Computation
Estimate the Distribution of Screened Parameter Values
Parametric and nonparametric statistical approaches can be used to estimate a percentile of a nutrient concentration distribution. In a parametric approach, you typically assume that observed concentrations are log-normally distributed, and estimate the mean and standard deviation of the available data. Then, you can compute percentiles of the log-normal distribution from those parameters (see Figure 1). In a nonparametric approach, you sort available data and directly estimate percentiles from the data based on ranking of individual samples. For example, if 100 measurements of nutrient concentrations are available, then the 90th highest concentration is an estimate of the 90th percentile of the distribution. In both of these approaches, you might need to treat repeated samples at individual sites differently than individual samples collected at different sites.
Figure 1. Example log-normal distribution of phosphorus concentrations for streams.
Selecting the Percentile
Your selection of the percentile value to use as the basis for establishing nutrient criteria is a critical decision. Consequently, you need to develop and document your rationale for making that decision.
Following are some factors for you to consider:
- The reference conditions selected in step 1 (e.g., least disturbed condition)
- The quantity and quality of the screened data used for creating the distribution
- The designated uses(s) of the resources
- The option to apply multiple lines of evidence
Reference conditions
The term minimally disturbed implies that virtually no human activities have affected conditions in the water bodies. The upper end of the range of data from those reference sites represents an upper threshold of a reference condition. The upper quartile of reference sites (i.e., the 75th percentile) represents a value with a margin of safety added that might exclude the effect of outliers, protect against errors in site selection that might have resulted in sites outside of expectation being selected, and serve as an initial recommendation of a sufficiently protective value. In contrast, in regions of pervasive human activity where no minimally disturbed sites can be identified and only least disturbed reference sites can be identified, you should select a lower percentile of the distribution to avoid establishing criteria representing degraded conditions.
Quantity and quality of data generated
The amount of data available, and the level of certainty that exists that the data accurately reflect the desired reference condition, influence your percentile choice and should be supported with scientific literature and other available information. For a small data set with greater heterogeneity, you might consider selecting a lower percentile to ensure that all types of water bodies are protected; and for a large data set with greater homogeneity, you might be able to choose a higher percentile. Classifying your water bodies accurately in step 2 and the amount of data available might also factor into percentile selection.
Uncertainty consideration and designated use
You can interpret selecting a percentile as a way to manage uncertainty that otherwise could result in falsely listing a water body as impaired, noting that a percentile also must be protective of designated uses. Using the 90th percentile reflects confidence that the data set used to derive the criteria is supportive of designated uses. The 90th percentile is more defensible as an appropriate concentration to specify the protection level magnitude if a state or tribe is confident that distribution of the screened data reflects minimally disturbed, biologically healthy reference conditions.
Multiple lines of evidence
Another option is to compare multiple lines of evidence to select an interim value. This option can help minimize the uncertainty associated with a single approach. Using the multiple lines of evidence approach, which combines two or all three of the approaches described, will produce criteria of greater scientific validity.
Note: When using multiple lines of evidence, you should independently compare the results of your computation to other approaches.
A state or tribe could derive TP and TN criteria by examining all the thresholds identified in the chosen approach (e.g., reference, stressor-response, modeling, literature values, ecoregional values, and existing state criteria approved by EPA), then comparing the thresholds of each approach independent of the others, with more weight given to indicators with greater precision and certainty.
If few or no data are available for a given water body type or region, reference conditions also can be predicted by inference or extrapolation of various models. Although extrapolation of models beyond their original calibration data can be risky, it might be the only option available to estimate reference conditions if no reference data exist or are unlikely to exist (e.g., in pervasively disturbed landscapes). In addition to statistical modeling to help determine reference conditions, you can use mechanistic models to estimate both nutrient loads and load reductions to achieve a targeted nutrient regime in a receiving water. Models are available to estimate nutrient loads from different land uses, transport of nutrients, and receiving water effects, including hypoxia and chlorophyll a concentrations.
If identifying reference sites proves difficult or a temporary estimate is needed until reference sites can be adequately described, you can use published values. Literature values can be used as criteria if a strong rationale is presented that demonstrates the suitability of the threshold value to the water body type of interest (i.e., the system of interest should share characteristics with the systems used to derive the published threshold values).
Estimate the Distribution of Screened Parameter Values
Parametric and nonparametric statistical approaches can be used to estimate a percentile of a nutrient concentration distribution. In a parametric approach, you typically assume that observed concentrations are log-normally distributed, and estimate the mean and standard deviation of the available data. Then, you can compute percentiles of the log-normal distribution from those parameters (see Figure 1). In a nonparametric approach, you sort available data and directly estimate percentiles from the data based on ranking of individual samples. For example, if 100 measurements of nutrient concentrations are available, then the 90th highest concentration is an estimate of the 90th percentile of the distribution. In both of these approaches, you might need to treat repeated samples at individual sites differently than individual samples collected at different sites.
Figure 1. Example log-normal distribution of phosphorus concentrations for streams.
Selecting the Percentile
Your selection of the percentile value to use as the basis for establishing nutrient criteria is a critical decision. Consequently, you need to develop and document your rationale for making that decision.
Following are some factors for you to consider:
- The reference conditions selected in step 1 (e.g., least disturbed condition)
- The quantity and quality of the screened data used for creating the distribution
- The designated uses(s) of the resources
- The option to apply multiple lines of evidence
Reference conditions
The term minimally disturbed implies that virtually no human activities have affected conditions in the water bodies. The upper end of the range of data from those reference sites represents an upper threshold of a reference condition. The upper quartile of reference sites (i.e., the 75th percentile) represents a value with a margin of safety added that might exclude the effect of outliers, protect against errors in site selection that might have resulted in sites outside of expectation being selected, and serve as an initial recommendation of a sufficiently protective value. In contrast, in regions of pervasive human activity where no minimally disturbed sites can be identified and only least disturbed reference sites can be identified, you should select a lower percentile of the distribution to avoid establishing criteria representing degraded conditions.
Quantity and quality of data generated
The amount of data available, and the level of certainty that exists that the data accurately reflect the desired reference condition, influence your percentile choice and should be supported with scientific literature and other available information. For a small data set with greater heterogeneity, you might consider selecting a lower percentile to ensure that all types of water bodies are protected; and for a large data set with greater homogeneity, you might be able to choose a higher percentile. Classifying your water bodies accurately in step 2 and the amount of data available might also factor into percentile selection.
Uncertainty consideration and designated use
You can interpret selecting a percentile as a way to manage uncertainty that otherwise could result in falsely listing a water body as impaired, noting that a percentile also must be protective of designated uses. Using the 90th percentile reflects confidence that the data set used to derive the criteria is supportive of designated uses. The 90th percentile is more defensible as an appropriate concentration to specify the protection level magnitude if a state or tribe is confident that distribution of the screened data reflects minimally disturbed, biologically healthy reference conditions.
Multiple lines of evidence
Another option is to compare multiple lines of evidence to select an interim value. This option can help minimize the uncertainty associated with a single approach. Using the multiple lines of evidence approach, which combines two or all three of the approaches described, will produce criteria of greater scientific validity.
Note: When using multiple lines of evidence, you should independently compare the results of your computation to other approaches.
A state or tribe could derive TP and TN criteria by examining all the thresholds identified in the chosen approach (e.g., reference, stressor-response, modeling, literature values, ecoregional values, and existing state criteria approved by EPA), then comparing the thresholds of each approach independent of the others, with more weight given to indicators with greater precision and certainty.
If few or no data are available for a given water body type or region, reference conditions also can be predicted by inference or extrapolation of various models. Although extrapolation of models beyond their original calibration data can be risky, it might be the only option available to estimate reference conditions if no reference data exist or are unlikely to exist (e.g., in pervasively disturbed landscapes). In addition to statistical modeling to help determine reference conditions, you can use mechanistic models to estimate both nutrient loads and load reductions to achieve a targeted nutrient regime in a receiving water. Models are available to estimate nutrient loads from different land uses, transport of nutrients, and receiving water effects, including hypoxia and chlorophyll a concentrations.
If identifying reference sites proves difficult or a temporary estimate is needed until reference sites can be adequately described, you can use published values. Literature values can be used as criteria if a strong rationale is presented that demonstrates the suitability of the threshold value to the water body type of interest (i.e., the system of interest should share characteristics with the systems used to derive the published threshold values).