A HAB mathematical model of competition between two algae species in the Yangtze River Estuary and its

adjacent waters

Qing Wang South China Sea Institute of Oceanology

Chinese Academy of Sciences Guangzhou, China

Liangsheng Zhu, Jinpeng Hu School of Civil Engineering and Transportation

South China University of Technology Guangzhou, China

Abstract—Field observations in high frequent harmful algal bloom (HAB) occurrence area around Yangtze River Estuary show that during HAB, nutrients concentration and their distribution are the main factors leading to the population succession between two main dominant HAB species, Skeletonema costatum (S.c) and Prorocentrum donghaiense (P.d). Based on such a succession mechanism, a HAB ecological mathematical model is developed by improving a 3D coupled hydrodynamic-ecological model (COHERENS). Compared with in-situ data, the numerical simulations represent the trend of dominant HAB species succession in this sea area and effects of marine nutrients and sea water temperature on competition between these two algae species.

Keywords-Yangtze River Estuary; population succession; harmful algal bloom; ecological mathematical model.

I. INTRODUCTION

With rapid development of economy, the number of estuarine and coastal engineering and industrial projects increase year by year, which seriously affect the coastal ecosystem balance. Especially in the Yangtze River Estuary and its adjacent waters, eutrophication has become an overwhelming phenomenon caused by frequent human activities, and consequently, large-scale harmful algal blooms occur more frequently here than ever before [1]. In recent years, many researches on conditions and mechanism of HAB in this area have been conducted, which make considerable progress in ecological adaptive strategies of representive HAB species, the relationship between eutrophication and HAB and the impact on the ecological environment of HAB [2]. Direct and qualitative understandings of HAB process in this area can be obtained from existing research results [3]-[5], which make it possible to conduct a more realistic numerical simulation of HAB process by providing a range of ecological parameters. The main numerical models up to date applied to simulation of HAB can be summarized as pure ecological system models [6]-[7] and coupled hydrodynamic-ecological models [8]-[10]. Compared with pure eco-system models, coupled models consider HAB as a physical, biological and chemical process of interaction, which is the mainstream research method. However, most numerical simulations of HAB focus on concentrations of the whole biomass or a single algal species, and few involve nutrient competition between two algae species.

Analysis of field survey data shows that during HAB in the Yangtze River Estuary and its agjacent water, the species exhibit a conspicuous succession trend “diatom-dinoflagellate-diatom” [11]. The main dominant HAB species involved in the succession are S.c and P.d with ecological niche differing from each other. Results from field mesocosm experiments [12] and culture experiments [13] indicate that: S.c is more competitive in a rich nutrient environment and has a wider adaptive temperature range (15°C-25°C); P.d can live in a low nutrient environment with population growth and has an obvious exponential growth phase under temperature range from 20°C to 25°C. These two algae have different nutritional storage ability [14], which decides that potential nutrient competition exists between them. Based on such a competition mechanism, a HAB ecological mathematical model is developed and applied to simulate the HAB species succession in high frequent HAB occurrence area around Yangtze River Estuary.

II. MODEL DESCRIPTION The maximum growth rate and the nutrient half-saturation

constants for growth dynamics of S.c are very different from those of P.d, which results in different reproductive capacity between them in nutrient sufficient conditions. Therefore, Michaelis-Menten equation [15] is chosen to parameterize the growth rate of these two algae species as below

NjCij

Njii CK

C+

= maxμμ (1)

where i is the growth rate of algae species, CNj is the concentration of nutrient, KCij is the half-saturation constant for nutrient uptake, i and j are used to classify the algae species and nutrients. In order to consider the effect of temperature on algae growth rate, an improved empirical formula is introduced here to parameterize temperature growth factor:

( ) riTi TTqeTf −−= (2)

where Tri is the reference temperature, qTi is the empirical coefficient, T is the sea water temperature. Consequently, Eq. (1) is updated to:

)(max TfCK

C

NjCij

Njii ⋅

+= μμ (3)

978-1-4244-7874-3/10/$26.00 ©2010 IEEE

Moreover, nutrient threshold conditions are used not only to force S.c HAB to dissipate, but to keep P.d in a continuous propagation. On the basis of the above theory, a HAB concept model of competition between two algae species is developed here by improving a hydrodynamic-ecological model COHERENS, into which four state variables of S.c (ASC), P.d (APD), phosphate (POS) and silicate (SIOS) concentration, together with their corresponding convection-diffusion equations, are added.

COHERENS is a three-dimensional multi-purpose numerical model for coastal and shelf seas. The hydrodynamic model is coupled to biological, resuspension and contaminant models, and resolves mesoscale to seasonal processes [16]. The hydrodynamic part of the model uses the momentum equations using the Boussinesq approximation and the assumption of vertical hydrostatic equilibrium, the continuity equation and the equations of temperature and salinity. The biological module cycles concentrations of organic carbon and nitrogen through microplankton and detrital compartments with associated changes in dissolved concentrations of nitrate, ammonium and oxygen. The concentrations are updated in time by solving a transport equation for each state variable whereby the biological interactions are included as source and sink terms and which takes account of vertical sinking and the physical transport by advection and diffusion. The general form of a transport equation for any state variable can be written as follows:

)()()()(

)()()(

ψβψλψλψλ

ψωψψψψ

=∂∂

∂∂−

∂∂

∂∂−

∂∂

∂∂−

∂∂+

∂∂+

∂∂+

∂∂+

∂∂

yyxxzz

tzw

yv

xu

t

HHT

s

(4)

where s is a “non-physical” sinking (or swimming) rate specific for the quantity , T is the vertical diffusion coefficient, H is the horizontal diffusion coefficient, and ( )is the source/sink term. The biological module with 8 independent state variables (microplankton carbon B, microplankton nitrogen N, detrital carbon C, detrital nitrogen M, dissolved nitrate NOS, dissolved ammonium NHS, oxygen O, zooplankton nitrogen ZN) is driven by several ecological processes (the growth of microplankton, meso-zooplankton grazing and excreting, nutrient uptake and nitrification, and detritus generation and remineralisation).

Source/sink terms of the four new state variables are seperately defined as:

ASCGASC asc ⋅−= )()( μβ (5) APDGAPD apd ⋅−= )()( μβ (6)

uBASCuAPDuS POasc

POapd

POPO −⋅−⋅−=)(β (7)

uBASCuS SIOasc

SIOSIO −⋅−=)(β (8)

where asc and apd, respectively, the growth rate of ASC and APD; G is grazing pressure; POuasc, POuapd and POu the phosphate uptake rate of ASC, APD and microplankton; SIOuasc and SIOu the silicate uptake rate of ASC and microplankton.

In the concept model of HAB, the microplankton field of COHERENS model is considered as a dynamic balance condition, while S.c and P.d are regarded as independent growth parts with abnormal rate (Fig. 1).

Figure 1 The concept model of HAB

III. MODEL CONFIGURATION The simulated area is the East China Sea(117-131°E, 24.5-

41°N). The horizontal resolution is 5 ×5 , and 10 sigma levels are defined vertically. Five open boundaries are respectively located in the Yangtze River Estuary (121°33 E, 31°00 N-31°27 N), the Osumi-Tokara Strait (129°00 E-131°00 E,28°30 N-31°00 N), the Tsushima Strait (129°00 E-130°00 E, 33°30 N-35°00 N), the Taiwan Strait and the east of Taiwan (117°00 E-123°00 E, 24°30 N). Ryukyu Island Chain is simplified as solid boundary. Bathymetry of the simulated area and open boundary locations are shown in Fig. 2. Model input data and sources are listed in Table I.

Figure 2. Bathymetry (unit: m) of the simulated area and open boundary locations marked with thick solid lines

The model is initialized with zero values for currents and sea surface elevation and integrated for 90 model days to simulate the spring HAB process with start date March 26.

hydrodynamic background

excreting grazinggrazing

remineralistionuptake

uptake

microplankton Skeletonema costatumProrocentrum donghaiense

ammonium nitratephosphate silicate

detritus

meso-zooplankton hydrodynamic background

hydrodynamic background

hydrodynamic background

TABLE I. MODEL INPUT DATA AND SOURCES

Variable Unit Source

Temperature °C World Ocean Atlas 2001

Salinity PSU World Ocean Atlas 2001

Wind speed m/s QuikSCAT

Precipitation rate kg/m2/s AMSR-E

Cloud cover — ICOADS

Relative humidity — ICOADS

Air temperature °C ICOADS

Chlorophyll mg/m3 World Ocean Atlas 2001

Nitrate mmol/m3 World Ocean Atlas 2005

Phosphate mmol/m3 World Ocean Atlas 2005

Silicate mmol/m3 World Ocean Atlas 2005

Oxygen mmol/m3 World Ocean Atlas 2005

ASC mmol C/m3 [17]

APD mmol C/m3 [18]

Grazing pressure day-1 [19]-[21]

RESULTS AND DISCUSSION Distributions of nutrients and algae concentrations in the

Yangtze River Estuary and its adjacent waters (Fig. 2. small box section) are separately shown in Fig. 3-7. When the model is integrated forward to March 27, concentrations of nitrate, phosphate and silicate respectively reach more than 4mmol/m3,0.4mmol/m3, 8mmol/m3, even in the offshore waters relatively far. The sea water temperature ranges from 13°C to 20°C at this time. Adequate nutrients and suitable temperature make the diatom occupy the position of competitive advantage and keep it in fast growth and reproduction.

Figure 3. ASC distribution (unit: mmol C/m3)

Consequently, S.c HAB occurs on April 2 with maximum concentration of 28 mmol C/m3. Along with nutrients largely consumed during the HAB, the growth rate of S.c gradually decreases to below its respiration rate and grazing pressure. As a result, the S.c HAB dissipates step by step in 23 model days and its concentration drops to below 1.5 mmol C/m3. Nitrate and silicate concentrations, at this moment, still remain higher than 3mmol/m3, while phosphate concentration drops to a lower level around 0.1mmol/m3. Then it can be concluded that the rapid consumption of phosphate is probably the main reason for the S.c HAB dissipation.

Figure 4. APD distribution (unit: mmol C/m3)

However, P.d, with better endurance of low-nutrient environment, gradually becomes the dominant species and maintains sustained growth. Around May 9, the P.d HAB breaks out with maximum concentration of 55 mmol C/m3.Nearly 14 days of gestation period for the P.d HAB is much longer than that for the S.c HAB (8 days), because of the big difference between their maximum growth rate. The P.d HAB lasts for about 30 model days and then enters into the stage of dissipation on June 19. As the sea water temperature increases to over 25°C, the growth of P.d is partly limited by the temperature growth factor and its concentration drops to about 0.5 mmol C/m3 due to its respiration rate and grazing pressure.

Figure 5. Nitrate distribution (unit: mmol/m3)

Figure 6. Phosphate distribution (unit: mmol/m3)

Figure 7.Silicate distribution (unit: mmol/m3)

Figure 8. Temperature distribution (unit: °C)

The concept model of competition between two algae species during HAB represents the main characteristic of dominant HAB species succession phenomenon in the Yangtze River Estuary and its adjacent waters. The model results suggest that phosphate threshold condition is the key reason for the dissipation of S.c HAB and the increasing sea water temperature limits to some extent the development of P.d HAB. In further study, the effects of irradiance, sediment and salinity on HAB should be concluded to make the numerical simulation more realistic.

REFERENCES

[1] Tang, DL, Di, BP, Wei, GF, Ni, IH, Oh, IM, and Wang, SF (2006). "Spatial, seasonal and species variations of harmful algal blooms in the South Yellow Sea and East China Sea," Hydrobiologia, Vol 568, No 1, pp 245-246.

[2] Zhou, MJ, and Zhu, MY (2006). "Progress of the Project Ecology and Oceanography of Harmful Algal Blooms in China," Advances in Earth Science, Vol 21, No 7, pp 673-679.

[3] X.R. Han, X.L. Wang, X. Sun, X.Y. Shi, C.J. Zhu, C.S. Zhang and R. Lu, “Nutrient distribution and its relationship with occurrence of red tide in coastal area of East China Sea,” Chinese Journal Of Applied Ecology, 14(7): 1097-1101, July 2003.

[4] Li, JT, Zhao, WH, Yang, DF, and Wang JT (2005). "Effect of turbid water in Changjiang(Yangtze) estuary on the growth of S.c," Marine Sciences, Vol 29, No 1, pp 34-37.

[5] Zhao, YF, Yu, ZM, Song, XX, and Cao, XH (2009). "Effects of Different Phosphorus Substrates on the Growth and Phosphatase Activity of S.c and P.d," Environmental Science, Vol 30, No 3, pp 693-699.

[6] Wang, HL, Feng, JF, and Shen, F (2002). "Nonlinear Dynamics Research of the Algal Model in Bohai Sea," Ocean Technology, Vol 21, No 3, pp 8-12.

[7] Huppert, A, Blasius, B, Olinky, R, and Stone, L (2005). "A model for seasonal phytoplankton blooms, " Journal of Theoretical Biology, Vol 236, Issue 3, pp 276-290.

[8] Ennet, P, Kuosa, H, and Tamsalu, R (2000). "The influence of upwelling and entrainment on the algal bloom in the Baltic Sea, " Journal of Marine Systems, Vol 25, Issues 3-4, pp 359-367.

[9] Griffin, LS, Herzfeld, M, and Hamilton, PD (2001). "Modelling the impact of zooplankton grazing on phytoplankton biomass during a dinoflagellate bloom in the Swan River Estuary,Western Australia," Ecological Engineering, Vol 16, Issue 3, pp 373-394.

[10] Solé, J, Estrada, M, and Emilio, GL (2006). "Biological control of harmful algal blooms:A modelling study," Journal of Marine Systems,Vol 61, Issue 3-4, pp 165-179.

[11] Zhang, CS, Wang, JT, Zhu, DD, Shi, XY, and Wang, XL (2008). "The prel iminary analysis of nutrients in harmful algal blooms in the East China Sea in the spring and summer of 2005," Acta Oceanologica Sinica, Vol 30, No 2, pp 153-159.

[12] Li, RX, Zhu, MY, Wang, ZL, Shi, XY, and Chen, BZ (2003). "Mesocosm experiment on competition between two HAB species in East China Sea," Chinese Journal of Applied Ecology, Vol 14, No 7, pp 1049-1054.

[13] Wang, ZL, Li, RX, Zhu, MY, Chen, BZ and Hao, YJ (2006). "Study on Population Growth Processes and Interspecific Competition of P.d and S.c in Semi-continuous Dilution Experiments," Advances in Marine Science, Vol 24, No 4, pp 495-503.

[14] Lu, SH, and Li, Y (2006). "Nutritional Storage Ability of Four Harmful Algae from the East China Sea," The Chinese Journal of Process Engineering, Vol 6, No 3, pp 439-444.

[15] Michaelis, L, and Menten, ML (1913). "Die kinetik der invertinwirkung," Biochem Z, Vol 49, pp 333-369.

[16] Luyten, PJ, Jones, JE, Proctor, R, Tabor, A, Tett, P, and Wild, AK (1999). "COHERENS-A Coupled Hydrodynamical-Ecological Model for Regional and Shelf Seas: User Documentation," MUMM Report, Management Unit of the Mathematical Models of the North Sea, pp 1-914.

[17] Xie, WL (2006). "Community Structure and Dynamics of Planktonic Diatoms in Typical Areas of East China Sea," Xiamen University, Xiamen.

[18] Chen, HL (2006). "A Survey on the red tides in the East China Sea in 2004 and species interaction of two causative HABs species," Jinan University, Guangzhou.

[19] Zhang, WC, and Wang, R (2000). "Microzooplankton and Their Grazing Pressure on Phytoplankton in Bohai Sea," Oceanologia Et Limnologia Sinica, Vol 31, No 3, pp 252-258.

[20] Sun, J, Liu, DY, Wang, ZL, Shi, XY, Li, RX, and Zhu, MY (2003). "Microzooplankton herbivory during red tide-frequent-occurrence period in Spring in the East China Sea," Chinese Journal of Applied Ecology, Vol 14, No 7, pp1073-1080.

[21] Zeng, XB, and Huang, BQ (2007). "Grazing Impact of Microzooplankton in Taiwan Strait and Its Contribution to Nutrient Regeneration," Journal of Xiamen University (Natural Science), Vol 46, No 2, 231-235.