Document Sample

Limnol. Oceanogr., 38(7), 1993, 1403-1419 0 1993, by the American Society of Limnology and Oceanography, Inc. A spectrally averaged model of light penetration and photosynthesis Thomas R. Anderson James Rennell Centre for Ocean Circulation, Natural Environment Research Council, Gamma House, Chilworth Research Centre, Chilworth, Southampton, U.K. SO1 7NS Abstract A model was developed which predicts the daily photosynthesis of a vertical pigment profile divided into a number of homogeneous layers. A spectral model (irradiance divided into a large number of wavebands) was used to derive simple empirical equations for calculating spectrally averaged values of two parameters- the vertical light attenuation coefficient and the chlorophyll-specific absorption of algae- for each layer as a function of its pigment content and position in the water column. The empirical equations are not dependent on the layer depths chosen, i.e. the same equations can be used for any given set of depths. The spectrally averaged parameters can be used with analytic integrals to give a compu- tationally rapid and accurate result. The model is therefore ideally suited for general circulation models. When choosing models of light penetration production in the water column by as much and photosynthesis for a given application, one as 50% or more (e.g. Sathyendranath et al. 1989; should consider the need for both accuracy and Platt and Sathyendranath 1991). The spectral computational efficiency of predictions. Some- properties of PAR must be considered to times both are required, particularly when em- achieve accuracy. Comprehensive models have bedding ecosystem models in general circula- been developed that divide PAR into a large tion models (GCMs) of the world’s oceans. number of wavebands and explicitly include The penetration of photosynthetically active the wavelength-dependent properties of vari- radiation (PAR) into seawater depends on the ous parameters which affect light attenuation nature of the light field and the absorbing prop- and photosynthesis (Morel 1988, 199 1; Sath- erties of water and substances present in it. yendranath and Platt 1988, 1989). Computa- Photosynthesis depends on the distribution of tional speed can be achieved with analytic so- algal pigments and their photosynthetic re- lutions for integrating photosynthesis over sponse to PAR. The complicated nature of depth and time. Currently available analytic these processes means that achieving a balance integrals, however, require PAR to be modeled between accuracy (achieved by introducing de- as a single entity and not split into wavebands. tail) and computational efficiency (achieved If the water column is divided into one or through simplicity) is not easy. more homogeneous layers, a spectrally aver- Both light attenuation and photosynthesis aged parameterization can be achieved by cal- are affected by the spectral properties of the culating an average value for each spectrally light field. For example, red wavelengths are dependent parameter in each layer. Platt and rapidly absorbed in the upper 10 m of the water Sathyendranath (199 1) used a spectral model column, whereas blue wavelengths penetrate (i.e. PAR divided into wavebands) to derive much deeper (Jerlov 1968). Furthermore, light the necessary average values and then used at different wavelengths is absorbed with dif- these to calculate daily water-column photo- ferent efficiencies by algae. The use of non- synthesis. They showed that one- or two-lay- spectral models of light attenuation and pho- ered models could be used with a correction tosynthesis can overestimate daily primary factor (which they suggested was small and stable) to yield satisfactory results, although their analyses were limited to water columns with uniformly distributed biomass. They also Acknowledgments showed that greater accuracy was achieved This research was supported by the Natural Environ- when several layers were modeled instead of ment Research Council and a grant from the IJ.S. DOE only one or two, because of the variation in (DE-FG02-90ER6 1053). I thank M. J. R. Fasham, A. Morel, and S. Sathyen- the spectral composition of PAR with depth. dranath for comments on the manuscript, and D. Ruiz- However, changes in the vertical distribution Pino for providing inspiration. of pigment or in the spectral properties of ir- 1403 1404 Anderson concentration and its position in the water col- Derived parameter to calculate light ab- umn. Daily photosynthesis can then be cal- sorption by algae: Eq. 13, dimension- culated by using the spectrally averaged values less in conjunction with analytic integrals. In ad- Spectrally averaged a# for layer L dition, the model is applicable to non-uniform Calculated a# just below ocean surface pigment profiles. It can be applied to any pro- for pigment concn G Chl-specific absorption of algae, m2 (mg file where the ocean is represented by one or Chl) - ’ more layers, each with a homogeneous chlo- Derived parameter: Eq. 9 rophyll content. Its application is, however, Chl-specific absorption of algae in wave- restricted to “case 1” waters, which are those band j, dimensionless in which ‘phytoplankton and their covarying Photosynthetic efficiency in white light, mg C (mg Chl) ’ h-’ (PEinst m-* products play the predominant role in deter- s ‘)-I mining optical properties, and the contribu- Maximum photosynthetic efficiency, mg tion due to other substances is small (Morel C (mg Chl)- i h ’ (PEinst m-2 s-l)-’ and Prieur 1977). Most oceanic waters are Chl biomass, mg m -3 Parameter for light attenuation due to case I. algal pigments, waveband j, m2 mg-’ A user-friendly listing of the FORTRAN Daylength, h code for the model is available on request. Quantum yield, mg C PEinst ’ Pigment biomass, mg m 3 Background Parameter for attenuation due to algal pigments, wavcband j Perhaps the most frequently used equation Downwelling PAR just below ocean sur- for the attenuation of PAR in ecosystem mod- face and at depth z, PEinst m-2 s-’ els is (e.g. Steele and Frost 1977; Hofmann and Scalar PAR, PEinst m-2 s ’ Ambler 1988; Fasham et al. 1990) Spectrally averaged k,,, for layer L, m- ’ Vertical attenuation coefficient, m -’ I, = I,exp( - kparz). (1) Diffuse attenuation coefficient for water of waveband j, m ’ I, is total PAR at depth z, I0 is the PAR just Daily depth-integrated photosynthesis, beneath the ocean surface, and k,,, is the ver- mgCm-2d ’ tical attenuation coefficient. (A list of notation Assimilation number, mg C (mg Chl)-’ h ’ is provided.) The value of k,,, is influenced by Total irradiance penetrating ocean sur- the different components of the optical system face, Einst m 2 d- ’ (water itself, phytoplankton, other substances). Depth of base of layer i, m A single exponential may be a poor approxi- Fraction downwclling PAR just below ocean surface and at depth z in wave- mation to the true irradiance distribution be- band j cause red wavelengths are rapidly absorbed in Fraction scalar PAR just below ocean the uppermost 10 m of the ocean, whereas blue surface in waveband j wavelengths are absorbed more slowly. An im- Polynomial coefficients for calculating proved prediction can be made with a double daily photosynthesis exponential (Paulson and Simpson 1977; Carr 1986): radiance impinging on the ocean surface cause I, = Io[R exp( - kaz) + (1 - R)exp( - kbz)]. the values of spectrally averaged parameters to change. To determine the new values in a (2) multilayered system, Platt and Sathyendran- k, and kb are attenuation coefficients, and the ath had to rerun their spectral model. constant R is determined empirically for var- The model described here extends Platt and ious water types. A similar arctangent approx- Sathyendranath’s approach. The novel aspect imation has been developed by Zaneveld and of the work is that simple empirical equations Spinrad ( 19 SO). Only rarely have such for- are derived for calculating spectrally averaged mulations for irradiance been used in phyto- values for two parameters-the vertical light plankton models (e.g. Fasham et al. 1983; Tay- attenuation coefficient and the chlorophyll- lor et al. 199 1). Different models of light specific absorption of algae-for any given lay- attenuation were compared by Simpson and er solely as a function of the layer’s chlorophyll Dickey (198 1), who concluded that the most Spectrally averaged model 1405 accurate method was to divide PAR into a Cullen (1990) has recast traditional P-I large number of spectral wavebands, each of curves such as Eq. 4 in terms of more physi- which is then independently attenuated. A good ologically based parameters, allowing spectral example is the model of Morel (1988), where influences on photosynthesis to be addressed. the photosynthetic spectrum is split into 61 The maximum photosynthetic rate, PB,, is wavebands. For a uniform pigment profile, generally considered to be independent of Morel’s model is wavelength (Pickett and Myers 1966). Param- eter aB can be recast as the following product (Platt and Jassby 1976; Platt 1986): I, = IO 5 ti,jexp[--(k,j + ~~Gu)z]. (3) j=l a”@> = 4,a,(O (6) G is pigment biomass (chlorophyll + pheo- a”(X) describes the spectral dependency of aB, phytin), kw,j is the diffuse attenuation coeffi- $A is the quantum yield, and a,(X) is the chlo- cient for water in waveband j, xj and rj are rophyll absorption cross-section. The assump- parameters that describe light attenuation by tion of a spectrally invariant quantum yield is phytoplankton pigments, and the wavelength reasonable when defined on a per photon basis, corresponding to band j (X, nm) is 395 + 5j. except at the extreme blue end of the PAR The coefficients o,,~ determine the fraction of spectrum (Lewis et al. 1985). The absorption total downwelling PAR just below the ocean spectrum, and hence the photosynthetic action surface in each of 6 1 wavebands and vary with spectrum, is markedly wavelength-dependent time of year, location, and atmospheric con- (e.g. Morel 199 1). Parameter a,(X) can be use- ditions. fully normalized to the maximum value of a,(X) The relationship between photosynthesis, observed in the PAR spectrum (e.g. Morel irradiance, and chlorophyll is commonly de- 199 1), after which the spectral dependence of scribed with photosynthesis-irradiance (P-I) aB is simply curves. If light extinction is described by a a*(h) a”(X) = aBmax (7) single light extinction coefficient (Eq. 1), then various P-I curves can be depth integrated (e.g. where anmax the maximum photosynthetic ef- is Platt et al. 1977). Recently, Platt et al. (1990) ficiency and a*@) the dimensionless chloro- derived a particularly useful algorithm that in- phyll absorption cross-section. tegrates photosynthesis with respect to both The light attenuation model developed here depth and time, assuming a sinusoidal pattern treats irradiance as a downwelling flux. When of irradiance over a day. The P-I curve on using a*(A) values, however, irradiance must which this integral is based is (Platt et al. 1980) be specified as a 2calar flux (Morel 199 1). Sca- lar irradiance, I(X), can be calculated from PB = P”,[l - exp( - ~r~l/P~,]. (4) downwelling irradiance as (Morel 199 1) PB is biomass-normalized photosynthesis, B is chlorophyll biomass, I is PAR, PB, is assim- f(A) = I($$. ilation number, and aB is the initial slope of the P-I curve. Moreover, Platt et al. (1990) k&X) is the downwelling attenuation coeffi- closely approximated their integral solution cient (which can be calculated from Eq. 3), and with a simple fifth-order polynomial, so depth- a(A) is (Morel, 199 1) integrated daily photosynthesis Pd is + a(X) = [a,+,(X) 0.06AChl(X)G0.65][l + 0.2v(X)] Pd = BDPB,,J(?rk,&i-&(I*)x. (9) (5) x=1 with I* is defined as ctBI,JPB,, D is daylength, Is is y(X) = exp[-0.014(X - 440)]. (10) noon irradiance just below the ocean surface, Prieur and Sathyendranath (198 1) tabulate and Q, are polynomial coefficients. Currently, values for parameters a,(A) and AC&). analytic depth integrals of photosynthesis with In the model developed here, all photosyn- formulations for light attenuation more com- thetic parameters require irradiance to be spec- plex than Eq. 1 are not available. ified as a scalar flux. If PAR is assumed to 1406 Anderson Note that a”(X) is influenced by G because of pigment 1.o its influence on k,,,(X). - (mg m-3 1 10.0 Model descriplion profile number The modeling approach adopted here in- 3 45 6 depth cm> volves deriving simple equations for calculat- - ing average values for the spectrally dependent 10 parameters k,,, and a# for any given layer in a layered vertical pigment profile. This param- 23 40 eterization then permits daily photosynthesis to be rapidly calculated with analytic integrals 61 such as Eq. 5. To derive equations for these parameters, it is necessary to determine the true spectral dis- tribution of PAR as a function of depth and chlorophyll distribution. The spectral model 123 of Morel (1988) was run to provide the best estimate of this. For a water column that is divided into a number of homogeneous ver- tical layers, this model is 200 ‘i - (kw,j+ XjGi’J) i=l Fig. 1. Six pigment profiles used to test the model (based on the GCM ofsarmiento et al. 1993). ’ (Uj- Ui-1) 1 encompass wavelengths between 400 and 700 x ew[-(kw,j + x~G,‘J)(z- ur-,>I nm (e.g. Morel 1991), Eq. 4 can be recast as r > 1, u. = 0. (14) PB = PB, -cxB,,,/PBm z is in the rth layer, and Gi and Ui denote the pigment biomass and depth of the base of layer )1 700 X a*(X)i(A) dX . i. Equation 3 can simply be applied for r = 1. s x=400 - Using this model ignores upward irradiance (11) due to backscattering. This irradiance is typ- Light attenuation is, however, modeled as a ically 0.3-3% of downward irradiance (Paul- downwelling flux. Equation 11 was converted son and Simpson 1977) and therefore can for this purpose as follows: probably be safely neglected. Values must be assigned to parameters as,j (the fraction of IO in each spectral band) before Eq. 14 can be PB = PB, -cY~,,,/P~,~ used. An unchanging spectral distribution just below the ocean surface was assumed (i.e. pa- 700 rameters w,y,jare constant), thereby allowing a a”(X)I(A) dX . (12) X general empirical model to be derived. This s x=400 distribution was obtained by running Gregg and Carder’s (1990) atmospheric model for a”(X) is a new parameter: maritime atmospheres. The synthesis of the model involved three a”(X) = a*(X) - ‘k,AV main stages: definition of the spectral distri- a@) . bution of irradiance just below the ocean sur- Spectrally averaged model 1407 face, derivation of equations for calculating an Table 1. Values of atmospheric paramctcrs. average k,,, for a layer as a function of its Prccipitable water, 2 cm position in the water column and its pigment Ozone, 0.35 cm content, and the derivation of equations for Visibility, 23 km calculating an average a” for a layer as for k,,,. Windspccd (instantaneous), 4 m s ’ The success of the new model in predicting Mean windspced (over 24-h period), 4 m s-’ daily photosynthesis was assessed for the six Relative humidity, 80% Air mass type, 1 hypothetical pigment profiles shown in Fig. 1. Atmospheric pressure, 1,000 mb The layer depths of these profiles are based on the North Atlantic GCM used by Sarmiento et al. (1993). The wide range of pigment dis- tributions encompassed by these profiles pro- 180, the fractions of quantum irradiance at vides a good test of the model. different wavelengths for zenith angles of 0” Spectral distribution below ocean surface- and 80”, as predicted by the model, are shown Running Morel’s ( 198 8) light extinction model in Fig. 2. The two distributions are remarkably (Eq. 3) requires that 61 values be assigned to similar. Because the spectral distribution of parameters o,,~, which define the spectral dis- irradiance was predicted to be relatively in- tribution (quantum units) of downwelling ir- sensitive to zenith angle, a midrange zenith radiance just below the ocean surface. It was angle of 45” was set to generate the spectral assumed that this spectral distribution does distribution just below the ocean surface in not change over time, in order to derive a gen- bandwidths of 1 nm, using Gregg and Carder’s eral empirical model. Baker and Frouin (1987) (1990) model. Parameters o,,~ were then cal- showed that the spectral distribution imme- culated by averaging across 5-nm wavebands. diately above the ocean surface varied little for Parameters o,, 1 and a,.61 were weighted by 0.5 a range of atmospheric and geometrical (sun because they are on the edge of the 400-700- geometry) conditions. Solar zenith angle has, nm spectrum (which actually divides into sixty however, been thought to significantly affect 5-nm intervals); the resulting values are listed transport across the air-sea interface (e.g. Mo- in Table 2. rel 199 1). The spectral solar irradiance model Derivation of k,,,- Having generated the of Gregg and Carder (1990) was implemented spectral distribution just below the ocean sur- to generate a spectral distribution just below face, my next step was to determine how ir- the ocean surface. Values of atmospheric pa- radiance is attenuated as a function of depth rameters were set mostly to those used by Mo- and the vertical pigment profile. If the water rel (199 1) and are listed in Table 1. With these column is divided into a number of layers, inputs and a day number (from 1 January) of each with a separate value of spectrally aver- 1 0.0053 13 0.0157 25 0.0164 37 0.0186 49 0.0190 2 0.0103 14 0.0156 26 0.0172 38 0.0186 50 0.0189 3 0.0108 15 0.0158 27 0.0178 39 0.0169 51 0.0183 4 0.0113 16 0.0163 28 0.0177 40 0.0178 52 0.0173 5 0.0014 17 0.0169 29 0.0174 41 0.0181 53 0.0182 6 0.0014 18 0.0156 30 0.0180 42 Cl.0187 54 0.0194 7 0.0107 19 0.0161 31 0.0180 43 0.0187 55 0.0191 8 0.0126 20 0.0169 32 0.0181 44 0.0186 56 0.0189 9 0.0127 21 0.0164 33 0.0179 45 0.0191 57 0.0188 10 0.0140 22 0.0170 34 0.0182 46 0.0188 58 0.0180 11 0.0154 23 0.0171 35 0.0180 47 0.0187 59 0.0164 12 0.0154 24 0.0163 36 0.0185 48 0.0190 60 0.0170 61 0.0089 1408 Anderson E s -50 ‘2 -0O” 3 .......... . 80” ai 0.001 1 I I I I jmIoo~l . , , . . , .~ 400 500 600 700 a 0.01 0.1 I 0 h b-0 e PAR (as fraction of surface) Fig. 2. Predicted spectral distribution of PAR just be- Fig. 3. Percentagedifference from the full spectral model low the ocean surface for zenith angles of 0” and 80”. of the irradiance profiles generated with the spectrally av- eraged model, with zero pigment, for n = 1, 2, 3, 4. aged kpar, then PAR at depth z is gression package (SAS 1990: procedure NLIN) r-l was used for this purpose. Resulting parameter L z [-ki(Ui - Ui- I)] values are shown in Table 3, and the relative i=l errors (the difference between resulting irra- x exP[-k(z - ur- 111 diance profiles and those generated from Mo- rel’s spectral model) are shown in Fig. 3. A r > 1, u. = 0. (15) vast improvement in accuracy was made when z is the rth layer and ki is the k,,, value for the two layers were used rather than only a single ith layer. For r = 1, Eq. 1 can be applied instead layer, with further gains for three and four lay- ofEq. 15. ers. A value of n = 3 was chosen as providing Consider the case where pigment is zero, and an acceptable level of accuracy balanced against so parameters ki are influenced solely by the the need to minimize the number of layers (in attenuation due to water itself. If the water order to minimize overall amounts of com- column (O-200 m) is divided into n layers, then putation). For convenience, the model was re- the question arises: how large should n be to parameterized for n = 3, but setting ul = 5.0 accurately simulate light attenuation with Eq. m and u2 = 23.0 m; the resulting ki values are 15? The true irradiance distribution for a zero also listed in Table 3. The predictive error for pigment profile was estimated by running Mo- these settings was only very slightly greater rel’s spectral model (Eq. 14). Then, least- than that shown for n = 3 in Fig. 3. squares best-fit values for parameters in Eq. Next, the effect of the vertical pigment pro- 15 (ki and Ui) were found for n = 1, 2, 3, 4 by file on light attenuation must be added to the fitting against the best estimate of the true dis- model. This addition is problematical, in that tribution for depths between 0 and 180.8 m the rate of light extinction at any depth z de- (the predicted 1% light level for zero pigment) pends not only on the pigment concentration with data points every 0.1 m. A nonlinear re- at that depth, but also to some extent on the Table 3. Fitted k, (m I) and u, (m) values for n = 1,2,3,4 and for n = 3 with U, and uZ set at 5.0 and 23.0 m rcspcctively. n k, k, k, k4 UI U2 % 1 0.06029 - - - - - 2 0.11833 0.02589 - - 7.64 - - 3 0.13553 0.04339 0.02236 - 4.60 22.28 - 4 0.14629 0.06736 0.03186 0.02093 3.08 10.15 35.84 3 0.13117 0.04 177 0.02233 - 5.00 23.00 Spectrally averaged model 1409 0 2 4 6 8 10 0 2 4 6 8 10 pigment in thin layer at 10 m (mg m-3) pigment in thin layer at 50 m (mg mD3) Fig. 4. Effect of pigment at depth z (in a very thin layer), and above depth z, on -dlogl/dz - - at depth z for two depths, predicted with the full spectral model. pigment profile above it (which influences the obtain ki values for each of the three layers for spectral properties of the light field). The rel- different pigment concentrations. A range of ative importance of these two factors, for O-15 mg m-3 was considered, with a square depths of 10 and 50 m, is shown in Fig. 4, root transformation to ensure a bias toward which was generated by applying Eq. 14. Here, smaller values which are more frequently en- -dlogZ/dz (k,,,) is plotted for various pigment countered in nature. Pigment was assumed to concentrations in a very thin (0.2 pm) layer at be uniformly distributed in the water column. depths of 10 (Fig. 4a) and 50 m (Fig. 4b) and Parameters kl, k2, and k3 were determined with also as a function of the pigment concentration least-squares fits (the same procedure as for (uniform distribution) from the surface to the zero pigment described above); the depth of thin layer. At both depths, - dlog1/dz was much the bottom layer used for fitting was either more strongly influenced by the pigment at 180.8 m (the 1% light level for zero pigment) depth z rather than the pigment profile above or the depth at which the 0.00 1% light level it, except when there was a very large concen- was reached if this was < 180.8 m. The re- ’ tration at depth z with a low pigment above. sulting fitted ki values are plotted against pig- This finding provides the foundation for a ma- ment concentration for each of the three layers jor simplifying assumption of the model: that (Fig. 5). The much higher values for the top k,,, at a given depth can be treated as inde- layer are caused by the rapid attenuation of pendent of pigment above that depth and is red light near the surface. Fifth-order poly- then a function of depth itself and pigment at nomials were fitted for each layer relating ki to that depth. It then follows that an average k,,, the square root of pigment concentration in can. be derived for any given layer, ki, which that layer. With uI = 5.0 m and u2 = 23.0 m, is influenced only by the position and chlo- k, , k2, and k3 are then rophyll content of the layer and not by the pigment profile above. ki = bo,i + bl,ic + b2,iC2 Having derived parameters u1 = 5.0 m, u2 + + b3,iC3+ bd,iC4 bs,iC5 (16) = 23.0 m, these were then fixed. Admittedly, where c = G1j2, mg m-3. Values for the coef- the optimum depths for these partitions will ficients are listed in Table 4. change for different pigment profiles, but the A three-layer model of light attenuation is need for a generalized model forces them to now complete: Eq. 15 and 16. It can be applied remain constant. If we accept the three-layer to any vertical profile with a given number of model as derived above, it is now possible to layers, each with a homogeneous pigment con- 1410 Anderson k Par 0.3 (m-9 0.2 0 1 4 9 16 pigment (mg m-3) PAR (as fraction of surface) Fig. 5. Fitted k,, values for 12= 3 for pigment con- Fig. 6. Percentagedifference from the full spectral model centrations between 0 and 15 mg m-3. Lines are fifth-order of irradiance predictions of the spectrally averaged model polynomial fits (Table 4). for the six pigment profiles of Fig. 1. tent. It is necessary to subdivide those layers w,,~ is the fraction of total downwelling irra- in the profile which encompass depths 5.0 and diance in waveband j at depth z (calculated 23.0 m unless model layers exactly match these from Eq. 14), and the remaining parameters depths. Consider the profiles shown in Fig. 1. correspond to those in Eq. 13 for waveband j. The uppermost layer of O-10 m must be sub- The a*, spectrum was that of Morel (199 1). divided into two layers of O-5 and 5-l 0 m. By Profiles of a#=for the six vertical pigment pro- pure coincidence, the depth of the second layer files of Fig. 1 are shown in Fig. 7. It is clear is 23 m, and so no subdivision of layers be- that a#=depends not only on the pigment con- neath the top layer is required. The three main centration at depth z, but also the pigment in layers dictated by u1 and u2 can be subdivided the water column above (e.g. profiles 2 and 3 further, in which case Eq. 16 is then applied both have a pigment concentration of 1.O mg separately to each sublayer. The percentage er- m-3 at 23 m, but have very different values for ror incurred by the new model when predicting a#=at that depth). The rate of change of a# with light attenuation for the six profiles shown in z, daVdz, depends on pigment concentration Fig. 1, as compared to that predicted with Mo- at depth z, on depth z itself, and on the pigment rel’s spectral model, is shown in Fig. 6. This profile above. It is also apparent that there are error was consistently small (< 10%) down to sudden changes in a#= which are caused by the 10% light level and < 20% down to the 1% changes in pigment concentration. For uni- light level. Errors do increase if even smaller form pigment profiles, the relative impor- light levels are investigated, but such increases tances of the pigment at depth z and the profile are relatively unimportant when calculating above are shown for two depths, 10 and 50 m, overall depth-integrated photosynthesis. in Fig. 8 (generated as for Fig. 4). At 10 m, Derivation of a# - A spectrally averaged val- pigment at depth z generally had a much larger ue of a# can be calculated at any depth based effect on da#ldz than pigment above (Fig. on the spectral distribution of light and the 8a), although the effect is less simple at 50 m pigment concentration (which affects k,,,) at (Fig. 8b). In the model it is assumed that daV that depth: dz is independent of the pigment profile above depth z. 61 m,,ja*jkpar,j Equations 14 and 17 were used to calculate a% = 2 a. - (17) j=l J da#/dz for pigment concentrations between 0 Table 4. Polynomial coefficients relating k, to square root of pigment in layer i: Eq. 16. i b,, , b,, b,, b 3, b 48 b 5.1 1 0.13096 0.030969 0.042644 -0.013738 0.00246 17 -0.00018059 2 0.04 1025 0.0362 11 0.062297 -0.030098 0.0062597 -0.0005 1944 3 0.021517 0.050 150 0.058900 -0.040539 0.0087586 -0.00049476 Spectrally averaged model 1411 Table 5. Coefficients g,-g,, for predicting da#ldz as a function of pigment and depth: Eq. 18. 1.0 g, = 0.048014 g, = 0.0027974 0.8 g, = 0.00023779 g, = 0.00085217 a# g3 = -0.023074 g* = -0.0000039804 0.6 g, = 0.0031095 g, = 0.0012398 g, = -0.0090545 g,, = -0.00061991 0.4 0.2 variations with depth (which cause the quo- tient k,,,la to change) are simulated by apply- o! 0 20 40 60 80 100 ing an offset to a# when crossing between mod- depth (m) el layers. The equivalent offset at the ocean Fig. 7. Depth dependence of a# for the six pigment surface was calculated for the pigment con- profiles of Fig. 1 calculated with the full spectral model. centrations of the two layers, and it was used. In reality this offset is depth-dependent, but and 15 mg m-3 (square-root bias) assuming the approach adopted here is a useful generic uniform pigment profiles and depths between approximation. 0 and 200 m (log bias). Results are shown in An average value of a# for any given model Fig. 9a. A quadratic equation was fitted to these layer L, a#L, can now be calculated by inte- data to describe da#/dz as a function of the grating Eq. 18 with respect to z through the square root of pigment concentration (c = G1j2) layer and dividing by two to give a value for and the natural logarithm of depth [v = log(z the layer midpoint (term 3 in Eq. 19), adding + l), m]: it to a# at the base of the layer above (terms 1 and 2), and then adding the offset (terms 4 and da#/dz(c,v) = g, + g,c + g,v + g,cv 5). + g,c2 + g,v2 + g,c3 1 UI.-1 + g,v3 + ggc2v + g10cv2. W-9 a#,, = asL-, + - daVdz(c, v) dz 2 s UI.-2 g,-g,, are the fitted coefficients; their values are listed in Table 5. Predicted values of da#/ 1 UL daVdz( c, v) dz dz for the same range of pigment concentra- + 2 s UL-, tions and depths are shown in Fig. 9b; com- parison with Fig. 9a shows a reasonable agree- + CGL - a#.,, ,--, ment. Sudden changes in a#= caused by pigment G, a#3, = a%+ a% = a#.,., (19) a) 0 2 4 6 8 10 0 2 4 6 8 10 pigment in thin layer at 10 m (mg m-3) pigment in thin layer at 50 m (mg m-3) Fig. 8. As Fig. 4, but on da#/dz. 1412 Anderson a> b> 10 100 200 10 100 200 depth (ml depth (ml Fig. 9. Dependence of da#ldz on depth and pigment concentration predicted with the full spectral model (a) and according to the fitted function (b) (Eq. 18). where a#S, is a# at the ocean GI surface calcu- lated for pigment concentration GL. The first = i (z + l)(g, + g2c + &C2 + &C3) integral term in Eq. 19 is only applied for L > 1. Equation 17 was used to generate a”,, L+fi -iz+ U(g3+ g4c + g9c2) values (Fig. 10). A polynomial equation was + “6 {z + 1 lk, + ia&) fitted to these data: UI. a#,, = h, + h,c + h2c2 + h3c3 + h,C4(20) +f,-iz+ ugs where c is G lj2. Values for the fitted coefficients 1UI.I are given in Table 6. (21) The integral terms in Eq. 19 solve as UI. where da#ldz(c, v) dz f,{z+ l}=(z+ l)log(z+ l)-(z+ (22) l), s UI.-I fi{z + l} = (z + l)log2(z + 1) - 2fi {z + 1},(23) o.7i 0.6 # a s,G 0.5 0.3 0 1 4 9 16 pigment, G (mg m-3) Fig. 10. Predicted a#,y,, as a function of pigment con- depth (m) centration calculated with full spectral model. Fitted line is the polynomial fit (Eq. 20). Fig. 11. As Fig. 6, but of predicted a#. Spectrally averaged model 1413 Table 6. Coefficients ho-h, for fitting a#s,,;as a function and for simplicity a value of G = 0 was as- of surface pigment: Eq. 20. sumed, giving h, = 0.36796 h, = -0.065276 ~Bnlax = 2.602 aBw. (26) h, = 0.17537 h, = 0.013528 h, = -0.0011108 The best estimate of daily water-column photosynthesis, against which the predictions of the spectrally averaged model were com- and pared, was obtained by executing the “full spectral model”: Gregg and Carder’s (1990) f,{z + 1) = (z + l)log3(z + 1) - 3f2{z + 1}.(24) atmospheric model to provide the total irra- Equations 19-24 can now be used to calculate diance and its spectral distribution just below the value of a# for any given layer, a#L. The the ocean surface, Morel’s (198 8) spectral errors in a#=incurred when compared with the model (Eq. 14) to attenuate light, and Platt et full spectral model for the six vertical profiles al.‘s (1980) P-I curve (Eq. 4) with spectrally of Fig. 1 are shown in Fig. 11 (bear in mind dependent parameters (Eq. 12) to calculate that a#=is constant within any one layer in the photosynthesis. The result, Pf (mg C me2 d-l), new model). Profile 3 showed significant pos- is then itive errors near the surface and large negative errors below 23 m. Predictions were generally within f 10% for the other profiles, except those with deep chlorophyll maxima which had er- rors as large as -20%. Calculating photosynthesis with the model Having derived simple equations for cal- culating spectrally averaged values for param- eters k,,, and a# for each model layer, we can Iz,tj is downwelling PAR at depth z, time t, and now test their ability to accurately calculate in waveband j and a#,j is a# at depth z in wave- daily water-column photosynthesis. Equations band j (derived from Eq. 13). The integrations 4 and 5 were used to model photosynthesis. were done numerically, with a time step of 5 The two parameters which define the P-I curve min and a depth interval of 10 cm. described by Eq. 4 are PB, and aR. Nonspectral The spectrally averaged model can be used measures of aR are commonly made in white to calculate daily photosynthesis, integrating light, with irradiance measured in scalar units. analytically with respect to depth, or both depth If white light is assumed to have the same and time. In the former case, daily photosyn- spectral distribution as irradiance just beneath thesis, Pk, (the subscript refers to spectrally the ocean surface, then the photosynthetic ef- averaged k,,, and a#), is (the basic integral is ficiency in white light, aRW,is provided by Platt et al. 1990) (25) ~Blnax is the maximum photosynthetic efficien- X CY, which occurs at X = 435 nm, and ij~,j is the s 0 D 2 (-1)x x.x! + 1 x=1 fraction of surface scalar irradiance in wave- band j, which can be calculated from param- x kLax a#LIL,t, l lP”,)x eters w,g,jand Eq. 8. Consequently, from a given value of ayBW, value for cyBmnX be calcu- a can - h%ax a%,L2 /P”,)“] dt. (28) lated. However, this calculation depends on I L.&l is the total PAR entering the layer at time pigment concentration, because of its impact t, and IL,r,2is the light leaving the layer (both on kpw For an aBWof 1, calculated values of calculated from Eq. 15). Total PAR just below ~Bnlaxrange from 2.602 for G = 0 to 2.371 for the ocean surface was calculated by running G = 10. Sensitivity to G is thus relatively low, the atmospheric model of Gregg and Carder. 1414 Anderson Table 7. Summary of daily integrations. Estimate Spectral distribution k “A a* Pf Gregg and Carder model Morel model Morel model pfi Paramctcrs w,~(fixed) Morel model Morel model Pk,,, Parameters w,,, (fixed) Spectrally averaged Spectrally averaged P kod Parameters w,~(fixed Spectrally averaged Spectrally averaged pk Paramctcrs w,~,,(fixed) Spectrally averaged Morel model PO Parameters w,, (fixed) Morel model Spectrally averaged If irradiance through the day is assumed to IZ,l is calculated by means of Eq. 15, with Gregg vary sinusoidally, then water-column photo- and Carder’s model to generate total irradiance synthesis can be analytically integrated with just below the ocean surface. The same equa- respect to time as well as depth with the ap- tion is used for Pkad,with a sinusoidal variation proximation of Platt et al. (1990) (Eq. 5). Daily of irradiance about the noon value. The nu- photosynthesis as. predicted by the spectrally meric solutions for Pk, and P,&dcalculated from averaged model, Pka& is then Eq. 30 consistently differed from the equiva- lent analytic solutions (Eq. 28 and 29) by 1.5% Pkad = 2 BLDPn,l(akL) or less (usually much less). L=l The difference Pka - Ps arises from three sources: the assumption of a set spectral dis- tribution just below the ocean surface and the differences associated with the parameteriza- tion of k,,, and a#. Thus, . (29) - ((XBm,,a”LZL,,,,lPBm)Xl I L,4, and IL, 4,2are the irradiances entering and 1 “p, pf= (DSp+ Dk + D,)/lOO. (31) leaving layer L at noon. A problem arises when comparing Ps, Pka, and Pkad:the methods for integrating over depth DSp,Dk, and D, are the % differences from the and time (i.e. numeric or analytic) differ. To spectral model (normalized to Pi) associated avoid this problem when comparing the dif- with the spectral assumption and the param- ferent daily estimates, I obtained all the results eterization of k,,, and a#, respectively, nor- displayed here by applying numeric integra- malized to the best estimate. The magnitude tions for both depth and time. The daily pho- of each was estimated as follows. tosynthesis can then be predicted from the D,,: The full spectral model was run (as for spectrally averaged model as Pf), except that the set spectral distribution just below the ocean surface (parameters w,,j) was imposed. If the resulting daily photosynthesis ha=&, is PJw, then D,, is L=l D UL X SS I=0 z=u,.- [ P%[l - exP(-~Hn,axa#LL,l DS,,= 1.00 Pfw - Pf . (32) + PBn,)] dz dt. Pf (30) DIC and Da: It is possible to run the full spec- tral model with the set spectral distribution (as Table 8. Latitudes and day numbers (from 1 January) for PfJ, except that the empirical equations of used to test the model. the spectrally averaged model for kT, and a#,_ Scc- Sce- can be imposed to determine either k,,, or a# nario Day nario Lat (“) Day (both at once would give Pka). The two result- ing figures, Pk (spectrally averaged k,,, but not : 70 0 172 310 e f 50 139 355 a#) and Pa, give an estimate of the relative impact of the parameterization of k,,, and a# : 60 172 264 E 80 70 240 210 on the difference Pka - Pp Dk and Da are then Spectrally averaged model 1415 layer 1 lzsl layer 3 0 layers 5,6,7,8 l!zzi layer 2 @j El layer 4 2 1.2 2 1.0 %I ‘3 0.8 E g 0.6 \ g 0.4 % 3 0.2 Ei Q 0.0 abc~abc~abc~abc~abdabc 1 2 3 4 5 6 profile number Fig. .12. Comparison between the full spectral model and the spectrally averaged model of predicted daily photo- synthesis for scenario e (50”, day number 355) for the six pigment profiles of Fig. 1: a-P!; b--P,,; C-P,,,. Dk= 100 pk - Pk - PjL pfi + pa - pfu The assumption of a sinusoidal irradiance pat- tern through the day, used to calculate Pk&, ,- a. introduces an additional source of error, Dd (33) (normalized to Ps, % units): and P - pka Dd= 100 ICad Pr ’ Da = 100 pa- pfi A summary of the different methods for cal- Pk - Pfw+ Pa - PJu . culating daily photosynthesis is given in (34) Table 7. Table 9. Best estimates of daily water-column photosynthesis (O-200 m), Pr, for the six vertical profiles (Fig. 1) and each scenario (Table 8). Units are mg C m-2 d- *. Profile Scenario I 2 3 4 5 6 410.33 1,269.67 345.56 219.38 156.32 E 2.76 99.83 12.42 39.56 11.53 4.38 2.82 : 63.22 130.81 270.07 852.78 238.99 121.82 82.24 543.26 1,689.39 464.79 277.37 194.53 e 25.26 111.53 359.48 101.29 44.03 28.90 f 120.01 495.39 1,535.99 420.02 ’ 259.88 183.94 492.57 1,545.ll 430.65 233.47 159.92 i 116.64 64.60 284.14 913.48 257.38 113.86 74.95 1416 Anderson -40 1 O a 0 d Fig. 13. Predicted errors associated with the spectrally averaged model for the six pigment profiles of Fig. 1 and eight scenarios of Table 8 divided into their subcomponents: D,, Dk, and D,. Results ber 35 5) was selected because it represents a The model was tested for the six pigment midlatitude site and was also investigated in profiles shown in Fig. 1 and for a wide range detail by Platt and Sathyendranath (1991) in of latitudes and day numbers (scenarios a-h), their layered model of water-column photo- corresponding to those examined by Platt et synthesis. Predictions of the spectrally aver- al. (1990), and listed in Table 8. Settings for aged model are compared to those of the full photosynthetic parameters are based on me- spectral model in Fig. 12. Values of P,are tab- dian values for midlatitude phytoplankton de- ulated in Table 9. Daily water-column pho- scribed by Harrison and Platt ( 1986); they are tosynthesis, Pka, was successfully predicted to PB = 2.39 mg C (mg Chl)-’ h-l, and CY~,,, = within - 10% of the best estimate, except for O.o”l mg C (mg Chl)-’ h-l (PEinst m-2 s-‘)-~. those profiles with deep chlorophyll maxima, It was assumed that chlorophyll biomass, B, which showed slightly larger errors. Using the was 80% of total pigment biomass, G (e.g. Trees daily approximation (sine irradiance assump- et al. 1986). tion), Pk&, changed the error in predictions by A single scenario was chosen for a detailed - 10%. Not only were the daily totals predicted analysis: to investigate the suitability of each with reasonable accuracy, but the vertical dis- of the two approximations for predicting daily tribution of the photosynthesis within the production in each model layer for each of the model layers was also predicted with success. six pigment profiles. Scenario e (50°, day num- Next, Pka was calculated for all the scenarios Spectrally averaged model 1417 averaged over the Table 10. Predicted errors associated with assuming a sinusoidal irradiance pattern, Ddand Ddc, six profiles for each scenario. Scenario D,,-~95% C.I. Dd< f95% C.I. : -0.11 kO.03 9.12kO.25 0.4564 46.4 1 51.49 0.4558 - 1.25k0.64 -0.02+0.01 i 11.22kO.19 17.18k0.66 55.16 20.98 23.79 66.98 - 1.34kO.73 -2.72t- 1.39 e 10.83f0.34 6.63 7.47 -0.BO-tO.45 f 12.34k1.46 53.57 61.76 - 1.99+: 1.01 hp 26.45kO.59 28.6 120.77 17.41 42.39 55.94 23.22 -1.92k1.09 -3.02+ 1.61 (a-h). For each scenario and profile, the dif- found by Platt et al. (1990), the sinusoidal as- ference Pk, - P,was split into its components: sumption overestimates the radiation entering Dsp, Dk, and Da. When observing these, one the water column per day. This error can be must remember that summing positive and corrected for by multiplying &ad by the quo- negative values will cause an overall reduced tient Qcc/QS, where Qcc is the total irradiance difference. Results are shown in Fig. 13. Dis- penetrating the ocean surface per day (Einst regarding profiles 5 and 6, Pka was within - 7% m-2 d-l) ca1 1 d using Gregg and Carder’s CU ate (and usually much less) of Pr for all scenarios model, and Q, is that calculated from a sinu- except b. Moreover, this success was due to all soidal function, with Gregg and Carder’s mod- three components of the difference (Dsp, Dk, el to calculate noon irradiance. The new ad- and Da) being small, and not to large values ditional error caused by assuming a sinusoidal of these components of opposite sign having irradiance, DdC,is then a compensating effect. The difference due to the parameterization of a#, Da, ranged between DdC= 100 PkadQG,/Qs - pku . (36) 10 and 20% for profiles 5 and 6 but was offset Pf to some extent by Dk, which was typically 3- 4% in these profiles, and of opposite sign to Predicted values of DdC,averaged for each sce- Da. The difference associated with the spectral nario, are also shown in Table 10. Assuming distribution, Dsp, was very marked in the case a sinusoidal irradiance now causes only a very of scenario b. This scenario is a high-latitude small negative error, because the higher irra- site (70”) with a very short day (5.2 h). The diances resulting from the sinusoidal assump- resulting zenith angles for radiation ranged en- tion were being used less efficiently for pho- tirely between 85 and 90”. Although not shown tosynthesis. Platt et al. (1990) showed that a in Fig. 2, zenith angles much greater than 80” sine-square approximation was more suitable cause a significant increase in the proportion for high latitudes (the analytical solution for of irradiance in the blue wavelengths, with less such a case was also presented). in the red. Because red light is rapidly absorbed by water at the top of the water column, this means that the spectral distribution defined by Concluding remark parameters o,,~ underestimates light available A model is presented here that is an empir- to phytoplankton for scenario b and, hence, ical approximation of Morel’s (1988, 199 1) also daily photosynthesis. spectral model of light attenuation and ab- Finally, the additional error caused by ex- sorption by phytoplankton (with Gregg and ploiting the daily approximation (i.e. by as- Carder’s 1990 atmospheric model to generate suming a sinusoidal pattern of irradiance dur- light at the ocean surface), used in conjunction ing the day) was assessed (I&). Results for the with Platt et al.‘s (1980) P-I curve (Eq. 4). The six profiles were averaged for each scenario new model is designed to predict daily pho- and are shown in Table 10. Assuming a si- tosynthesis for a vertical pigment profile di- nusoidal irradiance pattern introduced a vari- vided into a number of homogeneous layers able, and sometimes large (high-latitude sites and is computationally efficient. with long days), positive error. As was also The accuracy of the new model was assessed 1418 Anderson by comparison with the output of the full spec- Nevertheless, the spectrally averaged model tral model. It was tested for several vertical is a computationally efficient tool for predict- pigment profiles and scenarios (latitudes and ing water-column photosynthesis, which takes day numbers) and predicted daily water-col- account of the spectral influences on light at- umn photosynthesis to within 15%, and usu- tenuation and photosynthesis and how these ally to within 5%, of the spectral model (except are influenced by the vertical pigment profile. for profile b). It is particularly well suited for use in GCMs, It should be remembered that the new model where accuracy and computational speed of has only successfully approximated another predictions are at a premium. model. It is necessary to speculate on the suit- ability of incorporating the new model in glob- al-scale GCMs, i.e. on the general applicability References of the full spectral model as it was imple- ATLAS, D., AND T. T. BANNISTER. 1980. Dependence of mented to generate the approximation. When mean spectral extinction coefficient of phytoplankton running the spectral model, the phytoplankton on depth, water color, and species. Limnol. Oceanogr. parameters x, y, and a* were assigned fixed 25: 157-159. values for each of the 6 1 spectral wavebands. BAKER, K. S., AND R. FROUIN. 1987. Relation between In the real ocean, phytoplankton communities photosynthetically available radiation and total in- solation at the ocean surface under clear skies. Lim- are composed of different species with different nol. Oceanogr. 32: 1370-1377. characteristics and may be physiologically BRICAUD, A., A.-L. B~DHOMME, AND A. MOREL. 1988. adapting to their particular environment. Al- Optical properties of diverse phytoplanktonic species: gal absorption spectra differ significantly be- Experimental results and theoretical interpretation. J. Plankton Res. 10: 851-873. tween different phytoplankton groups accord- CARR, M. R. 1986. Modelling the attenuation of broad ing to the kinds and amounts of accessory band light down a water column. Statistician 35: 325- pigments accompanying chlorophyll a and pig- 333. ment packaging effects (Atlas and Bannister CLEVELAND, J.S.,M.J. PERRY, D.A. KIEFER,AND M.C. 1980; Bricaud et al. 1988). Photosynthetic light TALBOT. 1989. Maximal quantum yield of photo- synthesis in the northwestern Sargasso Sea. J. Mar. utilization efficiencies by phytoplankton ex- Res. 47: 869-886. hibit a spectral plasticity that can be associated CULLEN, J. J. 1990. On models of growth and photo- with changes in community structure and pho- synthesis in phytoplankton. Deep-Sea Res. 37: 667- tophysiology (Schofield et al. 199 1). Further 683. FASHAM, M. J. R., H. W. DUCKLOW, AND S. M. MCKELVIE. experimental evidence and modeling is re- 1990. A nitrogen-based model of plankton dynamics quired to assess the impact of this variation in the oceanic mixed layer. J. Mar. Res. 48: 59 l-639. on estimates of daily photosynthesis. Non- -, P. M. HOLLIGAN, AND P. R. PUGH. 1983. The spectral effects on phytoplankton parameters spatial and temporal development of the spring phy- toplankton bloom in the Celtic Sea, April 1979. Prog. can easily be incorporated in the model. For Oceanogr. 12: 87-145. example, Cleveland et al. (1989) suggested that GREGG, W. W., AND K. L. CARDER. 1990. A simple maximum quantum efficiency is proportional spectral solar irradiance model for cloudless maritime to the availability of inorganic nitrogen. Such atmospheres. Limnol. Oceanogr. 35: 1657-1675. an effect could be introduced by making aBw a HARRISON, W. G., AND T. PLATT. 1986. Photosynthesis- irradiance relationships in polar and temperate phy- function of nitrogen availability. The assump- toplankton populations. Polar Biol. 5: 153-l 64. tion of a fixed quantum yield throughout the HOFMANN, E. E., AND J. W. AMBLER. 1988. Plankton PAR range requires further validation. In ad- dynamics on the outer southeastern U.S. continental dition, the phytoplankton absorption spec- shelf. Part 2. A time-dependent biological model. J. Mar. Res. 46: 883-917. trum used in the model is based on laboratory JERLOV, N. G. 1968. Optical oceanography. Elsevier. cultures, whereas light attenuation is based on LEWIS, M. R., R. E. WARNOCK, AND T. PLATT. 1985. empirical relationships derived from in situ Absorption and photosynthetic action spectra for nat- observations. Future modeling work could ural phytoplankton populations: Implications for pro- perhaps involve using the same phytoplankton duction in the open ocean. Limnol. Oceanogr. 30: 794-806. absorption spectra to compute both light at- MOREL, A. 1988. Optical modelling of the upper ocean tenuation in the water and light absorbed by in relation to its biogenous matter content (case 1 phytoplankton. waters). J. Geophys. Res. 93: 10,749-10,768. Spectrally averaged model 1419 -. 199 1. Light and marine photosynthesis: A spec- SAS. 1990. SAS/STAT user’s guide, version 6, 4th ed. tral model with geochemical and climatological im- SAS Inst. plicatiohs. Prog. Oceanogr. 26: 263-306. SATHYENDRANATH, S., AND T. PLATT. 1988. The spectral - AND L. PRIEUR. 1977. Analysis of variations in irradiance field at the surface and in the interior of ockan color. Limnol. Oceanogr. 22: 709-722. the ocean: A model for applications in oceanography PAULSON, C. A., AND J. J. SIMPSON. 1977. Irradiance and remote sensing. J. Geophys. Res. 93: 9270-9280. measurements in the upper ocean. J. Phys. Oceanogr. -, AND -. 1989. Computation of aquatic pri- 7: 952-956. mary production: Extended formalism to include ef- PICKETT, J. M., AND J. MYERS. 1966. Monochromatic fect of angular and spectral distribution of light. Lim- light saturation curves for photosynthesis in Chlorel- nol. Oceanogr. 34: 188-198. la. Plant Physiol. 41: 90-98. - -, C. M. CAVERHILL, R. E. WARNOCK, AND PLATT, T. 1986. Primary production of the ocean water MI R. LEWIS. 1989. Remote sensing of oceanic pri- column as a function of surface light intensity algo- mary production: Computations using a spectral rithms for remote sensing. Deep-Sea Res. 33: 149- model. Deep-Sea Res. 36: 43 1453. 163. SCHOFIELD, O., AND OTHERS. 199 1. Variability in spectral -, K. L. DENMAN, AND A. D. JASSBY. 1977. Mod- and nonspectral measurements of photosynthetic light elling the productivity of phytoplankton, p. 807-856. utilisation efficiencies. Mar. Ecol. Prog. Ser. 78: 253- Zn E. D. Goldberg et al. [eds.], The sea. V. 6. Wiley. 271. -, C. L. GALLEGOS, AND W. G. HARRISON. 1980. SIMPSON, J. J., AND T. D. DICKEY. 198 1. Alternative Photoinhibition of photosynthesis in natural assem- parameterisations of downward irradiance and their blages of marine phytoplankton. J. Mar. Res. 38: 687- dynamical significance. J. Phys. Oceanogr. 11: 876- 701. 882. -, AND A. D. JASSBY. 1976. The relationship be- STEELE,J. H., AND B. W. FROST. 1977. The structure of tween photosynthesis and light for natural assem- plankton communities. Phil. Trans. R. Sot. Lond. Ser. blages of coastal marine phytoplankton. J. Phycol. 12: B 280: 485-534. 42 l-430. TAYLOR, A. H., A. J. WATSON, M. AINSWORTH, J. E. - AND S. SATHYENDRANATH. 199 1. Biological pro- ROBERTSON,AND D. R. TURNER. 199 1. A modelling duction models as elements of coupled, atmosphere- investigation of the role of phytoplankton in the bal- ocean models for climate research. J. Geophys. Res. ance of carbon at the surface of the North Atlantic. 96: 2585-2592. Global Biogeochem. Cycles 5: 15 1-l 7 1. - -- AND P. RAVINDRAN. 1990. Primary pro- TREES, C. C., R. R. BIDIGARE, AND J. M. BROOKS. 1986. d&ion biphytoplankton: Analytic solutions for dai- Distribution of chlorophylls and pheopigments in the ly rates per unit. area of water surface. Proc. R. Sot. northwestern Atlantic Ocean. J. Plankton Res. 8: 447- Lond. Ser. B 241: 101-l 11. 458. PRIEUR, L., AND S. SATHYENDRANATH. 198 1. An optical ZANEVELD, J. R. V., AND R. W. SPINRAD. 1980. An arc classification of coastal and oceanic waters based on tangent model of irradiance in the sea. J. Geophys. the specific spectral absorption curves of phytoplank- Res. 85: 49 19-4922. ton pigments, dissolved organic matter, and other particulate materials. Limnol. Oceanogr. 26: 67 l-689. SARMIENTO, J. L., AND OTHERS. 1993. A seasonal three- dimensional model of nitrogen cycling in the North Submitted: 10 November 1992 Atlantic euphotic zone. Global Biogeochem. Cycles Accepted: 27 April 1993 7: In press. Revised: 18 May I993

DOCUMENT INFO

Shared By:

Categories:

Tags:

Stats:

views: | 7 |

posted: | 9/1/2012 |

language: | Unknown |

pages: | 17 |

OTHER DOCS BY cuiliqing

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.