Application of Assimilative Capacity to the TMDL Process

The derivation of the amount of nutrients, sediments, pathogens, or other stressors that can be added to the waterbody without exceeding the criteria depends upon a number of factors (Figure 1).

Without man-derived (anthropogenic) inputs, there will still be a variety of inputs to the receiving water from the watershed and atmospheric deposition. Nutrients (manure and decomposition products), pathogens, and naturally derived toxins are derived from biological processes. Runoff from the watershed can carry nutrients from soil or rock along with sediment. Natural outcroppings from the watershed can be sources of hydrocarbons, metals, nutrients, and other materials. Atmospheric deposition can deliver particulates and nutrients that may have been transported very long distances.

The receiving environment will also act upon the materials transported into the waterbody. Dilution by the addition of water from the watershed will occur. Current outside the study area can also transport the materials introduced to the river. Many materials can be biodegraded or biotransformed so that they no longer have the original activity. Particulates and the materials that attached to them can be trapped as sediment and not be available to the water column. Organics such as benzene and related aromatics can volatilize, escaping from the water column to the atmosphere. At higher pHs, metals and some other materials can combine with carbonates and precipitate from the water column. The combination of the rates of the inputs and outputs results in a baseline concentration of the nutrient or other material regulated by the TMDL process. The difference between this level and the established criteria provides an indication of the additional materials that could be added. Of course, this baseline is not a constant but depends upon the seasonal and natural changes that occur in the watershed. Times of low precipitation will result in a lower amount of runoff from the watershed. The lack of precipitation in a watershed will also result in low flow and reduce the amount of dilution and the transport of the contaminants from the waterbody. In cases where the data are available, it is possible to


Assimilative capacity

Baseline concentration of regulated materials

Baseline concentration of regulated materials

Nonanthropogenic inputs Biological inputs (nutrients, pathogens, toxins) Runoff from watershed (nutrients, sediments, biological inputs from watershed)

Natural outcroppings (metals, hydrocarbons, nutrients) Atmospheric inputs (nutrients, particulates, long-range transport of materials).

Difference between this concentration and the regulatory limit is the assimilative capacity.









Figure 1 Diagram of the interactions that are part of determining the assimilative capacity of a receiving water.

Assimilative capacity


Baseline concentration of regulated materials

Nonanthropogenic inputs Biological inputs (nutrients, pathogens, toxins) Runoff from watershed (nutrients, sediments, biological inputs from watershed) Natural outcroppings (metals, hydrocarbons, nutrients)

Atmospheric inputs (nutrients, particulates, long-range transport of materials).

Receiving waters









Anthropogenic inputs

Original capacity c

Anthropogenic inputs Point sources: nutrients, toxics from manufacturing process, temperature, color, sediments, pathogens

Nonpoint sources: nutrients and sediments from urbanization; pesticides, herbicides, and fertilizer runoff from agriculture, disturbance of the channel and structure of the watershed.

Atmospheric inputs: nutrients, particulates, long-range transport of materials, acid precipitation.

Figure 2 Anthropogenic inputs add to the loading of the receiving water and start to encroach on the regulatory limit.

establish confidence intervals for the ranges that the input and output variables may take over time to provide a more realistic picture of the conditions of watershed and the waterbody.

Man-made nutrients, alterations to water flow, and other factors broaden the types of considerations (Figure 2). Point and nonpoint sources from human cultural activities add nutrients, contaminants, pathogens, and other materials to the receiving water. Points sources, such as outflows from manufacturing or municipal water treatment systems, can contribute elevated levels of metals in a refined form, novel toxicants, an increase in temperatures, dyes, and materials not normally found in nature. The place of input is also localized and at a concentration. Only the output processes at the point of introduction and those downstream are available to process the materials. Nonpoint sources such as those from agricultural areas or residential zones introduce other unique materials. Pesticides, herbicides, and fertilizer runoff can come from both areas. Antibiotics have been detected in agricultural runoff while pathogens can be obtained from a variety of sources. Agriculture, residential areas, and manufacturing regions can also alter the structure of the waterbody by channelization and pave changing the hydrodynamics of the system. Atmospheric inputs can bring contaminants from outside the watershed depositing them as they fall out of the atmosphere as particulates or in precipitation. Rain and snow both can be contaminated. Organics can be found as part of snow pack even in remote mountainous regions. It is unlikely that any site exists that does not receive a detectable amount of an anthropogenic contaminant.

In response to these inputs, an increase in the rates of degradation and other factors controlling the output of the material from the waterbody may occur. As the inputs of nutrients and organics increase, biodegradation and biotransformation rates of toxicants may also increase. However, the rates may reach a maximum depending upon temperature, oxygen concentration, flow rates, or other factors. In situations where the receiving water is already above the criteria, the factors that control the removal of the contaminant are likely to already be at a maximum.

In order to estimate the loading limits that will not exceed the criteria set for the receiving water, an expression formally connecting the features in Figure 2 in a causal relationship should be derived. Figure 3 illustrates the tools that have been used in order to accomplish this linkage. The goal is to be able to connect the loading to the final concentration of the contaminant in the water body. In this fashion specific limits on the amount and rates of loading can be established to ensure that the water-quality goals for the receiving water can be met.

The tools that have been used fall into three categories. The first set of tools are the use of mechanistic


Inputs of contaminants or other stressors

Translation of assimilative capacity to loadings

Mechanistic process models confirmed by site-specific data or data from other sites.

Water quality criterion limit

Calculated or measured concentration

Empirical models confirmed by site-specific data or data from other sites. Index linkages (regression based) are a form of this approach to modeling.

Inferences from other sites or past situations

Figure 3 Tools for connecting loads and water quality criteria.

mathematical models that have functions that describe the important features of the receiving water that control the concentration of the contaminant. Such a model includes input rates for the contaminant, degradation or sedimentation rates, volatilization rates, dilution factors, and other features that essentially turn Figure 2 into an equation for a specific situation. These models have the potential to be accurate and can address a number of issues very quickly. The downside is that a complete process model can take a lot of time to construct and the data may not exist. It may also not be clear what factors control some types of contaminants. When sufficient knowledge of the process is not available to construct a process model, then it is necessary to use alternative approaches.

Empirical models use regression techniques to connect input loadings to final concentration in the receiving waters. In some instances, these models may have many different components and a multiple regression equation used to define the relationships. There are also models that describe the relationship between inputs to the system and a specific type of water quality index. Indexes are numbers that composite many kinds of data and may not clearly represent the criteria established for the system of interest. The accuracy of empirical methods depends largely on the amount of data available and its origin. Data for several different receiving waters may have to be combined in order to have enough data to derive a reasonable regression. There may also be regionally specific factors that may not be included, or different bioregional regions may require different regressions in order to provide accurate predictions. Assumptions of the models and the source of the data used to derive the regression should be stated as part of the reporting process.

Simulation models, often incorporating segments that are process derived and some with empirical backgrounds, are among the most commonly used tools in estimating loadings that do not exceed the assimilative capacity of the receiving water. Table 2 lists some of the characteristics of those simulation models used for nutrients.

It is important that the models that are used are as transparent as possible, that is, that the underlying assumptions, constants, and calculations be available for review. This requirement precludes against the use of proprietary models that are not open source and have not met peer review. The model should also be as simple as meets the requirements of setting the loading limits.

In some instances there may be no mathematical relationship that has been derived for understanding the relationship between loading and final concentration in the water body. In this case, inferences may be drawn from the past or from other situations, but the uncertainty in these predictions is likely to be high.

When uncertainty is high in the relationship between loadings and the resulting concentration in the receiving water, a margin of safety (MOS) can be included in the process. This margin of safety is usually expressed as a percentage of the assimilative capacity. In the case of a regulatory limit of 20 mgl1 for total phosphorus, a 10% margin of safety would result in the goal for loadings would be not to exceed 18 mgl_1.

In summary, assimilative capacity is a means of tying loading from a number of sources to site-specific regulatory limits for receiving water. Assimilative capacity is tied directly to the TMDL process. The calculations that tie loading to in-stream concentrations are typically done by models that are designed for this purpose and are specific for the type of receiving water. Uncertainty in the predictive model is dealt with using an MOS to ensure that the receiving water concentration is not exceeded.

Table 2 Currently available models for calculating loadings and assimilative capacities for rivers, streams and lakes. The models and websites are current as of summer 2006





US Army Corp of CE-QUAL-RIV1 Engineers

Waterways CE-QUAL-W2 Experimental Station, Vicksburg





USEPA Ecosystems BASINS/QUAL2K Research Division


One-dimensional, dynamic flow and water quality model for streams Two-dimensional, vertical-longitudinal hydrodynamic water quality model for reservoirs Steady-state water and nutrient balance calculations in a spatially segmented hydraulic network which accounts for advective and diffusive transport and nutrient sedimentation Program allows estimation of tributary mass discharges (loadings) from sample concentration data and continuous flow records Data reduction and analysis of water quality data. Includes several eutrophication response variable calculations Two-dimensional (horizontal) and three-dimensional water quality model for coastal systems currently restricted to US Corp of Engineers use

This stream and river water quality model that assumes that the stream is well mixed Model includes the water column and the benthos of lakes products.cfm?Topic=model&Type=watqual qual2k.html wasp.html

See also: Sediments: Setting, Transport, Mineralization, and Modeling.

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