Mathematical models can be used to predict changes in ambient water quality due to changes in discharges of wastewater. In Bank work, the context is typically establishing priorities for reduction of existing wastewater discharges or predicting the impacts of a proposed new discharge. Although a range of parameters may be of interest, a modeling exercise typically focuses on a small number such as dissolved oxygen, coliform bacteria or nutrients.
Predicting the water quality impacts of a single discharge can often be done quickly and sufficiently accurately with a simple model, while regional water quality planning will usually require a model with a broader geographic scale, more data, and more complex model structure.
Water quality models are usually classified according to the model complexity, type of receiving water, and the water quality parameters (dissolved oxygen, nutrients, etc.) that the model can predict.
The more complex a model is, the more difficult and expensive it will be to apply to a given situation. Model complexity is a function of four factors.
The number and type of water quality indicators. In general, the more indicators included, the more complex the model will be. In addition, some indicators are more complicated to predict than others (see Table 1).
The level of spatial detail. As the number of pollution sources and water quality monitoring points increase, the data required and the size of the model also increase.
The level of temporal detail. It is much easier to predict long-term, static averages than to project short-term dynamic changes in water quality. In addition, point estimates of water quality parameters are usually simpler than stochastic predictions of the probability distributions of those parameters.
The complexity of the water body under analysis. Small lakes that 'mix' completely are less complicated than moderate-size rivers. These in turn are less complex than large rivers, which are less complicated than large lakes, estuaries, and coastal zones.
The level of detail required can vary tremendously across different management applications. At one extreme, managers may be interested in the long-term impact of a small industrial plant on dissolved oxygen in a small, well mixed lake. This type of problem can be addressed in a simple spreadsheet, and solved by a single analyst in a month or less. At the other extreme, if managers want to know the rate of change in Black Sea heavy metal concentrations that can be expected from industrial modernization in the lower Danube, the task will probably require many person-years of effort with extremely complex models, and cost millions of dollars.
For the indicators of aerobic status such as biological oxygen demand (BOD) and dissolved oxygen (DO) and temperature, simple, well-established models can be used to predict long-term average changes in rivers, stream, and moderate-size lakes. The behavior of these models is well-understood, and has been studied more intensively than have other parameters. Basic nutrient indicators such as ammonia, nitrate, and phosphate concentrations can also be predicted reasonably accurately, at least for simpler water bodies such as rivers and moderate-size lakes. Predicting algal concentrations accurately is somewhat more difficult, but is commonly done in the US and Europe, where eutrophication has become a concern in the past two decades. Toxic organic compounds and heavy metals are much more problematic. Although some of the models reviewed below do include these parameters, the behavior of these materials in the environment is still an area of active research.
Models can only cover a limited number of pollutants and care should be taken in the selection of parameters for the model to chose those which are both of specific concern in themselves and which are also representative of the broader set of substances which cannot all be modeled in detail.
As one might expect, the data requirements for different models increase with the complexity and scope of application. As shown in Table 2, all models require data on flows and water temperature. Static, deterministic models require point-estimates of these, and often use worst-case 'design flow' estimates in order to capture the behavior of pollutants under the worst plausible circumstances. For most management purposes, the worst case will be high summer temperatures (since these exacerbate problems with dissolved oxygen and algal growth), and low flows, resulting in high concentrations of BOD and other pollutants. Dynamic models will need time-series data on flows, temperatures, and other parameters.
In addition to hydraulic data, models require base-case concentrations of the water quality parameters of interest (e.g., dissolved oxygen, mercury, etc.). These are required both to calibrate the models to existing conditions, and to provide a base against which to asses the effects of management alternatives. They will also need discharges or loads of the pollutants under consideration from the sources (e.g., industrial plants) being studied. The types and amounts of data needed for a given application are specific to the management question at hand.
Example Water Quality Models
Table 3 contains information on five representative water quality models, according to the criteria in Table 1, while Table 4 contains a textual description of each model. A large number of water quality models have been developed for particular watersheds, project-specific analyses, and other specialized purposes. In many cases, models are developed and used only once, for a particular project. In other cases, models are available only as proprietary, commercial software packages. The models in Table 3 were selected because they have been applied in a wide variety of management analyses, and because public-domain versions of the software are readily available. The list is, therefore, not intended to be exhaustive. Instead, the models shown in the table should be viewed as a representative sample of models that might be applied to a particular management problem. The section on 'Sources for Additional Information' includes references for the models discussed and comprehensive surveys of water quality modeling. The five models shown are used here as examples of the much broader class of representative models available for use. Their inclusion in the table should not be viewed as an endorsement or recommendation by the World Bank.
The models shown vary from simple analytical models (WQAM) suitable for approximating the water quality effects of individual industrial plants, to complex models that include a wide variety of pollutants and pollution sources (WASP). Of the five models, WASP is the only model that is potentially capable of handling all types of water bodies, management analyses, and water quality parameters under consideration. The others may well be sufficient for a problem where WASP’s complexity is not needed.
It is extremely important to recognize that the models or software packages only provide a framework for the analyses. Data specific to the watershed, industrial plant(s), and management scenarios will need to be gathered on-site to make any model operational. An economic analog might be the use of input-output (I/O) analysis of a regional economy. Although the framework (I/O tables arranged by economic sector, etc.) is the same regardless of the region or management question being analyzed, the data required will be very specific to the problem at hand. To carry the analogy a bit further, both water quality and I/O models often require some customization when applied to localized problems. In the case of I/O models, particular economic sectors may be analyzed in more detail than others. Similarly, some water bodies and water quality constituents will receive more attention than others, depending on the problem at hand.
Hypothetical Example Application 1:
Modernizing a Petroleum Refinery in a Severely Degraded River Basin
A Latin American government has applied for a loan to upgrade the processing technology at a large oil refinery. Improvements in process technology are expected to decrease water-borne discharges of BOD and phenols by 50 percent. Use of a simple model (WQAM) shows that this will improve downstream dissolved oxygen levels slightly. Under the 10-year, 7-day design flow (the lowest flow for a one-week period in 10 years) WQAM analysis shows that dissolved oxygen levels will increase from 2 parts per million (ppm) to 2.5 ppm. Although WQAM cannot analyze phenol concentrations, ambient levels are already very low, due to a high dilution by flow in the river. Managers then use WQAM to asses the effects of added end-of-pipe treatment, which would increase dissolved oxygen levels from 2.5 to 3.0 PPM, and decide that further improvements will not significantly affect water quality, due to high levels of discharge from other sources. Requires 1-2 person-months to complete the analysis, assuming that requisite water flow and quality data are readily available. Approximate cost of the analysis is $10,000.
Hypothetical Example Application 2:
New Food Processing Plant in a Moderately Polluted Coastal Estuary
A new vegetable canning plant is planned for a moderately polluted tropical estuary. Use of a simple model (WQAM) shows that the mill’s discharges may have a significant effect on the estuary’s dissolved oxygen and nutrient levels. If the plant is brought on-line, dissolved oxygen would decrease from 4.5 to 3 ppm. which could cause problems for aquatic life and phosphorus concentrations could increase from 0.5 to 2.0 ppm, which, according to local experts, could lead to algal blooms and affect the local fishery. Next, a more complex model (WASP) is used to asses the effects in more detail. Affects as assessed in WASP are also deemed unacceptable. Since the plant is new and projected to have state-of-the-art pollution abatement equipment in place, it is found to be more cost-effective to upgrade a nearby municipal sewage treatment plant. Projected discharge reductions in the municipal plant are found to give acceptable water quality when analyzed with WASP. Requires 10-12 person-months to complete the analysis, assuming that requisite water flow and quality data are readily available. Approximate cost of the analysis is $100,000.
Hypothetical Example Application 3:
Regional Water Quality Enhancement Plan for a Moderate-Size River Basin
A Central European government has received a loan to perform long-term investment planning for industrial and municipal sewage treatment for a river basin of 20,000 square kilometers. The basin contains approximately 100 point sources, of which one quarter are industrial treatment plants. Increases in user fees are expected to pay for primary sewage treatment for all municipalities within 10 years. In addition, increases in emission fees should induce all industrial sources to install and operate primary sewage treatment plants within the same time frame. The central government has agreed that it will finance more advanced treatment facilities for a subset of municipalities out of general revenues. In addition, it will use the emission fees levied on industrial dischargers to finance advanced treatment works for some sources. Due to a shortage of investment capital, the government wishes to get as much improvement in water quality per amount invested as it can.
The government has decided to focus its water quality control efforts on dissolved oxygen and nutrients, and turn to toxic pollutants (a problem in some heavily industrialized areas) at a later date, when the economy is projected to improve. A survey of existing water quality data shows that dissolved oxygen is especially problematic downstream of two major cities, and that nutrient concentrations are of particular concern just below an industrial complex. Because of the large number of pollution sources, a simple approach using WQAM is rejected. At the same time, a model as complex as WASP is thought to be too expensive to calibrate and run for such a large area. In addition, since the government is formulating a long-term investment plan, it believes that the dynamic information provided by WASP or HEC-5Q is not required. Therefore, the government plans to use QUAL2E to project the water quality effects of different investment strategies.
QUAL2E can assess whether or not a particular combination of treatment plants will meet a set of water quality goals. In addition to a water quality model, a simple optimization model will also be required in order to assess which combination will meet the goals at least cost. The government decides to evaluate this using a simple spreadsheet model with a commercial optimization add-on. The results show a significant savings when compared to a strategy that requires all plants to have the same level of treatment. Requires 100-150 person-months to complete the analysis, assuming that requisite water flow and quality data are readily available. Approximate cost of the analysis is $1,000,000.
An actual example demonstrating the scale of savings that could be identified by an exercise like this is a study of the Nitra River, a tributary of the Danube River. Raising present dissolved oxygen levels to a minimum of 4 mg/l could be accomplished at a cost of about $13m using a mix of treatment systems to be provided for the major different discharges. To raise this DO value to a minimum of 6 mg/l would cost about $26m, with higher treatment requirements for most of the discharges. To bring all the discharges up to EU standards would cost about $65m, would achieve DO levels of about 7 mg/l and would also reduce nutrient levels in the river. The conclusions of the study noted an uncertainty in the results (because of data shortcomings) but concluded that the results 'strongly suggest that substantial cost savings are possible using a least-cost control policy'.
Management Objectives and Applications
Something that is often overlooked in real-world application of water quality models is that they are a means to achieve a set of management objectives, and not an end in themselves. In many cases, it may not be necessary to use a water quality model at all, even when one knows in advance that a project will affect water quality. Suppose that in Example 1, above, the local water quality was acceptable to local environmental authorities prior to upgrading the plant. Given that the plant upgrade will reduce discharges and so improve water quality, there would be no need for model results that will project the extent of projected water quality improvement. Instead, the fact that water quality will not become worse may be sufficient information for the problem at hand.
In other cases, the motivations of project managers and those of water quality modelers may not be in concert. If environmental regulations focus on long-term averages for dissolved oxygen and BOD, there may be little if any need for advanced water quality modeling that can predict concentrations of heavy metals and toxic organic compounds. Water quality analysts, however, may be more interested in performing complex analyses on metals and organics which are more of a technical challenge.
Managers should also remember that the accuracy of model projections is severely constrained by the quality and quantity of the available data used to calibrate and test the models. The hypothetical examples shown above explicitly assume that these data are readily available. This will often not be the case in practice. Although data on water quantity is often collected for larger water bodies, water quality information is often collected sporadically or not at all. This applies especially to algae and other biological information, heavy metals and toxic organic compounds, since scientific interest in this data is relatively new.
The lack of data can create three problems. The first, of course, is that a model cannot be calibrated and tested until a monitoring system has been designed and operated for a considerable length of time. The second is that water sample collection and analysis may be considerably more expensive than the modeling effort that it is designed to support. Finally, design of a monitoring system may fall prey to the same types of problems that can affect water quality modeling, including the lack of clear connections to management objectives and a tendency to excessive complexity.
Models are only an abstraction from the reality of a situation and the improper use or misinterpretation of outputs from a model can lead to imprecise or incorrect results. Any conclusions reached on the basis of a model should therefore always be checked for realism and common sense.
In summary, managers should be cautious about underwriting the development and application of water quality models. They should be clear about their management goals, and model application should clearly support those goals. In some settings, models may not be needed at all, while in others, simple models may suffice. Any model will require a substantial amount of supporting data, which may not be immediately available.
Sources for Additional Information
Although many textbooks and journal articles have surveyed water quality model development and application, most surveys are not readily accessible for non-specialists. Among the less technically oriented materials available, Wurbs (1995) provides an up-to-date survey of modeling techniques for water management (both quality and quantity), and has a useful guide to software packages. Novotny and Capodaglio (1995, in press) provide a survey of concepts used in water quality modeling, and an overview of available models. Thomann and Mueller (1987) is a standard text on the principles of water quality modeling, as is Orlob (1982).