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TECHNICAL REPORT
Heavy Metals in the Environment

Assessment of Uncertainty and Risk in Modeling Regional Heavy-Metal Accumulation in Agricultural Soils

^a Swiss Federal Institute of Technology (ETH Zürich), Institute of Terrestrial Ecology, Grabenstr. 3, CH-8952 Schlieren, Switzerland
^b Swiss Federal Institute for Environmental Science and Technology (EAWAG), Ueberlandstr. 133, P.O Box 611, CH-8600 Dübendorf, Switzerland

* Corresponding author (armin.keller{at}ito.umnw.ethz.ch)

Received for publication October 30, 2000.

	ABSTRACT

TOP ABSTRACT INTRODUCTION THEORETICAL BACKGROUND MATERIALS AND METHODS RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS REFERENCES

 
Present agricultural land use and atmospheric deposition may lead to heavy-metal accumulation rates in soils that may violate soil quality standards in the future. To undertake suitable preventive measures against heavy-metal enrichment, flux balances in agroecosystems and their uncertainties have to be assessed. For this reason we developed an empirical stochastic model, PROTERRA-S, that considers heavy-metal inputs through agricultural management as well as outputs by crop removal and leaching on a regional scale. In this manuscript we describe application of PROTERRA-S to the Sundgau region in Switzerland. Considering uncertainty in informational and natural variability, large variations of the aggregated regional cadmium and zinc balances were found, with standard deviations that were of the same order of magnitude as their average values. Uncertainty in the simulated net zinc flux originated mainly from uncertainty in the zinc concentrations of manure and crops and from uncertainty in atmospheric deposition of zinc. For cadmium, the main contribution to the total uncertainty came from uncertainty in crop concentration, regression functions to estimate Freundlich parameters, atmospheric deposition, and from spatial variation of soil pH and cation exchange capacity (CEC). For both zinc and cadmium, informational uncertainty in input data were large, indicating that significant uncertainty reduction could be achieved by additional data collection campaigns. A monetary risk value for the regional zinc accumulation rate in Sundgau was calculated to be on the order of 22 million Euro.

Abbreviations: CEC, cation exchange capacity • RTU, root of uncertainty • SRC, standardized regression coefficient • UIF, uncertainty impact factor

	INTRODUCTION

TOP ABSTRACT INTRODUCTION THEORETICAL BACKGROUND MATERIALS AND METHODS RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS REFERENCES

 
THE SUSTAINABILITY of current land use in agroecosystems can be assessed with respect to heavy-metal accumulation in soils by balancing their input and output fluxes. Many studies point to the fact that, at the present rate, agricultural land use may not be sustainable because of heavy-metal accumulations. Some examples include studies by von Steiger and Baccini (1990), Reiner et al. (1996), and Moolenaar and Lexmond (1998) at the field and farm scales, and Andersson (1992) and Schütze and Nagel (1998) at the regional and national scales.

To provide meaningful information for taking suitable preventive measures against heavy-metal accumulation in soils, the uncertainty and reliability of the inputs and the outputs have to be known (von Steiger et al., 1998). There are two major sources of uncertainty in a modeling study: the uncertainty caused by parameters and the uncertainty due to model error. To quantify the model error in modeling heavy-metal balances is demanding, as it requires long-term monitoring data. Instead, we focus on the uncertainty caused by input parameters in this work. Parameter uncertainties in heavy-metal balances for soils with agricultural land use may be "natural" (i.e., arising from spatial and temporal variation that is inherent in natural processes) or "informational" (i.e., arising from measurement errors or incomplete or unreliable data). In addition, a common source of informational uncertainty in heavy-metal balance models is the uncertainty introduced by regression functions to derive model input parameters. Consequently, realistic modeling requires simulation procedures that account for these data characteristics (Abbaspour et al., 1998).

Aside from the limited amount of data that is usually available for heavy-metal balance analyses, the informational uncertainty may also arise as a result of scale differences. Soil and agricultural data necessary for heavy-metal balance studies often refer to different spatial scales. Metal output fluxes by leaching, erosion, or crop uptake are generally estimated at a plot or field scale. Other data, in particular those concerning agricultural management (e.g., livestock and crop production), are usually only available at a regional scale (Moolenaar, 1998). These data cannot easily be assigned to geographic coordinates, contrary to basic soil information that is obtained from soil maps in a GIS.

Various models have been developed to assess heavy-metal balances of agricultural soils. Few attempts were made to address the sensitivity of model results based on parameter uncertainty (Boekhold and van der Zee, 1991; Palm, 1994; Moolenaar and Lexmond, 1998). Tiktak et al. (1999) and de Vries and Bakker (1998) determined the contribution of uncertain model input parameters to the total uncertainty of the model results. However, these models did not consider metal inputs from land management and their uncertainties.

Uncertainty analysis includes the following tasks: (i) determination of the uncertainty in the model input parameters, (ii) propagation of parameter uncertainty through the model taking account of cross correlations between uncertain parameters, (iii) analysis of the contribution of each uncertain component to the total uncertainty of the results, and (iv) analyses of alternative strategies to reduce the uncertainties and associated risks of inadequate management decisions. In general, while risk imparted by informational uncertainties must be reduced by further detailed investigations, the uncertainties caused by natural variation must be maintained for a realistic representation.

To address these tasks in the assessment of heavy-metal balances at the regional scale for agricultural land, we developed the empirical stochastic model, PROTERRA-S. The model is an extended version of PROTERRA (von Steiger and Obrist, 1993) that was designed for assessing phosphorus, cadmium, zinc, and copper balances of agricultural land over regions of some 100 km². The basic units of the balances are land-use systems, defined by livestock composition and cropping systems. Metal balances on the level of the land-use systems can be disaggregated to the level of individual crop types or aggregated to the regional level. To facilitate the performance of PROTERRA-S, the model could be linked to regional databases, such as agricultural statistics and soil information systems. The agricultural statistics of the land-use systems are coupled with the soil characteristics by a stochastic approach, considering each possible combination of soil type and fertilization management, both of which are related to livestock production and cultivated crops. Uncertain model input parameters can be treated as random variables, quantified with probability distributions, and propagated to model outputs using a Latin hypercube sampling scheme with correlated variables.

In this paper we demonstrate the applicability of the model and show how it deals with data and parameter uncertainty, illustrated by the regional aggregated zinc and cadmium balances for a case study.

	THEORETICAL BACKGROUND

TOP ABSTRACT INTRODUCTION THEORETICAL BACKGROUND MATERIALS AND METHODS RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS REFERENCES

 
Basic Equations
In the following, we briefly summarize the basic model equations. A detailed description of the PROTERRA-S model can be found in Keller et al. (2001). Heavy-metal balances calculated by PROTERRA-S are based on the following mass conservation equation proposed by van der Zee et al. (1990) and Boekhold and van der Zee (1991) for the plow layer of an agricultural soil:

[1]

where M (g ha^-1) is the total heavy-metal content, t is the time (yr), I_Atm (g ha^-1 yr^-1) is the metal input flux by atmospheric deposition, I_Agr (g ha^-1 yr^-1) is the sum of the metal input fluxes by agricultural activities, and k_C (yr^-1) and k_L (yr^-1) are the crop-uptake rate coefficient and the leaching-rate coefficient, respectively. The exponents m and n, are empirical parameters. The total metal content M is the sum of metal sorbed to the solid phase and metal dissolved in the soil solution:

[2]

where is the dry soil bulk density (kg m^-3), z is the depth of the plow layer (m), is the volumetric water content (L m^-3), and c_t (mg kg^-1) and c_s (mg L^-1) are the sorbed and dissolved metal concentrations of the soil, respectively. To convert M from mg m² to g ha^-1 a factor of 10 was used in Eq. [2]. PROTERRA-S considers agricultural metal inputs resulting from application of animal manure (I_Man), sewage sludge (I_Se), commercial fertilizer (I_CF), and pesticides (I_Pes), all expressed in g ha^-1 yr^-1:

[3]

Metal inputs with fertilizer applications are linked to the following phosphorus (P) balance:

[4]

Here, O_P,Crop (g ha^-1 yr^-1) is the P export with crop harvest or grazing, and I_P,tol (g ha^-1 yr^-1) represents an empirically determined rate of P surpluses in agroecosystems. I_P,Man, I_P,Se, and I_P,CF are the P inputs with manure, sewage sludge, and commercial fertilizers (g ha^-1 yr^-1), respectively. O_P,Crop, I_P,tol, I_P,Man, and I_P,Se are obtained from agricultural statistics and guidelines, nutrient balances on experimental farms, and from bookkeeping of wastewater treatment plants. I_P,CF is then calculated from these data according to Eq. [4], assuming that farmers usually follow the fertilization strategy recommended by the Swiss guidelines for water protection (Federal Office of Environment, Forests and Landscape, 1994). After the P balance is determined, metal inputs from fertilizer application are estimated from the P fluxes and from the ratios between metal and P concentrations of the fertilizers.

Assuming a linear relationship between the metal concentration in crop type i, c_Crop,i (mg kg^-1), and its concentration in soil, c_t (see, for comparison, Gerritse et al., 1983 and Kuboi et al., 1986), the uptake-rate coefficient k_C (yr^-1) of crop type i in Eq. [1] is given by:

[5]

where Y_i (kg ha^-1 yr^-1) is the yield (dry matter) of crop type i, and the exponent m in Eq. [1] is set equal to one. A linear relationship between metal concentration in the soil and in the crop does not hold in general. However, there is no significant difference between the assumption of linearity and nonlinearity at metal concentrations at or near background as in our case, so the linear assumption was used. Leaching of heavy metals from the plow layer into the subsoil, O_L (g ha^-1 yr^-1), is determined assuming equilibrium partitioning of metals between the adsorbed and dissolved phases described by Freundlich isotherms. As the dissolved amount of heavy metal in soil can usually be neglected, the leaching-rate coefficient is approximately given by:

[6]

where q_w (L m^-2 yr^-1) is the (Darcy) water flux at the lower boundary of the plow layer, and K_F (L kg^-1) and n (unitless) are the Freundlich parameters. These parameters are related to soil properties (van der Zee and van Riemsdijk, 1987; Buchter et al., 1989) and are derived from regression functions explained below.

Application of the Model
Metal balances are calculated in two steps. First, flux balances of heavy metals are simulated for individual land-use systems within the region of interest. Second, the input and output fluxes of these land-use systems are aggregated by their area fractions to estimate the average flux balance for the region. The land-use systems are the basic units for the areal balances, which are categories defined by the user of PROTERRA-S based on the available statistical databases. We classified the land-use systems by farm type (i.e., predominant livestock type and density) and by cropping systems (i.e., classes of crop types) (Keller et al., 2001).

Figure 1 illustrates the main components of the model, which are programmed in MATLAB Version 5.3 (Mathworks, 1999). These modules are linked to the software UNCSAM (Janssen et al., 1994), a package for efficient Monte Carlo sampling in combination with regression and correlation analysis to perform sensitivity and uncertainty analyses.

View larger version (101K): [in this window] [in a new window]   Fig. 1. Performance steps of the PROTERRA-S balance model.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION THEORETICAL BACKGROUND MATERIALS AND METHODS RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS REFERENCES

As a case study, we applied the model to the Sundgau, a rural region in the northwest of Switzerland. This region extends from the Swiss Jura in the southeast with hills to 800 m to the Rhine Valley in the northwest. Sundgau has an area of about 95 km² and includes 201 farms that cultivate about 36 km² of arable land. Pastures and meadows account for 49% of this area, agricultural crops 46% (dominated by bread and fodder cereals), and special crops (vineyards, orchards) 6%. Dairy farms and arable farms cover about 88% of the total agricultural area. The data used in this case study refer to the period from 1992 to 1997. The complete set of model input parameters used in this case study is available at http://www.ito.umnw.ethz.ch/SoilProt/staff/kellera or can be obtained from the corresponding author.

Derivation of Model Parameters
The Freundlich parameter, K_F in Eq. [6], was determined from GIS mapped soil properties using the relationship given by Elzinga et al. (1999):

[7]

where b_kf, b_pH, and b_CEC are empirical regression coefficients and is the regression error assumed to be normally distributed with mean zero and variance ² (Draper and Smith, 1981). Table 1 gives the values of the regression coefficients calculated based on a wide range of soils for cadmium and zinc. Given the calculated K_F values, we estimated the metal concentration in soil solution based on the Freundlich equation (see below for the estimation of the Freundlich coefficient n), and compared these estimated metal concentrations in soil solution with measured NaNO₃–extractable concentrations (Swiss Agency for the Environment, Forests and Landscape, 2001) from a regional soil survey by Bono (1999). For cadmium, the estimated concentrations were in the same range as the measured ones, while for zinc the regression function given by Elzinga et al. (1999) overestimated the respective measured values on average by a factor of five. Therefore, we adjusted the intercept, b_kf, of the regression function to fit the average of these measurements.

[8]

where b_n and b_npH are empirical coefficients. Taking estimated regression coefficients from the literature (Table 1), here denoted as _i and _k, the total variance of the predicted Freundlich coefficients, ²_Y, is given by:

[9]

where C_ik is the covariance matrix of the p regression variables and ² is the regression error. Random realizations of were drawn with Monte Carlo simulations to estimate ², taking into account the coefficient of determination of the regression functions, R², according to:

[10]

For each regression function the error term was assigned to the regression constants, that is, b_kf and b_n were treated as a normally distributed random variables with mean b_kf and variance ² and with mean b_n and variance ², respectively.

Uncertainty Analysis
In this case study, we initially considered 42 parameters as uncertain, thus we treated them as random variables (RV). A preliminary sensitivity analysis using stepwise backward regression (Zar, 1984) showed that uncertainty of about half of these random variables had negligible effect on the uncertainty of the model results. Therefore, 20 of the most sensitive parameters were retained as uncertain random variables. These are listed in Tables 2 and 3. Table 2 contains the sources of data from which the probability distributions given in Table 3 were inferred. It should be noted that the classification of parameter uncertainty into the categories of informational and natural in Table 2 indicates the predominant uncertainty type of the random variables. A sharp distinction between such categories, however, is not possible as each variable has a measure of both uncertainties. The selection of parameters, considered here as random variables, depends on the agricultural characteristics (e.g., the predominant crop types and livestock production of the Sundgau region). In other regions, estimates of cadmium and zinc fluxes may be sensitive to a different set of parameters because other types of crop and manure may dominate the uncertainty of these estimates.

View this table: [in this window] [in a new window]   Table 3. Random variables and correlation coefficients used in metal flux simulations. For an explanation of symbols see Appendix 1.

Correlations between uncertain input parameters may significantly affect the uncertainty of the model results. However, the amount of data usually available for heavy-metal balance studies does not support such analyses. We estimated correlations between random variables for which we had obvious indication that they were correlated, as shown in the last column of Table 3. The Spearman correlation coefficients listed in Table 3 were obtained from soil surveys (correlation between c_t and c_Crop, pH, CEC) and from the literature (correlation between c_t and metal concentration of fertilizers).

To propagate the uncertainties in the parameters through the model we used the Latin hypercube sampling technique (McKay et al., 1979). After some preliminary runs with different sample sizes of up to 600, we noticed that the results above 300 were very consistent. Thus, we made 400 model runs with PROTERRA-S. Based on the definitions of the probability functions, all possible combinations of soil characteristics and agricultural land-use types were taken into account by this approach. We performed the Latin hypercube sampling with and without taking parameter correlations into account, to determine the effect of such correlations on the model outputs. We used the procedure described by Janssen et al. (1992) for the Latin hypercube sampling with correlated parameters.

Determination of Uncertainty Contributions
To quantify how the uncertainties in model input parameters affect the uncertainty of the model results, various approaches have been proposed in the literature (e.g., Iman and Helton, 1992; Janssen, 1994). We employed a multiple regression model to evaluate the effect of each random variable X_i (listed in Table 3) on the regional net cadmium and net zinc balances (Y), of the form:

[11]

where b₀ and b_i are the regression coefficients, _j are the residual errors, p is the number of random variables, and N is the number of data points. The residuals are assumed to be normally distributed with zero mean and variance ². To obtain a relative sensitivity measure that is independent of the scale of the random variables, standardized regression coefficients, SRC, were calculated as (Janssen et al., 1994):

[12]

where _Y is the standard deviation of Y and is the standard deviation of the variable X_i. The SRC measures the relative change of Y for each parameter with respect to its standard deviation, due to a relative change in X_i with respect to its standard deviation, while keeping all other model parameters constant. To account for the influence of correlation between input parameters on the model output uncertainty, Janssen et al. (1994) introduced the so-called root of uncertainty, RTU:

[13]

where r_XiY is the correlation coefficient between parameter X_i and Y, and r_XiXk is the correlation matrix of the model input parameters. If no correlation between the model input parameters exists, the RTU_i equals approximately the SRC_i. The uncertainty measure RTU is only meaningful if the regression function shows a good linear approximation (i.e., the adjusted coefficient of determination R²_adj 1). Therefore, the assumptions of the regression analysis must be rigorously checked with respect to R²_adj as well as the residual errors. While the R²_adj gives information about the approximation of the linear regression to the model results, the residuals reveal if assumptions for the regression errors are valid. We checked the residuals by inspecting normal probability plots (quantiles of residuals versus quantiles of the standard normal distribution) and the plot of model results versus regression estimates.

Because the estimation of RTU by the least squares minimization method is very sensitive to outlier values, we applied the less-sensitive maximum likelihood (ML) estimation method in combination with a Huber-weighting function for the determination of the regression coefficients b_i that minimize the following quantity (Huber, 1981):

[14]

where (_j) is an arbitrary function of the residuals _j, and s is a scale parameter. The residuals _j depend on the estimated regression coefficients b_i, and are assumed to be independently distributed and follow the same distribution. The scale parameter s can be estimated by the (robust) median of absolute values, s_MAV (Huber, 1981):

[15]

The derivation of the function (_j) leads to the ML estimator function for b_i of the form:

[16]

where X is the matrix of the random variables and is a function that assigns weights, w_j, to the standardized residuals _j/s_MAV. There are various functions to obtain robust estimates for the b_i (Hoaglin et al., 1983). We used the following function proposed by Huber (1981):

[17]

[18]

where c is a tuning constant, which was set to a value of five in this study. The ML approach can be solved iteratively. In each iteration the ML estimator of the coefficients b given by are calculated according to:

[19]

where X^T is the transpose of the matrix X and W is a diagonal weighting matrix with diagonal elements given by:

[20]

The _j and s_MAV are recalculated in each iteration.

Risk Analysis
For our purposes, we define risk in monetary terms as the expected cost associated with the probability of failure at a given year:

[21]

where R(t) is the risk in year t, C_f(t) is the cost (Euro) that would arise as the consequence of failure in year t, and P_f(t) is the probability of failure in year t. In this study we define failure as the occurrence of a heavy-metal accumulation rate in excess of a critical rate. This critical rate was calculated as the tolerable metal accumulation during 200 years that would lead to a metal concentration in the plow layer equal to the Swiss guideline values (Swiss Agency for the Environment, Forests and Landscape, 2001).

The probability of failure was estimated by employing the same Monte Carlo simulation procedure as described above. The probability of failure can be reduced by decreasing the part of uncertainty that is associated with the informational components by improving data processing and additional surveys.

	RESULTS AND DISCUSSION

TOP ABSTRACT INTRODUCTION THEORETICAL BACKGROUND MATERIALS AND METHODS RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS REFERENCES

 
Heavy-Metal Fluxes
Model simulations showed an average enrichment of cadmium and zinc in the agricultural soils of the Sundgau region during the period considered (Table 4). The regional cadmium balance was mainly determined by atmospheric deposition (67% of total input) and by crop removal (43% of total input) (Fig. 2) . Leaching of cadmium was of minor importance because of the large sorption capacity and high soil pH values in the region. Cadmium inputs from commercial fertilizers were found to be relatively small due to the predominance of manure as fertilizer. About 60% of the total P input (21.8 kg P ha^-1 yr^-1) was provided by manure and about 40% by commercial fertilizers. The amount of P supplied with sewage sludge was almost negligible due to the small amounts applied within the region. It should be emphasized that even for extensively used meadows and pastures, where atmospheric deposition is the only relevant cadmium source, the regional cadmium balance indicates a slight accumulation in soil. In contrast to cadmium, the regional zinc balance was mainly governed by animal manure (64% of total input), followed by atmospheric deposition (31%) and crop uptake (31%) (Fig. 3) .

View larger version (35K): [in this window] [in a new window]   Fig. 2. Model results for the regional cadmium balance. (a) Input and output fluxes, where IMan = inputs by animal manure; ISe, ICF, and IPes = inputs with sewage sludge, commercial fertilizer, and pesticides, respectively; IAtm = atmospheric deposition; OCrop = output by crop removal; and OL = leaching. The boxes give the interquartile range (IQR). The horizontal bar in each box indicates the median. The length of the whiskers is 1.5 x IQR. Values outside these limits are plotted as points. (b) Net flux, where xmed = median flux. (c) Contribution of the uncertainty sources to total variance of the net flux, where RTU = root of uncertainty. For symbols of uncertainty sources, see Appendix 1.

View larger version (38K): [in this window] [in a new window]   Fig. 3. Model results for the regional zinc balance. (a) Input and output fluxes, where IMan = inputs by animal manure; ISe, ICF, and IPes = inputs with sewage sludge, commercial fertilizer, and pesticides, respectively; IAtm = atmospheric deposition; OCrop = output by crop removal; and OL = leaching. The boxes give the interquartile range (IQR). The horizontal bar in each box indicates the median. The length of the whiskers is 1.5 x IQR. Values outside these limits are plotted as points. (b) Net flux, where xmed = median flux. (c) Contribution of the uncertainty sources to total variance of the net flux, where RTU = root of uncertainty. For symbols of uncertainty sources, see Appendix 1.

Sources of Uncertainties
Propagation of uncertainties of the random variables through the model resulted in large variances of the regional aggregated net cadmium and net zinc fluxes. The coefficient of variation (CV) was about 120% for cadmium and about 50% for zinc.

The regression model used in this study to quantify the contribution of the uncertainty sources explained about 98% of the variance of the simulated net zinc flux (Fig. 4) . Thus, the linear approximation was appropriate in this case. Since there were few outliers that were identified by the Huber function, the maximum likelihood estimator for the regression coefficients, b_i, was quite similar for zinc to the corresponding least squares estimation. For cadmium, however, less of the variation was explained by the linear regression model (R²_adj = 0.73), and the residuals showed a slightly nonlinear structure (see Fig. 4). In particular, the regression model overestimated the negative net cadmium fluxes. Down-weighting of the observed outliers in the robust regression led to significant changes in some regression coefficients and hence, to changes in the corresponding uncertainty measure RTU.

View larger version (32K): [in this window] [in a new window]   Fig. 4. Control plots of the residual analyses: normal probability plot (left graphs) and plot of the model estimate versus the robust regression estimates (right graphs) for the regional net flux of (a) cadmium and (b) zinc. The observations plotted in grey refer to weighted residuals (Huber tuning constant c = 5).

Comparable results were obtained by Palm (1994), who coupled a hydrological model with a model for sorption and plant uptake to assess cadmium behavior for a soil profile. Cadmium uptake by plants was assumed to be proportional to root water uptake. He found that the partitioning of cadmium between sorption, leaching, and plant uptake was highly sensitive to sorption isotherms, whereas root distribution of plants and hydrological soil properties influenced the partitioning of these fractions only to a limited degree. However, the uncertainties in cadmium inputs were not taken into account in these two studies. As our case study shows, cadmium and zinc accumulation in agricultural soils may also be quite sensitive to the uncertainties in atmospheric deposition and fertilization management.

Our findings are also consistent with the findings of Boekhold and van der Zee (1991), who used a deterministic transport model to simulate cadmium accumulation in soil, leaching, and uptake by barley. They reported that leaching was very sensitive to the input rate, water flow, and sorption parameters. With time, however, this sensitivity decreased. Cadmium uptake by barley was very small, but in time became increasingly sensitive to flow and sorption parameters. From their analysis, Boekhold and van der Zee (1991) concluded that the input flux is the most sensitive parameter for short-term predictions of cadmium accumulation in soil, whereas for long-term predictions accumulation is also sensitive to variations of flow and sorption parameters. In our case, uncertainty of input fluxes explained about 42% of the total uncertainty of the regional net cadmium flux.

The uncertainty of the regional net zinc flux was primarily influenced by variations of zinc concentration in manure (RTU = 33.5%) and in crops (17.7%) as well as variations in atmospheric zinc deposition (15.8%), when parameter correlations were considered (Table 5). The large contribution from animal manure to the total uncertainty was mainly due to highly uncertain zinc concentrations in pig manure (23.1%) and in the manure from cattle and dairy cows (7.2%). Similar to uncertainty in cadmium uptake, uncertainty arising from metal uptake by grass grown on extensively used meadows yielded the largest RTU value (5.2%). In addition, a significant part of the uncertainty in the zinc balance resulted from spatial variation of soil pH and CEC (10.5%) and zinc concentration in soils (9.4%). The uncertainty resulting from regression of the Freundlich isotherms was less important for zinc than for cadmium. Both b_kf and b_n contributed only about 6.2% to the total variation of the regional net zinc flux. To sum up, about 58% of the total variation of the net zinc flux resulted from informational uncertainties, while 42% was caused by natural uncertainties. As in the case of cadmium, there is also a large potential for uncertainty reduction of the regional zinc balance by further detailed surveys and investigations.

Variation of heavy-metal concentrations in crops and in soils led to large uncertainties in the estimates of the crop uptake rate coefficients (Table 6). The largest rate coefficients were obtained for maize silage and intensively used meadows. For cadmium, the CVs of the rate coefficients ranged between 50 and 72%, while for zinc, values between 33 and 45% were found.

The Influence of Parameter Correlation
Correlations between the random variables had little effect on the regional net cadmium and net zinc fluxes. For individual land-use systems, however, their influence was quite significant. For example, for dairy farms (pastures and meadows, 0.2–1.0 cattle manure units [CMU] ha^-1 cattle) the standard deviation of the net zinc flux decreased from 220 to 198 g ha^-1 yr^-1 (median 378 g ha^-1 yr^-1) when parameter correlations were incorporated in the simulations (Fig. 5) .

View larger version (35K): [in this window] [in a new window]   Fig. 5. Frequency distributions of simulated net zinc fluxes for both with and without considering input parameter correlations. The left plot is is the regional balance, the right plot is for a specific land-use system (dairy farm types).

Model Uncertainty
The analysis of uncertainty propagation yields informational and natural uncertainties, which are conditional on the validity of the model apart from the calibration of its parameters. An additional source of uncertainty is the error in the model itself. Model uncertainty may arise by neglecting relevant processes such as linear nonlinear adsorption, choice of inadequate process descriptions such as steady-state or equilibrium, or specification of incorrect boundary conditions. In our case, metal fluxes with soil erosion or metal inputs by compost were not considered, although they may play an important role for the heavy-metal balance of certain agricultural soils. Moreover, simplification of the metal leaching processes (i.e., metal partitioning between the adsorbed and dissolved phases) and the choice of flux assessment methods for metal inputs through animal manure may lead to model uncertainties. Regarding the leaching process, the Freundlich regression functions used in this study tend to overestimate the metal concentrations in soil solution (see, for comparison, Elzinga et al., 1999). Therefore, we recommend calibrating these isotherms with local measurements if balance analyses indicate that model outputs are sensitive to these data.

In general, model uncertainty is assessed by comparison of different models or by comparison of model predictions with independent measurements (de Vries et al., 1998; Heuvelink, 1998). The latter validation approach was performed by Tiktak et al. (1998). They tested the validity of their model by comparing retrospective model predictions using historical cadmium inputs with present heavy-metal concentrations in soils of the Netherlands. They found that model predictions deviated, in general, by less than a factor of two from measured cadmium concentrations in soil.

Unfortunately, the data available are very limited for such a direct validation of regional scale flux models. For PROTERRA-S, this would require long-term monitoring, not only of soil conditions such as pH, organic matter content, and contaminant concentrations, but also of metal fluxes entering and leaving the soil. Consequently, model development and application must be linked to soil monitoring networks. Integration of modeling efforts into existing monitoring programs is also in the interest of such programs, as only models allow local extrapolation of metal inputs and outputs assessed at specific monitoring sites to other areas.

Reduction of Uncertainty in Heavy-Metal Balances
To reduce the uncertainty in metal balances, the two major types of uncertainty considered in this study are distinguished. While it is desirable to reduce the informational uncertainty, the natural uncertainty of parameters must be maintained for models to be realistic. To evaluate the potential gain that could result from the reduction of uncertainty in different parameters, we calculated the so-called uncertainty impact factor (UIF), defined as the ratio of the RTU to the metal fluxes (% of total input). For the regional cadmium balance the largest UIF values were found for the parameters pH, CEC (UIF = 1.3), and b_kf and b_n (UIF = 1.4), indicating that the contributions of these sources to the total uncertainty of the regional net cadmium flux were larger than the contribution of the leaching flux to the total input flux (Table 5). In contrast, the uncertainty of atmospheric deposition, which accounted for 67% of the total cadmium input, contributed only 16% to the total variation of the net cadmium flux (UIF = 0.3).

This finding illustrates that the UIF can be used as an indicator to express the contribution of the random variables to the total uncertainty, regardless of the magnitude of the affected metal flux. In our case, the uncertainty of the net cadmium flux could be reduced considerably if regional measurements were available to establish a local regression function for the prediction of the Freundlich parameters. In contrast, uncertainty resulting from the spatial variation of the soil pH and CEC can hardly be reduced. Since the agricultural data are not site specific, the model takes all possible combinations of soil characteristics and agricultural land use within the region into account. Site-specific agricultural data would provide heavy-metal balances for individual soil type/land-use combinations, and that would improve the accuracy of the simulated net fluxes substantially.

Risk Analysis
For a rough estimation of the risk involved in the current metal accumulation trends, we compared the simulated net metal flux of the regional balance and of specific land-use types with the critical accumulation rate. This estimation assumes that the rate of metal accumulation based on the five-year analysis holds for the next 200 years. This extrapolation only reveals the continuation of the status quo and does not include any future measures that would reduce or increase the rate of accumulation. In the case of zinc, a critical rate of 0.46 mg kg^-1 yr^-1 was obtained based on our calculations (Swiss guide value: 150 mg kg^-1 HNO₃–extractable zinc). For a conversion from flux (g ha^-1 yr^-1) to critical value (mg kg^-1 yr^-1) we used a soil depth of 0.2 m and a soil bulk density of 1300 kg m^-3. The distribution of the initial heavy-metal concentration (Table 3) for the region was based on measured values from data sources reported in Table 2. Figure 6 shows the predicted probability of failure based on different land-use systems. More details about the definition of the land-use classifications can be found in Keller et al. (2001). The probability of failure for the arable and dairy farms is zero, the probability of failure for the animal husbandry farms about 82%, and for the regional averaged balance about 3%. In an alternative presentation, metal accumulation in soil as estimated with the regional balance is compared with the soil treshold concentration (i.e., the Swiss guide value; Fig. 7) .

View larger version (23K): [in this window] [in a new window]   Fig. 6. Cumulative distribution function (cdf) of simulated zinc accumulation rates compared with the critical rate, where ccrit is the tolerable zinc accumulation during 200 years that would lead to concentrations equal to the Swiss guide value of 150 mg kg-1.

View larger version (15K): [in this window] [in a new window]   Fig. 7. Median zinc concentration in soil, ct, over time (solid line), based on the estimated regional accumulation rate compared with the soil threshold concentration (Swiss guide value). The 95% confidence interval is also given (small dashed line).

	SUMMARY AND CONCLUSIONS

TOP ABSTRACT INTRODUCTION THEORETICAL BACKGROUND MATERIALS AND METHODS RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS REFERENCES

 
We applied the stochastic model PROTERRA-S to the Sundgau region and assessed the aggregated cadmium and zinc balances in agricultural soils and their uncertainty sources in the regional scale. The results indicated that cadmium and zinc inputs on average exceeded the outputs and, thus, led to net accumulation of these metals in soil during 1992–1997. The regional balance, however, provided only a general trend of metal fluxes. To take preventive measures, more detailed analyses relating the land-use systems and individual soil types within the region would be more useful. The model is designed to estimate fluxes for five-year periods; therefore, it estimates accumulation trends only for these periods. For temporal predictions beyond that, a dynamic model based on a more sophisticated description of the cause and effect relationships between metal cycling in agroecosystems and soil processes is required.

Taking into account informational and natural uncertainties of the input parameters resulted in large uncertainties of the heavy-metal balances. The standard deviations of the regional net cadmium and net zinc fluxes were of the same order of magnitude as their average values. Using a maximum likelihood regression approach for uncertainty analysis, we quantified the contribution of uncertainty in model input parameters to the total variation of the net heavy-metal fluxes. Uncertainty in the simulated net zinc flux originated mainly from informational uncertainty in zinc concentrations of manure and crops and from natural uncertainty in atmospheric deposition of zinc. In the case of cadmium, primarily the latter two sources of uncertainty as well as the natural uncertainty of the soil pH, CEC, and the uncertainty in the regression function to estimate the Freundlich parameters were the sources for the large variation of the regional net cadmium flux.

The modeling results gave valuable insights for (i) suitable preventive strategies for specific inputs to reduce heavy-metal enrichment in soils and (ii) reducing uncertainty in balances by further investigations to determine highly sensitive parameters more accurately. In order to identify the potential of parameters for efficient uncertainty reduction in the estimated metal balances, we defined the uncertainty impact factor (UIF). A large potential for uncertainty reduction in the net cadmium fluxes was found in the Freundlich regression functions. To reduce model uncertainty, we concluded that long-term monitoring data of soil conditions, metal inputs and outputs, and agricultural practices are required. Such data were not available for this study and therefore model uncertainty had not been accounted for. To improve the reliability and precision of metal balances, we suggest that model development and application should be integrated into soil monitoring programs in the future.

A simple risk analysis was conducted in order to exemplify the potential benefits of uncertainty analyses in the soil pollution monitoring. The analysis showed large risks to be associated with the current trends in accumulation of heavy metals in soils. However, since these risks resulted to a great degree from informational uncertainties, substantial risk reduction could be achieved by determining sensitive model parameters more accurately.

Notation of Symbols
b_kf, b_nFreundlich regression coefficients (unitless)cmetal content (mg kg^-1)c_ttotal metal concentration in soil (mg kg^-1)c_ssoluble metal concentration in soil (mg L^-1)Ccovariance matrixCECcation exchange capacity (mmol_c kg^-1)C_fcost of failure (Euro)CVcoefficient of variation (%)regression residualsImetal input flux (g ha^-1 yr^-1)I_Pphosphorus input flux (g ha^-1 yr^-1)k_Ccrop-uptake rate coefficient (yr^-1)k_Lleaching-rate coefficient (yr^-1)K_F, nFreundlich parameters (L kg^-1 if n = 1)mempirical parameter (unitless)Mmetal content in soil (g ha^-1)Nnumber of data pointsOmetal output flux (g ha^-1 yr^-1)O_Pphosphorus ouput flux (g ha^-1 yr^-1)P_fprobability of failurepHsoil pH (unitless)q_wwater flux (L m^-2 yr^-1)volumetric water content (L m^-3)dry soil bulk density (kg m^-3)rSpearman correlation coefficientR²coefficient of determinationRrisk (%)RTUroot of uncertainty (%)²variancestandard deviationSRCstandardized regression coefficient (%)ttime (yr)UIFuncertainty impact factor (unitless)Xrandom variableYdry matter crop yield (kg ha^-1 yr^-1)zdepth of plow layer (m)

Process Indices
Agragricultural activitiesManmanureSesewage sludgeCFcommercial fertilizersPespesticidesAtmatmospheric depositionCropcropsLleachingI_Ptolphosphorus surplus

	ACKNOWLEDGMENTS

 
We are grateful to P.H.M. Janssen, National Institute for Public Health and Environmental Protection (RIVM), Bilthoven, the Netherlands, who provided the UNCSAM software package for efficient Monte Carlo simulations. We wish to thank the Swiss Federal Statistical Office, Bern, for providing the agricultural statistics, and the reviewers for their helpful comments.

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TOP ABSTRACT INTRODUCTION THEORETICAL BACKGROUND MATERIALS AND METHODS RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS REFERENCES

 

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