Chain food model

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Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 35, No. 6, p. 454-461 (June 1998)

TECHNICAL REPORT

Development of a Dynamic Food Chain Model DYNACONand Its Application to Korean Agricultural Conditions

WonTaeHWANG*,t, yuseong HO* nd MoonHeeHAN*** Department f Nuclear ngineering, KoreaAdvancednstituteof Science nd Technology**Department f EnvironmentalystemAnalysis, KoreaAtomicEnergyResearch nstitute

(Receivedctober 0,1997),Revisedebruary 3,1998)A dynamicoodchainmodelDYNACONasdevelopedo simulatehe radionuclideransfer n agri-cultural cosystems. YNACONstimateshe radioactivityn eachcompartmentf foodchains or hreeradionuclides,ineplantspeciesndfiveanimal roducts s a function f the depositionate. A numberof the parameteralues sed n thisstudyare epresentativefKorean griculturalonditions. hemodelwasexpressedycoupled ifferentialquationsnd the radioactivityn eachcompartment as olved s afunctionf ime ollowingn acute eposition. lthough YNACONsstructurallyased nexisting odels,it wasdesignedn order o simulatemore ealisticadionuclideehaviorn Korean griculturalonditionsand o save omputationime. t was oundhat the radioactivityn foodstuffsependstrongly n he dateofdeposition. comparativetudybetween YNACONnd an equilibrium odel howed ood greementfordepositionshat occur uringhe growingeason f plants.DYNACONs going o be implementedn aKoreaneal-timeose ssessmentystem ADAS.KEYWORDS:dynamicfood chain model, DYNACON,acute deposition, agriculturalecosystems, oreanagricultural onditions, ompartments, quilibriummodel

I. IntroductionFollowing a deposition of radionuclides, a terrestrialfood chain is a significant pathway which leads to in-ternal radiation exposure to humans. Deposition of ra-dionuclides may occur as a result of routine or acci-dental releases from nuclear power plants, nuclear fuel-cycle facilities and nuclear weapons testing. Mathemat-ical models that simulate the transfer of radionuclidesin food chains have been developed for various pur-

poses. In such models, the behavior of radionuclides isdescribed by transfers between compartments which rep-resent different parts of food chains. Equilibrium modelsdescribe steady-state radioactivity in compartments re-sulting from routine releases of radionuclides into theenvironment. The U.S. Nuclear Regulatory Commis-sion's Regulatory Guide 1.109 model(1), which we willcall the NRC model in this paper, is the most well-known equilibrium model. However, equilibrium modelsare not appropriate in cases of accidental releases. Inthese cases, the transfer of radionuclides between com-partments has to be considered dynamically since ra-dioactivity in compartments does not reach steady-statein a short time for long-lived radionuclides such as 137Cs(T1/2=30 years) and 90Sr (T1/2=-29 years). The Cher-

nobyl accident showed clearly the importance of seasonalinfluence on ingestion doses resulting from contaminatedfoodstuffs in nuclear accidents(2)(3). Thereafter, severaldynamic models have been developed to describe suchseasonal changes(4)-(7).We developed a dynamic food chain model DYNA-CON to support a Korean real-time dose assessmentsystem FADAS (Following Accident Dose AssessmentSystem)(8) which evaluates the radiological consequencesof a nuclear accident. The parameter values in food chainmodels are dependent on climatological, agricultural andother characteristics of a considered region. The majorfoodstuffs of Korea are significantly different from thoseof other countries. In particular, rice is a main food-stuff, and rice fields differ from ordinary fields with re-gards to agricultural practices as well as soil characteris-tics. Although the parameter values in DYNACON arerepresentative of Korean agricultural conditions, somevalues were taken from available foreign literature dueto the lack of site-specific data. DYNACON is struc-turally based on existing models such as RADFOOD(4)and PATHWAY(5),and it was designed in order to simu-late more realistic radionuclide behavior in Korean agri-cultural conditions and to save computation time.This paper describes the methods of modeling, thetransfer processes of radionuclides and the calculationresults of DYNACON. A comparative study betweenDYNACON and the NRC model is also provided.

* 371 -1 Kusong-dong , Yusong-gu, Taejon, KOREA 305-701.**150 D uckjin-dong, Yusong-gu , Taejon, KOREA 305-353.tCorresponding author, Tel. +82-42-868-2353 ,Fax. +82-42-868-2370, E-mail: wthwang@nanum .lcaeri.re.kr454


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Development of a Dynamic Food Chain Model 455

II. General Description of DYNACONDANACON s written in FORTRAN 77 and operatedon a personal computer. Currently, the model considersthree critical radionuclides (137Cs, 90Sr, 131I) n an acci-dent of nuclear power plants. Nine plant species and fiveanimalproducts are considered. Table 1 shows the food-stuffsconsidered in the model. Soil is divided into fourdifferent ompartments; surface soil (0-1cm), root zonesoil agricultural land: 1-25cm, pasture land : 1-15cm),fixedsoil (agricultural land: 1-25cm, pasture land: 1-15cm) and deep soil (agricultural land: >25cm, pastureland: >15cm). Figure 1 represents the transfer pro-cessesof radionuclides between different compartments.Inputs of the model are the initial radioactivity on the

ground, F (Bq,m-2), and the date at which a depositionhappens. Outputs of the model are the radioactivity offoodstuffs ollowing an acute deposition.III. Transfer Processes of Radionuclide1. Deposition and InterceptionRadionuclides released into the atmosphere when anuclear accident occurs are deposited onto plants andsoil surfaces. The ratio of the amount deposited ontoplants to the amount of total radionuclide deposition isdefinedas the interception fraction, f (9). Neglecting theinterception by ears or the fruit surfaces of plants, thefunctionaldependence between the interception fractionand the biomass of plant leaves, Bf (dry-kg,m-2), is ex-pressed as follows(10):

f=1-e-aBf, (1)where a: Foliar interception constant (m2,dry-kg-1).The term a is estimated from measurements of theratio of plant concentration (Bq,dry-kg-1) to the to-tal deposition (Bq,m-2). It is found to range from2.3 to 3.3m2,dry-kg-1 for forage crops(9). The value of3m2,dry-kg-1 is assumed for all plant species except forfruits(11).A lower value of 0.3m2,dry-kg-1 is assumedfor fruits(12). Logistic growth of plants is assumed to

estimate the time-dependent biomass of plants:dB/dt=kgB(Bmax-B/Bmax), (2)where kg: Growth rate constant (d-1, where d standsfor day)B: Current biomass (dry-kg,m-2)Bmax: Maximum potential biomass (dry-kg,m-2).Equation (2) is applied to all parts of a plant. There-fore, the time-dependent biomass of plant leaves and thatof edible parts are replaced by Bf and Be, respectively,instead of B. The value of kg is assumed to be 0.12 d-1for all plants(5). Equation (2) may be analytically solvedas follows:

Fig. 1 The transfer processes of radionuclides betweendifferent compartments considered in DYNACON

Table 1 Foodstuffs considered in DYNACON

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456W. T. HWANG et al.

B(t)=maxB0/(Bmax-B0)e-kgt+B0, (3)where B0: Initial biomass of plants (dry-kg,m-2).The value of B0 is assumed to be 0.07 dry-kg,m-2for pastures and 0.015 dry-kg,m-2 for other plants(5).Table 2 represents the growth characteristics of theplant species considered in DYNACON(13).2. Weathering and Growth DilutionAfter the deposition of radionuclides on plant surfaces,environmental removal processes such as wind, washoffand volatilization, will reduce the quantity of contamina-tion on plant surfaces. The weathering removal rate lwis assumed to be 2.77x10-2d-1 (T1/2=25d)(6). Also,the mass concentration of plants will be diluted withgrowth. The growth dilution rate lg is assumed to be3.47x10-2d-1 (T1/2=20d)(14).3. ResuspensionRadionuclides on soil surfaces may be resuspended bythe action of wind, rain or other disturbances, and sub-sequently deposited on plant surfaces where they are ab-sorbed further into the inner parts of the plant. Theresuspension factor RF (m-1) is defined as the ratioof air concentration (Bq,m-3) to the radioactivity onthe ground (Bq,m-2). Different approaches to estimatethe resuspension factor are applied to agricultural andpasture land. For agricultural land, a single value of1x10-5m-1 is used(5). However, resuspension is notconsidered for rice fields because rice fields contain waterat all times during the growing season. For pasture land,a time-dependent RF suggested by Linsley is used(15):

RF(t in days)=10-6e-0.01t+10-9. (4)Deposition of resuspended particles onto plant surfacesis estimated with the deposition velocity Vd m,d-1),which is measured as the ratio of deposition rate onto

plants (Bq,m-2,d-1) to the air concentration (Bq,m-3).A value of 173m,d-1 is used in this study(5). The trans-fer rate of radioactivity by resuspension, lre (d-1), from

the soil surface to the plant surfaces is expressed as fol-lows:

lre= RFVd. (5)4. Percolation

This process describes the downward movement of ra-dionuclides from the surface soil to root zone soil. Avalue of 1.98x10-2d-1 is assumed to be the transferrate by percolation lpc, which effectively reduces the ra-dioactivity of soil surface(5).5. TranslocationThe inner tissues or edible parts of plants absorb ra-dionuclides from plant surfaces. The absorbed radioac-tivity is assumed to remain within the inner tissues,except for the losses due to radioactive decay ld(d-1)and growth dilution. This process is a dominant pro-cess in the early phase following an acute deposition,while root uptake increases generally in accordance withtime for long-lived radionuclides. The translocation rates

lr of 137Cs,90Sr and 131I are assumed to be 5.5x10-3,1.0x10-3 and 8.5x10-3d-1, respectively(5).6. LeachingThis process describes the downward movement of ra-dionuclides from root zone soil to deep soil where rootuptake is unavailable. The leaching rate ll (d-1) is esti-mated as follows(16):

llfcRp/tLr(1+rr/tKd), (6)

where Rp: Percolation velocity of water in soil (m,d-1)fc: Constant (1.0x103 L,m-3)t: Volumetric water content of soil (L,m-3)Lr: Depth of root zone soil (m)r: Bulk density of root zone soil (dry-kg,m-3)Kd: Soil-water distribution coefficient (L,dry-kg-i).For the soil condition of Korea, the values of t and rr

Table 2 Growth characteristics of plants considered in DYNACON(13)

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are givenas 600 and 1,040, 270 and 1,180, and 270 L,m-3and 1,180 ry-kg,m-3 for rice fields, ordinary fields andpasture land, respectively(13). The distribution coeffi-cientKd is defined as the ratio of radioactivity in soil tothat in water in a soil-water system at equilibrium. Thevalues f Kd are assumed to be 1,000, 100 and 100L,dry-kg-1 for 137Cs,90Sr and 131I, espectively(6).The percolation velocity of water in soil Rp is givenby

Rp=fpP+I-E, (7)where fp: Available fraction of precipitation, which istotal precipitation minus surface runoffP: Average precipitation rate (m,d-1)I: Average irrigation rate (m,d-1)E: Average evaporation rate (m,d-1).The values of fp are assumed to be 0.8, 1.0 and 1.0for rice fields, ordinary fields and pasture land, respec-tively(13). The seasonal precipitation is 230.7, 604.3,263.1and 103.3mm for spring, summer, fall and win-ter, respectively(13). The total irrigation for rice fieldsis assumed o be 1,050mm during the growing season ofrice(13). he irrigation is neglected for plants growing inordinary fields or pasture land. Table 3 represents thedaily average evaporation rate in each month accordingto the field types in Korean agricultural conditions(13).7. Adsorption and DesorptionSome radionuclides may be fixed and immobile in soilby their adsorption to clay particles which leads to areduction in the effectiveness of root uptake by plants.To simulate the fixation of 137Csbetween the root zonesoil and the fixed soil compartment, the values 1.9x10-3and 2.1x10-4d-1 are assumed for the adsorption rate

ld and desorption rate lds, respectively(5).8. Root UptakeThe radioactivity in the edible parts of plants throughroot uptake is estimated by the plant-to-soil concentra-tion ratio CR, which is defined as the ratio of radioac-tivity per unit mass of plant (Bq,kg-1-dry plant) to ra-

dioactivity per unit mass of soil (Bq,kg-1-dry soil). Therate of root uptake lup (d-1) is considered to be depen-dent on the growth rate of plants including the edibleparts, which varies logistically(5):

lvp=dBt/dt)CR/rrLr, (8)where Bt: Total biomass including plant leaves and ed-ible parts (dry-kg,m-2).The values of CR are selected from a reference(17) nconsideration of the soil characteristics (clay, loam) ofKorea. For rice, they are assumed to have the samevalues as cereals due to the lack of information.9. Feedstuff Ingestion and Excretion of AnimalsThe transfer of radionuclides from feedstuffs into an-imal products is described by the transfer factor TF(d,kg-1 or d,L-1), which is defined as the fraction ofthe amount transferred from an animal's daily intakeof a radionuclide (Bq,d-1) to 1kg of animal product(Bq,kg-1) at equilibrium, and the biological excretionrate lb (d-1). These parameter values were adopted fromEGOSYS-87(6), a dynamic food chain model developedat GSF-Forschungszentrum fur Umwelt and Gesundheit,Germany. A detailed description of the modeling ap-proach is given in Eq. (18) of this paper. The feed-ing diets of animals vary greatly, but a single feedstufffor each animal is considered. It is assumed that cowsingest fresh pastures and soil during the grazing sea-son, which is equivalent to the growing season of pas-tures, and stored pastures during the non-grazing sea-son. It is assumed that pigs and poultry ingest cerealsas a feedstuff. The feedstuff ingestion rates of animals,FV, are 16.1 dry-kg,d-1 for dairy cows, 7.2 dry-kg,d-1for beef cows, 2.4 dry-kg,d-1 for pigs and 0.07 dry-kg,d-1for poultry(17). The assumed values for soil ingestion,FS, are 0.5 and 0.01 dry-kg,d-1 for dairy and beef cows,respectively(5).IV. Mathematical Formulations

The advantage of the compartmental approach for dy-namic food chain modeling is that each compartment canbe treated independently and described by a relativelysimple mathematical model(18). The compartmental sys-tem consists of a series of interconnected compartmentsrepresenting different parts of the food chain. The rate ofchange of the radioactivity in a particular compartmenti,Xi/dt (Bq,m-2,d-1 or Bq,dry-kg-1,d-1), is describedby the first-order differential equation as follows:

dXi/dt=SKj=1j=/ilijXi-XiSKj=1j=/ilij, (

9) where K: Number of compartmentslj: Transfer rate constant (d-1).A differential equation of this form is made for eachcompartment. Then, the numerical solutions of the cou-

pled differential equations are obtained with daily time

Table 3 Daily average evaporation rate according to thefield types applied in DYNACON(13)

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458 W. T. HWANG et al .

steps (i.e. Dt=1d) using Gear's stiff methods, which is agood algorithm to solve the first-order differential equa-tion system. DYNACON uses a FORTRAN subroutinecalled DGEAR, which is supplied by the InternationalMathematical and Statistical Libraries (IMSL)(19). Thedifferential equations for different compartments withboundary conditions are given as follows:Radioactivity on plant surfaces (XA):

(10)Radioactivity in the inner tissues (or edible parts) of

plants (XB):

(11)Radioactivity in the surface soil (XC):

(12)Radioactivity in the root zone soil (XD):

(13)Radioactivity in the fixed soil (XE):

(14)Radioactivity in the deep soil (XF):

(15)Radioactivity in vegetable foodstuffs at harvest,C*veg(Bq,wet-kg-1), is estimated as follows:

(16)where XA,h: Radioactivity on plant surfaces at harvest

(Bq,dry-kg-1)XB,h: Radioactivity in inner tissues at harvest(q,dry-kg-1)fw: Fraction of radioactivity remaining afterwashingfd: Ratio of dry to wet weight.

It is assumed that XA,h is zero except for leafy veg-etables. The value of fw is given as 0.5 for only leafyvegetables(5). The values of fd are summarized in Ta-

ble 2(13). Radioactivity after harvesting, Cveg Bq,wet-kg-1), decreases by radioactive decay with time:Cveg=C*velge-lat. (17)

The contamination of animal products may be causedby the ingestion of feedstuffs and soil. Therefore, theradioactivity in animal products, Canim (Bq,fresh-kg-1or Bq,L-1), can be expressed as follows:

(18)where N: Number of biological excretion ratesan: Fraction of biological excretion rate n

r: Bulk density of surface soil (1.18x103dry-kg,m-3)(13)Ls: Depth of surface soil subject to ingestion(1.0x10-2m).The first term including biological excretion rates rep-resents the contribution from previous feeding practicesof animals, and the remaining terms represent the con-tamination of animal products resulting from presentfeeding practices. It is assumed that XA is zero for ani-mal products which ingest cereals as a feedstuff.

V. Results and DiscussionRadioactivity in foodstuffs per unit deposition of ra-dionuclides (1Bq,m-2) was estimated using a dynamic

food chain model DYNACON. The 15th day of eachmonth was chosen as the date of deposition for the cor-responding month, except for November, where the 1stday was chosen to avoid overlap with the harvest of leafyvegetables.Figure 2 shows the integrated 137Cs concentrationin foodstuffs over 50 years following an acute deposi-tion as a function of the deposition month. It shows adistinct difference between the deposition in the grow-ing and non-growing seasons of plants. This is becausedeposition-translocation is a primary process in the con-tamination of foodstuffs, while root uptake is a relativelynegligible process. The largest difference in integratedradioactivity is observed in rice with 3 orders of mag-nitude. In general cases, the integrated radioactivity infoodstuffs increases steadily as the time of deposition isclose to the sowing date of plants due to the effects ofresuspension. However, the resuspension process is notconsidered in the case of rice, so the difference of in-tegrated radioactivity in deposition during non-growingseasons can hardly be observed.Figure 3 shows the integrated 90Sr concentrations infoodstuffs over the 50 years following an acute deposi-tion as a function of deposition month. It also showsa distinct seasonal dependence on the date of deposi-tion. However, the seasonal dependence of 90Sr is lessthan that of 137Csbecause of the relatively low translo-



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cation and high root uptake of 90Sr. Therefore, the vari-ationof integrated 90Sr concentrations in most foodstuffsfor deposition during non-growing seasons is hardly ob-served. Consequently, it is concluded that radioactivityin foodstuffs for 137Cs is generally higher than that for90Sr n depositions during the growing seasons of plants ,while he opposite is true for depositions during the non-growing easons of plants.Figure 4 shows the variation of radioactivity in milkand beef as a function of time following 131Ideposition onAugust 15th. Maximum radioactivity is reached withinseveral days after initial deposition. Thereafter, the ra-dioactivity n milk and beef rapidly decreases because ofthe short half-life of 131I (T1/2=8d) and the rapid excre-tion from animal products. Consequently, the short-lived131Is only important for foodstuffs with continuous pro-duction and short storage periods such as milk and beef.

From these results, it has been found that the radioac-tivity in foodstuffs depends strongly on the date of de-position. The difference in radioactivity of foodstuffsamong radionuclides is attributable primarily to phys-ical half-life and physiological mobility.

The results of DYNACON and the NRC model werecompared for 137Cs and 90Sr concentrations in leafy veg-etables and milk. The results of the NRC model maybe compared directly to those of DYNACON becausethe steady-state radioactivity per unit deposition rateis equivalent to the infinite time-integrated radioactiv-ity per unit acute deposition(20). The time-dependentradioactivity in foodstuffs obtained by DYNACON wasintegrated for 100 years. The input parameter valuesrequired in the NRC model were taken from those usedin DYNACON, when available. Otherwise, the defaultparameter values of the NRC model were used. The ra-dionuclide removal by washing in DYNACON was notconsidered. Since the results of the NRC model are es-timated using the input parameter values of the grow-ing season, the results of DYNACON are only comparedfor depositions that occur during the growing season ofplants. Figures 5(a) and (b) show the 137Cs and 90Srconcentrations in leafy vegetables estimated by two mod-els, respectively. During the growing season of leafy veg-etables, the results of DYNACON and those of the NRCmodel are within a factor of 5. Figures 6(a) and (b)are the 137Csand 90Sr concentrations in milk estimatedby two models, respectively. During the growing seasonof pastures, the results of DYNACON and those of theNRC model are within a factor of 10. The differenceof radioactivity in foodstuffs within an order of magni-tude between DYNACON and the NRC model resultsis not so large, even though there are differences in themathematical formulations and the considered transferprocesses in complex food chain models.In addition to the consideration of site-specific data

Fig. 2 137Cs concentrations in foodstuffs integrated over 50years as a function of the deposition month

Fig. 3 90Sr concentrations in foodstuffs over integrated 50years as a function of the deposition month

Same remarks apply here as to Fig. 2.

Fig. 4 Variation of 131Iconcentrations in milk and beef as afunction of time following an acute deposition (dateof deposition: Aug. 15th)

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in DYNACON, significant differences as compared withexisting dynamic food chain models are summarized asfollows: For the simulation of more realistic radionuclidetransfer in Korean agricultural conditions, (1) radionu-clide behavior in rice fields is considered to be differentfrom that in ordinary fields. Resuspension is the impor-tant contamination process for foodstuffs growing in or-dinary fields, but it is not considered for rice fields. Also,time-dependent leaching rate into deep soil is consideredaccording to the characteristics of agricultural practicefor different field types. (2) The resuspension factorof a single value is used for ordinary fields and time-dependent value is used for pasture land. This is becausea radionuclide is well mixed by tillage in ordinary fields,while it is not in pasture land. (3) The root uptake rateis assumed to be proportional to the total biomass in-cluding the edible parts of plants (see Eq. (8)), while thefoliar interception fraction is assumed to be proportionalonly to the biomass of plant leaves (see Eq. (1)). To savecomputation time, (1) time-dependent plant biomass is

obtained from an analytic solution neglecting the lossesof plant biomass resulting from the grazing of animalsand senescence effects, which were considered in PATH-WAY(5). (2) The radioactivity in animal products is alsoestimated by an analytic solution. Consequently, thenumber of coupled differential equations decreased.VI. Conclusions

This paper newly presented DYNACON, a dynamicfood chain model used to simulate the radionuclide trans-fer following an acute deposition on agricultural ecosys-tems. The parameter values in the model were adjustedto representative Korean agricultural conditions as muchas possible. The radioactivity in foodstuffs was esti-mated as a function of the date of deposition. As aresult, it was shown that the radioactivity in foodstuffsdepends strongly on the date of deposition. For rice, theintegrated 137Cs and 90Sr concentrations over 50 yearsshowed a maximum difference of 3 orders and an orderof magnitude, respectively, for the different dates of de-

(a) Time-integrated 137Cs concentration

(b) Time-integrated 90Sr concentrationFig. 5 Comparison of the results from DYNACON and anequilibrium model (NRC model) for time-integrated137Csand 90Sr concentrations in leafy vegetables

(a) Time-integrated 137Cs concentration

(b) Time-integrated 90Sr concentrationFig. 6 Comparison of the results from DYNACON and anequilibrium model (NRC model) for time-integrated137Csand 90Sr concentrations in milk



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position. This underlines the fact that a consideration ofthe realistic growth characteristics of plants is importantin food chain model predictions.

In DYNACON, the Korean foodstuffs were classifiedaccording to the growth characteristics of plant species.Since DYNACON is a dynamic model, it simulates morerealistic behavior of radionuclides in food chains follow-ing an acute deposition.

A comparative study between DYNACON and theNRC model showed that the results of both modelsagreed within an order of magnitude, although math-ematical formulations and considered transfer processesare different.

DYNACON is going to be implemented into a Koreanreal-time dose assessment system FADAS to evaluate theradiological consequences of nuclear accidents. It maybe used to determine the protective measures requiredagainst radioactive contamination of soil and foodstuffs.

[NOMENCLATURE]an: Fraction of biological excretion rate a, dimensionlessB: Biomass of plants (dry-kg,m-2)B0: Initial biomass of plants (dry-kg,m-2)Be: Biomass of edible parts (dry-kg,m-2)Bf: Biomass of plant leaves (dry-kg,m-2)

Bmax:Maximum potential biomass (dry-kg,m-2)Bt: Total biomass including plant leaves and edible parts(dry-kg,m-2)Canim: Radioactivity in animal products (Bq,fresh-kg-1)Cveg:adioactivity in vegetable foodstuffs (Bq,wet-kg-1)C*veg: adioactivity in vegetable foodstuffs at harvest(Bq,wet-kg-1)CR: Plant-to-soil concentration ratioE: Average evaporation rate (m,d-1)F: Initial radioactivity on the ground (Bq,m-2)FS: Soil ingestion rate of animals (dry-kg,d-1)FV: Feedstuff ingestion rate of animals (dry-kg,d-1)

f: Interception fraction of radionuclide to plantsf: Ratio of dry to wet weightfp: Available fraction of precipitationfw: Fraction of radioactivity remaining after washingI: Average irrigation rate (m,d-1)K: Number of compartmentsKd: Soil-water distribution coefficient (L,dry-kg-1)kg: Growth rate constant of plants (d-1)Lr: Depth of root zone soil (m)Ls: Depth of surface soil (m)N: Number of biological excretion ratesP: Average precipitation rate (m,d-1)

R: Percolation velocity of water in soil (m,d-1)RF: Resuspension factor (m-1)TF: Transfer factor into animal products (d,kg-1)Vd: Deposition velocity of resuspended particles (m,d-1)XA: Radioactivity on plant surfaces (Bq,dry-kg-1)XD: Radioactivity in the inner tissues of plant(Bq,dry-kg-1)XC: Radioactivity in the surface soil (Bq,m-2)XD: Radioactivity in the root zone soil (Bq,m-2)

XE: Radioactivity in the fixed soil (Bq,m-2)XF: Radioactivity in the deep soil (Bq,m-2)XA.h: Radioactivity on plant surfaces at harvest

(Bq,dry-kg-1)XB,h: Radioactivity in inner tissues at harvest(Bq,dry-kg-1)Xi: Radioactivity in compartment i (Bq,m-2 orBq,dry-kg-1)a

: Foliar interception constant (m2,dry-kg-1)t: Volumetric water content of soil (L,m-3)ld: Adsorption rate (root zone soil to fixed soil) (d-1)lb: Biological excretion rate from animal products (d-1)

l: Radioactive decay rate (d-1)ls: Desorption rate (fixed soil to root zone soil) (d-1)lg: Dilution rate for plant growth (d-1)llLeaching rate (root zone soil to deep soil) (d-1)lpcPercolation rate (surface soil to root zone soil) (d-1)lre:esuspension rate (surface soil to plant surfaces)

(d-1)ltr: Translocation rate (plant surfaces to edible parts)(d-1)lup: Root uptake rate (root zone soil to edible parts)(d-1)lw: Weathering removal rate (plant surfaces to surfacesoil) (d-1)

r: Bulk density of root zone soil (dry-kg,m-3)r: Bulk density of surface soil (dry-kg,m-3)

-EFERENCES-(1) U.S. Nuclear Regulatory Commission: RegulatoryGuide 1.109, (1977).(2) Muller, H., Prohl, G.: Proc. NEA Workshop on theInfluence of Seasonal Conditions Radiological Conse-

quences of a Nuclear Accident, p. 139 (1989).(3) Nuclear Energy Agency/OECD, reported by a Group ofConsultants: Influence of Seasonal and MeteorologicalFactors on Nuclear Emergency Planning, (1991).(4) Koch, J., Tadmor, J.: Health Phys., 50, 721 (1986).(5) Whicker, F. W., Kirchner, T. B.: Health Phys., 52, 717(1987).(6) Muller, H., Prohl, G.: Health Phys., 64, 232 (1993).(7) Abbott, M. L., Rood, A. S.: Health Phys., 66, 17(1994).(8) Han, M. H., et al., KAERI/RR-1737/96, (1996), [inKorean].(9) Charles, W. M.: NUREG/CR-1004, ORNL/NUREG/TM-282, (1979).(10) Chamberlain, A. C.: Atmos. Environ., 4, 57 (1970).(11) Miller, C. W.: Health Phys., 38, 705 (1980).(12) Pinder, J. E., III: Health Phys., 52, 707 (1987).(13) Lee, J. H., et al., KAERI/RR-998/90, (1990),[in Korean].(14) Peterson, H. T., Jr.: NUREG/CR-3332, ORNL-5968,(1983).(15) Linsley, G. S.: NRPB-R75, (1978).(16) Baes, C. F., III, et al.: ORNL-5785, (1984).(17) International Atomic Energy Agency: Technical Rep.Ser. No. 364, (1994).(18) Faw, R. E., Shultis, J. K.: "Radiological Assessment-Source and Exposures", PTR Prentice-Hall, EnglewoodCliffs, New Jersey, 523 (1993).(19) International Mathematical and Statistical Libraries:"MSL Library", Manual Vol. 1, IMSL Inc., (1984).(20) Whicker, F. W., et al.: Health Phys., 59, 645 (1990).

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