MARINE ECOLOGY PROGRESS SERIESMar Ecol Prog Ser

Vol. 269: 101–110, 2004 Published March 25

INTRODUCTION

In models of depth-integrated primary production,the rate of photosynthesis depends on the concentra-tion of chlorophyll, surface irradiance, and the pene-tration of solar irradiance with depth. In the simplestcase, water-column photosynthesis per unit surfacearea, ∫P (mg C m–2 h–1), is a function of irradiance at thesurface, integrated between 400 and 700 nm (photo-synthetically active radiation, EPAR, cf. Talling 1957),and its penetration is expressed as the nominal depthof the euphotic zone, zeu(PAR) (m), commonly definedas the depth at which EPAR is 1% of its value at the sur-face (Ryther & Yentsch 1957, Talling 1957, Platt &

Sathyendranath 1993, and review by Behrenfeld &Falkowski 1997):

(1)

where P Bmax is the maximum rate of photosynthesis

normalized to chlorophyll (mg C [mg chl]–1 h–1), B (mgchl m–3) is chlorophyll biomass in the surface layer, andthe dependence on irradiance is described as a func-tion of EPAR just below the surface, EPAR (0–), divided bythe saturation parameter for photosynthesis in units ofPAR irradiance, Ek(PAR). Direct measurements shouldbe used to constrain zeu(PAR); alternatively, zeu(PAR)has been related to total phytoplankton pigment in the

P P BEE

= ⋅ ⋅ ⋅ ƒ

−

∫ max ( )( )

( )B

euPAR

kPAR

PARz

0

© Inter-Research 2004 · www.int-res.com*Email: mlehmann@dal.ca

Spectrally weighted transparency in models ofwater-column photosynthesis and photoinhibition

by ultraviolet radiation

Moritz K. Lehmann*, Richard F. Davis, Yannick Huot, John J. Cullen

Centre for Marine Environmental Prediction (CMEP), Department of Oceanography, Dalhousie University, Halifax, Nova Scotia B3H 4J1, Canada

ABSTRACT: We present a simple method for describing the influence of variable attenuation of spec-tral irradiance, Kd(λ), on water-column photosynthesis and its inhibition by ultraviolet radiation (UV).The approach is based on weighted water transparency, a calculation introduced by Vincent et al.1998 (Ann Glaciol 27:691–696). Key results of a depth- and spectrally-resolved model of photosyn-thesis can be reproduced for a broad range of water types by simple parameterizations using a refer-ence solar irradiance spectrum at the surface and water transparency [1/Kd(λ)] weighted spectrallyfor biological effectiveness. Transparency that has been weighted spectrally by the normalized prod-uct of irradiance and photosynthetic absorption (PUR-weighted transparency, T W

PUR) describes spec-tral effects on photosynthesis in the water column. An empirical parameterization of transparencyweighted by the product of surface irradiance and the biological weighting function for inhibition ofphotosynthesis (T W

PIR), along with T WPUR, describes the inhibition of water-column photosynthesis rela-

tive to the uninhibited rate. Our approach is directly compared with an analysis that used weightedtransparency as an indicator of the potential for inhibition of photosynthesis by UV as influenced byvariations in chromophoric dissolved organic matter associated with climate change over the past6000 yr (Pienitz & Vincent 2000, Nature 404:484–487). Results demonstrate how weighted trans-parency, used as an indicator of potential inhibition, can be transformed into a predictor of biologicaleffects.

KEY WORDS: Weighted transparency · Photosynthesis model · Photoinhibition · Attenuation · Optical properties · CDOM

R e s a l e o r

Mar Ecol Prog Ser 269: 101–110, 2004

water column (Morel & Berthon 1989). See Table 1 forsymbols and definitions.

Regardless of the exact formulation of the photosyn-thesis-light relationship, estimates of depth-integratedprimary production are directly proportional to thedepth of 1% surface EPAR. However, the use of EPAR asthe measure of light is a simplification. It has beenrecognized for decades that irradiance weighted forabsorption by photosynthetic pigmentation (photo-synthetically utilizable radiation, EPUR, Morel 1978; seeEq. 6) is more relevant than EPAR as a measure of irradi-ance available for photosynthesis (e.g. Lewis et al.1985, Morel 1991). Errors associated with the use ofEPAR rather than EPUR are generally explored through

the use of depth-resolved numerical models; they canbe as large as 60% in waters with high chlorophyll con-centration (Sathyendranath et al. 1989). Nonetheless,currently-used, depth-integrated models following thegeneral form of Eq. (1) use EPAR and zeu(PAR), perhapsbecause a simple parameterization of zeu(PUR), thedepth of 1% surface EPUR, has not been developed inthis context.

More complete formulations of primary production(e.g. Arrigo 1994, Neale et al. 1998) take into accountinhibition of photosynthesis as a function of biologi-cally weighted UV radiation, i.e. photosynthesis-inhibiting radiation, E *PIR (see Neale 2000). This re-finement is essential for describing the environmental

102

Symbol Units Description

an, bn, cn Parameters of power functions to estimate results of photosynthesismodel; n = {1, 2} for a, and n = {1, 2, 3} for b and c

ap(λ) m–1 Spectral absorption coefficient of phytoplankton–ap m–1 Mean absorption coefficient of phytoplankton over 400 to 700 nmB mg chl m–3 Chlorophyll concentration Ek µmol quanta m–2 s–1 Saturation parameter for photosynthesisEPAR(0–) µmol quanta m–2 s–1 Scalar irradiance just below the surface integrated over 400 to

700 nmE *PIR(z) (dimensionless) Scalar irradiance weighted for inhibition of photosynthesisE PUR(z) µmol quanta m–2 s–1 Scalar irradiance weighted for absorption by photosynthetic

pigmentsEref(0–,λ) µmol quanta m–2 s–1 nm–1 Spectral scalar irradiance just below the water surfaceE400(0–,λ) (dimensionless) Spectral scalar irradiance just below the water surface normalized to

1.0 at 400 nmF(λ) (dimensionless) Factor of enhancement in surface irradiance due to ozone depletionKd(λ) m–1 Spectral diffuse attenuation coefficientKPAR m–1 Diffuse attenuation coefficient averaged over 400 to 700 nm from the

surface to the depth of 1% surface PARPpot(z) mg C m–3 h–1 Potential for primary production in the absence of inhibitionP(z) mg C m–3 h–1 Inhibited rate of photosynthesis∫P mg C m–2 h–1 Water-column integrated rate of photosynthesis∫P*pot m Water-column integrated potential rate of photosynthesis normalized

to B and PsB

∫P* m Water-column integrated inhibited rate of photosynthesis normalized to B and Ps

B

∆P/Ppot (dimensionless) Proportion of water-column photosynthesis lost due to photo-inhibition

P Bmax mg C [mg chl]–1 h–1 Maximum rate of primary production per unit chlorophyll in a

depth-integrated modelPs

B mg C [mg chl]–1 h–1 Maximum attainable rate of primary production per unit chlorophyll in the absence of photoinhibition

T WPIR m PIR-weighted transparency

T WPUR m PUR-weighted transparency

T*PI m PIR-weighted transparency according to Vincent et al. (1998)z m Depth below the water surfacezeu(PAR) m Depth of 1% EPAR(0–)zeu(PUR) m Depth of 1% EPUR(0–)ε(λ) (µmol quanta m–2 s–1)–1 Biological weighting function for the inhibition of photosynthesisε300(λ) (dimensionless) ε(λ) normalized to 1.0 at 300 nmλ nm Wavelength

Table 1. Symbols, units and definitions

Lehmann et al.: Biologically weighted transparency

effects of UV. For example, it provides a means toaccount for the influence of ozone depletion on water-column photosynthesis as well as natural variability ofattenuation by UV-absorbing, chromophoric dissolvedorganic matter (CDOM) (Arrigo & Brown 1996). Untilthe introduction of the approach described in thisstudy (Lehmann et al. 2000, Neale 2001), no depth-integrated model of UV-inhibition existed; the effectsof UV on depth-integrated photosynthesis could beevaluated quantitatively only through complicatednumerical models (e.g. Arrigo et al. 2003).

Here, we show that well-recognized limitations ofPAR-based models of depth-integrated primary pro-ductivity can be relieved by improving descriptions ofthe penetration of solar irradiance. We start with anapproach pioneered by Vincent et al. (1998), whodeveloped a straightforward method to assess theinfluence of variations in CDOM, and consequently thepenetration of UV, on water-column photosynthesis.We extend their work by developing a novel parame-terization of zeu(PUR) as a function of transparency, theinverse of the spectral diffuse attenuation coefficientfor downwelling irradiance, which we weight spec-trally for EPUR. We then describe a straightforwardrelationship between weighted transparency andwater-column photosynthesis as simulated by a spec-tral, depth-resolved model. Using a refinement ofweighted transparency as developed by Vincent et al.(1998), we parameterize relative values of photo-inhibition caused by UV radiation. To the best of ourknowledge, this represents the first application of bothphotosynthetically utilizable radiation and inhibitionof photosynthesis by UV in simple equations forestimating depth-integrated primary production.

As examples of practical applications of the parame-terizations, we calculated the effects of variations inwater-column transparency on photosynthetic produc-tion and the proportion of photoinhibition by UV usingoptical data from natural waters. Our approach is fur-ther explored in a re-analysis of data from an earlierapplication of weighted transparency using recon-structed optical properties for a sub-Arctic lake overthe past 6000 yr (Pienitz & Vincent 2000). Resultsdemonstrate how weighted transparency, previouslyused as an indicator of potential inhibition, can betransformed into a predictor of biological effects.

MATERIALS AND METHODS

Overview of the approach. To describe the effects ofvariations in water transparency on water-columnphotosynthesis, we used a reference solar spectrumand a function relating water transparency to CDOMand chlorophyll to calculate depth-resolved spectral

irradiance for 143 simulated water columns spanning abroad range of water types. For each case, 2 indiceswere constructed: transparency weighted for photo-synthetically utilizable radiation, T W

PUR (m), and trans-parency weighted for photosynthesis-inhibiting radia-tion, T W

PIR (m). Using a fully spectral numerical model,we calculated the rate of photosynthesis and its inhibi-tion by UV as functions of depth for each water col-umn. Resulting estimates of water-column photosyn-thesis, the uninhibited rate (i.e. without the inhibitionterm), and the fraction that is lost due to inhibitionof photosynthesis were related quantitatively to T W

PUR

and T WPIR through statistically determined empirical

functions. The resulting parameterizations, functionsof T W

PUR and T WPIR, were then used to predict the influ-

ence of water transparency on photosynthesis andphotoinhibition in natural bodies of water, usingmeasurements in lakes and ocean water, and a recon-struction of optical properties in a sub-Arctic lake overthe past 6000 yr (Pienitz & Vincent 2000).

This approach has roots in the earliest depth-integrated models of primary production (e.g. Ryther &Yentsch 1957, Talling 1957) and builds directly on thework of Vincent et al. (1998), who introduced weightedtransparencies. The method was originally describedby Lehmann et al. (2000), and aspects were incorpo-rated into a study by Neale (2001).

Water types. Water types were characterized byindividual attenuation spectra, Kd(λ) (m–1), con-structed using a functional dependence of Kd(λ) onchlorophyll and dissolved organic matter (DOM) con-centrations (Baker & Smith 1982). Each of 11 chloro-phyll concentrations (0.02, 0.05, 0.1, 0.5, 1, 2, 3, 4, 5,10, 15 mg m–3) was combined with each of 13 DOMconcentrations (0 to 50 g m–3), yielding 143 distinctwater types. These attenuation spectra were used topropagate through the water column a referencesolar irradiance spectrum (280 to 700 nm), modeledfollowing Gregg & Carder (1990), as extended intothe UV range by Arrigo (1994). The irradiance spec-trum is for a cloudless sky at 45° N on 21 March atnoon, with an ozone content of 366.1 DU. Scalar irra-diance just below the surface, Eref(0–,λ) (µmol quantam–2 s–1 nm–1), was calculated after Neale et al. (1998).

Weighted transparency. To obtain T WPUR (m), the

transparency, 1/Kd(λ), for each water type wasweighted by the normalized phytoplankton absorptionspectrum and scalar irradiance normalized to EPAR:

(2)

where

E EPAR refnm

nm

( ) ( , )– –0 0400

700

= ⋅∑ λ λ∆

T

K

a

aE

EPURW

dnm

nmp

p

ref

PAR

( )

( ) ( , )

( )

–

–= ⋅ ⋅ ⋅∑ 1 0

0400

700

λλ λ λ∆

103

Mar Ecol Prog Ser 269: 101–110, 2004

(µmol quanta m–2 s–1). We normalized photosyntheticabsorption, ap(λ) (m–1), by the mean absorption,

(m–1, where 301 is the number of wavelengths mea-sured), so that in white light EPUR = EPAR for anyabsorption spectrum (Markager & Vincent 2001).Morel (1978) normalized ap(λ) by the maximumabsorption, consistent with the fact that not all lightis utilized, i.e. EPUR < EPAR. We used an estimate ofphotosynthetic absorption derived from an excita-tion spectrum for in vivo chlorophyll fluorescence(Sakshaug et al. 1991).

Transparency was also weighted by the product ofsurface irradiance and a biological weighting function,ε(λ) ([µmol quanta m–2 s–1]–1), which reflects the effec-tiveness of UV wavelengths in inhibiting photosynthe-sis of a marine diatom (Cullen et al. 1992). Summingover the UV and visible wavelengths (280 to 700 nm)yields PIR-weighted transparency, T W

PIR (m):

(3)

Our formulation differs slightly from the one used byVincent and colleagues (Vincent et al. 1998, Pienitz &Vincent 2000), which, using our notation, is:

(4)

where ε300(λ) (dimensionless) is a biological weightingfunction (Cullen et al. 1992) normalized to equal 1.0 at300 nm, E400(0–,λ) (dimensionless) is the referencespectrum of solar irradiance just below the water sur-face normalized to equal 1.0 at 400 nm, F (λ) is a dimen-sionless factor accounting for spectral changes of theirradiance from the reference spectrum due to ozonevariability set to 1.0 for an ozone content of 330 DU,and ∆λ is 1 nm. The factor 1/111 (nm–1) provides theaverage weighted transparency between 290 and400 nm; we inserted this term for dimensional consis-tency with T W

PIR. The main difference between Eqs. (3)& (4) is that in our formulation, the weighting functionand the irradiance spectrum are not normalized. In ad-dition, F (λ) has been dropped; instead, we used an ir-radiance spectrum appropriate for the ozone levelstudied. As a result, our weighted transparencies willnot only be affected by the shape of the irradiancespectrum and weighting function but also by their ab-solute values. The latter is important when looking atchanges caused by variations in the magnitude of solarspectra or when comparing different weighting func-tions of similar shapes, but different amplitudes (Neale2000). In the present study, we evaluated only the in-

fluence of water transparency on depth-integratedphotosynthesis and its inhibition; effects of variationsin solar spectra and weighting functions have previ-ously been examined (Cullen et al. 2000) and will bereported elsewhere (J. J. Cullen et al. unpubl. data).

Numerical model of photosynthesis. Photosyntheticrates at solar noon were estimated for the 143 watertypes using a spectral model of photosynthesis andinhibition (Cullen et al. 1992), modified to use EPUR

instead of EPAR as described by Neale et al. (1998). Theuninhibited rate of photosynthesis (potential for photo-synthesis, Ppot(z), mg C m–3 h–1) at depth z (m) is mod-eled as a saturating function of irradiance, weightedfor absorption by photosynthetic pigments (EPUR(z),µmol quanta m–2 s–1):

(5)

where

(6)

The maximum attainable rate of photosynthesis, PsB

(mg C [mg chl]–1 h–1), was set to 1.0 so the numericalresult for Ppot(z) is equivalent to Ppot (z)/Ps

B (cf. Talling1957). The saturation parameter for photosynthesis interms of EPUR, i.e. Ek, was set to 150 µmol m–2 s–1. Theconcentration of chlorophyll, B (mg chl m–3), wasassumed uniform with depth, and its value was equalto that used to generate the corresponding attenuationspectrum for the water type.

After Cullen et al. (1992), the formulation of photo-synthesis is extended to include inhibition as a functionof the dose rate of photosynthesis-inhibiting radiation,E*PIR (dimensionless), to give the inhibited rate ofphotosynthesis, P(z) (mg C m–3 h–1):

(7)

where

(8)

Both Ppot(z) and P(z) were normalized to the productof B and Ps

B then integrated numerically over 100 inter-vals, distributed evenly between the surface andzeu(PUR), yielding normalized potential water-columnphotosynthesis, ∫P*pot (m), and normalized inhibitedwater-column photosynthesis, ∫P*(m):

(9)

(10)PP B

P z zz

*sB

(PUR)eu

d∫ ∫=⋅

⋅ ( )1

0

PP B

P z zz

potsB pot

(PUR)

*eu

d∫ ∫=⋅

⋅ ( )1

0

E z EK z

PIR refnm

nm* ( ) e d ( ) ( , )– – ( )= ⋅ ⋅ ⋅⋅∑ ε λ λ λλ

0280

700

∆

P z B PE z

E zE( ) e

( )sB – ( )

PIR

PURk

*= ⋅ ⋅ −

⋅

+( )1

1

1

E z

a

aE

K zPUR

p

pref

nm

nm

( ) e d ( )

( , )– – ( )= ⋅ ⋅ ⋅

⋅∑ λλ λ

λ0

400

700

∆

P z B PE z

Epot s

B( )

( ) ePUR

k –= ⋅ ⋅

−( )1

TK

E FPIRdnm

nm*

( )( ) ( , ) ( )–= ⋅ ⋅ ⋅ ⋅ ⋅∑1

1111

0290

400

300 400λε λ λ λ λ∆

TK

EPIRW

dnm

nm

ref ( )

( ) ( , )–= ⋅ ⋅ ⋅∑ 10

280

700

λε λ λ λ∆

a ap pnm

nm

( )= ∑1301 400

700

λ

104

Lehmann et al.: Biologically weighted transparency

Because biomass and photosynthetic parameters areassumed uniform with depth, water-column photosyn-thesis (mg C m–2 h–1) can be retrieved by multiplicationof ∫P* with the product of surface biomass and asuitable Ps

B.The proportion of water-column photosynthesis lost

due to inhibition, ∆P/Ppot (dimensionless), is:

(11)

Parameterizing the numerical calculations ofphotosynthesis. Normalized potential photosynthesisintegrated over depth (∫P*pot) was related to T W

PUR, andboth ∫P* and the relative inhibition of photosynthesis(∆P/Ppot) were related to T W

PUR and T WPIR by simple

parameterizations:

(12)

(13)

(14)

The parameters an to cn were determined for the143 water types by nonlinear least-squares fits usingthe Gauss-Newton method (implemented in MATLAB).The units of a1, b1, and c1 cancel out the awkwarddimensionality resulting from fractional exponents forT W

PUR and T WPIR. The fit between the parameterization

and the numerical simulation was evaluated by thecoefficient of determination for a regression (r2).

Application to natural waters. For a field applicationof the weighted transparency parameterizations, T W

PUR

and T WPIR were calculated for Kd spectra from 6 lakes in

Nova Scotia and from 7 stations, coastal and oceanic, inthe North Atlantic. The lake spectra were measuredduring summer 1999 with a profiling radiometer(OCI-200, Satlantic) using 6 channels (323, 338, 380,443, 490, and 555 nm; with bandwidths of 2 nm at halfmaximum for the first 2 channels and 10 nm for theothers). The depth profiles of downwelling irradiancefrom the 6 radiometer channels were corrected for theinstrument dark signal to eliminate the artificial non-linearity observed in plots of log-irradiance versusdepth (Morrow & Booth 1997). Then, attenuationcoefficients for the 6 wavelengths were estimated bylog-linear regression versus depth (Kirk 1994). The fullattenuation spectrum between 280 and 700 nm wasestimated by subtracting the contributions by chloro-phyll and water (following the model of Baker & Smith1982, using chlorophyll measured fluorometrically onsamples extracted in 90% acetone) from the Kd-valuesat the channel wavelengths, then fitting the residualattenuation spectrum to an exponential function todescribe attenuation by CDOM; the total attenuation

spectrum was reconstructed by adding chlorophyll andwater components back to the CDOM spectrum.

Marine irradiance profiles and chlorophyll concen-trations were obtained from diverse water types duringa cruise from Chesapeake Bay to the Gulf Stream inAugust 1997. Using a 13-channel profiling radiometer(SPMR, Satlantic, wavelengths 305, 325, 338, 380, 412,443, 490, 510, 532, 555, 670, 683, and 700 nm), attenua-tion coefficients for the channel wavelengths 325 to700 nm were estimated by log-linear regression versusdepth. Kd-values at 280 and 305 nm, the latter an insuf-ficiently sensitive channel of the SPMR, were estimatedby extrapolating an exponential fit through the valuesat 325, 338, and 380 nm. The entire spectrum was inter-polated linearly between the channel wavelengths.

Using measured chlorophyll concentrations andattenuation spectra, ∫P* and ∆P/Ppot were simulated thesame way as for the modeled water columns.

Reconstruction of historic spectral transparency andrelative photosynthesis. The second application of theweighted transparency parameterization used paleo-optical data for Queen’s Lake (sub-Arctic Canada,64° 07’ N, 110° 34’ W) from Pienitz & Vincent (2000). Dif-fuse downwelling attenuation coefficients were recon-structed at four wavelengths in the UV according to anempirical relationship with dissolved organic carbon(DOC) concentrations estimated over the past 6000 yr(Vincent et al. 1998). Clear-water attenuation (Baker &Smith 1982) at those wavelengths was subtracted fromthe Kd(λ) values. The results were fitted to an exponen-tial function of Kd(λ) versus DOC, then attenuation byclear water was added back to the entire spectrum togive an interpolation and extrapolation of Kd(λ) from 280to 700 nm. Assuming that absorption by chlorophyll con-tributed little to the empirical relationship between DOCand Kd(λ), which only considers UV wavelengths, weadded attenuation by 0.1 mg chl m–3 (Baker & Smith1982) to the reconstructed spectra to assess the contribu-tion of chlorophyll. To comply with the analysis of Pienitz& Vincent (2000), our parameterization was adapted tothe sub-Arctic environment by using their reference so-lar irradiance spectrum (290 to 325 nm) and extended itto 280 to 700 nm using a spectrum for that latitude fromthe irradiance model described above, scaled by theaverage ratio of the 2 spectra between 315 and 325 nm.

RESULTS AND DISCUSSION

Relationship between water-column photosynthesisand penetration of PUR

A large number of models express water-columnphotosynthesis using variations of Eq. (1). Notation anddetails vary, but models predict that for a given surface

P a T

P b T T

P P c T T

a

b b

c c

pot PURW

PURW

PIRW

pot PURW

PIRW

*

*

∫∫

= ⋅

= ⋅ ⋅

= ⋅ ⋅

1

1

1

2

2 3

2 3∆

∆P PP

Ppot

pot

= − ∫∫

1*

*

105

Mar Ecol Prog Ser 269: 101–110, 2004

irradiance, water-column photosynthesis, normalizedto surface chlorophyll and a maximum rate of normal-ized photosynthesis (e.g. ∫P*, in meters), varies directlywith a measure of light penetration. The depth of 1%surface PAR is a commonly used measure, and it istempting to estimate it using the Lambert-Beer Law:zeu(PAR) = 4.6/KPAR, with KPAR determined as thespectrally average Kd(λ) for surface water. This, how-ever, produces large errors, as the attenuation of PARchanges with depth — it is high near the surface, andwith depth it converges to the attenuation coefficientfor the wavelength of maximum transmission (Kirk1994). Furthermore, even with a KPAR appropriatelymeasured across the depth of the euphotic zone (Morel1988), the shortcomings associated with using EPAR in-stead of EPUR remain (Lewis et al. 1985, Sathyendranathet al. 1989, Laws et al. 1990, Markager & Vincent 2001).

We find that, in a uniform water column, the depth ofzeu(PUR) can be predicted well by a nonlinear functionof T W

PUR: zeu(PUR) = 5.26 T WPUR

1.08, r2 = 0.999, n = 143(Fig. 1A), using Kd(λ) from the surface. The simplepower function is smooth and monotonic, and the sim-

ulated data points show little scatter despite the broadrange of optical water types considered. Comparison ofzeu(PAR) with zeu(PUR) illustrates the improvement(Fig. 1B). The ratio zeu(PAR)/zeu(PUR) shows the errorassociated with using EPAR rather than EPUR to rep-resent irradiance for photosynthesis in a depth-integrated model. For the broad range of water typesconsidered, this error ranged from an underestimate ofabout 16% in very clear waters to an overestimate ofnearly 20% in waters with relatively shallow euphoticdepths. The implication is straightforward: in depth-integrated models of primary productivity, the expres-sion of light penetration as a function of PUR-weightedtransparency obviates the error associated with usingEPAR instead of EPUR in the light-penetration term.

General parameterization of uninhibited water-column photosynthesis

Eq. (1) and the strong relationship between zeu(PUR)and T W

PUR (Fig. 1A) suggest that for a given spectrum ofsolar irradiance at the surface, there should be a rela-tionship between uninhibited water-column photosyn-thesis and T W

PUR. Indeed, a simple power function ofT W

PUR could reproduce almost exactly the 143 calcula-tions of ∫P*pot representing a broad range of water types(r2 = 0.999, n = 143; Table 2):

(15)

General parameterization of water-column photosynthesis as influenced by UV

Existing PAR-based, depth-integrated models areinherently incapable of describing effects of UV onwater-column photosynthesis. Currently, this can onlybe done through spectrally resolved numerical model-ing (Arrigo 1994, Boucher & Prézelin 1996, Neale et al.1998). Inhibition-weighted transparency, T W

PIR, quanti-fies the effect of UV on photosynthesis and its penetra-tion with depth, so it was incorporated into a simplemodel similar to Eq. 15. The inhibited rate ∫P* isdescribed as a function of weighted transparencies:

(16)

As with Eq. (15), the simple function matched almostexactly the 143 results of numerical modeling (r2 =0.999, n = 143; Fig. 2C). In Eq. (16) the exponent ofT W

PIR, slightly greater than a value of 1, compared toalmost 0 for T W

PIR, indicates that most of the variabilityin water-column photosynthesis is explained by T W

PUR

alone (r2 = 0.997, n = 143; Fig. 2A). In essence, when

P T T* .. – .

∫ = ⋅ ⋅2 381 19 0 09

PURW

PIRW

P Tpot PURW*∫ = ⋅ .

.2 91

1 09

106

0.8

0.9

1

1.1

1.2

0 50 100 150 200

B

0

50

100

150

200

0 50 100 150 200

A

f(T

w

)P

UR

zeu(PUR)

z eu(P

AR

) / z

eu(P

UR

)

Fig. 1. (A) A simple power function of T WPUR predicts zeu(PUR):

zeu(PUR) = 5.26 T WPUR

1.08, r2 = 0.999, n = 143. (B) The ratiozeu(PAR)/zeu(PUR) for a given zeu(PUR). Each data point represents a water column with an individual Kd spectrumconstructed after Baker & Smith (1982) and a solar irradiance

spectrum for 45° N

Lehmann et al.: Biologically weighted transparency

only the influences of different water types are consid-ered, changes in the penetration of EPUR play a muchbigger role than photoinhibition in determining thevariability of water-column production. Interestingly,since attenuation coefficients for UV wavelengthscovary strongly with those in the visible range, T W

PIR

explains 95.5% of the variability in ∫P* (r2 = 0.955, n =143; Fig. 2B).

Proportional inhibition of water-column photosynthesis by UV

Studies of UV radiation and aquatic photosynthesisfocus primarily on estimating the proportional reduc-

tion of photosynthesis due to UV (e.g. Smith et al.1980). This inhibition is only a small fraction of ∫P*pot forthe wide range of water types considered (Fig. 3), andneither T W

PUR nor T WPIR can describe it precisely (T W

PUR:r2 = 0.172, n = 143; T W

PIR: r2 = 0.630, n = 143; Fig. 3A andB, respectively). In analogy to Eq. (16), proportionalinhibition of water-column photosynthesis, ∆P/Ppot,is described very well (r2 = 0.998, n = 143) by acombination of T W

PUR and T WPIR (Fig. 3C):

(17)

The exponents in Eq. (17) are close to –1.0 and 1.0,indicating that the inhibition of water-column photo-synthesis is strongly related to the ratio of T W

PIR to T WPUR

(r2 = 0.998, n = 143) as found by Neale (2001), whoadapted this approach (see also Fig. 5). The simpleparameterizations (Eqs. 16 & 17) are vastly easier touse and inherently more general than sensitivityanalyses of numerical models of photosynthesis andphotoinhibition.

Estimates of photosynthesis and photoinhibitionusing measured Kd spectra

Weighted transparency and the numerical solutionsfor ∫P* and ∆P/Ppot, all constrained with measuredattenuation spectra and chlorophyll concentrations,compare well with relationships for the modeledwater columns (circles and squares in Figs. 2 & 3).This is notable since it implies that the parameteriza-tion is not restricted to attenuation spectra specifiedby a particular model of Kd(λ) as a function of CDOMand chlorophyll.

∆P P T Tpot PURW

PIRW .

– . .= ⋅ ⋅0 24

1 08 1 01

107

Parameter Latitude45° N Sub-Arctic

a1 2.91 2.72a2 1.09 1.09

(r2) (0.999) (0.999)

b1 2.38 2.24b2 1.19 1.18b3 –0.09 –0.08

(r2) (0.999) (0.998)

c1 0.24 0.26c2 –1.08 –1.07c3 1.01 1.00

(r2) (0.998) (0.998)

Table 2. Parameters of the power functions constructed toestimate water-column photosynthesis (Eqs. 12 & 13) and theproportion of inhibition for different latitudes (Eq. 14). For eachfunction, r2 is the proportion of variability explained in the

results of 143 numerical simulations

0

10

20

30A

0

40

80

120

0 40 80 120

C

∫P* (Numerical simulation; m)

0

4

8

12

16B

Modeled water typesNova Scotian lakesMarine

0

3

0 4 80

0.4

0.8

0 4 8 0

4

8

0 4 8

Tw

(m)

PU

R

Tw

(m)

PIR

∫P*

= f

(Tw

, Tw

)P

IRP

UR

0 40 80 120 0 40 80 120

Fig. 2. (A) PUR-weighted transparency, T WPUR, is linearly proportional to the numerical solution for the normalized water-column

integral of inhibited photosynthesis, ∫P* (r2 = 0.997, n = 143). (B) PIR-weighted transparency, T WPIR, is related to ∫P* (r2 = 0.955,

n = 143). (C) A non-linear function of T WPUR and T W

PIR (Eq. 13 with parameters bn for 45°N from Table 2) describes variability ininhibited water-column photosynthesis normalized to biomass (r2 = 0.999, n = 143). Open circles and squares are added for com-parison and represent results where measurements of Kd(λ) were used to predict ∫P* in Nova Scotian lakes and marine systems,

respectively

Mar Ecol Prog Ser 269: 101–110, 2004

Reconstruction of historic relative photosynthesisand inhibition

The parameterizations for photosynthesis using thesub-Arctic irradiance spectrum (Eqs. 12, 13 & 14, withcoefficients in Table 2) were used to infer changes in∫P* and ∆P/Ppot due to optical variability in a generic,deep lake with the same historical evolution of opticalproperties as Queen’s Lake in northern Canada. Forthe time-series records (Fig. 4), ∫P* was multiplied by0.1 mg chl m–3 to retrieve common production dimen-sions, assuming Ps

B = 1 mg C [mg chl]–1 h–1. While theinferred rate of photosynthesis and ∆P/Ppot show thesame trends as T*PI reported by Pienitz & Vincent(2000, their Fig. 2d), the x-axis of our Fig. 4 is a quan-titative estimate of relative photosynthesis and ofphotoinhibition as influenced by variations in watertransparency, while T*PI is an indicator of the potentialfor photoinhibition with no explicit relationship to rela-tive photoinhibition per se. As in the analysis of Pienitz& Vincent, our estimates are based on the unrealisticassumptions that the weighting function for photoinhi-bition and, in our work, for chlorophyll concentration,absorption spectra, and photosynthetic parameters donot change over time. Nonetheless, the new quantita-tive context is useful for interpreting the reconstructionof optical conditions in terms of the ecological pressureassociated with variations in UV. Our parameteriza-tion indicates that since the transparency minimum,4.41 × 103 yr before present, photosynthesis (assuming0.1 mg chl m–3) increased by 1040%. In turn, the pro-portion of inhibition of photosynthesis increased by255%, to 0.069 from 0.027. During the same interval,the Pienitz & Vincent parameter, T*PI (Eq. 4) changedby 3658%. The temporal variation in T*PI overesti-mates inhibition of photosynthesis by UV, because, as

discussed by Pienitz & Vincent, periods of clear waterlead to changes in T W

PUR that partly compensateincreases in T W

PIR (Fig. 5).Our quantitative assessment indicates that variations

in weighted transparency alone can greatly overesti-mate the biological effects, more than tenfold in thiscase. Although we estimate less variability in inhibi-tion than suggested by changes in T*PI, our analysisdoes not affect the conclusions of Pienitz & Vincent(2000), i.e. that natural variability in water trans-parency has a greater influence on water-columnphotosynthesis and inhibition than even extremeozone depletion (Arrigo & Brown 1996, see alsoSchindler et al. 1996 and Leavitt et al. 1997).

108

0 0.04 0.08

T * (m)

B0

1

2

3

4

5

60 1 2

Inferred P(mg C m-2 h-1)

A

Age

(10

3 yea

rs b

efor

e pr

esen

t)

Inferred ∆P/Ppot

PI

Fig. 4. (A) Time series of inferred photosynthesis (∫P = ∫P*·B ·Ps

B, where ∫P* is calculated using Eq. 13, with para-meters bn for the sub-Arctic from Table 2) and (B) the propor-tion of photoinhibition, ∆P/Ppot (using Eq. 14, with para-meters cn for the sub-Arctic from Table 2), in a deep lake withthe same evolution of optical properties as Queen’s Lake insub-Arctic Canada. For comparison T*PI (Eq. 4) based onPienitz & Vincent (2000) is shown in Panel B (dashed line)

0

10

20

0

4

8

BModeled water typesNova Scotian lakesMarine

0

0.05

0.1

0.15

0 0.05 0.1 0.15

C

∆P/P (Numerical simulation)

Tw

(m)

PU

R

Tw

(m)

PIR

∆P/P

pot

= f(

Tw

, Tw

)P

IRP

UR

12

1630A

0 0.05 0.1 0.150 0.05 0.1 0.15

Fig. 3. (A, B) Relationship between the fraction of photosynthesis lost to inhibition, ∆P/Ppot, simulated numerically from a spectralmodel, and PUR- or PIR-weighted transparency (r2 = 0.187 and r2 = 0.233, n = 143), respectively. (C) Prediction of ∆P/Ppot by aparameterization of PUR- and PIR-weighted transparency (Eq. 14 with parameters cn for 45°N from Table 2, r2 = 0.998, n = 143).Open circles and squares are added for comparison and represent results where measurements of Kd(λ) were used to constrain

predictions of ∆P/Ppot in Nova Scotian lakes and marine systems, respectively

Lehmann et al.: Biologically weighted transparency

CONCLUSIONS

The use of weighted transparency to describe thetransmission of solar radiation through the water columnrepresents an effective tool for describing biological ef-fects as a function of surface-water optical properties.We demonstrated its usefulness by accurately estimatingthe depth of the 1% PUR level (Fig. 1A) in a range ofwater types, encompassing both Case 1, for which opti-cal properties are determined by phytoplankton pigmentand derivative products, and Case 2 waters, with anadditional CDOM component (Kirk 1994).

Our function of PUR-weighted transparency (Eq. 15)can directly estimate changes in water-column produc-tion as influenced by variations in water transparency.The depth of 1% surface EPUR expressed as a simpleterm is an effective substitute for the depth of theeuphotic zone in general equations of depth-integrated photosynthesis, as given in Eq. (1). Thiseliminates a well-recognized error associated with theuse of EPAR (Lewis et al. 1985, Sathyendranath et al.1989, Laws et al. 1990).

Transparency weighted for photosynthesis-inhibitingradiation (T W

PIR) is evaluated in the context of depth-integrated water-column photosynthesis and, in a sim-ple function with T W

PUR, reproduces almost exactly theresults of a depth-resolved, spectral model, whichincludes the effects of UV as described by a biologicalweighting function. This is, to the best of our knowl-edge, the first time that UV has been incorporated intodepth-integrated equations of photosynthesis (sensuPlatt & Sathyendranath 1993, Behrenfeld & Falkowski1997), and it allowed us to transform an indicator ofinhibiting radiation (Pienitz & Vincent 2000) into apredictor of relative photosynthesis and photoinhibi-tion by UV.

The utility of our method is in using 2 simple equa-tions, based on properties at the sea surface (Eqs. 16& 17), to replace thousands or millions of depth-resolved calculations of subsurface irradiance andbiological responses that are based on properties atthe sea surface. For many applications, such simplemodels may provide additional insight. For example,proportional inhibition of water-column photosynthe-sis is a function of T W

PIR�T WPUR (see also Neale 2001),

which is very difficult to generate through a sensitiv-ity analysis using numerical models (Arrigo & Brown1996).

This study focuses on the potential influences of vari-ability in water transparency on photosynthesis and itsinhibition by UV in the water column. This is accom-plished by keeping the other factors constant whileexamining the effects of varying water transparency.We have extended this analysis to encompass varia-tions in solar irradiance spectra and physiologicalparameters (Cullen et al. 2000, J. J. Cullen et al.unpubl. data). In a sensitivity analysis, Neale (2001)evaluated the effect of a suite of measured andmodeled parameters on the sensitivity of phytoplank-ton to photoinhibition at solar noon. He concludedthat T W

PIR and the weighting function used for photoin-hibition are of similar importance for photoinhibition.

Models of photosynthesis are essential tools forassessing the effects of environmental variability onthe physiological responses of phytoplankton (e.g.Arrigo & Brown 1996, Neale et al. 1998), because onlyin the rarest of cases can environmental effects onwater-column inhibition be determined experimen-tally. Our parameterizations of photosynthesis andinhibition are shortcuts to describe results of detailednumerical models. While the model used to construct aparameterization requires individual validation of theparameters describing photosynthesis versus irradi-ance and inhibition versus UV exposure, our method isnot dependent on the formulation of the photosynthe-sis model. Moreover, photosynthesis is but a singleexample for the application of the weighted trans-parency concept. The same analysis could be per-formed on any photochemical or photobiological pro-cess for which appropriate weighting functions exist,for example DNA damage (Huot et al. 2000, Pienitz &Vincent 2000), or photochemical production of DOC(Johannessen & Miller 2001).

Acknowledgements. This study was funded by NSERC(Research Partnerships, Research Grants), ONR, NOPP, andEnvironment Canada. We thank W. F. Vincent, who gener-ously provided data and many suggestions. Marine irradianceand chlorophyll data were kindly provided by M. Mallonnee,L. Harding and W. L. Miller. The manuscript was improved byconsidering the comments of C. Brown and 3 anonymousreviewers.

109

0 1 2

10 T * PI

T w PUR-1.07

0

1

2

3

4

5

6

Weighted transparency

Age

(103 y

ears

bef

ore

pre

sent

)

T w PIR1.0

Fig. 5. Time series of T*PI (Eq. 4, multiplied by 10 to fit scale)based on Pienitz & Vincent (2000), T W

PUR, and T WPIR, with the

latter 2 raised to their respective powers according to Eq. (14) and parameters cn in Table 2 for the sub-Arctic

Mar Ecol Prog Ser 269: 101–110, 2004

LITERATURE CITED

Arrigo KR (1994) Impact of ozone depletion on phytoplanktongrowth in the Southern Ocean: large-scale spatial andtemporal variability. Mar Ecol Prog Ser 114:1–12

Arrigo KR, Brown CW (1996) Impact of chromophoricdissolved organic matter on UV inhibition of primaryproductivity in the sea. Mar Ecol Prog Ser 140:207–216

Arrigo KR, Lubin D, van Dijken GL, Holm-Hansen O, MorrowE (2003) Impact of a deep ozone hole on SouthernOcean primary production. J Geophys Res Oceans 108:no. C5.10.1029/2001JC001226,2003

Baker KS, Smith RC (1982) Bio-optical classification andmodel of natural waters. Limnol Oceanogr 27:500–509

Behrenfeld MJ, Falkowski PG (1997) A consumer’s guideto phytoplankton primary productivity models. LimnolOceanogr 42:1479–1491

Boucher NP, Prézelin BB (1996) Spectral modeling of UVinhibition of in situ Antarctic primary production using afield derived biological weighting function. PhotochemPhotobiol 64:407–418

Cullen JJ, Neale PJ, Lesser MP (1992) Biological weightingfunction for the inhibition of phytoplankton photo-synthesis by ultraviolet radiation. Science 258:646–650

Cullen JJ, Davis RF, Huot Y, Lehmann MK (2000) Quantifyingeffects of ultraviolet radiation in surface waters. In: Oceanoptics XV: conference proceedings on CD-ROM. PrestigePublishing, Alexandria, VA

Gregg WW, Carder KL (1990) A simple spectral solar irradi-ance model for cloudless maritime atmospheres. LimnolOceanogr 35:1657–1675

Huot Y, Jeffrey WH, Davis RF, Cullen JJ (2000) Damage toDNA in bacterioplankton: a model of damage by ultra-violet radiation and its repair as influenced by verticalmixing. Photochem Photobiol 72:62–74

Johannessen SC, Miller WL (2001) Quantum yield for thephotochemical production of dissolved inorganic carbonin seawater. Mar Chem 76:271–283

Kirk JTO (1994) Light and photosynthesis in aquatic eco-systems. Cambridge University Press, Cambridge

Laws EA, DiTullio GR, Carder KL, Betzer PR, Hawes S (1990)Primary production in the deep blue sea. Deep-Sea ResPart A 37:715–730

Leavitt PR, Vinebrooke RD, Donald DB, Smol JP, SchindlerDW (1997) Past ultraviolet radiation environments in lakesderived from fossil pigments. Nature 388:457–459

Lehmann MK, Davis RF, Huot Y, Cullen JJ (2000) Biologicallyweighted transparency: a predictor for water columnphotosynthesis and its inhibition by ultraviolet radiation.In: Ocean optics XV: conference proceedings on CD-ROM. Prestige Publishing, Alexandria, VA

Lewis MR, Warnock RE, Platt T (1985) Absorption andphotosynthetic action spectra for natural phytoplanktonpopulations: implications for production in the openocean. Limnol Oceanogr 30:794–806

Markager S, Vincent WF (2001) Light absorption by phyto-plankton: development of a matching parameter for algalphotosynthesis under different spectral regimes. J Plank-ton Res 23:1373–1384

Morel A (1978) Available, usable, and stored radiant energy

in relation to marine photosynthesis. Deep-Sea Res 25:673–688

Morel A (1988) Optical modelling of the upper ocean in rela-tion to its biogenous matter content (Case I waters). J Geo-phys Res 93:10749–10768

Morel A (1991) Light and marine photosynthesis: a spectralmodel with geochemical and climatological implications.Prog Oceanogr 26:263–306

Morel A, Berthon JF (1989) Surface pigments, algal biomassprofiles, and potential production of the euphotic layer:relationships reinvestigated in view of remote-sensingapplications. Limnol Oceanogr 34:1545–1562

Morrow JH, Booth CR (1997) Instrumentation and method-ology for ultraviolet radiation measurements in aquaticenvironments. In: Häder DP (ed) The effects of ozonedepletion on aquatic ecosystems. R. G. Landes, Austin,p 31–44

Neale PJ (2000) Spectral weighting functions for quantifyingeffects of UV radiation in marine systems. In: de Mora S,Demers S, Vernet M (eds) The effects of UV radiation inthe marine environment. Cambridge University Press,Cambridge, p 72–100

Neale PJ (2001) Modeling the effects of ultraviolet radia-tion on estuarine phytoplankton production: impact ofvariations in exposure and sensitivity to inhibition.J Photochem Photobiol B Biol 62:1–8

Neale PJ, Davis RF, Cullen JJ (1998) Interactive effects ofozone depletion and vertical mixing on photosynthesis ofAntarctic phytoplankton. Nature 392:585–589

Pienitz R, Vincent WF (2000) Effect of climate change relativeto ozone depletion on UV exposure in subarctic lakes.Nature 404:484–487

Platt T, Sathyendranath S (1993) Estimators of primary pro-duction for the interpretation of remotely-sensed data onocean color. J Geophys Res 98:14561–14596

Ryther JH, Yentsch CS (1957) The estimation of phyto-plankton production in the ocean from chlorophyll andlight data. Limnol Oceanogr 2:281–286

Sakshaug E, Johnsen G, Andersen K, Vernet M (1991)Modeling of light-dependent algal photosynthesis andgrowth: experiments with Barents Sea diatoms Thalas-siosira nordenskioeldii and Chaetoceros furcellatus.Deep-Sea Res 38:415–430

Sathyendranath S, Platt T, Caverhill CM, Warnock RE, LewisMR (1989) Remote sensing of oceanic primary production:computations using a spectral model. Deep-Sea Res 36:431–453

Schindler DW, Curtis PJ, Parker BR, Stainton MP (1996) Con-sequences of climate warming and lake acidification forUV-B penetration in North American boreal lakes. Nature379:705–708

Smith RC, Baker KS, Holm-Hansen O, Olson RS (1980) Photo-inhibition of photosynthesis in natural waters. PhotochemPhotobiol 31:585–592

Talling JF (1957) The phytoplankton population as acompound photosynthetic system. New Phytol 56:133–149

Vincent WF, Laurion I, Pienitz R (1998) Arctic and Antarcticlakes as optical indicators of global change. Ann Glaciol27:691–696

110

Editorial responsibility: Otto Kinne (Editor), Oldendorf/Luhe, Germany

Submitted: July 4, 2003; Accepted: October 21, 2003Proofs received from author(s): March 15, 2004