BIOLOGICALLY WEIGHTED TRANSPARENCY: A PREDICTOR FOR
WATER COLUMN PHOTOSYNTHESIS AND ITS INHIBITION
BY ULTRAVIOLET RADIATION
Moritz K Lehmann, Richard F Davis, Yannick Huot, John J Cullen
Dept. of Oceanography, Dalhousie University, Halifax, N.S., Canada, B3H 4J1
ABSTRACT
Planktonic photosynthesis depends on the quantity and quality of the radiance
field in the euphotic zone. The rate of photosynthesis is a result of nonlinear interactions
between photosynthetically utilizable radiation (PUR) in the visible waveband, and
photosynthesis-inhibiting radiation (PIR), mostly in the ultraviolet (UV) bands. Several
spectrally-resolved numerical models describe photosynthesis as a function of PUR alone
and ignore inhibition by UV. More complete models include inhibition as a function of
biologically weighted UV radiation. This refinement is essential for describing the effects
of ozone depletion on photosynthesis as influenced by natural variability of absorption by
colored dissolved organic matter (CDOM).
A simple method for describing the influence of variable spectral attenuation
(kd(λ)) on water column photosynthesis is introduced for a very broad range of water
types. Key results of a fully resolved spectral model of photosynthesis can be reproduced
with simple parameterizations of a reference solar irradiance spectrum at the surface and
water transparency (i.e., 1/kd(λ)) weighted spectrally for biological effectiveness
consistent with PUR and PIR. Transparency weighted spectrally by the normalized
product of irradiance and photosynthetic absorption (PUR-weighted transparency, TwPUR)
describes spectral effects on photosynthesis in the water column. An empirical
parameterization of transparency weighted by the product of surface irradiance and the
biological weighting function for inhibition of photosynthesis (TwPIR), along with TwPUR,
describes the inhibition of water column photosynthesis relative to the uninhibited rate.
This parameterization of inhibition is new.
The use of weighted transparency may greatly simplify the calculation of water
column production and its inhibition as a function of solar irradiance and attenuation
coefficients in UV and visible wavelengths; potentially, this can be done on a global scale
using optical properties retrieved from ocean color and should be especially useful in
generalizing the influences of CDOM on UV-dependent processes.
INTRODUCTION
Optical measurements from remote or in situ platforms allow the determination of
important parameters for models of photosynthesis at various space and time scales. In
these models the rate of photosynthesis depends on irradiance and the concentration of
chlorophyll. The dependence on irradiance has been implemented with varying degrees
of complexity (e.g. Behrenfeld & Falkowski 1997). In the simplest case, photosynthesis
is a function of the integrated irradiance between 400 and 700 nm (photosynthetically
active radiation, EPAR c.f. Talling (1957)). Further detail is added if models account for
1
the fraction of EPAR that is actually absorbed by photosynthetic pigmentation, the
photosynthetically utilizable radiation, EPUR (Morel 1978, c.f. Lewis et al. 1985). For
example Sathyendranath et al. (1989) showed that EPAR-based models may overestimate
water column photosynthesis by up to 60% compared to EPUR models. More complete
formulations (e.g. Arrigo 1994, Neale et al. 1998) take into account photoinhibition of
photosynthesis as a function of biologically weighted UV radiation, i.e. photosynthesisinhibiting radiation, EPIR. This refinement is essential for describing the environmental
effects of ozone depletion on photosynthesis as influenced by natural variability of
attenuation by UV-absorbing colored dissolved organic matter (CDOM) (Arrigo and
Brown 1996).
We describe a simple method to determine the influence of water transparency on
two key results of fully spectral models of photosynthesis: water column integrated
production rate and photoinhibition of photosynthesis. The simple parameterization is
potentially useful for implementation in large scale models.
METHODS
For reference, a full numerical simulation of water-column photosynthesis was
performed for 99 optically distinct water types (Table 1). Two main results of this
simulation were retained: the water-column integrated rate of photosynthesis and the
percentage of water-column production lost to inhibition by UV radiation. In an attempt
to parameterize the numerical solution we constructed two types of weighted
transparency (here, transparency is defined as the inverse spectral diffuse attenuation
coefficient, 1/kd(λ)), based on the formulation by Vincent et al. (1998). One, TwPUR, was
spectrally weighted for biological effectiveness of solar irradiance consistent with EPUR,
the second, TwPIR, was weighted with a biological weighting function for photoinhibition.
The underwater optical environment was simulated using the functional
dependence of attenuation on chlorophyll and dissolved organic matter (DOM)
concentrations (Baker and Smith 1982): each of 11 chlorophyll concentrations (0.02 – 15
mg m-3) was combined with each of 9 concentrations of DOM (0 – 5000 mg m-3). These
attenuation spectra were used to propagate through the water column a reference solar
irradiance spectrum (280 – 700 nm), modeled after Gregg and Carder (1990) and
extended into the UV as in Arrigo (1994). The irradiance spectrum is for a cloudless sky
on March 21st at 45º N at noon, with a climatological ozone content of 366.1 DU (Van
Heuklon 1979). Scalar irradiance (E0 ref(λ) ) was calculated after Neale et al. (1998).
Photosynthetic rates were estimated for the 99 water types using a depth resolved
spectral model (Cullen et al. 1992). The potential for photosynthesis (Ppot(z)) is modeled
as a saturating function of irradiance, weighted for absorption by photosynthetic pigments
(EPUR(z)), Equation i). The maximum attainable rate of primary production, PBs, was set
to one so the numerical result for Ppot(z) is equivalent to P/PBs (Table 2 lists the values of
the parameters used in the photosynthesis model). The concentration of chlorophyll was
assumed uniform with depth and the values were equal to those used to generate the
corresponding attenuation spectrum for the water type. The formulation for Ppot(z) is
extended to include inhibition of photosynthesis as a function of the dose rate of
photosynthesis-inhibiting radiation (E*PIR, Equation vi) to give the inhibited rate of
primary production (P(z), Equation ii). The weighting function, ε(λ), used in the
2
calculation of E*PIR reflects the biological efficiency of UV wavelengths to inhibit
photosynthesis in a marine diatom (Equation (vi), Cullen et al. 1992). Both, Ppot(z) and
P(z) were normalized to chlorophyll and integrated to the depth where EPUR(0-) is reduced
to 0.1% to yield water column primary production (Equations iii and iv). The percentage
of water column photosynthesis lost due to inhibition (%inh) is calculated with Equation
(vii).
PUR-weighted transparency (TwPUR) of a water column is the product of the
inverse of the spectral attenuation coefficient, surface irradiance (E0 ref(λ,0-), where the
minus in the superscript designates irradiance just below the surface) relative to EPAR, and
the normalized photosynthetic absorption ( ap / ap ) integrated over the visible
wavelengths (400 to 700 nm). Note that we normalize photosynthetic absorption by the
mean absorption, in contrast to Morel (1978) who normalized by the maximum
absorption. Transparency weighted by the product of surface irradiance and the biological
weighting function for inhibition of photosynthesis integrated over the visible and UV
wavelengths (280 to 700 nm) yields PIR-weighted transparency (TwPIR), Equation (x).
Normalized photosynthesis integrated over depth (∫P*pot, and ∫P*) and the relative
inhibition of photosynthesis were separately fitted to the two weighted transparencies by
multiple linear regression on log-transformed variables. The goodness of fit was
evaluated by linear regression on the numerically modeled and predicted variables.
Table 1: The equations with parameters and units.
Ppot(z) (mg C m-3 h-1) Potential for primary
production in the absence of inhibition
P(z) (mg C m-3 h-1) Inhibited rate of primary
production
1
E
(z)  
B
B
-1 -1
(ii) P( z) = BPs 1 − exp − PUR
P
s (mg C (mg Chl) h ) Maximum
*
Ek  

1+ EPIR
attainable rate of primary production per
0.1% EPUR
unit chlorophyll in the absence of phoP
z)
(
pot
(iii) ∫ Ppot* = ∫
dz
B
toinhibition
Ps B
*
0
∫P
pot (m) Column-integrated normalized
0.1% E PUR
potential primary production
P( z)
*
*
(iv) ∫ P = ∫
dz
B
(m) Column-integrated normalized
∫P
Ps B
0
inhibited rate of primary production
EPUR(z) (µmol quanta m-2 s-1) Irradiance
where
weighted by absorption by
(v)
photosynthetic pigments
700
*
E
(z) (dimensionless) Weighted
ap ( λ )
PIR
−
E0 ref (λ ,0 )exp(−kd( λ ) z)dλ
EPUR (z) = ∫
irradiance
for inhibition of
ap
400
photosynthesis
Ek (µmol quanta m-2 s-1) Saturation
(vi)
parameter for photosynthesis; it is related
700
to the initial slope of the PBpot versus
E*PIR (z ) = ∫ ε ( λ ) E0 ref (λ ,0 − )exp(−kd ( λ ) z)dλ
EPUR relation, αB (mg C (mg Chl)-1
400
(µmol quanta m-2 s-1)-1 h-1), by Ek = PBs /
αΒ
E0 ref(λ, 0-) (µmol quanta m-2 s-1 nm-1)
Photosynthesis model
E
(z)  
(i) Ppot (z ) = BPsB 1− exp − PUR

Ek

3
Table 1 (continued)
Percent inhibition of photosynthesis

PB 
∫
(vii) %inh =  1−
100
B 


∫ Ppot 
PUR-weighted transparency
700
1 ap( λ ) E0 (λ ,0 − )
w
(viii) TPUR = ∫
dλ
ap EPAR (0− )
400 kd (λ )
700
−
(ix) EPAR (0 ) =
∫E
0 ref
−
(λ ,0 ) dλ
400
PIR-weighted transparency
700
1
w
ε ( λ ) E0 ref ( λ ,0− ) dλ
(x) TPIR = ∫
λ
k
(
)
280 d
Spectral scalar irradiance just below the
water surface
B (mg Chl m-3) Chlorophyll concentration
(uniform with depth)
z (m) Depth below the water surface
ap(λ) (m-1) Spectral absorption coefficient
of phytoplankton
ap (m-1) Mean absorption coefficient of
phytoplankton over 400-700 nm
ε(λ) (µmol quanta m-2 s-1)-1 Biological
weighting function for the inhibition of
photosynthesis
λ (nm) Wavelength
TwPUR (m) PUR-weighted transparency
TwPIR (m) PIR-weighted transparency
EPAR(0-) (µmol quanta m-2 s-1) Irradiance
just below the surface integrated over
400 to 700 nm
kd(λ) (m-1) Spectral diffuse attenuation
coefficient
Table 2: Values of parameters used in the
photosynthesis model
Parameter
B
P s
Ek
B
E0 ref(PUR,0-)
Value
1 mg C (mg Chl)-1 h-1
150 µmol quanta m-2 s-1
0.02, 0.05, 0.1, 0.5, 1, 2,
3, 4, 5, 10, 15 mg Chl m-3
1500 µmol quanta m-2 s-1
RESULTS AND DISCUSSION
Water-column integrated photosynthesis normalized to chlorophyll, ∫P* and ∫P*pot,
and its inhibition can be accurately predicted as a function of weighted transparency.
Most straightforward is the description of ∫P*pot by TwPUR (Figure 1). Both are linearly
related with a regression coefficient of r2 = 0.99.
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Figure 1: The relationship between a fully spectral numerical
simulation of the potential for photosynthesis in the water (∫P*pot, m, xaxis) and PUR-weighted transparency (TwPUR, m, y-axis). Both are
directly proportional with a linear regression coefficient of r2 = 0.99.
The data points are color-coded according to their DOM concentration
used to construct the individual attenuation spectra (see legend).
Owing to the relatively small fraction of photoinhibition, causing less than 15%
reduction of photosynthesis in the worst case (see x-axis in Figure 3), most of the
variability in ∫P* can still be described by PUR-weighted transparency (r2 = 0.998, Figure
2 left panel). Yet an exponential function of TwPUR and TwPIR is capable of describing ∫P*
with greater accuracy (r2 = 0.999, Figure 2 right panel). The exponential parameterization
in Equation (xi) was determined by multiple linear regression on the log-transformed
variables.
(xi)
1.20
w
estimated ∫ P * = 2.49 TPUR
w
TPIR
−0.11
Finally, the percentage of photosynthesis lost due to inhibition is described well
(r2 = 0.998) by combination of TwPUR and TwPIR similar to the one above (Figure 3 right
panel, Equation xii).
(xii)
w
estimated % inhibition = 22.91TPUR
− 1.07
w 0.99
TPIR
5
Figure 2: (Left panel) The numerical solution for the integral inhibited photosynthesis
(∫P*, m, x-axis) is linearly proportional to PUR-weighted transparency (TwPUR, m, yaxis), r2 = 0.998. (Right panel) TwPUR and PIR-weighted transparency (TwPIR, m) are
combined in a parameterization (y-axis), which describes variability in inhibited watercolumn photosynthesis normalized to biomass more accurately than TwPUR alone (r2 =
0.999 after regression on the transformed variables) (legend see Figure 1).
Figure 3: (Left panel) The relative amount of photosynthesis lost to inhibition
simulated numerically from a fully spectral model (x-axis) is poorly described by PIRweighted transparency (y-axis) alone. (Right panel) A parameterization of PUR- and
PIR-weighted transparency can more accurately predict the percentage of
photoinhibition (r2 = 0.998) (legend see Figure 1).
6
The prediction of the percentage of photoinhibition requires a combination of
both variables, TwPUR and TwPIR, as each one individually accounts for only 22.4% and
60.5% of the variability in log-space, respectively (see Figure 3 left panel for TwPIR versus
%inhibition).
Following dimensionless arguments carried forward by Talling (1957) water
column photosynthesis can be retrieved by multiplication of ∫P* with the product of
surface biomass and a suitable PBs.
The parameterizations described above hold for 99 different spectra of diffuse
attenuation, accounting for the wide range of chlorophyll and CDOM concentrations
investigated. The relationship between weighted transparency and photosynthesis are
therefore robust with respect to water type. The present results are representative for one
set of physiological parameters and a single reference irradiance. In the future we will
assess the sensitivity of the parameterization to variable Ek, to a number of biological
weighting functions and to changing solar irradiance to arrive at estimates for
photosynthesis integrated over a whole day (see Cullen et al., this volume).
CONCLUSION
For representative physiological and environmental conditions we demonstrated
an efficient and accurate method to predict water-column integrated results of spectrallyand depth-resolved models of photosynthesis. The parameterization of photoinhibition is
new and offers a straightforward way to assess the impact of UV radiation on
photosynthesis in waters with naturally varying CDOM concentrations (cf. Pienitz and
Vincent 2000). Global scale application of the method may be feasible once the
parameterization is expanded and tested.
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