Predicting median monthly chlorophyll-a concentrations

Limnologica 43 (2013) 169176

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Limnologica

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Predict cen

Peter H.a Department ob Swedish Univ regrun

a r t i c l

Article history:Received 12 MReceived in reAccepted 1 AuAvailable onlin

Keywords:Chlorophyll-aSeasonalityLakePhosphorusRegression moStatistical mod

nt whever,certaredicatitudakesere lbe usa mea

Introductio

Chlorophsampled in most lake monitoring programs. Chl-a is related tomany other water quality variables, e.g. phytoplankton biomass(Kazprzak et al., 2008) and Secchi depth (Hkanson and Boulion,2003). It is commonly used to indicate the trophic state in lakes andin some coument actionIn the Europthe main inhas been spits regardinPoikane et acators are ireleases gre(Schrier-Uijhas been re(e.g. Schindand agriculcan controlbodies.

Previousof Chl-a (Mby Marshalland another

CorresponE-mail add

ceduonce. The

Brownet al. (1998) concluded that there is no difference in the vari-ation between north and south Florida lakes and that the trophicstatus does not affect the variation ofmonthly concentration of Chl-a. Marshall and Peters (1989) pointed out that the air temperature,

0075-9511/$ http://dx.doi.ontries it is the only target indicator for lake manage-s related to eutrophication (Sndergaard et al., 2011).ean Commission Water Framework Directive, Chl-a isdicator of phytoplankton abundance and much effortent on dening reference conditions and Chl-a lim-g the ecological status of lakes (Carvalho et al., 2008;l., 2010). In addition, Chl-a and other trophic state indi-mportant determinants of the extent to which a lakeenhouse gases such as carbon dioxide and methanel et al., 2011). For a long time, total phosphorus (TP)cognized as the main promoter of Chl-a in many lakesler, 1974; Schindler et al., 2008). Because wastewaterture are sources of TP to lakes, regulating these sourcesalgae blooms and Chl-a concentrations in many water

studies have been made to examine the seasonalityarshall and Peters, 1989; Brown et al., 1998). A studyand Peters (1989) was made on north temperate lakesstudybyBrownet al. (1998)wasmadeonFlorida lakes.

ding author. Tel.: +46 18 4710000.ress: [email protected] (P.H. Dimberg).

which is affected by the latitude, could possibly inuence the tim-ing of spring blooms and Marshall and Peters (1989) developed amodel to calculate the bloom date by using annual air tempera-ture and Chl-a as in-parameters. Jones et al. (1998) concluded thatTP-Chl models which are designed with aggregated data (creatingmean or median values) have limited use when predicting singlemeasurements. There might also be a limited possibility of usingthese types ofmodels on individual lakes. Since TP does not explainall the seasonality of Chl-a in lakes there might be another param-eter, e.g. a physical, chemical and/or biological factor, which cancontribute to explaining variations in Chl-a concentrations (Joneset al., 1998).

There exist several statistical models to predict summer Chl-aconcentration from TP (e.g. from older works Jones and Bachmann(1976) to recent papers, e.g. Phillips et al. (2008)). Sakamoto(1966) was the rst study to introduce this type of model andVollenweider (1976)was an essential contributor.Many suchmod-els have been thoroughly tested, yielding high prediction accuracyin cross-systems surveys (Brown et al., 2000; Phillips et al., 2008).The use of statistical models has for many decades been importantfor predicting changes in Chl-a concentrations after TP concentra-tions have been altered in the lake water due to, e.g. increasedpopulation density or improved urban sewage treatment in the

see front matter 2012 Elsevier GmbH. All rights reserved.rg/10.1016/j.limno.2012.08.011ing median monthly chlorophyll-a con

Dimberga,, Julia K. Hytteborna, Andreas C. Bryhnb

f Earth Sciences, Uppsala University, Villav. 16, 752 36 Uppsala, Swedenersity of Agricultural Sciences, Department of Aquatic Resources, Skolgatan 6, 742 42

e i n f o

arch 2012vised form 17 July 2012gust 2012e 6 December 2012

delel

a b s t r a c t

Chlorophyll-a (Chl-a) is a plant pigmewater quality indicator for lakes. Howas measurements are concentrated tohow monthly Chl-a medians can be ptotal phosphorus concentrations and lfrom the literature. Data from 308 loligotrophic to hypertrophic, they w(North America). These models mayand for managing lakes in which Chl-

n

yll-a (Chl-a) is a common water quality variable

Thepromean ctrationm/locate / l imno

trations

d, Sweden

ich is used in many environmental monitoring programs as amonthly Chl-a data are often lacking inmanymonitored lakesin periods of the year. This study investigates two methods ofted (i) new monthly regression models from median summere, (ii) andwithmonthly constants added to regressionmodelswere used and the trophic status of the lakes ranged fromocated from northern Sweden (Europe) to southern Floridaeful for understanding the general Chl-a seasonality in lakessurements are not made over the whole year.

2012 Elsevier GmbH. All rights reserved.

re to evaluate the Chl-a seasonalitywas to compare thentration of Chl-a for each month to the annual concen-variation was expressed as a difference in percentage.

170 P.H. Dimberg et al. / Limnologica 43 (2013) 169176

drainage area. The TP-Chl-a models have been developed fromnumerous lakes with a wide range in the targeted variables (e.g.Jones and Bachmann, 1976). One limitation in these models is sub-stantial predictive errors when being used in some individual lakes(Smith and Shapiro, 1981). Model predictions can nevertheless beused as guidelines to how the lake will react after an increase ordecrease in TP concentrations. Seip et al. (1990) have investigatedthis and concluded that a reduction in P-limited lakes of TP with30g/l in shallow lakes and 14g/l in deep lakes will have a prob-ability of 80% for a positive response. Furthermore, the statisticalmodels canbeused to estimate Chl-a concentrations in a single lakewhen only TP concentration data are available (Smith and Shapiro,1981; Prairie et al., 1989). However, none of these models includelatitude for predictions of Chl-a concentration, which can be animportant parameter when explaining seasonality (Marshall andPeters, 1989; Jones et al., 1998).

Most of the models are designed from summer average valuesof TP and Chl-a, and are hence not useful for predicting seasonalityof Chl-a oveis a correlatpurpose wi

(i) develoption usidepend

(ii) from 11calculatdict mo

Theseapeach monthfrom 308 Eanalysis.

Materials a

FrequenA.

Lake waSweden (12of the lakedTPsummer 32745.06Nfollowing s(18), New Yranges of thTPsummer 255.4968.3Chl-a 2.26the latitudewith trophi

Table 2Range of data used. TPsummer are summermedians of TP, Chl-a aremonthlymedians,n=number of lakes. Note that the highest TPsummer is the same for all months sincethe lake with the highest TP during summer also had Chl-a data for all the months,respectively.

Month TPsummer [g/l] Chl-a [g/l] Latitude [N] n

January 3.0456.0 0.20147.50 2763.48 48February 3.0456.0 0.10156.40 2768.35 122March 2.0456.0 0.10152.00 2768.35 125April 2.0456.0 0.15149.00 2767.60 197May 2.0456.0 0.35379.00 2768.35 218June 2.0456.0 0.20251.00 2768.35 249July 2.0456.0 0.30235.05 2768.35 223August 2.0456.0 0.40349.00 2768.35 304September 2.0456.0 0.30169.20 2768.35 232October 2.0456.0 0.5599.00 2768.31 205November 3.0456.0 0.60163.00 2762.68 100December 2.0456.0 0.60252.00 2762.98 32

fromof thlakeT, 2ereAgrither, Ahlotter2000sonrovidetecervals, 23), antionstratitratirencered bin simet al-a vrd deont

uentviou% unludedereen cndenthe e

Table 1Statistical mod

Equation Reference Comment

ln(Chl) = 1.44 Carlson (1977) USlog(Chl) = 1.4 Jones and Bachmann (1976)log(Chl) = 1.1 Prepas and Trew (1983) Canadalog(Chl) = 1.0 Quiros (1990) Argentinalog(Chl) = 1.4 Vyhnlek et al. (1994) Slovakialog(Chl) = 1.0 Ostrofsky and Rigler (1987) Canadalog(Chl-a) = Phillips et al. (2008) Europelog(Chl-a) = Seip et al. (2000) Norwaylog(Chl-a) = Havens and Nrnberg (2004) Temperate, humiclog(Chl-a) = Havens and Nrnberg (2004) Temperate, clearlog(Chl) = 0.7 Nrnberg (1996) N. America, Europe, Asiar the year. Brown et al. (2000) have shown that thereion between monthly TP and Chl-a in Florida lakes. Theth this paper is therefore to

regression models for monthly Chl-a concentra-ng median summer TP concentration and latitude asent variables; andexisting statistical models (Table 1) and empirical datae typical month constants which could be used to pre-nthly Chl-a concentration with the existing models.

proacheswill bebasedonempiricalChl-amedians fromand TP medians from the summer (JuneAugust). Data

uropean and North American lakes will be used in the

nd methods

tly used terms and abbreviations are listed in Appendix

ter quality data from the United States (185 lakes),1 lakes) and Estonia (two lakes) were used. The rangesata fromtheUnitedStateswere forChl-a0.55379g/l,456g/l, longitude 111.5871.64W and the latitude. The data from the United States lakes come from thetates: Iowa (4), Florida (27), Minnesota (16), Michiganork (2), Utah (1), Vermont (116) and Wyoming (1). Thee lake data from Sweden were for Chl-a 0.1300g/l,350g/l, longitude 11.6123.35E and the latitude5N. The ranges of the lake data from Estonia were for7g/l, TPsummer 4049.5g/l, longitude 2627.5E and57.858.5N. This means that the data consists of lakesc status fromoligotrophic to hypertrophic and a latitude

rangevaluesStates(STOREdata wsity ofalso ga(1972)Annad1999,Bengtswere p

To dical intinterva(n=12centraconcenconcena diffecompamadeBrown

Chlstandaliers (MSubseqthe prethan 5be exclakes w

Whindepehalf of

els used in this paper, n=number of lakes used for the regressions.

n r2

9ln(TP)2.442 43 0.856log(TP)1.09 143 0.9546log(TP)0.661 34 0.818log(TP)1.943 97 0.7825log(TP)0.922 55 0.3935log(TP)0.728 49 0.63

1.026log(TP)0.455 1138 0.781.123log(TP)0.443 30 0.930.738log(TP)0.156 137 0.600.813log(TP)0.240 232 0.5999log(TP)0.25 180 0.6427 to 68.35N. Table 2 shows the ranges of the medianese data and their latitude for each month. The Uniteddata came from the Environmental Protection Agency011) and the major part of the data from Swedishgathered from the database at the Swedish Univer-cultural Sciences (SLU, 2011). Swedish lake data wereed from the following sources: Ahlgren (1971), Ahlgrengren andAhlgren (1973), Forsberg (1978), Rosn (1968),and Forssblad (2008, 2009, 2010), Cronberg et al. (1998,, 2001, 2002, 2003), Lundkvist (2002, 2003, 2004),(2005, 2006, 2007, 2008, 2009) and Estonian lake dataed by Keskkonnainfo (2011).t the difference of Chl-a variation at different geograph-ls, the data set was divided into three different latitude741N (n=32), 4155N (n=153) and 5568.35Nd a comparison of the seasonal variation of Chl-a con-was made using Wilcoxons test. The monthly Chl-aon was normalized compared to the median annualon for each latitude interval; the percentage in Chl-between different months and the annual value wasetween the latitude intervals. This approach has beenilar investigations by Marshall and Peters (1989) and

. (1998).alues of the data set which deviated more than 3viations from median Chl-amonth were treated as out-gomery et al., 2001) and rejected from the data set.ly, a new regression was made which was compared tos one. If the new r2-value changed drastically (by moreits) from the original r2-value then the outliers would. This happened in none of the cases and therefore all

included.onstructing a regression model, or validating againstt data, a higher r2 than those obtainedwhen comparingmpirical data setwith the other half cannot be expected

P.H. Dimberg et al. / Limnologica 43 (2013) 169176 171

due to inherent uncertainty (Hkanson, 1999). The empirical Chl-a data were randomly divided into two sets, i.e. Emp1 and Emp2,to calculate the highest expected r2-values for each month. Evenif the r2-value is high when constructing or validating a regres-sion model the predicted values may have a different distributionthan the empirical data which may not be accepted. The distri-butions are therefore tested with Wilcoxons test with the p-levelfor signicance set to 0.05. The analysis of data and regressionswere made by using the softwares R (www.r-project.org) and Mat-lab (www.mathworks.com). The statistical analysis was performedwith R and the preparation of data (calculating median values, etc.)was performed with Matlab.

The new monthly Chl-a regression model

To obtain monthly statistical models of Chl-a, one multipleregression for each month was made. Available Chl-a data from308 lakes were used to calculate monthly medians in each lakeand TP data from June to August were used to calculate sum-mer medians (TPsummer) in each lake. The different variables weretransformed to suit a normal distribution. For TPsummer and Chl-amonth, log-transformation was used which is typical for waterchemistry dsqrt-transfodata. Chl-athe explana

log(Chl-amo

Stabilitymonthly regaccording tand latitudeexcluded aThe coefciwas calculamuch it varregressionmcentrationswith empir

The monthlyfrom the lite

The statTPsummer w

dimensionless moderators. The same Chl-amonth and TPsummer datawhich were used in the new regression model (Eq. (1)) were used.

The procedure to calculate the constants is described below:

(1) An existing statistical model of Chl-a and TP from the literature(Table 1) was used to calculate a predicted Chl-a for every lakeof the data set (this was done for all the regressions in Table 1,respectively),

(2) The empirical Chl-a for a certain month was divided by the pre-dicted Chl-a for every lake to establish a characteristic constant,

Ccharacteristic =Chl-aempiricalChl-amodel

(2)

(3) A median value of the characteristic constants was calculatedfor each month and used as a uniform constant for a specicmonth,

Cuniform = median(Ccharacteristic 1...i) (3)where i is the number of the characteristic constant.

Theuniform-monthly constantwill be referred toas the constanting eregreneratuatiocal m

onth

difonswasst fonts groveering

s

comin F

N) asimilandStatitedbloolatitu

Fig. 1. Relativ (n=1Swedish and E ith thethat the rangeata (Hkanson and Peters, 1995) and for latitude thermationmaintained the best normal distribution of thewas the target variable and TPsummer and latitude weretory variables. The regression models had the form:

nth) = a1 log(TPsummer) + a2 sqrt(latitude) + intercept(1)

tests (Hkanson and Peters, 1995)weremade for everyression to clarify how sensitive these regressions wereo the intercept and the included data, Chl-amonth, TP. In the stability tests, 10% of the lakes were randomly

nd this was performed 10 times for each regression.ent of variation (CV; CV= standard deviation/median)ted for each parameter as a measurement on howies (Hkanson, 1999; Hkanson and Peters, 1995). Theodelswere also used to predict themonthly Chl-a con-

in four Swedish lakes and predictions were comparedical data.

constants for Chl-a prediction with existing modelsrature

istical regression models in Table 1 of Chl-a andere used to calculate monthly constants which act as

if nothfor alland geThe eqstatisti

Chl-am

TheWilcoxcedureThe teconstaan impconsid

Result

Thesented4155ratherto MayUnitedern Unspringlakes (

e Chl-a in three different geographical locations. Latitude 2741N (n=32), 4155Nstonian lakes (n=123). The median monthly Chl-a concentration is normalized ws of each individual month can be read from Table 2.lse is specically written. This procedure was repeatedssions in Table 1 for the months January to Decembered 12 differentmonth constants for every singlemodel.n for predicting Chl-a in 1 month using one existingodel is described as

= Chl-amodel constant (4)ferent statistical models have been tested withtest to clarify anymismatchof thedistribution, this pro-done in respectwhenusing andnot using the constants.r the statistical models by using and not using theave an indication whether including the constant wasment, and also if the improvement was good enoughthe magnitude for the predicted values.

parisonbetween the threegeographical intervals is pre-ig. 1. The northern lakes from United States (latitudend the Swedish and Estonian lakes (5568.35N) arearwitha twin-peakshape,witha springbloominMarcha summer bloom in July to September. The northern

es lakes seemtohaveanearlier springbloom.The south-States lakes (latitude 2741N) have an indication of am and the summer bloom starts earlier than northernde 4155N and 5568.35N). The seasonality does not

53) including lakes from the United States and 5568.35N includingmedian annual Chl-a concentration for each latitude interval. Note


Table 3Median annual concentrations for the three different geographical intervals.

Latitude [N] n Median annualconcentration[g/l]

CV-interval fordifferent months[%]

2741 32 15.2 1843004155 153 4.8 944335568.35 123 3.0 170563

Table 4Highest expected r2-values of Chl-awhen comparing Emp1with Emp2 for each lake,n=number of lakes. Emp1 is the Chl-a for one lake and one month and Emp2 is theChl-a for the same lake and same month but the empirical data comes from anothermeasurement.

Month r2e n

January 0.70 33February 0.77 117March 0.77 97April 0.71 162May 0.61 188June 0.78 226July 0.81 213August 0.90 302September 0.83 190October 0.75 200November 0.50 67December 0.76 29

differ signiChl-a (the Cwas largestthe Swedisvariation fointervals an

Table 4of the mediselected parexpected r2

and Fig. 2 s

Fig. 2. HighesEmp2. Emp1 isponding data

Table 5The new monthly regression models of log(Chl-a) for different months. a1 is theTPsummer and a2 is the latitude coefcient from Eq. (1). indicates that the param-eter was rejected at level p>0.05. The generic p-value for all the monthly regressionmodels are below 0.001.

Month r2 a2 a1 Intercept

January 0.66 0.26 0.71 1.39February 0.66 0.28 0.73 1.46March 0.66 0.43 0.46 2.86April 0.69 0.11 0.91 0.30May 0.62 0.88 0.40June 0.74 0.99 0.56July 0.80 1.16 0.72August 0.82 0.05 1.16 0.92September 0.77 1.06 0.48October 0.73 0.07 0.85 0.16November 0.53 0.11 0.73 0.56December 0.49 0.83 0.21

The new monthly regression models of Chl-a with TPsummer andlatitude as explanatory variables for January to December are pre-sented in Table 5. The p-values were below 0.001 for all of theregressions. The r2-values of the regressions for themonths Januaryto March, Juhighest exp0.11, 0.04,and Octobeest expectethe calculaexpected r2

titudr an

t andsenten caad foctob

summ

ues (valuly A

sionmfferecantly at p


Fig. 3. The 12 ur diffmean depth 1 th 3.6mean depth 1. . All tin the four lak

The r2-valup-value ran308 lakes wan r2-valuewhen Wilcodata.

The resuels from thethe distribuconstants aels from thwere rejecteical data forejected whever, this dthough theSeip et al. (output dataempirical m

sion

tinger halitywer

nt raed foe user the

Table 7The calculated1=passed thenot pass the te

Regression

Carlson (197Jones and BaPrepas and TQuiros (1990Vyhnlek etOstrofsky anPhillips et alSeip et al. (2Havens andHavens andNrnberg (1differentmodels used to illustrate the seasonal variation of Chl-a concentration in fo.6m. (B) Rotehogstjrnen, r2 = 0.63, latitude 58.82N, TPsummer 531g/l, mean dep4m. (D) Brunnsjn, r2 = 0.53, latitude 56.60N, TPsummer 524g/l, mean depth 5.3mes.

e for the 308 lakes ranged from 0.00 to 0.99 and theged from 0.05)of theChl-a season-en northern and southern lakes. However, the mediancentration differed. No certain conclusion can be madencentrations differ between the three geographicalne reason can be the higher temperature and radia-southern lakes. Another reason can be that the mixes

different trophic status inuence the result if they aredistributed between these three locations. It has beeny Marshall and Peters (1989) that eutrophic lakes have

he regression passed Wilcoxons test with and without the constant.t, 3 =did not pass the test with the constant but without, and 4=did

August September October November December

2 1.282 1.252 1.024 0.932 0.8911 1.342 1.302 1.063 0.971 0.9111 1.222 1.212 0.981 0.901 0.9814 27.922 27.532 22.822 20.642 23.1322 0.991 0.972 0.794 0.732 0.7014 1.922 1.892 1.532 1.412 1.6523 1.052 1.022 0.842 0.772 0.9012 0.792 0.782 0.642 0.582 0.6423 1.114 1.184 0.941 0.851 1.0813 1.104 1.154 0.941 0.821 1.0714 1.174 1.224 0.981 0.881 1.141


a higher variability of Chl-a than oligotrophic lakes. This also con-cerns the number of lakes used in the three different intervals of thelatitude, where a higher amount of lakes in each interval will givea more signicant result. However, since the CV-values are rathergreat betweannual conclatitude int

For the msion model(Table 3) it ipossible imthe data sesilica. Nitroof primary p2009). Silicasilica concespring and2001). Theof empiricaalso that thsions if othSplitting thtudedoes nto improveing the r2-vcan result incompared wthe subsettoo small itexists and wnecessary innot be founNovember ithe highestthe uncertaexpected r2

0.01 and NoThe stab

and Novemrejected asfor the othewas includmore imporconclusionlocated faring the coldthe latitudevalues for taffect the mWilcoxonsdicted dataThe reasonculation angeographicThis meanspredictChl-nd out if t

Even thooped it is pare used insame data fever, be strein northernhypertrophconstant thareas, thou

Seip et al. (2000) in combination with the constant could not berejected in any month.

In a warmer future, algal blooms are assumed to be prolongedand Chl-a concentrations may increase. The regression models

en TPperationd as a, e.gd to sa waredi

f exeand007)illusd tod thant mthats thaa. Thring

ion fobe unly tThe r.00 tohavedel.ande mathin-valurd dessededbya genIt is pof th

s, and byationon labe in

sion

regChl-

sed ong isalityve ttheal Chlso mratudsdoyeara, bued aherely men the different months it is possible that the medianentration is the samebetween at least the twonorthernervals.onths when the r2-value for the new monthly regres-

s (Table 5) is below the highest expected r2-values theoretically possible to improve the regressions. Oneprovement of the regressions is to expand the range oft, or to include another parameter such as nitrogen orgen may be a temporarily limiting or co-limiting factorroduction in lakes (Schindler et al., 2008; Conley et al.,is an important constituent in diatomblooms, andhigh

ntrations could mean high Chl-a concentrations duringautumn, particularly in lakes at high latitudes (Wetzel,reason not to use nitrogen or silica data was scarcityl nitrogen and silica data in the investigated lakes, ande user should not be restricted by using these regres-er measurements than TPsummer are missing in a lake.e data set into geographical sub-areas where the lati-ot need to be implemented is also onepotential solutionthe r2-value. However, focusing too much on increas-alue, by for example dividing the data set into subsets,less robust results, the distribution can be too narrowith the empirical data mainly due to less variation in

and also a smaller range in the data. If the variation iscan be difcult to conclude that a specic distributionhen applying, e.g. Wilcoxons test for those data muchformation can be missed (a variation which exists can-

d due to too fewdata or smaller data-range). InMay andt may be noted that the r2-values (Table 5) were aboveexpected r2-value (Table 4) and it is probably withininty span. It is appropriate to conclude that the highest-values for these cases may be slightly increased (May,vember, 0.03).ility tests (Table 6) showed that the latitude for Augustber causes uncertainty to the model because it wasa signicant parameter for some of the runs. However,r months the uncertainty was small where the latitudeed. The results in Table 6 indicate that the latitude istant for the colder season than the warmer season. Theis that when regressions are made for lakes which arefrom each other the latitude should be included dur-er months. Even though the uncertainties added fromare high for some months, the uncertainties in the r2-

hese months are low and perhaps the latitude does notodel predictions signicantly. This was supported bytest where no rejections were done between the pre-(Eq. (1)) and empirical data for all months except April.why April was rejected might be that the spring cir-d a spring bloom occur in different months at differental locations and that the largest difference is in April.that it is possible that summer TP cannot be used toa concentrations inApril, however, future studiesmighthis is restricted to this data set or in general.ugh the constants (Table 7) were statistically devel-

ossible that there might be different results when theyother areas; in these tests the results were tested on therom where the constants were made. It should, how-ssed that thedata setused in this study spans fromlakesSweden to southern Florida and from oligotrophic to

ic. One approach to determine which model with theat works best is basically by trial and error in differentgh here the models from Prepas and Trew (1983) and

betweas temsuggesbe usechangebe useto usewhen pkind owateret al., 2

Thebe useshowediffereposedmonthof Chl-monitodeviatels canusing oitude.from 0whichthe modictedthat thlies wihigh r2

standabe strecapturtigatelakes.butionmodelaffectethe releffectfuturelakes.

Conclu

Newality ofare basampliseasonmay saof howseasonwere athe litemethowholein Chl-producods if tmonthand Chl-a are not able to handle this kind of changeture is not included as an in-parameter in the model. Ais that latitude in the monthly regression models couldproxy for temperature to examine the effect of climate

. lower latitude than the actual latitude for a lake couldimulate a future Chl-a concentration. Another option isrmer month, for example the regression model for Maycting April. There are, however, large risks in doing thisrcise as the climate change will have an impact on thephosphorus cycle that are not well known (Blenckner.tration of how the new monthly regression models canpredict the seasonality of Chl-a concentration (Fig. 3)t they manage to capture the general patterns betweenonths during a year. Using these new models, it is pro-no measurement of TP is necessary during the othern the summer to obtain an overview of the seasonalityis may save time and money for nancially strappedgroups. The predicted values were within the standardr the most months and indicated that these new mod-sed to estimate Chl-a concentration for all the monthshe median TP concentration from summer and the lat-esult of the r2-values for all lakes individually ranged0.99 and this lead to an incorrect conclusion that lakesvery low r2-values do not give accurate results fromHowever, the r2-value indicates of how well the pre-empirical concur from month to month, which meansgnitude of the predicted value can still be accepted andthe standard deviation. In contrast, results with a verye can give predicted results which are far outside theviations but still follow the empirical pattern. It shouldthat temporal changes in both time and space is notthemodel and themodels shouldonly beused to inves-eral pattern of the Chl-a concentration in individualossible that the Gulf Stream is inuencing the contri-e latitude in the Swedish and Estonians lakes for the

d that northern lakes far from the Gulf Stream may bethe latitude in a somewhat different way. In this study,ship between the Gulf Stream and latitude and theirkes are beyond the scope of the paper and may in thevestigated of its impact in general patterns between

s

ression models have been developed to predict season-a concentration in awide range of lakes. The regressionsn median TP concentrations from the summer and notherefore needed during other periods of the year if theof the Chl-a concentration should be investigated. Thisime and money and still give an accurate descriptionChl-a varies during the year. Large, general patterns inl-a have been captured by these ndings. In this studyonthly constants computed for existing models from

re to predict monthly Chl-a concentration. These twoesnotexclude that empirical TPmeasurementsover themay be better for predicting and explaining seasonalityt the new regression model and the monthly constantsnd tested in this study can act as good alternative meth-is a lack of data or if the monitoring budget for makingeasurements is small.


Acknowledgements

The authorswould like to thank twoanonymouspeer-reviewerswhich greatly helped improving this article. The data providersare also ackcultural SciChrister LnAhlgren atlending outAnnadotterThe data frronmentalEnvironmentection AgeEnvironmen

Appendix A

The follothe paper.

Aggregated

Characteristconstant

Chl-aCV

Data

Empirical da

Gathered danp-Valuer2

TPUniform con

Wilcoxons

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Bengtsson, B., 2007. Lake Ringsjn, Water Studies 2007. Ecology Group, Landskrona,56 pp. Available online: http://www.ringsjon.se/usok rapport.asp (accessed20.05.11) (in Swedish).

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5.11)er, T., A, Janko007. Lal ChaC.D., Clorops. J. La.D., Hionshida an

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://dx.d, S., Alvarottkilke, Anowledged: Eva Willn at Swedish University of Agri-ences for providing data from their internal data base,nergren from Stockholm Vatten, Gunnel and IngemarDepartement of Limnology at Uppsala University forreports about Lake Norrviken and Lake Edssjn, Heleneat Regito for sending the reports about Lake Vombsjn.om SLU were collected within the Coordinated Envi-Research in Sweden, funded by the National Swedishtal Protection Agency; STORET, Environmental Pro-ncy, United States; Keskkonnainfo, Estonian Nationaltal Monitoring Programme database.

. List of terms and abbreviations

wing terms and abbreviations are used frequently in

data Empirical data which have been adapted, e.g. createdmean or median values for a certain time period

ic A constant representing one lake for one regressionmodel, see also uniform constantChlorophyll-a concentrationCoefcient of variation; Standard deviation dividedwith the mean valueOften referred to the 308 lakes which were used in thestudy. This data set contains TP, Chl-a and latitude

ta This can refer to either TP or Chl-a and isdemonstrating the concentration in one or severallakes for a certain time

ta Data collected from different data bases and literatureNumber of dataLevel of signicanceCoefcient of determinationTotal phosphorus concentration

stant A constant representing all lakes for one regressionmodel, see also characteristic constant

test Statistical test that compare the distribution of twodata sets

71. Limnological Studies in Norrviken, Edssjn, Oxundasjn, Mes-, Physical and Chemical Conditions, Phosphorus and Nitrogen Budget0. Department of Limnology at Uppsala University, Uppsala, 19 pp. (in

2. Limnological Studies in Norrviken, Edssjn, Oxundasjn, Messageical and Chemical Conditions, Phosphorus andNitrogen Budget 1971.nt of Limnology at Uppsala University, Uppsala, 17 pp. (in Swedish).hlgren, G., 1973. Limnological Studies in Norrviken, Edssjn and, Message No. 8, Environmental Factors, Nutrient Budget and Phy-Production 1972. Department of Limnology at Uppsala University,

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Predicting median monthly chlorophyll-a concentrationsIntroductionMaterials and methodsThe new monthly Chl-a regression modelThe monthly constants for Chl-a prediction with existing models from the literature

ResultsDiscussionConclusionsAcknowledgementsAppendix A List of terms and abbreviationsReferences

Documents

Predicting median monthly chlorophyll-a concentrations