\ A trophic state index for lakes1 THIS WATERIALI.tA r Be PROTecTED BYCOPYRIGHTI.A~ Robert E. Carlson . (T;T~:- "1?t 1.8.COD£) Limno IOglCal Research2 Center, University of Minnesota, Minneapolis 55455 Abstract A numerical trophic state index for lakes has been developed that incorporates most lakes in a scale of 0 to 100. Each major division (10, 20, 30, etc.) represents a doubling in algal biomass. The index number can be calculated from any of several parameters, including Secchi disk transparency, chlorophyll, and total phosphorus. My purpose here is to present a new ap- sometimes circumvented by classifying proach to the trophic classificationof lakes. lakes that show characteristics of both oli- This new approach was developed because gotrophy and eutrophy as mesotrophic. of frustration in communicatingto the pub- Two or three ill-defined trophic states lic both the current nature or status of lakes cannot meet contemporary demands for a and their future condition after restoration sensitive, unambiguous classification sys- when the traditional trophic classification tem. The addition of other trophic states, system is used. The system presented here, such as ultra-oligotrophic, meso-eutrophic, termed a trophic state index (TSI), in- etc., could increase the discrimination of the volves new methods both of defining index, but at present these additional divi- trophic status and of determining that status sions are no better defined than the first in lakes. three and may actually add to the confu- All trophic classification is based on the sion by giving a false sense of accuracy and division of the trophic continuum, however sensitivity. this is defined, into a series of classes I acknowledgethe advice and encourage- termed trophic states. Traditional systems ment of J. Shapiro in developing this index divide the continuum into three classes: and in preparing the manuscript. I also oligotrophic, mesotrophic, and eutrophic. thank C. Hedman and R. Armstrong for ad- There is often no clear delineation of these vice and H. Wright for help in manuscript .. divisions. Determinations of trophic state preparation. are made from examination of several di- verse criteria, such as shape of the oxygen Cu"ent approaches curve, species composition of the bottom The large number of criteria that have fauna or of the phytoplankton, concentra- been used to determine trophic status has tions of nutrients, and various measures of contributed to the contention that the biomass or production. Although each trophic concept is multidimensional, in- changes from oligotrophy to eutrophy, the volvingaspects of nutrient loading, nutrient changes do not occur at sharply defined concentration, productivity, faunal and places, nor do they all occur at the same floral quantity and quality, and even lake place or at the same rate. Somelakes may morphometry. As such, trophic status be considered oligotrophic by one criterion could not be evaluated by examining one or and eutrophic by another; this problem is two parameters. Such reasoning may have fostered multiparameter indices (e.g. Bre- 1Contribution 141 from the Limnological Re- search Center, University of Minnesota. This work zonik and Shannon 1971; Michalski and was supported in part by Environmental Protec- Conroy 1972). A multiparameter index is t I tion Agency training grant U910028. limited in its usefulnessbecause of the num- I · Present address: Department of Biological Sciences, Kent State University, Kent, Ohio ber of parameters that must be measured. 44242. In addition, the linear relationship assumed UMNOLOGY AND OCEANOGRAPHY 361 MARCH 1977, v. 22(2) 362 Carlson between the parameters in some of these I chose algal biomass as the key descrip_ indices does not hold as evidence presented tor for such an index largely because algal below indicates. bloomsare of concern to the public. An in- Alternatives to the multidimensional dex that is particularly sensitive to such trophic concept have been based on a sin- concern would facilitate communicationbe- gle criterion, such as the rate of supply of tween the limnologistand the public. either organic matter (Rodhe 1969) or nu- Values for algal biomass itself are diffi- trients (Beeton and Edmondson 1972) into cult to use in the index because biomassis a lake. Indices based on a single criterion a poorly defined term, usually in turn esti- potentially could be both unambiguous and mated by one or more parameters such as sensitive to change. However, there is cur- dry or wet weight, cell volume, particulate rently no consensus as to what should be carbon, chlorophyll, or Secchi disk trans- the single criterion of trophic status, and parency. I constructed the index using the it is doubtful that an index based on a sin- range of possible values for Secchi disk gle parameter would be widely accepted. transparency. In addition to having values easily transformed into a convenient scale, Basisfor a new index Secchi disk transparency is one of the sim- The ideal trophic state index (TSI) plest and most often made limnological should incorporate the best of both the measurements. Its values are easily under- above approaches, retaining the expression stood and appreciated. of the diverse aspects of trophic state found The relationship between algal biomass in multiparanleter indices yet still having and Secchi disk transparency is expressed the simplicity of a single parameter index. by the equation for vertical extinction of This can be done if the commonly used light in water trophic criteria are interrelated. The evi- dence is that such is the case. Vollenweider I"= Ioe-(k-+kt>.8, (1) (1969, 1976), Kirchner and Dillon (1975), whereIe= light intensityat the depth at and Larsen and Mercier (unpublished) which the Secchi disk disappears, 10=in- have developed empirical equations to pre- tensityof light strikingthe water surface, dict phosphorus concentration in lakes kw= coefficientfor attenuationof lightby from knowledge of phosphorus loading. water and dissolved substances, kb =coef- Sakamoto (1966) and Dillon and Rigler ficient for attenuation of light by particu- 1 (1974) have shown a relationship between late matter, and z depth at which the vernal phosphorus concentration and algal = .1 biomass,measured as chlorophylla concen- Secchi disk disappears. The term k'b can tration. Lasenby (1975) used Secchi disk be rewritten as aC, where a has the dimen- transparency to predict areal hypolimnetic sions of m2 mg-1 and C is the concentration oxygen deficits. If many of the commonly of particulate matter (mg m-B). Equation i used trophic criteria could be related by a 1 can then be rewritten as series of predictive equations, it would no longer be necessaryto measure all possible trophic parameters to determine trophic status. A single trophic criterion, e.g. algal and rearranged to form the linear equation biomass,nutrient concentration,or nutrient loading, could be the basis for an index from which other trophic criteria could be (~)(ln ~:) = kw+ aC. (3) estimated or predicted by means of the es- III is about 10% of 10 (Hutchinson 1957; tablished relationships. Alternatively, mea- Tyler 1968) and can be considered to be a surements of any of the trophic criteria constant. Alpha may vary depending on could be used to determine trophic status. the size and on the light-absorption and Co Trophic state index 363 100 o o . 100 120 o , , , , " . ", . ;> o 0 100 E o f 10 o " o '5. oo , PI 80 o , is . E . , - .'0' CI I . E .~"''''.. ., - , , , , nil 60 0 , , = .. , , s:>. .. a. 0.. 0L. f". 0' 0 o 0 s: 40 'f · u ... o .. 20-1 . Ie.. 0.1 1 10 100 . Secchi Disk Transparency em) .<: ... 0. "'. ......-.. ... _8. 2 G 7 8 9 10 11 12 13 Secch i Disk Transparency (meters) Fig. 1. Relationship between Secchi disk transparency and near-surface concentrations of chloro- phyll a. Insert: log-log transformation of same data. Dashed line indicates slope of 1.0. light-scattering properties of the particles, ency is inverselyproportional to the sum of but intuitively one would expect the value, the absorbance of light by water and dis- which is the reciprocal of the amount of solved substances (k",) and the concentra- particulate matter per square meter in the tion of particulate matter (C). In many water column above the Secchi disk, not lakes studied, k",is apparently small in re- to vary as a function of algal concentration, lation to C, and hyperbolic curves are ob- and for this discussion it is considered a tained when Secchi disk transparency is constant plotted against parameters related to algal According to Eq. 3, Secchi disk transpar- biomass, such as chlorophyll a (Fig. 1). 364 Carlson Constructionof the index At the same time it retains the original I defined trophic states for the index meaning of the nomenclatural trophic sys- using each doubling of algal biomass as the tem by using major divisions (10, 20, 30, criterion for the division between each etc.) that roughly correspond to existing state, i.e. each time the concentration of concepts of trophic groupings. algal biomass doubles from some base Adc1ltion of other parameters value, a new trophic state will be recog- nized. Because of the reciprocal relation- The regression of Secchi disk against ship between biomass concentration and chlorophylla and total phosphorus was cal- Secchi disk transparency, each doubling in culated from data readily available. The biomass would result in halving transpar- number of data points and the number of ency. By transforming Secchi disk values parameters used can be expanded. The to the logarithm to the base 2, each bio- data used came from Shapiro and Pfann- mass doubling would be represented by a kuch (unpublished), Schelskeet al. (1972), whole integer at Secchi disk values of 1 Powers et al. (1972), Lawson (1972), Me- m, 2 m, 4 m, 8 m, etc. gard (unpublished), and Carlson (1975). I felt that the zero point on the scale Chlorophyll a (Fig.