Multi-watershed nonpoint source pollution management through coupling Bayesian-based 1 simulation and mechanism-based effluent trading optimization 2 3


 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 can be under additional challenges and yield considerable economic and environmental benefits. 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.

where superscripts "  " and "  " represent the lower and upper bounds of an interval parameter Subject to:  In above model,    (Huang et al., 2000). Then the 252 interval solutions can be gained by solving two sub-models in sequence. The ecological environment of Daguhe and Moshuihe watersheds is extremely vulnerable 297 because of the excessive nutrient emission. The improper allocation of discharge permits strategy 298 may lead to the inefficiency of environmental management even lead to the issue of hot spots. 299 Instead, effluent trading would contribute to allocate discharge permits with optimal economic 300 benefits or enhanced environmental benefits. In addition, those with pollution sources that are not 301 easy to mitigate or who choose to heighten production can purchase the unused permits deriving 302 from the others within the trading system, without paying huge environmental penalties. TP and 303 NH3-N are selected as water quality indicators.

305
As shown in Figure 2, firstly, six reaches have been demarcated in the two watersheds for 306 avoiding the issue of hot spots in trading, including 4 reaches in Daguhe watershed and 2 reaches 307 in Moshuihe watershed (Xu, 2004;Ning et al., 2017). Secondly, there are 18 major pollution 308 sources in the two watersheds, including 10 nonpoint sources in Daguhe watershed (i.e. four 309 agricultural zones, three livestock and poultry industry zones and three fishery zones) as well as 310 one agricultural zone in Moshuihe watershed. Besides, seven companies in Moshuihe watershed 311 are also considered. The planning period in this study is one year (2021), and the discharge 312 permit trading of three levels of water availability (high level (w = 1), low level (w = 2) and 313 medium level (w = 3)) is respectively planned. In study area, TP and NH3-N discharge permits 314 would be allocated to 18 pollution sources in two watersheds, which include multiple human 17 activities (i.e. agriculture, livestock and poultry industry, fishery and company). The initial allocation is based on the proportion of their own ecological, economic benefits and pollutant 317 emissions. BS-METM can be formulated under three trading mechanism cases. Under Case 1, the 318 discharge permits are forced to be traded only within the pollution sources from the same 319 watershed. Under Case 2, cross-watershed effluent trading is allowed, which means that the The objective is to maximize the ultimate net system benefit, which is calculated with the total 332 environmental penalty and the total initial net system benefit which removes the cost. The

333
ultimate system net benefit considers the total initial net system benefits and the total 334 environmental penalties of agriculture, livestock and poultry industry, fishery and company. The 335 constraints to be complied with can be divided into the following groups: 2. Constraints for NH3-N permit reallocation Constraints (7j)-(7m) and (7n) Constraints (7j)-(7m) and (7n)-(7q) can contribute to ensure that the selling TP and NH3-N 368 discharge permits from pollution sources should be larger than the initial permits they possess, 369 respectively.  Markov chains comprising 20,000 iterations for each parameter, and the first 10% of which 449 would be removed as burn in period. Their prior densities were designed to be uniform within 450 their limits as shown in Table 1.
Place Table 1 here  Table 2 shows loading distributions and the associated probabilities for 470 TP and NH3-N, respectively.
Place  In this study, totally 9 scenarios based on each trading mechanism are examined considering 26 three levels of water availability (w) and three environmental allowance-violation risk levels (p).

479
The trading ratio is introduced to ensure that the water quality between the trading sources is 480 equivalent. It is determined according to the hazard degree of pollutants produced by each 481 industry, the location of pollution sources and the water quality standard of the discharged 482 watershed.

484
In tables 3 to 6, the results are provided in forms of "selling amount/purchasing amount". The Place Tables 3 to 6 here The excess total TP and NH3-N emissions from agricultural zones, total TP and NH3-N emissions, 503 system net benefits and total trading amounts are investigated under the three environmental 504 allowance-violation risks (p). Table 7 shows the total excess TP and NH3-N emissions from 505 agriculture at different p. The results indicate that generally the total excess TP and NH3-N 506 emissions from agriculture would be decreased as p is increased except for the scenarios under no 507 excess TP and NH3-N. Table 8 shows the total excess TP and NH3-N emissions at different p. 508 From the results, the total excess TP and NH3-N emissions would also be decreased as p is 509 increased accordingly. For example, under Case 1 and w = 2, the total excess TP emissions would 510 be decreased from 521.48 ton to 520.30 ton as p is raised from 0.01 to 0.1. Figure 7 shows the net 511 system benefits at different p. The results illustrate that net system benefits would be increased as 512 p is improved due to the decreased total excess TP and NH3-N emissions. For example, under 513 Case 1 and w = 2, the net system benefits would be RMB¥ 17947.415×10 6 (p = 0.01) and 514 RMB¥ 17947.578 ×10 6 (p = 0.1). Figure 8 shows the total TP and NH3-N trading amounts at 515 different p. The results indicate that TP and NH3-N trading amounts under p = 0.01 are higher 516 than those under p = 0.1 because the decreased total excess pollution emissions would decrease 517 the desire for TP and NH3-N permits trading program. Above results imply that the total excess 518 TP and NH3-N emissions from agricultural zones would be decreased when p is raised. Then the 519 total excess TP and NH3-N emissions would be decreased, leading to the increased net system 520 benefits and decreased total trading amounts.
Place Tables 7, 8  The total trading amounts, excess total TP and NH3-N emissions and system net benefits are 526 investigated under three levels for water availability (w). From the results in Figure 8, when the 527 level of water availability varies from low to high, the total TP and NH3-N trading amounts 528 would increase. For example, under Case 2 and when p takes 0.01, the NH3-N trading amounts 529 would be 54.87 ton and 1139.11 ton when w = 2 and w = 1, respectively. This is mainly because 530 the existence of demand and more supply for TP and NH3-N permits when the level of water 531 availability is high. The demand represents the existence of excess pollution emissions from 532 many pollution sources which need to require more pollution permits. The supply represents that 533 the total surplus TP and NH3-N permits would be increased by 0.76 ton and 1287.49 ton before 534 trading when the level of water availability rises from low to high. This implies that the effluent 535 trading would be promoted in high level of water availability. The total excess TP and NH3-N 536 emissions would be decreased when the level of water availability is raised due to the increased 537 total trading amounts ( Firstly, from the results in Table 8 17970.639×10 6 (Case 2), 17970.028×10 6 (Case 3). Based on the above results, trading cases 558 perform better than non-trading case in high level of water availability. This is mainly because 559 the trading cases can achieve the optimal configuration for pollution permits. Secondly, the total 560 excess TP and NH3-N emissions under Cases 1 and 2 would be higher than those under Case 3 561 when w = 2 (Table 8) 17947.768×10 6 (Case 3). The above results imply that the system in low level of water 568 availability is suitable for non-trading mechanism. This is mainly because there is almost no 569 surplus pollution discharge permits for all pollution sources in low level of water availability.

30
Thirdly, the total excess TP emissions under Cases 1 and 2 would be higher than those under 571 Case 3 when w = 3 (Table 8) 17963.080×10 6 (Case 3). The above results indicate that trading cases perform better than 580 non-trading case in medium level of water availability. This is mainly because trading cases can 581 achieve the optimal configuration for pollution permits.  TP permits under Case 1 would almost be equivalent to those under Case 2 when w = 1 ( Figure   591 9). The above results imply that the TP trading under Case 2 can better achieve pollution permits' 592 optimal configuration than Case 1. In addition, the total excess NH3-N emissions would be same 31 under Cases 1 and 2 when w = 1 ( Case 2 when w = 3. This is mainly because the certain surplus pollution permits would be traded

List of Table Captions
Table 1 Sensitive parameters of SWAT model for TP and NH3-N Table 2 TP and NH3-N loading distribution and the associated probabilities (unit ton) Table 3 The detailed trading process for TP under Case 1 when p = 0.01 and w = 2 Table 4 The detailed trading process for NH3-N under Case 1 when p = 0.01 and w = 2 Table 5 The detailed trading process for TP under Case 2 when p = 0.01 and w = 2 Table 6 The detailed trading process for NH3-N under Case 2 when p = 0.01 and w = 2 Table 7 Total excess TP and NH3-N emissions in agriculture under three cases (ton)   Table 3 The detailed trading process for TP under Case 1 Table 5 The detailed trading process for TP under Case 2