# Extraction of Photosynthesis Parameters from Time Series Measurements of In Situ Production: Bermuda Atlantic Time-Series Study

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## Abstract

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## 1. Introduction

^{14}C method in 1952 by Steemann Nielsen [1]. Shortly afterwards followed the quantification of primary production by means of mathematical models based on the first principles of phytoplankton physiology [2,3]. Decades later, we find ourselves with global scale maps of phytoplankton production represented by daily carbon uptake at our disposal [4,5,6,7]. Such maps are made possible by combining satellite measurements of chlorophyll concentration with primary production models forced by photosynthetically-available surface radiation [8,9]. Complementary estimates based on satellite phytoplankton carbon and growth rates have also been developed [10]. At their core, chlorophyll-based models are founded on knowledge of the photosynthesis–light relationship, which enables the calculation of primary production.

^{14}C enriched phytoplankton samples at a set of light intensities and thereby constructing a photosynthetic response curve [11]. The photosynthesis irradiance function is used to represent the results of these experiments and to describe the photosynthetic response to changes in available light [12,13]. This is accomplished by the non-linear fitting of a prescribed photosynthesis irradiance function to the measurements. The information extracted from the procedure establishes the physiological parameters, which determine the optimum choice of photosynthesis irradiance function from amongst the infinite family of possible functions. These are termed photosynthesis parameters [14,15].

^{14}C enriched samples in incubation bottles suspended along a line at predefined depths during the incubation period [17,18]. In this case, the measurements correspond to production integrated in time over the period of incubation, and under natural, variable, irradiance conditions. The standard incubation time is the daylength, and the standard total depth interval is the photic zone [14]. The photosynthesis parameters can be extracted from the measured production profile in a similar fashion to that from incubations under controlled light conditions [19]. The former approach, in which the parameters are extracted from experiments under controlled light conditions, was introduced some decades ago, whereas the latter one was introduced more recently [16].

## 2. Materials and Methods

#### 2.1. Model of the Production Profile

^{−3}h

^{−1}), is expressed as a rate in carbon units [14,17]. As a measure of phytoplankton biomass throughout this paper, hereafter denoted B, we employed the chlorophyll concentration (mg Chl m

^{−3}), which is the appropriate measure of biomass for chlorophyll-based models. The chlorophyll molecule couples light with the photosynthetic unit; it is ubiquitous in all phytoplankton taxa and is easily measurable, making it a useful operational index of phytoplankton biomass [34]. As a measure of available light, we took the downward irradiance integrated over the visible portion (400–700 nm) of the spectrum, I (W m

^{−2}), which is the photosynthetically-active radiation (PAR), easily measured at sea by optical profilers, and can also be modelled relatively easily by knowing just the surface light field and the optical properties of the water column [35,36]. Once B and I are known, what remains to model primary production is the relationship between P and I, i.e., the photosynthesis light function.

^{−1}(W m

^{−2}) h

^{−1}), and the assimilation number, ${P}_{m}^{B}$ (mg C (mg Chl)

^{−1}h

^{−1}) [15,37,38]. With this relationship at hand we proceeded to modeling the instantaneous production at depth, $P(z)$. For this we needed knowledge of the underwater light field and we employed a simple model:

#### 2.2. Bermuda Atlantic Time-Series Study Data Set

^{−2}using Smith and Morel’s procedure [42]. Out of the 151 cruises, the first full set of measurements we used was from 13 February, 1992 and the last was from 20 May, 2012. The sampling depths for the cruises were 0, 20, 40, 60, 80, 100, 120 and 140 m, for both chlorophyll and primary production. Optical profiles were sampled continuously. Surface PAR was measured with a 2 s interval over the course of daytime for the 87 mentioned cruises. The chlorophyll and primary production data are available at http://batsftp.bios.edu/BATS/bottle/, and the optical data are available at ftp://ftp.eri.ucsb.edu/pub/org/oceancolor/BBOP/. Information on the method used to measure chlorophyll concentration can be found at bats.bios.edu/methods/chapter14.pdf, and information on the method for primary production can be found at bats.bios.edu/methods/chapter18.pdf. Detailed information on the profiling spectroradiometers used to measure vertical optical profiles can be found in Allen et al. [43] in the Material and Methods section, along with other references therein. A thorough review of the BATS measurements was provided by Lomas et al. [44].

## 3. Results

#### 3.1. Determining the Attenuation Coefficient

#### 3.2. Photosynthesis Parameters Extraction

^{−1}h

^{−1}. The mean of the initial slope was 0.3, the median was 0.26 and the standard deviation was 0.27, all expressed in mg C (mg Chl)

^{−1}(W m

^{−2}) h

^{−1}distribution spread mainly from 0.1 to 0.5 mg C (mg Chl)

^{−1}(W m

^{−2}) h

^{−1}, with a peak around 0.2 mg C (mg Chl)

^{−1}(W m

^{−2}) h

^{−1}, and only a small number of parameter values fell outside these limits. The ${P}_{m}^{B}$ distribution ranged mainly from 2 to 15 mg C (mg Chl)

^{−1}(W m

^{−2}) h

^{−1}, with a peak at 5 mg C (mg Chl)

^{−1}h

^{−1}and few values outside this range. As there were more ${P}_{m}^{B}$ values estimated, the distribution of ${P}_{m}^{B}$ is more reliable than the distribution of ${\alpha}^{B}$. With time, as more measurements become available it is expected that these distributions will show a more coherent structure.

#### 3.3. Estimation of Watercolumn Production

^{−3}, with a standard deviation of 0.032 mg Chl m

^{−3}. The mean depth of the deep biomass maximum, ${z}_{m}$, was 99 $\mathrm{m}$, with a standard deviation of 21 $\mathrm{m}$. The mean width of the biomass peak $\sigma $ was 22 m, with a standard deviation of 12.5 m and finally, the mean height of the biomass peak, H, was 0.377 mg Chl m

^{−3}, with a standard deviation of 0.265 mg Chl m

^{−3}.

#### 3.4. Estimation of Growth Rates

^{−1}. For each cruise, we calculated ${\mu}_{m}$, and the results are given in Figure 5, expressed as per day growth rate, by multiplying the hourly rate from Equation (12) by the daylength, D. In fact, using this method, we determined the maximum daily growth rate. The distribution of the maximum daily growth rate was skewed to the right. The mean value was 0.7 d

^{−1}, the median was 0.62 d

^{−1}and the standard deviation was 0.39 d

^{−1}. The minimum value was 0.13 d

^{−1}and the maximum was 1.67 d

^{−1}. For 118 profiles, the maximum daily growth rate was below one per day, and for 33 profiles, it was above one per day.

^{−1}with $\chi $ in the range of 100–200 mg C (mg Chl)

^{−1}requires ${P}_{m}^{B}>25$ mg C (mg Chl)

^{−1}h

^{−1}, i.e., above the theoretical maximum calculated by Falkowski [53]. Here, did not observe such high assimilation numbers (Figure 1b), but the histogram shows a right-hand tail with values well above 10 to 15 mg C (mg Chl)

^{−1}h

^{−1}, which implies the possibility of high growth rates, at least on occasion. The bulk of our results are consistent with those of Casey et al. [54], who reported growth rates in the Sargasso Sea equal to $0.42\pm 0.17$ d

^{−1}, based on nitrogen uptake rates. The reader is referred to Table 2 in Casey et al. [54] for more literature values on the growth rates in the Sargasso Sea, which are all consistent with the ones reported in this work, although obtained by different methods.

#### 3.5. Seasonal Cycle

^{−1}h

^{−1}, where $j=0,1,2,\dots ,365$ is the Julian day. Judging by the figure, the representation of the seasonal cycle by the sum of two sine functions is well suited for the assimilation number.

^{−1}h

^{−1}, in spring. A more recent compilation [21] revised the mean value for spring slightly upwards, to 5.92, which is quite close to the value that we found for ${P}_{m}^{B}$ in early spring (March, in Figure 6). However, instead of this being a maximum, the seasonal cycle in Figure 6 shows the value in March of ~6 mg C (mg Chl)

^{−1}h

^{−1}to be a minimum, with a maximum of ~12 mg C (mg Chl)

^{−1}h

^{−1}being reached in summer. The differences may indicate that sporadic data from ships fails to capture the full extent of seasonal variations in photosynthesis irradiance parameters, such as those revealed here. These differences have immediate implications for the computation of marine primary production based on remotely-sensed chlorophyll concentration combined with photosynthesis irradiance parameters (e.g., Sathyedranath et al. [24]).

#### 3.6. Application to Remote Sensing

## 4. Discussion

^{−1}h

^{−1}. The same authors [9] also reported that the initial slope, ${\alpha}^{B}$, ranged from 0.017 to 0.806 ± 0.46 mg C (mg Chl)

^{−1}(W m

^{−2})

^{−1}h

^{−1}. These ranges coincide well with the distribution given in Figure 1. The values of ${P}_{m}^{B}=7.41\pm 2.09$ mg C (mg Chl)

^{−1}h

^{−1}reported by Forget et al. [70] for the Sargasso Sea are also in line with the values shown in Figure 1b. However, the values reported by the same authors for ${\alpha}^{B}=0.097\pm 0.024$ mg C (mg Chl)

^{−1}(W m

^{−2})

^{−1}h

^{−1}fall on the lower end of values given in Figure 1a. The numerous values for ${\alpha}^{B}$ and ${P}_{m}^{B}$ reported by Platt et al. [71] for the Northwest Atlantic obtained by photosynthesis light experiments all match well with the ones reported in this work. Platt et al. [71] reported that ${P}_{m}^{B}$ went from about 1 to 12 mg C (mg Chl)

^{−1}h

^{−1}and ${\alpha}^{B}$ from roughly 0.01 to 0.2 mg C (mg Chl)

^{−1}(W m

^{−2})

^{−1}h

^{−1}(the reader is referred to Figure 3a in Platt et al. [71]). We conclude that the values recovered here from in situ production measurements are in a reasonable range for the open ocean and are consistent with previous, direct estimates based on photosynthesis irradiance measurements at sea.

^{−1}(W m

^{−2})

^{−1}h

^{−1}and ${P}_{m}^{B}$ as 1.7 to 5.0 mg C (mg Chl)

^{−1}h

^{−1}for this region of the Atlantic. According to the results presented here (Figure 1), these ${P}_{m}^{B}$ values fall in the lower end of the parameter distributions. Furthermore, rather than applying fixed values for the assimilation number for each season, our results (Figure 7) allowed a smoothly-varying function to be applied to account for seasonal variation in the parameter when computing primary production using satellite data. These considerations further emphasise the importance of being able to evaluate the seasonal cycle in ${\alpha}^{B}$ as well.

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Histograms of estimated parameter values: (

**a**) distribution of the initial slope, ${\alpha}^{B}$, obtained from 87 cruises and (

**b**) distribution of the assimilation number, ${P}_{m}^{B}$, obtained from 138 cruises. The abscissa corresponds to the parameter values and the ordinate gives the percentage of cruises that fell into a certain interval of parameter values.

**Figure 2.**Comparison of the model versus measured production at depth obtained by combining the measured data with the estimated parameter values. The abscissa corresponds to the ratio of daily production at depth ${P}_{T}^{B}(z)$ to the maximum possible production, ${P}_{m}^{B}D$. The ordinate gives the dimensionless irradiance, ${I}_{\ast}^{m}{e}^{-Kz}$. The continuous curve is recognized as the ${f}_{z}({I}_{\ast}^{m}{e}^{-Kz})$ function. The coordinates of each point are $({\tilde{P}}_{T}^{B}({z}_{n})/{P}_{m}^{B}D,{\alpha}^{B}{\tilde{I}}_{0}^{m}{e}^{-\tilde{K}{z}_{n}}/{P}_{m}^{B})$, where ${\alpha}^{B}$ and ${P}_{m}^{B}$ are the estimated parameters for each profile. The ${r}^{2}$ value between the measured normalized production and the modeled normalized production is 0.95. In total, there are 1049 points.

**Figure 3.**Comparison of the model and measured normalized daily watercolumn production obtained by combining the measured data with the estimated parameter values. The abscissa is the dimensionless irradiance, ${I}_{\ast}^{m}$, and the ordinate is the ratio of normalized watercolumn production to ${P}_{m}^{B}D/K$. The continuous curve is the $f({I}_{\ast}^{m})$ function (10). The coordinates of each point are $({\tilde{P}}_{Z,T}^{B}\tilde{K}/{P}_{m}^{B}D,{\alpha}^{B}{\tilde{I}}_{0}^{m}/{P}_{m}^{B})$, where ${\alpha}^{B}$ and ${P}_{m}^{B}$ are the estimated parameters for each profile. The ${r}^{2}$ between the measured normalized watercolumn production and the modeled normalized watercolumn production is 0.97.

**Figure 4.**(

**a**) Scatter plot of measured $\tilde{B}$ and modelled biomass B with the shifted Gaussian function. There are, in total, 1049 points. (

**b**) Scatter plot of measured ${\tilde{P}}_{Z,T}$ and modeled ${P}_{Z,T}$ watercolumn production with the analytical solution for the shifted Gaussian biomass. There are, in total, 138 points. The grey line on both plots represents the 1:1 model versus the measurement ratio.

**Figure 5.**Histogram of the estimated maximum daily growth rate, ${\mu}_{m}$, obtained from 138 cruises based on Equation (12) and here multiplied by the daylength, D, to convert hourly into daily rates. The value of the carbon-to-chlorophyll ratio $\chi $ is 146 mg C (mg Chl)

^{−1}, taken from Maranon (2005).

**Figure 6.**Estimated seasonal cycles for the BATS station. The thin curves represent the monthly averages on each Julian day, which were calculated from the daily values, 15 days prior and 15 days post a given Julian day. The thick curves are the fits of a sum of two sine functions (superimposed onto an annual mean) to the monthly averages. (

**a**) Seasonal cycle of ${P}_{m}^{B}$ (blue) and ${B}_{Z}$ (orange). (

**b**) Seasonal cycle of ${P}_{Z,T}^{B}$ (red).

**Figure 7.**Comparison of the measured (grey curve) versus the modelled seasonal cycle of watercolumn production based on remotely sensed-chlorophyll with the time-dependent assimilation number, ${P}_{m}^{B}(t)$ (blue curve), and the average assimilation number, $\langle {P}_{m}^{B}\rangle $ (dashed blue curve).

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kovač, Ž.; Platt, T.; Sathyendranath, S.; Lomas, M.W. Extraction of Photosynthesis Parameters from Time Series Measurements of In Situ Production: Bermuda Atlantic Time-Series Study. *Remote Sens.* **2018**, *10*, 915.
https://doi.org/10.3390/rs10060915

**AMA Style**

Kovač Ž, Platt T, Sathyendranath S, Lomas MW. Extraction of Photosynthesis Parameters from Time Series Measurements of In Situ Production: Bermuda Atlantic Time-Series Study. *Remote Sensing*. 2018; 10(6):915.
https://doi.org/10.3390/rs10060915

**Chicago/Turabian Style**

Kovač, Žarko, Trevor Platt, Shubha Sathyendranath, and Michael W. Lomas. 2018. "Extraction of Photosynthesis Parameters from Time Series Measurements of In Situ Production: Bermuda Atlantic Time-Series Study" *Remote Sensing* 10, no. 6: 915.
https://doi.org/10.3390/rs10060915