Journal of Environmental Management 84 (2007) 427–446
Watershed-based point sources permitting strategy and
dynamic permit-trading analysis
Shu-Kuang Ning
a, Ni-Bin Chang
b,aDepartment of Civil and Environmental Engineering, National University of Kaohsiung, Kaohsiung 811, Taiwan, ROC bDepartment of Civil and Environmental Engineering, University of Central Florida, Orlando, FL 32816, USA
Received 15 October 2004; received in revised form 14 June 2006; accepted 20 June 2006 Available online 23 August 2006
Abstract
Permit-trading policy in a total maximum daily load (TMDL) program may provide an additional avenue to produce environmental benefit, which closely approximates what would be achieved through a command and control approach, with relatively lower costs. One of the important considerations that might affect the effective trading mechanism is to determine the dynamic transaction prices and trading ratios in response to seasonal changes of assimilative capacity in the river. Advanced studies associated with multi-temporal spatially varied trading ratios among point sources to manage water pollution hold considerable potential for industries and policy makers alike. This paper aims to present an integrated simulation and optimization analysis for generating spatially varied trading ratios and evaluating seasonal transaction prices accordingly. It is designed to configure a permit-trading structure basin-wide and provide decision makers with a wealth of cost-effective, technology-oriented, risk-informed, and community-based management strategies. The case study, seamlessly integrating a QUAL2E simulation model with an optimal waste load allocation (WLA) scheme in a designated TMDL study area, helps understand the complexity of varying environmental resources values over space and time. The pollutants of concern in this region, which are eligible for trading, mainly include both biochemical oxygen demand (BOD) and ammonia-nitrogen (NH3-N). The problem solution, as a consequence, suggests an array of waste load reduction targets in a well-defined WLA scheme and
exhibits a dynamic permit-trading framework among different sub-watersheds in the study area. Research findings gained in this paper may extend to any transferable dynamic-discharge permit (TDDP) program worldwide.
r2006 Elsevier Ltd. All rights reserved.
Keywords: Environmental resources; Pricing theory; Optimization; Simulation; Shadow price; Permit trading; TMDL; Water quality management
1. Introduction
A discharge permit program to regulate possible viola-tion of surface water quality standards is a managerial tool in the traditional command and control system worldwide. Both technology-based and water quality-based controls have been implemented through a permitting process in many countries. While the former must specify a minimum level of treatment required based on an assessment of the achievability of control technologies by individual cate-gories of dischargers, the latter is achieved through the integration of the chemical-specific, whole-effluent toxicity, and biological criteria approaches. But population growth
and economic development in the past decades have placed increasing demands on the environment making it more difficult for discharge permit programs to maintain the required water quality standards. Market-based ap-proaches, such as air or water quality permit trading, might provide more flexibility and hold higher potential to acquire environmental benefit greater than what would otherwise be achieved under more traditional regulatory approaches (USEPA, 1997).
Since the US Environmental Protection Agency (USE-PA) issued its ‘‘emissions trading policy (ETP)’’ in 1986, most applications of this approach have been in SOx or NOxtrading for air pollution control (Solomon, 1998). The ETP has been found to achieve desirable cost reductions or environmental benefits in many recent applications (Kling, 1994; Bohi and Burtraw, 1998; Farrell, 2000). In 2005, www.elsevier.com/locate/jenvman
0301-4797/$ - see front matter r 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jenvman.2006.06.014
Corresponding author. Tel.:+1 407 7547521. E-mail address:nchang@mail.ucf.edu (N.-B. Chang).
USEPA issued the federal rule allowing cap and trade policy to reduce mercury emissions from coal-fired power plants. In line with air pollutant trading, trading principles have also been sanctioned by USEPA for water pollution control since the early 1980s. USEPA has since then formalized the concept into a framework to guide effective implementation of water pollutant trading (USEPA, 1996, 2003). USEPA also supports trading that involves nutrients (e.g., total phosphorus and total nitrogen) or sediment loads which has the potential to improve water quality and achieve ancillary environmental benefits if trading pro-grams are properly designed (USEPA, 1997). To achieve this goal, a ‘‘pollutant offset system (POS)’’ is designed to be a transferable permit program in which transfers of discharge permits are subject to the restrictions that no violations of water quality standards occur at any receptor point in a river basin (Letson, 1992).
Water quality trading allows one source to meet its regulatory obligations by using pollutant reductions created by another source that has lower pollution control costs on a watershed basis. Such trading could effectively capitalize on economies of scale and the control cost differentials among sources. Permit trading under the total maximum daily load (TMDL) policy scenario offers decision makers an additional avenue to produce environ-mental benefits, which closely approximates what would be achieved through a command and control approach, with relatively lower costs. Many transferable discharge permit (TDP) programs therefore offer a trading platform, in which effluent permits issued to dischargers in terms of a single pollutant may be transferred among them as a free market commodity (Houck, 2002). Extended choice of permit trading, such as dynamic permit programs, may even contribute more to environmental resource manage-ment. Dynamic permit programs (i.e., flow variable discharge permits), being viewed as an alternative permit strategy, have the potential for meeting the water quality standards at even lower social cost. They allow discharge rates that increase and decrease according to changes in the assimilative capacity of river reaches associated with different magnitudes of flow rate over seasons. Yet permits for several pollutants, which are traded as individual commodities or grouped together, could be more difficult to characterize and apply. In any circumstances, trades could be relatively easier among point sources than nonpoint sources because the design of a watershed point/nonpoint abatement trading system might involve even higher technical complexity and managerial uncer-tainties (Zhang and Wang, 2002). However, a policy maker, while aiming for better environment and efficient waste management, has to understand all possible mechan-isms and related constraints.
In the setting of trading arrangements, there are varying degrees of complexity related to the number of partners involved, the location of those partners, the pollutant or reduction traded, and the form of the trade. Variables for structuring or evaluating trading programs in a
watershed-based trading system might include selection of pollutants, structure of trade, units of trade and minimum quantities, eligible traders, size of trading area, trading ratio, monitoring requirements, banking and inter-pollutant trades, calculating loads, assuring real trades, trade approvals, enforcement and responsibility, registration system, verification of credits, and public information (Marshall, 1999). Trading ratio is defined as how many units of pollutant reduction a source must purchase from the other source in order to receive credit for one unit of load reduction. Transaction price or cost is expenses for trading participants need to pay for one unit of load reduction that occurs only as a result of trading. In the past, trading programs allowed point sources facing higher pollution control costs to meet their regulatory obligations by purchasing environmentally equivalent pollution reduc-tions from another source at lower cost. Yet the trading ratio between point and nonpoint sources was discussed from the viewpoint of economics (Malik et al., 2001; Horan, 2001). For more comprehensive pollution offset system design, please refer to seminal economics literature on modeling the pollution offset permit market (Krupnick et al., 1983;McGartland, 1988). The optimal trading ratio depends on the relative costs of enforcing point versus nonpoint reductions and the uncertainty associated with nonpoint loadings (Malik et al., 2001). In actual trading programs, the trading ratios are usually adjusted upward in response to nonpoint uncertainties. This fact conflicts with the purpose of encouraging more nonpoint controls. Given no detailed technical discussions of how these pollution loadings were calculated in line with possible trade-offs, a public choice model was used to explain the contradiction with respect to a divergence of social and public risk perceptions, and found that a trading market encourages economically suboptimal nonpoint source controls (Horan, 2001). Nowadays, one of the important considerations that might affect the effective trading mechanism among point sources dischargers is to determine the dynamic transaction prices and trading ratios in response to seasonal changes in the assimilative capacity in the river. This information cannot be retrieved without using technically sound and scientifically credible methods.
The current TMDL process normally distributes por-tions of the river assimilative capacity to various pollution sources, including natural background sources and a margin of safety, so as to maintain the officially required water quality standards. The total pollution loadings limited to a water body, which are of significance for permit trading, can be derived from point, nonpoint, and background sources via various simulation analyses to meet different needs (USEPA, 1997). As part of the watershed-based permitting strategy, WLA schemes have been extensively discussed based on total allowable pollution loadings in a TMDL program (Pickett, 1997; Parry, 1998). The design of various permit-trading systems previously, including single-pollutant-based TDPs (Brill et al., 1984), time-varying discharge permits (Eheart et al.,
1987), flow variable discharge permits (Noss and Glad-stone, 1987), TDPs for control of multiple pollutants (Lence et al., 1988), two pollutant and bi-seasonal pollution offset systems (Letson, 1992), and weighted sum TDPs (Lence, 1991), had illustrated some critical steps theoretically for developing appropriate WLA schemes associated with various dynamic conditions. Advanced case studies associated with multi-temporal spatially varied trading ratios among point sources to manage water pollution basin-wide hold considerable potential for industries and policy makers alike.
This paper aims to present an integrated simulation and optimization analysis for generating spatially varied trad-ing ratios and evaluattrad-ing seasonal transaction prices. It is designed to configure a permit-trading structure basin-wide and provide decision makers with a wealth of cost-effective, technology-oriented, risk-informed, and commu-nity-based management strategies. This work therefore might be viewed from two perspectives in systems analysis for the enhancement of point source controls. The basic QUAL2E simulation model, applicable to any pollutant and media, is the first step towards an integrated policy making platform. Such a platform gives decision makers the insight to analyze various scenarios basin-wide. The optimal WLA scheme in the second step sheds light on the possibility of pricing environmental resources (i.e., assim-ilative capacity) and using market based trades for water quality management in a designated TMDL study area. The proposed modeling system was applied in a case study in the Kao-Ping River Basin, south Taiwan, which helps decision makers understand the complexity of varying environmental resources values over space and time and the potential for using permit trading. The pollutants of concern in this region, which are eligible for trading, mainly include biochemical oxygen demand (BOD) and ammonia-nitrogen (NH3-N). The effect of uncertainty, prevalent in most situations, on model solutions is also analyzed using linear programming-based sensitivity ana-lysis. This may ensure that no hotspots are created due to discharge uncertainty on a watershed level over seasons and guide regulators in developing optimal regulations in different situations. The next section documents the case study in greater detail.
2. Case study
The case study is arranged as follows. Subsection 2.1 explains the site situation in the first TMDL program in Taiwan and pinpoints some implementation aspects of watershed based pollutant trading. It is then followed by a Subsection 2.2 illustrating the methodology, in which estimation of trading ratios and pricing strategies based on a benefit–cost analysis are presented sequentially. The section ends with results and discussion presented in Subsection 4.
2.1. Site description and implementation perspective 2.1.1. Site description
In Taiwan, 129 rivers may be found of which 21 of them are classified as primary rivers and 29 as secondary rivers. With two-thirds of the island being mostly rugged mountains in the eastern area, the rivers in Taiwan generally have big slopes, low storage capacity, and large carrying capability of suspended solids while flowing through gently rolling plains in the western region. The water year in a hydrological sense can be divided into two seasons. The wet season covers the time period from May to October, and the remaining time in a year is the dry season. The average precipitation is 2150 mm annually, which is about 2.6 times the world average; however, 70% of it occurs during the wet season from May to October in each year (i.e., the rainy season is mostly during the southwest monsoon from June to August). Uneven rainfall across seasons has resulted in the need for water resources redistribution in winter and early spring. Diversion across natural boundaries of river basins has been planned on a long-term basis. Even though most of the wastewater effluents discharged from municipalities, industrial sites, and livestock farms comply with the effluent water quality standards, the river water quality often cannot meet the officially required water quality levels with respect to attainable uses due to seasonal changes in the assimilative capacity of the river.
The Kao-Ping River Basin, which is the study area in this paper, is the largest river basin in Taiwan. It flows approximately 140 km and drains towards the south part of the Taiwan Strait. With an area of 3256 km2, including major administrative regions of Kaohsiung and Pingtung Counties, the main stream of Kao-Ping River originates from four small tributaries: Chi-San River, Liao-Nung River, Cho-Kou River, and Ai-Liao River (see Fig. 1). From the confluence to the union with those tributaries at the location of Li-Ling Bridge, the river carries the name Kao-Ping River. But Liao-Nung River and Kao-Ping River are generally regarded as the integrated main stream of Kao-Ping River in many watershed management practices. The period of high flow rate in the stream usually occurs in late spring and summer due to monsoons and typhoons. During the monsoon period, the flow in Kao-Ping River increases to a level approximately 8–12 times higher than its flow during the dry season.
The drainage area in the Kao-Ping River Basin is primarily used for agricultural production. Crops that are produced from the agricultural fields include: rice, sugar cane, pineapple, and a variety of vegetables. Livestock farming is an active agricultural activity. A number of small- and medium-scale industrial parks also exist in the downstream areas. In addition to meeting the water demand for agricultural production and industrial manu-facturing processes, water pumped from the river system is also essential for drinking and personal hygiene in this region. Concern and attention in water resources
management has been directed primarily to the uneven distribution of rainfall and stream flows over the dry and wet seasons associated with contamination of drinking water supplies. Currently, the transfer of water resources from the main stream of Kao-Ping River to its neighboring Tseng-Wen River Basin is an indispensable solution to improve the reliability of high quality water supply for two big coastal cities—Tainan and Kaohsiung (Ning et al., 2001).
2.1.2. Implementation perspective
The degree of water pollution defined for water quality management is classified by four categories, including ‘‘no pollution’’, ‘‘mild pollution’’, ‘‘median pollution’’, and ‘‘severe pollution,’’ in Taiwan. The downstream area of
Kao-Ping River has been falling into the category of ‘‘severe pollution’’ for many years, although it has long been used as the sole source of potable water in south Taiwan. The river in the downstream area has a long history of higher BOD and NH3-N pollution due to inadequate disposal of manure from the livestock farming and domestic wastewater disposal. Continuous discharge of industrial organic matter, stock manure, and degradable domestic wastewaters into flowing waters in the middle and downstream areas, where most water intakes are located, has resulted in the need for an effective managerial policy for improving the water quality condition. Such a need eventually motivated the Environmental Protection Ad-ministration (EPA) in Taiwan to declare the middle and
lower streams of this river system as the first TMDL region in 1999, which requires immediate development of a restoration program.
Pollutant dischargers are mainly classified as either point or nonpoint sources. Point sources are defined as the ones having direct and measurable emissions at particular sites, such as industrial parks, municipal waste treatment plants, etc., while nonpoint sources are the ones with diffused emissions that are difficult to measure, such as agricultural or storm-water runoffs. Among the various possibilities of carrying out permit trading, the one between point sources is thought to be simpler and achievable. Within the scope of this TMDL program, actions regarding the reduction of wastewater discharges from livestock farming and the expansion of sewer systems in five mid-size cities in the middle stream of Kao-Ping River were considered at first. While the enhancement of WLA in the receiving water body was of concern, the development of policy instru-ments, such as effluent taxes and marketable/transferable permits, was also taken into account officially.
There are two ways to make a trade happen. Trades can occur in the context of individual point source permits. In this case, different point sources have individual pollutant permits based on either technology or water-quality-based standards and treatment cost differentials encourage trading between various point sources located at different sites. On the other hand, trades may also occur through the development of TMDL or other equivalent analytical framework. In this case, a regional analysis in terms of trading ratios and transaction prices, common to all the point sources in a sub-basin, need to be established up front for all sub-basins involved in the TMDL program. This provides a holistic approach to comparing the costs of the baseline responsibilities necessary to achieve water quality goals to the benefits possibly achieved in different alternatives of WLA. Parties to the trade then negotiate with each other under the best WLA settings so as to satisfy the ultimate goals of restoration optimally. Crucial parameters that affect the economics of trading in this case are trading ratios, transaction prices, number of participants, availability of cost and benefit data, and uncertainties related to the assimilative capacity due to uneven stream flow rate. From the polluter’s perspective, it makes multiple options available for meeting the systematic goal in addition to having to simply go by the choice of installation of advanced end-of-pipe treatment facilities. From the deci-sion makers’ perspective, trading a particular amount of a pollutant among point sources in different sub-basins, which is able to reduce its total discharge more than that specified by the regulation, may speed up the restoration process. Once the integrated simulation and optimization framework is developed in the next section, it may open up the option of exploring various managerial scenarios to finalize the best WLA settings and determine the associated trading ratios and transaction prices region wide over seasons.
2.2. Methodology
QUAL2E is an USEPA-developed water quality model that has gained wide acceptance as a planning tool in watershed studies. It has been applied for several water quality management studies in the Kao-Ping River Basin since 1998 (Ning et al., 2001). The first effort was to calibrate and verify this water quality simulation model (i.e., a QUAL2E model) for the estimation of river assimilative capacity and evaluation of pollution preven-tion projects (Ning et al., 2001). The inclusion of nonpoint source pollution impact later on made the QUAL2E simulation model capable of extending the assessment with respect to both point and nonpoint source pollution loadings with the aid of the GWLF model (Ning et al., 2002, 2006). The creation of an optimal expansion strategy for a water quality monitoring network further extended the assessment potential (Ning and Chang, 2002, 2004, 2005). But a sound decision analysis for environmental management has to count on both technical and economic information, simultaneously. To support a cost-effective TMDL study,Chen et al. (2002)conducted a comparative analysis of methods to represent uncertainty in estimating the cost of constructing wastewater treatment plants, which summarized all the existing cases of domestic and industrial wastewater treatment plants in Taiwan. On the other hand, the benefits associated with water quality improvement in the river system can be drawn directly from an assessment using the fuzzy contingent valuation (FCV) method (Chen et al., 2005). These previous studies represent the culmina-tion of a 3-year research effort in support of this dynamic permit-trading analysis.
TMDLs offer a great opportunity for permit trading among point sources or even between point and nonpoint sources. There are two types of systems analyses that can be used to aid in the permit-trading assessment. The main assumption of the first one is that given that the waste reduction level and trading ratio are known using any type of simulation model, such as the QUAL2E or WASP5 model for water quality management, the impacts of the trading option and technology option can be collectively or separately quantified to identify the most cost-effective action via the use of an optimization model (i.e., a mixed integer programming (MIP) model). Additionally, this type of systems analysis can be applied to integrate the Gaussian plume model with the optimization model for air quality management too. For example, the model developed by Farrell et al. (1999)for NOxbudget, which is a MIP model with an objective of cost minimization for all sources, falls into this category. It tends to select the combination of control technologies for each plant to yield the lowest cost or to maximize the net present worth for an individual boiler over a period of time. The unique feature in this type of setting is that it may permit the banking of trades over time in the analysis, which is not suitable for water quality management. The second type of systems analysis aims to deal with the pollution offset permit design by exploring
the correlations and interactions between transaction prices and trading ratios simultaneously without regard to any pre-fixed waste reduction scheme determined solely by a simulation analysis. In this case, use of an integrated simulation and optimization approach would be beneficial for modeling the correlations and interactions between transaction prices and trading ratios. This would allow the decision makers to foresee the changes in environmental resources values (i.e., the value of assimilative capacity in the river) over seasons and alter the trading ratios dynamically according to the varying assimilative capacity. Since most previous studies focus on the first type of systems analysis (Farrell et al., 1999), it is therefore prudent to systematically analyze the second type of systems analysis at this juncture.
The following numerical example was thus prepared to demonstrate the knowledge, expertise, skill, and technol-ogy required for assessing the interactions between transaction prices and trading ratios in response to time-varying river assimilative capacity in Kao-Ping River, south Taiwan. It is an extension of a series of companion studies in watershed management in this region as all the relevant databases in the literature are supportive (Ning et al., 2001;Chen et al., 2002; Ning and Chang, 2002, 2004; Chen et al., 2005).
The practical implementation of this study was assessed by four scenarios or cases reflecting the situations of dry season at present, dry season in the target year of restoration, wet season at present, and wet season in the target year of restoration individually according to the future water resources redistribution and pollution pre-vention actions (i.e., the target year is 2010 in this study) (Ning et al., 2001). The sub-basin-based trading scenarios may provide a comparative basis for trading between any paired point sources between downstream and middle stream areas, leading to simplify the complexity of the trading structure in the proposed TMDL study area. Given that the water resources redistribution and pollution prevention actions are known (Ning et al., 2001), the integrated modeling efforts would involve employing a two-stage analysis in an iterative scheme. The first-stage analysis involves the use of a QUAL2E simulation model to estimate the trading ratios pairwise among all sub-basins. The second-stage analysis applies an optimization model to search for the optimal WLA scheme and corresponding shadow prices associated with each water quality constraint in the MIP model. The MIP can then be formulated as a benefit–cost analysis framework for pricing river assimilative capacity, which helps identify the varying value of the environmental resource—river assimilative capacity—over space and time.
The problem solution, as a consequence, correlates shadow prices in MIP with transaction prices in TMDL within 13 sub-basins in the study area. It conforms to the idea that shadow price in a linear programming-based model designed for resources management would reflect marginal resources value in a system (i.e., implied
economic value) with respect to a set of trading ratios prescribed by a pollutant fate and transport process in a simulation model. The objective function value in the optimization model would at least approximate the maximum net benefit or minimum net costs given all water quality constraints can be satisfied. Additional efforts designed to evaluate the sensitivity in the context of optimization may become essential due to the varying assimilative capacity over time.
2.2.1. Estimation of trading ratios
Trading ratios incorporate one or more of the following scientific and policy principles: relative value, address ‘‘leaks’’, margin of safety, and differential water quality impacts (USEPA, 1996). Increasing the ratio can provide a much larger environmental improvement and safety margin. However, if the ratio is too high, it will lessen or eliminate the cost advantages of trading and consequently could prevent effluent trades from occurring (Jarvie and Solomon, 1998).
The trading ratios among sub-basins with respect to a prescribed fate and transport process of target pollutants (i.e., BOD and NH3-N here) in the river reaches can be derived by the QUAL2E simulation model directly. To achieve this calculation, information on industrial dis-charge, municipal point sources, and effluents from livestock farming in the Kao-Ping River Basin was collected according to the certified permit and water right programs. Then, the river system was further characterized hydraulically and environmentally for modeling purposes. Sampling campaigns were performed during the dry and wet seasons in a previous study (Ning et al., 2001). Sampling in the period of low flows gave a proper worst-case scenario, yielding estimations of high pollutant concentrations, while sampling in the period of high flows presented an optimistic scenario, characterizing the upper bound of stream assimilative capacity. The modeling process using QUAL2E in this study excludes the consideration of photosynthesis and respiration of at-tached aquatic plants since they are not influential in this river system.
With a database containing over 10 years of records of the Kao-Ping River system, a thorough investigation of stream flow duration, hydrological pattern, drainage area, reach dimension and pattern, and schedule of ongoing and future engineering projects for water resources redistribu-tion and polluredistribu-tion prevenredistribu-tion acredistribu-tions was performed (Ning et al., 2001). The modeling effort first required selecting a designed stream flow based on a representative water year according to a thorough hydrological monitoring database. With the existing certified water rights analysis program, a sequential allocation of available water resources to a series of end users in agricultural, industrial, and domestic sectors was performed. The impact of the proposed diversion action in the Kao-Ping River system was then estimated for the target year. Consequently, final estimation of the resultant stream flow at different locations in either dry or
wet season may be predicted (Ning et al., 2001). In this analysis, the designed stream flow for the assessment of assimilative capacity in the future target year is Q50in the Kao-Ping River system. This would imply that only 50% probability exists for a seasonal stream flow to exceed the designed stream flow within a selected season (i.e., dry season or wet season in this study). The ratio of stream flows between dry and wet seasons turns out to be slightly smaller after considering the proposed diversion action of water resources over the natural boundaries (Ning et al.,
2001; Chen and Chang, 2006). Finally, the estimated
spatio-temporal distribution of stream flows in the river basin would become a firm basis for assessing the possible interactions between transaction prices and trading ratios. Hence, the trading ratio with respect to the fate and transport of target pollutants between two sub-basins can be drawn pairwise from a series of QUAL2E simulation runs. This output, accounting for the embedded nonlinear interactions between dissolved oxygen (DO) and nutrients (BOD/NH3) in the natural system, may provide a set of scientifically reliable reference bases to build up an environmental relationship matrix linking any two sub-basins together in the study area for trading. Such a matrix is deemed valuable for the subsequent optimization analysis.
2.2.2. Pricing strategies based on a benefit–cost analysis The optimization analysis was designed by a ‘‘zone uniform treatment’’ approach searching for the optimal WLA scheme among all sub-basins with respect to BOD and NH3-N simultaneously. The costs and benefits terms in line with various tradeoffs between differing sub-basins can be linked together and assessed as a whole in the proposed optimization framework. Table 1 defines the planning scenarios at present and in the target year associated with dry and wet seasons in the context of a benefit–cost analysis.
Knowledge gained in previous studies was incorporated as an integral part of the formulation in the optimization model (Ning et al., 2001; Chen et al., 2002, 2005). The objective function in the optimization model was designed
to minimize the costs for wastewater treatment and maximize the benefit due to in-stream water quality improvement while meeting water quality standards in all river reaches of concern. The associated shadow price linking each water quality constraint with the resource value of assimilative capacity in each river reach is a valuable index which reflects the possible transaction price in a transferable dynamic-discharge permit (TDDP) programs. It follows the idea raised by Freeman (1993) delineating how the values of these environmental and resource service flows emerge as shadow price from the solution of a welfare maximization problem. With such an assessment, estimating the possible market value of an environmental resource becomes much easier, which aids in decision making in the optimization context. The varying economic value of the environmental resource—river assimilative capacity—over space and time can then be elucidated via the optimization outputs. Once the optimal WLA scheme for all sub-basins in the study area is derived, the decision-making problems explored by the optimiza-tion model may include: (1) what would be the scale of shadow prices with respect to varying location and time in the river system? and (2) what is the waste reduction strategy for water pollution control associated with each sub-basin in the study area? The following optimization runs will cover the four planning scenarios aforementioned and answer these two questions.
The next few sub-sections are comprised of three parts. The first part focuses on the derivation of benefit and cost functions for use in the optimization analysis. The second part formulates the optimization model and performs the assessment of shadow price associated with each water quality constraint. The third part emphasizes the sensitivity analysis.
2.2.2.1. Benefit and cost functions. In the context of a benefit–cost analysis, the goal is to compare all of the benefits of the proposed program or policy to all of the costs. If the sum of all the benefits is greater than the sum of all the costs, then the program or policy is one of the candidates for decision makers to choose from. Shadow
Table 1
Planning scenarios for optimization analysis Selective items of
engineering project and control program
Case 1 dry season (present)
Case 2 dry season (target year)
Case 3 wet season (present)
Case 4 wet season (target year) Chin-Ho weir V Chiu-Chuang weir V Chi-Hisan weir V Yuan-Mei weir V Ai-Liao weir V Kao-Ping weir V
pig farming deduction program
V V
sewage treatment system V V
price associated with the water quality constraint may be viewed as the marginal cost of river assimilative capacity in this analysis (Freeman III, 1993;Salzman and Thompson, 2003). Assumptions being made here to simplify the benefit–cost analysis include: (1) the derived benefit for a whole population would be proportional to the derived benefit per person, (2) there is no need to wait until sufficient people are in the basin to initiate this scheme so that the total benefit can be used to offset the total cost, (3) there is no need to keep changing the quality standards to insure a positive net benefit as defined in the model, and (4) the treatment cost would not be a function of the population in this basin. Extended benefit–cost analysis with or without the inclusion of optimization or simulation analysis can be found elsewhere in the literature (Lind, 1995;Hollingworth and Mullins, 1995;Munda, 1996;Leu and Lin, 1998).
In decision analysis, the valuation of non-market service flows with regards to esthetic, ecological, and recreational values has generally become an essential part of bene-fit–cost analysis in water quality management programs and policies (Chen et al., 2005). Yet the in-stream water quality can be viewed as a fuzzy resource so that the valuation of such a resource should allow the interest
groups or affected parties to present more flexible and influential human judgment. The benefit function applied in this paper is directly drawn from a previous assessment based on the FCV method (Chen et al., 2005). Thus, the individual benefit function reflecting the implied economic value (B) is defined in terms of the possible improvement of BOD and DO in the river due to any measures, such as TMDLs, as shown below (Chen et al., 2005):
BðNT$=capita yearÞ
¼460 þ 231 DO 409 LnðBOD5Þ. ð1Þ
Besides, accurate prediction of construction and opera-tion costs of wastewater treatment facilities could signifi-cantly impact the economic feasibility at various levels in a water pollution control program. Therefore, an under-standing of the previous development of wastewater treatment plants and of the related construction and operation costs of those facilities becomes critical to handling an effective regional water pollution control program.Table 2lists part of the cost database excerpted from a previous study (Chen et al., 2002). The cost analysis, incorporating a complete database with 48 domestic wastewater treatment plants and 29 industrial
Table 2
Cost database applied for optimization analysis
Design for BOD5 removal Design for NH3-N removal
No. BOD5 (kg/day) Construction cost (million NT$)
Operating cost (million NT$)
No. NH3-N (kg/day) Construction cost (million NT$) A1 100 0.450 2.700 B1 605 800 A2 438 4.400 5.920 B2 500 1150 A3 625 6.890 10.960 B3 543 560 A4 750 3.910 9.696 B4 129 420 A5 800 4.460 10.380 B5 343 600 A6 825 3.010 7.040 B6 66 190 A7 875 4.810 18.520 A8 1250 12.330 8.540 A9 1250 9.190 13.340 A10 1500 14.220 11.060 A11 1500 9.330 — A12 1750 11.810 12.080 A13 2500 15.150 18.500 A14 2600 13.930 20.740 A15 2750 7.000 — A16 2750 10.930 17.556 A17 3000 13.370 12.444 A18 3000 13.370 14.074 A19 3000 18.330 — A20 3000 16.620 16.608 A21 3125 14.220 — A22 3125 20.930 11.112 A23 3750 18.520 — A24 4000 21.260 21.978 A25 5250 12.410 32.534 A26 5650 15.480 22.962 A27 6250 19.480 26.178 A28 6250 34.780 — A29 8375 32.440 27.704
wastewater treatment plants in Taiwan, implements a cost estimation procedure using fuzzy set theory. However, with the aid of an enlarged database compiled later on, the conventional least-squares regression method was applied to derive additional cost regression equations for use in this optimization analysis. The supplementary analysis covers 29 wastewater treatment plants designed mainly for BOD removal and 6 advanced wastewater treatment plants designed for NH3-N removal. Figs. 2(a) and (b) present two sets of scatter plots and associated regression equations of construction cost with respect to BOD and NH3-N removal rate. Fig. 3 shows a combined effort for deriving a regression equation of operation cost in terms of BOD and NH3-N removal simultaneously. With these three regression plots, the research findings clearly indicate that the newly derived linear regression equations exhibit fairly robust cost estimation with respect to R2 criteria (Chen et al., 2002). The derived equations are thus summarized below:
C1;BOD¼4:0141 þ 0:0033WBOD, (2a)
C2;BOD¼7:6155 þ 0:0030WBOD, (2b)
C1;NH3N¼230:95 þ 0:8401WNH3N, (3a)
C2;NH3N¼7:6155 þ 0:0030WNH3N, (3b)
in which C1 is the total construction cost of wastewater treatment (million NT$); C2is the total operation cost of
wastewater treatment on a yearly basis (million NT$/year); and WBODand WNH3Nare the total removal of BOD and
NH3-N in a wastewater treatment process (kg BOD5/day or kg NH3-N /day).
2.2.2.2. Optimization analysis. Systems analysis for water quality management often involves using optimization models for screening a variety of alternatives in association with technical, policy, economic, and institutional factors. The spectrum of applications may include WLA for water pollution control (Chen and Chang, 1998), optimal deployment of water quality monitoring stations (Ning and Chang, 2002, 2004; Ning et al., 2006), and planning, design and operation of regional sewer systems (Chang and Hernandez, 2006). A variety of functional forms for optimization analyses were derived and assessed to ensure the credibility and reliability in applications (Margeta, 1984; Vieira and Lijklema, 1989; Lee and Wen, 1996a, b; Chang et al., 1996a, b;Cardwell and Ellis, 1996;Somlyo´dy,
1997; Jolma et al., 1997; Onur et al., 1999; Chen and
Chang, 1998; Schu¨tze et al., 1999; Dorn and Ranjithan, 2003). To test the robustness of these strategies or to assess an independent policy, simulation analyses were often used to pinpoint insightful features on a river basin scale (Grayson et al., 1994;Hosoi et al., 1996;Ning et al., 2001). For policy makers who are responsible for handling TMDL programs, trading opens up new avenues to achieve better environmental goals at lower overall cost for which the policy maker has various parameters, such as trading ratios, trading transaction prices, and number of partici-pants, at his disposal. Linear programming-based analyses, driven by environmental and economic criteria, may ensure that the goal of final waste reductions can be achieved through the use of a ‘‘zone uniform treatment’’ approach in which river assimilative capacity is explicitly divided into a series of proportionate shares among sub-basins geogra-phically via an integrated simulation and optimization analysis (Chen and Chang, 2006). Such an optimal WLA scheme considers that the impact of pollution discharge at different sub-basins of a river system may differ in their abilities to assimilate the quantity and quality of the effluents because of varying flow rate and river environ-ment. The optimization model can be designed to maximize
(a) (b) 0 5 10 15 20 25 30 35 40 0 2000 4000 6000 8000 10000 W (kg-BOD5 / day) C1 (million NT$ ) C1=4.0141+0.0033×W R2=0.7168 0 100 200 300 400 500 600 700 800 900 0 100 200 300 400 500 600 700 W (Kg-NH3-N/day) C1 (million NT$) C1=230.95+0.8401×W R2=0.7942
Fig. 2. (a) Scatter plots of total construction cost with respect to BOD removal. (b) Scatter plots of total construction cost with respect to NH3-N removal. 0 5 10 15 20 25 30 35 0 2000 4000 6000 8000 10000 W (kg-pollutant / day) C2 (million NT$ / year) C2= 7.6155+0.0030×W R2 = 0.7152
Fig. 3. Scatter plots of annual total operation cost with respect to BOD and NH3removal.
the net benefit (i.e., aggregate social welfare) or minimize the net treatment cost, while ensuring all the effluents generated in those sub-basins are treated for compliance with the water quality standards in all reaches collectively. Thus, the possible benefit gained and cost saved in the context of the proposed zone uniform treatment model must be substantial such that the shadow price represents the economic value that should be economically paid off when gaining an additional unit of assimilative capacity in a specified reach. This study therefore goes by a two-stage analysis in which a simulation model provides dynamic trading ratios in both wet and dry seasons in the first stage, and the optimization model with a zone uniform treatment scheme identifies the shadow price associated with each reach of concern in the second stage. Thus, the shadow price drawn here may provide a firm basis for permits trading among those sub-basins located in the middle stream and downstream areas—the nonattainment re-gion—in the Kao-Ping River system, given the fact that information on trading ratios is available.
In the following model formulation, the objective function is defined to maximize the net benefit, while the constraint set consists of mass balance for stream flow, mass balance for pollutants and water quality constraints. The choice variable (i.e., decision variable) that appears in both the objective function and the constraint set is the total pollutant removal by weight (Wmi) in each sub-basin. The time frame applied in the objective function is equivalent to the life cycle of wastewater treatment facilities. But initial investment can be amortized and cash flows from different expenditure can be aggregated on an annual basis. As a result, the objective function is made up of both benefit and cost components in conjunction with the functional forms derived beforehand. The model formulation in the context of the WLA scheme may then be used to suggest allowable discharge levels from individual sub-basins to the river system and enables decision makers to look into the spatio-temporal distribu-tion of WLA across all sub-basins at the same time. Sensitivity analysis associated with such a benefit–cost analysis framework may enable us to justify relevant uncertainties in regard to any specific scenario of WLA. Within the modeling system, the river system of interest is classified as several river reaches and each reach is discretized into several elements to ease the calculation. The monetary value used in the modeling analysis is the new Taiwan dollars (NT$), and the currency rate of US Dollars was 1US$ ¼ 33NT$ in 2005 on average. The model is thus formulated for addressing the multi-pollutant impacts as below: Max ¼ X i X m X t Bm ð1 þ rÞtPOPi X i X m Cm1Wmiþ X t Cm2Wmi ð1 þ rÞt ! ð4Þ s.t.:
(A) Mass balance constraint for stream flow: This con-straint ensures the mass balance principle with regard to the flow rate must be held in each reach,
Qi¼Qði1Þþqiq0
i 8i 2 R [ R0 (5)
(B) Mass balance constraint for pollutants of concern: This constraint ensures the mass balance principle with regard to the pollutants of concern must be held in each reach.
QiLmi¼Qði1ÞLmði1ÞXmði1ÞþqiLmiq0iLmiXmi 8i 2 R; m, (6)
Lmi ¼F ðW0;miWmiÞ=qi 8i 2 R; m, (7)
W0;mi¼WmiþW0mi 8i 2 R; m. (8)
(C) Water quality constraint: This constraint guarantees the compliance with the prescribed water quality standards with respect to all pollutants of concern in each sub-basin,
Lmipð1 ÞLmi;std 8i 2 R; m. (9)
(D) Technical constraint: This constraint provides a reasonable range of removal efficiency for all pollu-tants of concern from an engineering perspective,
Wmi¼W0;mipZm 8i 2 R; m. (10)
(E) Nonnegativity constraint: All decision variables are nonnegative.
in which r is the interest rate (%); Bmis the derived per capita benefit based on several designated water quality improvement measures that ameliorate the water quality condition in association with both BOD and DO levels (NT$/capita/year) (i.e., see Eq. (1)); POPiis the population who benefit from the water quality improvement measures in sub-basin i (capita); T is the average life time of wastewater treatment facilities (year); R is a set of all elements connected to the outlet of sub-basins; R0 is a set
representing the rest of the elements which do not have a direct connection to the outlet of sub-basins; Cm1 is the amortized construction cost of wastewater treatment facilities for removing mth pollutant of concern (million NT$) (i.e., see Eqs. (2)–(3)); Cm2 is the annual operating cost of running wastewater treatment facilities for remov-ing mth pollutant of concern (million NT$) (i.e., see Eqs. (2)–(3)); F is a conversion factor associated with the yearly time frame (unitless); Wmiis the total removal by weight of mth pollutant of concern in the ith element connected with a sub-basin (kg BOD5/day); Qiis the flow rate in the end of each ith element (cms); Qi1 is the inflow at the starting point of each ith element (cms); qi is the inflow of
wastewater within the ith element (cms); qi0 is the water withdrawn from the ith element (cms); Lm(i1) is the concentration of mth pollutant of concern in the (i1)th element connected with a sub-basin (mg/L); Lmi is the concentration of mth pollutant of concern in the ith element connected with a sub-basin (mg/L); Xmi is the residual water pollution impact of the mth pollutant of concern in the ith element connected with a sub-basin (unitless) (i.e. there is a close tie between a trading ratio and a corresponding Xmi); W0,miis the total waste load of mth pollutant of concern by weight in the ith element connected with a sub-basin (kg pollutant/day); Wmiis the total waste reduction of mth pollutant of concern by weight in the ith element connected with a sub-basin (kg pollutant/day); Wmi0 is the total mth pollutant of concern by weight discharged into the ith element connected with a sub-basin (kg pollutant/day); ti is the time required for stream flow passing through the ith element connected with a sub-basin (day); Lmi,std is the prescribed water quality standard of mth pollutant of concern in the ith element connected with a sub-basin (mg/L); e is the percentage used for the margin of safety (%); and Zmis the optimal removal efficiency of the mth pollutant of concern in wastewater treatment. 3. Sensitivity analysis
Flow rate in the river bears the largest portion of uncertainties in this analysis. Sensitivity analysis was organized to examine the stability of transaction prices (i.e., the shadow prices). Four additional scenarios designed for sensitivity analysis were arranged to correlate the uncertainty in flow rate regimes with changes in corresponding shadow prices in these river reaches. Differing design flow rate (Q50) conditions with respect to the levels of 0.7Q50, 0.9Q50, 1.1Q50, or 1.3Q50were adopted in these four scenarios, respectively. Thus, each indepen-dent optimization run organized with respect to a specified design flow rate slightly deviating from Q50 may be performed to generate a set of transaction prices basin-wide. Work conducted in this sub-section thus reflects systematic uncertainties at the watershed level that might affect the dynamic permit-trading scheme.
4. Results and discussion
For ease of demonstration, the sub-basins of concern in this study were numerically assigned from 1 to 13 (seeFig. 4). Polluters within the same sub-basin may be subject to the common permit-trading ratios in relation to those in other sub-basins in the TMDL program. The trading ratio between each paired sub-basin was drawn from a series of QUAL2E simulation runs with respect to the target pollutant. The outputs were summarized by using a hybrid two-dimensional matrix organized in terms of both BOD and NH3-N associated with both dry and wet seasons simultaneously (seeTable 3). Ratios listed inTable 3reveal the relative impacts of wastewater discharge into the river
in different seasons comparatively. For example, the ratio of 1.832:1, as indicated at the lower-left corner ofTable 3, means 1.832 units of BOD waste load reduction in sub-basin 13 is equivalent to 1.000 unit of BOD waste load reduction in sub-basin 1 in the dry season. This also implies that the polluters in sub-basin 13, where was classified as a zone with severe pollution in the context of a zone uniform treatment approach, need to pay more in order to acquire the same allowance or credit as compared with those located in sub-basin 1. On the other hand, it also means for one unit of BOD waste load disposed of into the river in sub-basin 1, only a fraction of 0.546 (i.e. 1/1.832) of BOD waste load could eventually appear in the river reaches connected with sub-basin 13 due to the effects of diffusion, dispersion, and transformation in the fate and transport process. A similar conclusion can be drawn with respect to any paired sub-basins listed in Table 3. Overall, planning scenarios arranged for these two dry seasons assessed in different years may exhibit completely different trading ratios, which reflect the full impact of implementation of water redistribution and pollution prevention actions. So over the time horizon the variations of water quantity and quality in each reach would be obvious and different costs and benefits terms incurred due to such variations would definitely impact the final decision making.
To protect water quality in the proximity of water intakes located downstream and primeval forests in the middle and upstream area, decision makers would prob-ably not allow the trades to happen between upstream and downstream sources. Hence, possible transactions may most likely occur around the vicinal sub-basins, since the trading ratios between them may not have too much disparity. Marginal advantages can still be gained in such trading though. Given the fact that most forested land, grassland, and orchards are located around the upstream and middle stream areas, and industrial parks and cities are scattered around the downstream areas in the Kao-Ping River Basin, the opportunity of permit trading between point and non-point sources could be very slim. If such trading happens, it could result in some hot spots in downstream areas. Even though the control cost for non-point sources is generally less than that for non-point sources such trading should not be applied. This is also the main reason why we excluded the trading scenarios between point and non-point sources in the beginning.
Based on the planning scenarios arranged inTable 1, the optimization model would be able to incorporate highly nonlinear interactions between BOD, DO, and NH3-N in the water body and deliver such links into the water quality constraints in an effort to achieve possible tradeoffs between relevant costs and benefits terms. The problem solution, as a consequence, considers the impacts of water resources redistribution within and between two river systems and manifests a large variety of water quality con-ditions due to the natural variations of flow rate between dry and wet seasons and the man-made impacts from water resources redistribution and pollution prevention actions.
Such an optimization model is proved useful to cover greater flexibility in representing the complexity of various possible management alternatives in the Kao-Ping River Basin, south Taiwan.
The software package LINGOswas used as a computer solver in this analysis.Table 4lists the optimal solution of WLA with respect to various cases, in which case 1 is the most critical one in this study. Differing planning scenarios may result in different WLA schemes and associated utilization patterns of assimilative capacity. In general,
once the situation of water pollution impact in the dry season can be controlled, the water quality in the wet season may be confirmed. Table 5 summarizes all the optimal WLA patterns corresponding to these prescribed cases.
The associated costs and benefits terms in most sub-basins may then be assessed collectively to justify the final decisions. There are some negative values of net benefits in some sub-basins. This is due to the fact that the population residing in those sub-basins is too low to accumulate
Table 3 Matrix of tr ading ratio in terms of BO D and NH 3 -N
Table 4 Optimal control st rategy by zone uniform treatm ent appro ach wi thin the TMDL stud y area of the Kao-P ing Rive r Basi n No. of draina ge basin Case 1 (dry seas on) C ase 3 (we t seas on) Remo val efficiency (%) Remo val by weight (kg /day ) C ost (1 0 6NT$) Be nefit (1 0 6NT$) Ne t total be nefit (1 0 6NT$) Remo val efficiency (%) Remo val by weight (kg/d ay) C ost (1 0 6NT $) Be nefit (1 0 6NT $) Ne t total be nefit (1 0 6NT $) BO D N H3 -N BO D N H3 -N BOD NH 3 -N BOD NH 3 -N (a) Present 1 95.00 28.31 1,844 .95 44.08 420.3 3 224.5 9 195.7 4 0.00 0.00 0.00 0.00 0.00 224.5 9 224.5 9 2 95.00 69.50 470.0 0 104.52 425.8 7 272.8 4 153.0 3 0.00 0.00 0.00 0.00 0.00 272.8 4 272.8 4 3 53.72 86.10 2,196 .88 1,257.46 1,493 .56 683.3 0 810.2 6 0.00 0.00 0.00 0.00 0.00 683.3 0 683.3 0 4 0.00 80.30 0.00 178.97 474.8 1 94.64 380.1 8 0.00 0.00 0.00 0.00 0.00 94.64 94.64 5 50.02 85.81 589.3 5 534.30 805.8 3 110.8 5 694.9 8 0.00 0.00 0.00 0.00 0.00 110.8 5 110.8 5 6 49.42 87.87 257.9 7 286.60 577.8 1 56.21 521.6 0 0.00 0.00 0.00 0.00 0.00 56.21 56.21 7 10.74 89.62 504.4 0 5,834.68 5,438 .14 497.5 3 4,940 .61 0.00 0.00 0.00 0.00 0.00 497.5 3 497.5 3 8 0.00 63.46 0.00 132.53 434.2 0 78.74 355.4 7 0.00 0.00 0.00 0.00 0.00 78.74 78.74 9 0.00 0.00 0.00 0.00 0.00 270.9 1 270.9 1 0.00 0.00 0.00 0.00 0.00 270.9 1 270.9 1 10 64.38 90.65 6,788 .01 5,716.53 5,551 .03 1,065 .03 4,486 .01 0.00 0.00 0.00 0.00 0.00 1,065 .03 1,065 .03 11 0.00 11.05 0.00 18.38 334.3 7 426.1 4 91.77 0.00 0.00 0.00 0.00 0.00 426.1 4 426.1 4 12 70.80 91.09 7,655 .27 11,180.76 10,35 9.40 3,822 .76 6,536 .63 0.00 22.04 0.00 2,064 .81 2,124 .00 3,822 .76 1,698 .77 13 93.93 92.97 7,569 .09 5,834.08 5,680 .71 873.2 3 4,807 .48 0.00 0.00 0.00 0.00 0.00 873.2 3 873.2 3 Total 27,87 5.93 31,122.90 31,99 6.07 8,476 .77 23,51 9.30 0.00 2,064 .81 2,124 .00 8,476 .77 6,352 .78 (b) Ta rget year 1 0.00 0.00 0.00 0.00 0.00 224.5 9 224.5 9 0.00 0.00 0.00 0.00 0.00 224.5 9 224.5 9 2 0.00 0.00 0.00 0.00 0.00 272.8 4 272.8 4 0.00 30.07 0.00 33.02 347.1 8 272.8 4 74.34 3 0.00 0.00 0.00 0.00 0.00 683.3 0 683.3 0 0.00 0.00 0.00 0.00 0.00 683.3 0 683.3 0 4 0.00 0.00 0.00 0.00 0.00 94.64 94.64 0.00 0.00 0.00 0.00 0.00 94.64 94.64 5 0.00 0.00 0.00 0.00 0.00 110.8 5 110.8 5 0.00 0.00 0.00 0.00 0.00 110.8 5 110.8 5 6 0.00 0.00 0.00 0.00 0.00 56.21 56.21 0.00 0.00 0.00 0.00 0.00 56.21 56.21 7 0.00 0.00 0.00 0.00 0.00 497.5 3 497.5 3 0.00 0.00 0.00 0.00 0.00 497.5 3 497.5 3 8 0.00 0.00 0.00 0.00 0.00 78.74 78.74 0.00 0.00 0.00 0.00 0.00 78.74 78.74 9 0.00 0.00 0.00 0.00 0.00 270.9 1 270.9 1 0.00 0.00 0.00 0.00 0.00 270.9 1 270.9 1 10 0.00 0.00 0.00 0.00 0.00 1,065 .03 1,065 .03 0.00 0.00 0.00 0.00 0.00 1,065 .03 1,065 .03 11 0.00 0.00 0.00 0.00 0.00 426.1 4 426.1 4 0.00 0.00 0.00 0.00 0.00 426.1 4 426.1 4 12 35.22 22.88 3807 .64 346.49 752.3 3 3,822 .76 3,070 .44 0.00 0.00 0.00 0.00 0.00 3,822 .76 3,822 .76 13 90.68 83.55 7307 .98 2241.05 2,529 .59 873.2 3 1,656 .36 0.00 0.00 0.00 0.00 0.00 873.2 3 873.2 3 Total 11,11 5.62 2,587.54 3,281 .92 8,476 .77 5,194 .86 0.00 33.02 347.1 8 8,476 .77 8,129 .59 *The currenc y ratio is 33 NT$/1 US$ in 2005.
enough implied economic value via water pollution control while the costs required for NH3-N removal are relatively high.Fig. 4shows the shadow prices distribution in terms of different locations and time when both BOD and NH3 -N are taken into account. Since assimilative capacity in most areas is not a binding resource, its associated shadow prices are equal to zero (i.e., no sensitivity in an economic sense).
Given such pricing structures, the benefits gained via the improvement of water quality in the river must be substantial enough to justify the necessary administrative efforts required to develop a sound permit-trading program. To increase the administrative feasibility, using a uniform treatment approach with equity concerns might merit more credit than applying a zone uniform treatment approach in the short-run. But the cost incurred in a uniform treatment approach should be higher than any other approach. In any circumstance, possible considera-tion of a TDP for ammonia-nitrogen in the downstream area is highly recommended to reduce the nitrogen impact resulting from pig farming in the long run. Otherwise, the disposal fee (or effluent tax) mandated for effluent discharge in terms of NH3-N or BOD could be used as an alternative policy instrument for achieving the same goal. Both policy instruments (i.e., effluent tax and permit trading), however, help internalize the external cost from the societal point of view.
Sensitivity analyses addressing the uncertainties of assimilative capacity via the use of shadow prices may confirm the reliability of the research findings as described above. In the original settings, Q50 is the design flow rate for both simulation and optimization analyses. A decrease of 30% (0.7Q50) and 10% (0.9Q50) and an increase of 10% (1.1Q50) and 30% (1.3Q50) of the original design flow rate would be a realistic test for sensitivity analyses. Shadow prices associated with all the changes are listed inTable 6.
Figs. 5(a) and (b) further summarize the percentage
changes of shadow prices in response to the variation of design flow rate. In any circumstances, if such a variation
in flow regime can change the shadow price from zero to a non-zero value, the impact is deemed critical, and hence the variation is expressed by ‘‘100%’’ inFigs. 5 and 6. On the contrary, if such a variation in flow regime can change the shadow price from a nonzero value to zero, the impact is also deemed critical, and hence the variation is expressed by ‘‘100%’’ in Figs. 5 and 6. The situation of shadow prices in the dry season at present (i.e. case (1)) is the most sensitive one in terms of both pollutants. It can be seen that the change of design flow rate in case (1) may even result in a structure change of shadow prices when pricing the environmental resources (i.e., assimilative capacity). In cases (2)–(4), the shadow prices associated with BOD and NH3-N decrease with the increase of design flow rate due to the increasing assimilative capacity. Conversely, low-ering the design flow rate may cause a decrease in assimilative capacity. This is evidenced by the changes in the corresponding shadow prices in the 13th sub-basin in case (3), as indicated inFig. 5, and in the 2nd and 11th sub-basins in case (3), as indicated inFig. 6. Although some of the shadow prices in various sub-basins decrease with the increase of design flow rate, such as the 5th and 13th sub-basins associated with BOD and the 3rd, 4th, 5th, 7th, 11th, 12th, and 13th sub-basins associated with NH3-N, the others cannot conform to such a general rule-of-thumb. For example, in the 4th sub-basin, the shadow price associated with BOD in the scenarios of using 0.7Q50and 0.9Q50actually decrease as compared to the case of using Q50in case (1), as indicated inFig. 5.
Owing to the trade-offs between costs and benefits in the context of optimization, the 2nd and 3rd sub-basins in the middle and upstream areas need to reduce pollution loadings in order to diminish the stress on less assimilative capacity downstream. Yet the shadow price associated with NH3-N in the 8th sub-basin is not consistent with such an observation in case (1), as indicated in Fig. 6. When the design flow rate was changed from 1.1Q50 to 1.3Q50, the shadow price associated with NH3-N actually increased from zero to 999.8 NT$/kg. It is mainly because the
Table 5
A summary of the waste load allocation in this study (unit: kg-pollutant/day)
No. of drainage basin Dry season at present Wet season at present Dry season on-target year Wet season on-target year
BOD NH3-N BOD NH3-N BOD NH3-N BOD NH3-N
1 97.10 111.63 1,942.06 155.71 383.06 9.46 383.06 9.46 2 24.74 45.87 494.73 150.39 127.88 109.82 127.88 76.80 3 1,892.99 203.00 4,089.88 1,460.46 806.04 72.14 806.04 72.14 4 709.05 43.92 709.05 222.89 125.32 12.34 125.32 12.34 5 588.99 88.35 1,178.34 622.65 197.00 17.39 197.00 17.39 6 263.99 39.58 521.96 326.19 48.82 7.87 48.82 7.87 7 4,192.40 675.92 4,696.80 6,510.60 64.42 61.98 64.42 61.98 8 84.94 76.33 84.94 208.86 28.96 28.44 28.96 28.44 9 0.74 0.86 0.74 0.86 26.97 0.14 26.97 0.14 10 3,755.50 589.87 10,543.51 6,306.40 308.05 292.90 308.05 292.90 11 216.95 147.96 216.95 166.34 28.94 74.75 28.94 74.75 12 3,156.85 1,093.96 10,812.12 9,569.37 7,004.73 1,167.72 10,812.37 1,514.21 13 489.07 441.21 8,085.16 6,275.29 750.89 441.24 8,058.87 2,682.29
Table 6 Outpu ts of sen sitivity ana lyses of sha dow pric es (unit: NT$/k g-pollu tant No. of dra inage basin BOD NH 3 -N Case 1: dry seas on at pre sent Case 2: dry season on -target yea r Case 1: dry seas on at present Case 2: Dry seas on on -target year Q50 0.7 Q50 0.9 Q50 1.1 Q50 1.3 Q50 Q50 0.7 Q50 0.9 Q50 1.1 Q50 1.3 Q50 Q50 0.7 Q50 0.9 Q50 1.1 Q50 1.3 Q50 Q50 0.7 Q50 0.9 Q50 1.1 Q50 1.3 Q50 1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2 0.0 0.7 0.7 0.7 0.0 0.0 0.0 0.0 0.0 0.0 101.1 96.6 95.9 103.8 102.8 0.0 2149 .7 0.0 0.0 0.0 3 0.0 1.3 0.8 1.0 1.0 0.0 0.0 0.0 0.0 0.0 142.0 164.6 145.6 141.2 124.2 0.0 0.0 0.0 0.0 0.0 4 12.9 3.8 3.7 3.0 2.8 0.0 0.0 0.0 0.0 0.0 424.8 515.3 452.9 400.3 379.8 0.0 0.0 0.0 0.0 0.0 5 1.1 1.3 1.2 1.0 1.0 0.0 0.0 0.0 0.0 0.0 145.4 173.5 149.5 142.6 134.8 0.0 0.0 0.0 0.0 0.0 6 2.5 1.3 2.7 2.4 2.2 0.0 0.0 0.0 0.0 0.0 263.3 330.7 276.7 55.5 231.0 0.0 0.0 0.0 0.0 0.0 7 0.0 5.6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 382.1 437.0 386.7 0.0 0.0 0.0 0.0 0.0 0.0 0.0 8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 595.3 689.4 635.9 0.0 999.8 0.0 0.0 0.0 0.0 0.0 9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 10 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 314.7 373.4 324.3 816.2 0.0 0.0 0.0 0.0 0.0 0.0 11 0.6 0.0 0.8 0.0 0.7 0.0 0.0 0.0 0.0 0.0 4786.5 6004.2 5102.1 4528.3 4130.7 0.0 0.0 0.0 0.0 0.0 12 18.7 18.7 14.9 12.5 10.9 0.6 0.7 0.6 0.5 0.5 847.5 1005.4 888.5 813.9 762.5 847.5 1005 .4 888.4 813.6 762.9 13 21.3 26.3 22.4 21.0 19.0 21.3 25.6 22.4 20.4 19.0 2843.5 3416.9 2992.2 2722.0 2534.8 2843.5 3416 .6 2992 .0 2722 .0 2534.6 Case 3: wet season at presen t Case 4: wet seas on on-target year Case 3: wet seas on at pre sent Case 4: wet seas on on-ta rget year Q50 0.7 Q50 0.9 Q50 1.1 Q50 1.3 Q50 Q50 0.7 Q50 0.9 Q50 1.1 Q50 1.3 Q50 Q50 0.7 Q50 0.9 Q50 1.1 Q50 1.3 Q50 Q50 0.7 Q50 0.9 Q50 1.1 Q50 1.3 Q50 1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2149.7 0.0 0.0 0.0 1164.4 1449 .7 1264 .5 998.3 468.9 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 7 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 10 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 11 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 24638.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 12 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 18902.1 19852.7 19148.1 18699.2 18390.6 0.0 0.0 0.0 0.0 0.0 13 0.0 141.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
increase of design flow rate causes the diminution of pollution reduction in the upstream area, as shown in the 7th sub-basin, and the accumulated pollution loadings associated with NH3-N system wide would call for more waste reduction associated with NH3-N downstream. These capricious regions could be treated as the highest sensitive areas for pricing the assimilative capacity in the TMDL program. Finally, given the changing natural environment and engineering infrastructure, the pricing
model may estimate time- and location-varying shadow prices (transaction prices) associated with BOD and NH3 -N using an iterative or re-optimization process in support of a permit-trading market over time.
5. Conclusion
Work presented in this article analyzed watershed-based permitting strategy and water pollutant trading scenarios
drainage basin
shadow prices variation (%)
0.7Q 0.9Q 1.1Q 1.3Q -100 -80 -60 -40 -20 0 20 40 60 80 100 -100 -80 -60 -40 -20 0 20 40 60 80 100 drainage basin
shadow prices variation (%)
0.7Q 0.9Q 1.1Q 1.3Q -100 -80 -60 -40 -20 0 20 40 60 80 100 1 3 5 7 9 10 11 12 13 drainage basin
shadow prices variation (%)
0.7Q 0.9Q 1.1Q 1.3Q -100 -80 -60 -40 -20 0 20 40 60 80 100 drainage basin
shadow prices variation (%)
0.7Q 0.9Q 1.1Q 1.3Q
dry season at present
dry season at target year
wet season at present
wet season at target year (1) (2) (3) (4) 2 4 6 8 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7 8 9 10 11 12 13
in a TMDL program at the watershed level. It uses a two-stage analysis framework to assess two vital water quality indicators (i.e., BOD and NH3-N) in association with a given number of participants (i.e., 13 sub-basins). Estima-tions of trading ratios are proved useful and informative via the use of QUAL2E simulation analysis accounting for the dynamic features of the river system. Such a simulation tool may further support the possible changes system wide, which can be assessed through a re-optimization or an
iterative process resulting in different WLA schemes. The use of the zone uniform treatment approach for optimizing the WLA in the watershed plays a central role in multiple criteria decision making. The criteria of concern in the study include cost, benefit, location of effluent discharge, time-varying pricing strategy, multiple pollutants, and administrative feasibility. Pricing assimilative capacity in response to spatial and temporal variations in a river system via the use of shadow price is deemed feasible. In
-100 -80 -60 -40 -20 0 20 40 60 80 100 1 3 5 7 9 10 11 12 drainage basin 13
shadow prices variation (%)
0.7Q 0.9Q 1.1Q 1.3Q -100 -80 -60 -40 -20 0 20 40 60 80 100 drainage basin
shadow prices variation (%)
0.7Q 0.9Q 1.1Q 1.3Q -100 -80 -60 -40 -20 0 20 40 60 80 100 drainage basin shadow pricesvariation (%) 0.7Q 0.9Q 1.1Q 1.3Q
dry season at present
dry season at target year
wet season at present
-100 -80 -60 -40 -20 0 20 40 60 80 100 drainage basin
shadow prices variation (%)
0.7Q 0.9Q 1.1Q 1.3Q
wet season at target year (1) 2 4 6 8 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7 8 9 10 11 12 13 (4) (2) (3)
