# Sensitivity of Chlorophyll Variability to Specific Growth Rate of Phytoplankton Equation over the Yangtze River Estuary in a Physical–Biogeochemical Model

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## Abstract

**:**

## 1. Introduction

## 2. Data and Methodology

#### 2.1. Model and Data

#### 2.2. Experiment Design

^{3}/s) of the Yangtze River is first converted into a Gaussian distributed precipitation rate (unit: m/s) around the river mouth based on a spatial scale, which is a parameter related with model resolution and taken as 120 km (60 km for L1 domain) in our study. This method was used in many other studies in which the complex estuary dynamics cannot be explicitly resolved in coarse resolution ocean models [38,39,40,41]. Then, different nutrients are added in the physical–biogeochemical model, by multiplying the discharge with the observed nutrients concentration (nitrate: 41.9 mmol/m

^{3}average from January 1963 to December 1999; silicate: 95.6 mmol/m

^{3}, and phosphate: 0.21 mmol/m

^{3}average from January 1963 to December 1984; Liu et al. [31]), and assuming the added nutrients will be mixed in the top 10 m of the water column. In this way, we can convert the river discharge into the change of nutrient concentration rate (unit: mmol/m

^{3}·s).

^{−1}, but it changes from 0 to 5.0 d

^{−1}for Case 3, when temperature changes from 0 to 30 °C. Case 2 and Case 3 are used to estimate the growth of picoplankton and diatoms. The growth rate of Case 4 and Case 5 specific growth rate of phytoplankton equations gradually increase from 0 to 1.0 d

^{−1}, when temperature changes from 0 to 30 °C. The difference between the Case 4 and Case 5 is that when temperature exceeds 22 °C, the growth rate of Case 5 is a constant and does not increase with the increase of temperature [47,48]. Rates of growth given by Case 1–3 are much higher than Case 4–5.

## 3. Results

#### 3.1. Comparison of SST with ECCO2 SST Product

#### 3.2. Comparison of Chlorophyll with Observation

^{3}, with the bias of varying from −0.19 mg/m

^{3}to 0.31 mg/m

^{3}, and the correlation coefficients are all above 0.7. The comparison between Case 5 and SeaWiFS is better than the comparisons between Case 1–4 and SeaWiFS. From the above comparisons, we find that Cases 1–4 are all overestimated chlorophyll, and Case 5 is the closest to SeaWiFS.

^{3}over the near shore, and it gradually decreases to low value in the open sea. In terms of temporal evolution, chlorophyll concentration increases from April to July, and decreases in August over the region of 29° N–32° N, 122.5° E–124° E. The region of high chlorophyll concentration (higher than 5 mg/m

^{3}) extends northeastward gradually from April to July, and is caused by freshwater discharge, especially in the region of 29° N–32° N, 122.5° E–124° E [52,53]. Although there exist large differences in the magnitude of chlorophyll concentration between Cases 1–3 and SeaWiFS, the spatial distributions of Cases 1–3 all have high values near the shore and low values offshore (Figure a1–e3). For Case 4, the chlorophyll concentration ranging in 0–10 mg/m

^{3}, and the value gradually increases from April to August. Case 5 shows the same spatial distribution to SeaWiFS, and the magnitude of concentration is also from 0 to 5 mg/m

^{3}. However, the chlorophyll concentration of Case 5 is significantly lower than Case 4 from June to August, which may be related to the fact that the SST exceeded the optimal temperature of phytoplankton growth of 22 °C. The above analysis shows that the model which uses the fifth specific growth rate of phytoplankton equation can reproduce the spatial distribution of chlorophyll on seasonal timescales over the Yangtze River estuary.

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) The outer model domain covers the whole Chinese coastal region and part of western Pacific. The range of the black rectangle is the inner one (27° N–36° N, 119° E–128° E). (

**b**) The inner model domain covers the Yangtze River estuary and part of East China Sea. The black rectangle (29° N–32° N, 122.5° E–124° E) is the area we analyzed.

**Figure 2.**Growth rate changes with temperature for five forms of specific growth rate of phytoplankton equation, Case 1 to 5.

**Figure 3.**Monthly SST of ECCO2 from April to August (13-year average from 1998–2010) of Yangtze River estuary (

**a**–

**e**, top row). The (

**f**–

**j**) are the same as (

**a**–

**e**), but for the model results.

**Figure 4.**The seasonal cycle of ECCO2 SST and model result from April to August averaged over 29° N–32° N, 122.5° E–124° E from 1998 to 2010.

**Figure 5.**Comparisons of chlorophyll from model (five cases) against SeaWiFS from April to August (13-year average from 1998–2010) within the area of 29° N–32° N and 122.5° E–124° E. The figures in the first row (

**a1**–

**e1**) are for Case 1 and SeaWiFS. The figures in the second row (

**a2**–

**e2**) are from Case 2 and SeaWiFS. The figures in the third row (

**a3**–

**e3**) are from Case 3 and SeaWiFS. The figures in the fourth row (

**a4**–

**e4**) are from Case 4 and SeaWiFS. The figures in the fifth row (

**a5**–

**e5**) are from Case 5 and SeaWiFS. The correlation coefficient (R), root mean square error (RMSE) and bias between model and SeaWiFS are shown in each figure.

**Figure 6.**Monthly chlorophyll concentration of SeaWiFS from April to August (13-year average from 1998–2010) of Yangtze River estuary (

**a**–

**e**, top row). The (

**a1**–

**e5**) are the same as (

**a**–

**e**), but for the model results (five cases). The figures in the second row (

**a1**–

**e1**) are for Case 1. The figures in the third row (

**a2**–

**e2**) are from Case 2. The figures in the fourth row (

**a3**–

**e3**) are from Case 3. The figures in the fifth row (

**a4**–

**e4**) are from Case 4. The figures in the sixth row (

**a5**–

**e5**) are from Case 5.

**Figure 7.**The seasonal cycle of 1998–2010 averaged chlorophyll concentration from SeaWiFS and model result (Case 5) over 29° N–32° N, 122.5° E–124° E.

**Table 1.**The initial conditions for the coupled physical–biogeochemical model for the Yangtze River estuary.

Parameter Description | Value | Data Source |
---|---|---|

Nitrate (NO3)/mmol·m^{−3}Silicate (Si(OH)4)/mmol·m ^{−3}Phosphate (PO4)/mmol·m ^{−3}Oxygen (O2)/mmol·m ^{−3} | World Ocean Atlas 2005 (WOA05) [21] | |

Ammonium (NH4)/mmol·m^{−3} | 0.0001 mmol·m^{−3} | Xiu and Chai [20] |

Total alkalinity (Talk)/mmol·m^{−3} | GLODAP dataset [25] | |

Total CO2 (TCO2)/mmol·m^{−3} | 0.0001 mmol·m^{−3} | Xiu and Chai [20] |

Semi-labile DOC (SDOC)/mmol·m^{−3} | surface to bottom: decreases according to a hyperbolic tangent function from 15 mmol·m^{−3} to 0.01 mmol·m^{−3}. | |

Labile DOC (LDOC)/mmol·m^{−3} | 0–500 m: 2.0 mmol·m^{−3}; 500 m to bottom: 0.01 mmol·m^{−3}. | |

Colored labile dissolved organic carbon (CLDOC)/mmol·m^{−3} | 0.0001 mmol·m^{−3} | |

Labile DON (LDON)/mmol·m^{−3} | 9.95 | |

Semi-labile DON (SDON)/mmol·m^{−3} | 15.38 | |

Colored semi-labile (CSDOC)/mmol·m^{−3} | 0.4 | |

Detritus-nitrogen (DDN)/mmol·m^{−3} | 0.0001 mmol·m^{−3} | |

Detritus-silicate (DDSI)/mmol·m^{−3} | 0.0001 mmol·m^{−3} | |

Detritus-carbon (DDC)/mmol·m^{−3} | 0.0001 mmol·m^{−3} | |

Bacteria nitrogen (BAC)/mmol·m^{−3} | surface to bottom: decreases according to a hyperbolic tangent function from 0.03 mmol·m^{−3} to 0.01 mmol·m^{−3}. | |

Small phytoplankton (S1)/mmol·m^{−3} | 0.0001 mmol·m^{−3} | |

Diatoms (S2)/mmol·m^{−3} | 0.0001 mmol·m^{−3} | |

Coccolithophorids (S3)/mmol·m^{−3} | 0.0001 mmol·m^{−3} | |

Chlorophyll in small phytoplankton (chl1)/mg·m^{−3} | 0.0001 mg·m^{−3} | |

Chlorophyll in large phytoplankton (chl2)/mg·m^{−3} | 0.0001 mg·m^{−3} | |

Coccolithophorids chlorophyll (chl3)/mg·m^{−3} | 0.0001 mg·m^{−3} | |

Carbon in small phytoplankton (C1)/mmol·m^{−3} | 0.0001 mmol·m^{−3} | |

Carbon in large phytoplankton (C2)/mmol·m^{−3} | 0.0001 mmol·m^{−3} | |

Coccolithophorids carbon (C3)/mmol·m^{−3} | 0.0001 mmol·m^{−3} | |

Micro zooplankton (ZZ1)/mmol·m^{−3} | 0.0001 mmol·m^{−3} | |

Meso zooplankton (ZZ2)/mmol·m^{−3} | 0.0001 mmol·m^{−3} | |

zz1-carbon (ZZC1)/mmol·m^{−3} | 0.0001 mmol·m^{−3} | |

zz2-carbon (ZZC2)/mmol·m^{−3} | 0.0001 mmol·m^{−3} | |

Particulate inorganic carbon (DDCA)/mmol·m^{−3} | 0.0001 mmol·m^{−3} |

**Table 2.**Five kinds of the specific growth rate of phytoplankton equations in the coupled model (${\mathrm{T}}_{\mathrm{opt}}$ = 22 °C).

Cases | Specific Growth Rate of Phytoplankton Equations | Source |
---|---|---|

Case 1 | Q10 = ${\mu}_{0}$·1.0 | Eppley [6] |

Case 2 | $\mu $ = ${\mu}_{0}$·e^{(0.069·(T-Topt))} | Zhou et al. [29] |

Case 3 | $\mu $ = ${\mu}_{0}$·0.69·(1.066^{T}) | Eppley [6] |

Case 4 | $\mu $ = ${\mu}_{0}$·e^{(−4000.0·(1.0/(T+273.15)−1.0/303.15))} | Geider [43]; Moore et al. [44]; Fujii et al. [45] |

Case 5 | $\mu $ = ${\mu}_{0}$·e^{(−4000.0·(1.0/(T+273.15)−1.0/303.15))}$\mu $= ${\mu}_{0}$·e ^{(−4000.0·(1.0/(Topt+273.15)−1.0/303.15))} (T > 22 °C) | Lin [47]; Li [48] |

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**MDPI and ACS Style**

Wu, Q.; Wang, X.; Xiu, P.; Chai, F.; Chen, Z.
Sensitivity of Chlorophyll Variability to Specific Growth Rate of Phytoplankton Equation over the Yangtze River Estuary in a Physical–Biogeochemical Model. *Atmosphere* **2022**, *13*, 1748.
https://doi.org/10.3390/atmos13111748

**AMA Style**

Wu Q, Wang X, Xiu P, Chai F, Chen Z.
Sensitivity of Chlorophyll Variability to Specific Growth Rate of Phytoplankton Equation over the Yangtze River Estuary in a Physical–Biogeochemical Model. *Atmosphere*. 2022; 13(11):1748.
https://doi.org/10.3390/atmos13111748

**Chicago/Turabian Style**

Wu, Qiong, Xiaochun Wang, Peng Xiu, Fei Chai, and Zhongxiao Chen.
2022. "Sensitivity of Chlorophyll Variability to Specific Growth Rate of Phytoplankton Equation over the Yangtze River Estuary in a Physical–Biogeochemical Model" *Atmosphere* 13, no. 11: 1748.
https://doi.org/10.3390/atmos13111748