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Journal of Environmental Quality 30:1976-1989 (2001)
© 2001 American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America

TECHNICAL REPORT
Heavy Metals in the Environment

A Stochastic Empirical Model for Regional Heavy-Metal Balances in Agroecosystems

A. Keller*,a, B. von Steigerb, S.E.A.T.M. van der Zeec and R. Schulina

a Swiss Federal Institute of Technology (ETH Zürich), Institute of Terrestrial Ecology, Grabenstr. 3, CH-8952 Schlieren, Switzerland
b Ecole Polytechnique Fédérale de Lausanne (EPF Lausanne), CE-Ecublens CH-1015 Lausanne, Switzerland
c Wageningen Univ., Environmental Sciences, Soil Quality, P.O. Box 8005, 6700 EC Wageningen, The Netherlands

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

Received for publication October 24, 2000.

   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Mass flux balancing provides essential information for preventive strategies against heavy-metal accumulation in agricultural soils that may result from atmospheric deposition and application of fertilizers and pesticides. In this paper we present the empirical stochastic balance model, PROTERRA-S, that estimates heavy-metal and phosphorus accumulation in agricultural soils on the regional level. The basic units of these balances are land use systems defined by livestock production and cultivated crops. The model is designed to use available databases, such as regional agricultural statistics and soil information systems. In a case study, we assessed the phosphorus, cadmium, and zinc balances for the Sundgau region, Switzerland. The regional P requirements of crops were mainly supplied by animal manure (56%) and commercial fertilizers (40%). Net cadmium fluxes of the land use systems ranged from 1.0 g ha-1 yr-1 (dairy and mixed farm types) to 17.8 g ha-1 yr-1 (animal husbandry systems), whereas the regional net cadmium flux was only 1.4 g ha-1 yr-1. The regional net zinc flux was 605 g ha-1 yr-1. The smallest net zinc flux of 101 g ha-1 yr-1 was found for an arable farm type, whereas for animal husbandry systems fluxes up to 39.8 kg ha-1 yr-1 were estimated. Comparison of model results with reported metal balances of experimental farms shows that identification of agricultural land with high risks of heavy-metal accumulation benefits from stratification of heavy-metal balances according to land use systems while accounting for their P fertilization plans. Consequently, the model may support sustainable management of heavy-metal cycles in agricultural soils.

Abbreviations: CEC, cation exchange capacity • CMU, cattle manure unit • LUS, land use system


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
THEORY
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
SOIL surveys assess pollution only after it occurred. They cannot provide preventive strategies against metal accumulation in soil. Heavy-metal inputs into agricultural soils due to atmospheric deposition and application of commercial fertilizers, animal manure, sewage sludge, and pesticides take place at a rather slow rate but on large areas. Hence, it may take decades to detect accumulation trends in soil by repeated sampling with statistical significance. Such contamination may not be of concern in terms of immediate toxicity effects as in the case of "hot spot" pollution of hazardous waste and industrial sites. Yet, it is the ubiquitous character and the increase of heavy-metal flows through the soil system that may cause serious problems for soil fertility, ground water quality, and food chains. The only adequate strategy to deal with slow large-scale accumulation of heavy metals in soils is to prevent such contamination. The instrument of mass flux balancing is essential to achieve sustainable management of the metal regime of agricultural soils in the long term as it enables the anticipation of metal enrichment in soil (Schulin, 1993). In this respect, the balance approach is useful to derive indicators for sustainable soil quality as well as for other environmental compartments (Gilbert et al., 1996; Moolenaar et al., 1997; van der Zee and de Haan, 1998).

Various methods have been proposed to assess metal balances for agricultural soils. A general purpose of (static) mass balance studies is to identify important metal input and output fluxes in order to detect soil pollution risks (von Steiger and Obrist, 1993; Moolenaar and Lexmond, 1998; de Vries and Bakker, 1998). Additionally, dynamic models have been developed to predict long-term behavior of heavy metals in soil (van der Zee et al., 1990; Boekhold and van der Zee, 1991; Harmsen, 1992; Palm, 1994; Moolenaar et al., 1998; Tiktak et al., 1998).

Apart from the degree of process modeling involved, these balance approaches differ primarily with respect to the spatial scale (field, farm, region, nation), their temporal scale of interest (static or dynamic approach), and with regard to their combination with available model databases. Models based on mechanistic descriptions of soil processes (Boekhold and van der Zee, 1991; Palm, 1994) have been restricted to applications on the field scale, because of the large input data requirements. Empirical models, with simplifications related to data availability, are commonly developed for the farm scale (e.g., Moolenaar and Lexmond, 1998) or the regional scale (e.g., von Steiger et al., 1998; Tiktak et al., 1998). The regional scale is particularly appropriate for monitoring and controlling metal fluxes in agroecosystems because this spatial scale corresponds with the socioeconomic scale of communities and farms (i.e., for decision-making and regional policies regarding arable management systems) (Fresco, 1995). Therefore, the regional scale appears to be an appropriate target scale for translating model results into sustainable management of heavy-metal cycles by farmers and other land managers.

However, model development for regional agroecosystems requires that agricultural data are coupled with soil characteristics, taking into account reliability and accuracy of input data that may influence model results considerably. Soil characteristics can usually be obtained from georeferenced soil maps (site-specific data) representing interpolated soil data on gridcell maps using geostatistical methods. The agricultural metal inputs, however, cannot always be derived for a comparable resolution. The spatial pattern of these inputs depends on the spatial distribution of agricultural characteristics such as livestock production, crop types, and fertilization management. Typically, this information is not available at field level (non–site specific data). Thus, these non–site specific metal inputs resulting from agricultural activities cannot directly be linked to the site-specific soil information maps. For instance, the dynamic balance model for the long-term response of heavy-metal contents to regional inputs developed by Tiktak et al. (1998) uses average agricultural metal inputs. The main advantage of this model is that regional differences in metal accumulation can be identified and trends of future metal contents predicted. The influence of different agricultural land use, however, is averaged out.

To take into account agricultural characteristics in balances and to provide preventive strategies against heavy-metal accumulation in regional agroecosystems, von Steiger and Obrist (1993) developed the empirical model PROTERRA for the assessment of phosphorus, cadmium, zinc, copper, and lead balances in regional agroecosystems of about 100 km2. We extended this model incorporating leaching of heavy metals and set the empirical model in a stochastic framework to account for parameter uncertainty. This stochastic empirical model, PROTERRA-S, considers each possible combination of site-specific soil characteristics and non–site specific fertilization management. The basic units of the balances are land use systems defined by livestock composition and cultivated crops. The balance model is linked to available regional databases, such as agricultural statistics and soil information systems. Since the agricultural database is updated every 5 yr in Switzerland, the model estimates temporal average balances for 5-yr periods to consider changes in regional boundary conditions such as increasing use of waste fertilizers or change in agricultural land-use characteristics.

The objective of this paper is to present the empirical stochastic balance model for regional agroecosystems and to assess the magnitude of cadmium and zinc fluxes for a case study in Switzerland. Other heavy metals can be assessed by the balance model as well. In addition, key assumptions of the model are discussed and the model results are compared with other heavy-metal balance studies.


   THEORY
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Model Structure
Figure 1a presents the input, internal, and output flows that are in general considered in heavy-metal balances on a farm scale. While some mass flow data can be obtained from bookkeeping sheets of the farms, most of the data necessary to calculate the indicated heavy-metal flows directly are usually not available or very time consuming to obtain (von Steiger and Obrist, 1993). Based on available databases, PROTERRA-S uses the balance scheme delineated in Fig. 1b, separating the mass flows determined from non–site specific agricultural management data and mass flows determined from site-specific soil data. The balance of the agricultural management gives the net input of metals into the soils by agricultural land use, here referred to as crop production.



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  		Fig. 1. General balance scheme for (a) the farm scale and (b) the regional balance model PROTERRA-S.

 
The model relates the metal fluxes associated with fertilizer inputs to the management of the soil P balance, making empirically based assumptions about farmer fertilization strategies (Table 1). We chose P as the key element of the nutrient management because (i) metals are primarily present in P and N–P fertilizers and hardly in N fertilizers and (ii) P fertilization plans of the farmers depend primarily on the P requirements of crops. On the basis of the relationship between the metal fluxes and the P fertilization plans, the model can make use of available regional agricultural statistics (e.g., livestock production, crop type areas, amounts of sewage sludge used) (Table 2). Moreover, the model takes regional characteristics of fertilization management into account that can be obtained from agricultural consultants and guidelines.


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  		Table 1. Mass flux assessment and modeling approaches used in PROTERRA-S.

 

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  		Table 2. Available databases used in PROTERRA-S.

 
Levels of Flux Balances
According to Swiss agricultural statistics, farms are grouped by predominant livestock type and density (per unit area of farm land) into farm types, which are denoted here by the index i (Table 3). For each farm type the statistics also provide the total numbers of different kinds of livestock. The area of agricultural land, Ai, belonging to each farm type is grouped by cropping systems (i.e., into three crop classes, denoted by index j, see Table 3). Using k as the index for individual crops, Aik denotes the total agricultural area of the region on which crop type k is produced within the ith farm type. This databasis is available for each region in Switzerland, where a region refers here to an administration unit comprising several communities. Typically a region has an area in the order of some 100 km2.


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  		Table 3. Land use systems (LUSij) as the basic units of the PROTERRA-S model. All combinations of farm type i and cropping system j are considered.

 
Given these databases, so-called land use systems (LUS) were defined as the basic balance units. A LUSij is defined as the agricultural land of a region belonging to the same farm type i and the same cropping system j. It should be noted that metal transfer between farms of the same LUS (e.g., by exchanging feed crops, livestock, or manure) has no influence on the balance setup by the model because they remain internal. In other words, PROTERRA-S treats the farms grouped in the same LUS together as a larger composite farm in terms of the schemes depicted in Fig. 1b.

The model disaggregates balances from the level of the LUSij to the level of specific crop types k within a farm type i as well as aggregates the LUSij balances according to their area fraction Aij to the regional level. It is obvious that such an aggregation of the input and output fluxes of the LUS results in loss of details. The specific livestock and crop production characteristics are averaged out. Therefore, the aggregated heavy-metal balances indicate only a general trend of the region.

Model Equations at the Level of the Land Use Systems
The change of a heavy-metal content M (g ha-1) in a completely mixed soil layer (i.e., the topsoil or plow layer in the case of arable soils) during a time period {Delta}t (yr) is given for each LUSij by:

[1]
where IAtm (g ha-1 yr-1) is the regional aggregated metal input flux by atmospheric deposition, IAgr,ij (g ha-1 yr-1) is the net input flux of the LUSij from agricultural activities, and OL (g ha-1 yr-1) is the metal loss by leaching that is evaluated for the predominant soil types of the region and aggregated according to their area fraction. Fluxes such as metal transfer by soil erosion are not considered here, but might also be included (Harmsen, 1992). Because the databases do not provide site-specific cross information between the basic agricultural balance units, LUSij, and the soil type units, we used a stochastic balance approach considering each possible combination of soil type and agricultural management of the LUS.

Leaching
The total heavy-metal content M (g ha-1) in a plow layer is the sum of sorbed metal amount to the solid phase and (truly) dissolved amount in the soil solution:

[2]
where {rho} is the dry soil bulk density (kg m-3), z is the depth of the plow layer (m), {theta} is the volumetric water content (L m-3), and ct (mg kg-1) and cs (mg L-1) are the sorbed and dissolved metal concentrations of the soil, respectively. Partitioning between adsorbed and dissolved metal phase is described by a Freundlich type isotherm given by:

[3]
where KF (L kg-1) and n (unitless) are constants. The term KF is related to soil properties (van der Zee and van Riemsdijk, 1987; Buchter et al., 1989; Elzinga et al., 1999), and can be expressed by a regression function of the form:

[4]
where bKf is the adjusted Freundlich coefficient, bg is the empirical coefficient of g basic soil properties xg that are considered in an appropriate regression function (e.g., involving soil pH and cation exchange capacity [CEC]). The dissolved metal concentration cs is approximately given by:

[5]
and considering only convective transport, the leaching flux can be written as:

[6]
where kL (yr-1) is the leaching rate coefficient, given by:

[7]

and where qw (L m-2 yr-1) is the (Darcy) water flux at the lower boundary of the plow layer.

Crop Production
The net metal input from the crop production process in each LUS is given by:

[8]
where IMan is the input flux by animal manure application, ICF is the input flux with commercial fertilizer, ISe is the input flux with sewage sludge, IPes is the input flux by pesticides, and OCrop is the output flux by crop removal, which are all expressed in g ha-1 yr-1.

Metal inputs with fertilizer application, IMan, ICF, and ISe, are determined on the basis of the following P balance:

[9]

Here, OP,Crop (g P ha-1 yr-1) is the P uptake of crops (only harvested parts) and IP,tol (g P ha-1 yr-1) is an additional P input that accounts for present P surpluses in agroecosystems. IP,Man, IP,Se, and IP,CF are the P input fluxes through manure, sewage sludge, and commercial fertilizers, respectively (all in g P ha-1 yr-1). Phosphorus losses by surface runoff and leaching are not considered here separately; these processes are assumed to be accounted for by updating the P fertilization plans for every balance period.

The P demand of crops in Eq. [9] can be specified based on available statistical data for each LUS, whereas the data for fertilizer refer to larger units. Manure production can be inferred from livestock statistics for farm types. Bookkeeping of wastewater treatments plants allows us to determine the metal and P fluxes entering the environment by sewage sludge disposal for communities. Likewise, trade statistics may give information about the amounts and types of commercial fertilizers sold in a region. How fertilizers are distributed across the agricultural land depends on the decisions of the farmers.

In order to estimate the distribution of fertilizers between the LUS, PROTERRA-S assumes that farmers in average use the following fertilization strategy, which is recommended by the Swiss Guidelines for Water Protection (Federal Office of Environment, Forests and Landscape, 1994). (i) All the manure produced by a specific farm type is applied to the cropping area belonging to that farm type. On agricultural land, where sufficient nutrients can be supplied with animal manure alone, other fertilizers are avoided. (ii) If the produced manure is insufficient to supply the P demands of crops, waste fertilizer such as sewage sludge is used (quantity is restricted to 5 Mg dry matter every 3 yr). (iii) Commercial fertilizer is used to provide the P demand for crops that is still required after manure and sewage sludge have been distributed.

Phosphorus Balance
Average P removal for cropping systems j is calculated for each farm type i as:

[10]
where Aijk (ha) is the area of the crop type k within LUSij, Aij (ha) is the total area of LUSij, and Yk (kg dry matter ha-1 yr-1) and cP,k (mg P kg-1) are the yield and P concentration of the crop type k. It should be noted that averaging the P removals of crop types for cropping systems may lead to small errors in the P balance, and consequently in the metal balances of the LUS. Partitioning of manure quantity between the cropping systems j is determined by the P demand of the cropping systems, OP,Crop,ij, and a preference factor, {alpha}Man,j (%). A weighting matrix {lambda}Man,ij can therefore be defined as:

[11]

The total quantity of P to be distributed with manure, QP,Man (kg P yr-1), for each farm type i may be calculated from:

[12]
where nl (unit) is the number of livestock type l and fP,l (kg P unit-1 yr-1) is the amount of P produced per unit of livestock type l that is assumed to be independent of the farm type. Applying the fraction {lambda}Man,ij of this amount to LUSij, the P input flux by manure is then given by:

[13]

If within a farm type IP,Man is larger than OP,Crop, it is assumed that manure is not distributed on areas of other farm types. Thus, manure application may lead to excessive P input on some LUS. If the manure produced is insufficient to cover the P demands of the crops, the quantity IP,need (g P ha-1 yr-1), which is given by:

[14]
is positive. In this case, the given sewage sludge quantity of the region is distributed proportionally to the remaining demand IP,need across the area on which sewage sludge is accepted, {alpha}Se,j (%). This empirical factor accounts for the fact that sewage sludge is not accepted by all farmers and is assumed to be independent of the farm type. The fraction of sewage sludge entering the LUSij, {lambda}Se,ij, is then given by:

[15]
with the constraint that for LUSij with negative IP,need,ij values, the weight {lambda}Se,ij is set to zero, and that for all LUSij, {lambda}Se,ij must sum up to one (mass conservation). The P supply provided by sewage sludge, IP,Se (g P ha-1 yr-1), is then given by:

[16]
where QSe (Mg dry matter yr-1) is the regional sewage sludge quantity and cP,Se (kg P Mg-1) is the P concentration of the sewage sludge. Following the fertilization strategy, commercial fertilizer provides the remaining P requirement for crops that is given by:

[17]

[18]
for the areas where sewage sludge is applied. On agricultural areas where sewage sludge is not accepted, Aij (1 - {alpha}Se,j), IP,CF,ij is calculated likewise except that IP,Se,ij in Eq. [17] and [18] is set to zero.

Heavy-Metal Inputs
Once the fertilizer inputs have been partitioned between the LUS, the metal inputs through fertilization are determined from the P fertilizer inputs and from the ratios between metal and P concentrations of the fertilizers. Thus, the metal input through manure is calculated according to:

[19]
where xM,Man,l (g metal per kg P) is the ratio between metal M and P concentrations in manure of livestock type l. Likewise, the metal input with sewage sludge on the fraction of land where this is accepted is calculated according to:

[20]
where xM,Se (g metal per kg P) is the ratio between metal and P concentration in sewage sludge. The metal input with commercial fertilizer equals to:

[21]
where xM,CF (g metal per kg P) is the ratio between metal and P concentration in commercial fertilizer. Finally, the metal input with pesticides, IPes (g ha-1 yr-1), is estimated as:

[22]
where qPes (L ha-1 yr-1) is the quantity of pesticide for the crop type k recommended by agricultural guidelines, and cPes (g metal per L) is the metal concentration in pesticide obtained from product information.

Crop Uptake and Harvest
Metal outputs with harvest (including grazing) are calculated as:

[23]
if data of the metal concentration of the crop type k, cCrop,k (mg kg-1 dry wt.), are available. In a general form, with regard to the total metal concentration in soil, OCrop can be written as (Boekhold and van der Zee, 1991):

[24]
where kC is the crop uptake rate coefficient and m is an empirical parameter. Under the assumption of a linear relationship between cCrop and ct, which might be valid for nonpolluted soils, the crop uptake rate coefficient for the specific crop type k is according to:

[25]
and the parameter m becomes 1. Alternatively, cCrop can be derived by a (nonlinear) regression function of the form:

[26]
that might be advisable for polluted soils. Here b0k and b1k are regression coefficients. In this case, the crop uptake rate coefficient is given by:

[27]
and the parameter m becomes b1k. The regression approach can be extended by other basic soil properties, such as the soil pH, clay content, or organic matter content of the soil (e.g., Eriksson, 1990).

Model Extension
Based on the availability of regional agricultural statistics the PROTERRA-S balance approach is used to calculate the change of a heavy-metal content in soil during a time period {Delta}t (yr). Therefore, characteristics of the regional agricultural land use are assumed to be constant for that time step. Temporal variation of metal fluxes during that period is averaged out and not considered in the model. Such variation may result from seasonal variability of crop yield or from variation of annual atmospheric metal deposition. Substituting Eq. [7], [8], and [25] in Eq. [1], the PROTERRA-S model can be extended for assessing continuous temporal changes in heavy-metal balances in the form (Boekhold and van der Zee, 1991):

[28]
where Itot (g ha-1 yr-1) is the sum of the metal input fluxes considered in the model. Boekhold and van der Zee (1991), Moolenaar et al. (1997), and Tiktak et al. (1999) derived analytical solutions for such a dynamic balance approach for certain values of m and n. Harmsen (1992) presented analytical solutions regarding various chemical reactions that determine the relationship between the solubility of heavy metals and their accumulated contents in soil.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
As a case study, we applied the model to the Sundgau, a rural region south of Basel in northwestern Switzerland (Fig. 2) . This region extends between the Swiss Jura in the Southeast with hills up to 800 m in altitude and the Rhine valley in the Northwest. The region covers 95 km2 and comprises 16 communities of the Cantons Basel-Land and Solothurn.



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  		Fig. 2. Distribution of agricultural land (1-ha gridcells) in the Sundgau region, Switzerland (total area = 95 km2).

 
Agricultural Statistics
The agricultural land of the region covers about 36 km2, distributed among 201 farms. Pastures and meadows accounted for 49%, agricultural crops, dominated by bread and fodder cereals, for 46%, and special crops for 6% of this area. The average farm area of 18 ha was slightly larger than the national average of 13.8 ha (1995). Thirty-nine percent of the farms were smaller than 10 ha, and about equal fractions of 20% of the farms fell into the classes of 10 to 20, 20 to 30, and >30 ha. The average livestock density of the region was about 0.93 cattle manure units (CMU) ha-1, which is only slightly smaller than the Swiss average of 1.2 CMU ha-1 (1995). (The cattle manure unit is based on the nutrient quantities for a dairy cow weighing 600 kg: 105 kg N yr-1, 15 kg P yr-1). Thus, with respect to livestock production and farm characteristics, the Sundgau region is quite typical for Switzerland.

Table 4 presents the agricultural statistics of the LUS in our case study for the period 1992 through 1997. Dairy farms (0.2–1 CMU ha-1, cattle; 1–2 CMU ha-1, cattle) and arable farms (<0.2 CMU ha-1 and 0.2–1 CMU ha-1, poultry) covered about 88% of the total agricultural area. Dairy farms are characterized by the combination of plant and animal production (meat, milk). Besides pastures and meadows the land of these farms was mainly used for growing bread and fodder cereals and silo and green maize in crop rotation. Arable farms were characterized by the dominance of crop rotation land on which mainly bread and fodder cereals, potatoes, and rape were produced, while grassland and special crops (vegetables and vineyards) played a minor role. On a few farms, comprising 2% of the total area, livestock density was >2 CMU ha-1. These intensive husbandry systems are characterized by animal breeding. Crops grown on these farms were primarily fodder cereals, silo maize, and green maize.


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  		Table 4. Agricultural statistics of the Sundgau case study (3560-ha total area).

 
Assumptions used to model the farmers' fertilization strategies were as follows. The tolerable P surplus, IP,tol, was set equal to the Swiss average of 13 kg P ha-1 yr-1, estimated by Spiess (1999). Assuming that manure was preferably distributed on pastures and meadows and only marginally on special crops, the weights for {alpha}Man were set at 2 for pasture and meadows, 1 for agricultural crops, and 0.2 for special crops ({alpha}Man = [2, 1, 0.2]). Sewage sludge was assumed to be accepted on 50% of the grassland area and on 30% of the crop rotation area ({alpha}Se = [0.5, 0.3, 0]). The complete data set of the model input parameters used in this case study (e.g., metal and phosphorus concentrations in crops and fertilizers and crop yield) is available at http://www.ito.umnw.ethz.ch/SoilProt/staff/kellera (verified 21 June 2001).

Soil Data and Freundlich Regression Function
Soil types and soil pH, organic matter (OM), clay content, carbon content, and CEC of the Sundgau region were derived from 1:5000 GIS-based soil maps. Predominant soil types in the area of the Swiss Jura are Humic Cambisols, Calcaric Cambisols, and Rendzic Leptosols, while in the northwestern part of the region Haplic Luvisols, Stagnic Luvisols, as well as Humic Cambisols and Calcaric Cambisols are the most frequent soil types. Measured metal concentrations in soil and additional soil properties were available from regional soil surveys of the cantonal Environmental Protection Agency (Table 5). Additional measurements were available from plots of the Swiss National Soil Monitoring Network (Keller and Desaules, 1999).


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  		Table 5. Sample statistics for measured soil properties and metal concentrations (Bono, 1993, 1999) in agricultural soils of the case study area.

 
Following the approach proposed by Elzinga et al. (1999), we calculated Freundlich distribution coefficients KF from the mapped soil properties using linear regression of KF on soil pH and CEC values. For cadmium we applied the regression function given by Elzinga et al. (1999) and Tiktak et al. (1999):

[29]
and estimated the cadmium concentration in soil solution using Eq. [5]. These soluble cadmium estimates were in the same range as the NaNO3–extractable concentrations (Swiss Agency for the Environment, Forests and Landscape, 2001) measured by the cantonal Environmental Protection Agency (see Table 5). For zinc, however, 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 of the regression function to fit the average of these measurements. This resulted in the following modified equation:

[30]

The exponent n of the Freundlich equation was estimated using the following regression equation given by Buchter et al. (1989) for both metals:

[31]

Parameter Uncertainty
To estimate the uncertainty in model predictions, designated input parameters were treated as random variables described by normal or log-normal probability distributions (Keller et al., 2002). Using a Latin Hypercube sampling scheme with correlated variables a large number of equally probable realizations of the model input data were generated. The PROTERRA-S model was run for each set of realizations, which yields model outputs that are also random variables. In this study, we applied the program UNCSAM (Janssen et al., 1994), which is a package for efficient Monte Carlo sampling in combination with regression and correlation analysis to perform sensitivity and uncertainty analyses on a large variety of simulation models. The balance model is programmed using MATLAB Version 5.3 (Mathworks, 1999).


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Phosphorus Balances
On LUS with livestock densities larger than 2 CMU ha-1, P requirements of crops were met by animal manure alone. For these animal husbandry farm types, large P surpluses ranging from 108 to 580 kg P ha-1 yr-1 were found. For dairy and arable farm types, additional P inputs through sewage sludge (3.2–8.8 kg P ha-1 yr-1) and commercial fertilizer (5.5–20.8 kg P ha-1 yr-1) were required to meet the crop demands. On arable farms the P inputs through these fertilizers were largest. Phosphorus uptake of the cropping systems ranged between 17.3 and 26.9 kg P ha-1 yr-1, while the regional crop uptake was 19.6 kg P ha-1 yr-1. In total, 56% of the regional P input was supplied by animal manure and 40% by commercial fertilizers, whereas sewage sludge contributed only about 5%.

Cadmium Balances
Net cadmium fluxes varied between 1.0 g ha-1 yr-1 for agricultural crops on farms with a livestock density of 1 to 2 CMU ha-1 poultry and 17.8 g ha-1 yr-1 for pastures and meadows on farms with a livestock density of >2 CMU ha-1 pig (Table 6). Excluding the LUS with predominant pig breeding, the range of the net cadmium flux in the LUS decreased considerably (median 1.0–3.4 g ha-1 yr-1) and was close to the regional net cadmium flux of 1.4 g ha-1 yr-1 (Fig. 3) .


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  		Table 6. Median and standard deviation of simulated cadmium input and output fluxes for selected land use systems (LUS). Units are g ha-1 yr-1 unless otherwise noted.

 


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  		Fig. 3. Simulated cadmium balance for the regional scale. 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. 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; OL = leaching; and xmed = median flux.

 
Differences between the LUS were large. On arable farm types, atmospheric deposition and commercial fertilizers were the dominant cadmium sources. For example, on LUS12 (<0.2 CMU ha-1, agricultural crops) the total cadmium input (i.e., the sum of the input sources) was caused by atmospheric deposition (62%) and commercial fertilizer (26%). Of this total cadmium input, 16% was exported again by crop removal and 21% lost by leaching according to our estimates. The remaining 63% of the total cadmium input accumulated in the plow layer or topsoil. Regarding the cadmium outputs, removal by crops was larger on pastures and meadows (1.4–2.2 g ha-1 yr-1) than on crop rotation land (0.6–1.6 g ha-1 yr-1). Model simulations yield on average uptake rate coefficients of 4.7 x 10-4 yr-1 for bread cereals, 2.3 x 10-4 yr-1 for fodder cereals, 33.9 x 10-4 yr-1 for sugar beet, and 40.3 x 10-4 yr-1 for maize. For intensively fertilized meadows, average uptake rate coefficients were 22.7 x 10-4 yr-1 for extensive meadows and 17.5 x 10-4 yr-1 for pastures. Thus, the average flux of cadmium uptake varies strongly between crops.

On dairy farms and animal husbandry farms, cadmium inputs through commercial fertilizers were less important than inputs through manure. As on arable farms, cadmium balances were governed by atmospheric deposition and harvest export. The regional cadmium balance was dominated by atmospheric deposition (64% of total input) and crop removal (37%), while leaching (22%), commercial fertilizer (18%), and manure (17%) were less important (see Fig. 3). Cadmium imports by disposal of sewage sludge were rather small in the case study. Model estimates for leaching showed that most of the cadmium entering the soil was accumulating due to the large sorption capacity and almost neutral soil pH values across the region. Using regression Eq. [30] and Eq. [32], estimated Freundlich parameters KF and n were 207 ± 122 L kg-1 and 0.68 ± 0.05, respectively, which resulted in an average leaching rate, kL, of 1.4 x 10-5 ± 2.5 x 10-4 yr-1.

Input parameter uncertainty led to standard deviations in the range of one-third to one-half of the corresponding median values for the cadmium sources manure, sewage sludge, and atmospheric deposition as well as for crop removal (see Table 6). The largest coefficients of variation (CV) were found for cadmium input through commercial fertilizer application (90–230%) and output by leaching (300%). As a consequence, standard deviations of the resulting net cadmium fluxes were in general on the same order of magnitude as their median values and for some LUS nearly twice as high. The CV of the regional balance (120%) was slightly lower than of the indivdual LUS due to the averaging effect.

On 56% of the total agricultural area cadmium accumulation in soil as indicated by the LUS balances was smaller than the regional average of 1.4 g ha-1 yr-1 (Fig. 4) . However, net cadmium fluxes for some LUS representing 2.5% of the total area (about 90 ha) revealed large cadmium inputs. Extrapolating the current regional accumulation trend linearly into the future, we defined a critical accumulation rate as the tolerable cadmium accumulation during 200 yr that would lead to a concentration of 0.8 mg kg-1 of HNO3–extractable cadmium in the plow layer (Swiss guide value; Swiss Agency for the Environment, Forests and Landscape, 2001). On the basis of our simulations this guide value would be exceeded on about 1.1% of the total area (ca. 40 ha) in 200 yr. However, comparing the 90% confidence intervals (5 and 95 percentiles) of the net cadmium flux of the LUS with the critical rate (Fig. 4), inputs may have been unacceptably high on 8% of the agricultural area of the Sundgau region.



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  		Fig. 4. Area-cumulated cadmium net fluxes of the land-use systems and the regional balance. The estimated 90% confidence intervals for the land use systems are also given.

 
Zinc Balances
Net zinc fluxes varied by three orders of magnitude. The smallest net zinc fluxes were found for an arable farm type (101 g ha-1 yr-1 on pastures and meadows), whereas largest net zinc fluxes up to 39.8 kg ha-1 yr-1 were discovered for animal husbandry farms (Table 7). Dairy farm types showed net zinc fluxes in the range of 349 to 614 g ha-1 yr-1, which is in the magnitude of the regional average of 605 g ha-1 yr-1 (Fig. 5) . Ratios between net fluxes of individual LUS and the regional average varied from 0.1 up to 67. This large variation was mainly a result of differences in livestock production with the associated zinc input through manure. This input was particularly important on farms with intensive husbandry of the livestock types pig, calf, and cattle. On arable farming systems, atmospheric deposition and sewage sludge were the dominant inputs. On the regional level, about two-thirds of the total zinc inputs entered the agricultural land through manure application and about one-third with atmospheric deposition (see Fig. 5).


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  		Table 7. Median and standard deviation of simulated zinc input and output fluxes for selected land use systems (LUS). Units are g ha-1 yr-1 unless otherwise noted.

 


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  		Fig. 5. Simulated zinc balance for the regional scale. 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. 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; OL = leaching; and xmed = median flux.

 
Average zinc uptake by crops was usually twice as high on pastures and meadows as for agricultural crops. Uptake rate coefficients, kC, were 37.8 x 10-4 yr-1 for intensively fertilized meadows and 28.4 x 10-4 yr-1 for extensively used meadows and pastures, whereas simulations showed lower uptake rate coefficients for bread cereals (14.3 x 10-4 yr-1) and for fodder cereals (12.2 x 10-4 yr-1). Leaching was of some importance for zinc balances of arable farming systems. Simulations showed a leaching rate, kL, of 3.5 x 10-6 ± 2.4 x 10-5 yr-1, resulting from estimated Freundlich KF values of 587 ± 219 L kg-1 and n values of 0.68 ± 0.05.

Coefficients of variation were much lower for the zinc than for the cadmium fluxes (cf. Keller et al., 2002). Standard deviations of the zinc uptake by crops and the zinc input flux through sewage sludge ranged from 10 to 30% of the corresponding median values of the LUS, while standard deviation for atmospheric deposition was about 45%. Largest variation of zinc fluxes (30–90%) was obtained for zinc inputs through manure and commercial fertilizer and for leaching. For arable farm types this resulted in a CV of 70 to 220% for the net zinc fluxes, for dairy farm types and intensive husbandry systems the CV was 40 to 70%, while the CV of the net zinc flux of the entire region was 46%. Thus, the CV of the net cadmium flux was nearly three times as high as the CV of the net zinc flux at the regional level.

On about 90% of the total area, zinc accumulation in the soil of the LUS was estimated to be smaller than the regional average (Fig. 6) . If present zinc accumulation would continue at the estimated regional rate, the critical zinc flux would be exceeded on about 4% (143 ha) of the total area (Swiss guide value for HNO3–extractable Zn concentration: 150 mg kg-1; Swiss Agency for the Environment, Forests and Landscape, 2001).



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  		Fig. 6. Area-cumulated zinc net fluxes of the land-use systems and the regional balance. The estimated 90% confidence intervals for the land use systems are also given. For graphical presentation, original metal flux values were transformed adding Ytrans.

 

   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
CONCLUSIONS
 REFERENCES
 
Validity of the Model
Comparison with Other Heavy-Metal Balance Studies
Our results at the regional level are in good agreement with regional and national balance studies in European agroecosystems. An overview of these studies has been given by Moolenaar (1998). Further metal balance investigations on a national level were recently presented by Schütze and Nagel (1998) for Germany, and by Chambers et al. (1998) for England and Wales. According to these studies, net cadmium accumulation in European agricultural soils varied between 0.2 and 3.7 g ha-1 yr-1 and net zinc accumulation between -61 and 1083 g ha-1 yr-1. The regional net cadmium and net zinc flux found in our case study are well within these ranges, despite the differences in balance system definitions, types of databases, and methods of flux assessment used. Considerable variability could be expected also due to differences in agricultural and environmental characteristics (e.g., atmospheric deposition levels) of the compared systems.

To evaluate the model validity with respect to the LUS balances, we compared the estimated input and output fluxes on the level of the LUS with metal balance studies on individual farms, which determined metal fluxes experimentally (e.g., Richner and Moos, 1989; von Steiger and Baccini, 1990; Reiner et al., 1996; Bayerische Landesanstalt für Bodenkultur und Pflanzenbau, 1997; Moolenaar and Lexmond, 1998). The range of metal input and output fluxes reported by these studies agreed well with the LUS balances of our study.

Reiner et al. (1996) studied 24 experimental farms in Austria that were different in their farming systems as well as in their fertilization management. For farms with manure and commercial fertilizer application they determined net fluxes between 3.1 and 6.6 g ha-1 yr-1 for cadmium and 231 to 2800 g ha-1 yr-1 for zinc, and P net removals from -14 kg ha-1 yr-1 up to P surpluses of 33 kg ha-1 yr-1. The smallest net metal fluxes were obtained for arable farm types and the largest for pig and mixed farm types. Analysis of variance of the net fluxes revealed that the classification by farm type and fertilization management explained 55% of the total variation of the net fluxes for cadmium and about 70% for zinc and P. These results are very similar to our case study, although in our case classification by farm type and cropping systems did not explain quite as much variation between the LUS balances (i.e., about 60% of the total variation for zinc but only about 30% for cadmium).

Also, the findings of Moolenaar and Lexmond (1998) are in good agreement with the results of our case study. They compared different farming systems in the Netherlands, and concluded that on arable farming systems heavy-metal balances were predominantly influenced by agricultural crops and the selection of fertilizers, whereas for dairy farming systems feed management in combination with the amount of fodder crop production were of main importance. On mixed farming systems fertilization management affected metal balances significantly; larger fertilizer inputs were found on grassland than on arable land. Similar metal input patterns on experimental farms were also observed by Richner and Moos (1989), Steiger and Baccini (1990), and Bayerische Landesanstalt für Bodenkultur und Pflanzenbau (1997).

Model Sensitivity to Fertilizer Management
As heavy-metal inputs with fertilizer are coupled with P fertilization in PROTERRA-S, the influence of the assumptions about fertilization management on the metal balances has to be evaluated. Based on fertilization guidelines in Switzerland (Federal Office of Environment, Forests and Landscape, 1994), the model predicted a regional P flux through commercial fertilizer of 12.4 kg P ha-1 yr-1. This is on the same magnitude as the corresponding national average value of 8.5 kg P ha-1 yr-1 for Switzerland in 1995 (Spiess, 1999).

Net zinc fluxes of the cropping systems were sensitive to the manure distribution parameter {alpha}Man, in particular zinc balances for dairy, mixed, and animal husbandry farms. In contrast, net cadmium fluxes of the LUS were in general only slightly influenced by different {alpha}Man values. Changing the sewage sludge distribution parameter, {alpha}Se, affected only the cadmium and zinc balances of arable farming systems substantially. The net metal fluxes at regional level were rather insensitive to varying assumptions about manure and sewage sludge distribution between the LUS.

Model Simplifications
Another aspect of model validity is the choice of the estimation methods for heavy-metal fluxes in combination with available input data. In particular, we used simplified flux assessment methods to estimate leaching and manure input. Leaching depends sensitively on the partitioning of heavy metals between the solid and the liquid phase. In this study, we estimated the partitioning by the Freundlich isotherms given by Elzinga et al. (1999), which were derived by linear regression using a wide range of different soils. The results show that these estimates were sufficient as a first guess to start with the analyses, because the model results were rather insensitive to leaching. Elzinga et al. (1999) reported that for cadmium and zinc their proposed regression functions tended to overestimate the metal concentrations in soil solution. Therefore, we recommend that others calibrate these isotherms with their own measurements if balance analyses indicate that the model outputs depend very sensitively on these data. This may in particular be the case if soils are much more acidic than in the Sundgau region.

Metal input by manure is usually determined either from balances of the animal production process, focussing on the metal inputs by feed concentrates, or using representative values of measured metal concentrations in manure (e.g., Menzi and Kessler, 1998; Nicholson et al., 1999). Reiner et al. (1996) compared these two approaches in the above-mentioned study, and found deviations almost on the order of one magnitude between the estimates for zinc fluxes. For the P fluxes, however, the calculation approaches led to almost similar results. These findings were also confirmed by Menzi and Kessler (1998), who reported that the concentration ratios between heavy metal and phosphorus in manure were found to be the most constant parameters in manure for various livestock types in a wide variety of farms. Thus, we consider linking metal input by manure to P input using this ratio in combination with livestock data as a very reliable flux assessment method.

Using the Model as a Consulting Tool
Most heavy-metal balance studies at the regional or national level use aggregated data of livestock and crop production, and of fertilizer and pesticide application for the study area. Thus, these balances do not take into account the diversity of the agricultural management within the balance area. PROTERRA-S differs from these models because it stratifies the agricultural land of a region by farm types and cropping systems and relates metal input fluxes through fertilizers to the P nutrient management. Another approach for a regional balance model has been taken by Tiktak et al. (1998) as mentioned above. Basic units of their balance model are 500- x 500-m2 gridcells, and metal fluxes of land-use types are estimated by weighting the average for this spatial resolution. They found that the net cadmium fluxes were more sensitive to soil types than to land-use types. This finding indicates that variation of heavy-metal inputs and outputs between land use systems might be averaged out if the agricultural data are aggregated to larger units. On the other hand, a large-scale spatial distribution pattern of metal fluxes is reproduced by their model.

In contrast, PROTERRA-S estimates balances for non–site specific LUS considering agricultural management. Therefore, the model is particularly suited to be used as a consulting tool: Areas with an unacceptable metal accumulation risk can be identified, and the influence of optimized fertilization management (e.g., calculation of scenarios to reduce P surpluses) and changes in livestock and crop production on the heavy-metal input fluxes of specific LUS can be evaluated. Further detailed investigations are desirable to validate the estimated heavy-metal input fluxes and to assess the present soil quality. In this respect, the fields that belong to the non–site specific LUS can be identified according to their farm type affiliation.

Moreover, the influence of increasing use of waste fertilizer on the metal balances can be predicted by the model. Reiner et al. (1996) showed that related to conventional fertilization plans (i.e., with animal manure and commercial fertilizer), application of composts and sewage sludge doubled cadmium accumulation in soil and increased zinc accumulation even by a factor of five. Moolenaar and Lexmond (1998) found that metal inputs with compost can far exceed the combined input with commercial fertilizer and manure. In our case study, a fivefold amount of the regional sewage sludge quantity would lead to a slight increase of the regional net zinc flux from 605 g ha-1 yr-1 to 758 g ha-1 yr-1, while the net zinc fluxes for arable farm types would increase by factors between five and nine.

Calculation of Steady-State Concentrations and Critical Loads
Temporal alterations of heavy-metal concentrations in soil may lead to changes in the relationship between estimated input and output fluxes until steady-state conditions are reached (i.e., input fluxes equal the output fluxes and accumulation rate in soil becomes zero). Constant heavy-metal input fluxes that are at present larger than the output fluxes may result in an increasing leaching rate and increasing crop uptake rates in the future, whereas the accumulation rate may decrease in time (Boekhold and van der Zee, 1991; Palm, 1994).

Given the estimated leaching rate coefficients, crop uptake rate coefficients, and metal inputs, steady-state metal concentrations in soil can be obtained solving Eq. [28] numerically. Under the assumption that metal input fluxes and rate coefficients kC and kL are constant in time, crop removal is linear (m = 1), and Freundlich isotherms are nonlinear (n = 0.68), regional average total concentrations in the Sundgau soils toward steady state were 0.71 mg kg-1 for cadmium and 120 mg kg-1 for zinc. These steady state concentrations, which would be reached in about 1600 yr (cadmium) and about 950 yr (zinc), are below the corresponding Swiss guide values. However, while for arable farm types (e.g., LUS12), the estimated zinc concentration at steady state of 89 mg kg-1 (1430 yr) would be below the guide value, on mixed farm types (e.g., LUS61), the steady state concentration of zinc (343 mg kg-1 in 810 yr) would exceed it.

Therefore, it is desirable to define such metal inputs that would lead to steady-state concentrations in soil that are acceptable for soil fertility, ground water quality, and food chains (i.e., the so-called critical loads) (de Vries and Bakker, 1998; Paces, 1998). PROTERRA-S approximates for individual LUS the critical input fluxes with atmospheric deposition and/or through fertilizers, given the critical accumulation rates defined above (see Fig. 4 and 6). Alternatively, at the balance level of the crop type k, critical metal inputs with regard to crop quality standards can be calculated.


   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
REFERENCES
 
Identification of the dominant factors that influence heavy-metal balances depends primarily on the spatial resolution of the mass flux assessment and, therefore, on the aggregation process used for model input data. It is shown that metal balances varied largely between the LUS resulting from differences in the agricultural farming systems and their fertilization management. The estimated cadmium and zinc balances of the LUS were in good agreement with reported metal balance studies on experimental farms. Therefore, we concluded that stratification of heavy-metal balances according to agricultural management systems and linking the metal inputs through fertilizers with the P balances of these strata seem to be useful approaches to account for agricultural characteristics in modeling metal accumulation in soil. The balances for the LUS give more detailed insights in factors that dominate metal accumulation in agricultural soil, whereas large-scale balances indicate an average situation and may be used for economic analyses.

The model can be used as a regional consulting tool to identify the areas with the highest metal accumulation risk and to evaluate the effect of preventive actions against metal enrichment in soil (e.g., the influence of optimized fertilization management on the heavy-metal cycles). Further detailed investigations may then be carried out to validate the model estimates. Moreover, based on the critical accumulation rates defined for a certain time period, critical metal inputs can be obtained, preventing harmful effects on soil fertility and crop quality.


   ACKNOWLEDGMENTS
 
This work was partly funded by the Swiss Programme on Environment of the Swiss National Science Foundation (No. 5001-044759). 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 the agricultural statistics.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 




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