Resuspension and redistribution of radionuclides during grassland and forest fires in the Chernobyl exclusion zone: part II. Modeling the transport process

Journal of Environmental Radioactivity 87 (2006) 260e278 www.elsevier.com/locate/jenvrad

Resuspension and redistribution of radionuclides during grassland and forest fires in the Chernobyl exclusion zone: part II. Modeling the transport process V.I. Yoschenko a,*, V.A. Kashparov a, S.E. Levchuk a, A.S. Glukhovskiy a, Yu.V. Khomutinin a, V.P. Protsak a, S.M. Lundin a, J. Tschiersch b a

Ukrainian Institute of Agricultural Radiology (UIAR), Mashinobudivnykiv str.7, Chabany Kyiv-Svjatoshin distr, Kyiv region 08162, Ukraine b GSF-National Research Center for Environment and Health, Institute of Radiation Protection, D-85764 Neuherberg, Germany Received 21 June 2005; received in revised form 7 December 2005; accepted 15 December 2005 Available online 14 February 2006

Abstract To predict parameters of radionuclide resuspension, transport and deposition during forest and grassland fires, several model modules were developed and adapted. Experimental data of controlled burning of prepared experimental plots in the Chernobyl exclusion zone have been used to evaluate the prognostic power of the models. The predicted trajectories and elevations of the plume match with those visually observed during the fire experiments in the grassland and forest sites. Experimentally determined parameters could be successfully used for the calculation of the initial plume parameters which provide the tools for the description of various fire scenarios and enable prognostic calculations. In summary, the model predicts a release of some & from the radionuclide inventory of the fuel material by the grassland fires. During the forest fire, up to 4% of 137Cs and 90Sr and up to 1% of the Pu isotopes can be released from the forest litter according to the model calculations. However, these results depend on the parameters of the fire events. In general, the modeling results are in good accordance with the experimental data. Therefore, the considered models were successfully validated and can be recommended for the assessment

* Corresponding author. Tel.: þ380 44 526 2444; fax: þ380 44 526 4502. E-mail addresses: [email protected] (V.I. Yoschenko), [email protected] (V.A. Kashparov), [email protected] (J. Tschiersch). 0265-931X/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jenvrad.2005.12.003

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of the resuspension and redistribution of radionuclides during grassland and forest fires in contaminated territories. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Model development; Biomass burning; Plume rise; Radioactive aerosol; Resuspension; Deposition

1. Introduction Various radionuclides at very high concentrations are deposited inside the Chernobyl exclusion zone. Some of these nuclides were deposited during the Chernobyl accident directly onto trees and bushes; others were transferred by root uptake from the contaminated soil to the vegetation. The exclusion zone is covered mostly (almost 2/3 of the total area) by forests and grasslands. It is estimated that several percents of the initially deposited radionuclides are contained in the biomass of the grasslands and even more in the biomass of the forests. These radionuclides currently fixed in the biomass may potentially be mobilized by wildland fires. The aim of the investigation is to quantify the resuspension, transport and deposition of the relevant radionuclides during grassland and forest fires in the Chernobyl exclusion zone. Previous studies on fire resuspension (Kashparov et al., 2000) had been performed outside the Chernobyl exclusion zone giving only data on the nuclide 137Cs. Now, the focus of the investigation is on the potential impact of the radionuclides 90Sr, 238Pu and 239þ240Pu. Part I of this study (Yoschenko et al., 2006) reports the experimental results obtained during controlled fires at three experimental sites in that area (referred as grassland plots #1, #2 and forest plot #3), and provides the necessary array of empirical data for the development and verification of the corresponding mathematical models. In distinction to other observations in the exclusion zone, the data were obtained in the course of prepared fires at well described plots under recorded meteorological conditions, which enable a systematical modeling of the results of each fire event. Part II of the study shows the development of apt modeling tools for the description of the atmospheric transport of the investigated radionuclides by the wildland fires in the ecosystems of the Chernobyl zone. 2. Method of model adaptation The radioactivity spreading during the fire from the burning area involves at least three mechanisms: an initial plume rise, its transportation and the deposition of the aerosol particles. To describe the last two mechanisms, various mathematical models are usually applied, which differ mainly in the consideration of the atmospheric conditions and the related dispersion. The first mechanism, the initial plume rise from various sources, including the buoyant plumes released from a burning area, was primarily formalized by Briggs (1965) and later modified by himself (Briggs, 1968, 1972, 1984) and others (Rodi, 1982; Azarov, 1996). In the present work, the main effort is spent to select and redevelop a physically-based model of the initial plume rise that would operate with empirically measured parameters and to reveal the ways of how to account for the specific fire conditions. 2.1. Initial plume rise In our earlier studies (Kashparov et al., 2000), the initial rise of the radioactive plume was modeled using the mathematical formalization proposed by Talerko (1990). However, the

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List of symbols AS AV(x,y,z) C CP CW Dry F F(x) FStokes g¼ 9.8 m s
2 h HMix I(x,y) J m MS NAV NAS P Q R(z) R0 Rp St SD STD Te Ti(z) U(z) U0 U10 Ugust Uz UD Vt VF W(z) W0 WP x y

the deposition density, Bq m
2; the airborne activity concentration, Bq m
3; the entrainment parameter; the specific heat, J kg
1 K
1; the resistance factor of the plume; the dry mass fraction of the fuel; the buoyancy flux parameter; a function of the radioactive cloud depletion due to the deposition; the Stokes resistance force, N; the gravitational acceleration; the initial height of the point source, m; the thickness of the above-ground homogenized air layer (mixing layer), m; the deposition intensity to the ground surface, Bq m
2 s
1; the specific heat release from the fuel, J kg
1; the particle mass, kg; the fuel mass content per unit area, kg m
2; the number of observation points of the airborne concentration; the number of observation points of the deposition density; the air pressure, Pa; the energy released per time unit during the fire, J s
1; the radius of the plume, m; the initial radius of the plume, m, R0 ¼ R(0); the aerodynamic particle radius, m; the area burned per time unit, m2 s
1; the signed value of deviation; the standard deviation; the ambient air temperature, K, Ti(z)
Te ¼ DT(z); the temperature in the plume, K; the wind speed, m s
1; the wind speed at the ground surface, m s
1, U0 ¼ U(0); the wind speed at 10 m height, m s
1, U10 ¼ U(10); the wind speed at the ground surface during gusts, m s
1; the vertical gradient of the wind speed, s
1; the unsigned value of deviation; the volume of air that is heated in the layer of the height HMix per time unit, m3 s
1; the velocity of the fire front, m s
1; the vertical velocity of the particles in the plume, m s
1; the vertical velocity of the particles at the upper edge of the mixing layer, m s
1, W0 ¼ W(HMix); the particle deposition velocity, m s
1; the horizontal coordinate (distance along the plume axis), m; the horizontal coordinate (normal to the plume axis), m;

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z Zmax a

b(z) f h q re ri(z) rp si(x) S U

263

the vertical coordinate (height above the ground surface), m; the final elevation of the plume, m; the release coefficient which specifies the radionuclide fraction released into the atmosphere (related to the radionuclide inventory in the biomass fuel); the angle between the trajectory tangent and the x-axis; the completeness of fuel burning (the fuel fraction that is combusted); the air viscosity, kg m
1 s
1; the energy necessary for the evaporation of the moisture from the fuel mass unit, J kg
1; the air density outside the plume, kg m
3; the air density inside the plume, kg m
3; the bulk density of the particle, kg m
3; the dispersion along the i-axis, m; the areal activity density (or activity density of the fuel) in the source of release, Bq m
2; the intensity of release, Bq s
1.

attempt of the application of the same approach in the present study showed the necessity of a revision of the model because it calculated a non-realistic high initial ascend of the radioactive aerosols even in case of grassland fires, when the visual height of the plume did not exceed 10e20 m. A revised basic system of equations was derived using the same fundamental considerations as in above-mentioned papers and in this research its description is given in brief below. 2.1.1. Basic system of equations A flat ground-based source of release is approximated by a round area of the radius R0. This approximation is based on the empirical fact that the plumes usually form an almost round cross-section at some height irrespective of the shape of the source of release. We consider a 2-d problem assuming that the particles move in the plume in two directions: vertical, along z-axis, with a velocity of W, and horizontal, along x-axis, which coincides with the direction of the wind speed U. Further, we assume that the source of release has a vertical dimension of HMix, which corresponds to the thickness of the above-ground homogenized air layer (mixing layer) above the burning fuel material during the fire. Visually, HMix might be estimated as the flame height. Within this layer, the temperature of release Ti is constant exceeding the ambient air temperature Te by DT. At the upper edge of the mixing layer, the fire products have only the vertical constituent of the velocity, W0. The following system of equations is derived from the requests of the force and impulse balance on each element of the plume. The thermodynamic legality is taken into account and a linear dependence of the air entrainment velocity on the linear velocity in the plume is assumed (Kachurin, 1973). This approach was proposed by Talerko (1990), only the factor Ti/Te is introduced into the corresponding terms in Eqs. (1) and (2) to adjust the relation of the release to the ambient air temperature: x€W 2


CW U 2 Ti gDT þ x_ ¼ 0 Te 2pRTe

ð1Þ

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dW=dz ¼

gDT CTi CW U 2
W4
x_ Te W RTe 2pRW42

ð2Þ

gTi DTCTi 4
RTe CP Te

ð3Þ

dDT=dz ¼
dTe =dz



 R g gDT dR=dz ¼ C=R 4 ð2 þ DT=Te Þ
1=P dP=dz

2 CP Te Te W 2 42

ð4Þ

where x_ ¼ dx=dz; x€ ¼ d2 x=dz2 ; qffiffiffiffiffiffiffiffiffiffi 4ðzÞ ¼ 1=sin bðzÞ ¼ 1 þ x_2 ; the air pressure P is assumed to be equal inside and outside the plume. The system of Eqs. (1)e(4), along with the above-mentioned initial conditions, describes the plume trajectory in the xz-plane, as well as the dependences of the vertical air velocity, the overheating in the plume and the plume radius R on the elevation. A linear dependence of the wind speed on the elevation dU=dz ¼ Uz ; Uðz ¼ 0Þ ¼ U0 ;

ð5Þ

is added to the above system of equations. Expression (5) represents a simplified approach, but it gives a wind profile in the observed plume elevation range, which is quite similar to the one calculated according to the widely used power-law equation (Irwin, 1979) UðzÞ ¼ U10 ðz=10Þ

P

ð6Þ

2.1.2. Initial parameters of the plume 2.1.2.1. Air overheating. The biomass which potentially may be burned is considered as the fuel. We propose the following expression to calculate the air overheating DT0 ¼ DT(0):   ð7Þ DT0 ¼ Q= Cp M ; where Q is the energy released per time unit during the fire, in J s
1, M is the mass of gas (air and evaporated water), which is heated from Te to Ti (0) per time unit, in kg s
1. Q ¼ ½Jf
qð1
DryÞMS St ;

ð8Þ

In the above expression, fMSSt means the combusted amount of fuel per time unit, in kg s
1. Therefore, the first term in the expression, JfMSSt, corresponds to the total energy release per time unit. Some part of this energy is absorbed in the fuel itself for the evaporation of the moisture and thus must be subtracted from the total energy release. It is assumed that all moisture will be evaporated, which reflects the experimental results (Yoschenko et al., 2006). This is described with the second term, q(1
Dry)MSSt, where q denotes the energy for the evaporation of the moisture from the fuel mass unit, J kg
1, which is calculated using the specific heat

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for water, 4200 J kg
1 K
1, and the specific evaporation heat, 2.26  106 J kg
1 (Landau et al., 1969): q ¼ 4200ð373
Te Þ þ 2:26  106 :

ð9Þ

Then, M ¼ Vt re þ MS fSt ð1
DryÞ;

ð10Þ

where the first constituent in the right part of the equation means the mass of air that is heated in the layer of the height HMix per time unit, and the second constituent corresponds to the mass of water that is evaporated from the fuel material per time unit, in kg s
1. The air volume that is heated per time unit can be expressed as Vt ¼ ðU0 =VF þ 1ÞHMix St :

ð11Þ

The product HMixSt in (11) is the air volume above the burning area in the absence of wind, and St/VF is the width of the fire front. Multiplied by U0HMix, this width determines the air volume that comes into the fire zone per time unit. The approach for the calculation of the initial temperature in the plume is a kind of idealization. The application of the concept of HMix enables to assess the mass and temperature of the heated air, but it does not reflect any local heterogeneities of the heating process. Thus it can be considered as a way for the estimation of averaged or effective overheating values. Also, we did not take into account that some part of the released energy dissipates outside the HMix layer in air, trees and soil. However, the calculation of the temperature in the plume using the expressions (7)e(11) is simple and gives realistic values. 2.1.2.2. Plume radius and velocity. The value of the initial plume radius is calculated from the continuity request of the air flux and the assumption that the fire front is split into several separate equal parts (the number of such parts is denoted as Branching). The whole volume of the heated air is entrained in several equal plumes of radius R0: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Vt R0 ¼ ; pW0 Branching

ð12Þ

where Vt/W0 is the total burning area. With this assumption we ignore any possible interaction between the plumes released from the neighboring parts of the fire front. In our opinion, this assumption works in the case of low fire intensity, however, its limitations remain unclear. The calculation of the plume trajectories at various input parameters showed that they depend on the product R0W0, and are almost stable at R0W0 ¼ Const (assuming reasonable other calculation parameters). Therefore, the next step in the parameter evaluation is the attempt to estimate W0 by observations. Here, it is assigned W0 ¼ 0.1 m s
1 for the grassland fires, and W0 ¼ 0.5 m s
1 for the forest fire, which is concluded from the visual observations of the plume formation during the fire experiments (Yoschenko et al., 2006). However, it is obvious that the main uncertainty is related to the factor Branching, which can be interpreted either as an observation result or as the adjusting parameter of the calculation.

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2.1.2.3. Vertical gradient of the wind speed. Generally, U(z) values in the lower layer of the troposphere depend on the meteorological conditions and the landscape. They can either be measured in experiments or calculated theoretically (for instance, see Bruyatsky, 2000). However, in both cases, their determination is rather complicated. Here a simplified scheme is proposed that is based on the following assumptions:  the wind speed in the lower air layer rises linearly with the height (thus the problem is reduced to the assessment of Uz defined in (5) while U0 is measured in the experiment);  the Uz value conforms to an inequality U0 þ Uz  15  Ugust :

ð13Þ

The inequality (13) means that we assume that the wind speed at the level of the tree tops (15 m, Yoschenko et al. (2006)) does not exceed the wind speed observed above the ground surface at the gusts. The proposed inequality is a first approach for the estimation of the wind speed gradient in the absence of direct measurements. Taking into account that the grassland plots are located in the same landscape as the forest plot, it is proposed, in addition, to assign the same Uzto all performed fire experiments. 2.1.3. Initial rise of ‘‘heavy’’ aerosol particles In the consideration made above it is supposed that the rise of aerosol particles is identical with the whole plume rise. This is reasonable for radionuclides in the atomic state, which behave as gas. Obviously, considering the resuspended radioactive particles of ash, resin, water and non-burned rests of the fuel material, we have to take into account their sedimentation due to the gravity force, mg. On the other hand, the Stokes resistance force also acts on the moving particles. This force is expressed as (Landau et al., 1969) FStokes ¼ 6phRp WP :

ð14Þ

It is assumed that the particles are spherical with the density rp of 1000 kg m
3 which is a common convention in classifying the aerodynamic diameter and using the activity median aerodynamic diameter (AMAD) concept for the assessment of the size of radioactive particles (ICRP, 1994). The balance of forces FStokes ¼ mg ¼ 4=3pR3p rp g

ð15Þ

is valid for the relatively small particles after a negligible period of time, and the particles gain the velocity (derived from Eqs. (14) and (15)) WP ¼ grp R2p =ð4:5hÞ:

ð16Þ

The dependence of the particle vertical coordinate zp on the time is calculated as the integral zp ðtÞ ¼

Z

t

ðW
WP Þ dt: 0

ð17Þ

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The particle ascent can be divided into a set of discrete intervals ziþ1
zi with the average particle velocity of (Wiþ1 þ Wi)/2 inside the i-th interval. The particle passes the i-th interval in the period of Dti ¼ 2 (ziþ1
zi)/(Wiþ1 þ Wi). Then the integral in (17) can be rewritten as the sum:

zp ðjÞ ¼

j
X

Dti

i¼0

  Wiþ1
Wi
WP ; 2

ð18Þ

which provides the possibility to calculate the particle trajectory in the coordinate plane (zx). The measured deposition velocity can be also utilized as WP in Eqs. (17) and (18). The introduction of WP in expression (18) results in a downward bias of the particle trajectory. However, our calculations have shown that this effect is not significant for the aerosol particles in the typical size range (up to 10 mm) and elevation range where the Stokes velocity does not exceed W. Even for a deposition velocity of some 10 cm s
1, the zp(x)-curve at the above-mentioned distances is still located in the range of z(x)  R(x). 2.1.4. Final elevation of the plume The final elevation of the plume asymptotically approximates to some maximal value Zmax. For ‘‘heavy’’ aerosols, there is the maximal plume rise determined by the expression WðZmax Þ ¼ WP :

ð19Þ

For the whole plume, it can be proposed that the maximal rise Zmax is such that xðZmax Þ ¼ xlim ;

ð20Þ

where x(z) is a certain parameter of the plume (for instance, the overheating, the velocity of rise, the angle between the trajectory and ground surface, etc). 2.2. Transportation and deposition of the radioactive aerosol To model the transport process, a standard Gauss model (IAEA, 1980) is applied with the following assumptions: the volumetric source of release has the vertical dimension Zmax  R(Zmax). Within this range, the airborne activity concentration in the plume is described by the normal distribution with the maximum located in Zmax. In the horizontal plane, the source shape and activity distribution are identical to those of the burning plot, and its horizontal coordinates are ‘‘shifted’’ by x(Zmax) along the x-axis as compared to the plot coordinates; - the fire event is a short-term source of release; - variations of the wind speed (except gusts) can be neglected; - the airborne activity concentration and the deposition density at each point are calculated as the superposition of the various particle size fractions. -

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The airborne concentration field for an arbitrary source shape can be described by the integral of the point source function (Gusev and Beliayev, 1991; Bruyatsky, 2000): Gðx; y; zÞ ¼

FðxÞ 2 expð
y2 =2s2y Þ½expð
ðz
h þ WP x=UÞ =2s2z Þ 2psy sz U 2

þ expð
ðz þ h
WP x=UÞ =2s2z Þ

ð21Þ

where the point source coordinates are defined as 0,0,0. F(x) is a function of the radioactive cloud depletion due to deposition (Gusev and Beliayev, 1991), 2 3 Z x pffiffiffiffiffiffiffiffiffi 1 FðxÞ ¼ exp4
2=p WP =U expð
h2 =2s2z Þ dx5 ð22Þ 0 sz Here, the initial height of the point source h can assume any value in the range Zmax  R(Zmax). Then the airborne activity concentration, in Bq m
3, is calculated as AV ðx; y; zÞ ¼ UGðx; y; zÞ;

ð23Þ

where the intensity of release (source strength) U is U ¼ St Sa;

ð24Þ

depending on the size of the burning area St, the areal activity density S and the release coefficient a. The deposition rate to the ground surface, in Bq m
2 s
1, is calculated as Iðx; yÞ ¼ WP AV ðx; y; 0Þ:

ð25Þ

For well defined meteorological conditions the dispersion parameters are tabulated in reference books (e.g., Gusev and Beliayev, 1991). The final point of modeling is the determination of the radionuclide fractions a released into the atmosphere during the fires. 2.3. Concept of the virtual point source of release The airborne activity concentration at any point of the plume trace is the superposition of the concentrations caused by the releases from point sources, resulting in activities which are normal distributed in the vertical cross-section of the plume. On the other hand, the distribution of the airborne concentration in the vertical plane from the point source of release is also described by the normal law. Thus, for any meteorological condition it is possible to find the coordinates of virtual point sources such that the above distributions will coincide at the end of the phase of the initial plume rise with the actual source of release (Fig. 1). This virtual source will be attributed to the total intensity of release of the entire set of actual point sources forming the plume cross-section. The introduction of the virtual point source significantly reduces the further calculations. To realize this concept, the dependence sz(x) is formulated according to Gusev and Beliayev (1991) and Xv is found at which 3sz(Xv) ¼ R(Zmax). The horizontal coordinate of the virtual point source is calculated as X0 ¼ XðZmax Þ
Xv :

ð26Þ

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Plume from the virtual point source of release

Virtual point source of release

X0

Actual source of release

269

Z

X(Zmax)

Normal distribution of the aerosol airborne concentration by height

X

Phase of the initial plume rise

Fig. 1. Scheme of the concept of the virtual point source of the radioactive smoke release.

2.4. Calculation parameters and algorithm The parameters for the model calculation that are interpreted as deterministic are presented in Table 1. Some of these parameters represent widely cited reference data, while other parameters, despite their stochastic nature, are considered as deterministic because their variation in the reasonable ranges does not impact significantly the calculated result. Concerning the stochastic parameters (Table 2), it is necessary to identify both their variation range and their distribution pattern, which is not always determined in the experimental observations. For simplification, a uniform distribution within the experimentally measured variation range is supposed. WP values in Table 2 are presented by the corresponding ranges of the experimental results. In this case, each value calculated according to Eq. (25) is the effective value that averages the velocity range. Because of the lack of large data arrays of this parameter, its distribution is set as uniform in the given range. For S, the given values represent the areal activity density of the principal fuel material, namely grass þ litter in the grassland plots and litter þ fallen branches in the forest plot. The transport calculation from the source for each radionuclide is carried out by MonteCarlo algorithm, which includes the following steps: 1. The fire area is divided into j elementary cells DxiDyi, i ¼ 1.j. 2. Start the calculation loop by DxiDyi. 3. According to the distribution patterns presented in Table 2, a spontaneous set of parameters is generated. 4. DT0 and R0 are calculated according to Eqs. (7) and (12). Then the initial plume rise is calculated using the basic system of Eqs. (1)e(5) taking into account Eqs. (18) and (19). The calculations are done using the adaptive step Runge-Kutta method (Boglayev, 1990). 5. The coordinates of the virtual point source of release are determined. This source is attributed to the release intensity according to Eq. (24) with the assumption a ¼ 1. 6. The airborne radionuclide concentrations (above-surface) and deposition intensities at the observation points are calculated according to Eqs. (21), (23) and (25).

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Table 1 Deterministic parameters for the radionuclide transport model during the fire experiments Parameter

Source

CP (J kg
1 K
1) re at 293 K (kg m
3) h (kg s
1 m
1) Te (  C) 1/P (dP/dz) (m
1) CW C J (J kg
1) f Dry HMix (m) Branching Plot area (m2) MS (kg m
2) St (m2 s
1) VF (m s
1) W0 (m s
1) Uz (s
1) U0 (m s
1) Wind direction (  ) Diffusion category

Landau et al. (1969) Koshkin and Shirkevi (1975) Landau et al. (1969) Yoschenko et al. (2006) Landau et al. (1969) Kochin et al. (1963) Bruyatsky (2000) Dusha-Gudym (1999) Kuchma et al. (2002) Rikhter et al. (2002) Observation/estimate Observation/estimate Yoschenko et al. (2006) Yoschenko et al. (2006) Yoschenko et al. (2006) Yoschenko et al. (2006) Observation/estimate Observation/estimate Yoschenko et al. (2006) Yoschenko et al. (2006) Yoschenko et al. (2006)

Plot #1

22.3

1  107 0.3 0.3 0.3 20 3600 1.1 2 0.067 0.1 0.1 2 Table 2 C

Plot #2 1006 1.3 1.8  10
5 16.2 1.14  10
4 0.9 0.24 1  107 0.3 0.3 20 5400 1.55 3 0.115 0.1 0.1 2 340

Plot #3

26.5

2  107 0.3 0.8 1 10 8770 2.15 1.62 0.052 0.5 0.1 3 Table 2 E

7. The steps 3e6 are repeated n times. The values for the airborne concentration and deposition rate obtained at each observation point at step 6 are stored in the array. For n obtained values of each parameter, the mean value and STD are calculated. 8. The steps 2e7 are repeated j times (for every elementary rectangle DxiDyi). The airborne concentration and deposition rate values obtained at each observation point in step 7 are summarized and their sums are divided by j in order to estimate the corresponding integral values of the release from the whole plot,1 and the STD is calculated. Values of the deposition density AS are derived as a product of the integral value of the deposition rate I and the fire duration (in seconds); 9. The value of the release coefficient a is calculated by minimization of the functional PNAS  exp 2 NAV NAS X X  2 k¼1 ASk exp 2 FðaÞ ¼ aASk
ASk þPNA  exp aAVk
Aexp ;  Vk 2 V k¼1 k¼1 k¼1 AVk

ð27Þ

where the index exp is used to indicate the experimental values at the observation point k. 1 The measured airborne concentration AV is the ratio of the total sampled activity A at the filter during the sampling period (fire duration) T to the sampled air volume V. At the sampling rate n, m3 s
1, the sampled volume is nT. Assuming that the burning time of the elementary rectangle is ti, which causes the airborne concentration AVi in the observation point, and taking into account that ti/T is equal to the ratio of the elementary rectangle area DxiDyi to the total fire area S, we can see that j j P P AV nti X AVi j j X A i¼1 i ¼ AVi ti =T ¼ AVi Dxi Dyi =S ¼ i¼1 ; AV ¼ ¼ V nT j i¼1 i¼1 i.e. the integral value of AV is a sum of the values from each elementary rectangle divided by the number of the rectangles j.

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Table 2 Stochastic parameters for the radionuclide transport model during the fire experiments (according to Yoschenko et al. (2006) and real-time observation/estimate) Parameter 

Wind direction ( ) Ugust (m s
1) Probability of U0b WP 137Cs (m s
1) WP 90Sr (m s
1) WP 238Pu (m s
1) WP 239þ240Pu (m s
1) S 137Cs (kBq m
2) S 90Sr (kBq m
2) S 238Pu (Bq m
2) S 239þ240Pu (Bq m
2)

Distributiona

Plot #1

Plot #2

Plot #3

Multi-modal Uniform Uniform Uniform Uniform Uniform Uniform Normal Normal Normal Normal

180 (0.58); 185 (0.42) 2e4 0.9e0.95 0.026e0.053 0.16e0.57 0.001e0.063 0.001e0.095 290  190 190  140 720  400 1600  1200

Table 1 3e7 0.9e0.95 0.13e0.35 0.09e0.6 0.07e0.28 0.08e0.26 120  80 110  60 87  60 190  140

120 (0.07); 140 (0.52); 165 (0.41) 6e7 0.78e0.82 0.006e0.05 0.002e0.027 0.0035e0.078 0.0029e0.052 140  50 180  60 280  120 600  230

a

Multi-modal e multi-modal with the median value of each mode; the probability of each mode is given in brackets; Uniform e uniform within the presented range; Normal e normal distribution, mean  2 STD. b The probability of Ugust is calculated as (1
probability of U0).

The minimization procedure means that we search for the value of a at which the whole set of the modeled values will have the smallest deviation from the empirical data. For this purposes, the sums of the squares of the deviations in each observation point are calculated. Since the absolute values of AV and AS differ by several orders of magnitude, the ratio of PNAS 

 exp 2 k¼1 ASk PNAV  exp 2 k¼1 AVk is introduced in the second term in the right part of Eq. (27) for normalization. In this approach, all the deviations have the same weight. In principle, several forms of the functional can be constructed, and the proposed one was chosen because it provides a simple way to compare modeled and observed values for the whole set of observation points. For all plots, the number of runs n was equal to 5000, while the number of cells j was 360, 540 and 877 for the plots #1, #2 and #3, respectively. 3. Modeling results and discussion The results obtained in the fire experiments (Yoschenko et al., 2006) were used for the evaluation of the proposed model. The ability of the model was tested to predict the resuspension and transport of radionuclides during wildland fires. The end points of modeling have been the determination of the release coefficient a for each radionuclide and the evaluation of the modeling quality using the two criteria defined as follows: the signed value of deviation, SD   N xmodel
xexp P k k xexp k SD ¼ k¼1 100% N and the unsigned value of deviation, UD

ð28Þ

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N xmodel
xexp

P k k xexp k¼1 k 100% UD ¼ N

ð29Þ

where N ¼ NAV þ NAS and xmodel and xexp are values of the airborne concentration or the deposition density at the observation point k determined by the model and the experiment, respectively. The calculated trajectories of the plume match well with those observed in the experiments. In Fig. 2 the forest fires plumes are calculated as example for the mean wind velocity and for the wind gusts. The plume rises higher at low wind velocity, while the gusts force the plume to pass lower over the ground surface. Fig. 2 also depicts the plume trajectories calculated according to Brigg’s (1972) equation for neutral and unstable atmospheric conditions, zðxÞ ¼

1:6F1=3 x2=3 U

ð30Þ

where the buoyancy flux parameter gR20 W0 DT0 ð31Þ Te is calculated using the approaches for the determination of the initial plume parameters specified above. In general, the present calculation results are similar to those predicted by Eq. (30), but the Briggs’ curves rise slower in the beginning, and the maximum elevation is observed much farer from the source of release (at distances of approximately 160 m and 130 m at the mean wind speed and at the gusts, respectively). However, the new approach enables to calculate the temperature, velocity and radius of the plume, and can be applied for heavy aerosols as well. The comparison of the modeling data and the experimental results is shown in Figs. 3e5. In each plot, values of both, the airborne radionuclide concentration and the deposition density are presented to visualize the consistency of model and experiment. The cluster in the upper right part of the plot corresponds to the deposition density values and the other cluster consists of the airborne concentration values. Vertical and horizontal bars at each value represent the uncertainties of the modeled and measured results, respectively. The data of all Pu isotopes for each grassland fire were combined (238þ239þ240Pu) because of their limited number (for the forest fire more results are available and 238Pu and 239þ240Pu are presented separately). The evaluation of the modeling quality according to Eqs.(28) and (29) are presented in Table 3, as well as the release magnitudes of each radionuclide during the fire experiments. The modeling results of the grassland fires show that F¼

 the model predictions are close to the empirical data (Table 3). Generally, the SD and UD values are comparable to the STD of the experimental and modeling results which demonstrate the good agreement between model and experiment;  the worst consistency of the model predictions with the empirical data is observed near the source of release and, especially, inside the source (Figs. 3 and 4), which results from the virtual point source concept;

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273

60

a)

z, m

40

20

0 -20

0

20

40

60

80

40

60

80

x, m 60

b)

z, m

40

20

0 -20

0

20

x, m Fig. 2. Model calculation of the plume rise above the forest site: the present model (thick lines, contour ¼ centerline  s) and Briggs equation (thin lines, centerline) at the mean wind speed (a) and at the gusts (b).

 the released fraction of 90Sr was the same in the two experiments, while the release of the 137Cs and Pu isotopes in the second grassland fire experiment was twice as much as in the first experiment. In general, the model predicts a release of some & from the radionuclide inventory of the fuel material by the grassland fires;  the applied models describe satisfactorily the studied processes and can be proposed for the prediction of the radionuclide redistribution over flat terrain during grassland fires. However, the modeling results can be lower than the experimental values near the source of release, which shows the limitations of the model. The deviation of the model results near the source of release is due to neglected processes which are more relevant in the near zone of the fire. E.g., the model does not take into account that some part of the airborne activity in this area can be associated with giant particles (pieces of grass, etc.) which settle from the plume due to their high deposition velocity. Convective turbulent eddies can also redistribute some part of the released radioactivity near the source of release while we consider only the transport in the plume. The impact of local heterogeneities of the burning plot is higher close to the plot.

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274

1000 137Cs

model

100 10 1 0.1 0.1

1

10

100

1000

100

1000

0.1

1

experiment 1000 90Sr

model

100 10 1 0.1 0.1

1

10

experiment 1 238+239+240Pu

model

0.1

0.01

0.001

0.0001 0.0001

0.001

0.01

experiment Fig. 3. Model predictions vs experimental data for the grassland fire at plot #1: experimental result and model calculation of the airborne activity concentration in Bq m
3 (,) and the deposition density in Bq m
2 (-) are given for each observation spot.

The modeling results match well with the experimental data obtained during the forest fire (Fig. 5). The deviation between the empirical data and the model predictions is the lowest for 137 Cs, while for the other studied radionuclides the deviation is more than 100% (but lower than one order of magnitude) at 5e7 observation positions. At all these positions, the model predictions exceed systematically the measured values, and one might assume that some local obstacles (which are ignored in the modeling exercises) may have caused the low experimental values. If these locations are not considered, the model criteria SD and UD are only half as high as those reported in Table 3. The stochastic pattern of the actual plume transport and the measurement uncertainties are additional sources of discrepancy between model and experiment. Besides the above

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1000 137

model

100

Cs

10 1 0.1 0.01 0.01

0.1

1

10

100

1000

10

100

1000

experiment 1000

model

100

90Sr

10 1 0.1 0.01 0.01

0.1

1

experiment

model

0.1 0.01

238+239+240Pu

0.001 0.0001 0.00001 0.00001

0.0001

0.001

0.01

0.1

experiment Fig. 4. Model predictions vs experimental data for the grassland fire at plot #2: experimental result and model calculation of the airborne activity concentration in Bq m
3 (,) and the deposition density in Bq m
2 (-) are given for each observation spot.

discussed process idealizations, some assumptions were made which may have impact on the modeling quality:  the fuel material inventory per unit area and its thermal characteristics are the same at any part of the burning area;  the fire front is split into round sources of equal size;  shielding effects and turbulences caused by the tree crowns and trunks are ignored;  the forest fire is of the surface type, i.e. the periods of crown fire are ignored;  when applying the Gauss model (including the wind velocity) the atmospheric surface layer is of uniform characteristic. Also, the use of the virtual point source concept entails the possibility of an underestimation of the airborne concentration and fallout densities in the starting stage of the plume rise

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100 137

model

10

Cs

1 0.1 0.01 0.01

0.1

1

10

100

10

100

0.01

0.1

experiment 100

model

10

90Sr

1 0.1 0.01 0.01

0.1

1

experiment 0.1 238Pu

model

0.01 0.001 0.0001 0.00001 0.00001

0.0001

0.001

experiment 1

model

0.1

239+240Pu

0.01 0.001 0.0001 0.00001 0.00001

0.0001

0.001

0.01

0.1

1

experiment Fig. 5. Model predictions vs experimental data for the forest fire at plot #3: experimental result and model calculation of the airborne activity concentration in Bq m
3 (,) and the deposition density in Bq m
2 (-) are given for each observation spot.

(Fig. 1). But in general, the utilized models provide reasonable predictions and can be recommended for the estimation of the radioecological impact of wildland fires in the Chernobyl exclusion zone. 4. Conclusions The developed model for the initial rise of the radioactive smoke plume (1)e(5) satisfactorily describes the studied process. The predicted trajectories and elevations of the plume match

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Table 3 The model quality criteria signed value of deviation (SD), unsigned value of deviation (UD) and release coefficient (a) assessing the model predictions for the three fire experiments Quality criteria

Radionuclide 137

90

Grassland fire (plot #1) SD (%) UD (%) a (%)


30 66 0.062


11 46 0.15


14 61 0.033

Grassland fire (plot #2) SD (%) UD (%) a (%)

67 109 0.14

160 190 0.16

2 72 0.069

Forest fire (plot #3) SD (%) UD (%) a (%)


10 21 4.2

46 55 2.9

9 57 0.78

Cs

238

Sr

Pu

239þ240

Pu

40 71 0.77

with those visually observed during the fire experiments in the grassland and forest sites and those predicted according to Brigg’s equation. The utilization of the measured parameters in expressions (7), (12) and (13) for the calculation of the initial plume parameters is a great advantage of the model as it provides the tools for the description of various fire scenarios and enables prognostic calculations. In absence of detailed data on the local weather conditions and surface characteristics, the Gauss model can be satisfactorily applied to characterize the aerosol transport in the atmosphere. In general, the modeling results are in good accordance with the experimental data. Therefore, the considered models were successfully validated and can be recommended for the assessment of the resuspension and redistribution of radionuclides during grassland and forest fires in contaminated territories. During the grassland fires the released radionuclide fraction from the fuel material (litter and grass) into the atmosphere can be estimated as follows: 137Cs and 90Sr e up to some &; Pu e up to 1 &. During the forest fires, up to 3e4% of 137Cs and 90Sr and up to 1% of the Pu isotopes can be released from the forest litter. The released fraction of the radionuclides during the forest fires may even be bigger if the source of release is a large-scale and is a very intensive fire, since in this case a bigger burn-up of the combustible material can be expected. Acknowledgements The presented studies were carried out within the frameworks of the project #1992 funded by the Science and Technology Center in Ukraine (STCU). The authors kindly appreciate the support they met from the STCU, as well as the assistance of the Administration of the Exclusion zone in the organization and of the fire brigades in the realization of the experimental works. References Azarov, S.I., 1996. Estimation of the atmospheric pollution by Biology Radioecology 36, 506e515 (in Russian).

137

Cs in forest fires in the Chernobyl zone. Radiation

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Boglayev, Yu.P., 1990. Calculus Mathematics and Programming. Book Company ‘‘Visshaya Shkola’’, Moscow, 544 pp. (in Russian). Briggs, G.A., 1965. A plume rise model compared with observations. Journal of the Air Pollution Control Association 15, 433e438. Briggs, G.A., 1968. CONCAWE meeting: discussion of the comparative consequences of different plume rise formulas. Atmospheric Environment 2, 228e232. Briggs, G.A., 1972. Discussion: chimney plumes in neutral and stable surroundings. Atmospheric Environment 6, 507e510. Briggs, G.A., 1984. Plume rise and buoyancy effects. In: Randerson, D. (Ed.), Atmospheric Science and Power Production. U.S. Dept. of Energy, Springfield, VA, pp. 327e366. DOE/TIC-27601, DE84005177. Bruyatsky, Ye.B., 2000. Theory of Atmospheric Diffusion of the Radioactive Releases. Institute of Hydromechanics of NAS of Ukraine, Kiev, 444 pp. (in Russian). Dusha-Gudym, S.I., 1999. Radioactive Forest Fires. A Reference Book. Moscow, VNIIClesresurs, 160 pp. (in Russian). Gusev, N.G., Beliayev, V.A., 1991. Radioactive Releases into the Biosphere: A Manual. Book Company ‘‘Energoatomizdat’’, Moscow, 256 pp. (in Russian). IAEA, 1980. Atmospheric Dispersion in Nuclear Power Plant Siting: A Safety Guide. International Atomic Energy Agency, IAEA. Safety Series No 50-SG-53, Vienna, Austria. ICRP, 1994. Publication 66. Human Respiratory Tract Model for Radiological Protection. Annals of the ICRP 24. Pergamon Press, Oxford. Irwin, J.S., 1979. A theoretical variation of the wind profile power-law exponent as a function of surface roughness and stability. Atmospheric Environment 13, 191e194. Kachurin, L.G., 1973. Physical Principles of Influence on the Atmospheric Processes. Gidrometeoizdat Publishing House, Leningrad (in Russian). Kashparov, V.A., Lundin, S.M., Kadygrib, A.M., Protsak, V.P., Levtchuk, S.E., Yoschenko, V.I., Kashpur, V.A., Talerko, N.N., 2000. Forest fires in the territory contaminated as a result of the Chernobyl accident: radioactive aerosol resuspension and exposure of firefighters. Journal of Environmental Radioactivity 51, 281e298. Kochin, N.E., Kibel, I.A., Roze, N.V., 1963. Theoretical Hydromechanics, P.1. Physmatgiz Publishing House, Moscow (in Russian). Koshkin, N.I., Shirkevi, M.G., 1975. Reference Book for Elementary Physics. Nauka Publishing House, Moscow, 256 pp. (in Russian). Kuchma, N.D., Bednaya, S.M., Arkhipov, N.P., 2002. Long-term radioecological consequences of the forest fires in the radioactive contaminated territories. In: Prevention, Elimination and Consequences of the Fires in the Radioactive Contaminated Territories. Collection of the Scientific Works 54. Institute of Forest of NAS of Belarus, Gomel, pp. 155e158 (in Russian). Landau, L.D., Akhieser, A.I., Lifshitz, E.M., 1969. Course of the Basic Physics. Mechanics and Molecular Physics. Nauka Publishing House, Moscow, 400 pp. (in Russian). Rikhter, I.E., Klimchik, G.Ya., Akunovich, E.G., 2002. Pyrological characteristics of the surface fuel material in the heather and mossy pine woods. In: Prevention, Elimination and Consequences of the Fires in the Radioactive Contaminated Territories. Collection of the Scientific Works 54. Institute of Forest of NAS of Belarus, Gomel, pp. 64e67 (in Russian). Rodi, W., 1982. Turbulent Buoyant Jets and Plumes. HMT (The science and applications of heat transfer). Pergamon Press, 172 pp. Talerko, N.N., 1990. Calculation of radioactive admixture ascent from Chernobyl NPP accidental unit. Meteorology and Hydrology 19, 39e46 (in Russian). Yoschenko, V.I., Kashparov, V.A., Protsak, V.P., Lundin, S.M., Levchuk, S.E., Kadygrib, A.M., Zvarich, S.I., Khomutinin, Yu.V., Maloshtan, I.M., Lanshin, V.P., Kovtun, M.V., Tschiersch, J., 2006. Resuspension and redistribution of radionuclides during grassland and forest fires in the Chernobyl exclusion zone. Part I. Fire experiments. Journal of Environmental Radioactivity 86, 143e163.