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Chapter 4: Selection and Characterization of Reference ConditionsEstablishment of reference conditions is key to biological assessment and biocriteria programs. Reference conditions are a representation of the biotic potential for lakes in the absence of human activity or pollution. The attainment of aquatic life use is evaluated against the expectations of the reference condition as expressed in the biocriteria. Reference conditions are expectations on the status of biological communities under minimal anthropogenic disturbances and pollution. The expectations are usually based on the status of reference sites, which might be subject to anthropogenic influences. Ideally, reference sites are minimally impacted by human pollution and disturbance. The care that states use in selecting reference sites and developing reference condition parameters, together with the survey techniques employed, will bear directly on their ability to defensibly assess a waterbody. At a minimum, reference conditions should be identified for each of the lake classification categories developed for a state. As pointed out in Section 3.2.4, the definition of reference condition differs between natural lakes and artificial reservoirs. The general sequence of reference condition characterization is to first assemble a panel of experts and make a preliminary classification of lake resources within a region. Following classification, sampling sites are selected, and habitat and biological data are obtained from those sites (either from existing data bases or from a survey). The preliminary classification is reconciled with the biological data to ensure that the final classification is biologically meaningful, and the reference conditions are characterized as part of the biocriteria development process. 4.1 Regionalization and Preliminary ClassificationThe regional differences in biological communities across the United States must be accounted for in the development of biological monitoring programs. This is done by comparing the biology of lakes to a regional reference condition. As biological conditions change across the country, the reference conditions will change also. To account for the regional differences in biological communities, and also for the differences that result from structural differences in biological habitat (either natural or caused by human activities), USEPA recommends that states classify lakes into categories and that a reference condition should be developed for each of the lake categories. Biotic index comparisons can then be made within each category, and inappropriate biological comparisons between different classes will be avoided. Moreover, the aquatic life expectations of waterbodies are tempered by realistic regional expectations; there is no attempt to set a single numeric aquatic life designated use standard for the entire nation. Lakes vary widely in size, shape, and ecological characteristics, and a single reference condition that applies to all lakes would be misleading. The purpose of classification is to group similar lakes together: i.e., to prevent comparison of apples and oranges. By classifying lakes the variability of biological measures within classes is reduced and the variability among classes is maximized. Classification invariably involves professional judgment to arrive at a workable system that separates clearly different ecosystems, yet does not consider each lake a special case. The intent of classification is to identify groups of lakes that, under ideal conditions, would have comparable biological communities. As far as possible, classification should be restricted to those characteristics of lakes that are intrinsic, or natural, and not the result of human activities. 4.1.1 Definition of the ResourceMost large reservoirs, and some natural lakes, are on rivers and might be considered large pools in the rivers rather than lakes. At what point does a pool become a lake? For the purpose of lake bioassessment, it is when distinctly lake-like flora and fauna occur (i.e., phytoplankton and zooplankton). Phytoplankton require a water retention time of 3 days or more (Uhlmann 1971). Microzooplankton (e.g., rotifers) have generation times roughly twice that of phytoplankton cells; therefore, the minimum retention time for zooplankton to develop may be approximately 1 week. For the purposes of bioassessment described here, a lake is any inland body of open water with some minimum surface area free of rooted vegetation and with an average hydraulic retention time of more than 7 days. These characteristics distinguish lakes from small ponds and wetlands, and from riverine pools (natural or artificial) that retain their lotic character. The distinction between lake and small pond is arbitrary, and the minimum size for a waterbody to be considered a lake must be set by resource agencies. For practical reasons, this document does not explicitly consider emergent wetlands at the margins of lakes. Bioassessment methods for wetlands are being developed separately by USEPA and other agencies. The unit of assessment and sampling (the sampling unit) is, most commonly, a definable, relatively self-contained basin of a lake. Most lakes have a single basin and thus will consist of a single sampling unit. Larger lakes, and especially reservoirs, have embayments, arms, and basins that are hydrologically isolated from the main body of the lake. Each isolated basin can be considered a separate sampling unit because of restricted water flow between basins. Large lakes can thus comprise several sampling units. Alternatively, a state may wish to define the sampling unit as an area or point in space (e.g., 1m2). Most reservoirs are also divided into three zones - riverine, transitional, and lacustrine - to reflect differences among these zones (Thornton 1990b). Each zone is a separate sampling unit; in large reservoirs, zones might be represented in each major arm (TVA 1994). 4.1.2 Basic RulesThere is no single “best” classification, nor are resources available to determine all possible differences between all lakes in a region. The key to classification is practicality within the region or state in which it will be applied; local conditions determine the appropriate classes. Classification will depend on regional experts familiar with the range of lake conditions in a region, as well as biological similarities and differences between the lakes. Ultimately, classification can be used to develop a predictive model of lake characteristics that affect the values of the biological metrics and indices in reference sites. There are two fundamental approaches to classification, a priori and a posteriori (Conquest et al. 1994). The a priori approach consists of developing logical rules for classification based on observed patterns in characteristics of the objects. Thus, classifying lakes on ecoregion, surface area, and maximum depth would be an a priori, rule-based classification. The a posteriori approach develops groups from a data base of observations from the sites. The classification is restricted to those sites and variables in the data base and typically involves cluster analysis to develop the groups. The a posteriori approach is useful for exploratory analysis of a substantial data set, but it is not appropriate for operational assessment and management, where a site’s class must be established from prior information (e.g., maps) before intensive data are collected. A few general rules for the development of a priori lake classification include: In a priori classification, lake characteristics that are readily affected by human activities or are a biological response to physical or chemical conditions should not be used as classification variables. Such responses might include trophic state, chlorophyll, or nutrient concentrations. For example, in the Northern Lakes and Forests ecoregion of Minnesota, lake trophic state is characteristically low whereas in the nearby Northern Glaciated Plains ecoregion, trophic state is relatively high (Heiskary 1989). The classification variable in this case is ecoregion, and trophic state is a response to ecoregion. A eutrophic lake in the Northern Lakes and Forests is considered impaired, but a eutrophic lake in the Northern Glaciated Plains is not considered impaired. Using trophic state as a classification variable could lead to misclassifications and inappropriate assessments. As shown in the example above, the best classification variables are those which are readily obtained from maps, bathymetric charts, or regional water characteristics, such as alkalinity or hardness. 4.1.3 Considerations for Reservoirs
Distribution - Reservoirs are most numerous in regions with few natural lakes: the nonglaciated parts of North America (except Florida) have the largest numbers of reservoirs (Thornton 1990a). Form - The form or shape of the basin and watershed may be the most important distinction between natural and artificial lakes. Shape substantially influences the hydrology and water quality of reservoirs. Large reservoirs are drowned river valleys and tend to be long and deep with numerous embayments from tributaries. The watersheds of reservoirs are typically much larger than those of natural lakes and contribute greater sediment loads. Longitudinal gradient - Reservoirs have characteristics typical of both lakes and streams within the same basin. They are more like streams at the head where major tributaries enter and are more like lakes near the dam (Thornton 1990b). Turbidity and loading - Reservoirs are typically more turbid, and they receive more nutrients and organic matter from their tributary streams than do most natural lakes. Management - Reservoirs were built and are managed for specific purposes: hydro-power, irrigation, flood control, fisheries, and multiple uses. Management might include extreme water level fluctuations, fish stocking, and other effects not present in natural lakes. Most of the differences between reservoirs and natural lakes are resolved in classification of the lake resource. The needs for which reservoirs were designed dictate many attributes of these waterbodies. Operational strategies can influence reservoir characteristics and resultant water quality (Kennedy and Walker 1990, Kennedy et al. 1985). The release of water from deep in the water column increases heat gain and the dissipation of materials accumulated in bottom waters (Martin and Arneson 1978, Wright 1967). Surface releases dissipate heat and retain materials. These and other operational differences can provide a basis for grouping reservoirs because reservoirs operated similarly can be expected to exhibit similar limnological responses, even when compared across large, heterogeneous regions. 4.1.4 Hierarchical FrameworkThis protocol is not intended to develop a classification scheme applicable to the entire United States. Overviews of global lake classification systems are in Hutchinson (1957) and in Leach and Herron (1992). Classification must be regional, and regional expertise must be used to determine those classification variables which are useful in a region. A useful classification scheme is hierarchical, beginning at the highest (regional) level and stratifying as far as necessary (Conquest et al. 1994). The procedure is to classify lakes at the highest level (usually geographic), and then to continue stratification in the classification hierarchy to a reasonable point. Although several possible classification levels are outlined below, in practice, only one, or at most two, relevant levels would typically be used. Classification should be parsimonious to avoid proliferation of classes that do not contribute to assessment. One or two relevant levels of the hierarchy will yield the best classification scheme. The proposed hierarchical scheme below applies to both natural lakes and reservoirs. Geographic Region - The geographic region (e.g., ecoregion, physiographic province) determines landscape-level features such as climate, topography, regional geology and soils, biogeography, and broad land use patterns. Ecoregions are based on geology, soils, geomorphology, dominant land uses, and natural vegetation (Hughes and Larsen 1988, Omernik 1987) and have been shown to account for variability of water quality and aquatic biota in several areas of the United States (e.g., Barbour et al. 1996a, Barbour et al. 1996b, Heiskary et al. 1987, Hughes et al. 1994, Ohio EPA 1987). Because of the importance of geography in determining aquatic biota, the National Research Council’s Aquatic Restoration Committee made the following recommendation (NRC 1992): The committee believes that goals for restoration of lakes need to be realistic and should be based on the concept of expected conditions for individual ecoregions. Further development of project selection and evaluation techniques based on ecoregion concepts and refinement of ecoregion definitions and descriptions should be encouraged and supported by the U.S. Environmental Protection Agency. Many of the characteristics below that can be used as classification variables are often subsumed by ecoregion. For example, watersheds are often similar within ecoregions, having been formed by the regional geomorphology, and water quality characteristics such as alkalinity are determined by regional bedrock and soils. Within ecoregions, it might be sufficient to classify using only lake basin morphology (e.g., depth, area, development ratio): anthropogenic or natural origin; or management objective.
Watershed Characteristics - Watershed characteristics affect lake hydrology, sediment and nutrient loads, alkalinity, and dissolved solids. As noted above, many watershed characteristics are relatively uniform within an ecoregion and may not be necessary if ecoregions were the primary classification variable. Watershed characteristics that may be used as classification variables include:
Lake Basin Characteristics - Lake basin morphology influences lake hydrodynamics and lake responses to pollution. Characteristics of some reservoirs change with age, particularly regional shoaling and silting of aged reservoirs subject to high sediment loads (O’Brien 1990). Morphological metrics include:
Lake Hydrology - Lake hydrology forms a basis for water quality. Mixing and circulation patterns influence nutrient retention and the development of hypoxia. Hydrological factors include:
Characteristic Water Quality - Lakes can be classified by characteristic water types into categories, such as marl lakes, alkali lakes, ombrotrophic bog lakes, and others. Many water quality characteristics are relatively uniform within an ecoregion and as the result of regional, watershed, basin, and hydrologic characteristics. Water types are determined by the following water quality variables:
Human actions (e.g., discharges, land use) alter water quality, especially sediment and nutrient concentrations, but they can also affect alkalinity, salinity, conductivity, color, and DOC. Care must be taken that classification according to characteristic water types reflects natural conditions and not anthropogenic impacts. For example, if a lake is highly turbid due to poor land management practices, it should not be classified as highly turbid. Rather, it should be classified as it would have been in the absence of poor land use. 4.2 Establishing Reference ConditionsFive elements are used to establish lake reference conditions for biological monitoring and biological criteria: (1) expert consensus, (2) biological survey of sites, (3) paleolimnology, (4) evaluation of historical data, and (5) prediction of expected conditions using ecological models (Table 4-1).
4.2.1 Expert ConsensusExpert consensus is essential in supporting the information and data interpretation derived from the other approaches. It provides a balanced and comprehensive assessment of all of the information and promotes the optimum criteria when properly done. A panel of experts is assembled before any other steps are implemented, to guide the process and to select the best methods appropriate to the region for characterizing reference conditions. The panel should consist of skilled aquatic biologists, physical scientists, fisheries biologists, and natural resources managers.
In significantly disrupted areas where no candidate reference sites are acceptable, a form of this expert consensus is a workable alternative to establish reference expectations. Three or four biologists can be convened for each assemblage to be used in the assessment. Each expert should be familiar with the lakes of the region. Based on their collective expertise, they are asked to develop a description of the assemblage to be expected if the lakes were relatively unimpacted. This description, developed by consensus, will necessarily be more qualitative than quantitative, but will allow development of metrics and metric scoring. 4.2.2 Biological SurveyThe recommended empirical approach is to use a population of reference lakes to establish conditions that will be used to identify and calibrate metrics. Pairwise comparison of two lakes leads to the trivial conclusion that they are different (Hurlbert 1984). All monitoring sites, reference or impaired, can vary over time and space for natural reasons. A central measure from a composite of several reference sites is used to base expectations to account for natural variability and uncertainty. Statistically, this means that the status of a lake is judged by comparing the lake (the “test site”) to a population of reference sites. In hypothesis-testing terminology, the null hypothesis examines whether the test lake is a member of the population of reference sites. A critical requirement for the use of reference conditions in biocriteria is the USEPA antidegradation policy, which protects against incremental deterioration of waterbodies and reference conditions. An observed downward trend in reference sites cannot be used to justify relaxing reference expectations, reference conditions, and the associated biological criteria. Once established, biocriteria may only be refined in a positive direction in response to improved conditions. To characterize reference conditions, surveys of both reference sites and known impaired sites are made for both biota and physical habitat. These data are needed to determine gradients of conditions (from best to impaired) for the purpose of measurement calibration and discrimination. The raw data must be evaluated within the ecological context (waterbody type and size, season, geographic location, and other elements) that defines what is expected for similar waterbodies.
Candidate metrics are developed from the key biological attributes, and the effects of stressors on specific metrics must be understood (USEPA 1996a). Those measurements that have a monotonic response to a gradient of conditions (from unimpaired to heavily impaired) will be the best candidates for assessing biological impairment. Therefore, ambient sites other than reference sites should be surveyed as part of the data base. Selection and confirmation of the measurements must address the ability to differentiate between impaired and unimpaired sites. Minimally Impaired Reference SitesReference sites must be carefully selected because they will be used as a benchmark against which test sites will be compared. The conditions at reference sites should represent the best range of minimally impaired conditions that can be achieved by similar lakes within the region. The reference sites must be representative of the region, and relatively least impacted compared to other lakes of the regions. Sites that are undisturbed by human activities are ideal reference sites. However, land use practices and atmospheric pollution have so altered the landscape and quality of water resources nationally that truly undisturbed sites are rarely available. In fact, it can be argued that no unimpaired sites exist. Therefore, a criterion of “minimally impaired” must be used to determine the selection of reference sites. In regions where minimally impaired sites are significantly degraded, the search for suitable sites should be extended over a wider area. Stringent criteria might require using park or preserve areas for reference lakes. Criteria for reference lakes will also pertain to the condition of the watershed, as well as the lake itself. If relatively unimpaired conditions do not occur in the region, the selection process could be modified to be more realistic and reflect attainable goals, such as the following: Land use and natural vegetation - Natural vegetation has a positive effect on water quality and hydrological response of streams. Reference lakes should have at least some percentage of the watershed in natural vegetation. Riparian zones - Zones of natural vegetation alongside the lakeshore and streams stabilize shorelines from erosion and contribute to the aquatic food source through allochthonous input. They also reduce nonpoint pollution by absorbing and neutralizing nutrients and contaminants. Watersheds of reference lakes should have at least some natural riparian zones regardless of land use. Best management practices - Urban, industrial, suburban, and agricultural nonpoint source pollution can be reduced with successful best management practices (BMPs). Watersheds of reference lakes should have BMPs in place provided that the efficacy of the BMPs has been demonstrated. Discharges - Absence or minimal level of permitted discharges (NPDES) into surface waters. Management - Management actions, such as extreme water level fluctuations for hydropower or flood control, can significantly influence lake biota. Reference lakes should be only minimally impacted by management activities. Predefined reference conditions for lakes have been used in Minnesota to determine ambient phosphorus criteria (Heiskary 1989). Maine uses a similar approach in regulating the water quality of streams and uses a reference standard of aquatic life as naturally occurs (Davies et al. 1993). If a fixed definition of reference condition is deemed to be overly restrictive or an impractical ideal, then an empirical working definition is an alternative. For example, because natural conditions for reservoirs cannot be defined, the best existing conditions are used instead. This approach is also useful in ecoregions with little or no contiguous stands of natural vegetation remaining, such as in the agricultural Midwest. Choosing the best sites requires at least a representative survey (or better, a census) of lake watershed variables in the ecoregion. Individual lakes with the best conditions, such as the greatest percentage of forest or natural vegetation, the lowest percentages of agricultural and urban land use, etc., are chosen as reference sites.
Without antidegradation safeguards, the best available approach might allow continual deterioration. For example, construction and development in a lake watershed that is one of the “best” in a region might cause biological degradation of the lake. If the set of “best” lakes in the ecoregion have suffered similar degradation, they might still be the reference sites, but the new reference condition will be degraded relative to its earlier state. For example, Maine has a antidegradation policy that requires that lakes remain stable or improve in trophic state (Courtemanch et al. 1989, NALMS 1992). An effective antidegradation policy can promote continually improving conditions. The selected reference lakes should be representative of each of the classes, and a sufficient number of lakes are then sampled to enable characterization of each class. A general “rule of thumb” for optimal sample size is 10-30 lakes per class, and each lake is a sampling unit (see Chapter 9 for estimating power and sample size). In regions where all lakes are impacted, the 10 to 30 relatively least impacted lakes of each class (e.g., ecoregion) are sampled, where “best” is determined by least anthropogenic disturbance or impacts, but not by most desirable biota. In regions where the population of unimpaired reference lakes is large, a stratified random sampling scheme (lakes in each class selected randomly) will yield an unbiased estimation of reference conditions. “Stressed Reference Sites” - Effective metrics respond to environmental degradation and allow discrimination of impaired sites from the reference expectations. Metrics that do not respond are not useful in bioassessment. Response is determined by sampling a set of stressed sites in the same way as the reference sites - in effect, sampling a set of “stressed reference” sites. Lakes with known problems, such as nutrient loading, thermal pollution, toxic sediments, or urban land use, are good candidates for “stressed reference” sites. There should be several in each class or lake ecoregion for adequate tests of metric responses. Because impaired lakes are frequently objects of monitoring by natural resource agencies, data might already exist to test the biological metrics. However, the sampling methods for reference and impaired lakes should be comparable. Sampling and Data Analysis - One or more of the recommended tiers of biological assemblages are sampled and identified. It is imperative that reference sampling include all assemblages that will be used in operational sampling and assessment. Sampling methods are described in Chapters 4 and 5; data analysis is described in Chapter 6. Reference Conditions from Distributions of Biological MetricsIf sufficient minimally impaired reference sites do not exist or cannot be found, reference conditions can be selected from an entire population of sites. This approach is especially relevant for human-made impoundments and reservoirs, where no least-impaired systems exist, as well as for resources subject to strong and relatively uniform human impacts, such as lakes in large urbanized areas or in heavily agricultural regions. The approach was developed by Karr et al. (1986) for the Index of Biotic Integrity (IBI). It has since been applied to estuary assessment (Engle et al. 1994, Ranasinghe et al. 1994) and reservoir assessment (TVA 1994). A representative sample of lakes is taken from the entire population. Sites that are known to be severely impaired may be excluded from the sample, if desired. The population distribution of each biological metric (Chapter 5) is determined, and the 95th percentile of each metric is taken as its reference value. The range from the minimum possible value (usually 0) to the reference value is trisected, and values in the top third of the trisected range are taken to be similar to reference conditions. Scoring of metrics is explained more fully in Chapter 6. A central assumption of the population approach is that at least some sites in the population of lakes are in good condition, which will be reflected in the highest scores of the individual metrics. Because there is no independent definition of reference (independent of biological status), reference conditions defined in this way must be taken as interim and subject to future reinterpretation. Again, antidegradation safeguards must be in place to prevent deterioration of the reference standard. Periodic examination of the reference standards for trends can detect deterioration or improvement. Strictly speaking, the distributional approach is circular because the reference biological conditions are characterized as the best of existing biological conditions, without consideration of impacts. This is necessary when reference criteria cannot be defined a priori, or when all lakes under consideration are equally impaired. The object of the method is to develop a measurement standard for assessment of lakes. Its validity must then rest on external confirmation of the response of metrics to stressors, usually from published or other independent studies.
Following the initial classification of the lakes in a region, biota are surveyed to determine those aspects of the classification that are relevant in explaining biological variability among lakes. The objective of the survey is to determine the final classification and to characterize the biota of each of the lake classes. Analysis of biological data includes testing classes developed in the initial classification, as well as aggregating classes as necessary to obtain a parsimonious classification that accounts for the greatest amount of biological variability. The survey may use existing data, although a new survey allows careful selection of reference sites representative of each of the classes of lakes. 4.2.3 PaleolimnologyAn alternative to characterizing present-day reference conditions is to estimate historic or prehistoric pristine conditions. In many lakes, presettlement conditions can be inferred from fossil diatoms, chrysophytes, midge head capsules, cladoceran carapaces, and other remains preserved in lake sediments (e.g., Charles et al. 1994, Dixit et al. 1992). Fossil diatoms are established indicators of historical lake alkalinity, salinity, and trophic state (e.g., Hall and Smol 1992). Diatom frustules, composed of silica, are typically well preserved in lake sediments and easy to identify. However, remains of other organisms are problematic because of incomplete preservation. Paleolimnological investigations can be performed in lakes in which identifiable remains are preserved, and the sediments can be dated to the period of interest (Charles et al. 1994). In some lakes, sediments are subject to scouring, resuspension, or periodic drying and are not suitable for coring. Most lakes have a quiescent depositional area in the deepest profundal waters, and these sediments receive material from both pelagic and littoral zones, as well as from the surrounding watershed. Reservoirs meeting the depositional criteria can also be analyzed in this way, yielding a history of the reservoir. However, historical conditions in a reservoir might or might not be a desired reference condition. Design of paleolimnological studies to determine reference conditions can range from basic to complex. The simplest procedure is to analyze only the top and bottom of a sediment core, and to make a comparison of assemblages to determine if there has been a significant shift in taxa composition. If there is little difference, then there has probably been relatively little change in major ecological characteristics in the lake. If there are significant differences, then further investigation may be warranted, including quantitative inference of past water chemistry conditions (Charles and Smol 1994). The more informative approach is to analyze several sediment intervals from a sediment core that has been dated (usually Pb-210), and infer specific past conditions. This design leads to understanding of the magnitude, rate, and timing of change and can be related to specific watershed or in-lake events. Using paleolimnology to characterize lake reference conditions requires selection of a time period for the reference. In general, the time period should be as close to the present as possible when anthropogenic impacts on the lakes were minimal. If there is concern that background conditions may have varied substantially, a few to several presettlement time periods could be analyzed to determine natural variability. In most cases this variability is relatively small compared with changes following European settlement. The greatest advantage of paleolimnology is that a sample of reference sites can be selected without regard to present conditions in the lakes. Thus, there is usually no need to select “least-impaired” lakes because nearly all lakes in the selected reference period are least-impaired by definition. Reference sites are selected such that each lake class has at least 5 to 10 representative lakes. Reference sites should be representative of their respective class. Transitional, exceptional, or uncertain lakes should not be included in the reference sample. The population approach to defining reference conditions means that a single site is never taken as a representative reference for an entire class. Similarly, the condition at only 1 time period of a single lake may not represent a reference for its present condition. Ecosystems are not constant in time, even in the absence of disturbance, and the condition of a single lake is likely to change in the course of a century. Therefore, samples of past conditions at several points in time are more likely to characterize reference conditions than a single sample. Sampling and Data Analysis - Sediment diatoms are the recommended assemblage for paleolimnological determination of reference conditions because preservation of frustules is excellent and identification is based solely on the frustules. Other assemblages (e.g., cladocerans, midges) are not recommended at this time because preservation is incomplete and identification of fragments is problematic. Cores are taken from the representative lakes and analyzed as described in Appendix C. 4.2.4 Historical DataSome lakes have extensive historical data bases from the early to mid-20th century, typically on water quality, diatoms, zooplankton, or fish. However, historical data may not represent undisturbed conditions, and the biological data and auxiliary historical information should be examined carefully to ensure that the data actually represent conditions better than at present. Cultural eutrophication has occurred since neolithic peoples first settled on lakeshores, and in many American waterbodies cultural eutrophication was most pronounced in the 1950s and 1960s. Historical data might not always be representative of lakes in a region because the lakes were selected for special reasons (e.g., unique lakes, near laboratory, site of water intake, etc.). Universities, municipal water supply departments, and other agencies are often good sources of long-term lake water quality data. It might be possible to augment present-day reference site data with historical data. 4.2.5 Modeling ApproachesSeveral modeling approaches can be used, including mathematical models (logical constructs following from first principles and assumptions), statistical models (built from observed relationships between variables), or a combination of the 2. The degree of complexity of mathematical models to predict reference conditions is potentially unlimited, with attendant increased costs and loss of predictive ability as complexity increases (Peters 1991). Mathematical models are complex and untestable hypotheses (Oreskes et al. 1994, Peters 1991). Nevertheless, models to predict water quality in rivers and reservoirs from first principles of physics and chemistry have been quite successful (e.g., Kennedy and Walker 1990). Statistical models can be fairly simple in formulation, such as the Vollenweider model, the Morphoedaphic Index, and others (Vighi and Chiaudani 1985, Vollenweider 1975, Mazumder 1994), to predict trophic status, but they require a sufficiently large data base to develop predictive relationships. If enough data exist to construct a statistical model, it is likely that there are lakes that can serve as reference sites.
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