coupling 1d monte-carlo simulations and geostatistics to...

Ž .Journal of Contaminant Hydrology 32 1998 25–39

Coupling 1D Monte-Carlo simulations andgeostatistics to assess groundwater vulnerability to

pesticide contamination on a regional scale

Marc Soutter ), Andre Musy´Institute of Land and Water Management, Swiss Federal Institute of Technology, EPFL-Ecublens, 1015

Lausanne, Switzerland

Received 29 August 1997; revised 1 September 1997; accepted 1 September 1997

Abstract

A method to predict groundwater vulnerability to pesticide contamination on a regional scalehas been developed and applied to a part of the upper Rhone river valley in Western Switzerland.

Ž .Stochastic application of deterministic pesticide leaching models Monte-Carlo , along withgeostatistical interpolation techniques, were used to map both vulnerability levels and uncertain-

Žties. The various tested leaching models numerical and analytical solutions of the convection–dis-.persion equation, capacitive model lead to similar outcomes. The resulting maps show very high

vulnerabilities. However, uncertainties are large, ranging from 20–30% for vulnerability indicesŽ . Ž .between 0 and 1. Variations in pesticide properties 40–50% , water table depth 30–40% and

Ž .organic carbon content 20% account for almost all the uncertainties on predicted contaminationlevels. q 1998 Elsevier Science B.V. All rights reserved.

Keywords: Groundwater; Pesticide; Convection–dispersion

1. Introduction

Non-point source pollution of groundwater by various agricultural by-products consti-tutes a major environmental problem since gradual decrease of water quality mayimpair, in the long term, its use as drinking water supply. The diffuse and progressivenature of pesticide accumulation makes the control or management of this kind of

) Corresponding author. Fax: q41-21-693-37-39.

0169-7722r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved.Ž .PII S0169-7722 97 00075-2

( )M. Soutter, A. MusyrJournal of Contaminant Hydrology 32 1998 25–3926

pollution difficult. In most cases, evidence of pollution or benefits resulting from pestcontrol take several years to become perceptible. State-wide andror regional groundwa-ter vulnerability assessments could, therefore, help to promote contextually adaptedpreventive actions and become an efficient tool for natural resources management.

Identifying highly vulnerable areas implies a systematic evaluation of the contamina-tion potential over a wide region. Such an approach is, therefore, related to the more

Ž .general issue of the coupling or integration of geographical information systems GIS ,environmental databases, and simulation models, that aim not only at developingpredictive tools for management purposes but also at achieving a better understanding ofthe processes involved.

Groundwater vulnerability to non-point sources has been the subject of considerableŽ .attention in the past decade, with attempts at regional assessments by Aller et al. 1987 ,

Ž . Ž . Ž . ŽKhan and Liang 1989 , Meeks and Dean 1990 , Loague et al. 1989 , Loague 1991,. Ž . Ž .1994 , Petach et al. 1991 , Bleeker et al. 1995 , to mention just a few. The coupling

Ž .issue has emerged more recently and was reviewed by Corwin and Wagenet 1996 .The application of macro-scale simulation models to account for larger, mega-scale

processes, especially when the latter include transport in an unsaturated soil, faces threeŽ . Ž .major problems Jensen and Mantoglou, 1992 : i validity of the partial derivatives

Ždescribing the processes at macro-scale e.g., Richards’ equation or the convection–dis-. Ž .persion equation when applied to describe the global behavior, ii definition of the

‘mean’ parameters used by these equations and determination of ‘representative’ valuesŽ .and iii quality of the outputs, i.e., uncertainties.

The approach presented in this paper combines local simulations of pesticide leachinginto the groundwater with subsequent interpolation of the resulting local vulnerabilitylevels. It, therefore, overcomes the first two problems mentioned above, since macro-scalemodels are applied to macro-scale processes with measurable macro-scale parameters.However, taking uncertainties into account is still needed if the vulnerability maps thatmay be drawn are to be used as agricultural management tools. This may be achieved

Ž . Ž .either i by stochastic modelling, ii by a stochastic application of deterministic modelsŽ . Ž .Monte-Carlo , or iii by error propagation methods in the case of analytical solutions.The availability and the widespread use of deterministic models dictated our choice ofthe Monte-Carlo method. Its principle consists of sampling repeatedly an output

Ž . Ž .Ys f X , . . . , X for various sets of inputs X , . . . , X , which are randomly generated1 n 1 n

according to the probability density functions that define the variables X , . . . , X .1 n

When applied successively to several soil profiles, this method produces localŽprobability distributions of a vulnerability index mass ratio of the amount of pesticide

.reaching the water table to the amount of pesticide applied on soil surface . InterpolationŽ .of these local distributions by geostatistical tools kriging, stochastic imaging provides

an estimated groundwater vulnerability index distribution over the whole area.Ž .The research reported in the present article intended i to evaluate the potential and

Ž .limitations of the selected approach, ii to evaluate relative and respective effects ofvarious sources of uncertainties on the final results and, as a by-product, determine the

Ž .key variables on which data collection should focus, and iii to compare variousleaching models to ascertain how far simplification in process description affects

Ž .predicted contamination Soutter, 1996; Soutter and Pannatier, 1996 .

( )M. Soutter, A. MusyrJournal of Contaminant Hydrology 32 1998 25–39 27

2. Simulation models

Ž .The main processes involved in pesticide behavior in soils are i biological degrada-Ž . Ž .tion, ii chemical degradation, iii sorption by the organic and mineral constituents of

Ž . Ž . Ž .the solid matrix, iv uptake by plant roots, v volatilization and vi flow-relatedŽ .diffusion, dispersion and convection processes Musy and Soutter, 1991 . They are

described in mathematical form by a standard convection–dispersion equation:

E C E E CL LuqrK f q´ K s q u D u ,qŽ . Ž .OC OC HE t E z E z

E h u E CŽ . LqC K u q1 qD t ´ K "QŽ . Ž .L a Hž /ž /E z E z

w 3 xwhere C denotes the pesticide concentration in the liquid phase kgrm , u the waterLw 3 3 x w 3 xcontent m rm , r the bulk density kgrm , K the partition coefficient of theocw 3 x w xpesticide m rkg , f the organic carbon content of the soil kgrkg , K the modifiedoc H

w xHenry’s constant of the pesticide y , i.e., the ratio of its vapor pressure density to itsw 3 3 x Ž .aqueous solubility, ´ the saturation deficit m rm , D u ,q the diffusion–dispersion

w 2 x Ž . w x Ž .coefficient m rs , K u the hydraulic conductivity of the soil mrs , h u its matricw x w 2 x Ž .pressure m , D the molecular diffusion coefficient in air of the pesticide m rs , t qa

w xthe tortuosity factor of the soil y and Q a sink term accounting for degradationprocesses, most frequently according to first order kinetics.

Pesticide fate may be simulated using more or less simplified models. Numericalsolution of the convection–dispersion equation above, e.g., using the computer code

Ž .LEACHM Hutson and Wagenet, 1992 , represents the most advanced alternative,whereas solving analytically a simplified version of that equation would be the most

Ž .basic one attenuation factor; Rao et al., 1985 . In the latter case, simplification resultsfrom the assumptions of steady flow at field capacity along with a purely convectivetransfer process and instantaneous phase equilibrium. The attenuation factor AF may be

Ž .expressed for a stratified soil as follows Soutter, 1996 :

nC 1nAFs sexp y r d RF uŽ .Ž .Ý i i i fc iC q0 is1

where C and C are the pesticide mass applied at the soil surface and leached into the0 nw x Ž .groundwater respectively kg , q the net recharge rate usually on an annual basis

w x w y1 xmrd , and, for the various soil layers i, r denotes the degradation rate d , d thew x w 3 3 x w xthickness m , u the field capacity m rm and RF a retardation factor y expressingfc

Ž .the specific mobility of the pesticide in the soil u being the saturated water content ,s

r f K u y u KŽ . Ž . Ž .i oc oc s fc Hi i iRF s1q qi

u uŽ . Ž .fc fci i

Ž .The capacitive model LEACHA; Addiscott, 1977 represents an intermediate optionŽin that transport processes are accounted for by a cascade of reservoirs or cells, or thin


.soil layers with specified discharge rules rather than by the convection–dispersionmechanisms: water fluxes between two adjacent cells are determined to achieve hy-draulic potential equilibrium whereas solute fluxes are computed according to waterfluxes and available solute concentrations.

3. Data processing

The use of these simulation models in a Monte-Carlo process requires the preliminarydetermination of the probability density functions describing the various parametersinvolved, i.e., soil properties, pesticide properties, water table depth and climatecharacteristics.

The 2 km-wide and 10 km-long study area selected for the present research is locatedin the upper Rhone river valley, between the cities of Martigny and Sion, in Southwest-ern Switzerland, about 460 m above sea level. Data on soil and groundwater werecollected within the framework of the foreseen construction of ten hydropower unitsŽ .project HYDRO-RHONE along the Rhone river, which flows from the NE to the SWŽ .Fig. 1 .

3.1. Soil properties

Ž .Soil data for the study area consist of 196 soil profile descriptions Fig. 1 down to aŽdepth of one to two meters including thickness, color and textural class determined by

.hand for each soil layer and other features such as iron or organic matter traces andpresence of gravel andror stones. Soils are mostly sandy to silty with a low claycontent.

Soil characteristics are defined, according to textural class and depth, by probabilityŽdensity functions that were derived from a statistical analysis analysis of variance,

. Žfitting of multivariate distributions carried out on the parameters particle size distribu-.tion, organic matter content, pH, CEC, etc. measured on the 511 soil samples that were

Ž .collected throughout the valley Soutter, 1996 .Hydraulic properties of each soil layer and for each Monte-Carlo run are obtained by

Ž .applying either the pedotransfer functions derived by Cosby et al. 1984 or thoseŽ .derived by Rawls and Brakensiek 1988, 1985 to the randomly generated soil character-

Ž .istics Fig. 2 . The use of such regressive relationships, established on the basis of verylarge sets of soil samples but without any specific link to the area under consideration, isquestionable. Although considerable soil data was available, there was only very little

Ž .evidence to justify or reject their use: comparing the distributions of predicted vs. fieldŽ . Žmeasured saturated hydraulic conductivities Fig. 3 shows a rather good agreement an

order of magnitude reduction between field and laboratory measurements is not uncom-. 1mon . Rawls and Brakensiek’s pedotransfer functions seem to better reproduce the

overall variability of saturated hydraulic conductivity and were therefore preferred.

1 Primarily due to loss of structure in the sampling process and during transport.

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Ž .Fig. 1. Study area along with piezometer and soil profile locations contourlines below 600 m, steps20 m .


Fig. 2. Random generation of soil hydrodynamic properties.

However, assuming that soil sampling had not been carried out, i.e., if empiricalprobability density functions 2 were used to describe soil characteristics, the predictedhydraulic properties would remain realistic only with Cosby’s pedotransfer functions. 3

The complete groundwater vulnerability assessment was performed for both casesŽi.e., fitted and empirical pdf’s, respectively, along with Rawl’s and Coby’s pedotransfer

.functions to further evaluate the overall influence of soil sampling.ŽBesides dispersivity log-uniform probability distribution ranging between 1–100

.mm , all diffusion–dispersion related soil properties that cannot be predicted usingŽpedotransfer functions were kept constant at a mean value see sensitivity analysis,

.Section 4 .

2 Triangular distributions with parameters selected according to the intrinsic logic of the soil classificationŽ .basically a transition from coarse to fine textures .

3 Unrealistic values appeared with Rawls and Brakensiek’s pedotransfer functions when the very tightlognormal distributions of organic matter content were replaced by a necessarily broader ‘empirical’ triangulardistribution.


Fig. 3. Cumulative probability density functions of saturated hydraulic conductivity as calculated for the soilŽ .samples and measured in the field 288 augerhole infiltration or pumping tests .

3.2. Groundwater

Groundwater data include 17,046 observations of water table heights in 743 piezome-Ž .ters between the summer 1983 and the spring 1986 Fig. 1 . Water table fluctuations

Ž .remain in most cases smaller than 1.0 m with mean depths of 1.1 m in summer JulyŽ .when snowmelt has boosted water levels and 1.7 m in winter January . The behavior of

Žthe water table is mainly influenced by the variations of water level in the river 1–2 m. Ž .above water table level , although heavy rainfall )20 mmrday may lead to signifi-

Žcant but erratic rises of the water table. The groundwater flows parallel to the river 1‰.slope , except in a few places along the edge of the valley.

Assuming sinusoidal fluctuations between minimal and maximal water table heightsseems quite reasonable. However, such behavior may be taken into account only whensolving the convection–dispersion equation numerically. For the other two models,water table level was assumed to remain constant throughout the year, at a depthrandomly chosen according to a uniform probability distribution between the minimaland the maximal values.

Since there are no piezometric data available on most soil profiles, minimum andmaximum water table heights had to be interpolated from neighboring piezometric data.

Ž .This was achieved in three steps: i removing the trend due to the slope by fitting aŽ .trend surface to mean water table heights, ii cokriging the residuals of the minimum

Ž .and maximum water table heights and iii transforming the estimated residuals back towater table heights using the trend surface equation. As shown by Fig. 4, spatial

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Fig. 4. Experimental variogram and cross-variogram surfaces for the residuals of the water table minimum and maximum elevations. Residuals relate to a trendsurface fitted to the water table mean levels.


Table 1Parameters of the linear model of co-regionalization

2w x w x Ž . w xVariable Model Sillrslope m Rangerpower m Direction Ns0 8 Anistropy ratio

Rmax Nugget 0.038 y y ySpherical 0.088 1200 330 1.6Linear 4.8e–05 1 330 6.8

Rmin Nugget 0.018 y y ySpherical 0.066 1200 330 1.6Linear 3.45e–05 1 330 6.8

Rmax– Rmin Nugget 0.0045 y y ySpherical 0.045 1200 330 1.6Linear 3.3e–05 1 330 6.8

continuity of the residuals R is highly anisotropic with the major axis of anisotropybeing parallel to the direction of the valley. The random response of water table to heavyrainfall may be discerned in the less pronounced spatial correlation exhibited by themaximum water table heights. Table 1 shows the parameters of the linear model of

Ž .coregionalization Journel and Huijbregts, 1978 that was fitted to these variogramsurfaces. Standard error of kriging remained generally below 0.05 m so that kriged watertable heights were considered as exact.

3.3. Climate

Climate data are provided on a daily basis by four stations; Martigny-ville, Mar-tigny–Batiaz, Sion and Sion airport according to Table 2. There are significant differ-ences in climate between the cities of Martigny and Sion, distant by 25 km: a strong

Ž .reduction of annual and monthly rainfalls y20% on average and a 30–40% increase inŽ .potential evapotranspiration ETP . Thus, the positive annual water balance in Martigny

becomes slightly negative in Sion.The 1960–1969 time period was selected since rainfall and evapotranspiration data

are available both for Martigny and Sion. This period is characteristic of average climateŽ .conditions. In the case of daily time step models LEACHA and LEACHM , spatial

variability of climate was taken into account by weighing daily rainfall and ETP dataaccording to the distance between the stations and the soil profile under consideration.Using the attenuation factor, those weights were applied to the parameters of the

Table 2Availability of climate data on a daily basis

Ž .Station Rainfall Evapotranspiration Primault, 1981

Martigny-ville 10.1900–12.1977 yŽ . Ž .Martigny–Batiaz 1.1960–12.1969 778 mmryr 1.1960–12.1969 495 mmryr

9.1989–12.1994Ž . Ž .Sion 10.1900–12.1977 600 mmryr 1.1901–12.1977 650 mmryr

Sion airport 1.1969–12.1994 1.1978–12.1994


Table 3Ža .Parameters of the uniform log-uniform pdf’s describing pesticide properties

Pesticide 1 Pesticide 2 Pesticide 3

min max min max min maxa y1w xDegradation rate d 0.0001 0.001 0.0001 0.001 0.001 0.01

3 y1w xPartition coefficient dm kg 10 100 100 200 10 100

Ž .normal probability density functions that were fitted to the annual net recharge rates ofeach station.

3.4. Pesticide properties

Pesticide properties identified as being among the primary determinants of thecontamination of a shallow water table are the degradation rate and the partition

Ž .coefficient see Section 5, sensitivity analyses . Three ‘generic’ pesticides were, there-fore, selected for simulation purposes. Pesticide 1 can be considered as very persistent

Ž .and very mobile, although its properties Table 3 reflect quite well the diversity ofobserved values for commonly used pesticides such as atrazine, simazine and glyphosateŽ .Rao and Davidson, 1980 . Pesticides 2 and 3 are, respectively, less persistent and lessmobile variations of pesticide 1. All other pesticide properties were kept constant at a

Žmean value except that solubility was allowed to vary between 50–5000 mgrl log-uni-.form distributions .

In the case of the LEACHM and LEACHA models, pesticides were applied at a rateof 2 kgrha on April 15 of each year at the surface of a bare soil. Pesticide degradationrates, decreasing linearly by a factor of 10 from the soil surface to an average watertable depth, were applied to solution phase only.

4. Selective sampling, sensitivity analysis and Monte-Carlo process

Identifying the key variables of a simulation model by sensitivity analysis is ofŽprominent interest since it helps to collect data in a more efficient way regarding time

.andror cost and to reduce uncertainties on the outputs by getting more preciseinformation on the essential input variables. Sensitivity analysis usually consists ofobserving the sensitivity of the response Y to variations in one input variable X whilethe others are kept constant. However, the limits of that technique are reached quite

Žquickly as soon as the number of input variables becomes large exponent of the power.function defining the requested number of simulations . Combining a selective sampling

Ž .technique such as Latin hypercube sampling McKay et al., 1979 and stepwiseregression techniques overcomes this problem.

The principle of Latin hypercube sampling consists of dividing the probability densityfunction of each variable involved in the model into k equally probable intervals andthen to choose at random a value in each one of those intervals. Thus, the sampling


Table 4Sensitivity analysis: % variation in the output explained by variations in the inputs

Ž .AF Leach-M fLeach-A

% Cumulative % Relative % Cumulative % Relative

Degradation rate 67.30 67.30 44.70 44.70Water table depth 69.90 9.60 62.45 17.75Partition coefficient 82.80 5.90 74.56 12.11

aOrganic carbon content 89.20 6.40 81.97 7.41Net annual recharge rate 92.50 3.30

aOrganic matter contentr1.724.

process ensures that the full plausible range of each input variable is represented andthat more probable sub-ranges are given more weight.

The ordered samples of each variable are randomly permuted, 4 all the ith valuesbeing combined to form a vector of inputs to the model. Stepwise forward regression isthen applied to the ranks of the output Y as a function of the ranks of the inputs X . Thisi

leads to classifications of the input variables according to the degree of monotonicity oftheir dependence to the output Y, or, in other words, to rank them according to the

Žtendency shown by an increase of the input to systematically induce an increase or.decrease of the output.

The application of this sensitivity analysis technique to the leaching models describedin Section 2 showed that cumulative pesticide fluxes were mainly dependent uponpesticide degradation rate, water table depth, pesticide partition coefficient and organic

Ž .carbon content of the soil Table 4 . Unexpectedly, the other variables involved,especially hydrodynamic characteristics of the soils and pesticide solubility did, in

Ž .comparison, only have a very marginal effect on long-term 10 yr pesticide build-upŽ .Soutter and Musy, 1997 .

Latin hypercube sampling also proved to be very efficient in reducing the number ofsimulations required in a Monte-Carlo process to get the resulting distributions reason-

Ž .ably stabilized from 300–500 to 50 simulations in the case of the LEACH models .

5. Interpolation of local distributions

The local distributions of groundwater vulnerability for the various simulated condi-Ž .tions Table 5 are generally spread over a wide range of values. Especially for high

Ž .contamination levels pesticide 1 , the spreading is reduced and the distributions showŽnegative skewness using mean values in a single calculation would, therefore, lead to

.underestimation of the median vulnerability .

4 In fact, if the input variables cannot be considered as independent, random permutation has to beinfluenced to avoid unrealistic combinations, such as bringing together a high porosity with a low hydraulic

Žconductivity. This is done by reordering the samples to induce predefined rank correlation structure Iman and.Conover, 1982 .


Table 5ŽCharacteristics of the selected simulation scenarios fixed values were chosen at the center of the former

.variation range

Case Pesticides Water table Soils Climate Models

1 variable variable Experimental pdf’s and Rawls interpolation AF, Leach-A, Leach-M2 fixed variable Experimental pdf’s and Rawls interpolation AF, Leach-A3 fixed fixed Experimental pdf’s and Rawls interpolation AF, Leach-A4 fixed fixed Empirical pdf’s and Cosby interpolation AF, Leach-A5 fixed fixed Experimental pdf’s and Rawls constant AF, Leach-A

The spatial continuity of the various fractiles of those distributions systematicallyŽ .shows a banding effect Fig. 5 due to the sampling design, since most soil profiles are

Ž .located along cross sections Fig. 1 . In each of the above-mentioned simulationscenarios, the various fractiles of the simulated local distributions show intrinsicco-regionalization, that is all their variograms and cross variograms are proportional tothe same model. As a consequence, the distribution of the vulnerability index at a givenpoint of the study area can be established by kriging independently the various fractiles

Žof the local distributions rather than by cokriging all of them Journel and Huijbregts,.1978 .

In the case of the attenuation factor, the prominent effect of the pesticide degradationrate along with occasional moisture deficits induce so much variability among the localdistributions that any analysis of spatial continuity of the lowest fractiles is impaired. Ina similar way, simulating the behavior of less contaminating pesticides often leads tomore widely spread distributions of the groundwater vulnerability indices. As a conse-quence, the statistics that underlie spatial continuity modelling become less meaningfulŽ .‘butterfly wing’ shaped h-scatterplots . Finally accounting for spatial uncertainty by a

Ž .Fig. 5. Variogram surfaces for the medians of the local distributions Case 1, pesticide 2 .


Ž 5.Monte-Carlo interpolation process stochastic imaging proves to be very time con-suming and CPU intensive. This is in great part due to the lack of knowledge regardingthe minimum numbers of fractiles and iterations that would be required to get significantresults. However, the minimal variability of soil properties and their small effect onsimulated vulnerability indices leads us to consider spatial uncertainty as a minorcontribution to global uncertainty.

6. Results and conclusions

Groundwater vulnerability indices predicted using three different kinds of leachingmodels were similar, with the noticeable exception of the attenuation factor in the case

Ž .of the less contaminating pesticide pesticide 3 . The mathematical form and theŽ .sensitivity analysis of the attenuation factor Table 4 both show that pesticide degrada-

tion rate is a key variable. Thus, a small decrease in persistence drastically reduces thevulnerability index for the attenuation factor model as compared to the other models.

ŽMaps of the median vulnerability indices show very high contamination levels Fig..6 , with up to 60–90% of the applied pesticide moving into the groundwater in the case

of pesticide 1. Highest vulnerability levels can be found in the central zone of the studyarea where water table levels are not as deep. However, uncertainties 6 on the predictedmedian values are also very high, reaching values up to "0.2–0.3 for vulnerabilityvalues ranging between 0–1. Moreover, the smallest uncertainties relate to locationswhere cumulative pesticide fluxes reach the most extreme values. The comparison of themaps drawn for pesticides 2 and 3, respectively less mobile and less persistent thanpesticide 1, shows that these two aspects have a similar effect on the median values,

Ž .whereas the spreading of the local distributions i.e., uncertainties is much moresensitive to water table depth in the first case than in the second.

Keeping pesticide properties and water table depths fixed results in almost nochanges in the maps of median values. The related uncertainty maps show that some40–50% of the global uncertainties are accounted for by uncertainties in pesticideproperties, 30–40% by uncertainties in water table position and the 20% left by

Žuncertainties in soil characteristics essentially organic carbon content, as shown by the.results obtained for a tracer .

The high resulting vulnerability levels are somewhat perplexing since to our knowl-edge no groundwater contamination evidence has ever been reported in that area. Three

Ž .elements seem to explain, at least to some extent, this apparent paradox: i modelŽ .deficiencies e.g., neglecting processes that affect the fate of pesticides on soil surface ,

Ž . Žii lack of knowledge regarding degradation processes in natural conditions valuesreported for the same pesticide may vary across several orders of magnitude between

. Ž .laboratory and field trials, cf. Rao and Davidson, 1980 , and iii huge volume of theŽ .aquifer over 500 m estimated depth implying possibly important dilution.

5 Repeated kriging of the whole area along a random walk, each new estimate being added to the krigingŽ .system see for example, Bourgault et al., 1997 .

6 Considered here as the difference between the 95% and the 5% quantities.


Ž .Fig. 6. Vulnerability maps for three ‘generic’ pesticides along with their uncertainty maps case 1 .

Beyond the consistency issue, interpretation of those vulnerability assessments raisethe question of admissible pesticide fluxes into the groundwater: Do we have to considerall but the zero flux as a potential threat to drinking water supplies or does the systemhave some natural capacity of self-cleansing? To determine the critical pesticide flux alink with a groundwater model would obviously be needed.

References

Addiscott, T.M., 1977. A simple computer model for leaching in structured soils. J. Soil Sci. 28, 554–563.Aller, L., Bennett, T., Lehr, J.H., Petty, R.J., Hackett, G., 1987. DRASTIC: A standardized system for

evaluating ground water pollution potential using hydrogeologic settings, U.S. Environ. Prot. Agency, Ada,OK, EPAr600r2-87r035.

Bleeker, M., Degloria, S.D., Hutson, J.L., Bryant, R.B., Wagenet, R.J., 1995. Mapping atrazine leachingŽ .potential with integrated environmental databases and simulation models. J. Soil Water Conserv. 50 4 ,

388–394.


Bourgault, G., Journel, A.G., Rhoades, J.D., Corwin, D.L., Lesch, S.M., 1997. Geostatistical analysis of a soilsalinity data set. Adv. Agronomy 58, 241–292.

Corwin, D.L., Wagenet, R.J., 1996. Applications of GIS to the modelling of nonpoint source pollutants in theŽ .vadose zone: a conference overview. J. Environ. Qual. 25 3 , 403–411.

Cosby, B.J., Hornberger, G.M., Clapp, R.B., Ginn, T.R., 1984. A statistical exploration of the relationships ofŽ .soil moisture characteristics to the physical properties of soils. Water Resour. Res. 20 6 , 682–690.

Hutson, J.L., Wagenet, R.J., 1992. Leaching Estimation And Chemistry Model, Version 3, User Manual,Cornell Univ., Ithaca, NY.

Iman, R.L., Conover, W.J., 1982. A distribution-free approach to inducing rank correlation among inputŽ .variables. Commun. Statist.-Simula. Computa. 11 3 , 311–334.

Jensen, K.H., Mantoglou, A., 1992. Future of distributed modelling. Hydrol. Processes 6, 255–264.Journel, A.G., Huijbregts, C.J., 1978. Mining geostatistics, Academic Press, London, 600 pp.Khan, M.A., Liang, T., 1989. Mapping pesticide contamination potential. Environ. Manage. 13, 233–242.Loague, K., 1991. The impact of land use on estimates of pesticide leaching potential: assessments and

uncertainties. J. Contam. Hydrol. 8, 157–175.Loague, K., 1994. Regional scale groundwater vulnerability estimates: impact of reducing data uncertainties

Ž .for assessments in Hawaii. Ground Water 32 4 , 605–616.Loague, K., Yost, R.S., Green, R.E., Liang, T.C., 1989. Uncertainty in a pesticide leaching assessment for

Hawaı. J. Contam. Hydrol. 4, 139–161.¨McKay, M.D., Beckmann, R.J., Conover, W.J., 1979. A comparison of three methods for selecting values of

Ž .input variables in the analysis of output from a computer code. Technometrics 21 2 , 239–245.Meeks, Y.J., Dean, J.D., 1990. Evaluating groundwater vulnerability to pesticides. J. Water Resour. Plann.

Ž .Manage. 116 5 , 693–707.Musy, A., Soutter, M., 1991. Physique du sol. Collection Gerer l’environnement, 6, Presses Polytechniques et´

Universitaires Romandes, Lausanne. 335 pp.Petach, M.C., Wagenet, R.J., Degloria, S.D., 1991. Regional water flow and pesticide leaching using

Ž .simulations with spatially distributed data. Geoderma 48 3–4 , 245–269.Primault, B., 1981. Extension de la validite de la formule Suisse de calcul de l’evapotranspiration, Arbeits-´ ´

berichte SMA No. 103, Zurich.¨Rao, P.S.C., Davidson, J.M., 1980. Estimation of pesticide retention and transformation parameters required in

Ž .nonpoint source pollution models. In: Overcash, M.R., Davidson, J.M. Eds. , Environment impact ofnonpoint source pollution, Ann Arbor Sci. Publ., Ann Arbor, MI, pp. 23–67.

Rao, P.S.C., Hornsby, A.G., Jessup, R.E., 1985. Indices for ranking the potential for pesticide contaminationof groundwater. Proc. Soil Crop Sci. Soc. Fla. 44, 1–8.

Rawls, W.J., Brakensiek, D.L., 1985. Prediction of soil water properties for hydrologic modelling. In: Jones,Ž .E., Ward, T.J. Eds. , Watershed Management in the Eighties. Proc. Symp. ASCE, Denver, CO, 30

April–2 May 1985, ASCE, NY.Rawls, W.J., Brakensiek, D.L., 1988. Estimation of soil water retention and hydraulic properties. In:

Ž .Morel-Seytoux, H.J. Ed. , Unsaturated flow in hydrologic modeling, theory and practice, KluwerAcademic Publ., Dordrecht, pp. 275–300.

Soutter, M., 1996. Prediction stochastique a l’echelle regionale des risques de contamination des eaux´ ` ´ ´souterraines par des pesticides, These EPFL no. 1487, Swiss Federal Institute of Technology, Lausanne,`150 pp.

Soutter, M., Pannatier, Y., 1996. Groundwater vulnerability to pesticide contamination on a regional scale. J.Ž .Environ. Qual. 25 3 , 439–443.

Soutter, M., Musy, A., 1997. Pesticide leaching models: sensitivity analyzes and Monte-Carlo simulationsŽ .using Latin hypercube sampling, Water Resour. Res. Subm. .

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