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e c o l o g i c a l m o d e l l i n g 2 1 0 ( 2 0 0 8 ) 247–252

avai lab le at www.sc iencedi rec t .com

journa l homepage: www.e lsev ier .com/ locate /eco lmodel

odeling a wetland system: The case of Keoladeoational Park (KNP), India

ikas Rai ∗

S 532, Department of Physics, Indian Institute of Technology at Delhi, Hauz Khas, Delhi 110016, India

r t i c l e i n f o

rticle history:

eceived 18 May 2006

eceived in revised form

4 July 2007

ccepted 26 July 2007

ublished on line 29 October 2007

eywords:

lood plain wetland

ystems modeling

conomic values

a b s t r a c t

A model for the wetland part of KNP is presented and analyzed. Two-dimensional parameter

scans suggest that this minimal model possesses dynamical complexities. Per capita avail-

ability of water to “bad” biomass (W1) is one of the most vital parameters. One can ensure

good health of the park by restricting the par capita availability of water to low values. Get-

ting the “bad” biomass removed by granting permits to villagers should go hand in hand

with water management and conservation activities. The model presented in this paper

may be helpful in designing the timing and nature of human interventions in the form of

implementation of well worked out policies in future.

© 2007 Elsevier B.V. All rights reserved.

cological health

redator–prey interaction

imulations

ynamical complexities

wo-dimensional parameter scans

. Introduction

he Ramsar convention adopted the following definition ofetlands. Wetlands are areas of marsh, fen, peatland or water,hether natural or artificial, permanent or temporary withater that is static or flowing, fresh, brackish or salty includ-

ng areas of marine water, the depth of which at low tide doesot exceed 6 m. This definition suggests that wetlands couldive rise to varieties of values. Wetlands also act as pollutionssimilation agents for nitrate pollution created by up-stream

griculture. Thus they provide a positive externality benefit.he aquatic system of KNP belongs to such a system.

There are various kinds of wetlands. Some well-knownetland types are (1) fresh water coastal wetlands, (2) flood-lain wetlands and (3) constructed wetlands. The aquatic

∗ Tel.: +91 11 26591351; fax: +91 11 26582037.E-mail address: rvikas41@hotmail.com.

304-3800/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.ecolmodel.2007.07.031

part of KNP belongs to the second category. It has beenfound that tourist traffic and ecological value of the park arenon-linearly related. Chopra and Adhikari (2004) have shownthat conservation efforts increase the attractiveness of thepark beyond a certain level. They have also indicated thatthe impact may be cumulative and, therefore, more thanproportionate income is expected.

The Keoladeo National Park is a man-made system.It is located on the Indo-Gangetic Plain near the town ofBharatpur(27◦13′N, 77◦32′E). It is a Ramsar and designatedWorld Heritage site. It has an interesting history. This man-

made park was declared as National Park in 1981. The relativeimportance of three constituent ecosystems (wetland, grass-land and woodland) has evolved over time. This evolutionhas been primarily driven by human interventions over more

i n g

part of aquatic fauna inhabiting the same wetland. The thirdassumption implies that birds feed only on “good” biomass.They hardly feed on any species, which have been clubbed in“bad” biomass. This assumption serves as a foundation stone

248 e c o l o g i c a l m o d e l l

than hundred years now. The wetland area of the park coversa central depression of about 8.5 km2, which is divided bydykes into a number of compartments or blocks. Apart fromrainfall, the park receives water released into it throughthe Ghana canal. This canal originates in the Ajanbund, aseasonal reservoir of water to the south of the park. Theseasonal floods in the northern rivers upstream cause theannual inundation of the park.

The economic value of the park emanates primarily fromthe presence of two kinds of birds: resident and migratory.The seasonal rainfall and the water that is let into the parkin July–August initiate a period of increased biomass growth.The tourism value of this park is determined by its wetlandnature. It provides a large habitat for birds among which themigratory species, namely, the Siberian crane, constitutes theflagship species. The biomass is divided into two categorieswith reference to the migratory birds: “Good” and “Bad”. In1985, a report from Bombay Natural History Society suggestedthat grazing per se was not damaging the ecology of the park.On the contrary, the excess growth of Paspalum restricted thegrowth of bulbs, tubers and roots (Vijayan, 1991). Avifaunasuch as Siberian cranes that fed on these found that their habi-tat had become less friendly. The probability of grassland firesalso increased. This report by BNHS persuaded the manage-ment of the park to grant permits for villagers to enter the parkfor extraction of grasses in summer months. The issuance ofpermits started in 1986.

In course of time, the cost of the control of bad biomass bynon-biotic means arose and the subsidy from the governmentalso arose. This subsidy is viewed as the excess of expendi-ture over revenue collected by the management of the park.The most expensive item was the creation of open water bod-ies, which were the required habitats for several bird speciesincluding the Siberian crane.

The other notable human intervention that the KNP wassubjected to after 80s was intensive agriculture in the catch-ment. The increased agricultural activities affect the wetlandadversely in two respects: (a) a reduction in water flow intothe park and (b) the deterioration in the quality of water dueto the chemical fertilizer upstream. This also causes deathsof birds due to poisoning (Chopra and Adhikari, 2004). A bet-ter understanding of inter-relationships between populationof birds and different kinds of biomass and the factors drivingtheir change over time would enable us to take better policydecisions for the management of the park. One of the mainobjectives of the present paper is to present a model which canlink up the ecological and economic values (use and recreationvalues) in such a way that a balance can be struck between thetwo. The paper presents a model of the wetland, which pro-vides clear perspectives on future management strategies andpolicy decisions.

2. The model

A wild grass species Paspalum distichum is the most dominant

species, which depletes oxygen in the open water bodies inthe park. The fishes and the water-fowl are the species mostsuffered. The other suffered species are that of floating veg-etation: Nymphoides indicum, Nymphoides cristatum, Nymphaea

2 1 0 ( 2 0 0 8 ) 247–252

nouchali and Nymphaea stellat (Shukla and Dubey, 1996). ThePaspalum and its family acts as a “bad” biomass for the birds(resident and migratory) and floating vegetation. The floatingvegetation and other useful species are clubbed together inthe category “good” biomass. I propose the following model todescribe the temporal evolution of the wetland part of KNP.

dG

dt= aG − bG2 − cGB − d

GP

G + D(1)

dB

dt= eB − B2

W1− a2GB (2)

dP

dt= −�P + �

GP

G + D1, (3)

where a is the reproductive growth rate of the “good” biomass(G) and b measures the severity of the intra-specific competi-tion among individuals of “good” biomass. The ratio of a to bdefines carrying capacity to good biomass. The carrying capac-ity is neither constant nor a continuously varying function;instead, takes a discrete set of values in simulations reportedin the present paper. The d is the maximum of the rate atwhich the bird population (P) consumes the “good” biomass.D is a measure of the half-saturation constant. Similarly, e rep-resents the rate of reproductive growth for the “bad” biomass(B) and W1 denotes the per capita water availability for B.The parameters c and a2 measure the intensity of competi-tion between “good” and “bad” biomasses. The � and � aremortality rates and conversion coefficients for the bird species(resident as well as migratory). D1 is the half-saturation con-stant appearing in the numerical response of the predator P.It may be noted that dynamics of G and P is cast as that ofa system known as R–M system (Rosenzweig and MacArthur,1963; Rai, 2004).

The underlying assumptions of the model are the follow-ing:

(1) The growth rate of the bad biomass is limited by the percapita availability of water.

(2) “Good” and “bad” biomasses are in competition forresources like nutrients, water, light, etc.

(3) The bird population dies out exponentially in the absenceof the “good” biomass.

The second assumption represents a fact of KNP as both are

Fig. 1 – The basic interactions between the differentcomponents of the model.

g 2 1 0 ( 2 0 0 8 ) 247–252 249

fif

3

Thgaso

�

sf

vAJcsmysccloavppnst

F

3.2.1. Evapo-transpirationThe water body in the park loses a substantial quantityof water through evapo-transpiration. The highest monthlyloss occurred in May 1984 (2.99 × 106 m3) and the lowest

e c o l o g i c a l m o d e l l i n

or the model presented and is in conformity with the real-ty in the wetland part of KNP. Field data is presented in theollowing section in support of the first assumption.

Fig. 1 depicts the interactions characterizing this model.

. Methodology and field data

he economic value of an ecological system depends on itsealth. This paper attempts to obtain conditions, which yieldood health of the park. If choices of the parameter valuesre made in such a way that the following condition on theystem parameters is satisfied, the G–P subsystem oscillatesn a stable limit cycle.

< �

((a/D1b) − 1(a/D1b) + 1

)(4)

The following basal values of parameters were used forimulation experiments, which aim at knowing the conditionsor good and bad health of KNP.

a = 0.2, b = 0.002, c = 0.005, d = 0.5, e = 0.2, D = D1 = 20,

� = 0.05, � = 0.1 and W1 = 10, a2 = 0.003.

These values of model parameters are relative. For actualalues, the reader is referred to references Chopra anddhikari (2004), Jorgensen (1979), Jorgensen et al. (1991),

orgensen et al. (1995), Jorgensen et al. (2001). These have beenhosen in such a way that the G–P subsystem oscillates on atable limit cycle with period 1 year which signifies the visit ofigratory birds in months of November and December each

ear. This choice of the parameter values also takes into con-ideration the fact that G and B compete for a number ofommon resources. At the basal values of parameters, all theomponents of the system display persistent periodic oscil-ations. The densities of “bad” biomass are lower than thatf the bird population. The system behavior was scanned in–W1 and e–W1 two-dimensional parameter spaces keepingalues of rest of the parameters at their basal values. Thesearameters are controllable and, therefore, were chosen for

arameter scans. The results obtained are described in theext section. In the following, data on water availability is pre-ented. It clearly shows that the per capita water availabilityo B will be a crucial parameter.

ig. 2 – Quantity of water released from Ajanbund into KNP.

Fig. 3 – Biomass of aquatic macrophytes in KNP (gm/m2).

3.1. Water sources

Water from a temporary reservoir, Ajanbund situatedabout 1 km south-west of the boundary, is taken to KNPthrough a narrow canal in months of July–September. Fig. 2shows the annual water inflow from the reservoir during1984–1988.

The water input from the reservoir showed wide fluctua-tion lowest being (0.017 × 106–15 × 106 m3) during 1966–1990.

Another appreciable source of water is rain. It occurs manlyduring the period June–September. The average annual rainfallin Bharatpur from 1901 to 1990 was approximately 655 mm.During 1980s, the overall rainfall was 495.7 mm. The onlymajor input from precipitation is the rain directly received inthe water-spread area. The sources of loss of water are givenin the following paragraphs.

3.2. Losses

Fig. 4 – Two-dimensional parameter scans showing theconditions for good and bad health of the wetland. Goodhealth means that G and P maintain higher densities thanB. When densities of “bad” biomass are comparable orhigher to that of Z, it is inferred that the system is in a stateof bad health.

250 e c o l o g i c a l m o d e l l i n g 2 1 0 ( 2 0 0 8 ) 247–252

Fig. 5 – Two-dimensional parameter scans showing theconditions for good and bad health of the wetland. Goodhealth means that densities of G and P oscillate andmaintain higher densities than that of B. When densities of“bad” biomass are comparable or higher to that of Z, it isinferred that the system is in a state of bad health; b1 wasfixed at 0.001 and a1 was varied between 0.1 and 0.5.

Fig. 6 – Parameter scans showing how carrying capacity togood biomass and per capita availability of water to badbiomass affects the dynamical behavior of the aquaticsystem of KNP. The carrying capacity of the good biomass

Fig. 7 – Different population densities changes with timefor the following parameter values: a = 0.2, b = 0.002,c = 0.005, d = 0.5, e = 0.2, D = D1 = 20, � = 0.05, � = 0.1 and

the rate of reproductive growth of G is low and the per capitaavailability for B is higher (cf. Fig. 4). In contrast to this, B decaysto 0 at higher per capita availability of water when e = 0.1. Athigher values of this parameter, system exists in a state of bad

is plotted on the X-axis. The per capita availability of waterto bad biomass is on the Y-axis.

(0.15 × 106 m3) during January and February 1987 (Chopra andAdhikari, 2004).

3.2.2. InfiltrationThe overall average rate of infiltration for the aquatic areawas 0.062 mm/h (44.64 mm/month). It was estimated during1984–1988 that an average loss of 0.3% of the total water budgetwas due to infiltration (BNHS Study, 1991).

There exists high monthly variation of average biomass ofmacrophytes. Fig. 3 shows monthly variation of macrophytesfor the period (1984–1988). A grass species P. distichum is amajor constituent of the total aquatic biomass in the park.

4. Results

Simulation results on this model are presented in Figs. 4–6 astwo-dimensional parameter scans. The paper’s main concern

W1 = 30. It signifies the good health of the park as B isalways lower than P.

is to figure out conditions (represented by parameter values)for good health of the park. The good health is defined byparameter values, which give rise to fluctuating G and P. Thefluctuations in the densities of these populations are such thatthey maintain higher values than those of the “bad” biomass(B) for all time. It can be noted from Fig. 4 that the systemcollapses at 0.4. At these parameter values, G and P oscillateand B goes to extinction. Both Figs. 4 and 5 suggest that thereexist dynamical complexities and discontinuities in the sys-tem’s behavior. The system is dragged into bad health when

Fig. 8 – Different population densities changes with time atparameter values: a = 0.2, b = 0.002, c = 0.005, d = 0.5, e = 0.4,D = D1 = 20, � = 0.05, � = 0.1 and W1 = 35. It signifies the badhealth of the park as B is comparable to P.

e c o l o g i c a l m o d e l l i n g 2 1

Fig. 9 – Different population densities change with time atparameter values: a = 0.2, b = 0.002, c = 0.005, d = 0.5, e = 0.5,Dh

hehtvttwdwisatc(aF

5

FmrpgwocvcO“tht

= D1 = 20, � = 0.05, � = 0.1 and W1 = 30. Since, B is alwaysigher than P, it signifies bad health of wetland part of KNP.

ealth when per capita availability of water (W1) is more. At= 0.4, B and Z become comparable. This is one kind of badealth scenario. When e is increased further, this trend con-inues for higher values of per capita availability of water. Atery high values of this parameter, bad biomass representshe dominant group of species and, therefore, bird popula-ion decays to low densities (see Fig. 5). Fig. 6 presents a studyhich aims at examining how changes in a, the specific repro-uctive growth rate of G, affects the behavior of the wetlandhen its intra-specific competition coefficient is set at half of

ts basal value. The basal values of parameters are those whichatisfy inequality Eq. (4). It can be noticed from this figure thatn exchange between conditions of good and bad health hasaken place (compare Figs. 4 and 6). Good health conditionsontinue to W1 = 30 and bad health scenario appears at K = 200a = 0.2) for values of W1 ranging from 30 to 40. Typical situ-tions of good and bad health of the system are depicted inigs. 7–9.

. Discussion and conclusion

rom ecological as well as economic point of view, W1, is theost crucial parameter. It is all about managing this limiting

esource which is essential for all species whether it is macro-hytes or avians. It is clear from Fig. 5 that one can ensureood health of KNP by restricting the per capita availability ofater to “bad” biomass to low values. For intermediate valuesf a, the “bad” biomass goes to extinction, thus, the systemollapses. The system regenerates only when a acquires aalue equal to 0.4. This simple system is repleted with dis-ontinuities and dynamical complexities (see Figs. 4 and 5).ne is supposed to restrict the reproductive rate of growth of

bad” biomass to 0.2. If it goes beyond this value, then con-rolling the per capita availability of water to bad biomassolds the key to good health of the park. This means thathe removal of Paspalum by villagers should go hand in hand

0 ( 2 0 0 8 ) 247–252 251

with water management and conservation measures in thepark.

Plantation of plants like babul (local name) and cacti (localname) in the terrestrial area of the wetland is recommended.These plants consume less amount of water and provide sub-stances of economic value. For example, babul gives gum likesubstance, which is of considerable medicinal value. Similarly,cacti provides a fuel of high calorific value because of presenceof high calorific value because of presence of hydrocarbonsin high quantity in its sap besides normal cellulose whichmakes most of its body. Inside the wetland, plantation of slowgrowing floating vegetation and emergent plants which havemedicinal value and consume less amount of water should beencouraged.

Earlier authors have concerned themselves with otheraspects of the wetland, e.g., Shukla and Dubey (1996), Shukla(1998) examine the consequences of wetland degradation tothe species which depend on the resources that are derivedfrom this aquatic system. Shukla (1998) points out that anincreasing effort is required to control wild grasses, especiallyP. distichum. This is a key observation, which is more impor-tant for the economic value (use as well as recreational) ofKNP. The model presented in the present paper suggests waysand means to control the wild grasses in an efficient manner.A recent modeling effort by Simonit et al. (2005) investigatespressures built up by needs of reallocation of wetland and riceproduction caused by presence of an international hydroelec-tric power project in the area.

Most of the recent modeling efforts are devoted to evalua-tion of performance of constructed wetlands for the treatmentof wastewater. One of the modeling approaches (Marsili-Libelliand Checchi, 2005) models a constructed wetland as an infi-nite number of continuously stirred reactors (CSTR) assuminga wetland to possess many through-flow channels flanked byside regions of limited flow. This approach to model the dis-persed flow and pollution reaction dynamics consists of twosteps: (1) setting up the model structure and (2) identificationof the best performance models based on approximate param-eter confidence regions based on Fisher Information Matrix(FIM) or Hessian Matrix. The models are calibrated with datasets from several constructed wetlands with widely differinghydraulics and pollution removal characteristics. The identifi-cation method assists in the selection of best combination ofhydraulics and kinetics to obtain robust yet simple models forhorizontal subsurface constructed wetlands. The model pre-sented in the present paper assumes entire wetland as a largeCSTR. It assumes that the spatial structure of the wetland doesnot influence the temporal dynamics. Thus data requirementsfor parameter estimation are moderate and the model can beeasily implemented on any modern-day personal computer.The model enables one to figure out how to create a balancebetween ecological health of KNP and the economic benefitsaccruing from it. As long as well-mixed conditions prevail inthe wetland, Monod kinetics serves as a workable hypothesis(Monod kinetics is used to model the interaction between the“good” biomass and the bird population). The model presented

in the paper is a general one, specifically tailored to a flood-plain or constructed wetland wherein per capita availabilityof water is a critical parameter. It may not be applicable to afreshwater coastal wetland.

i n g

r

252 e c o l o g i c a l m o d e l l

Acknowledgements

The author wishes to thank Profs. Kanchan Chopra and S.S.Saluja for invigorating discussions. An anonymous reviewer’scomments improved the presentation of ideas contained inthe paper.

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Jorgensen, S.E., Halling-Sorensen, B., Nors-Nielsen, S., 1995.Handbook of Environmental and Ecological Modeling. CRCPress, Scottsdale, Az, 672 pp.

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Jorgensen, Chuo, S.E., Kikun, Cha, Katima, J.H.Y., 2001.Application of Wetland Systems and Waste StabilizationPonds in Water Pollution Control. Der es Salam University, Deres Salam, 225 pp.

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of rice in Esteros del Ibera. Argentina Ecol. Model. 188,123–144.

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