tn_{p^{\prime}p} , \, tn_{ip} , \, tn_{np} , \, tn_{mp}$	NH3-N trading ratio of transaction from fishery zone $p^{\prime}$, agricultural zone $i$, livestock and poultry industry zone $n$ and company $m$ to fishery zone $p$, respectively
$tn_{m^{\prime}m} , \, tn_{im} , \, tn_{nm} , \, tn_{pm}$	NH3-N trading ratio of transaction from company $m^{\prime}$, agricultural zone $i$, livestock and poultry industry zone $n$ and fishery zone $p$ to company $m$, respectively
$tn_{ii^{\prime}} , \, tn_{nn^{\prime}} , \, tn_{pp^{\prime}} , \, tn_{mm^{\prime}}$	NH3-N trading ratio of transaction from agricultural zone $i$ to $i^{\prime}$, from livestock and poultry industry zone $n$ to $n^{\prime}$, from fishery zone $p$ to $p^{\prime}$ and from company $m$ to $m^{\prime}$, respectively
$p_{h}$	Constraint-violation probability
$PE_{r}$	The quantity of energy in per kg of crop $j$ (kcal/kg)
$LE_{r}$	The quantity of required energy in per livestock $r$ (kcal/one)
$DP$	Total population in Daguhe watershed
$MP$	Total population in Moshuihe watershed
$NE$	The quantity of required energy for per person from the crop in each year (kcal/one/a)
$CE_{j}$	The quantity of digestible protein in per kg of crop $j$ (g/kg)
$LP_{r}$	The quantity of required digestible protein for per livestock $r$ in each year (g/one/a)
$NP$	The quantity of required digestible protein for per person (g/one/a)
$TPA_{iw} , \, TPL_{nw} , \, TPS_{pw} , \, TPC_{mw}$	Allowance of TP emission for agricultural zones, livestock and poultry industry zones, fishery zones and companies within the two watersheds in level w (ton)
$TNA_{iw} , \, TNL_{nw} , \, TNS_{pw} , \, TNC_{mw}$	Allowance of NH3-N emission for agricultural zones, livestock and poultry industry zones, fishery zones and companies within the two watersheds in level w (ton)
$TPG_{w}$	Allowance of TP emission in Daguhe watershed in level w (ton)
$TNG_{w}$	Allowance of NH3-N emission in Daguhe watershed in level w (ton)
$TPGF_{qw}$	Allowance of TP emission in reach q, Daguhe watershed in level w (ton)
$TNGF_{qw}$	Allowance of NH3-N emission in reach q, Daguhe watershed in level w (ton)
$TPW_{w}$	Allowance of TP emission in Moshuihe watershed in level w (ton)
$TNW_{w}$	Allowance of NH3-N emission in Moshuihe watershed in level w (ton)
$TPWF_{ow}$	Allowance of TP emission in reach o, Moshuihe watershed in level w (ton)
$TNWF_{ow}$	Allowance of NH3-N emission in reach o, Moshuihe watershed in level w (ton)
$TPT_{w}$	Allowance of TP emission in both watersheds in level w (ton)
$TNT_{w}$	Allowance of NH3-N emission in both watersheds in level w (ton)