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CHARACTERIZATION OF THE TROPHIC CONDITIONS OF

MARINE COASTAL WATERS WITH SPECIAL REFERENCE

TO THE NWADRIATIC SEA: PROPOSAL FOR A TROPHIC

SCALE, TURBIDITY AND GENERALIZED WATER

QUALITY INDEX

R. A. VOLLENWEIDER,1,2* F. GIOVANARDI3, G. MONTANARI1 AND A. RINALDI1

1Laboratory `M. M. Daphne II', Emilia Romagna Region, Centre for Marine Research, Cesenatico (Forli), Italy2National Water Research Institute, Canada Centre for Inland Waters, Burlington, Ontario, Canada

3ITALCOPO' S.P.S. S.p.A., Parma, Italy

SUMMARY

In pursuing earlier attempts to characterize the trophic state of inland waters, a new trophic index (TRIX)based on chlorophyll, oxygen saturation, mineral and total nitrogen and phosphorus, and applicable tocoastal marine waters, is proposed. Numerically, the index is scaled from 0 to 10, covering a wide range oftrophic conditions from oligotrophy to eutrophy. Secchi disk transparency combined with chlorophyll,instead, de®nes a turbidity index (TRBIX) that serves as complementary water quality index. The twoindices are combined in a general water quality index (GWQI). Statistical properties and application ofthese indices to speci®c situations are discussed on examples pertaining to the NW Adriatic Sea. It isbelieved that these indices will simplify and make comparison between di�erent spatial and temporaltrophic situations of marine coastal waters more consistent. # 1998 John Wiley & Sons, Ltd.

KEY WORDS eutrophication; trophic indices; Adriatic Sea

1. INTRODUCTION

The harmful e�ects of eutrophication on the coastal marine environment worldwide are welldocumented (Vollenweider et al., 1992; REDTIDE Newsletters, various). Since marine coastaleutrophication has become more frequent over recent years, words like `oligotrophy', `meso-trophy' and `eutrophy' (a terminology largely developed by limnologists to characterize thetrophic conditions of inland waters) have also become more frequent in the marine literature.There is general agreement that oligotrophy means nutrient poor (�low productivity) andeutrophy means nutrient rich (� high productivity) waters. However, little is said regarding `howproductive', and where the boundaries between categories are to be set.

Trophic condition of vast marine areas, like the Mediterranean, vary considerably fromregion to region and within regions (UNESCO, 1988; Vollenweider et al., 1996). In coastal areas

CCC 1180±4009/98/030329±29$17.50 Received 4 June 1997# 1998 John Wiley & Sons, Ltd. Revised 21 December 1997

ENVIRONMETRICS

Environmetrics, 9, 329±357 (1998)

* Correspondence to:R. A. Vollenweider, National Water Research Institute, 867 Lakeshore Road, Burlington, Ontario,Canada L7R 4A6.

manifestations of eutrophication show not only various patterns of spatial inshore±o�shore andalong shore gradients, but often also considerable year to year variations in both intensity andextension, especially if they are under the direct in¯uence of major rivers like some heavilyeutrophied coastal stretches of the NW Adriatic Sea (Rinaldi and Montanari, 1988; Degobbisand Gilmartin, 1990; Franco and Michelato, 1992; Vollenweider et al., 1992). Yet, an objectivetrophic characterization of bodies of waters with a few catchwords remains a trying matter in anycase, since attempts of this sort inevitably imply a rather arbitrary fusion of qualitative andquantitative judgement elements. Therefore, the use made of the trophic terminology by variousauthors often hinges on the authors' objectives, intentions and/or personal beliefs, rather than onthe application of a set of criteria agreed upon by convention. As the development of a trophicreference system properly tuned to the marine environment is still unsettled (Giovanardi andTromellini, 1992; Ignatides et al., 1992; Innamorati and Giovanardi, 1992), misapplication of thelimnological terminology to marine waters is even more likely to occur. This creates not onlyuncertainties between researchers, but also di�culties about the way the essence of ®ndings areconveyed in a single manner to administrators and to the public at large. For such reasons theneed was felt to devise a method that would permit to synthesise key data into a simple numericexpression to make information comparable over a wide range of trophic situations, whileavoiding the subjectivity in the usage of traditional trophic terminology. This is the objective ofthe present paper.

2. CONCEPTUAL FRAME

There have been numerous e�orts to typify and compare the trophic conditions of bodies ofinland water (e.g. Thienemann, 1928; Naumann, 1932; AÊ berg and Rodhe, 1942; Sawyer, 1947;Elster, 1962; Vollenweider, 1968; Shannon and Brezonik, 1972; Carlson, 1977; Uhlmann, 1979;Vollenweider and Kerekes 1982; Hillbricht-Ilkowska, 1984; SchroÈ der, 1991). Some of thepertinent criteria used by authors entail general features, others instead are more speci®c. Also,various attempts have been made to scale parameters, and to correlate the respective quantitieswith the perceived trophic conditions of waters in terms of an index. Of particular interest to thefollowing development are those that are based on a few parameters most commonly measured inroutine surveillance studies in both fresh and marine waters, such as: nutrients, phytoplanktonbiomass, transparency, and a few others. Among the respective indices to mention:

(1) Uhlmann/Verduin's Index using carbon, nitrogen and phosphorus;(2) Carlson's Index using chlorophyll, total phosphorus, Secchi transparency;(3) SchroÈ der's Correlation Model that considers a variety of nutritional and environmental

factors in a correlative way;(4) The OECD Classi®cation which de®nes trophic categories probabilistically using total

phosphorus, average chlorophyll, peak chlorophyll, Secchi transparency.

The speci®cations of these indices (or models) are summarized in Appendix 1. Each one hasmerits as well as limitations. From a methodological point of view, all have in common that fordata elaboration more or less complex transformations and/or statistical summaries of theoriginal data are used. For the purpose of synthetically characterizing marine trophic conditions,Uhlmann's model is too general, but would have the advantage that the basic equation couldeasily be adjusted to include other nutrients, such as trace elements using the same algorithm;

ENVIRONMETRICS, VOL. 9, 329±357 (1998) # 1998 John Wiley & Sons, Ltd.

330 R. A. VOLLENWEIDER ET AL.

however, the correct scaling of such factors remains as yet unresolved. Also, except in brackishwaters of high pH, carbon in marine waters is hardly limiting; thus, Uhlmann's model reducesin practice to phosphorus and nitrogen, whereby it is even not entirely clear which forms ofphosphorus and nitrogen (inorganic, soluble, total) should be used for calculation. SchroÈ der'smodel, which in its conception is the most interesting, cannot easily be modi®ed for the marineenvironment. Carlson's index and the OECD concept, instead, require relatively modestmodi®cations. Earlier attempts (Giovanardi and Tromellini, 1992) to apply the OECD method-ology to coastal marine waters showed promising avenues, yet, had still as objective to classifywaters within a system of trophic categories (cf. Appendix 4).

The most important objection to transfer limnological models unmodi®ed to marine condi-tions are neither salinity nor biotic di�erences, but stems from the fact that limnological trophiccriteria intend to characterize lakes in their entirety. Lakes, by their very nature, are limited in sizeand volume, and as such are relatively well de®ned entities. Except in very large and/or elongatedlakes, gradients in lacustrine waters are normally modest, wherefore in most cases a representativedescription of their conditions can be obtained from measurements at a few strategically welllocated stations and the respective depth pro®les. Accordingly, the derived trophic character-istics are usually thought to apply to the body of water as a whole, and not just to a limitedfraction of it.

Except for certain areas, such as enclosed bays, lagoons, certain estuaries, etc., this conceptionis largely inappropriate for the marine environment. For coastal areas adjacent to majordischarge sources in particular, where the prevailing currents, inshore±o�shore exchanges,weather and wind conditions, tidal e�ects, upwelling, etc., continuously modify chemical±biological and physical divergencies over relatively short distances (1±100 km; time scale, days toweeks) a purely numeric scale that makes it possible to score the trophic properties of watersstation by station, and/or sequential in time, would be preferable to categorical denominators.Such a conception is closest to Carlson's, and in some sense the following development may beconsidered as a modi®cation of it.

3. DESIGN OF A TROPHIC SCALE FOR MARINE WATERS

3.1. Basic design principles

There are various modalities of contriving indices to characterize a phenomenon either qualita-tively or quantitatively, or both. Conditions that pertain to all valid indices are: (a) relevance ofthe index components for identifying the phenomenon in a meaningful way, (b) limitation ofvalidity within a speci®ed ambience and/or a numerical range de®ned by boundary values.

One of the simplest way to devise a numerical index is to express its component values Xi as afraction of the speci®ed validity range, i.e.

Xi � �Mi ÿ Li�=�Ui ÿ Li� �1�

where Mi�measured value of parameter m, Ui� upper limit, Li� lower limit. Accordingly, ifMi� Li , Xi� 0; if Mi�Ui , Xi� 1. Values outside this range are not de®ned.

# 1998 John Wiley & Sons, Ltd. ENVIRONMETRICS, VOL. 9, 329±357 (1998)

TROPHIC CONDITIONS OF MARINE COASTAL WATERS 331

A composite index Xc that is derived from more than one component parameter, say n, can beexpressed either as sum, or as average of the partial Xis, each one with its own upper and lowerlimits U and L, that make up the total index, i.e.

Xc � �1=n�Xi�n1

��M ÿ L�=�U ÿ L��i �2�

If instead one wishes to express an index di�erentiated by degrees (0, 1, 2,. . .k) rather than asfraction between 0 and 1, (1/n) in the above equation is replaced by (k/n), k being the number ofdegrees. Also, depending on the underlying statistical distribution of parameters the values,M,Uand L may be appropriately transformed.

3.2. Approach and criteria for a practical trophic index

In developing the above general framework in terms of an explicit trophic index, the followingprinciples have been observed: Component parameters of the index should (a) be meaningful interms of both, production and production dynamics, (b) encompass major causal factors, (c) be aroutine measurement in most marine surveys.

3.2.1. Comments

Chlorophyll is a substitute parameter for autotrophic phytoplankton biomass and as suchcommonly measured; yet, chlorophyll per se is not an expression of production dynamics.Primary production measured by either the 14C or the oxygen technique, or both, supplementedby measurements of community respiration, would be desirable. However, these are not routinelymeasured. On the other hand, productive systems show noticeable variation in oxygen saturation;low productive systems normally do not. Hence, aD%0 (deviation of oxygen saturation from100%) can be taken as an indicator for the production intensity of the system, encompassingboth phases of active photosynthesis and phases of prevailing respiration. Whereas variations inpH are normally correlated with productivity, its sensitivity for the purpose is low. Among thecausative factors, total nitrogen and total phosphorus are the most representative parameters.Yet, total nitrogen is often not routinely measured. Mineral components, instead, are usuallymeasured, and may be taken as substitute for the totals. The same would apply to total anddissolved mineral phosphorus, but substitution of mineral phosphorus for totals is morequestionable. Silica, trace metals, and other production controlling factors, which could besupplementary indicators, are not routinely measured, and are in any case more di�cult toincorporate into a trophic index.

Problems regarding the suitability of salinity, temperature and transparency, and questionsabout interchangeability, will be discussed below.

3.3. The trophic index TRIX

For the actual development and validation of the proposed trophic index, data collected between1982 and 1993 along the Emilia-Romagna coast have been used as reference. As a whole, thesedata cover a broad array of trophic situations that range from often highly eutrophic inshore to



oligotrophic conditions o�shore (Emilia-Romagna Region Annual Reports 1982±1994). Selectedportions of it have been explored in several examples reported in this paper.

The kind of temporal parameter variations that are found in coastal waters of Emilia-Romagna (cf. Figure 1) is exempli®ed with Figure 2(a) and (b), which refers to a special study ata ®xed station 3 km o�shore of Cesenatico, where from June 1986 to October 1987 almost dailysamples were taken. Because of its representativeness and the broader use made of this materiallater on, statistical summaries of relevant parameters (percentile distribution, averages, standarddeviation, maximum, minimum) and a respective correlation matrix are given in Tables I and II.These, and supplementary multiple regressions, served among others to characterize the numericenvironment, to score correlations between parameters, to identify potential redundancy, and tonarrow down the selection of parameters. Though several trophic indicators, such as chlorophylland nutrients, would be signi®cantly correlated with, for example, salinity, temperature andtransparency, by themselves these latter factors are not trophic indicators. They may be useful

Table I. Adria St.314 1986±87 Surface daily measurements. Statistical summaries

pH TEMP SAL %02 aD%0 ChA NO3 NO2

AVG 8.4 18.0 32.5 105.1 13.1 11.3 267.2 11.2STD 0.1 6.9 2.9 18.1 13.5 21.9 480.6 17.0MAX 8.8 27.1 37.4 176.9 79.4 194.1 4600.0 215.0MIN 8.0 3.8 16.2 20.6 0.0 0.4 0.1 0.1GeoM 8.4 16.2 32.4 103.5 ± 5.4 138.5 5.7

NH4 MinN PT PO4 mN/P TRSP PO*

AVG 22.1 300.5 20.8 5.6 288.8 3.5 12.8STD 25.1 497.9 10.5 4.8 597.4 1.7 6.8MAX 220.0 4776.0 60.0 34.0 3870.0 8.3 47.5MIN 0.1 6.1 2.0 0.1 1.0 0.4 5.3GeoM 12.4 174.1 18.1 2.9 68.6 ± 11.5

Percentile distribution of original data; N� 461

05% 10% 25% 50% 75% 90% 95%

pH 8.18 8.23 8.32 8.41 8.50 8.60 8.66TEMP 5.5 7.0 12.4 20.2 24.2 25.5 26.2SAL 26.5 28.0 31.8 33.3 34.2 35.6 36.1%02 81.6 87.4 95.2 102.4 113.3 127.9 142.4aD%0 0.8 1.5 4.0 8.5 16.8 32.0 44.2ChA 1.3 1.7 2.7 4.4 9.6 27.4 40.1NO3 30 40 66 133 288 479 885NO2 0.1 1.1 3.0 7.5 13.5 20.0 33.8NH4 1 3 8 16 27 43 65minN 47 63 89 157 326 550 928PT 7 9 13 19 27 36 40PO4 0.1 0.1 2.0 4.0 8.0 11.8 15.0mN/P 9.3 13.6 21.6 42.1 192 903 1799TRSP 0.9375 1.25 2 3.5 5 6 6.5PO 6.42 6.88 8.31 10.7 14.8 22.4 27.3

Units in mg/m3 where applicable; Temp in 8C; Sal in %0; Oxygen in % Saturation; D%0 in ABS values; Transparency in(ÿ) meter; *River Po in 100 m3/sec



Figure 1. Emilia-Romagna coast of the NW Adriatic Sea: surveillance grid stations and designated station groups.Inshore groups: G1, G2, G4, G5, G7; O�shore groups: G3, G6, G8



Figure 2. (a) Daily variation of salinity(%), chlorophyll (mg/m3) and oxygen saturation (%) measured from June 1986to October 1987 at St. 314 (Group 6) 3 km o�shore, 0.5 m below surface. Lacking data have been linearly interpolated.

(b) Mineral nitrogen N7 (NO3 � NO2 � NH4) and total phosphorus; mg/m3



for demarcating boundary conditions, assessing overall water quality, or be used in predictivemodelling. Variation in salinity and an array of correlated factors are controlled by the River Poand local rivers, and by the current dynamics that in their co-action determine the speci®ccharacteristics of the coastal system. In multiple regression, salinity, for example, makes outsome 40±50% of all variability, but outside the region this would not necessarily hold. Thebearing of temperature on trophic conditions is doubtful; high production may occur any timeindependent of season and temperature. Transparency, instead, is a complex factor, whichneeds to be considered separately (see below). Therefore, it would be unwise to include suchfactors into a trophic index for which generality is claimed. Conversely, from the matrix canalso be seen that ± beside other relationships ± dissolved mineral phosphorus and nitrogen arehighly correlated with their respective totals; therefore, if deemed necessary, dissolved compo-nents and totals may be used interchangeably to some degree, but not simultaneously to avoidredundancy.

After careful considerations of this sort, the following set of parameters, listed under threeheadings, were selected as useable components of a trophic index:

(a) Factors that are direct expressions of productivity:Chlorophyll `a': [Ch: mg/m3]Oxygen as absolute [%] deviation from saturation: [abs j 100±%0 j � aD%0]

Table II. Adria St.314 1986±87 Surface daily measurements. Correlation matrix

pH TEMP SAL %02 aD%0 ChA NO3 NO2

pH 1.000 ÿ0.016 ÿ0.527 0.596 0.238 0.388 0.155 0.112TEMP 1.000 0.108 ÿ0.159 ÿ0.040 ÿ0.325 ÿ0.511 ÿ0.410SAL 1.000 ÿ0.581 ÿ0.356 ÿ0.460 ÿ0.516 ÿ0.445%02 1.000 0.500 0.559 0.313 0.181aD%0 1.000 0.575 0.248 0.083ChA 1.000 0.391 0.232NO3 1.000 0.796NO2 1.000

Continues: NH4 MinN PT PO4 mN/P TRSP PO

pH ÿ0.246 0.141 ÿ0.052 ÿ0.199 0.126 ÿ0.0454 0.055TEMP ÿ0.372 ÿ0.526 ÿ0.119 ÿ0.361 ÿ0.013 0.30967 0.145SAL 0.031 ÿ0.512 ÿ0.224 ÿ0.095 ÿ0.064 0.39411 ÿ0.290%02 ÿ0.214 0.297 0.180 ÿ0.004 ÿ0.028 ÿ0.3036 0.020aD%0 0.088 0.246 0.153 0.058 ÿ0.075 ÿ0.4121 0.113ChA ÿ0.038 0.384 0.082 0.035 ÿ0.019 ÿ0.4379 0.035NO3 0.120 0.999 0.233 0.310 0.025 ÿ0.3236 0.065NO2 0.104 0.807 0.216 0.341 ÿ0.031 ÿ0.2504 0.036NH4 1.000 0.170 0.218 0.432 ÿ0.032 ÿ0.0935 ÿ0.106minN 1.000 0.243 0.332 0.021 ÿ0.3257 0.058PT 1.000 0.620 ÿ0.285 ÿ0.2434 ÿ0.096PO4 1.000 ÿ0.411 ÿ0.226 ÿ0.127mN/P 1.000 0.04066 0.059TRSP 1.000 0.207PO 1.000

Signi®cance of correlation: P(95%) r� 4 0.095; P(99%) r� 4 0.120; N� 461.



(b) Nutritional factors:(i) Totals

Total nitrogen: [NT: mg/m3]Total phosphorus: [PT: mg/m3]

(ii) AvailableDissolved inorganic nitrogen as N-(NO3 � NO2 � NH3): [DIN�mN: mg/m3]Dissolved inorganic phosphorus as P-PO4: [DIP� PO4: mg/m3]

(c) Supplementary water quality factor:Transparency: [Secchi depth: m]

The components selected for the proposed index are those listed under (a) and (b) above,whereby among the nutritional factors, respectively, two (nitrogen and phosphorus) are selectedaccording to availability of data. The desirable combination are: NT and PT(1), mN and PT(2),mN and PO4(3), in this order; the least desirable, NT and PO4, instead is of little interest.Transparency is used for a supplementary index.

For the de®nition of the upper and lower limits of parameters, one can use either MEAN+2.5 STD, or any other boundary, or robust statistics if the data distribution is uncertain. In anycase, it is desirable to exclude extreme values that occur rarely; otherwise there is the risk that thestatistical con®dence intervals become too large to permit discrimination between di�erentTRIX. The example given in Tables I and II shows further that data distribution of almostnone of the trophic parameters is normal. Whereas the actual distribution should be evaluatedseparately for each parameter, experience shows that simple log transformation approximatesnormal distribution for most parameters of interest (see also Section 4.1). Accordingly, usinglogarithms (10log) rather than untransformed values, the basic structure of the trophic indexTRIX reads

TRIX � �k=n�Xi�n1

��log U ÿ log L�=�log M ÿ log L��i �3�

To simplify calculation, the ranges have been standardized to 3 log units, anchoring the lower,and with this also the upper limits of validity for each parameters as listed in Table III.Introducing these values into the above equation, and ®xing the number of classes to 10, oneobtains by rearranging

TROPHIC INDEX � �LOG�Ch*aD%�O*N*P� ÿ �ÿ1�5��=1�2 �4�

3.4 Calculation, sensitivity and noise of TRIX

A ®rst calculation example using Eq.(4) and data of the same survey is given in Table IV in whichfor the nutritional parameters the three combinations mentioned above are used.1 The syllogismis straight forward, yet, as expected the three indices di�er numerically. How far these di�erencesare signi®cant but interchangeable will be discussed in Section 4. For the time being it is su�cient

1In order to distinguish between di�erent TRIXs one may use the following symbols: TRIX(NT,PT), TRIX(DIN,PT) orTRIX(mN,PT), TRIX(DIN,DIP) or TRIX(mN,PO4); or simply TRIX(NP), TRIX(nP), TRIX(nP), where the uppercases stand for the totals, the lower cases for mineral nitrogen (minN) and mineral phosphorus (essential PO4),respectively.



to keep in mind that, in a strict sense, though, only indices calculated at the same basis arecomparable.

The second example referring to station St.314 introduced above permits a more thoroughassessment of the statistical properties, the contribution of the components to variation, anddiscrimination between TRIXs calculated at the same basis. Using mineral nitrogen and total

Table III. De®nition of the proposed trophic index; lower and upper limits, and range within which thetrophic index is de®ned

Limits and ranges Min log units Max log units Range Step(linear) (linear) log units range/10

(A) Principal parameters:(1) Chlorophyll a ÿ0.5 2.5 3 0.3

(0.32) (316)

(2) D%O-Saturation ÿ1 2 3 0.3abs[100-%O] (0.1) (100)

(3) Total Nitrogen 0.5 3.5 3 0.3[NT] (3.2) (3160)

(4) Total Phosphorus ÿ0.5 2.5 3 0.3[PT] (.32) (316)

Sum of logs of the principal parameters ÿ1.5 10.5 12 (1.2� 4*.3)

Trophic index� (log[Ch*aD%0*N*P]7 [ÿ1.5])/1.2

(B) Alternative parameters:3(a) Dissolved Mineral Nitrogen 0.5 3.5 3 0.3[N(NO3 � NO2 � NH4)] (3.2) (3160)

4(a) Dissolved Mineral Phosphorus ÿ0.5 2.5 3 0.3[P(PO4)] (.32) (316)

(C) Additional water quality parameter:

(5) Transparency*) ÿ0.5 1.5 2 ±(Secchi Disc in m) (0.32) (31.6)

(Linear) concentrations in mg/m3.* See text.

Table IV. Calculation example of trophic indices sample on 3.3.92 at St.314 surface

ChA % Oxygen NT PT mN PO4mg/m3 saturation mg/m3 mg/m3 mg/m3 mg/m3

Analytical data 22.3 184 728 14 343 5

Trophic score Trophic index

TRIX(NT,PT) log(Ch*D%0*NT*PT)� 7.28 (7.28 � 1.5)/1.2� 732TRIX(mN,PT) log(Ch*D%0*mN*PT)� 6.95 (6.95 � 1.5)/1.2� 7.04TRIX(mN,PO4) log(Ch*D%0*mN*PO4)� 6.51 (6.51 � 1.5)/1.2� 6.88



phosphorus Figure 3 displays the temporal variation of TRIX jointly with the two principleaggregate components, log(Ch*aD%0) and log(mN*PT), and the log of the ratio (Ch*aD%/(mN*PT), which represents a utilization e�ciency coe�cient. Numerically TRIX varies from3.33 to 8.67, giving a range of 5.34 with MEAN� 5.507+0.889; distribution is close to normal.Accordingly, the amplitude of ¯uctuation of TRIX over a 16 month period appears to besu�ciently large to permit discrimination between highs and lows. Regarding aggregatecomponents log(mN*PT) is signi®cantly correlated, though at a low level, with log(Ch) and log(Ch*aD%0), but not with log(aD%0). The low correlation is due to the fact that over certainperiods biomass and biomass activity vary in concert with nutrients, while in other periods theopposite is the case (cf. Figure 3). Because of the generally high N/P ratio, log(mN*PT) contri-butes on average some 60±65% to TRIX, thus raising its average level, but the actual variationsof TRIX are controlled to 75% by log(Ch*aD%0).

For heuristic purposes, the result of using PO4 instead of PT is shortly discussed. Theapparently high variability of log(PO4) is somewhat misleading: it results from the fact thatin order to avoid log(0) the value 0.1 has been assigned to data51; this shifts the mode toclass 0-1. Accordingly, also the contribution of log(Ch*aD%0) to the total variation of TRIXreduces to only 52%. While this seems more equilibrated, its real meaning has to be interpreted incontext.

Figure 3. Variation of the trophic index TRIX(mN,PT), its main aggregate components [(log(mN*PT), log(Ch*D%0)];and log (Ch*D%0/mN*PT), calculated for the same data and period as Figure 2. See text.



3.4.1. Noise vis-aÁ-vis total variation of TRIX

The previous arguments are yet insu�cient to answer the question whether, for example, twocontiguous estimates of TRIX are statistically di�erent. There are several ways to deal with thisproblem. Among these, some ideas from control theory (Woodall and Adams, 1989) have beenborrowed. To note, however, that the necessary assumption underlying the theory, i.e. that overprolonged periods of time, say one year, the system is `in statistical control', that is a steady staterandom process, is not strictly valid in our case, in as far as the total systems variability is theresultant of two processes: (a) ¯uctuations due to external forcing functions (e.g. nutrient supply,insolation, temperature, mixing, etc.) that control the broad features of the system, (b) randomnoise within the system superposed over (a). Therefore, the question levels down to distinguishbetween systems ¯uctuations and random noise. Variations that remain within the amplitudes ofrandom noise are considered as statistically not di�erent.

A rough approximation to estimate random noise can be made from the moving range Ri oftwo successive observations X, i.e.

Ri � abs jXi ÿ Xi-1 j ; i � 1; 1; 3; . . .m;

where the mean is,

R � �1=m�Xi�m1

Ri

and the (unbiased) population s (sample size n� 2)� 0.8865*R. Further, the `upper and lowercontrol limits', within which the system would ¯uctuate `normally', is then given byMean(X)+2.6595*R.

Using the data of the example in question, the (unadjusted) average noise range R would resultas 0.372+0.347, the population s as 0.330, and the control limits as +0.989. Clearly, s� 0.330over all changes is smaller than the STD of the TRIX statistics (s� 0.889); yet s due to noisealone must be even smaller because of the inclusion in the R-statistics of changes that are dueto systems ¯uctuation. Thus, assuming for a next approximation that variations 5+0.55(�1.65*0.33; P(90%)) are due to systems ¯uctuations and adjusting the R-series accordingly, theaverage noise range would reduce to Re� 0.320+0.254, and the unbiased population s to 0.284.Calculating instead the Ris as di�erence against the 7 day moving average, Re reduces further to0.297+0.278, and s to 0.263. Plotting of data in various ways shows that ± regardless ofprocedure ± the distribution of Ris is close to exponential up to about 1, above which a clearthough weak break can be noted. The cumulative frequence of Ris4 1 makes up about 5% of thetotal. Accordingly, it seems safe to conclude that s due to random noise is around 0.26 to 0.29,and that two contiguous TRIXs are distinct, if their di�erence is 50.85 (53*s). By implication,this also would validate the assumed scaling resolution of 1 at a scale 0±10 for a single case asadequate, while a ®ner resolution, say 1 at a scale 0±100, would not be.

Further, it is reasonable to conclude that, if a sequence of TRIX values in the above exampleslies outside the 4.5±6.5 range (Mean(X)� 5.5), the system over that phase is mainly dominatedby external forcing functions. This is clearly the case during the early months of 1987(TRIXs4 6.5: period of high water load, low salinity and high nutrient supply); conversely,values of TRIXs5 4.5 have been found on several occasions over the year to coincide with,beside other conditions, turbidity and wave height due to strong winds.



3.5 The turbidity index TRBIX

Whereas water transparency (Secchi disk transparency) is an important quality parameterthat cannot be ignored, it also cannot be incorporated into a trophic index using the samealgorithm as for the other factors. This is because transparency is the resultant of at least threecomponent functions that determine light absorption and scattering: (a) water plus waterdissolved substances, (b) biomass, (c) mineral turbidity (Bukata et al., 1991a). We may assumethat except in particular situations the functions under (a) do not contribute essentially to thevariability of transparency in marine waters, which leaves biomass and turbidity to be considered.If absorption and scattering are solely due to biomass, then waters at any value of transparencyare optically `biomass saturated', that is to say there exists a quanti®able relationship betweenSecchi disk transparence and maximum possible biomass. If mineral turbidity is present, thenwaters cannot be optically `biomass saturated', i.e. actual biomass concentrations are below theirpotential.

Re-elaborating data from the OECD programme, a simple relationship between transparencyand chlorophyll under approximate conditions of optical saturation in terms of chlorophyll, hasbeen derived as,

TRSP�p� � 30=Ch��7� �5�[approximate validity range: Chlorophyll 0.2 to 300 mg/m3; TRSP 48 to 0.3 m]

From this relationship2 a `Turbidity/Chlorophyll Ratio' is de®ned as the ratio between thepotential (p) and the actual (a) transparency, i.e. TRBR� TRSP(p)/TRSP(a), and the turbidityindex calculated as the log to the basis 2 of TRBR,

TRBIX � log2�TRBR� �6�The simple interpretation of this index is that waters are optically `biomass saturated' with regardto chlorophyll if TRBIX� 0; if TRBIX� 1 chlorophyll and other turbidities would be aboutequal; if TRBIX� 2 chlorophyll would make out about 1/4, etc.

In Figure 4 both TRIX(mN,PT) and TRBIX are plotted for St.314. The following pointsshould be noted: (a) as a mean, waters at this station are not optically `biomass saturated' interms of chlorophyll; hence, average phytoplankton biomass density is below its potential exceptin occasions of algal blooms, noticeably during the spring situation of 1987 coincident withhighest values of TRIX in the follow of freshwater supply and development of a bloom ofdiatoms. (b) On the other hand, values of TRBIX in excess of 2±3 coincide, with a few exceptions,with situations of wave height records exceeding 5±6 feet measured ca 10 km o�shore. Duringsuch situations, sediments are visibly stirred up along shores up to about 5 km o�shore. Theexcellent agreement between the various patterns con®rms the validity of TRBIX (as de®nedabove) as a measure of the relative presence of mineral turbidity.

3.6. Generalization

Figure 5 instead shows the relationship between TRIX and TRBIX for the same data. Whereasthere exists a general inverse tendency between the two indices ± as onewould expect ± the scatter

2A preferable estimate of the chlorophyll concentration to be used would be the average concentration of chlorophyll inthe water column from 0 m to the depth of the Secchi disk.



Figure 4. (a) Variation of TRIX and the turbidity index TRBIX (upper half). Generalized Water Quality Index (lowerhalf). See text. (b) Wave height exceeding 5 feet, measured at AGIP Tower 10 km o�shore Cesenatico



diagram shows that in e�ect single data vary largely independently.3 Accordingly, the combina-tion of TRIX and TRBIX thought as components of a vector would characterize thewater qualityof coastal waters more generally. By subdividing the vector space arbitrarily into four quadrantsthrough the location de®ned by the averages of TRIX and TRBIX, respectively, the overall waterquality properties may then be speci®ed as (moving counterclockwise from the lower leftquadrant):

(1) below average trophy and average turbidity;(2) below average trophy and above average turbidity;(3) above average trophy and average turbidity;(4) above average trophy and below average turbidity.

The temporal ¯uctuations of this generalized water quality index is depicted in the lower halfof Figure 4.

Figure 5. Scatter diagram of TRIX versus TRBIX. See text

3The few values of TRBIX<0 is due to the simplicity of the de®nition of TRSP(p). At low values of chlorophyll perhaps amodel of the form TRSP(p)�K/(a � b*Ch)c, [TRSP(p)! 65 for Ch! 0], may be more realistic. Yet, the propertuning of the coe�cients would require additional data.



3.7. Some further applications of TRIX

There are at least three other ways of using TRIX:

(a) To evaluate the long-term trophic evolution at a given station over several years. Figure 6(a)provides an example at an inshore station, Figure 6(b) one at an o�shore station. In the ®rstcase one notes a rather weak seasonal pattern and randomly ¯uctuating conditions; o�-shore, instead the seasonal variations are much more pronounced with highs mainly duringspring and lows in summer-fall. Besides, from 1990 on there seems to be a trend towardlower TRIX values. Variations of this sort can easily be correlated with long-term variationsin river ¯ow, meteorological and/or other conditions. In fact, the negative trend mentionedis likely to be attributed to decrease of nutrient supply over these years, due in part to dryweather as well as to a point source phosphorus control programme implemented overrecent years.

(b) To map the spatial trophic pattern found within an area at a given date. As an exampleFigure 7 refers to the trophic situation encountered along the Emilia-Romagna coast inSeptember 1993. The trophic indices have been calculated station by station (see Figure 1);isolines have been plotted using the mapping programme SURFER VER.4.14 (Golden

Figure 6(a). Caption opposite



Software Inc. 1989). The ®gure highlights the areal di�erentiation in either directions,inshore±o�shore and north±south. To mention the high values of TRIX(55.6) adjacent tothe River Po delta, its progressive decrease north±south, and the advection of o�shorewater at the height of Cesenatico indicated by TRIX values 43.6. The picture can also beinterpreted as a north±south sequence of three vortices of about 30 km in diameter.

(c) To characterizing the average trophic conditions by areal sectors over prolonged periods oftime. This forms the basis for regional comparison. Some of the pertinent aspects regard-ing this question are summarized in the following section.

4. STATISTICAL FEATURES USING TRIX APPLIED TO DIVERSE SITUATIONS

Data used for the purpose of the discussion were collected from 1982 to 1993 at 38 stations thatcovered the whole coastal area between the Po delta in the north and Cattolica in the south, andfrom inshore to 20 km o�shore. Instead of treating data station by station, stations that at thebasis of multivariate analyses (Giovanardi and Tromellini, 1992) were thought to be relativelyhomogeneous have been merged into eight groups, ®ve inshore (G1, G2, G4, G5, G7) and three

Figure 6(b).

Figure 6. (a) Typical pluriannual variation of TRIX at an inshore station (St. 14, Group 6). (b) Variation at an o�shorestation (St. 1019, Group 8). Note the spring highs versus the summer low



Figure 7. Areal mapping of TRIX for the 1993 September situation found in Emilia-Romagna coastal waters extendingfrom the River Po delta to Cattolica, and upto 20 km o�shore. For station grid see also Figure 1



o�shore (G3, G6, G8) (see Figure 1). For reasons that only from 1989 on were consistentmeasurements of total nitrogen made, summary data are reported separately for two temporalperiods: (a) from 1982 to 1988; (b) from 1989 to 1993. The wide variety of situations allows thestudy of questions about data distribution, stabilization of variance, and discrimination betweenmeans, groups, and temporal evolution.

4.1. Data distribution and normalization

As already mentioned in Section 3.3, simple log transformation was considered adequate tonormalize data distribution of individual parameter series. This assumption has further beentested using Box & Cox transformations (Box and Cox, 1964) and maximum likelihood estimatescon®rmed the use of the transformation. Yet, what may be true for high resolution data series, asconsidered in previous sections, does not necessarily apply to sets collected over several years atlower time resolution. Moreover, regarding TRIX as a linear composite of the four components,normality and independence of the component series is a prerequisite that TRIX summarizes andmaintains any statistical property of the original variables.

The kind of cumulative distribution one obtains using log transformation for the four compo-nents Ch, aD%0, mN and PT is exempli®ed on Group 4, period (a) from 1982 to 1988 (datamerged from three stations) as shown in Figure 8(a). Clearly, normalization is not perfect, inparticular not for the ®rst two components; still, the data as a whole line up su�ciently well alongthe respective computer produced interpolation lines. Thus, the corresponding distribution ofTRIX, shown in Figure 8(b) results as normal.

4.2. Discrimination and conversion between corresponding series of TRIX

How di�erent are the three estimates of TRIX(mN-PO4; mN-PT; NT-PT) estimates? Is it possibleto relate di�erent estimates of TRIX by simple conversion? Figure 9, pertaining to group (G2)given as example, shows that the respective cumulative distributions are su�ciently distinct topermit discrimination between the respective populations, albeit di�erences tend to decrease withincreasing values of TRIX. We attribute this to the fact that, at higher concentrations of totalnitrogen and phosphorus, a relatively larger fraction is present in dissolved form. Digressionwould be somewhat more noticeable for station situated further south (G6, G7, G8). Numerically,the di�erences between the population means of TRIX(NT,PT) and TRIX(mN,PT) resultsas 0.393+0.78, between TRIX(NT,PT) and TRIX(mN,PO4) as 1.000+0.111, and betweenTRIX(mN,PT) and TRIX(mN,PO4) as 0.693+0.105, respectively (see Table V). Accordingly,conversion, using the appropriate factors, would therefore not cause serious errors if applied tothe population as awhole; applied to single data simple conversion is more questionable, however.

4.3. Variance stability; discrimination between groups

Inspection of Table V shows generally a remarkable consistency of variance as measured by theSTD, regardless of group, period, actual mean, and number of data. Taken at face value thereseems to be two patterns, however: (1) TRIX(mN,PT) of all inshore groups plus G8 haveSTD5 1; (2) STD of G3 and G6, instead, are 41. The same applies also to TRIX(mN,PO4),though the STDs of this latter are generally higher when compared to the former. Yet, the overall



average STD of TRIX(mN,PO4)� 1.056+0.150 would statistically not di�er from that ofTRIX(Mn,PT)� 0.945+0.148.

A more rigorous analysis of variance of TRIX(mN,PT), taking into account the number ofdata in each group, gives a mean square between groups of 80.6 and a means square withingroups of 0.8865, resulting in a F-value of about 90, and a mean STD over all the data of 0.9415.Accordingly, discrimination between groups seems well assured. Yet, plotting STD against theirmeans (see Figure 10) shows a somewhat more di�erentiated pattern: the STDs of inshore groupsare independent of their means regardless of whether the ®rst (1982±88) or second period(1989±93) is considered, whereas for the three o�shore groups (G3, G6, G8) the STD is a linearfunction of the mean. Accordingly, it is justi®ed to consider inshore groups as statisticallyhomogeneous, while o�shore groups as de®ned in this study are not. One of the reasons for thedivergency between the inshore groups us di�erence in the respective hydrodynamic regime, that

Figure 8(a)



is to say di�erences in the frequency patterns, and the extent to which waters are a�ected byevents of freshwater supply and inshore±o�shore water mass exchange.

The main conclusions one can draw from these analyses are:

(1) The variance within and between all inshore groups is quite stable giving a STD for allinshore groups of ca. 9. Accordingly, group data would line up parallel in a cumulativeprobability diagram separated by their means; group means can be distinguished from eachother.

(2) Thus, the north±south di�erentiation (decreasing trophy from G1 to G7) is real.(3) Similarly, the perceived decrease in trophy between the ®rst and second period is real for all

inshore groups.

Figure 6(b).

Figure 8. (a) Cumulative distribution of TRIX components of station group 4 (data 1982±1988): (1) chlorophyll;(2) absolute %-deviation from oxygen saturation (aD%0); (3) total phosphorus; (4) dissolved mineral nitrogen,

(b) Corresponding distribution of TRIX



(4) The divergence from this pattern of the o�shore groups G3, G6, and G8 is likely aconsequence of the fact that these groups are not homogeneous in themselves, and shouldbe further subdivided. By extension, if stations are united into groups, internal homo-geneity should be tested ®rst.

(5) If the procedure proposed in this paper is applied to other areas and other data sets,appropriate tests of validation are necessary.

5. DISCUSSION

No index is a perfect substitute for the original data and thorough understanding of theproperties and workings of the system that the index represents. The more complex a system, theless it can be described by a few numbers or catchwords. Marine ecosystems are indeed complex.

Figure 9. Cumulative distribution for the three alternatives of TRIX, station group 2: (1) TRIX(mN,PO4);(2) TRIX(mN,PT); (3) TRIX(NT,PT) (data 1989±1993)



Nonetheless, judiciously used simpli®cations, such as indices, can convey useful messages to boththe professional and the public at large. For example, the earthquake scales of Mercalli/Richterhave proven to be an e�ective instrument of this sort. Scaling the trophic index 0±10, we proposea measure that may perform a similar function regarding the trophic conditions of coastal marineareas. The trophic index (TRIX) combined with a turbidity index (TRBIX), and supplementedby a general water quality characterization that includes microbiological conditions (a subjectwhich is not under discussion in this paper), will be of special bene®t to environmental managers,health o�cials and tourist operators.

Speaking in more technical terms, in designing a trophic index we have tried to be as simple aspossible without sacri®cing scienti®c rigor. However, this does not clear a critical evaluation of

Table V. Three versions of TRIX by station groups and two observation periods

Group* Period** TRIX A TRIX B TRIX C(mN,PT) (mN,PO4) (NT,PT)

Mean STD N Mean STD N Mean STD N

G1 1 6.388 0.658 74 5.603 0.748 74 ± ± ±2 5.983 0.833 562 5.429 0.871 563 6.276 0.778 471

G2 1 6.189 0.910 613 5.460 1.023 7012 5.865 0.824 579 5.269 0.870 583 6.229 0.769 483

G3 1 5.551 1.287 126 4.716 1.316 1392 5.289 1.157 235 4.606 1.224 235 5.532 0.985 204

G4 1 5.760 0.895 376 4.920 1.044 4182 5.421 0.895 410 4.857 0.984 412 5.802 0.764 345

G5 1 5.668 0.944 766 4.914 1.007 8602 5.383 0.944 455 4.807 1.029 458 5.730 0.830 352

G6 1 4.767 1.044 37 3.979 1.264 462 4.795 1.102 439 4.155 1.190 440 5.276 0.939 377

G7 1 5.222 0.932 474 4.455 1.089 5012 5.026 0.913 639 4.409 1.042 642 5.350 0.826 516

G8 1 4.198 0.823 25 3.365 1.055 302 4.449 0.954 186 3.825 1.146 187 4.963 0.772 151

AverageSTD

Mean 0.9447 1.0564 0.8329SD 0.1432 0.1457 0.0791N 16 16 8

TRIX A±TRIX B TRIX C±TRIX A TRIX C±TRIX BAveragedeviatesbetweenTRIX

Mean 0.693 0.393 1.000STD 0.105 0.078 0.111N 16 8 8

* cf. Figure 1; ** Period 1� 1982±1988, Period 2� 1989±1993.



both single aspects of how the trophic index has been conceived, and of the overall utility andlimitations of it.

5.1. Parameter selection

One may challenge the appropriateness of any of the parameters selected, and their restrictionto essentially 4±5. It has already been mentioned that among the parameters that stand forproductivity (chlorophyll and aD%0) primary production as such has not been consideredbecause the techniques involved do not normally lend themselves to routine measurements. Also,phytoplankton biomass (biovolume), active and inactive, broken down into main components(e.g. diatoms, dino¯agellates, etc.), would certainly be preferable to using only one single pigmentas substitute of biomass density. Further, measurements should be extended over vertical pro®lesat least down to the 1% light level, not be restricted to subsurface samples.

Regarding nutrients one may doubt whether totals or the dissolved fractions are preferable.However, this would immediately open other questions, some methodological (e.g. limitationsof sensitivity using say auto-analyzers for orthophosphate, etc.), others conceptual, as forexample, about the necessity to measure dissolved organic nitrogen and phosphorus in additionto the mineral components. Dissolved organics may indeed become a resource in periods of lowavailability of mineral components.

Figure 10. TRIX(mN,PT): Means and STD by groups (see Table V and Figure 1) separated by periods of collection:(a) 1982±88, (b) 1989±93. Note di�erence between inshore and o�shore groups



5.2. Range, lower and upper limits, and changes of parameters

The ranges adopted in our design have been such to cover a wide spectrum of possible situations.Still, the limits of some parameters may be too narrow, or too wide. If one wishes to change them,then Eqs (3) and (4) for calculating TRIX have to be adjusted accordingly. The same applies ifone adds, changes or deletes a parameter. While theoretically all this is possible, it is to be notedthat redesigned estimates of TRIX remain not strictly comparable to ours. Yet, as long aschanges relative to the designated ranges are small, the deviation from our TRIX will not be tooserious.

How far TRIX correctly re¯ects low productive waters is still to be tested. Perhaps a slightlymore appropriate model that avoids the arbitrary setting of lower limits could be achievedsubstituting log(x) by log(x � 1), (x� Ch, aD%0, NT, PT, mN, PO4, respectively). Also failingsof TRIX, recurring when a larger fraction of the population does not conform to normaldistribution and/or having unusual modes, may be minimized.

5.3. Other distribution models

Whereas simple log transformation to normalize parameter distribution was satisfactory in ourcase, di�erent transformations may be required in others. For example, Heyman et al. (1984)tested several distribution models (log, b-, g) and found g-distribution to be most appropriate forfresh waters. Ignatides et al. (1992) used Box & Cox transformations (Box and Cox, 1964) forGreek waters. These transformations, though powerful, require appropriate computer software,however.

5.4. Trophic Index as de®ned above

With the selection of both chlorophyll and aD%0 as components of TRIX, a certain level ofredundancy is introduced. Also, there seems to be a certain imbalance in our design as to thecontribution to variability of log(Ch*aD%0) vis-aÁ -vis the log(N*P) component. Yet, ponderingthe meaning that should be given to a trophic index, these are not serious problems in ouropinion. In fact, one is probably more interested in TRIX as an expression of actual productivity,to say in what the system does, rather than in what the system potentially could do, albeit bothaspects have their importance. Because of factors other than nutrients that control productivity,nutrients are often not utilized to their maximum potential. Therefore, a TRIX that wasdominated by nutrients would seem to be less satisfactory as an index that re¯ects the actualdynamics of the system.

5.5. Supplementary Indices

Regarding utilization of, and imbalances within, the resources available to the system, such asspeci®c nutrients, light availability, e�ect of mixing, biotic factors, possible toxicity, a.o., ratiosbetween single and aggregate components are of interest. The N/P ratio is commonly used asindicator for either nitrogen or phosphorus limitation, but TRIX per se does not make distinctionof this sort. Two indices worth mentioning in this context, which may be taken as comple-mentary modules to TRIX, are (a) Dobson's two indices de®ned by (minN � PON)/PON and(PO4 � POP)/POP, respectively (Dobson, 1994). Single, as well as the ratio between the two



indices give an indication about the likely prevailing limitation. (b) Innamorati's location ofwaters in aCartesian diagramde®ned by the coordinates log(Ch/minN) and log(Ch/PO4) providesimmediately two derived additional indices: minN/PO4 and Ch/(minN*PO4)0�5 (Innamoratiand Giovanardi, 1992). Though not identical, the interpretation of the latter is similar to that ofthe ratio log[(Ch*aD%0)/(N*P)] (see Figure 3), both being a coarse measure of relative nutrientutilization.

5.6. Turbidity index

The way of estimating `potential transparency' and the `turbidity ratio' using chlorophyll andSecchi disk transparency may be questionable. Indeed it would be more appropriate to useattenuation (absorption and scattering) spectra and to decompose them into contributing com-ponents. Cross-section absorption coe�cients of phytoplankton biomass in terms of chlorophyll(m2/mg) are well known, ranging from 0.01 to 0.03 on average over the visible spectrum (seee.g. Bukata et al., 1991b); hence, by di�erence the water � turbidity fraction can be roughlyestimated. However, measurements of this sort are not routine, while Secchi disk measurementsare common place.

5.7. Vector indices

Instead of using simple averaging an equally justi®able model to conceive TRIX would beconsidering the partial indices as components of a multidimensional vector V,

V � �S�xi�2�0�5 i � 1; 2; 3 . . . n

An added advantage of vector indices would be the ease of grouping waters according tosimilarity de®ned by their location in the vector space. The principle of such an approach hasalready been introduced with the combination of TRIX and TRBIX in a more general waterquality index. Water quality characterization by vectors may be preferable in many otherinstances. For example, mention has been made of the need to characterize biomass by theircomponents. Thus, instead of trying to incorporate such components into a single index, one maytreat them as complementary modules of a more general vector in a fashion similar to that of theturbidity/chlorophyll ratio.

A step further in this direction are multivariate analyses as, for example, used by Shannon andBrezonik (1972) for lakes, and Giovanardi and Tromellini (1992) for marine areas. Thesemethods are quite powerful, but the rationale for not having pursued them in the present contextis simplicity of design and interpretation, to say, the de®nition of a trophic index should be keptat a level that makes it possible to obtain TRIX from the original data with but a few additionalcalculations.

ACKNOWLEDGEMENTS

The data used for calibrating TRIX and TRBIX are from the data archive of the Laboratory`DAPHNE II' at the Centre for Marine Research, Cesenatico (Fo), Italy. We wish to thankA. Ghetti, C. R. Ferrari, V. Pagan and D. Pagan, who, beside G. Montanari and A. Rinaldi, wereinvolved in collecting the data used in this study.



APPENDIX 1

(1) Uhlmann/Verduin index

Developing ideas of Verduin (1964) and Uhlmann and Albrecht (1968) propose a simple index,Y, that permits to rank waters according to their trophic potential while accounting for the mostproduction limiting nutritional factor: For this the authors adapted the following equation,

Y � Ym�1-2ÿc��1-2ÿn��1-2ÿp�;in such a way thatY results between 05 1. The exponents c, n, and p are de®ned as ratios betweenactual concentration of carbon, nitrogen and phosphorus, respectively, and their relative use inphytoplankton according to the Red®eld Ratio, i.e. c� C/42; n�N/7.2; p� P/1. The xs (x� c,n, p, respectively) are then re-scaled setting the highest ratio x! x0 � 7, and adjusting theremaining two xs accordingly. Thus, the factor with the highest x0 (which represents the leastproduction limiting nutrient) becomes (1±277)� 0.99, so that the value of Y is determined solelyby the remaining factors. In most circumstances the least production limiting factor is carbon,but may also be nitrogen or phosphorus. The calculated Ys can then be correlated with, sayphytoplankton biomass, or chlorophyll.

(2) Carlson/Walker/Porcella index

Carlson (1977) considers three parameters (chlorophyll a; total phosphorus; Secchi trans-parency). The raw data are transformed by appropriate equations to meet the condition that thetransformed lowest and highest range values for the three factors equal 0 and 100, respectively.The range boundaries are set in a way to encompass almost all possible actually foundmeasurements. The scaling is done as following:

Equations: Ranges:I(ChA)� 9.81*1n(ChA) � 30.6 (ChA�mg chlorophyll; 0.04 to 1180 mg/m3)I(PT)� 14.42*1n(PT) � 4.15 (PT�mg total; 0.75 to 768 mg P/m3)I(SD)� 60±14.42 (SD) (SD� Secchi depth in m; 64 to 0.0625 m)

Accordingly, any transformed value will result between 05 100. Walker (1979) and Porcellaet al. (1980) enlarged the number of parameters considered to include also hypolimnetic oxygendepletion rates, and others.

(3) SchroÈ der's Correlation Model

SchroÈ der's model (1991) di�ers from the previous indices, in as far as the author distinguishes threeparameter criteria: parameters that either characterize (a) anabolic processes, and/or (b) catabolicprocesses [chlorophyll; dissolved phosphorus P-PO4, particulate phosphorus, total phosphorusPT, dissolved nitrogen/P mN/P, nitrate-nitrogen, iron Fe; NH4-N, NH4/mN, dissolved organicN/dissolved inorganic N DON/mN, total nitrogen, chemical oxygen demand]; (c) ambientparameters [lake surface A0 , mean and maximum depth z and zmax , altitude above sea level,epilimnetic temperature Te and temperature over ground Tg , extinction at E260 , and sum of sun-shine S in relation to long term averages S*, S/S*]. From systematic correlation of various para-meter combinations (using log transformations) with chlorophyll, and progressive elimination ofnot signi®cant correlations, the author derived two state equations (anabolic and catabolic,



respectively). Paired plotting of the respective coordinate values, calculated from the equations foreach lake separately, puts each lake in a characteristic region along a 1 :1 axis, thought to re¯ect itsdistinctive trophic conditions. Substantial deviation from the 1 :1 relation would further indicateother properties (e.g. dystrophy�1; polymixis�1).

(4) The OECD Classi®cation

This classi®cation (Vollenwider and Kerekis, 1982) was built on a few parameters (total P; yearlyaverage chlorophyll; peak chlorophyll; Secchi transparency), evaluating for each parameter themost likely range and boundary values regarding ®ve trophic categories (ultra-oligotrophic,mesotrophic, eutrophic, hypertrophic). Recognizing that a ®xed boundary categorization wouldbe too rigid, it was proposed to replace it by an open boundary system, attaching to eachlogarithmically scaled parameter a class probability derived from respective class frequencyhistograms. The normalized class probabilities are spaced by a factor of 3 for total phosphorus,average and peak chlorophyll, and by a factor of two for Secchi transparency. In essence, thisapproach relates a subjective qualitative class judgement with a parametric objective quantity.Beside status de®nition, the OECD approach considered also the relation to nutrient loading. AsChapra and Reckhow (1979) showed, also this relationship can be expressed in probabilisticterms. Shannon and Brezonik (1972), instead, used stepwise additive and multiplicative, as wellas canonical regression analysis.

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