carlson trophic state index

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A trophic state index for lakes1

Robert E. Carlson

Limnological Research Center, University of Minnesota, Minneapolis 55455

AbstractA 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 doublingin algal biomass. The index number can bc calculated from any of several parameters,including Secchi disk transparency, chlorophyll, and total phosphorus.

My purpose here is to present a new ap-proach to the trophic classification of lakes.This new approach was developed becauseof frustration in communicating to the pub-lic both the current nature or status of lakesand their future condition after restorationwhen the traditional trophic classificationsystem is used. The system presented hcrc,termed a trophic state index (TSI), in-volves new methods both of definingtrophic status and of determining that statusin lakes.

All trophic classification is based on thedivision of the trophic continuum, howcvcrthis is defined, into a series of classestermed trophic states. Traditional systemsdivide the continuum into three classes:oligotrophic, mesotrophic, and cutrophic.There is often no clear delineation of thesedivisions. Determinations of trophic stateare made from examination of several di-verse criteria, such as shape of the oxygencurve, species composition of the bottomfauna or of the phytoplankton, conccntra-tions of nutrients, and various measures of

biomass or production. Although eachchanges from oligotrophy to eutrophy, thechanges do not occur at sharply definedplaces, nor do they all occur at the sameplace or at the same rate. Some lakes maybe considered oligotrophic by one criterionand eutrophic by another; this problem is

1 Contribution 141 from the Limnological Re-search Center, University of Minnesota. This workwas supported in part by Environmental Protec-

tion Agency training grant U910028.’ Present address: Department of BiologicalSciences, Kent State University, Kent, Ohio44242,

sometimes circumvented by classifyinglakes that show characteristics of both oli-go trophy and cutrophy as mesotrophic.

Two or three ill-defined trophic statescannot meet contemporary demands for ascnsitivc, unambiguous classification sys-tem. The addition of other trophic states,such as ultra-oligotrophic, meso-eutrophic,etc., could increase the discrimination of theindex, but at present these additional divi-sions arc no better defined than the firstthree and may actually add to the confu-sion by giving a false sense of accuracy andsensitivity.

I acknowledge the advice and encourage-ment of J. Shapiro in developing this indexand in preparing the manuscript. I alsothank C. IIedman and R. Armstrong for ad-vice and H. Wright for help in manuscriptpreparation.

Current approaches

The large number of criteria that havebeen used to determine trophic status hascontributed to the contention that the

trophic concept is multidimensional, in-volving aspects of nutrient loading, nutrientconcentration, productivity, faunal andfloral quantity and quality, and even lakemorphometry. As such, trophic statuscould not be evaluated by examining one ortwo parameters. Such reasoning may havefostered multiparameter indicts (e.g. Bre-zonik and Shannon 1971; Michalski andConroy 1972). A multiparameter index is

limited in its usefulness because of the num-ber of parameters that must be measured.In addition, the linear relationship assumed

LIMNOLOGY AND OCEANOGRAPIIY 361 MARCH 1977, V. 22(2)



362 Carlson

between the parameters in some of theseindices does not hold as evidence presentedbelow indicates.

Alternatives to the multidimensionaltrophic concept have been based on a sin-gle criterion, such as the rate of supply ofeither organic matter ( Rodhe 1969) or nu-trients (Beeton and Edmondson 1972) intoa lake. Indices based on a single criterionpotentially could be both unambiguous andsensitive to change. However, there is cur-rently no consensus as to what should bethe single criterion of trophic status, andit is doubtful that an index based on a sin-gle parameter would be widely accepted.

Basis for a new index

The ideal trophic state index (TSI )should incorporate the best of both theabove approaches, retaining the expressionof the diverse aspects of trophic state foundin multiparameter indices yet still havingthe simplicity of a single parameter index.This can be done if the commonly usedtrophic criteria are interrelated. The evi-

dence is that such is the case. Vollenweider( 1969, 1976)) Kirchner and Dillon ( 1975))and Larsen and Mercier (unpublished)have developed empirical equations to pre-dict phosphorus concentration in lakesfrom knowledge of phosphorus loading.Sakamoto (1966) and Dillon and Rigler(1974) have shown a relationship betweenvernal phosphorus concentration and algalbiomass, measured as chlorophyll a conccn-tration. Lasenby (1975) used Secchi disk

transparency to predict areal hypolimneticoxygen deficits. If many of the commonlyused trophic criteria could be related by aseries of predictive equations, it would nolonger be necessary to measure all possibletrophic parameters to determine trophicstatus. A single trophic criterion, e.g. algalbiomass, nutrient concentration, or nutrientloading, could be the basis for an indexfrom which other trophic criteria could beestimated or predicted by means of the es-tablished relationships. Alternatively, mea-surements of any of the trophic criteriacould be used to determine trophic status.

I chose algal biomass as the key descrip-tor for such an index largely because algalblooms are of concern to the public. An in-dex that is particularly sensitive to suchconcern would facilitate communication be-tween the limnologist and the public.

Values for algal biomass itself are diffi-cult to use in the index because biomass isa poorly defined term, usually in turn esti-mated by one or more parameters such asdry or wet weight, cell volume, particulatecarbon, chlorophyll, or Secchi disk trans-parency. I constructed the index using therange of possible values for Secchi disktransparency. In addition to having valueseasily transformed into a convenient scale,Secchi disk transparency is one of the sim-plest and most often made limnologicalmeasurements. Its values are easily under-stood and appreciated.

The relationship between algal biomassand Secchi disk transparency is expressedby the equation for vertical extinction oflight in water

1, = Ioe-(hu+b)~, (1)

where I, = light intensity at the depth atwhich the Secchi disk disappears, I0 = in-tensity of light striking the water surface,k, = coefficient for attenuation of light bywater and dissolved substances, kb = coef-ficient for attenuation of light by particu-late matter, and x = depth at which theSecchi disk disappears. The term kb canbe rewritten as aC, where a! has the dimen-sions of m2 mg-l and C is the concentrationof particulate matter (mg m-3). Equation1 can then be rewritten as

and rearranged to form the linear equation

= k, + aC. (3)

I, is about 10% of I0 (Hutchinson 1957;Tyler 1968) and can be considered to be aconstant. Alpha may vary depending onthe size and on the light-absorption and



Trophic state index 363

I I I I I I01 1 10 100

Secchi Disk Transparency (m)

Secchi 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,but intuitively one would expect the value,which is the reciprocal of the amount ofparticulate matter per square meter in thewater column above the Secchi disk, notto vary as a function of algal concentration,

and for this discussion it is considered aconstant.

According to Eq. 3, Secchi disk transpar-

ency is inversely proportional to the sum ofthe absorbance of light by water and dis-solved substances (k,) and the concentra-tion of particulate matter (C). In manylakes studied, k, is apparently small in re-lation to C, and hyperbolic curves are ob-

tained when Secchi disk transparency isplotted against parameters related to algalbiomass, such as chlorophyll a (Fig. 1).



364 Carlson

Construction of the index

I defined trophic states for the indexusing each doubling of algal biomass as thecriterion for the division between eachstate, i.e. each time the concentration ofalgal biomass doubles from some basevalue, a new trophic state will be recog-nized. Because of the reciprocal relation-ship between biomass concentration andSecchi disk transparency, each doubling inbiomass would result in halving transpar-ency. By transforming Secchi disk valuesto the logarithm to the base 2, each bio-mass doubling would be represented by awhole integer at Secchi disk values of 1m, 2 m, 4 m, 8 m, etc.

I felt that the zero point on the scaleshould be located at a Secchi disk (SD)value greater than any yet reported. Thegreatest value reported by Hutchinson(1957) is 41.6 m in Lake Masyuko, Japan.The next greatest integer on the log2 scaleis at 64 m. A trophic state index ( TSI )value of 0 at 64 m is obtained by subtract-ing the log, of 64 from an indexing numberof 6, giving a final TSI equation of

TSI = 10(6-logs SD). (4

The value is multiplied by 10 to give thescale a range of 0 to 100 rather than 0 to10. Two significant digits are all that canbe reasonably expected. The completedscale begins at 0 at SD = 64 m, with 32 mbeing 10; 16 m, 20; 8 m, 30; etc. The theo-retical limit is indefinite, but the practicallimit is 100 or 110 (transparency values of6.4 and 3.2 cm).

The scale is intentionally designed to benumerical rather than nomenclatural. Be-cause of the small number of categoriesusually allot ted in nomencla tural systems,there is both a loss of information whenlakes are lumped together and a lack ofsensitivity to trophic changes. This problemis alleviated as more and more trophicstate names are added, but the system soonbecomes so encumbered that it loses its

appeal. The scale presented here, a nu-merical classification with more than 100trophic categories, avoids these problems.

At the same time it retains the originalmeaning of the nomenclatural trophic sys-tem by using major divisions (10, 20, 30,etc.) that roughly correspond to existingconcepts of trophic groupings.

Addition of other parameters

The regression of Secchi disk againstchlorophyll a and total phosphorus was cal-culated from data readily available. Thenumber of data points and the number ofparameters used can be expanded. Thedata used came from Shapiro and Pfann-kuch (unpublished), Schelske et al. ( 1972))Powers ct al. ( 1972), Lawson ( 1972), Me-gard (unpublished), and Carlson ( 1975).

Chlorophyll a ( Fig. 1) does not give alinear fit to the model predicted in Eq. 2.A nonlinear element in the relationship ne-ccssitated a log-log transformation of thedata. The resulting equation is

In SD = 2.04 - 0.68 In Chl (5)(r = 0.93, n = 147),

where SD transparency is in meters andChl a concentration is in milligrams percubic meter taken near the surface. Onepossible explanation for this exponentialrelationship may be that as algal densityincreases, the algae become increasinglylight limited. In response to lower lightper unit cell, more chlorophyll may be pro-duced ( Steele 1962).

When all available data were included,the regression of total phosphorus (TP inmg m-” ) against the reciprocal of Secchidisk transparency yielded

SD = 64.9/TP(r=0.89, n=61).

(6)

Total phosphorus should correlate bestwith transparency when phosphorus is themajor factor limiting growth. Correlationsmay be poor during spring and fall over-turn when algal production tends to belimited by temperature or light. Prelimi-nary use of the above regression coefficients

in the index suggested that the equationdots predict the average seasonal relation-ship between total phosphorus and trans-




Table 1. Completed trophic state index andits associntcd parameters.

Surface SurfaceSecchi phosphorus

TSI disk (m) (mg/m31chlorophyll

(mg/m3)

0 64 0.75 0.0410

z1.5 0.12

;o2

0.348 0.944 12 2.6

2:2 24 6.41 4 8 20

78::0.5 96 560.25

;zc154

90 0.12 427100 0.062 760 U83

parency, but its predictions for phosphorus

are too high in spring and fall and toolow during summer. Because the equationis to be used in an index where agreementof correlated parameters is emphasized, Idecided to use only summer values in theregression to provide the best agreement oftotal phosphorus with algal parameters dur-ing the season when sampling would nor-mally be done.

There were not enough data availablefor phosphorus and transparency during

July and August to produce a meaningfulregression. Instead, chlorophyll was rc-gressed against total phosphorus and theresulting equation combined with Eq. 4 toproduce a phosphorus-transparency equa-tion. The chlorophyll-total phosphorus forJuly and August data points yielded

In Chl = 1.449 In TP - 2.442 (7)(r=0.846, n=43).

This equation is similar to that derived by

Dillon and Rigler ( 1974) for the relation-ship between vernal total phosphorus andsummer chlorophyll:

In Chl = 1.449 In TP - 2.616. (8)Combining 5 with 7 produced

In SD = 3.876 - 0.98 In TP, (9)or approximately

SD=48(l/TP). (10)

This equation was used in the index,The trophic state index can now be com-

puted from Secchi disk transparency, chlo-

rophyll, or total phosphorus. Thetional forms of the equations are

computa-

TSI( SD) = 10 6 -g, (11)

TSI(Ch1) = 10(

6-2.04 - 0.68 In Chl

In 2 >, (12)

and

TSI(TP) =lO (13)

The completed scale and its associated pa-rameters are shown in Table 1.

Using the index

Seasonal TSI values for several Minne-sota lakes are plotted in Fig. 2. The TSIvalues for total phosphorus tended to fluc-tuate less than those for the biological pa-rameters, which approached the valuesbased on phosphorus during July and espe-cially August and September. The extremefluctuations in the TSI based on biologicalparameters in May and June may resultfrom springtime crashes in algal popula-tions. In Lake Harriet, the chlorophyll andSecchi disk TSI values rcmaincd below thephosphorus TSI throughout summer. Thisdivergence of the biological TSI valuesfrom the phosphorus TSI cannot yet be ex-plaincd, but it does emphasize one of thestrongest advantages of individually deter-mined trophic indices. All parameters whentransformed to the trophic scale shouldhave the same value. Any divergence fromthis value by one or more parameters de-mands investigation. For example, is itreally true that Lake Harriet is P limited,since it seems to be producing less biomassthan the phosphorus levels would suggest?Thus, the TSI scale not only classifies thelake but can serve as an internal check onassumptions about the relationships amongvarious components of the lake ecosystem.

To use the index for classifying lakes re-quires that a single number be generated

that adequately reflects the trophic statusof the lake. It should be emphasized thatthe number generated is only an index of



366 Carlson

Fig. 2. Seasonal variation in trophic state in-dices calculated from Secchi disk transparency( 0 ), chlorophyll a ( 0 ), and total phosphorus( x ) for three M innesota lakes in 1972.

the trophic status of a lake and does notdefine the trophic status. In other words,chlorophyll or total phosphorus are not con-sidered as the basis of a definition of trophicstate but only as indicators of a more

broadly defined concept. The best indi-cator of trophic status may vary from laketo lake and also seasonally, so the best in-dex to use should be chosen on pragmaticgrounds.

Secchi disk transparency might be ex-pected to give erroneous values in lakescontaining high amounts of nonalgal par-ticulate matter, in highly colored lakes(those with a high k,), and in extremelyclear lakes where 7c, again is an importantfactor in light extinction. The advantageof using the Secchi disk is that it is an ex-tremely simple and cheap measurement andusually provides a TSI value similar to thatobtained for chlorophyll.

Chlorophyll a values are apparently freefrom interference, especially if the valuesare corrected for phiophytin. It may bethat the number derived from chlorophyllis best for estimating algal biomass inmostlakes and that priority should bc given forits use as a trophic state indicator.

Accurate index values from total phos-phorus depend on the assumptions thatphosphorus is the major limiting factor for

algal growth and that the concentrationsof all forms of phosphorus present are afunction of algal biomass. The former as-sumption does not seem to hold during

spring, fall, or winter (Fig. 2) nor is thelatter the case in lakes having high ortho-phosphorus values (such as some lakes re-ceiving domestic sewage) or in highly col-ored lakes where some forms of phosphorusmay be tied up with humic acids (Moyerand Thomas 1970). The advantage of thephosphorus index is that it is relativelystable throughout the year and, because ofthis, can supply a meaningful value duringseasons when algal biomass is far below its

potential maximum.In instances where the biological TSIvalues diverge from that predicted by thephosphorus index, it is not satisfactory toaverage the different values, as the resultingvalue would neither represent the trophicstate predicted by the nutrient concentra-tion nor the biological condition estimatedfrom biological criteria. I suggest that forpurposes of classification priority be givento the biological parameters, especially the

chlorophyll index, during summer, and per-haps to the phosphorus values in spring,fall, and winter, when the algae may belimited by factors other than phosphorus.These priorities would result in about thesame index value during any season of theyear.

Some period should be identified duringwhich samples should be taken for lakeclassification. It might be argued that sam-plcs should be taken throughout a calen-dar year to include all variations in trophicstatus, but this would require the switchingof index parameters during the year, asmentioned above, and the large number ofsamples required might limit the usefulnessof the index.

Basing the index on samples taken dur-ing spring or fall turnover would providea phosphorus index based on mean phos-phorus concentration, a measurement usedin most predictive loading models. IIow-

ever, some disadvantages of limiting sam-pling to overturn periods are the brief oreven nonexistent overturn in some lakes




and the possibility of a lessened agreementwith the biological parameters. In addition,mean phosphorus concentrations could becalculated at any time if appropriate mor-phometric data were available. An alter-native might be to take epilimnetic sam-ples during summer stratification, whenthere should be the best agreement betweenall of the index parameters. This wouldallow confidence in comparisons betweenstudies that used different parameters. Thisperiod would also coincide, in temperatelakes, with peak recreational usage, increas-ing the utility of the index in communicat-ing the meaning of the classification to the

general public.A calculation of TSI values from the

yearly data for Lake Washington (Fig. 3),supplied by W. T. Edmondson, also illus-trates the utility of the scale. In 1957, thelake was receiving 57% of its phosphorusfrom sewage effluent, and there was a no-ticeable deterioration in water quality.Sewage diversion began in 1963, and by1968, 99% of the sewage had been divertedfrom the lake (Edmondson 1970). Al-though the data plotted in Fig. 3 show theincrease and decrease in nutrients and re-sulting biological changes, the rates ofchange differ considerably for each param-eter. Chlorophyll a seems to be only slightlyaffected until 1961, whereas Secchi disktransparency shows a drastic decrease be-tween 1950 and 1955. Conversely, aftersewage diversion in 1963, chlorophyll ashows a dramatic decrease, while there isa 3-year lag before Secchi disk transpar-ency changes noticeably. These discrepan-cies in rates of response are the result ofthe inverse relationship between chlorophyllconcentration and transparency. Secchidisk transparency is very sensitive to bio-mass changes at low concentrations, butis insensitive at high concentrations, Ifonly chlorophyll had been measured duringthe 195Os, it might have seemed that sig-nificant changes in the lake did not occuruntil after 1961. When chlorophyll valuesare converted to TSI, however, they canbe seen to be responding rapidly to enrich-ment, and the changes parallel those in the

Secchi Disk Trons~orency

Chlorophyll ax

Total Pimsphorus

Fig. 3, Top: Yearly changes in average sum-mer values of three parameters in Lake Wash-ington, Seattle, Washington. Below: Data trans-formed into trophic state index values.

TSI values based on transparency. The TSIvalues predicted by total phosphorus closelyparallel the biological TSI values, addingstrength to the argument that phosphoruswas the key nutrient in determining thebiological trophic state of Lake Washing-ton.

Discussion

The trophic index presented here hasseveral advantages over previous attemptsat trophic classification.

The scale is numerical rather than no-menclatural, allowing a large number of in-dividual lake classes rather than three tofive distinct ones. This allows sensitivityin describing trophic changes. The major



368 Carlson

trophic divisions have a logical basis,namely the doubling of concentrations ofsurface algal biomass, which should makethe trophic state classification more ac-ceptablc theoretically.

Although the scale itself is constructedfrom a single paramctcr, the mathematicalcorrelation with other parameters allowssome latitude in selecting the best one fora given situation, The use of correlatedparameters also allows trophic comparisonsbetween lakes where different types of datawcrc collected in different studies. Calcu-lation of the index for more than one pa-rameter for a given lake also serves as aninternal check both on methodology andon assumptions as to relationships betweenparameters.

The data used can be minimal or cxten-sive, depending on the level of accuracy de-sired and the resources available. Secchidisk values alone can give a trophic stateclassification, information that can be col-lected even by nonscientists in public-par-ticipation programs at little expense ( Sha-piro et al. 1975). If the survey is more

extensive, data on chlorophyll and totalphosphorus can provide supplementary oralternative index values. The index numbergives both the public and the limnologista reasonably accurate impression of a lake’swater quality. For the layman, the num-ber may have little meaning at first, but itcan readily be transformed into Secchitransparency, which is easily understood.By analogy, the Richter scale hasmeaning for people other than seismolo-gists. For the limnologist the index canbc an aid in communication between him-self and other scientists. With only theTSI value, a reasonable estimate can bemade of the Secchi disk transparency,chlorophyll, and total phosphorus.

The index can be used as a predictivetool in lake-management programs. If themean total phosphorus after nutrient abate-ment can be predicted with loading-rate

equations such as those of Vollenweider( 1969, 1976), then a new TSI can easily becalculated and the biological conditions of

the lake estimated. This should prove ofvalue to groups interested in determininghow much nutrient abatement is necessaryto reach a desired trophic condition.

The index can bc used for regional classi-fication of all surface waters, includingstreams and rivers. Any body of watercould bc classified using the total phos-phorus index, which is essentially a predic-tor of potential algal biomass. Hutchinson(1969) suggested that lakes and theirdrainage basins should be consideredas trophic systems, where a eutrophicsystem is one in which the potentialconcentration of nutrients is high. The in-dcx allows the classification of that poten-tial concentration for a watershed or re-gion, at least on the basis of phosphorus.Such a classification could develop anawareness of regional patterns in trophicpotential, and could then also allow regionaltrophic standards to be the basis of rationalmanagement.

Finally, a trophic state index is not thesame as a water quality index. The termquality implies a subjective judgment that

is best kept separate from the concept oftrophic state. A major point of confusionwith the existing terminology is that eu-trophic is often equated with poor waterquality. Excellent, or poor, water qualitydepends on the use of that water and thelocal attitudes of the people. The definitionof trophic state and its index should re-main neutral to such subjective judgments,remaining a framework within which vari-ous evaluations of water quality can bemade. The TSI can be a valuable tool forlake management, but it is also a valid scien-tific tool for investigations where an objec-tive standard of trophic state is necessary. Ihope that the index can serve as a standardof trophic measurement against which com-parisons can be made between the manychemical and biological components of thelake system that are related to trophicstatus. The result could be a more com-

plete and dynamic picture of how thesecomponents relate to one another and tothe lake ecosystem as a whole.




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RODIIE, W. 1969. Crystallization of euttophi-cation concepts in northern Europe, p. 50-64. In Eutrophication : causes, consc-quenccs, corrcctivcs. Natl. Acad. Sci. Publ.1700.

SAKAMOTO, M. 1966. Primary production byphytoplankton community in some Japaneselakes and its dependence on lake depth. Arch.Wydrobiol. 62 : l-28.

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DU~LON, P. J., AND F. I-1. RIGLER. 1974. Thephosphorus-chlorophyll relationship in lakes.Limnol, Oceanogr. 19 : 767-773.

EDMONDSON, W. T. 1970. Phosphorus, nitro-gen, and algae in Lake Washington after di-version of sewage. Science 169 : 690-691.

HUTCHINSON, G. E. 1957. A treatise on lim-nology, v. 1. Wiley.

-. 1969. Eutrophication: Past and pres-cnt, p. 17-26. In Eutrophication: Causes,consequences, correctives. NatI. Acad. Sci.Publ. 1700.

KIIWIINEH, W. B., AND P. J. DILLON. 1975. Anempirical method of estimating the retentionof phosphorus in lakes. Water Resour. Res.11: 182-183.

LASENBY, D. C. 1975. Dcvelopmcnt of oxygendeficits in 14 southern Ontario lakes. Limnol.Oceanogr. 20 : 993-999.

LAWSON, D. W. 1972. Temperature, trans-

parency, and phytoplankton productivity inCrater Lake, Oregon. Limnol, Oceanogr. 17 :410-417.

MICIIALSKI, M. F., AND N. CONROY. 1972.Water quality evaluation-Lake Alert study.Ontario Min. Environ. Rep. 23 p,

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Announcement

SCHELSKE, C. L., L. E. VELDT, M. A. SANTIAGO,AND E. F. STOERMER. 1972. Nutrient en-richment and its effect on phytoplankton pro-duction and species composition in Lake

Superior. Proc. 15th Conf. Great Lakes Res.1972 : 149-165.

SIIAPJRO, J., J. B. LUNDQUIST, AND R. E. CARLSON.1975. Involving the public in limnology-an approach to communica tion. Int. Ver.Theor. Angew. Limnol. Vcrh. 19: 866-874.

STEELE, J. IX 1962. Environmental control ofphotosynthesis in the sea. Limnol. Oceanogr.7 : 137-150.

TYLER, J. E. 1968. The Secchi disc. Limnol.Oceanogr. 13: l-6.

VOLLIWWEIDER, R. A. 1969. Possibilities andlimits of elementary models concerning thebudget of substances in lakes. Arch. Hydro-biol. 66: 1-36.

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Submitted: 5 February 1975Accepted: 18 November 1976

Pacific Section, American Society of Limnology and Oceanography, Inc.

The Pacific Section will meet 12-16 June 1977 at San Francisco StateUniversity, San Francisco, California. A symposium on “The San Fran-cisco Bay” is scheduled for 13 June. Symposia on “Coastal upwelling”and “Ecology of western streams and rivers” arc planned for 15 June,

carlson trophic state index

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