A model on the carbon cycling in Lake Taihu, China

A model on the carbon cycling in Lake Taihu, China

Ecological Modelling 222 (2011) 2973–2991 Contents lists available at ScienceDirect Ecological Modelling journal homepage: www.elsevier.com/locate/e...

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Ecological Modelling 222 (2011) 2973–2991

Contents lists available at ScienceDirect

Ecological Modelling journal homepage: www.elsevier.com/locate/ecolmodel

A model on the carbon cycling in Lake Taihu, China Hu Weiping a,∗ , Sven Erik Jørgensen b , Zhang Fabing c , Chen Yonggen d , Hu Zhixin e , Yang Longyuan a a

Nanjing Institute of Geography and Limnology, Chinese Academy of Sciences, 73 East Beijing Road, Nanjing 210008, China Copenhagen University, University Park 2, 2100 Copenhagen, Denmark c The Environment Monitoring Centre of Shanghai, 1 NanDan Road, Shanghai 200030, China d Zhejiang Forestry University, 88 North Huancheng Road, Linan 311300, China e University of Anhui, 3 Feixi Road, Hefei 230039, China b

a r t i c l e

i n f o

Article history: Available online 15 June 2011 Keywords: Carbon cycling Carbon speciation Carbon dioxide flux Water–air interface Lake Taihu

a b s t r a c t A model of the carbon cycling in Lake Taihu was developed based on the previous developed model EcoTaihu Model, which couples the hydrology, the nutrient cycling and a number of biological processes. The carbon cycling model (abbreviated CCM) has in addition to the states variables of the EcoTaihu Model, the carbon in phytoplankton, zooplankton, fish, macroplant, hydrogen carbonate carbon, carbonate carbon, dissolved carbon, abiotic organic carbon in water, organic carbon in sediment, soluble organic carbon in pore water, inorganic carbon in sediments, soluble inorganic carbon in pore water and pH. The calibration and validation of the CCM showed that the model results are in good accordance with the observations (from the period February17 to December. 5, 2003). It implies that the model can be used to assess the variation of the carbon dioxide flux at the water–air interface, and to find the pH value of the lake water as function of time. According to the model, the carbon dioxide flux at the water–air interface has clear, diurnal variations. Eutrophied water is a sink for the atmospheric carbon dioxide due to the phytosynthesis during the summer. Due to the terrestrial input of carbon to the lake, Lake Taihu is, however, a source of atmospheric carbon dioxide. The total annual flux is almost equal to the terrestrial input of carbon to the lake. © 2011 Elsevier B.V. All rights reserved.

1. Introduction The concentration of carbon dioxide (CO2 ) in the atmosphere has increased from a pre-industrial value of 280 ppmv to current value of 385 ppmv. Carbon dioxide is a green house gas (Zhang, 2005). Thus, the processes determining the atmospheric CO2 concentration has become one of the key issues of scientific research. The ocean is an important sink of CO2 with a net flux of 2.19 GtC a−1 (Orr, 1993), corresponding to almost half of the total discharge of CO2 to the atmosphere by human activities (Yan and Liu, 2001). Although lake areas only account for 0.5% of water surface in the world (Yan and Liu, 2001), far less than oceans area, they may still have great influence on the budget of the atmospheric CO2 because lakes are much closer to the human carbon dioxide emission. The following amounts of carbon are absorbed by lakes per year: organism organic carbon is about 0.036 GtC a−1 , dissolved organic carbon is 0.015 GtC a−1 and, dissolved inorganic carbon deposited in lakes is 0.026 GtC a−1 (Downing et al., 1993). About 70% of the carbon comes from the atmosphere, i.e. that the world’s lakes are able to absorb 0.0532 GtC a−1 from atmosphere, corresponding to almost 10% of the sum of 0.632 GtC a−1 of the

∗ Corresponding author. Tel.: +86 25 86882180; fax: +86 25 57714759. E-mail address: [email protected]iglas.ac.cn (H. Weiping). 0304-3800/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2011.04.018

inorganic and organic carbon inputs from the rivers to the oceans (Meybeck, 1993). Carbon dioxide is fundamental for the photosynthesis in lacustrine ecosystem (Jørgensen, 1988). It is therefore a very important nutrient in the lacustrine ecosystem (Dahl-Madsen and StrangeNielsen, 1974; Jørgensen, 1976; Wetzel, 2001) and has a great influence on the growth of phytoplankton and macroplants in water. When carbon dioxide is consumed by the photosynthesis, its partial pressure in water decreases, resulting in a flux of carbon dioxide from the atmosphere to the water. When the photosynthesis ceases for example during the night, while the respiration continues, the partial pressure of carbon dioxide in water increases, resulting in a flux of carbon dioxide from water to atmosphere. The fluxes of carbon dioxide between the atmosphere and water and will change the pH value of water (Panizzuti and Tartari, 1995; Wang, 2000) and thereby influence the water quality and the growth of producers. Development of a carbon cycling model for lakes would therefore not only be beneficial for a wider understanding of the role of lakes for the CO2 exchange between the atmosphere and the hydrosphere but also improve the lake management in general. A model of lacustrine carbon cycling based on the verticalcompressed three-dimensional ecological model of Lake Taihu, China (the EcoTaihu Model) is presented in this paper. The following two sections describe in details the model. The results of

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H. Weiping et al. / Ecological Modelling 222 (2011) 2973–2991

Yincunga

6

3

Zhushan Bay

Zhoutie

Meicun

4

5

1

9

Dafu Wangyu River Junzhang Gonghu Bay 2 Xiaogong Island

Tuoshan

13

Dagong Island Tortois

Jiaosha

Dapu

S

0

Meiliang Bay

Fenshui

Zhihugang rRiver

HuDai

N

Wuxi

7 10

Lake

Suzhou

Taihu 8

Mudu

Mansha

Pingtai Island

Yinshan

Xu River

Xukou Changsh

Henshan

Hengjing

Zhushan Jiapu

Shoushan

Dalei Island

Ducun

Dongtingxishan Dongtingdongshan East Taihu Bay

Xintang

12

Dapu River Xiaolei Island Xiaomei 11

Dongjiao mouth Miaogang Qidu Sampling site

Huzhou Fig. 1. Map of Lake Taihu and sampling.

the model calibration are given in Section 3. Discussion of the results including the determination of the carbon dioxide fluxes is presented in Section 4. Finally, the conclusions are presented in Section 5. 2. Conceptual model of the carbon cycling in Lake Taihu, China Lake Taihu (Fig. 1) is a typical large shallow lake with an area of 2338 km2 and a mean depth of 1.89 m (Hu et al., 2006). Its drainage basin covers an area of 36,500 km2 (Sun et al., 1993) and holds a population of 34.5 million, eight large cities and 31 counties or county cities (Yang et al., 2003). Its western and northern part are hyper eutrophicated with a dominance of phytoplankton, while the eastern part and Dongtaihu Bay are mestro-eutrophic with dominance of macroplant communities. Here the water quality is relatively good. The carbon in freshwater ecosystem is mainly in form of inorganic carbon, while a smaller amount is in form of organic compounds as dissolved and particulated detrital carbon, or as carbon of living biota (Wetzel and Likens, 1991). For Lake Taihu the inorganic carbon is 47–70% of the total carbon. It is mainly hydrogen carbonate carbon (HCO3 − ), dissolved carbon dioxide (CO2 ) and carbonate carbon (CO3 2− ), accounting for 95.3–97.9%, 1.3–4.5% and 0.2–0.8% of total dissolved inorganic carbon, respectively (Hu and Fan, 2008). The dissolved organic carbon of Lake Taihu has an annual mean concentration of 3.76–8.97 mg/L and accounts for 16.5–25.3% of the total carbon, (Hu and Fan, 2008). The particulate carbon, with an annual mean concentration of 1.42–8.26 mg/L, accounts for 7.0–36.2% of total carbon in 2003 (Hu and Fan, 2008). The highest concentrations of dis-

solved carbon dioxide, hydrogen carbonate carbon are found in the northern and western parts of the lake, where the main rivers have their inflows, while the lower concentrations of dissolved carbon dioxide, hydrogen carbonate carbon are in the eastern part of the lake and in Dongtaihu Bay, where the outflowing rivers are located (Hu and Fan, 2008). The dissolved organic carbon is highest in the north-western part, Meiliang Bay, and in the southern part during spring, in the northern part of the lake during summer, in north western part during autumn and winter, while it is lowest mainly in the eastern part where there is a significant coverage of macroplant vegetation (Hu and Fan, 2008). The CO2 flux from the water to the atmosphere shows significant diurnal variations not only in the northern part but also in the southern part of the lake. It is negative from 8:00 to 17:00 or 18:00, and positive from 19:00 to 8:00 next day (Zhang et al., 2004; Li et al., 2005; Chen et al., 2006). The respiration and photosynthesis of fresh water ecosystem have obviously great influence on the exchange of CO2 between the water and the atmosphere. There are four different pathways for the exchange of CO2 between lake water and the atmosphere. The first is the turbulent diffusion at the water–air interface, the second is the transfer of carbon dioxide in air bubble, and the third is the photosynthetic carbon fixation by macroplant such as aquatic floating plants, leaf floating plants and by phytoplankton at the surface. The last pathway is the carbon release due to the respirations of the macroplants, phytoplankton, zooplankton, fish and the microorganism. The organic carbon has two possible sources, autogenetic or allochthonous (Wetzel and Likens, 1991). The allochthonous organic carbon input to Lake Taihu includes:

H. Weiping et al. / Ecological Modelling 222 (2011) 2973–2991

Input of carbon

Output of carbon

air CO2

HCO3

C

Phytoplankton carbon

Zooplankton carbon

Fish carbon

C Macroplants carbon

Abiosis organic carbon CO3

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C

Inorganic carbon in sediments

Organic carbon in pore water

Organic carbon in sediments

Inorganic carbon in pore water

Fig. 2. Conceptual model of the carbon cycling in Lake Taihu, China.

(1) the dissolved organic carbon in the drainage water originated from the decomposition of terrestrial vegetation in the drainage area; (2) organic carbon in the detritus of terrestrial vegetation directly transported to the lake by the wind; (3) organic carbon in man-made organic waste in the drainage water; and, (4) organic carbon from sediment by resuspension.

(3) secondary consumers, fish and, (4) bacteria to account for the entire flow of carbon in the food web of Lake Taihu. According to the presentation of the relevant processes, the carbon cycling of Lake Taihu is shown in Fig. 2. 3. Equations of the carbon cycling in Lake Taihu

The autochthonous organic matter in shallow lake such as Lake Taihu is due to planktonic production and phytosynthesis of macroplants. The allochthonous inorganic carbon sources of Lake Taihu include: (1) the dissolved and particulate carbon originated from the decomposition of terrestrial vegetation and detritus transported to the lake by runoff, (2) carbon dioxide diffusion at the water–air interface; (3) inorganic carbon from sediments due to resuspension and diffusion across the water–sediments interface (Hu and Fan, 2008). The sources of the autochthonous inorganic carbon comprise: (1) the inorganic carbon originated from decomposition of detrital organic carbon, (2) the inorganic carbon originated from the mineralization of organic carbon in sediments. The output of organic carbons includes: (1) outflow of organic carbon via the rivers, (2) mineralization of organic carbon in the lake, and, (3) the organic carbon output due to fishing. Inorganic carbon output includes: (1) outflow of inorganic carbon via rivers, (2) carbon dioxide transfer at air–water interface. Thus, the model to describe carbon cycling in Lake Taihu should include all the above mentioned biological and chemical transfer processes and the carbon transportation processes by advection and diffusion. Consequently, the model should include: (1) the producers, phytoplankton and macroplants, (2) primary consumers, zooplankton,

3.1. The transportation equations for dissolved and particulate carbon in Lake Taihu Like the cyclings of nutrient nitrogen and phosphorus (Hu et al., 2006), the cycling of carbon in forms of dissolved and particulate carbon in Lake Taihu can be expressed by the advection–diffusion equation plus the terms of sources or sinks (Hu et al., 2002; Dong and Wang, 1994; Pu and Wang, 2000)

 w0  ∂C ∂C ∂C ∂C  +u +v + w× − H ∂t ∂x ∂y ∂ 

= Eh

∂2 C ∂2 C + ∂x2 ∂y2



+

1 ∂ H 2 ∂



Ez

∂C ∂

 + S − R + ε(c)

(1)

where C represents concentration of dissolved CO2 (CO2 in mg/L), HCO3 − carbon (HCO in mg/L), CO3 2− carbon(CO3 in mg/L), phytoplankton carbon (AC in mg/L), zooplankton carbon (CZ in mg/L), abiotic organic carbon (OC in mg/L), x (in cm), y (in cm) and  represent the coordinate in eastern, northern direction and vertical direction, respectively, t is time (in s), H (in cm) is the water depth, w0 (in cm/s) is the settling velocity of algae, inorganic and organic carbon, w* (in cm/s) is the water velocity in the  direction, Eh (in cm2 /s) is the horizontal diffusion coefficient, EZ (in cm2 /s) is the vertical diffusion coefficient, S and R (mg/L/s) are the sources and sink term of the advection and diffusion respectively, ε(c) is a small deviation generated from the transfer of the x, y, z coordinate system to the x, y,  coordinate system. The details of the coordinate system transfer have been described by Hu et al., 2006. Eq. (1) could also be used to express the transportation of hydrogen ions without the sink and source term. The transfers between different form of inorganic carbon and the concomitant variation of hydrogen iron (HI, in unit of mg/L) are excluded in Eq. (1), which will be discussed below. ε(c) could be expressed as



ε(c) = Eh

−2

2 ∂2 c H ∂x∂

∂c 1 ∂H ∂ H 2 ∂x





∂h ∂H − ∂x ∂x

∂H ∂h − ∂x ∂x



 +

+

∂2 c 1 ∂ 2 H 2

∂c 1 ∂ H





∂h ∂H − ∂x ∂x

∂2 H ∂2 h − 2 2 ∂x ∂x



2

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H. Weiping et al. / Ecological Modelling 222 (2011) 2973–2991

Table 1 Sink terms of Eq. (1) for the state variable dissolved carbon dioxide, phytoplankton carbon, zooplankton carbon, abiotic organic carbon. State variable

Unit

Symbol

Context

Expression

Dissolved carbon dioxide

mg/L

CO2

Uptaken by phytoplankton Fixation by macroplants

(I/(I + 300)) × Atk × (CO2 /(CO2 + Acs)) × ((alcmax − (CA/BP))/(alcmax − alcmin)) × BP (I/(I + 500)) × AStk × (CO2 /(CO2 + Ascs)) × ((SCmax − SC/SB)/(SCmax − SCmin)) × (SB/HeightSB ) × IfSB (T) where

0

T < T minSB (T − T minSB )/(TopSB − T minSB ) T minSB ≤ T ≤ TopSB e−SB |T −TopSB | T > TopSB GRAZal-ZOO × BZ(BP − KBPmin )/(BP + KBPhs ) × (CA/BP)

fSB (T ) = Phytoplankton carbon

mg/L

Zooplankton carbon

mg/L

Abiosis organic carbon

+

2 ∂2 c H ∂y∂

−2

CA



CZ

mg/L

∂h ∂H − ∂y ∂y

∂c 1 ∂H ∂ H 2 ∂y



Grazed by zooplankton Mortality Respiration

OC

 +

∂H ∂h − ∂y ∂y

Predation n by fish

Deathal × fd-al (T) × CA AVCF × BP × fa (T) where, RC × (CA/(BP

−×|alcmax)) e al T −Topal | T ≤ Topal fa (T ) = 1.0 T > Topal GRAZZOO-FISH × BF × (BZ − KBZmin )/(BZ + KBZhs ) × CZ/BZ

Mortality Respiration

DeathZOO × BZ × CZ ZLC × (CZ/(BZ × zlcmax))ZVCF × BZ

Organic carbon decomposition Grazed by zooplankton

k20 exp(Ca (T − 20)) × OC

∂2 c 1 ∂ 2 H 2

 +



∂c 1 ∂ H

∂h ∂H − ∂y ∂y



GRAZBD-ZOO × BZ × ((BD − KBDmin )/(BD + KBDhs ) × (OC/BD)

2

∂2 H ∂2 h − 2 2 ∂y ∂y

 (2)

The sink and source terms of the Eq. (1) for different state variables of the model are presented in Tables 1 and 2. The parameters applied in Tables 1 and 2 are listed in Table 3. Compared with biological and physical processes, the transfer between different speciations of carbonate system is rapid. When the chemical equilibrium of the carbonate system is affected by biological processes, such as the phytoplankton and macroplant uptake of carbon dioxide and the release of carbon dioxide due to respiration of the organism, and by physical processes, the chemical equilibrium will be re-established very rapidly. Thus, the carbonate system is considered always to be in chemical equilibrium. It implies that the transfer processes can be excluded from the

sinks and sources in control Eq. (1) for the state variables hydrogen carbonate carbon, carbonate carbon, dissolved carbon dioxide and hydrogen ions. The determination of the concentrations of hydrogen carbonate carbon, carbonate carbon, dissolved carbon dioxide and hydrogen ions are made in two steps in the model. The first step is calculations of the concentrations of the hydrogen carbonate carbon, carbonate carbon, dissolved carbon dioxide and hydrogen ions by use of Eq. (1) based on biological and physical processes. The second step is to calculate the new chemical equilibrium of the carbonate system. According to Wang (2000), the chemical equilibrium is based o the following processes: CO2 + H2 O = H2 CO3 = H+ + HCO3 − = 2H+ + CO3 2−

(3)

The concentrations in mol/L of dissolved CO2 , hydrogen carbonate ions, carbonate ions, and hydrogen ions are denoted [CO2 ]0 , [HCO3 − ]0 , [CO3 2− ]0 , [H+ ]0 respectively before the carbonate system is affected by physical and biological processes, while the concentrations of dissolved CO2 , hydrogen carbonate ions, carbonate ions, and hydrogen ions are denoted by [CO2 ]t , [HCO3 − ]t , [CO3 2− ]t , [H+ ],

Table 2 Source terms of Eq. (1) for state variable dissolved carbon dioxide, phytoplankton carbon, zooplankton carbon, abiotic organic carbon. State variable

Symbol

Context

Expression

Dissolved carbon dioxide

CO2

Organic carbon decomposition phytoplankton respiration

Zooplankton respiration Fish respiration

k20 exp(Ca (T − 20)) × OC AVCF RC × (CA/(BP × BP × fa (T)

−×|alcmax)) e al T −Topal | T ≤ Topal fa (T ) = 1.0 T > Topal SVCF PSRC = RSC

× (SC/(BP × SCmax)) × (SB/HeightSB ) × fS (T) 1 T > 38 fS (T ) = e−0.1(38−T ) T ≤ 38 ZLC × (CZ/(BZ × zlcmax))ZVCF × BZ FLC × (CF/(BF × Flcmax))FVCF × (BF/H)

Macrophyte respiration

Phytoplankton carbon

CA

Uptake by phytosynthesis

(I/(I + 300)) × Atk × (CO2 /(CO2 + Acs)) × ((alcmax − CA/BP)/(alcmax − alcmin) × BP

Zooplankton carbon

CZ

Grazing on detritus Grazing on phytoplankton

GRAZBD-ZOO × BZ × ((BD − KBDmin )/(BD + KBDhs )) × (OC/BD) GRAZal-ZOO × RZOO × BZ × ((BP − KBPmin )/(BP + KBPhs ) × (CA/BP)

Organic carbon

OC

Zooplankton mortality Fish mortality Phytoplankton mortality Undigested phytoplankton grazed by zooplankton Undigested zooplankton preyed upon by fish

DeathZOO × BZ × CZ DeathFISH × CF Deathal × fd-al (T) × CA GRAZal-ZOO × (1 − RZOO ) × BZ × (BP − KBPmin )/(BP + KBPhs ) GRAZZOO-FISH × (1 − RFISH ) × BF × (BZ − KBZmin )/(BZ + KBZhs ) × (CZ/BZ)

H. Weiping et al. / Ecological Modelling 222 (2011) 2973–2991

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Table 3 Parameters of the model. Symbol

Description

Value

Unit

Note

Acs

Half saturation constant of carbon dioxide assimilated by phytoplankton via photosynthesis Maximum ratio of carbon to biomass in phytoplankton Minimum ratio of carbon to biomass in phytoplankton Half saturation constant of carbon dioxide assimilated by macroplants via photosynthesis Uptake velocity of macroplants for carbon dioxide due to its photosynthesis Uptake velocity of phytoplankton for carbon dioxide due to its photosynthesis The power coefficient of influence of the ratio of carbon to biomass in phytoplankton on the releasing of carbon dioxide Influence coefficient of water temperature on the decomposition of abiotic organic carbon The environmental capacity of macroplants biomass Death rate of phytoplankton Death rate of fish (including excretion and respiration) Mortality rate of zooplankton Extension coefficient of macroplants Rate of respiration of fish Maximum ratio of carbon to biomass in fish Upward velocity of phytoplankton in case of no wind The power coefficient of influence of the ratio of carbon to biomass in fish on the releasing of carbon dioxide Rate of zooplankton grazing on detritus Predation rate of fish on macroplants Prey rate of fish on zooplankton The intrinsic growth rate of macroplants Velocity of the decomposition of abiosis organic carbon at temperature Half saturation constant of detritus grazed by zooplankton Minimum concentration of detritus grazed by zooplankton The half saturation constant of zooplankton concentration of fish for preying upon phytoplankton The minimum zooplankton concentration of phytoplankton concentration available to the prey of zooplankton Half saturation constant of macroplants preyed on by fish The minimum density of macroplants for fish preying on Rate of phytoplankton respiration Food coefficient for fish feeding on zooplankton Rate of the macroplants respiration Food efficiency for fish feeding on macroplants Food coefficient of phytoplankton grazed by zooplankton Maximum ratio of carbon to biomass in macroplants Minimum ratio of carbon to biomass in macroplants Diffusion rate of inorganic carbon from pore water to lake water Influence factor of dissolved oxygen on the releasing of carbon dioxide from sediments Influence factor of dissolved oxygen on the releasing of organic carbon from sediments Velocity of melting of the sedimentary organic carbon The power coefficient of influence of the ratio of carbon to biomass in macroplants on the releasing of carbon dioxide Minimum water temperature for macroplants survival The optimum water temperature that the phytoplankton can grow The optimum water temperature for macroplant to grow Velocity of the decomposition of organic carbon in pore water Velocity of the decomposition of organic carbon in sediments Settling rate of phytoplankton Settling rate of inorganic carbon Settling rate of abiotic organic carbon Rate of respiration of zooplankton Maximum ratio of carbon to biomass in zooplankton The power coefficient of influence of the ratio of carbon to biomass in zooplankton on the releasing of carbon dioxide The influence coefficient of water temperature on phytoplankton respiration Influence coefficient of water temperature on the decomposition of organic carbon in sediments and pore water The influence coefficient of water temperature on macroplant Diffusion velocity of organic carbon in pore water to overlay water Transfer rate of sedimentary inorganic carbon to pore water Light Water temperature Grazing rate of zooplankton on phytoplankton The transfer constant for density to height of macroplants

0.05

mg/L

Calibration

0.45 0.28 0.2

gC/Gd W gC/Gd W mg/L

Calibration Calibration Calibration

1

d−1

Calibration

−1

Alcmax Alcmin Ascs AStk Atk AVCF Ca CSB Deathal DeathFISH DeathZOO ESB FLC Flcmax Float FVCF GRAZBD-ZOO GrazSB-FISH GRAZZOO-FISH GrowthSB k20 KBDhs KBDmin KBZhs KBZmin KSBhs KSBmin RC RFISH RSC RSF RZOO SCmax SCmin Sedicwrv SeDoIcvt SeDoOcvt Sedroc SVCF TminSB Topal TopSB VPrex VSrex wBP wIC wOC ZLC zlcmax ZVCF  al S  SB Sedocwrv sedric I T GRAZal-ZOO HeightSB

1.5

d

Calibration

2



Calibration

0.0665



C−1

Calibration 2

2 0.11 0.003 0.04 1000 0.00015 0.45 0.000008 2

kg/m d−1 d−1 L/mg/d s/cm2 d−1 gc/gb cm/s –

Calibration Calibration Calibration Calibration Calibration Calibration Calibration Calibration Calibration

0.09 0.1 0.1 0.16 0.0202

d−1 d−1 d−1 d−1 d−1

Calibration Calibration Calibration Calibration Calibration

2 0.1 1

mg/L mg/L mg/L

Calibration Calibration Calibration

0.1

mg/L

Calibration 2

0.05 0.001 0.4 0.71 0.018 0.1 0.7 0.5 0.0095 0.00001 0.5

kg/m kg/m2 d−1 g/g d−1 gF/gS g/g gC/Gd W gC/Gd W m/d –

Calibration Calibration Calibration Calibration Calibration Calibration Calibration Calibration Calibration Calibration Calibration

0.5



Calibration −1

0.00001 2

d –

Calibration Calibration

5 28 20 1.84 × 10−6 1.84 × 10−6 0.000004 0.0009 0.000009 0.002 0.4 2



C C ◦ C d−1 d−1 cm/s cm/s cm/s d−1 gC/Gd W –

Calibration Calibration Calibration Calibration Calibration Calibration Calibration Calibration Calibration Calibration Calibration

0.03

1/◦ C

Calibration

0.0665



Calibration

0.0023 0.00001 0.000001 – – 0 1

1/◦ C d−1 d−1 ␮E/cm2 ◦ C d−1 m3 /kg



C−1

Calibration Calibration Calibration Forcing function observed Forcing function observed Hu et al., 2006 Hu et al. (2006)

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H. Weiping et al. / Ecological Modelling 222 (2011) 2973–2991

Table 3 (Continued) Symbol

Description

Value

Unit

Note

KBPhs

The phytoplankton concentration half saturation constant for zooplankton to prey upon phytoplankton The minimum phytoplankton concentration available to the zooplankton’s prey upon phytoplankton Concentration of detritus Biomass of fish Biomass of phytoplankton Zooplankton biomass Concentration of carbon in fish Carbonate carbon concentration Hydrogen carbonate carbon concentration Concentration of hydrogen iron Biomass of macroplants Density of carbon in form of macroplants

2

mg/L

Hu et al. (2006)

0.1

mg/L

Hu et al. (2006)

– – – – – – – – – –

mg/L mg/L mg/L mg/L mg/L mg/L mg/L mg/L kg/m2 kg/m2

State variable State variable State variable State variable State variable State variable State variable State variable State variable State variable

KBPmin BD BF BP BZ CF CO3 HCO HI SB SC

respectively, at the new chemical equilibrium. The following equations are valid at chemical equilibrium: [HCO3 − ]t [H+ ]t = K1 [H2 CO3 ]t [CO3 2− ]t , [H+ ]t [HCO3 − ]t

(4)

= K2

(5)

2− [H+ ]t = [H+ ]0 + ([CO2− 3 ]t − [CO3 ]0 ) − ([H2 CO3 ]t − [H2 CO3 ]0 )

(6)

[H2 CO3 ]t + ([CO3 2− ]t + [HCO3 − ]t ) = ([H2 CO3 ]0 + [CO3 2− ]0 + [HCO3 − ]0 )

(7)

where K1 and K2 are the first and the second dissociation constants of carbonic acid. They are functions of the temperature by the following expressions: K1 = 10(0.0057T −6.5269)

(8)

(0.009T −10.584)

K2 = 10

(9)

There are four Eqs. (4)–(7) for determination of four unknown variables [CO2 ]t , [HCO3 − ]t , [CO3 2− ]t , [H+ ]t . The boundary conditions in vertical direction at the water–air interface for the state variables AC, CZ, CO3 , OC, HCO, HI, CO2 , corresponding to  = 1, are: −EZ ∂AC + (F − wBP )AC = 0 H ∂

(10)

−EZ ∂CZ = 0, H ∂

(11)

∂CO3 −EZ − wIC × CO3 = 0 × H ∂

(12)

∂OC −EZ − wOC × OC = 0 × H ∂

(13)

−EZ ∂HCO =0 H ∂

(14)

−EZ ∂HI =0 H ∂

(15)

∂CO2 −EZ × = KT (CO2 − [CO2 ]air ) H ∂

(16)

where F is the upward rate of phytoplankton. F is dependent on the wind speed by the following expression: F = Fa (1.2 × 10−3 ×



U 2 + V 2 + Float

(25)

where U, V describe the eastern component and northern component, respectively, of wind speed. Fa is a constant which is

0.00153. Float is upward velocity of phytoplankton in case of no wind.  in Eq. (16) is the rate coefficient of carbon dioxide transfer between water and carbon dioxide, KT is the transfer velocity of carbon dioxide at the water–air interface at the temperature T. [CO2 ]air is the concentration of CO2 in water at equilibrium with the carbon dioxide in the atmosphere according to Fan et al. (2003). CO2 in the concentration of CO2 in water. It can be calculated from the observations of alkalinity, pH and water temperature (Fan et al., 2005; Wang, 2000). The left side of Eq. (16), the transfer velocity of carbon dioxide, can be determined by the observations of the CO2 and [CO2 ]air . Table 4 shows the transfer rate of carbon dioxide at the water–atmosphere interface in different parts of Lake Taihu. The transfer rate increases with the wind speed. The maximum, minimum and mean of the transfer rate are 0.762, 0.012, 0.23 m/d, respectively, in the centre of the lake, 1.344, 0.035, 0.565 m/d, respectively, in Dongtaihu Bay, 5.98, 0.091, 2.43 m/d, respectively, in Meilianghu Bay, and 5.34, 0.254, 1.763 m/d in the littoral zone. KT in Eq. (16) is not a constant, but a function of the wind speed, which can be expressed by Schmidt’s number, as proposed by Liss and Merlivat (1986), Tans et al. (1990), and Wanninkhov (1992). Thus the following equations are proposed to determine the transfer rate of carbon dioxide as function of the wind speed:



KT =

0.17 × U10 (600/Sc)

2.0/3.0

(2.85 × U10 − 9.65)(600/Sc)

1.0/2.0

U10 < 3.6m/s : U10 > 3.6m/s

(17)

where U10 represents the wind speed at an altitude of 10 m above water surface, Sc is Schmith’s number. The boundary conditions at the sediments-water interface, i.e. in the case of  = 0 are: −EZ ∂AC + (F − wBP ) × AC = −wBP × AC H ∂

(18)

∂CO3 −EZ × − wIC × CO3 = −wIC × CO3 H ∂

(19)

∂CO2 EZ × = Sedicwr v × (1000 × ICw − CO2 (−h)) H ∂ ×



SB T + 273 × 1.0 − 280 CSB



× SeDoIcvt,

(20)

∂CZ −EZ × =0 H ∂

(21)

∂HCO3 −EZ =0 × H ∂

(22)

∂HI −EZ × =0 H ∂

(23)

H. Weiping et al. / Ecological Modelling 222 (2011) 2973–2991

2979

Table 4 Transfer rate of carbon dioxide in Lake Taihu. Location

Wind speed (m/s)

Water temperature (◦ C)

Transfer rate (m/d)

Location

Wind speed (m/s)

Water temperature (◦ C)

Transfer rate (m/d)

Dongtaihu bay Dongtaihu bay Dongtaihu bay Dongtaihu bay Dongtaihu bay Dongtaihu bay Dongtaihu bay Dongtaihu bay Dongtaihu bay Littoral zone Littoral zone Littoral zone Littoral zone Littoral zone Littoral zone Littoral zone Meilianghu Bay Meilianghu Bay Meilianghu Bay

3.0 4.0 4.1 3.1 1.2 2.2 3.3 4.1 2.7 6.8 8.7 6.9 6.1 5.0 4.1 2.8 4.0 4.8 1.6

17.4 17.4 17.4 17.3 17.1 16.9 16.7 16.7 16.8 14.1 13.9 13.9 14.7 15.8 16.9 16.9 15.9 16.2 16.1

0.889 0.370 0.035 0.329 0.180 0.896 1.344 0.477 0.566 0.012 0.266 0.762 0.320 0.026 0.068 0.122 3.979 4.272 0.091

Meilianghu Bay Meilianghu Bay Meilianghu Bay Meilianghu Bay Meilianghu Bay Meilianghu Bay Meilianghu Bay Meilianghu Bay Meilianghu Bay Meilianghu Bay Littoral zone Littoral zone Littoral zone Littoral zone Littoral zone Littoral zone Littoral zone Littoral zone Littoral zone

1.8 1.8 0.7 3.9 3.1 4.0 2.2 3.1 2.6 2.6 4.3 1.8 1.7 2.7 5.0 3.3 3.3 4.0 6.3

15.8 16.0 15.9 15.8 17.3 17.3 17.1 16.9 16.9 17.2 31.2 33.0 34.8 34.2 33.7 33.0 33.5 35.6 36.8

1.633 3.512 0.213 1.658 3.689 0.672 0.605 1.218 5.977 4.016 1.173 2.703 2.370 0.309 0.254 0.616 0.419 2.677 5.347

EZ ∂OC × = Sedocwr v × (1000 × OCw − OC(−h)) H ∂ ×



T + 273 SB × 1.0 − 280 CSB



× SeDoOcvt,

and from macroplants:

(24)

where contents of Sedocwrv, Sedicwrv, SeDoIcvt, SeDoOcvt are listed in Table 3. The horizontal boundary conditions of the model could be expressed as, ∂(V × C) =0 ∂n

(26)

which means that matter flux at the boundary is 0. V is the rate of the water current, while C represents state variables such as dissolved carbon dioxide (CO2 ), hydrogen carbonate carbon (HCO), carbonate carbon (CO3 ), abiotic organic carbon (OC), phytoplankton (AC), zooplankton (ZC) and hydrogen ion. The boundary condition at the river inflow is expressed as C = C0

(27)

which indicates that the concentration at the river inflow is equal to the concentration in the river water. The boundary condition at the river outflow is: ∂C =0 ∂n

(28)

which means that there are no gradient concentrations at the boundary.

According to Hu et al. (2006), it is assumed that fish is evenly distributed in vertical direction. Thus, the equation for determination of the fish carbon in a water cell is:

1 H

3.3. Macroplant carbon differential equation According to the conceptual model, the changes of macroplant carbon are determined by the uptake of carbon dioxide by phytosynthesis, releasing of carbon dioxide by respiration, mortality, and predation by fish. The increase of macroplants carbon is expressed like the macroplant phosphorus in (Hu et al., 2006) with P replaced by C: ∂SC = ESB ∂t

−h

CZ × BF(BZ − KBZm ) dz BZ(BZ + KBZhs )



∂2 SC ∂2 SC + 2 ∂x ∂y2



(29)

where GrowthSB is the growth rate which is dependent on the water temperature, the solar radiation, the nitrogen and phosphorus levels in macroplants (Hu et al., 2006). The first right term of Eq. (32) expresses the horizontal increase of macroplants. The second right term of Eq. (32) is the uptake of carbon dioxide due to macroplant phytosynthesis: it is expressed as

HeightSB

SUC = GrazZOO-FISH × Rfish

(31)

The second term of the right of Eq. (29) is the fish carbon loss due to fish respiration, which is listed in Table 2 in the source term of the dissolved carbon dioxide. The loss of carbon due to fish mortality is the third right term in Eq. (29), which has already been described in Table 2 as the source of abiotic organic carbon. The fourth right term in Eq. (29) is the loss of carbon due to fishery. Here Fishf is a parameter which accounts the fishery pressure. As Eq. (29) does not include the state variable space derivatives, no boundary limitation or boundary condition is needed to obtain a solution of the equation.

The first right term SCF of Eq. (29) is the source term. It is composed of the carbon from zooplankton:



SC(SB − KSBmin ) SB(SB + KSBhs )

+ SUC − GrowthSB × SB/CSB × SC − CBFSB − Psrc × HeightSB (32)

3.2. fish carbon differential equation

∂CF = SCF − Frc − CFM − Fishf × CF ∂t

GrazSB−fish × BF × RSF ×

(30)

f (I) × AStk ×

sc max −SC/SB CO2 × CO2 + Ascs sc max −sc min

0

× SB/HeightSB × fSB (T )dz

(33)

H. Weiping et al. / Ecological Modelling 222 (2011) 2973–2991

(34)

(35)

Equation

(dICs /dt) = wIC × CO3 + VSrex es (T −20) × OCs − sedric × ICs

(dICw /dt) = sedric × ICs − Sedicwr v × (ICw − ((CO2 (−h)/1000)) × ((T + 273)/280)) × ((1.0 − (SB/CSB)) × SeDoIcvt + VPrex es (T −20) × OCw

(dOCs /dt) = wBP × AC × wOC × OC − VSrex es (T −20) × OCs − sedroc × OCs + GrowthSB × SB/CSB × SC + GrazSB−FISH (1 − RSF )((BF × SC)/SB)) × (SB − KSBmin /(SB + KSBhs )) (36)

(dOCw /dt) = sedroc × OCs − Sedocwr v × (OCw − (OC/1000)) × ((T + 273)/280)) × (1.0 − (SB/CSB)) × SeDoOcvt − VPrex es (T −20) × OCw

Unit

mg/cm2

mg/cm2

mg/cm2

mg/cm2

Symbol

ICs

ICw

OCs

OCw

Inorganic carbon in sediments Dissolved inorganic carbon in pore water Content of organic carbon in sediments Dissolved organic carbon in pore water

CBFSB = GrazSB-FISH × BF ×

State variable

The third right term is the loss of macroplant carbon due to macroplant mortality. The fourth right term covers the macroplants grazed by fish, which can be described by the following formula: SC(SB − KSBmin ) SB(SB + KSBhs )

The fifth term is the loss of macroplant carbon by respiration, which has been listed in Table 2. The parameters in Eq. (32) are listed in Table 3.

The sediments pools of different forms of carbon are extremely important components for the lacustrine carbon cycling. According to Fig. 1, there are four different pools of carbon in the sediment: inorganic carbon and organic carbon in sediment, dissolved organic carbon and inorganic carbon in pore water. The differential equations for the four pools are listed in Table 5 with the parameters listed in Table 3. The first right term of Eq. (34) is the settling of inorganic carbon, while the second right term and the third term are the decomposition of organic carbon in sediments and the transfer of inorganic carbon from the sediment to the pore water. The first right term of Eq. (35) is the same as the third term of Eq. (34). The second right term of Eq. (35) is the diffusion of the inorganic carbon in pore water to the lake water and the third term is the decomposition of organic carbon in pore water. The first and the second right terms of Eq. (36) are the settlings of algae and organic carbon respectively. The third right term is the same as the second right term in Eq. (34). The fourth term of Eq. (36) is the diffluence of organic carbon in sediments to pore water. The fifth term is the mortality of macroplant. The first right term of Eq. (37) is the same as the fourth right term of Eq. (36). The second term of Eq. (37) is the diffusion of the organic carbon in pore water to the lake water.

3.5. Numerical calculation of the model The staggered-grid finite-difference method adopted to consider the water current and conservative matter transportation presented by Hu et al. (1998, 2006) is applied to the model for carbon cycling in Lake Taihu. The East-west axis and North-South axis for Lake Taihu are both divided into 68 sections, with each section 1 km wide and 1 km long. The water column is divided into five equal layers. The details of the discretization of the differential equations are presented in (Hu et al., 1998).

3.6. Differential equations for other state variables From the above differential equations for carbon cycling in Lake Taihu have as variables u, v, w, and BP, SB, BZ, BF. These variables are related to , NP, PP, NZ, PZ, NF, PF, BD, ND, PD, SN, SP, NS, PE, PW, DO. These symbols describe water surface displacement, nitrogen in phytoplankton, phosphorus in phytoplankton, nitrogen in zooplankton, phosphorus in zooplankton, nitrogen in fish, phosphorus in fish, content of detritus in water, detrital nitrogen in, detrital phosphorus, nitrogen in macroplant (submerged plant), phosphorus in macroplant, exchangeable nitrogen in sediment, exchangeable phosphorus in sediments, soluble phosphorus in pore water, dissolved oxygen, respectively. The equations and the calculation methodology have been described in Hu et al. (2006) and the details can be obtained from the reference. They are therefore not included in this paper.

Table 5 Differential equations of inorganic carbon, organic carbon in sediments, dissolved organic carbon and inorganic carbon in pore water in sediments.

3.4. Carbon in the sediments and pore water

(37)

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H. Weiping et al. / Ecological Modelling 222 (2011) 2973–2991

3000

30 20

17-Nov

17-Oct

17-Sep

17-Aug

17-Jul

17-Jun

17-May

10 0

17-Nov

17-Oct

17-Sep

17-Aug

17-Jul

17-Jun

17-May

17-Apr

17-Mar

500

40

17-Apr

1000

50

17-Mar

-3

1500

17-Feb

2

PAR (μE/cm )

2000

60

17-Feb

Precipitation (10 m)

70

2500

0

2981

Date

Date Fig. 3. Photosynthetic solar radiation (PAR) in Lake Taihu Basin 2003. (data source: Taihu Laboratory for Lake Ecosystem Research, Chinese Academy of Sciences).

Fig. 5. Precipitation in Lake Taihu Basin in 2003. (data source: Taihu Laboratory for Lake Ecosystem Research, Chinese Academy of Sciences).

4. Model calibration

4.4. The initial values of the state variables

4.1. Time span

The water current and the water surface displacement at all grid points were initially set to be zero. The initial values of phosphate phosphorus, chlorophyll a, nitrate nitrogen, nitrite nitrogen, ammonia nitrogen, dissolved oxygen, TN, TP and zooplankton at grid points were determined by the following expression:

1.0/

i

4.5. Key parameters for the numerical calculations The time steps for water current and water surface displace calculation was set to be 120 s, while the time steps for calculations of matter transport (such as nitrogen, phosphorus, dissolved oxygen, biomass, etc.) were set to be 1200s. The horizontal space steps in

Date Fig. 4. Water temperature in Lake Taihu in 2003. (data source: Taihu Laboratory for Lake Ecosystem Research, Chinese Academy of Sciences).

20 16 12 8

17-Nov

17-Oct

17-Sep

17-Aug

0

17-Jul

4

17-Jun

-3

Evaporation (10 m)

17-Nov

17-Oct

17-Sep

17-Aug

17-Jul

17-Jun

17-May

17-Apr

17-Mar

40 35 30 25 20 15 10 5 0

17-Feb

Water temperature(ºC)

Photosynthetical radiation increased generally from the winter to summer in 2003, but it did not increased as significantly as in 1997 (Fig. 3). Water temperature increased from February 17 to August 4 2003. It reached the highest temperature of 36.5 ◦ C on August 4, which was 3.5 ◦ C higher than the maximum water temperature in 1997. It decreased after August 4 and faster than it increased before August 4 (Fig. 4). There were four large-scale rainfalls during the calibration period (Fig. 5). The total precipitation was 833 mm, more than the low precipitation in 1978 (722.6 mm), but less than the high precipitation in 1977 (1309.4 mm). The maximum daily precipitation was 60.4 mm/d, which occurred on June 29. The evaporation in the period was very stable. The total evaporation was 847.72 mm during the calibration period, which is slightly more than the precipitation (Fig. 6).

j

17-May

4.3. Physical feature during calibration time

(38)

where C0 is the concentration at a grid point (x, y) at initial time, x, y are the coordinates of grid point, i and j is the serial number of the monitoring station according to Taihu Laboratory for Lake Ecosystem Research.(xi , yi ) are the coordinates at the monitoring station i, C0 (xi , yi ) is the monitoring concentration at site i. The dissolved carbon dioxide, hydrogen carbonate carbon, carbonate carbon, abiotic organic carbon at grid points were also determined by Eq. (38) according to the values of dissolved carbon dioxide, hydrogen carbonate carbon, carbonate carbon, abiotic organic carbon at sampling sites respectively. They were obtained from the monitoring results of the water temperature, pH and alkalinity (Fan et al., 2003). As the carbon and nutrients in sediments are not the focus of this research, and as they change relatively slow, the initial value of the sediment state variables were estimated from the data in 1997.

17-Feb

The data set used for the model calibration holds the same indexes as that for the model published by Hu et al. (2006), except that time period in this case is from 17 February 2003 to 17 December 2003. During the period, the different forms of carbon in the influent rivers, effluent rivers, and in the lake were observed.

× Ci0 (xi , yi )

(x − xj )2 + (y − yj )2

17-Apr

4.2. Data sets

 1.0/ (x − x )2 + (y − y )2 i C0 =  i 

17-Mar

For the calibration and validation of the model the period from 17 February 2003 to 17 December 2003 was applied. The data set is of good quality and covers almost 1-year.

Date

Fig. 6. Evaporation in Lake Taihu in 2003. (data source: Taihu Laboratory for Lake Ecosystem Research, Chinese Academy of Sciences).

H. Weiping et al. / Ecological Modelling 222 (2011) 2973–2991 35

30

30

25

Biocarbonate carbon (mg/L)

Biocarbonate carbon (mg/L)

2982

25 20 15 10 5

1#

0

2.17

20 15 10 5

2#

0

3.15

4.16

5.15

6.15

7.15

8.15

9.15 10.15 11.15

2.17

3.15

4.16

5.15

30

30

25

25

20 15 10 5 0 2.17

3# 4.16

5.15

6.15

7.15

8.15

9.15 10.15 11.15

8.15

9.15 10.15 11.15

8.15

9.15 10.15 11.15

8.15

9.15 10.15 11.15

15 10 5

4# 2.17

9.15 10.15 11.15

3.15

4.16

5.15

6.15

7.15

Date 35 30

25

Biocarbonate carbon (mg/L)

Biocarbonate carbon (mg/L)

8.15

0

3.15

30

20 15 10

5#

0

2.17

7.15

20

Date

5

6.15

Date

Biocarbonate carbon (mg/L)

Biocarbonate carbon (mg/L)

Date

25 20 15 10

6#

5 0

3.15

4.16

5.15

6.15

7.15

8.15

2.17

9.15 10.15 11.15

3.15

4.16

5.15

Date

6.15

7.15

Date 35

25

Biocarbonate carbon (mg/L)

Biocarbonate carbon (mg/L)

30 20

15

10

5

7#

0

2.17

25 20 15 10

8#

5 0

3.15

4.16

5.15

6.15

7.15

8.15

9.15 10.15 11.15

Date

2.17

3.15

4.16

5.15

6.15

7.15

Date

Fig. 7. Comparison of calculated bicarbonate carbon and observed bicarbonate carbon in the period from February to 7 December 2003.

X-direction and Y-direction were 1 km and the step in -direction is 0.2, i.e., the water column is divided into five layers. The horizontal and vertical coefficients of diffusion and viscosity were chosen to be 50,000 cm2 /s and 4.0 cm2 /s, respectively. Wind drag coeffi-

cient was 0.0013 cm2 /s. When the model calculations are made by the ThinkPad X31 IBM notebook PC, it takes 9 h for the calibration. The values of parameters obtained for the carbon cycle model are summarized in Table 3.

H. Weiping et al. / Ecological Modelling 222 (2011) 2973–2991

0.50

1#

Carbonate carbon (mg/L)

Carbonate carbon (mg/L)

0.70 0.60 0.50 0.40 0.30 0.20 0.10

2# 0.40 0.30 0.20 0.10 0.00

0.00 2.17 3.15 4.16 5.15 6.15 7.15 8.15 9.15 10.15 11.15

2.17 3.15 4.16 5.15 6.15 7.15 8.15 9.15 10.15 11.15

Date

Date 0.60

3#

Carbonate carbon (mg/L)

Carbonate carbon (mg/L)

0.60 0.50 0.40 0.30 0.20 0.10 0.00 2.17 3.15 4.16 5.15 6.15 7.15 8.15 9.15 10.15 11.15

0.50

4#

0.40 0.30 0.20 0.10 0.00 2.17 3.15 4.16 5.15 6.15 7.15 8.15 9.15 10.15 11.15

Date

Date 0.60

5#

Carbonate carbon (mg/L)

Carbonate carbon (mg/L)

0.50 0.40 0.30 0.20 0.10 0.00

0.50

6#

0.40 0.30 0.20 0.10 0.00 2.17 3.15 4.16 5.15 6.15 7.15 8.15 9.15 10.15 11.15

2.17 3.15 4.16 5.15 6.15 7.15 8.15 9.15 10.15 11.15

Date

Date 0.35

7#

Carbonate carbon (mg/L)

Carbonate carbon (mg/L)

0.40 0.35

2983

0.30 0.25 0.20 0.15 0.10 0.05

0.30

8#

0.25 0.20 0.15 0.10 0.05 0.00

0.00 2.17 3.15 4.16 5.15 6.15 7.15 8.15 9.15 10.15 11.15

Date

2.17 3.15 4.16 5.15 6.15 7.15 8.15 9.15 10.15 11.15

Date

Fig. 8. Comparison of calculated carbonate carbon and observed carbonate carbon in Lake Taihu (solid line observation, broken line model output).

4.6. Model results 4.6.1. Inorganic carbon and abiotic organic carbon Figs. 7–10 compare the model results for the hydrogen carbonate carbon, dissolved carbon dioxide, abiotic organic carbon, and carbonate carbon with the observed results at the eight selected stations. The time-averaged deviation between the model results and observations and the ranges of the four state variables are

listed in Table 6. These model results are considered acceptable, except the sampling site 1. The variation ranges for carbonate carbon at the eight sites are bigger than for hydrogen carbonate, dissolved carbon dioxide, and abiotic organic carbon. The bigger deviation of carbonate carbon may be introduced when carbonate carbon concentrations are calculated by the use of the observed results of alkalinity, pH and temperature (Fan et al., 2003).

2984

H. Weiping et al. / Ecological Modelling 222 (2011) 2973–2991

0.6

0.6 0.4 0.2

0.5 0.4

(mg/L)

Dissolved carbon dioxide

0.8

(mg/L)

Dissolved carbon dioxide

1.0

0.3 0.2 0.1

1# 0.0

2#

0.0 2.17

3.15

4.16

5.15

6.15

7.15

8.15

9.15 10.15 11.15

2.17

3.15

4.16

5.15

Date

0.3 0.2 0.1

(mg/L)

Dissolved carbon dioxide

(mg/L)

Dissolved carbon dioxide

0.4

7.15

8.15

9.15 10.15 11.15

7.15

8.15

9.15 10.15 11.15

7.15

8.15

9.15 10.15 11.15

0.3 0.2 0.1

4#

3# 0.0 2.17

3.15

4.16

5.15

6.15

7.15

8.15

2.17

9.15 10.15 11.15

3.15

4.16

5.15

Date

6.15

Date 2.0

0.6

0.4 0.3 0.2 0.1

1.5

(mg/L)

Dissolved carbon dioxide

0.5

(mg/L)

9.15 10.15 11.15

0.4

0.0

Dissolved carbon dioxide

8.15

Date

0.5

1.0

0.5

5#

6#

0.0

0.0 2.17

3.15

4.16

5.15

6.15

7.15

8.15

2.17

9.15 10.15 11.15

3.15

4.16

5.15

Date

6.15

Date

0.5

0.5

0.4

0.4

0.3 0.2 0.1

0.3

(mg/L)

Dissolved carbon dioxide

(mg/L)

7.15

0.5

0.6

Dissolved carbon dioxide

6.15

0.2 0.1

7#

8#

0.0

0.0 2.17

3.15

4.16

5.15

6.15

7.15

8.15

9.15 10.15 11.15

Date

2.17

3.15

4.16

5.15

6.15

Date

Fig. 9. Comparison of calculated dissolved CO2 and observed dissolved CO2 in the period from 17 February to 7 December 2003.

Figs. 7–10 show that the major part of the abiotic carbon in Lake Taihu is hydrogen carbonate carbon, while carbonate carbon is a minor part of the abiotic carbon. The abiotic organic carbon is about 6 mg/L, less than the hydrogen carbonate carbon. Dissolved carbon dioxide carbon varies widely and has a lower concentration at the high water temperature.

4.6.2. pH Fig. 11 compares the model results and the observed values for pH at field sites 1–8. The difference between the two sets of values are less than 7% relatively except for field sites 6 and 1, which are both close to the river inflows (Table 6). The model results for pH agree generally with the observations very well and are

12.0

12.0

10.0

10.0

Organic carbon (mg/L)

Organic carbon (mg/L)

H. Weiping et al. / Ecological Modelling 222 (2011) 2973–2991

8.0 6.0 4.0 2.0

1#

8.0 6.0 4.0 2.0

2#

0.0

0.0 2.17 3.15 4.16 5.15 6.15 7.15 8.15 9.15 10.15 11.15

2.17 3.15 4.16 5.15 6.15 7.15 8.15 9.15 10.15 11.15

Date 12.0

10.0

10.0

Organic carbon (mg/L)

Organic carbon (mg/L)

Date 12.0

8.0 6.0 4.0 2.0

3#

0.0

8.0 6.0 4.0 2.0

4#

0.0 2.17 3.15 4.16 5.15 6.15 7.15 8.15 9.15 10.15 11.15

2.17 3.15 4.16 5.15 6.15 7.15 8.15 9.15 10.15 11.15

Date

10.0

12.0

8.0

10.0

Organic carbon (mg/L)

Organic carbon (mg/L)

Date

6.0 4.0 2.0

5# 0.0

8.0 6.0 4.0 2.0

6#

0.0

2.17 3.15 4.16 5.15 6.15 7.15 8.15 9.15 10.15 11.15

2.17 3.15 4.16 5.15 6.15 7.15 8.15 9.15 10.15 11.15

Date

9.0

9.0

8.0

8.0

Organic carbon (mg/L)

Organic carbon (mg/L)

Date

7.0 6.0 5.0 4.0 3.0 2.0 1.0

2985

7#

7.0 6.0 5.0 4.0 3.0 2.0 1.0

0.0

8#

0.0

2.17 3.15 4.16 5.15 6.15 7.15 8.15 9.15 10.15 11.15

Date

2.17 3.15 4.16 5.15 6.15 7.15 8.15 9.15 10.15 11.15

Date

Fig. 10. Comparison of calculated abiosis organic carbon and observed abiosis organic carbon in the period from 17 February to 7 December 2003.

fully acceptable compared with other diffusive model results of pH; see for instance Panizzuti and Tartari (1995) The influences of the cations [Ca2+ ], [Mg2+ ], [Na+ ], [K + ] and [NH4 + ], and the anions [HSO4 − ], [SO4 2− ], [NO3 − ] and [C1− ] on the net alkalinity and mineral acidity have not been taken into account in the model in

contrast to Panizzuti and Tartari’s model. pH is, however, mainly determined by the production of phytoplankton and submerged plants, which is included in the presented model of Lake Taihu. Panizzuti and Tartari’s model is furthermore based on observation of cations [H+ ], [Ca2+ ], [Mg2+ ], [Na+ ], [K + ] and [NH4 + ], and the anions

0.52 −3.46 to 4.61

9.79 −44.25 to 41.57

14.72 −21.43 to 44.59

9.41 −41.37 to 56.81

−9.25 −153.79 to 64.37

H. Weiping et al. / Ecological Modelling 222 (2011) 2973–2991

Site 8

2986

[HSO4 − ], [SO4 2− ], NO3 − ],[C1− ], HCO3 − , CO3 2− , which of course is a complication. 5. Discussion

0.86 −2.69 to 4.77 −0.49 −6.22 to 15.01

4.40 −33.51 to 23.11

−68.32 −300.91 to 45.30

−1.83 −8.70 to 2.41

Time averaged Range

Time averaged Range

Time averaged Range

HCO

CO3

pH

0.05 −3.83 to 4.13 −0.73 −3.72 to 3.07 −0.51 −6.45 to 4.55

0.38 −5.25 to 4.95

14.48 −61.34 to 55.33 −26.13 −266.12 to 65.01 10.40 −49.01 to 58.41 −27.35 −274.83 to 34.93 −1.42 −100.20 to 56.70

2.38 −115.67 to 49.38

9.41 −10.82 to 34.90 −10.05 −47.93 to 23.76

−2.84 −47.60 to 26.52 Time averaged Range OC

14.37 −4.41 to 38.29 11.36 −0.54 to 34.94 20.84 4.06 to 38.98

22.10 −0.85 to 47.61

5.79 −45.51 to 45.77 3.98 −45.48 to 41.39 3.54 −57.86 to 38.98 −7.98 −57.78 to 27.59 4.38 −43.40 to 34.87

−6.50 −73.42 to 39.76

−21.69 −143.09 to 71.07 11.20 −68.47 to 73.04 2.36 −133.03 to 66.68 0.28 −104.77 to 70.98 14.07 −56.44 to 81.32 15.71 −112.45 to 78.04 24.98 −41.33 to 85.14 Time averaged Range CO2

Site 1 Description Variable

Table 6 Model deviation between model results and observations for carbon (%).

Site 4 Site 3 Site 2

Site 5

Site 6

Site 7

5.1. Other carbon cycling modelling approaches At present, several models have been developed to determine the influence of the aquatic ecosystems on the global carbon cycle, but most of them have focused on the sea (Pu and Wang, 2000; Hu et al., 2004), while the models of carbon cycling in lakes either focus on the total lake carbon budget (Richey et al., 1978; Wetzel and Likens, 1991; Wetzel, 2001; Holzbecher and Nutzmann, 2000; Eugeni Barkan et al., 2001; Johannes et al., 1998; Wachniew and Rozanski, 1997; Dillon and Molot, 1997) or on the lacustrine carbon cycling (Panizzuti and Tartari, 1995; Dean, 1999; Bird et al., 1999; Cioffi and Gallerano, 2000; Chen et al., 2001; Hollander and Smith, 2001; McKenna et al., 2006). For example, Fan et al. (2003, 2005) proposed a model to describe the relationship between water–air flux and the partial pressure of carbon dioxide, and McKenna’s models (2006) only dealt with the carbon cycling through the food web without consideration of the inorganic carbon speciation and the fluxes of carbon dioxide across water-atmosphere interface. Mukherjee et al. (2007) have developed a model for inorganic carbon speciation in an aquarium. Although these model results are consistent with the measured values, it could not be applied for a large shallow lake, even for a small windy lake, as they consider that the transfer of carbon dioxide from the atmosphere to the water is a relatively slow process and the major carbon reserve for aquatic plants is the carbonate alkalinity system of the water. Furthermore, the model depends highly on the observation of pH. The one dimensional model proposed by Hollander and Smith (2001) is based on the isotope C13 , but the water–air carbon dioxide exchange is not included. Cioffi and Gallerano (2000) have proposed a model which couples hydrological, biological processes with inorganic carbon forms as the model state variables and includes also the water–air carbon dioxide exchange. Unfortunately, the results on carbon cycling were not presented in the paper. The carbon cycling model developed in this paper describes not only the lacustrine carbon transfer in water but also the flux of carbon dioxide at the water–air interface. It has coupled the hydrodynamic, biological and chemical processes, and been calibrated by a data set of almost 1-year at different sites. It can therefore be applied to describe the carbon cycling in Lake Taihu. 5.2. Diurnal variations of water–air carbon dioxide flux Fig. 12 describes the model results of the diurnal variation of the carbon dioxide flux at the water–air interface at three different sites (Fig. 13) in Lake Taihu during the spring. The carbon dioxide flux follows the diurnal changes. The upward carbon dioxide flux decreases at daytime due to the phytosynthesis and increases at night due to the respiration. The maximum upward carbon dioxide flux is almost at dawn 5:00–6:00 a.m. The results are consistent with the diurnal flux observations in Lake Taihu (Zhang et al., 2004), which supports the validation of the model. It can also be seen, that the diurnal variations of upward carbon dioxide flux at the three different sites are quite different. The biggest diurnal variation of the flux was at the site with macrophyte, followed by the site with relatively high eutrophication, while the smallest variation was at the central part of Lake Taihu without macrophytes and with relatively lower eutrophication. The site with macroplants has the highest phytosynthesis at daytime and the highest respiration at night because of the high biomass of macrophytes. The dissolved carbon dioxide concentration decreased the least at

9.0

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H. Weiping et al. / Ecological Modelling 222 (2011) 2973–2991

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2.17 3.15 4.16 5.15 6.15 7.15 8.15 9.15 10.15 11.15

Date

Date

Fig. 11. Comparison of calculated pH and observed pH in Lake Taihu.

daytime and increased the least at night, due to the low phytoplankton concentration in the central part of Lake Taihu. The same explanation can be applied to the variation of the carbon dioxide flux in summer (see Fig. 13). As the water temperature in summer was much higher than in the spring, the phytosynthesis and respiration at the three sites in summer were much stronger than during the spring. In summer the carbon dioxide

fluxes became negatives in daytime, indicating that the lake water was an atmospheric sink of carbon dioxide at all the three sites. The carbon dioxide fluxes were positive at night and the lake water were therefore a source of atmospheric carbon dioxide. The source of carbon dioxide at night at the southern site was bigger than that at the other two sites. It is noticeable that carbon dioxide flux at the site in Meiliang Bay was quantitatively consistent with

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10 5

Meiliang Bay

Lake center

14 12 10 8 6 4 2 0

0 11:00 16:00 21:00 2:00 7:00 12:00 17:00 22:00 3:00

8:00

Time (Apri. 25-27)

12:00 17:00 22:00 3:00 8:00 13:00 18:00 23:00

Time (Apr. 21-22,2003)

Flux of CO2 (mg/m 2/h)

15

Flux of CO2(mg/m2/h)

Flux of CO2(mg/m 2/h)

16 20

40

South of Lake Taihu 30 20 10 0 -10 11:00 14:00 17:00 20:00 23:00

2:00

5:00

8:00 11:00

Time (Apr.23-24)

Fig. 12. The diurnal variations of the flux of carbon dioxide on water–air interface at three sites in spring.

Fig. 13. The location of observation sites for water-air carbon dioxide flux and the subarea in Lake Taihu.

the observed results, which is a support for the reliability and the applicability of the model.

5.4. Horizontal distribution of carbon dioxide flux on the water–air interface

5.3. The day-by-day change of carbon dioxide flux at the water–air interface during the year 2003

In order to describe the horizontal distribution of carbon dioxide flux at the water–atmosphere interface, Lake Taihu is divided into seven zones, which are shown in Fig. 15:

Fig. 14 shows day-by-day changes of the sum of the carbon dioxide flux at the water–air interface from February17 to December 5, 2003. The pattern of the day-by-day changes of the sum of carbon dioxide fluxes at Meiliang Bay observation site was similar to the pattern at the lake centre site. The sum of carbon dioxide fluxes at the site in Meiliang Bay and the centre of Lake Taihu has a tendency to decrease during the period from February 17 to July 17. The site with macroplants was, however, quite different from the sites, as the daily sum of carbon dioxide fluxes have a tendency to decrease. The water body was, however, always a weak source of atmospheric carbon dioxide.

(1) Meliang Bay, locating in the northern part of Lake Taihu, is the eutrophic area with two big inflowing. The two rivers contributed relatively large discharge of total carbon. (2) Gonghu Bay located in Northeast of Lake Taihu with half of its area covered by macroplant vegetation. (3) The eastern part with the highest time-average flux. (4) Dongtaihu Bay is covered by macroplant and has pen fish cultures. It has a relatively high carbon accumulation in the sediment due to pen fish cultures and the macroplant.

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Table 7 Water–air interface fluxes of carbon dioxide in seven different zones of Lake Taihu. Zone

Whole Lake Taihu

Meiliang Bay

Gonghu Bay

The eastern epigeal part

Dongtaihu Bay

South part

Northwest Centre part part

Sum of flux in 292 days (106 kg/km2 ) Time-averaged flux (ton/km2 d) Maximum water to air flux (ton/km2 d) Maximum air to water flux (ton/km2 d)

258.709 0.38 2.36 −0.54

10.153 0.27 3.74 −1.53

28.705 0.50 3.97 −2.24

55.831 0.62 2.59 −0.96

36.025 0.57 2.93 −1.05

40.476 0.23 2.82 −0.39

37.814 0.49 1.91 −0.02

49.706 0.28 1.82 −0.19

-1

Carbon flux (mgC·m ·h )

70

-2

50 30 10 -10 Model output

-30

Observation

-50 18:00 23:00

4:00

9:00

14:00 19:00

0:00

5:00

10:00 15:00 20:00

1:00

6:00

11:00

Time(July 10-13,2003) Carbon flux (mgC/m /h)

Lake center 2

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0

:0 0 21

:0 16

:0

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00

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00 1:

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15

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00

10

5:

00

0

0:

:0

0

00

:0

19

14

9:

0

00 4:

:0 23

18

:0

0

-50

Time (July 10-13,2003) South of Lake 80 70

Carbon flux (mgC/m2 /h)

60 50 40 30 20 10

0 :0 21

16

:0

0

0 :0 11

00 6:

00 1:

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15

:0

0

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10

00 5:

00 0:

0 19

:0

0

00

:0

9:

00 4:

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14

-20

23

18 :

00

-10

0

0

Time (July 10-13,2003) Fig. 14. The diurnal variation of flux of carbon dioxide on water–air interface in summer.

(5) The north-western part is the hyper-eutrophic area of Lake Taihu, with more carbon discharge than Meiliang Bay. (6) The southern part of Lake Taihu is the transition area between phytoplankton domination and macroplants domination. There are three large inflowing rivers yielding one third of the entire annual input of the total drainage area runoff. (7) The central part with relatively little photosynthetic activity. The total carbon dioxide flux across the water–atmosphere interface during 292 days and the average carbon dioxide flux in

the seven different zones obtained by use of the model are listed in Table 7. It can be seen that the maximum space-averaged carbon dioxide flux is about 25.83 mg/m2 /h in the eastern epigeal part, while it is 23.75 mg/m2 /h in Dongtaihu Bay, 20.83 mg/m2 /h in Gonghu Bay, and 20.42 mg/m2 /h in northwest part of the lake. The three big fluxes were all in the area covered by macroplants vegetation. The fourth highest space-averaged carbon dioxide flux is in the hyper-eutrophic area with the highest discharge of carbon. The minimum of the space-averaged carbon dioxide flux is about 9.58 mg/m2 /h, which is in the southwest part. The

H. Weiping et al. / Ecological Modelling 222 (2011) 2973–2991

• The model results of pH values are acceptable with the biggest time-averaged deviation less than 16%, and a good coverage of the mechanism of pH explaining the changes. The model can be used to calculate the pH value in water in Lake Taihu.

250 200

North of Lake Taihu

150 100 50 0

Acknowledgements

-50 17-Nov

17-Oct

17-Sep

17-Aug

17-Jul

17-Jun

17-May

17-Apr

17-Mar

-100 17-Feb

Water-air interface 2 flux of CO 2 (ton/km )

2990

200

Centre of Lake Taihu

150 100 50

References

0 -50 17-Oct

17-Nov

17-Oct

17-Nov

17-Sep

17-Jul

17-Aug

17-Jun

17-May

17-Apr

17-Feb

-100 17-Mar

Water-air interface flux of CO2 (ton/km 2 )

Date

Date 600

of CO 2 (ton/km 2 )

Water-air interface flux

This work has been carried out within the frame work of the major projects of Chinese Academy of Sciences (KZCX1-SW-01-15) and the research project “A demonstrative research on lake ecosystem structurally dynamic model of Lake Taihu” (NSFC: 30670351). The authors also would like to thank Søren Nors Nielsen, Faculty of Pharmaceutical Sciences, University of Copenhagen for the help when the corresponding author was in Denmark.

South of Lake Taihu

500 400 300 200 100 0

17-Sep

17-Aug

17-Jul

17-Jun

17-M ay

17-Apr

17-M ar

17-Feb

-100

Date Fig. 15. The day-by-day change of carbon dioxide flux on water–air interface.

space-averaged carbon dioxide fluxes in Meiliang Bay and the centre of the Lake Taihu are almost the same. The total carbon dioxide fluxes on water–atmosphere interface is about 258.709 × 106 kg in 292 days, which is almost equal to the net input of carbon dioxide discharged to the lake. It implies that the terrestrial input of carbon has great influence on the carbon dioxide flux at the water–atmosphere interface. 6. Conclusion From the model description, its calibration and the discussion, the following can be concluded: • The presented carbon model has coupled the hydrodynamic, biological and chemical processes successfully, with the model output of different carbon speciation consistent with the observed results. It can be use to find the variations of the carbon dioxide flux at the water–air interface; • The carbon dioxide flux on the water–air interface shows distinct diurnal variations. Eutrophied water is a carbon dioxide sink for the atmosphere due to the phytosynthesis during the summer. Due to the terrestrial input of carbon; Lake Taihu is, however, a source of carbon dioxide to atmosphere on an annual basis. The total flux in a year is almost equal to the terrestrial input of carbon. Terrestrial input of carbon has therefore great influence on the carbon dioxide flux at the water–air interface.

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