Developing Total Maximum Daily Loads Under Uncertainty: Decision Analysis and the Margin of Safety
2008; Wiley; Volume: 140; Issue: 1 Linguagem: Inglês
10.1111/j.1936-704x.2008.00027.x
ISSN1936-704X
Autores Tópico(s)Water Quality and Pollution Assessment
ResumoSection 303(d) of the U.S. Clean Water Act (CWA) (U.S. Code 1972) details requirements for individual states and the U.S. Environmental Protection Agency (EPA) to quantify existing contaminant levels and to take measures to improve water quality in impaired and threatened water bodies. These requirements include listing all impaired water bodies and conducting Total Maximum Daily Load (TMDL) analyses for all listed water bodies (33 U.S. Code 1313). TMDLs must be developed with stakeholder participation and consensus that often highlights conflicts between environmental and economic objectives (Chen et al. 2004). Local and regional socio-economic impacts, limited scientific ability to evaluate and predict future water quality, hydroclimatic and ecological variation, and rapid changes in regional demographics and land use are difficult to assess. Indeed, implementing regulations needs to be a dynamic process (Maguire 2003); TMDL decisions are made under significant uncertainty with various associated risks that must be evaluated over time. A plan must be developed to reduce pollutant input to the stream to a level below the TMDL with some margin of safety, by allocating the assimilative capacity of the stream for a particular pollutant among all sources. A report released by the National Research Council examining the scientific basis of the TMDL program, specifically suggests use of a, "Bayesian framework to determine preliminary probability distributions of impairment that can help direct monitoring efforts and reduce the quantity of monitoring data needed for making listing decisions at a given level of reliability" (National Research Council 2000). The report also specifically calls for a reconsideration of the use of margin of safety in the TMDL program, such that is becomes based on uncertainty analysis, rather than arbitrary assignment. These recommendations are addressed in this paper within a Bayesian Decision Network framework. Guidance documents provided by EPA (EPA 1991, 1997) represent the TMDL allocation problem as shown in Equation 1. The Clean Water Act requirement to take into account, "any lack of knowledge concerning the relationship between effluent limitations and water quality," (section 303(d)(1)(c)) presents an interesting opportunity to explore decision analysis in a risk management context. Of particular interest is the "margin of safety" shown in Equation 1. The margin of safety is presented in the Clean Water Act as follows: Such load shall be established at a level necessary to implement the applicable water quality standards with seasonal variations and a margin of safety which takes into account any lack of knowledge concerning the relationship between effluent limitations and water quality (CWA 303(d)(1)(c), emphasis added). Guidance from EPA regarding the margin of safety is generally sparse. One EPA TMDL guidance document states that the margin of safety "is normally incorporated into the conservative assumptions used to develop TMDLs…" (EPA 1991). It is not clear from this guidance what makes an assumption conservative enough to satisfy margin of safety requirements. Presumably this decision is left to an EPA regulator tasked with approving the TMDL. Other EPA guidance suggests that, "If the margin of safety needs to be larger than that which is allowed through the conservative assumptions, additional margin of safety can be added as a separate component of the TMDL." Here again is missing any guidance as to when conservative assumptions are not enough, or how much margin of safety needs to be added. In practice there is no consistent meaningful application of a margin of safety. Of 13 approved TMDLs listed on an EPA web site (http://www.epa.gov/OWOW/tmdl/case.html), six give no mention of a margin of safety, one arbitrarily set the margin of safety at 50 percent of the maximum load, and the remaining six simply include the following statement: The margin of safety … was incorporated through the conservative assumptions used during TMDL development. If these conservative assumptions had been deemed insufficient, an additional margin of safety would have been added. (Colorado Department of Environmental Quality 1997). These examples of guidance and sample TMDLs from EPA do not explicitly address the Clean Water Act requirement that the margin of safety should explicitly account for uncertainty. Conservative assumptions are only useful in a decision-making context when one can quantify how conservative the assumptions are. Additionally, the arbitrary addition of a number or a percentage to the anticipated load does not explicitly account for uncertainty in the load estimate itself. The Clean Water Act implies that lack of knowledge concerning the relationships in a watershed may result in an unsatisfactory estimate of contaminant load. This uncertain estimate carries with it the possibility or risk of violation of the water quality standard. The margin of safety is intended to reduce this risk of violation to some acceptable level. If one can quantify the risk of violating a stream standard given different management options, then risk serves as a means to evaluate alternatives. Each state and the EPA will potentially invest hundreds of millions of dollars in the TMDL program over the next several years (EPA 1996). Given the current five-year renewal cycle for TMDLs, this expenditure could continue indefinitely. A risk-based approach to the margin of safety has the potential to improve TMDL decision-making and ultimately reduce costs. This approach will be demonstrated through a synthetic TMDL case study in a following section. The TMDL program faces several challenges. One of the most significant of these is associated with socioeconomic analysis. The local and regional socioeconomic impacts of regulating land use and other activities as part of a TMDL are as yet unclear. This is problematic because the Clean Water Act specifically requires that an assessment be made of the "economic and social costs of meeting Clean Water Act objectives in each state" as well as the "economic and social benefits of such achievement." Another significant TMDL challenge is associated with uncertainty in data and models. In many cases, there is rather limited data on water quality and quantity and associated causative factors. The scientific ability to assess current and predict future water quality is limited given this paucity of data as well as the wide range of hydroclimatic and ecological variation and rapid changes in regional demographics and land use. Because of this, TMDL decisions are typically made under considerable uncertainty. In light of these requirements and challenges, there is a need for consistent and broadly applicable TMDL guidance. EPA has developed several guidance documents, such as Guidance for Water Quality based Decisions: The TMDL Process (EPA 1998a). Additionally, several states have also developed guidelines (e.g. Idaho Department of Environmental Quality 1999). These documents provide general principles for monitoring, priority ranking, and targeting of water bodies and TMDL development. EPA has also produced and released a GIS-based computer program, Better Assessment Science Integrating point and Nonpoint Sources (BASINS) (EPA 2001), which can be used to model contaminant input to streams from point and nonpoint sources. These and other EPA modeling tools (such as those listed in EPA 1998b) are provided to assess current and predict future in-stream water quality. Although EPA documents and models provide general guidance, they do not explicitly address the social and economic impact of TMDL allocation decisions or risk and uncertainty. A decision analytic framework for TMDLs that addresses these issues using probability analysis and Bayesian networks is explored in the remainder of this paper. Bayesian networks (Pearl 1988) are graphical, probabilistic models that explicitly account for risk and uncertainty in complex systems where causes and effects can be identified. A directed acyclic graph is used to represent the cause and effect relationships between variables in the system. Relationships between variables are defined through conditional probability distributions. This type of probabilistic framework lends itself to modeling complex systems of interrelated variables where relationships between variables are defined with some uncertainty. Additionally, Bayesian networks can be used to link decision variables to multiple separate endpoints. In this way, the probable effect of decisions can be propagated throughout the network and quantified at every variable. Equally useful is the ability of a Bayesian network to propagate the probable effect of an observation of any variable in the system to all other variables. A more complete introduction to Bayesian networks and their use is given in Pearl (1988) and Jensen (1996). There is some precedent for using Bayesian networks in watershed management, though not specifically for TMDLs. Haas and Cleaves (1997) applied a Bayesian network-based water eutrophication model on the Mokelumme River watershed in northern California. Additionally, work by Reckhow (1994, 1999) and Borsuk et.al (2001, 2004) demonstrates the application of Bayesian network uncertainty analysis on the Neuse River watershed. One of the motivations for using a Bayesian network in TMDL analysis is to produce results that can be interpreted in the context of risk and uncertainty. The TMDL equation (1) is usually interpreted in a very deterministic manner, suggesting that the total allocated pollutant load can never exceed the water quality standard. However, most state water quality regulations do allow for some exceedance of water quality standards (e.g. "only one out of the most recent ten observations shall exceed the water quality standard.") This inconsistency between TMDL guidance and water quality standards needs to be rectified. One approach is to recast Equation 1 in terms of risk of violating the standard: Here, the probability, P, of the total load from point (WLA) and nonpoint (LA) sources exceeding the TMDL, or water quality standard, must be less than some level of acceptable risk (LAR). This type of risk analysis is explored further in the context of a synthetic case study in a following section. Another motivation for applying Bayesian networks to TMDLs is because they provide a clear representation of the interconnections between management options, intermediate variables, water quality measures, and economic and ecological outcomes of interest. The first step to developing a Bayesian network model for TMDL decision analysis is to identify the outcomes or endpoints of interest. These may include economic costs and benefits to specific stakeholder groups as well as significant physical, chemical, or biological indicator variables. Next, management alternatives that may have an effect on these endpoints must be identified. Finally, a conceptual, causal network model of the system is developed that clearly identifies the physical and mechanistic connections between management alternatives, pollutant sources, natural and anthropogenic influences, intermediate variables, and important endpoints and outcomes of interest. This initial structure must be then be tested for validity and modified as needed so that all conditionally independent variables are represented as such. The drainage network of a watershed forms a natural structure around which to build a Bayesian network. Control points at stream confluences can be useful intermediate nodes in the network when they represent the state of the contaminant at that point. Figure 1 shows a network of control points extracted from a portion of the hydrologic network of the Teton River in eastern Idaho. Such a diagram defines the flow of information through the physical network to control points of interest for decision-making. Extraction of a network of control points from a hydrologic network. A portion of the hydrologic network of the Teton River watershed in eastern Idaho is shown in (A). A network of control points for probability modeling of a particular contaminant (e.g. sediment) extracted from the hydrologic network is shown in (B). This is extended to a Bayesian network in Figure 2. With the addition of management options, socioeconomic, ecological, and other endpoints to the network diagram, the Bayesian network becomes a complete graphical representation of the cause and effect relationships associated with a particular set of management decisions. Figure 2 shows how the Teton River Bayesian network might look for management of sediment loads. In this network diagram, rectangular nodes represent three management options. These include "BMP Implementation,""Reduce Road Density," and "Reduce Road Usage." The first management option, "BMP Implementation" is an agricultural "best management practice" in which farmers along Darby Creek control access of cattle to the stream. The two remaining management options relate to Forest Service management of unpaved roads used by recreators in the upper part of the Teton River. In this example, road density and road usage directly impact bank stability, which, in turn, impacts sediment loads in the upper Teton River. A possible Bayesian network for sediment management in the Teton River watershed. Management options (rectangular), endpoints (diamond-shaped) and intermediate nodes (rounded rectangles) complete the network. Diamond-shaped nodes represent endpoint outcomes of decisions. Agricultural costs and benefits result from BMP management and recreational costs and benefits result from management of Forest Service roads. Finally, attainment of the Salmonid spawning beneficial use of the Teton River at control points 3 and 4 is also represented in the network. The size of a Bayesian network, and hence the number of variables that need to be characterized to populate it, grows rapidly as one moves downstream or considers more processes. However, recognizing that the state of the process at a particular node is known conditional on the state of the upstream nodes, it is possible to "cut" the intermediate nodes out of the system. This allows one to focus in on the direct problems of consequence. For example, if all that is needed is an estimate of the management options impact on Salmonid spawning, then the Bayesian network in Figure 2 could collapse down into four nodes: the three management options and the beneficial use attainment node. However, it is likely that an analyst will also be interested in the risk of violation of the sediment water quality standard at the control points. In this case the full network may be needed. Note that even when a large network representation is produced, each node only depends on a few others. In this way, the Bayesian network is used to decompose a large and complex problem into a series of smaller problems that can be solved sequentially, and potentially more easily. Once a Bayesian network structure is defined, several sources of information can be used to populate the conditional probability distributions that connect network nodes. Potential sources of information include: at-site data or data from similar water bodies, results of mechanistic model simulations, expert opinion, and stakeholder surveys. Each of these sources of information will have varying degrees of reliability that may need to be explicitly accounted for in the conditional probability distributions. A primary goal of TMDL development is to accurately characterize the relationships between the physical, biological, chemical, and socioeconomic aspects of the system. Such a characterization should provide decision-makers with an assessment of the probability of beneficial use attainment and stakeholder costs and benefits under current conditions as well as under different management actions, climate conditions and changes in demographics or land use. In an ideal case, characterization of the system through conditional probability distributions would be completed though the use of historical at-site data. For example, measurements of the target contaminant at the control point under a variety of historical conditions could be used to estimate the conditional probability distribution relating those conditions to contaminant levels. In most cases, adequate at-site data for such a characterization are not available. Often this leads to the use of mechanistic watershed and receiving waters loading models to estimate contributions from different sources at specified control points under existing or projected conditions. Such models are intended to quantitatively describe different components of the hydrologic balance in the watershed including overland flow, infiltration, subsurface flow and channel flow. Physical, chemical and biological processes attendant to the fate and transport of contaminants through the hydrologic system can also be modeled. A computer model such as QUAL2E can be used for in-stream routing of contaminants (Brown 1987). Ames et al. (2005) use such an approach to derive conditional probability distributions for Phosphorous in East Canyon Creek, Utah using Monte Carlo simulations. Unfortunately, scarcity of data often makes the calibration and validation of such models difficult. Natural variability of meteorological parameters used to drive such models compounds the uncertainty associated with their use. Consequently such models are best used in a diagnostic rather than predictive context. Specifying scenarios for natural variability (e.g., climate) and for management options (e.g., land use) and their respective likelihood can provide a diagnostic context. Factors that complicate the use of deterministic mathematical models include, but are not limited to, natural and human induced variability in loadings, seasonal variation in anticipated biological response, and the possibility of catastrophes or rare occurrences not accounted for in the model. In cases where at-site data are limited and mechanistic models are not suitable, information from similar water bodies can be used as part of a regional analysis to estimate the probable at-site conditions. This approach involves the use of a database of regional historical data and a set of nonparametric algorithms and classification methods to identify causal relationships in similar watersheds. The following steps could be followed to do this kind of analysis: (1) assemble a database on past loads and river flows over the river network; (2) identify key physical attributes of the watershed or reach in terms of drainage area, soil type, vegetative cover, land use, mean discharge, point loads, etc.; (3) identify similar reaches based on these attributes at other locations in the regional database; (4) develop probabilistic relationships for potential loading by sources given the selected attributes using similar reaches. An analysis such as this was used to estimate the concentration of phosphorous in tributaries to the Teton River based on physical characteristics of the tributary sub-watersheds. Characterization of point source loads can be done through the use of National Pollution Discharge Elimination System permit monitoring records at point source discharge facilities. These records can be used to estimate the average load of a contaminant to the receiving water as well as seasonal, diurnal, and annual variations. A probability distribution derived from such data may need to be augmented with data from similar point sources. For example, it may be that an estimate of the load from a point source under a new management alternative is needed. In this case, one could use data from a similar point source where the management option has been implemented (e.g. a similar wastewater treatment plant that is already using a proposed treatment method.) Another challenge for point source load estimation is accounting for potential upsets or equipment failures. These low probability events have the potential for being the most damaging to a natural system. In many cases, standard measures of economic welfare can be used as a metric to assess stakeholder cost or benefit levels. For example, profit levels for a factory owner or rancher can be used to quantify the costs or benefits resulting from specific management actions. Additionally, measures of consumer welfare can be used to quantify the benefits or costs incurred by recreational users of a water body as a result of different water quality levels. For example, the number of fish in the stream could be an indicator that contributes to recreational user welfare. Socioeconomic analysis can also be used to develop models of human behavior in response to uncertain variables. In this way, the operation of a farm or factory in response to climate or prices, for example, could be modeled in the Bayesian network as a predictor of pollutant loading from those sources. A Bayesian network framework for TMDL assessment provides a structured way to deal with issues of uncertainty and equitability as part of a collaborative management process. A key precept of this approach is that the focus is on the main interrelationships between variables, recognizing that available information is and will be incomplete. Thus the sensitivity of outcomes to decisions can be analyzed. For instance, a decision may be to collect additional data on nonpoint source contaminant loads. The question is whether it is useful to invest in this data collection effort. Given an initial assessment of the nonpoint source load and a proposed monitoring plan, the Bayesian network may be used to estimate the likelihood that that the collection of additional data will significantly change the nonpoint source load estimate. This is a type of sensitivity analysis where the effects of changes in one part of the system (e.g. fertilizer application on a farm) are propagated probabilistically throughout the system (e.g. to an estimate of stream loading). Such an analysis can be particularly useful when data collection funds are limited and must be directed where the resulting information is most likely to be important. Take as another example the decision to establish a riparian buffer of a certain width along a stream segment to reduce the amount of nonpoint source pollutants reaching the stream. For such a decision, an analyst may choose complex modeling of surface-subsurface flow interactions, leaching processes, overland flows and pollutant transport for a variety of climatic scenarios. In a probabilistic modeling framework, the analyst could also use the results from prior applications of such models or historical at-site data or data from other stream reaches where a similar situation exists. Whatever the source of information chosen, the focus is organizing and analyzing system interconnections in the context of a decision process rather than on detailed modeling of the ambient processes themselves. A Bayesian network approach focuses on risks associated with watershed management activities. Such risk can be defined in terms of cost (what is the probability that the management plan will cost a certain amount?), standard violation (what is the probability that temperature will exceed some value for a particular period of time?), or ultimate stream health (what is the probability that observed numbers of macro-invertebrates will be less than expected?) In each case, the goal of watershed management is to reduce risk to a level that is acceptable to the affected parties — local stakeholders and regulators alike. A complete Bayesian network can be used to evaluate the cost, benefit, and risk associated with management options. Costs and benefits derived by or allocated to each stakeholder for each management option can be identified. Ultimately, decision-makers are presented with the probability of success (or risk of failure) of each management option and can presumably make decisions that have a low risk of failure and a high probability of benefiting stakeholders in an equitable manner. Consider a watershed with a single stream as illustrated in Figure 3. Assume that the only designated beneficial use of the stream is "coldwater biota" and that it has historically supported a blue ribbon trout fishery. Additionally, assume that the stream is 303(d) listed for only one pollutant, biochemical oxygen-demanding organic matter (BOD). BOD loadings to the stream tend to reduce the amount of dissolved oxygen available to trout, thereby impacting the trout fishery. For water quality accounting purposes, the stream has been divided into three reaches corresponding to three divisions in the watershed (Figure 3). A TMDL would potentially have to be written for each of these 3 reaches. For the purposes of this case study, only conditions at the outlet of the watershed will be considered. Diagram of a synthetic watershed for TMDL analysis. In this watershed, a single stream passes through U. S. Forest Service lands, cattle grazing lands and urban lands. A nonpoint source (cattle ranch) and a point source (sugar beet factory) are identified. Additionally, two management alternatives are shown. These include forming a riparian buffer in the grazing lands to separate cattle from the stream, and building a wastewater treatment plant at the sugar beet factory. Three sources of BOD loading to the stream are considered. These include natural unregulated sources, primarily in the Forest Service lands; a diffuse, nonpoint source along the length of Reach 2 associated with cattle at the ranch; and one point source, the sugar beet factory. It is assumed that there is no interest in trying to control the natural sources of BOD to the stream, but that some regulation of loads due to the ranch and the sugar beet factory may be needed to maintain dissolved oxygen water quality standards at the watershed outlet. The possibility of such regulation on the rancher and factory owner gives them a strong interest to participate in the TMDL development process for this stream. Another significant stakeholder group in this scenario is composed of recreational anglers who use the blue ribbon trout fishery in Reach 3. This stakeholder group does not significantly impact water quality, but benefits from water quality improvements and is highly supportive of actions that would reduce loadings of BOD to the stream. In addition to the factory owner, the rancher, and the trout anglers, federal and state agencies such as the EPA and state Department of Environmental Quality are also stakeholders in this process. Typically the primary interest of the agency stakeholders is successful completion of the TMDL process, rather than some particular interest associated with sugar beets, trout, cattle, or BOD. The set of load allocation management alternatives should include all options and combinations of options available to the decision-makers in the system. This set of all management options is likely to be large and of high dimension. Some options may not result in BOD allocations that satisfy the TMDL requirement, or do so only at prohibitive cost to the stakeholder community. This cannot be fully determined until the impact of each option is assessed through modeling of the physical and socioeconomic system. The challenge for the EPA, Department of Environmental Quality and stakeholders is to identify management options that ex ante appear to provide a high likelihood of meeting the management objectives. Other considerations for reducing the set of options to be considered may be political. For instance, best management practices (BMPs) can be implemented through incentive-based EPA and National Resource Conservation Service programs. If BMPs on the cattle ranch appear to have a high probability of reducing BOD and satisfying the TMDL, they are a logical choice to be considered in the set of management options that are examined in detail. It may be the case that few legally enforceable load allocation options are available. In this event, other considerations can be used to focus on the management options that are most likely to provide a solution to the TMDL management problem. For example, informal estimates of point and nonpoint BOD loading or informed guesses as to the costs of reducing BOD loading can reduce the set of management options to be considered. For this case study, only management alternatives at the ranch and at the sugar beet factory are considered. In particular, the rancher has two alternatives, either do nothing (status quo) or implement a BMP. The proposed BMP, as shown in Figure 3, involves building fences to create a riparian buffer zone of a specified width along the stream to protect it from direct inputs of cattle manure. Management alternatives available to the factory owner include operating under existing NPDES permits (status quo) or building a wastewater treatment facility. The proposed wastewater treatment facility requires a significant expenditure by the factory owner to treat effluent waters, reducing BOD loadings. Potential management scenarios for the TMDL include all four combinations of the available management alternatives at the ranch and factory. Each of these scenarios translates into a different risk for violation of the dissolved oxygen standard in the stream and also to markedly different costs and benefits to the different stakeholders. A simple Bayesian network representation of this example case study is shown in Figure 4. Here the management alternatives described previously are shown as rectangular nodes in the diagram labeled Ranch BMP and Factory Mgmt. Ranch BMP has two potential states, Status Quo and Impose Riparian Buffer. If the option Impose Riparian Buffer is selected, the probable BOD loading from the ranch decreases. This presumably results in the probability of higher
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