Modeling Groundwater-Surface Water Interaction and Contaminant Transport of Chlorinated Solvent...

Modeling groundwater-surfacewater interactions including effectsof morphogenetic depressionsin the Chernobyl exclusion zoneA.C. Bixio Æ G. Gambolati Æ C. Paniconi Æ M. Putti Æ V.M. Shestopalov

V.N. Bublias Æ A.S. Bohuslavsky Æ N.B. Kasteltseva Æ Y.F. Rudenko

Abstract Morphogenetic depressions or ‘‘dishes’’in the Chernobyl exclusion zone play an importantrole in the transport of water and solutes (in par-ticular the radionuclides 137Cs and 90Sr), functioningas accumulation basins and facilitating their transferbetween the surface and subsurface via return flow(under conditions of high soil water saturation) andinfiltration. From a digital elevation model (DEM) ofthe 112-km2 study area, 583 dishes (covering about10% of the area) are identified and classified intofour geometric types, ranging in size from 2,500 to22,500 m2, and with a maximum depth of 2 m. Thecollective influence of these depressions on thehydrology of the study basin is investigated with acoupled model of three-dimensional saturated andunsaturated subsurface flow and one-dimensional(along the rill or channel direction s) hill-slope andstream overland flow. Special attention is given tothe handling of dishes, applying a ‘‘lake boundary-following’’ procedure in the topographic analysis, alevel pool routing algorithm to simulate the storageand retardation effects of these reservoirs, and ahigher hydraulic conductivity in the topmost 3 m ofsoil relative to non-dish cells in accordance withfield observations. Modeling the interactions be-tween the surface and subsurface hydrologic regimes

requires careful consideration of the distinctionbetween potential and actual atmospheric fluxes andtheir conversion to ponding, overland flow, andinfiltration, and this coupling is described in somedetail. Further consideration is given to the treat-ment of snow accumulation, snowmelt, and soilfreezing and thawing processes, handled via linearand step function variations over the winter monthsin atmospheric boundary conditions and in uppersoil hydraulic conductivities. A 1-year simulation ofthe entire watershed is used to analyze the watertable response and, at the surface, the ponding headsand the infiltration/exfiltration fluxes. Saturationpatterns and return flow and seepage fluxes aresimilar between the dishes and the main channelnetworks, with, as expected, preferential infiltrationin the dishes.

Keywords Chernobyl Æ Groundwater Æ Modeling ÆSurface water

Introduction

Atmospheric fallout from the Chernobyl accident in April1986 caused radioactive contamination in the large terri-tories of Ukraine and Belarus. The major impact to theenvironment was concentrated within a 30-km radiussurrounding the Chernobyl nuclear power plant (NPP).Following a local government resolution, the area sur-rounding the NPP where gamma exposure doses exceeded20 mrad/h was evacuated. This area forms the so-calledChernobyl exclusion zone (CEZ), which today comprisesapproximately 70 km2 located mostly on the west side ofthe NPP. Recent observations taken within the CEZrevealed the important role of ‘‘zones of fast vertical mi-gration’’ in the penetration into groundwater of long-livedradionuclides, such as 137Cs and 90Sr, released during theaccident (Shestopalov and others 1999). These anomalouszones, common in many areas of the Ukraine, Belarus, andPoland as well as other countries, are manifested as to-pographic depressions, either round (‘‘dishes’’) or linear(‘‘combs’’), with depths varying from centimeters tometers and planimetric dimensions ranging from a few

Received: 10 June 2001 / Accepted: 10 September 2001Published online: 28 March 2002ª Springer-Verlag 2002

A.C. Bixio Æ G. Gambolati Æ M. Putti (&)Dip. Metodi e Modelli Matematici, Universita di Padova,via Belzoni 7, 35131 Padova, ItalyE-mail: [email protected].: +39-049-8275919Fax: +39-049-8275995

C. PaniconiCRS4, Sesta Strada Ovest, Z.I. Macchiareddu,09010 Uta (CA), Italy

V.M. Shestopalov Æ V.N. Bublias Æ A.S. BohuslavskyN.B. Kasteltseva Æ Y.F. RudenkoRadioecological Center, National Academy of Sciencesof Ukraine, 55-b Gonchar St., Kyiv 252054, Ukraine

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162 Environmental Geology (2002) 42:162–177 DOI 10.1007/s00254-001-0486-7

to several hundred square meters (Fig. 1). Notwithstand-ing their limited cumulative area (they occupy no morethan 10% of the CEZ), these depressions drain more than60% of the total surface runoff. The hydrogeologicalcharacteristics of these depressions are also peculiar: theporous formation in its central portions has vertical per-meabilities that are, on average, three to five times largerthan the surrounding areas. During precipitation andsnowmelt events a large amount of surface water accu-mulates inside the dishes and the high hydraulic gradients,in combination with the high permeabilities, create a zoneof preferential vertical flow, with infiltration rates thatexceed those of the surrounding areas by as much as oneorder of magnitude (Shestopalov and others 1996).Mobilization and redistribution of 137Cs and 90Sr occursbecause of surface runoff, causing accumulation of theseradionuclides in the depressions. The mineralogical com-position of the soil, with high pH and high metal oxideconcentrations, enhances the mobilization and penetrationof the nuclides into the soil along these pathways and fromthere into the underlying phreatic Quaternary aquifer.Evidence of contamination of this aquifer has been re-ported by Bugai and others (1996, 1997) and Shestopalovand others (1995), with 137Cs contamination levels up to10 5 kBq/m3 under the cooling pond of the NPP.Concentrations of up to 15 Bq/m3 were also measured inthe deeper confined aquifer in the vicinity of the pumpingstation used to produce potable water for the city ofPrypiat. The causes of this contamination were traced backto leakage of the radionuclides from the phreatic aquiferbecause of incorrect sealing of the well casings(Shestopalov and others 1995).A simulation tool capable of describing the processes ofradionuclide surface redistribution and infiltration intothe groundwater in such a complex system needs to beable to simulate the water behavior in both the surface andsubsurface environments. In this paper we present aphysically-based distributed catchment-scale model for

the simulation of coupled surface runoff and subsurfaceflow, and describe its implementation and application tothe Chernobyl exclusion zone basin.The model is based on coupling Richards’ equation forvariably saturated porous media and a diffusion waveapproximation for surface water dynamics. The numericalscheme uses a finite element saturated-unsaturated sub-surface flow solver, FLOW3D (Paniconi and Putti 1994;Paniconi and Wood 1993), and a surface DEM-based finitedifference module, SURF_ROUTE (Orlandini and Kosso1996). Starting from a DEM discretization of the catch-ment surface and a corresponding three-dimensional gridof the underlying aquifer, atmospheric input (precipitationand evaporation data) is partitioned into surface andsubsurface components by the FLOW3D module on thebasis of the prevailing flux and pressure head values cal-culated at the surface. The overland flux values calculatedby FLOW3D at the grid nodes are transferred to the DEMcells and implemented as sink or source terms in theSURF_ROUTE module, which routes this surface waterand calculates the resulting ponding head values, whichare, in turn, used as boundary conditions in FLOW3D.Retardation and storage effects caused by lakes ordepressions are also implemented, giving a completedescription of the catchment flow dynamics.

Experimental evidence

Several field campaigns were conducted within the CEZover the past few years to understand the importance ofthe anomalous depressions in the hydrological behavior ofthe Chernobyl basin. We will summarize these activitieswith the aim of presenting evidence for preferential infil-tration patterns of radionuclides from the depressionstowards the Quaternary aquifer. The data from thesecampaigns has been used for the determination of thehydrological parameters and for calibration of the coupledsurface–subsurface flow model described later.

Geophysical studiesGeophysical studies of the anomalous depressions wereperformed using georadar and radon–thoron emanationprofiling, electromagnetic surveying and seismo-acousticsounding. Several observation sites with different mor-phological characteristics were selected to study thestructural peculiarities of the depressions in the CEZ anddeposits that form them, and to ascertain the depth of thegeodynamic origin of these unusual structures. An exampleof the results of the elaboration of the data obtained at theStari Shepelichi experimental site by means of georadarand radio–thoron-based techniques is reported in Fig. 2.The upper picture shows a vertical cross section of thedepression that interprets the georadar survey performedto a depth of 5 m. The equipment used for this activityconsisted of a SIR-2 complex, equipped with an antennaoperating at 300 MHz frequency. Post-processing of fielddata was accomplished with the program Radan (Shest-opalov and others 1999). The central part of the picture

Fig. 1Typical distributions of the anomalous depressions in the Chernobylexclusion zone. The water flow directions and the depressionsubcatchments are also indicated

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Environmental Geology (2002) 42:162–177 163

shows evidence of disintegration structure in the activezone of the depression. In good correlation with this resultare the radon–thoron emanation profiling data obtained ata depth of 0.5 m with an alpha–beta analyzer of NC-4286gamma-spectrometer. The middle and bottom plots in thefigure show the variation in radon–thoron ratio and radoncontent, respectively. These measures are used as an indi-cation of disintegrated zones and are related to the inten-sity of the geodynamic processes that occurred in thedeeper crystalline basement (Shestopalov and others 1999).The technique is based on measuring radon and thoronactivities at the soil surface. Because of the differences inhalf-life period between radon and thoron gases (3.5 daysand 54 s, respectively) the emanations recorded at thesurface cannot come from deposits that are deeper than10 m for radon and 0.5 m for thoron. Thus, the statisticalpredominance of emanations from the ‘‘deeper’’ radon gasover the ‘‘shallower’’ thoron gas (high radon/thoron ratio)indicates enhanced escape of radon gas because of thehigher permeabilities found in the depressions.The right-hand-side of the figure shows a planar view ofthe observation site indicating also the position of thedifferent survey profiles. Results from seismo-acoustic(shock method, depths to 50 m) and electromagnetic(depths to 600 m) surveys at various experimental siteshave shown that the zones of rock disintegration under-lying the central zone of the depressions may reach adepth of 100–500 m.

Infiltration dataHydrogeological experiments were performed at five ob-servation plots in the CEZ, using piezometric wells, lysi-meters for the determination of water infiltration rates, andsuction pressure gauges installed at different depths withinthe unsaturated zone (0–2 m). Summary results of this ac-tivity, performed during 1995 at the Stari Shepelichi site, areshown in Fig. 3. Yearly averages of the infiltration rates areplotted on a cross section of the depression, together with

groundwater levels measured at approximately monthlyintervals from March to November 1995. The maximuminfiltration rate reaches a value of more than 800 mm/yearwhereas the total annual precipitation does not exceed600 mm/year. This shows the importance of overland andsubsurface water flowing into the depression. The ground-water table in the central part reacts quickly to variations ofprecipitation intensity, and large spreading cupola areformed after spring snowmelt and after summer rainstorms.

Radionuclide activity measurementsSurface concentrations of Chernobyl-born radionuclides(90Sr and 137Cs) within the CEZ reach levels up to 106 Bq/m2. This situation provides a good starting point for un-derstanding the relative properties of radionuclide verticaltransport in the central and background zones of thedepressions. For this purpose 1 m deep pits were exca-vated at the Veresok and Liutegh sites. The location ofthese pits is shown in Fig. 2. Soil samples were taken at1 cm spaced intervals and analyzed in the laboratory.Figure 4 reports the vertical distribution of the 90Sr(Veresok site) and 137Cs (Liutegh site) concentrations. Upto two orders of magnitude differences in the activity levelsbetween the central and background zones are stillnoticeable at 1 m depth, showing the important role ofthese depressions as vehicles for radionuclide infiltrationtowards the Quaternary aquifer.

Description of the mathematicalmodel

Coupled subsurface flow and surface runoff can bemathematically described by a system of two partialdifferential equations, one describing the flow of water inthe vadose and groundwater zones (Richards’ equation)

Fig. 2Geophysical experimental evi-dence (georadar profile, radoncontent, radon–thoron ratio)relative to profile GREP 1 at theStari Shepelichi site. The planarview of the depression with itselevation (m a.s.l.) is shown inthe right figure together with theGREP sections (dashed lines) andthe locations of the two pitswhere 137Sr concentration mea-surements were periodicallytaken

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164 Environmental Geology (2002) 42:162–177

and the other describing the surface hydrologic responseof the catchment (hill-slope and channel flow). Couplingarises because the overland flow rate is affected by pre-cipitation (evaporation) and infiltration (exfiltration)rates. In turn, infiltration (exfiltration) in the soil is af-fected by ponding heads that result from surface routing.In formulating the mathematical model, we assume thathill-slope flow concentrates in rills or rivulets. In this wayboth channel and hill-slope flow can be described by aone-dimensional convection–diffusion equation definedon the rill or channel network using different parametervalues to distinguish between the two flow regimes.The system of partial differential equations is made up ofthe water mass balances for the subsurface in the form ofRichards’ equation and for the surface catchment in theform of a convection–diffusion equation complementedwith a Manning-type relationship that takes account ofdissipation. It takes the form:

r Swð Þ @w@t ¼ r � KsKrw Swð Þ rw þ gsð Þ½ �þqs hð Þ ð1Þ

@Q

@tþ ck

@Q

@s¼ Dh

@2Q

@s2þ ckqL h; wð Þ ð2Þ

where rðSwÞ ¼ SwSs þ / @Sw

@w ; Sw wð Þ is the water saturationof the porous medium, Ss is the aquifer specific storagecoefficient, / is porosity, w is pressure head, t is time, r isthe gradient operator, Ks is the saturated hydraulic con-ductivity tensor, Krw(Sw) is the relative hydraulic con-ductivity function, gz=(0,0,1)T, z is the vertical coordinatedirected upward, and qs represents distributed source orsink terms (volumetric flow rate per unit volume). Thesurface water is routed using Eq. (2) along each single hill-slope or channel link using a one-dimensional coordinatesystem s defined on the drainage network. In this equation,Q is the discharge along the channel link, ck is the kine-matic wave celerity, Dh is the hydraulic diffusivity, qL is thelocal source/sink term and h is the water depth (ponding

Fig. 4Vertical distribution of 90Sr (Ve-resok site) and 137Cs (Liuteghsite) concentrations in the upper1 m of soil: 1 center of thedepression; 2 depression border(background)

Fig. 3Annual averaged infiltration rates and vari-ations of groundwater levels for the subsur-face aquifer at the Stari Shepelichidepression: a infiltration rates (mm/year);b surface profile of the depression zone;c groundwater depth variations in time(depths are calculated with respect to thelowest elevation value in the depression anddates are reported as dates and months).Three zones can be distinguished dependingon the infiltration rates: the central or activezone (A); the transition zone (B); the slopingzone (C); and the background zone (D). Thesix wells used for piezometric measurementsare shown with dashed lines

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head). Note that qs includes the contributions of the in-coming (by infiltration) or outgoing (by exfiltration) waterfluxes into the porous medium through the soil surface.These fluxes are nonlinear functions of the surface pond-ing heads through the characteristic curves of the soil. Thesource/sink term of the diffusion-wave equation, qL, in-cludes the local contribution to the surface flow (overlandflow rate) from the subsurface, which is a nonlinearfunction of ponding and pressure heads at the groundsurface.The simultaneous solution of the coupled system ofequations for the unknown vector (Q,w) or (h,w) requiresthe consideration of these nonlinear dependencies; addi-tional nonlinearities arise in the Sw(w) and Krw(Sw) char-acteristic curves in Richards’ equation.

FLOW3D Richards’ equation solverFLOW3D is a three-dimensional finite element model forflow in variably saturated porous media, applicable to boththe unsaturated and saturated zones. The characteristicrelationships Krw(Sw) can be specified using the vanGenuchten and Nielsen (1985), Brooks and Corey (1964),or Huyakorn and others (1984) expressions. Equation (1)is highly nonlinear because of the pressure head depen-dencies in the storage and conductivity terms, and is lin-earized in the code using either Picard or Newton iterationpanput93b (Paniconi and Putti 1994). Tetrahedral ele-ments and linear basis functions are used for the discret-ization in space, and a weighted finite difference scheme isused for the discretization in time. The code handlestemporally and spatially variable boundary conditions,including seepage faces and atmospheric inputs, and het-erogeneous material properties and hydraulic character-istics.For the treatment of the atmospheric boundary conditions,the input flux values are considered ‘‘potential’’ rainfall orevaporation rates, and the ‘‘actual’’ rates, which depend onthe prevailing flux and pressure head values at the surface,are dynamically calculated by the code during the simu-lation. Overland flow, defined as the flow rate that ispresent at the surface and that can be routed via the sur-face model, is calculated at every time step from the bal-ance between potential and actual fluxes.Automatic switching of surface boundary conditions froma specified flux (Neumann) to a constant head (Dirichlet)condition, and vice versa, is implemented to correctly re-produce the physical phenomena occurring at the surface.For example, in the case of precipitation, if a surface nodebecomes saturated because of infiltration excess, thefraction of precipitation that does not infiltrate and re-mains at the surface (ponding head) becomes the overlandflow to be routed via the surface module. The boundaryconditions in this case switch from Neumann (atmo-sphere-controlled) to Dirichlet (soil-controlled) type. Ifprecipitation intensity decreases, so that the magnitude ofactual (computed) flux across the soil surface exceeds themagnitude of the atmospheric flux, the boundary condi-tion switches back to a Neumann type. If a surface nodebecomes saturated because of saturation excess (the water

table reaches the surface), and there is an upward fluxacross the soil surface (return flow), the overland flow iscalculated as the sum of precipitation and return flux. Theentire amount of water that remains at the surface or ex-filtrates from the subsurface is then transferred for routingto the DEM-based surface runoff module, which, in turn,returns, after surface propagation, the ponding headdistribution to FLOW3D.

SURF_ROUTE surface runoff solverThe surface hydrologic response of a catchment is con-sidered as determined by the two processes of hill-slopeand channel transport, operating across all the hill-slopesand stream channels forming a watershed and includingstorage and retardation effects of pools or lakes and in-filtration/evapotranspiration and exfiltration effects fromsubsurface soils.

Hillslope and channel processesWe assume that hill-slope flow concentrates in rills orrivulets that form and modify during the runoff event as afunction of slope, runoff characteristics and soil erodibil-ity. To minimize the computational effort and economizeon the number of model parameters, the rill formationsare lumped at the DEM elemental scale into a single con-ceptual channel. Each elemental hill-slope rill and networkchannel is assumed to have bed slope and length thatdepend on location within the extracted transport net-work, and a rectangular cross section whose width variesdynamically with discharge according to the scalingproperties of stream geometry as described by the ‘‘at-a-station’’ and ‘‘downstream’’ relationships first introducedby Leopold and Maddock (1953).The distinction between hill-slope and channel flow isbased on the ‘‘constant critical support area’’ concept asdescribed by Montgomery (1993). Rill flow is assumed tooccur for all those cells for which the upstream drainagearea A does not exceed the constant threshold value A*,whereas channel flow is assumed to occur for all those cellsfor which A equals or exceeds A* .A routing scheme developed on the basis of the Muskin-gum–Cunge method with variable parameters is used todescribe both hill-slope rill and network channel flows,with different distributions of the Manning roughnesscoefficients to take into account the different processesthat characterize the two physical phenomena (Orlandiniand Rosso 1996). The model routes surface runoff down-stream from the uppermost DEM cell in the basin to theoutlet, following the previously determined drainage net-work. A given grid cell will receive water from its upslopeneighbor and discharge it to its downslope neighbor, withthe inflow or outflow rate qL at any catchment cell givenby:

qL ¼ qDxDy=Ds

where q is the local contribution to surface runoff, ascalculated by FLOW3D, Dx and Dy are the cell sizes, and Dsis the channel length within the cell. Inflow hydrographsand overland fluxes qL are routed into each individual

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channel via the convection–diffusion flow Eq. (2), dis-cretized by the Muskingum–Cunge method to yield:

Qkþ1iþ1 ¼ C1Qkþ1

i þ C2Qki þ C3Qk

iþ1 þ C4qkLiþ1

ð3Þ

where Qk+1i+1 is discharge at network point (i+1)Ds and

time (k+1)Dt, qkLiþ1

is the overland flow rate at the (i+1)stspace interval and time kDt, and the routing coefficients Ci

depend on ck, on the temporal interval Dt, on the channellength Ds, and on the numerical scheme. Once the in andout discharge at each cell is determined, the cell waterdepth, or ponding head h, can be calculated from simplelocal mass balance considerations.

Topographic depressionsIsolated topographic depressions (‘‘pits’’) in the catchmentDEM can be attributed to the presence of pools or lakes, orcan be interpreted as erroneous or missing data. Depres-sions cannot be handled by automatic drainage networkextraction procedures, and depitting techniques are gen-erally used to modify the elevation values and to regularizethe DEM. These depitting schemes correct DEM errors andcan also be used in steep basins, where the flow is mainlydriven by slope and where slight artificial modifications oftopography will not significantly change surface flow pat-terns. However, when depressions play an important rolein the formation of surface and subsurface fluxes theseprocedures introduce inconsistent flow directions and donot correctly reproduce the storage and retardation effectsof pools and lakes on the catchment response. This typi-cally happens in relatively flat areas where flow patternsare strongly influenced by small slope changes.In this work topographic depressions are treated as follows.Initially the location of the pits is identified from the DEMand from prior field information. A ‘‘lake boundary-fol-lowing’’ procedure of Mackay and Band (1998) is employedto isolate and correct for potential breakdown in the sub-sequent drainage network extraction process. By thisprocedure, each cell along the boundary of the pit (alsocalled ‘‘buffer cells’’) acts as a depression point for all thecatchment cells draining into the pit. To ensure correct flowpaths in the area, the drainage direction in all the buffercells is forced to form a circulation path that drains into asingle cell (the lake outlet cell). A flow path algorithm, incombination with a ‘‘slope tolerance’’-based correctionprocedure to account for the remaining erroneous depres-sions, is then applied to the modified DEM that excludes thecentral cells of the depression. The storage and retardationeffects of the pit are accounted for by transferring withinfinite celerity all the water drained by the buffer cells tothe lake outlet cell, which is now treated as a reservoir. Allthe geometrical and physical characteristics of the depres-sion are thus attributed to this cell. Outflow from this cell iscalculated by solving, by a level pool routing procedure, thecontinuity equation for the reservoir:

@V

@t¼ I tð Þ O hð Þ ð4Þ

where V is the storage volume of the reservoir, I and O arethe incoming and outgoing discharges, functions of time

and of water elevation (above a reference level) in the res-ervoir h*, respectively. The reservoir water elevation thusdetermined is then assigned to all the lake cells and used inFLOW3D as ponding head, whereas the discharge from thereservoir is the outgoing flux at the cell to be used inSURF_ROUTE.

Coupling between the surface and subsurfacemodules

The explicit in time nature of the Muskingum–Cungediscretization scheme allows the construction of the fol-lowing non-iterative algorithm for the solution of Eqs. (1)and (2):for tk=0 to tmax with step Dt:

• Solve Eq. (2) using qkL as input to the SURF_ROUTE

model, obtaining Qk+1 and from this the distribution ofponding heads hk+1;

• Use hk+1 and precipitation/evaporation input at timetk+1 to set up boundary and initial conditions forFLOW3D (‘‘boundary conditions updating’’), and solveEq. (1) for wk+1;

• Calculate (again with FLOW3D) the overland flux qk+1L

using wk+1 and the balance between atmospheric inputsand actual fluxes.

In practice, because of the explicit conditionally stablediscretization scheme applied to solve the surface routingmodule, the first step in the above algorithm is sub-dis-cretized into smaller time steps whose size is estimatedbased on the Courant stability criterion.The algorithm needs to be initialized, and this is done bysetting an initial condition in terms of qL for Eq. (2). If thiscondition, as often happens, is not known a priori, it canbe calculated from an initial run of FLOW3D, which willevaluate a first guess for the overland flow based on theactual atmospheric input. In this case, an initial distribu-tion of w, generally more easily known, needs to bespecified.After the initialization of the algorithm, at every time-stepexchange of information regarding the subsurface fluxcontributions to surface ponding (calculated by FLOW3Dand passed on to SURF_ROUTE) and the nodal pressurehead values corresponding to ponded surface cells(SURF_ROUTE to FLOW3D) occurs. This exchange isstrongly linked to the control algorithm in the subsurfacemodule that checks for and switches surface boundaryconditions from soil-driven to atmosphere-driven regimesand vice versa. It is this algorithm that flags each surfacenode according to whether it is currently ponded, satu-rated, below saturation, or air-dry, calculates the ‘‘actual’’infiltration/exfiltration fluxes, and determines the overlandflow rate to be passed to the SURF_ROUTE module.Physically, the distinction between a surface node being‘‘saturated’’ or ‘‘ponded’’ is made via the input parameter‘‘pond_head_min’’, which is assigned the threshold pres-sure head value a surface node must attain to be consid-ered ponded, in the sense of having water available forrouting by the overland flow module. The value of

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pond_head_min can be set to account for the amount ofwater that can remain trapped in microtopographic fea-tures of the surface. Algorithmically, the introduction ofthe parameter pond_head_min allows us to activate theSURF_ROUTE module only when there is surface wateravailable for routing, rather than at every time step.

Implementation and applicationof the model to the Chernobyl site

The numerical model was applied to simulate the hydro-logical response of a watershed within the Chernobylexclusion zone during a typical hydrological year. Thephysical phenomena of snow accumulation and progres-sive freezing of the upper soil during winter, and snowmeltand soil thawing during spring, are taken into account aswill be explained below.

Delineation of the study domain and treatmentof the dishes

The watershed indicated in Fig. 5 was chosen within theCEZ. It extends for 111.5 km2 on the right bank of thePrypiat River, and is delimited to the north by the PrypiatRiver itself, to the west by the Sakhan River, to the southby moraine hills, and to the east by the cooling pond of thenuclear plant and by a small river. The territory is rela-tively flat, with elevations varying from 98 to 152 m a.s.l.,and is crossed by a dense network of drainage channelsdischarging into the Prypiat River; many dishes of roundand elongated shape, with planimetric dimensions varyingbetween 50 and 150 m and depths of 0.5–2 m, characterizethe area. Vertically, the domain extends to a depth of 27 mand includes the unconfined Quaternary aquifer underlainby the low-permeability Kiev marl formation (Fig. 6).

A 50·50-m resolution DEM of the selected domain wasobtained by digitizing available 1:50,000, 1:25,000, and1:10,000 maps and interpolating the digitized points usinggeographic information system (GIS) software. The DEMcontains a total of 44,606 cells, with its highest point(151.90 m) in the moraine hills and its lowest point(98.99 m) at the outlet of the Prypiat River from the basin.An artificial increase of 0.5 m in the elevation of the cellsalong the eastern and western boundaries of the domainwas necessary to guarantee a unique outlet cell. Thisincrease did not significantly alter the surface flow char-acteristics of the study domain because any water fluxesthrough these boundaries are considered to be negligible.Treatment of the dishes within the DEM was a complextask because they were too numerous to be clearly iden-tified and digitized from the topographic maps, and toovaried in dimension and shape to be considered individ-ually. These difficulties were overcome by identifying alimited number of dish ‘‘classes’’, each class of definedshape, dimension, and 50·50-m DEM cell geometry, at-tributing each depression of the study domain to one ofthese classes, and randomly distributing the dish classes ortypes over the previously digitized DEM in such a way asto preserve the original density of dishes (derived fromsatellite images) and their actual class distribution.Applying this procedure, four dish classes or types (Fig. 7)were identified: the first type has a round shape with di-ameter of approximately 50 m (one DEM cell) and 0.5 mmaximum depth; the second has an elongated shape withmain planimetric dimensions of 50 and 150 m (1·3 DEMcells) and depth varying between 0.5 and 1.5 m; the third isround with a diameter of 150 m (five DEM cells in total)and depth of 0.75–1.5 m; and the fourth is also roundwith a diameter of 150 m (3·3 DEM cells) and depth of

Fig. 5The watershed study site within the Chernobyl exclusion zone

Fig. 6Vertical schematization of the study domain showing the predomi-nant layers and their depths, which are considered constant withrespect to the ground surface. Porosity n and saturated hydraulicconductivity Ks values are assumed constant in each layer. The porousmedium is considered to be isotropic

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0.75–2.0 m. The discretization of the four dish typesguarantees a reasonable simulation accuracy of the flowdynamics in both the surface and subsurface models with amanageable size of the computational grid. A smaller DEMcell dimension would provide better spatial resolution, butwith highly increased computational costs. However,simulation in a small subcatchment showed that the 50·50cell is enough to capture the effects of the depression at thescale of interest. The ‘‘buffer’’ cells and the ‘‘reservoir’’ cellfor each dish type were determined as shown in Fig. 8. Thestudy domain was subdivided into eight zones character-ized by different densities of each dish type. In total, 583dishes were obtained, as shown in Fig. 9. The surface

drainage network automatically extracted from the DEMof the basin with all the dishes is shown in Fig. 10.

Definition of model parametersModel parameters for the soil, hill-slope, and channelcharacteristics were obtained from a combination of fieldmeasurements, prior calibration experiments, valuesreported in the literature, and a number of short-time(10 days) simulations. Given that the artificial drainagechannel network within the study domain has been com-pletely abandoned since the nuclear accident and vegeta-tion growth has been left uncontrolled, only hill-slope flowwas considered in the model, with a low Manning rough-ness coefficient (ks=1 m1/3/s). Leopold and Maddock

Fig. 7Schematization of the four dish classes or types, indicating the depthof each cell (in cm) within these representative dishes

Fig. 8Buffer cells and reservoir cell (R) for the four representative dishtypes

Fig. 9Distribution of the 583 dishes over the study basin (dish cells areshown in red, whereas buffer cells are yellow)

Fig. 10Surface drainage network for the study basin extracted from the dish-processed DEM. The picture shows the drainage direction in eachcell as a small arrow. The drainage channels are obtained byreleasing 100 uniformly distributed particles over the network andadvecting them until they reach the outlet (unitary speed ofpropagation is assumed over each link)

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(1953) scaling coefficients, as derived from the literature,are W=2, P=2, b‘‘=d’’=0.26, and b‘‘=d’’=0.5 . The hydro-geological properties of the soil, derived by the solution ofthe inverse problem in steady and unsteady conditions(Shestopalov 1998), are summarized in Fig. 6. The char-acteristic curves of the unsaturated zone were derivedfrom experimental measurements fitted with the UNSODAand RETC models (Leij and others 1996; van Genuchtenand others 1991) using the family of curves described byHuyakorn and others (1984; a=0.05, b=2, c=2, Swr=0.333,and n=1), with the final parameter values refined by cali-bration on a number of short-time simulations.To simulate the freezing and thawing of the upper soillayer during winter and spring periods, and their effects oninfiltration/exfiltration phenomena, the saturated hydrau-lic conductivity value of the upper loamy sand layer waslinearly decreased from its actual value to zero over theperiod 15–30 December (progressive icing of soil and di-minished capacity for water exchange between the surfaceand the subsurface), was kept at zero for the months ofJanuary, February, and March (soil completely frozen and,consequently, no infiltration or exfiltration is possible),and was linearly increased back to its actual value from 31March to 15 April (progressive thawing of soil and re-establishment of groundwater–surface water interactions).

3-D grid and boundary and initial conditionsIn discretizing the study domain the 44,606 DEM cellsresulted in 45,216 surface nodes and 89,212 triangles. Thevertical discretization of the domain into eight layers, asindicated in Fig. 6, produced a 3-D grid with a total of406,944 nodes and 2,141,088 tetrahedra. The numericalmodel allows the user to assign different hydrogeologicalproperties (porosity, hydraulic conductivity, etc) not onlyvertically (layer by layer), but also laterally according toan attribute index assigned to each 2-D surface triangle. Ifthe index is ‘‘1’’ for all triangles, then the porous mediumis (laterally) homogeneous; if the index ranges, forinstance, from ‘‘1’’ to ‘‘12’’, then the porous medium is

heterogeneous with 12 different material types (horizon-tally). For the CEZ application, five material types wereused, one for each of the four dish classes, plus one for thenon-dish or ‘‘background’’ cells. The saturated hydraulicconductivity of the upper 3 m of soil for the dishes was setat a value five times higher than the background value(1.75 and 0.35 m/day, respectively).The base and lateral boundaries of the 3-D domain wereconsidered to be impermeable, so that all surface andsubsurface flow is directed towards the watershed outletcell. These boundary conditions are justified by the role ofnatural water divide played by the moraine hills and by therivers and channels delimiting the watershed, by the verylow regional hydraulic gradients characterizing the Qua-ternary aquifer, and by the very low conductivity of theunderlying marl formation. This is confirmed by theresults of a regional groundwater modeling study showingthat the flow in the Quaternary aquifer is mostly deter-mined by surface recharge (Shestopalov and others 1999).The atmospheric boundary conditions (treated by themodel as ‘‘potential fluxes’’, as described earlier) werederived from observed rain and snow data for the year1997. Average daily potential evaporation rates were cal-culated by the Thornthwaite formula (Chow 1964) usingobserved temperature data.The atmospheric boundary conditions were set to zeroduring the freeze months (1 January to 30 March), therebynullifying any infiltration or runoff generation during thisperiod. The actual snowfall over this 3-month period wasaccumulated, transformed into equivalent water height,and supplied as ‘‘snowmelt’’ input to the model between 30March and 15 April assuming a linear in time melting ofthe accumulated snow volume.A 1-year simulation, without taking into account thefreezing–melting mechanism, was run using the observedatmospheric inputs to establish initial conditions at 1January. The piezometric and ponding head distributionsresulting from this simulation are shown in Figs. 11 and12.

Fig. 11Initial conditions: the phreaticlevels

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Simulation resultsThe coupled model was run for a 1-year simulation pe-riod and took 4,013 time steps for the subsurface prob-lem, varying in length between 4.32 s and an upper limitof 2.4 h (the time-step size is dynamically updated

according to nonlinear convergence behavior, increasingif convergence in the solution of Richards’ equation isachieved in few iterations and decreasing if convergenceis slow), with an average value of 4.46 iterations per timestep. The surface problem was solved in 79,210 timesteps, for an average of about 20 sub-discretization timesteps within each time step of the overall coupled solu-tion algorithm.Figure 13 shows the time-step sizes for the subsurface andsurface modules and the number of nonlinear iterations inFLOW3D for the 1-year simulation, along with a histogramof the potential precipitation–evaporation fluxes. Asexpected, the subsurface problem requires a smaller timestep and a higher number of nonlinear iterations wheneverthe atmospheric potential flux is intense, or when itchanges from precipitation to evaporation or vice versa.The time step required for stability of the surface solver isgenerally larger whenever the surface network is relativelyempty and flow velocities are low (implying small Courantnumbers).In Figs. 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, and 24 theresults of the simulation in terms of phreatic level, surfaceponding heads, and actual infiltration–exfiltration fluxes

Fig. 12Initial conditions: surface ponding heads distribution

Fig. 13Atmospheric forcing (atmpot),time step lengths for the sub-surface (dt-flow3d) and surface(dt-surfroute) modules, andnonlinear FLOW3D iterationsfor the 1-year simulation

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across the surface are shown for selected simulation times.We can observe that:

• At time 90 days (30 March), because of the zero atmo-spheric fluxes imposed during the antecedent freezemonths, the ponded areas are reduced relative to theinitial conditions (1 January) because the surface wateris routed to the outlet with no additional inputs arrivingfrom either atmosphere or subsurface. The pondingheads along the Prypiat River, for instance, have beenreduced from 7–13 cm on 1 January to 0.5–3 cm. Thewater-table levels, on the other hand, remain essentiallyunaltered owing to the reduced permeability applied tothe upper soil during the freeze period.

• At time 100 days (10 April), in response to precipitationand the release of accumulated snow over the freezemonths, the extent of ponding over the study domainand the ponding head values increase significantly(to 3–30 cm along the Prypiat River), and the drainagenetwork is more pronounced. The actual fluxes are

Fig. 14Phreatic levels at time 90 days

Fig. 15Ponding heads at time 90 days


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predominantly infiltration, with intensities varying be-tween 0.02 and 0.05 m/day. Preferential infiltration isclearly evident in the main channels of the drainagenetwork (values up to 0.1 m/day) and in some of thedishes (values up to 0.2 m/day). Exfiltration (return flowand seepage) is localized at the base of the moraine hillsand along the channels. The phreatic levels remainsubstantially unaltered because the soil has only par-tially thawed (i.e., saturated hydraulic conductivities arestill below their actual values). This implies that theincrease in ponded areas is caused by the ‘‘infiltrationexcess’’ mechanism rather than ‘‘saturation excess’’;

• At time 107 days (17 April), the precipitation peak(0.0194 m/day) causes an overall increase in pondingheads (6–50 cm along the Prypiat River) and a slight risein water-table levels, which now reach the soil surface inthe central part of the basin. In this area there is thus

Fig. 18Actual fluxes at time 100 days



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saturation excess runoff generation, while the morainehills are still in unsaturated conditions, with infiltrationintensity equal to the rainfall rate. The flux map showshow infiltration and exfiltration phenomena of varyingintensities predominate over different portions of thebasin, with seepage and return flow prevailing at thebase of the hills and laterally along the main channel ofthe network;

• At time 120 days (30 April), after 3 days of potentialevaporation (–0.001 m/day), large areas of the basin areno longer ponded and the phreatic surface is slightlylowered in the central-eastern region. Water depths inthe channels are not substantially altered, whereas in theunsaturated up-slope or hill areas the actual evaporation(–0.0005 m/day) is less than the potential rate becausethe water content in the soil is not sufficient to satisfy




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completely the atmospheric demand. Exfiltration pre-vails in the basin, but some preferential infiltration stilloccurs in some of the dishes and in the main channels ofthe network.

Figure 25 shows the hydrograph at the outlet cell of thebasin together with the atmospheric potential fluxes. Wecan observe that the hydrological response of the basin ishighly correlated with the storm and interstorm events andthat the delay time between peak rainfall and simulateddischarge at the outlet varies between 1 and 2 days.

Conclusions

The simulation results are consistent with field observa-tions made of the role of the morphogenetic depressions inthe hydrological response of the Chernobyl exclusion zonebasin to rainfall, snowmelt, and interstorm events. Thesetopographic dishes accumulate water via surface runoff

and return flow or seepage, and allow preferential migra-tion of this water into the subsurface because of theirhigher permeabilities. Although they cover only a smallportion of the basin in terms of total area, their ubiquityand sheer number suggest that these depressions can exerta strong influence, not only on the hydrologic regime ofthe CEZ, but also on the transport of hazardous contam-inants such as long-lived radionuclides.The simulation results presented here were focused on thefirst 4 months of a 1-year simulation in order to illustratethe numerical handling and hydrological role of snowfall,snowmelt, soil freezing, and soil thawing. These processescan be handled in a simple manner by using the hydraulicconductivity and atmospheric flux parameters to effec-tively block surface and subsurface flow during peakwinter months and to gradually reduce or increase thesupply of water during brief transitional freezing andthawing periods. The simulations were also focused oninvestigating the collective influence of the morphogeneticdepressions; with additional observation data on individ-ual dishes, smaller scale simulations can be used to ex-amine in detail the impact of these preferential infiltrationzones, quantifying the roles of geometry and heterogene-ity, and assessing the adequacy of the simple handling ofseasonal processes implemented here. Further studiescoupling the flow regime computed here with a transportmodel for radionuclides are also needed to more fullyaddress the significance of the morphogenetic depressionsand their ground and surface water impacts.The coupled surface–subsurface flow model is shown to bea useful tool for analyzing detailed interactions betweensurface water and groundwater at the catchment scale. Animportant feature of the model for the Chernobyl appli-cation is the treatment of topographic depressions orlakes, in a pre-processing step during the DEM analysis todefine and classify the dishes and the overland flow pathsaround them, and in the simulation algorithm for thestorage and release of incoming water from both surface



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and subsurface contributions. The model also handles, viaautomatic switching of surface boundary conditions fromDirichlet to Neumann type, the complex exchanges be-tween potential atmospheric inputs, surface ponding, andsubsurface fluxes that determine the partitioning of rain-fall into runoff and infiltration and the generation ofsurface saturation, overland flow, and seepage.The subsurface module is 3-D, nonlinear, and implicit intime whereas the surface module is 1-D and explicit intime. Nonetheless the CPU time required to solve thesurface component was actually greater than the CPU forthe subsurface component because of the sub-discretiza-tion time steps required for stability of the surface solver.Spatial discretization of the 112-km 2 study area resulted in44,606 50·50-m DEM cells, each cell subdivided into twotriangles and vertically replicated to yield a 3-D grid of406,944 nodes and 2,141,088 tetrahedra. This represents alarge-scale problem for a typical workstation, requiringdays or weeks of simulation turnaround time and largememory requirements and, therefore, is more effectivelyexecuted (hours or days of turnaround) on a high-end ormultiprocessor computer.

Acknowledgements This work has been partially funded by theINCO Programme of the European Commission (project RaCoS,grant number IC15-CT96-0211). The fourth author also ac-knowledges the support of the Italian Ministry of the University(project ISR8, C11-B) and the Sardinian Regional Authorities.

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