Nutrients Seasonal Variation and Budget in Jiaozhou Bay, China: A 3-Dimensional Physical–Biological Coupled Model Study

Abstract

A 3-D biological model was developed and coupled to a hydrodynamic model, i.e., Princeton Ocean Model, to simulate the seasonal variation and budget of dissolved inorganic nitrogen, phosphate, and silicate in Jiaozhou Bay. The modeled nutrients distribution pattern is consistent with observation. Silicate, the most important limiting element for phytoplankton growth, is characterized by consumption in spring, increase in summer and autumn, and accumulation in winter, whereas dissolved inorganic nitrogen and phosphorous have increasing trend with low rates in spring, due to excessive river loads. Phytoplankton plays an important role in nutrient renewal by photosynthesis and respiration processes. During an annual cycle, 7.83 × 10³ t N, 0.28 × 10³ t P, and 3.93 × 10³ t Si are transported to the bay’s outer sea, i.e., the Yellow Sea, suggesting that Jiaozhou Bay is a significant source of nutrients for the Yellow Sea. The spatial distribution of nutrients is characterized by vertically homogeneous profiles, with high concentration inside the bay and low concentration toward the bay channel. These features are mainly governed by strong turbulent mixing, fluvial influx, water exchange rate, and Yellow Sea water intrusion. Numerical experiments suggest that the government should pay enough attention to proper layout of sewage drainage.

Appendix

The phytoplankton (Dia, i.e., diatom), nutrients [i.e., dissolved inorganic nitrogen (DIN), phosphate (DIP), and silicate (SIL)], zooplankton (Zoo), and detritus (Det) are included in the biological model (Fig. 2). The state variables obey the following equations in x–y–σ coordinate:

$$ \frac{{d{\left( {{\text{Dia}} \cdot D} \right)}}} {{{\text{d}}t}} = {\text{dif}}{\left( {{\text{Dia}}} \right)} + D \cdot {\left( {{\text{PR}}_{{{\text{Dia}}}} - {\text{RS}}_{{{\text{Dia}}}} - {\text{GR}}_{{{\text{Dia}}}} - {\text{MO}}_{{{\text{Dia}}}} } \right)} $$

(A-1)

$$ \frac{{{\text{d}}{\left( {{\text{Zoo}} \cdot D} \right)}}} {{{\text{d}}t}} = {\text{dif}}{\left( {{\text{Det}}} \right)} + D \cdot {\left( {{\text{PR}}_{{{\text{Zoo}}}} - {\text{RS}}_{{{\text{Zoo}}}} - {\text{MO}}_{{{\text{Zoo}}}} } \right)} $$

(A-2)

$$ \frac{{{\text{d}}{\left( {{\text{Det}} \cdot D} \right)}}} {{{\text{d}}t}} = {\text{dif}}{\left( {{\text{Det}}} \right)} + D \cdot {\left( {{\text{EX}}_{{{\text{Det}}}} - {\text{MI}}_{{{\text{Det}}}} } \right)} $$

(A-3)

$$ \frac{{{\text{d}}{\left( {{\text{DIN}} \cdot D} \right)}}} {{{\text{d}}t}} = {\text{dif}}{\left( {{\text{DIN}}} \right)} + D \cdot {\left( {{\text{RE}}_{{{\text{DIN}}}} + {\text{RM}}_{{{\text{DIN}}}} - {\text{UT}}_{{{\text{DIN}}}} } \right)} $$

(A-4)

$$ \frac{{{\text{d}}{\left( {{\text{DIP}} \cdot D} \right)}}} {{{\text{d}}t}} = {\text{dif}}{\left( {{\text{DIP}}} \right)} + D \cdot {\left( {{\text{RE}}_{{{\text{DIP}}}} + {\text{RM}}_{{{\text{DIP}}}} - {\text{UT}}_{{{\text{DIP}}}} } \right)} $$

(A-5)

$$ \frac{{{\text{d}}{\left( {{\text{SIL}} \cdot D} \right)}}} {{{\text{d}}t}} = {\text{dif}}{\left( {{\text{SIL}}} \right)} + D \cdot {\left( {{\text{RE}}_{{{\text{SIL}}}} + {\text{RM}}_{{{\text{SIL}}}} - {\text{UT}}_{{{\text{SIL}}}} } \right)}, $$

(A-6)

where, D is water depth and arithmetic operator dif is the diffusion term.

The governing equations of biological processes are as follows. The photosynthesis PR_Dia is expressed by

$$ {\text{PR}}_{{{\text{Dia}}}} = r^{{{\text{Dia}}}}_{{\text{P}}} \cdot e^{{r^{{{\text{Dia}}}}_{{{\text{TP}}}} {\left( {T - T_{0} } \right)}}} \cdot r^{{{\text{Dia}}}}_{{\lim it}} \cdot \frac{I} {{I^{{{\text{Dia}}}}_{0} }}e^{{1 - \frac{I} {{I^{{{\text{Dia}}}}_{0} }}}} \cdot {\text{Dia,}} $$

(A-7)

where, $r^{{{\text{Dia}}}}_{{\text{P}}}$ denotes the maximum growth rate, $r^{{{\text{Dia}}}}_{{{\text{TP}}}}$ the temperature-dependent coefficient; I and $I^{{{\text{Dia}}}}_{0}$ the available and optimum light intensity for Dia growth, respectively. The available light intensity at the depth of z is assumed to be of negative exponential decrease, with depth deepening: $I{\left( z \right)} = I_{{\text{s}}} \exp ^{{ - k_{i} z}}$, where I _s is the surface light intensity. According to Weng et al. (1992), the coefficient k _i should be smaller in the shallow region. Therefore, k _i  = 0.7–0.04D, if D ≤ 15 m; otherwise k _i  = 0.1. The nutrients limitation follows the Michaelis–Menten kinetics: $r^{{{\text{Dia}}}}_{{\lim \;it}} = \min {\left( {\frac{{{\text{SIL}}}} {{{\text{SIL}} + K^{{{\text{Dia}}}}_{{{\text{SIL}}}} }},\frac{{{\text{DIN}}}} {{{\text{DIN}} + K^{{{\text{Dia}}}}_{{{\text{DIN}}}} }},{\text{ }}\frac{{{\text{DIP}}}} {{{\text{DIP}} + K^{{{\text{Dia}}}}_{{{\text{DIP}}}} }}} \right)}$, where $K^{{{\text{Dia}}}}_{{{\text{DIN}}}} ,K^{{{\text{Dia}}}}_{{{\text{DIP}}}}$, and $K^{{{\text{Dia}}}}_{{{\text{SIL}}}}$ are, the half saturation constant for DIN, DIP, and SIL, respectively. The respiration RS_Dia is expressed as:

$$ {\text{RS}}_{{{\text{Dia}}}} = r^{{{\text{Dia}}}}_{R} e^{{r^{{{\text{Dia}}}}_{{{\text{TR}}}} {\left( {T - T_{0} } \right)}}} \cdot {\text{Dia}} $$

(A-8)

where, $r^{{Dia}}_{R}$ and $r^{{Dia}}_{{TR}}$ are maximum respiration and temperature-dependent coefficient. Dia is grazed by ZOO through Ivlev function:

$$ {\text{GR}}_{{{\text{Dia}}}} = r^{{{\text{Dia}}}}_{g} Q^{{{{\left( {t - 10} \right)}} \mathord{\left/ {\vphantom {{{\left( {t - 10} \right)}} {10}}} \right. \kern-\nulldelimiterspace} {10}}}_{{10}} {\left( {1 - e^{{ - \lambda {\text{Dia}}}} } \right)} \cdot Zoo, $$

(A-9)

where, $r^{{Dia}}_{g}$ is the grazing rate of ZOO at 10°C, and temperature-dependent coefficient, λ is Ivelev constant. The Dia mortality is described as a simple linear function:

$$ {\text{MO}}_{{{\text{Dia}}}} = r^{{{\text{Dia}}}}_{M} \cdot {\text{Dia,}} $$

(A-10)

where, $r^{{{\text{Dia}}}}_{M}$ is mortality rate.

The Zoo assimilated and unassimilated parts, PR_Zoo and RS_Zoo, are set to be proportional to GR_Dia:

$$ {\text{PR}}_{{{\text{Zoo}}}} = \alpha \cdot {\text{GR}}_{{{\text{Dia}}}} $$

(A-11a)

$$ {\text{RS}}_{{{\text{Zoo}}}} = {\left( {1 - \alpha } \right)} \cdot {\text{GR}}_{{{\text{Dia}}}} , $$

(A-11b)

where α is the assimilation percentage of Zoo grazing. The Zoo mortality is described as:

$$ {\text{MO}}_{{{\text{Zoo}}}} = r^{{{\text{Zoo}}}}_{M} \frac{{{\text{Zoo}}}} {{{\text{Zoo}} + {\text{K}}_{{{\text{Zoo}}}} }} \cdot {\text{Zoo,}} $$

(A-12)

where, $r^{{{\text{Zoo}}}}_{M}$ is the maximum death rate, and K _Zoo is the half-saturation constant for Zoo mortality.

Mineralization of detritus is proportional to its concentration:

$$ {\text{MI}}_{{{\text{Det}}}} = r^{{{\text{Nit}}}}_{{{\text{Det}}}} \cdot {\text{Det,}} $$

(A-13)

where, $r^{{{\text{Nit}}}}_{{{\text{Det}}}}$ is mineralization rate. The dead Dia and Zoo, and the unassimilated part of Zoo grazing are considered as the influx for Det:

$$ {\text{EX}}_{{{\text{Det}}}} = {\text{MO}}_{{{\text{Dia}}}} + {\text{MO}}_{{{\text{Zoo}}}} + {\text{RS}}_{{{\text{Zoo}}}} $$

(A-14)

The mineralization from detritus to DIN, DIP, and SIL are, respectively, expressed by

$$ {\text{RM}}_{{{\text{DIN}}}} = {\text{C}}_{{{\text{NC}}}} \cdot {\text{MI}}_{{{\text{Det}}}} \cdot n^{{{\text{NC}}}} $$

(A-15a)

$$ {\text{RM}}_{{{\text{DIP}}}} = {\text{C}}_{{{\text{PC}}}} \cdot {\text{MI}}_{{{\text{Det}}}} \cdot n^{{{\text{PC}}}} $$

(A-15b)

$$ {\text{RM}}_{{{\text{SIL}}}} = {\text{C}}_{{{\text{SiC}}}} \cdot {\text{MI}}_{{{\text{Det}}}} \cdot n^{{{\text{SiC}}}} $$

(A-15c)

where, n ^NC, n ^PC, and n ^SiC are concentration ratios inside Dia body of N/C, P/C, and Si/C, respectively; C _NC , C _PC, and C _SiC are atomic weight ratios of N/C, P/C, and Si/C, respectively.

The uptake of nutrients by phytoplankton is linked to photosynthesis processes:

$$ {\text{UT}}_{{{\text{DIN}}}} = {\text{C}}_{{{\text{NC}}}} \cdot {\text{PR}}_{{{\text{Dia}}}} \cdot n^{{{\text{NC}}}} $$

(A-16a)

$$ {\text{UT}}_{{{\text{DIP}}}} = {\text{C}}_{{{\text{PC}}}} \cdot {\text{PR}}_{{{\text{Dia}}}} \cdot n^{{{\text{PC}}}} $$

(A-16b)

$$ {\text{UT}}_{{{\text{SIL}}}} = {\text{C}}_{{{\text{SiC}}}} \cdot {\text{PR}}_{{{\text{Dia}}}} \cdot n^{{{\text{SiC}}}} $$

(A-16c)

The nutrient releases from plankton, RE_DIN, RE_DIP, and RE_SIL for DIN, DIP, and SIL are related to Dia respiration as following:

$$ {\text{RE}}_{{{\text{DIN}}}} = {\text{C}}_{{{\text{NC}}}} \cdot {\text{RS}}_{{{\text{Dia}}}} \cdot n^{{{\text{NC}}}} $$

(A-17a)

$$ {\text{RE}}_{{{\text{DIP}}}} = {\text{C}}_{{{\text{PC}}}} \cdot {\text{RS}}_{{{\text{Dia}}}} \cdot n^{{{\text{PC}}}} $$

(A-17b)

$$ {\text{RE}}_{{{\text{SIL}}}} = {\text{C}}_{{{\text{SiC}}}} \cdot {\text{RS}}_{{{\text{Dia}}}} \cdot n^{{{\text{SiC}}}} $$

(A-17c)

The surface (σ → 0) and bottom (σ → 1) boundary conditions for biological variables are:

$$ \frac{{K_{{\text{H}}} }} {D}{\left( {\frac{{\partial {\text{Dia}}}} {{\partial \sigma }},\frac{{\partial {\text{Det}}}} {{\partial \sigma }}} \right)} = 0.\,\;,\; \to {\text{ }}0 $$

(A-18a, b)

$$ \frac{{K_{{\text{H}}} }} {D}{\left( {\frac{{\partial {\text{Dia}}}} {{\partial \sigma }},\frac{{\partial {\text{Det}}}} {{\partial \sigma }}} \right)}{\text{ }} = {\text{ }}0.{\text{ }},{\text{ }}\sigma {\text{ }} \to {\text{ }} - 1 $$

(A-18c, d)

$$ \frac{{K_{{\text{H}}} }} {D}{\left( {\frac{{\partial {\text{Din}}}} {{\partial \sigma }},\frac{{\partial {\text{Dip}}}} {{\partial \sigma }},\frac{{\partial {\text{Sil}}}} {{\partial \sigma }}} \right)}{\text{ }} = {\text{ }}{\left( {{\text{sur}}{\left( {{\text{Din}}} \right)},{\text{sur}}{\left( {{\text{Dip}}} \right)},{\text{sur}}{\left( {{\text{Sil}}} \right)}} \right)}{\text{ }},{\text{ }}\sigma {\text{ }} \to {\text{ }}0 $$

(A-18e, f, g)

$$ \frac{{K_{{\text{H}}} }} {D}{\left( {\frac{{\partial {\text{Din}}}} {{\partial \sigma }},\frac{{\partial {\text{Dip}}}} {{\partial \sigma }},\frac{{\partial {\text{Sil}}}} {{\partial \sigma }}} \right)}{\text{ }} = {\text{ }}{\left( {{\text{bot}}{\left( {{\text{Din}}} \right)},{\text{bot}}{\left( {{\text{Dip}}} \right)},{\text{bot}}{\left( {{\text{Sil}}} \right)}} \right)}{\text{ }},{\text{ }}\sigma {\text{ }} \to {\text{ }} - 1, $$

(A-18h, i, j)

where, sur and bot denote atmospheric deposition and nutrients flux from water–sediment interface, respectively; K _H is the vertical eddy diffusion coefficient. The values of biological parameters are shown in A-1.