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TECHNICAL REPORTS
Heavy Metals in the Environment

Mapping the Probability of Exceeding Critical Thresholds for Cadmium Concentrations in Soils in the Netherlands

^a W. de Vries, Alterra, Green World Research, P.O. Box 47, 6700 Wageningen, the Netherlands
^b Agricultural University Wageningen, Duivendaal 10, P.O. Box 37, 6700 AA Wageningen, the Netherlands
^c National Institute of Public Health and the Environment, P.O. Box 1, 3720 BA Bilthoven, the Netherlands

* Corresponding author (d.j.brus{at}alterra.wag-ur.nl)

Received for publication April 24, 2001.

	ABSTRACT

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

 
The probability of exceeding critical thresholds of Cd concentrations in the soil was mapped at a national scale. The critical thresholds in soil were based on food quality criteria for Cd in crops or in organs of cattle (Bos taurus), and were calculated by inverting a regression model for the Cd concentration in the crop, with the Cd concentration in soil, soil organic matter (SOM) content, clay content, and pH as predictors. The probability of exceeding the critical threshold for Cd in soil per node of a 500- x 500-m grid was approximated by Monte Carlo simulation, using the estimated cumulative distribution functions (cdf) of SOM, clay, pH, and Cd as input. The cdfs were estimated by simple indicator kriging with local prior means. For SOM, clay, and pH, detailed maps of soil type and land use were used to define subregions with assumed constant local means of the indicators (a priori distributions). The cdfs were sampled by Latin hypercube sampling. We accounted for correlation between the actual and critical Cd concentrations in soil by drawing Cd values from cdfs conditional on SOM and clay. The estimated probability for grassland is negligible, even in areas with high Cd concentrations in soil, and for maize (Zea mays L.) land the probability is almost everywhere smaller than 5%. For arable soils, however, these probabilities commonly are larger than 5% when sugar beet (Beta vulgaris L.) or wheat (Triticum aestivum L.) is taken as a reference crop, and locally exceed 50%.

Abbreviations: cdf, cumulative distribution function • ccdf, conditional cumulative distribution function • LGN3⁺, landuse database of the Netherlands • SOM, soil organic matter content

	INTRODUCTION

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

 
THERE IS WORLDWIDE concern about the dispersion of heavy metals such as Cd, Pb, Cu, and Zn into the rural environment through atmospheric deposition and the use of agrochemicals and manure. For the Netherlands, Van Driel and Smilde (1981) reported high heavy metal concentrations in recent river sediments that grossly exceeded the concentrations considered acceptable for cultivated soils. Somewhat later, Wiersma et al. (1986) reported high concentrations of Cd and Pb in cereals, often exceeding the proposed maximum allowable concentrations for human consumption in the Netherlands. In 1991 critical thresholds for heavy metal concentrations in agricultural soils were published (Landbouwadviescommissie milieukritische stoffen, 1991). These thresholds, referred to as LAC values, serve as a warning system: if the heavy metal concentrations in the soil exceed these thresholds, then there is a substantial probability that the quality standards for heavy metal concentrations in the crop or organs of cattle are exceeded. Four land use types are defined, and for each land use type two LAC values are presented, one for sand and one for clay or peat. Within these soil parent material categories the LAC is a constant.

Recently, a new method has been proposed to calculate critical thresholds of heavy metal concentrations in soils derived from quality standards for Cd in crops used for human consumption or as fodder, or for Cd in organs of cattle. The core of the method is the use of regression models to predict the heavy metal concentration in crops from heavy metal concentrations in soils, soil organic matter content, clay content, and pH as predictors. In many soils, these basic soil properties govern the transfer of heavy metals from soils to crops. For Cd, these regression models describe the variation of the metal concentration in various crops reasonably well. Therefore, the new method is a promising tool to derive soil quality standards related to health risks from Cd.

Contrary to the LAC values, the new critical thresholds also vary within soil parent material categories, because the basic soil properties SOM, clay, and pH vary within these categories. The aim of this study was to make maps of the new critical thresholds for Cd concentration in soils, and of the probability that the actual Cd concentration in soils exceeded these new critical thresholds. This was done for the dominant land use types in the Netherlands: grassland, maize land, and arable land. The critical thresholds for Cd in soils and the probability of exceeding the critical threshold for Cd in soil at a given location was valuated for the actual land use at that location.

	MATERIALS AND METHODS

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

 
Basic Soil Properties and Land Use
The uptake of heavy metals in soils by a crop is controlled by soil organic matter (SOM) content, clay content, and pH. Basically, these soil properties largely determine the concentrations of heavy metals in pore water, and therefore the amount of heavy metals available to crops. Measurements of these basic soil properties have been derived from the Soil Information System of the Netherlands. From this database we selected all points with a laboratory measurement of these properties on samples taken from the topsoil, beneath the sod layer, if present, from the surface, to about 25 cm below the surface. Soil organic matter was determined by loss on ignition, clay was determined gravimetrically, and pH was determined in a 1 M KCl solution. The total number of points (measurements) was 4105 for clay, 4051 for SOM, and 4187 for pH. These measurements have been used to estimate frequency distributions for grouped units of the Soil Map of the Netherlands at a scale of 1:50 000.

We also required information about the actual land use because uptake of heavy metals varies for different crops, and because land use may affect the concentrations of heavy metals in soils. Previous research has shown, for instance, that Cd concentrations in uncultivated soils are less than in soils under cultivation (Van Drecht et al., 1996). In this study we used the land use database LGN3⁺, which is derived from satellite imagery from 1995 and 1997, topographic maps, and statistics on agriculture of the Centraal Bureau voor Statistiek (Thunnissen and de Wit, 2000). The 25- x 25-m pixels were aggregated to pixels of 500- x 500-m by calculating the land use class with the largest area.

Cadmium Data
Various datasets on Cd concentrations were used (Table 1). The first five datasets of Table 1 were also used by Tiktak et al. (1998) to estimate means of 500- x 500-m blocks. These datasets were supplemented by the data of the National Soil Quality Monitoring Network (sampling rounds 1993, 1994, and 1995), data of the Soil Quality Monitoring Networks of the provinces of Groningen, Friesland, Drenthe, Gelderland (sampling round 1998), Flevoland, Utrecht, Noord-Holland, Zuid-Holland, and Noord-Brabant, and a dataset collected in an occasional project in the province of Zeeland. The total number of measurements was 4094. The size and shape of the sampled plots (geostatistical support) differs between the datasets. Common supports are squares of 20 x 20 m² (IB, IB/RIKILT, CCRX), 100 x 100 m² (PSM-DRa), 150 x 150 m² (ZLD), fields or forest stands (BLGG, PSM-GR, PSM-DR, PSM-GLD, SC-DLO), or all fields of a farm (NSM, PSM-NBR). Also, the depth and thickness of the sampled layer differs between the datasets. Commonly used layers are 0 to 20 cm for arable soils or 0 to 5 cm for grassland (BLGG, IB, IB/RIKILT), and 0 to 10 cm (regardless of land use). Soil samples were destructed with either HNO_3, HCl, or aqua regia, and analyzed with flame atomic absorption spectrometry or the inductive coupled plasma technique. For the IB/RIKILIT dataset the soil samples were ashed at 450°C (Wiersma et al., 1986). Similar to Tiktak et al. (1998), we did not correct for differences in sampling depth or extraction method.

All datasets were collected to assess baseline concentration levels, that is, concentration levels commonly found in soils at that time. Places that are known or suspected to be heavily polluted by point sources were either not sampled or omitted afterward. We also omitted samples taken from the recent flood plains along the rivers Maas and Rhine, and two outliers having a Cd concentration larger than the mean plus four times the standard deviation.

Critical Thresholds for Cadmium Concentrations in Soils Derived from Quality Standards for Crops
Quality standards in crops are the starting points for calculating critical thresholds of heavy metals, in this case cadmium, in soils. Once a model is derived that relates Cd concentration in crops to soils, then the soil Cd concentrations that result in exceeding the quality standards in crops can be estimated.

For arable land, wheat and sugar beet were taken as reference crops. For potatoes (Solanum tuberosum L.), a third commonly grown crop on arable soils in the Netherlands, there was no relation between Cd concentrations in soil and in potatoes. The Cd concentration in grass, maize, wheat, and sugar beet was modeled by the Freundlich equation:

[1]

where Q_plant and Q_soil are the Cd concentrations (mg kg^-1 dry matter) in the crop and the soil, respectively, A is the Freundlich constant, and B is a nonlinearity coefficient. We assumed that log(A) is a linear function of pH, log(SOM), and log(clay):

[2]

where pH is the soil pH (pH_KCl), SOM is the soil organic matter content (in %), and clay is the soil clay content (in %). Combining Eq. [1] and [2] gives:

[3]

Moreover, we took account of different values for B at different Cd concentrations in soil, by fitting a continuous piecewise linear model with one knot (Montgomery and Peck, 1992):

[4]

where Q_knot is the Cd concentration in the soil at the knot, and I_knot is an indicator having a value of 1 when Q_soil > Q_knot, and 0 in other cases. Eq. [4] can also be written as:

[5]

For each crop, all possible models were fitted, and the best model was selected on the basis of Mallow's C_p, under the following constraints (Montgomery and Peck, 1992): Q_soil must be part of the model, B and C must be positive, and A₁ and A₃ must be negative.

Note that when a piecewise linear model is not significantly better than a single linear model without a knot, a model is selected without the last term of Eq. [4]. The best location of the knot was estimated by fitting models for a range of values for the knot, then selecting the model with the smallest residual variance. Table 2 shows the estimated regression coefficients, the estimated knot, the percentage of variance accounted for, and the residual variance of the selected models.

View this table: [in this window] [in a new window]   Table 2. Estimated regression coefficients, percentage of variance accounted for (R2adj), and residual variance (2) of (piecewise) linear regression model for log(Cd) in four crops. n, Number of measurements; A0–A3, B, C, see Eq. [4]; –, not fitted.

[6]

Note that the critical threshold concentration in the soil depends on pH, SOM, and clay, and as a result varies in space, because the coefficient A depends on pH, SOM, and clay. For Q_plant,crit we inserted the quality standard for Cd in fodder, which equals 1.0 mg kg^-1 for grass and 0.5 mg kg^-1 for maize and sugar beet, or the quality standard for Cd in food for human consumption, which equals 0.15 mg kg^-1 for wheat (Projectgroep veterinaire milieuhygiene, 1997).

Critical Threshold for Cadmium Concentrations in Soils Derived from Quality Standards for Organs of Cattle
For grasssland, we also calculated critical thresholds for Cd in soil from the food quality standard for Cd in the kidney of cattle. Kidney appeared to be the most critical organ for Cd. In this case not only the transfer of Cd from soil to crop must be considered, but also the transfer from crop to cattle and Cd uptake through direct ingestion of soil. The internal Cd concentration of the kidney (mg kg^-1) was thus calculated as (Projectgroep FBS, 1999):

[7]

where M_grass and M_soil are the amounts of grass and soil consumed, respectively (kg d^-1), f_pa is the transfer coefficient of Cd in grass to animal via roots, and f_sa is the transfer coefficient of Cd in soil to animal. Uptake of Cd from drinking water was ignored because its contribution is negligibly small. The Cd concentration in grass was modeled in the same way as in maize and wheat (see previous section). Table 2 shows the model selected. Note that for grass the piecewise linear model was not significantly better than the model without the knot, Eq. [3]. Substitution of Q_grass by Q_soil and rewriting gives the following equation for calculating the critical threshold in soil from the critical threshold in kidney:

[8]

Note that Q_soil,crit is on both sides of the equation, and therefore must be calculated by iteration. The values used for M_grass and M_soil were 15 and 0.5 kg d^-1, respectively (Projectgroep veterinaire milieuhygiene, 1997). Following Projectgroep FBS (1999) we assumed that the transfer of Cd from soil or grass into the kidney is equal, that is, f_sa = f_pa, and equals 2.99. Again, Q_soil,crit varies in space because the Cd concentration in grass is determined by the pH and the SOM of the soil (Table 2). The food quality standard for Cd in kidney is 2.5 mg kg^-1 (Projectgroep veterinaire milieuhygiene, 1997).

Estimating the Actual and Critical Cadmium Concentrations in Soils by Simple Indicator Kriging with Local Prior Means
General Approach
If we know the values of the three basic soil properties in the regression model at a given point, then we can calculate the critical threshold concentration of Cd in soil, and we can establish if the actual Cd concentration in the soil at this point is above or below the critical threshold. The Cd concentrations and the soil properties were interpolated to map the probability that the critical threshold for Cd concentrations in the soil is exceeded. In establishing the probability of exceeding the critical threshold concentration, the uncertainty in both the interpolated Cd concentration and in the critical threshold were taken into account. Conventional kriging techniques focus on deriving optimal estimates of the contaminant concentration and the associated variance of the estimation error. To estimate the probability that the Cd concentration exceeds the critical threshold, we need the entire probability distributions of Cd and the soil properties at points. We may assume that the estimation errors follow normal distributions, but this is unrealistic in many situations. Other solutions are to use disjunctive kriging (Von Steiger et al., 1996) or indicator kriging (Goovaerts et al., 1997; van Meirvenne and Goovaerts, 2000). We chose indicator kriging because it can accommodate measurements less than the detection limit.

The cumulative distribution functions (cdfs) for SOM, clay, pH, and Cd were estimated for all 500- x 500-m grid nodes with agriculture according to LGN3⁺. All cdfs were estimated by simple indicator kriging with local prior means (Goovaerts, 1997, p. 284–331). The method is described in four steps: (i) choosing a number of cutoff values, (ii) indicator coding of measurements, (iii) estimating the local prior means, (iv) updating the local prior means.

Earlier investigations (e.g., Bak et al., 1997; Tack et al., 1997; McGrath and McCormack, 1999) have shown that the Cd concentration in the soil is related to the clay and SOM content. The previous section showed that for a given crop the critical threshold of the Cd concentration in soil is a function of SOM, clay, and pH. Therefore, to calculate the probability that the actual Cd concentration exceeds the critical threshold, the correlation between the actual and critical Cd concentrations was taken into account. We did this by drawing Cd values from conditional cumulative distribution functions (ccdfs), that is, cumulative distribution functions conditional on soil parent material defined in terms of SOM and clay. Basically, all updated cumulative distribution functions are conditional on the measurements in the neighborhood of the grid node. Nevertheless, we only use the term conditional cumulative distribution function for Cd, which is conditional on the SOM and clay value at the grid node, whereas we use the term cumulative distribution function for SOM, clay, and pH. The exact values for SOM and clay at a grid node are unknown, and therefore we have to estimate all possible ccdfs of Cd at each node.

Choosing Cutoff Values
The indicator approach starts with choosing cutoff values that provide a reasonable discretization of the frequency distribution. We chose the nine deciles of the sample histogram as cutoff values. As we have special interest in large concentrations, we included two extra cutoff values in the upper tail of the distribution, the 95th percentile (P95) and 99th percentile (P99) (Table 3).

Estimating Local Prior Means
The indicators are used to estimate cumulative frequencies, that is, areal fractions with values less than the cutoffs. The estimated cumulative frequencies are used as a priori estimates of the cumulative probabilities at points. For example, the estimated cumulative frequency of Cd concentrations 0.25 mg kg^-1 is 0.40, and consequently at any point in the Netherlands the a priori cumulative lower probability of 0.25 Cd mg kg^-1 can be estimated by 0.40. For SOM, clay, and pH, it is unrealistic to assume constant cumulative frequencies throughout the Netherlands. In geostatistical terms, it is unrealistic to assume that the means of the indicators are constant throughout the Netherlands. The soil map of the Netherlands at a scale of 1:50 000 was thus used to define subregions with assumed constant local means of the indicators. Soil organic matter and pH are influenced by land use, so for these two properties the soil map was combined with the land use database LGN3⁺. The resulting map units were grouped into 14, 13, and 13 categories for SOM, clay, and pH, respectively. The cumulative frequencies (means of indicators) for these categories were estimated by the measurements derived from the soil information system.

For Cd we considered four categories of parent material (Table 4) as well as two land use practices (cultivated and uncultivated). For uncultivated clay, uncultivated peat, and uncultivated peaty clay there were too few measurements (<100) to obtain reliable estimates of the cumulative frequencies. For these soil parent material categories no distinction was made in land use, resulting in five categories: uncultivated sand, cultivated sand, clay (undifferentiated), peat (undifferentiated), and peaty clay (undifferentiated). The local means of the indicators for Cd were estimated with the parent material (SOM and clay) and land use as recorded at the sample locations, and not as depicted on maps because of impurities and spatial variation within map units. Note that we could use the BLGG data (Table 1) with unknown geographical coordinates to estimate the local means of the indicators.

1. Estimate the parameters of the lognormal distribution by maximum likelihood estimation, using all data including the censored data (Akritas et al., 1994);
   
2. For any censored measurement, independently draw one random value from the part of the distribution that is less than the detection limit;
   
3. Backtransform all values, including the randomly drawn values;
   
4. Calculate the percentage of measurements less than the 11 cutoffs (means of indicators);
   
5. Repeat Steps 2 to 4 one-hundred times, leading to 100 estimates of the indicator means;
   
6. Calculate the averages of the 100 estimates of the indicator means.
   

Figure 1 shows the local prior means for the five categories.

View larger version (22K): [in this window] [in a new window]   Fig. 1. Cumulative frequency distributions of Cd (mg kg-1) in the topsoil for categories defined in terms of soil parent material and land use.

For all sample locations except the BLGG data (geographical coordinates unknown), the vector with residuals was calculated. Next, the residuals were interpolated one by one to the grid nodes, that is, first the residuals of the first indicator were interpolated, then those for the second indicator, etc. For interpolation we used the program kt3d with the option simple kriging and expected value 0 of GSLIB (Deutsch and Journel, 1998). Experimental variograms were also estimated with GSLIB. Parameters of variogram models were estimated by weighted least squares, using the number of pairs as weights (Table 5). Fitted models were spherical with nugget (22 times), double spherical with nugget (16 times), and pure nugget (6 times). A double spherical model can be described by:

[9]

where (h) is the semivariance between points with mutual distance h, c₀ is the nugget variance, c₁ is the first structured variance component, a₁ is the first range, c₂ is the second structured variance component, and a₂ is the second range.

[10]

where F(z_k|s₀) and F(z_k|s_i) are the a priori lower cumulative probabilities for z_k at the grid node x₀ and at the measurement location x_i, respectively, (x_i) is the simple kriging weight of the measurement location x_i, and I(x_i;z_k) is the random indicator variable for the cutoff value z_k at location x_i.

The exact values of SOM and clay at the nodes are unknown, and this implies that the a priori distributions of Cd are unknown. We only know the cdfs of SOM and clay at the nodes, thus we can sample these cdfs a large number of times and determine the soil parent material category for each pair of SOM and clay so that we obtain a probability for each parent material category and the associated a priori distribution. Ignoring the uncertainty about land use, we have in principle four possible a priori distributions at each node. All four have been updated by adding the interpolated residuals leading to four series of K conditional cdf (ccdf) values per node.

Each (conditional) cdf value must lie in the interval [0,1] and each series of K (conditional) cdf values must be nondecreasing. We checked for these constraints, and order-relation deviations have been corrected by averaging the upward and downward corrections (Deutsch and Journel, 1998, p. 81–86).

To simulate values by sampling the (conditional) cdf we need a complete (conditional) cdf, not only the cumulative probabilities at cutoff values. For soil property values between the smallest and largest cutoff, the (conditional) cumulative probabilities were interpolated linearly. For Cd and pH, probabilities less than the smallest cutoff were extrapolated by a power function (Goovaerts, 1997, p. 280). The exponent of the power function was estimated from the data by linear regression. Table 6 shows the estimated powers and arbitrarily chosen minima. There were very few measurements less than the smallest cutoff for SOM and clay. This implies that the a priori probabilities for the smallest cutoff were nearly 0. Consequently, we extrapolated linearly to a minimum of 0 for these properties. For all soil properties and Cd, the (conditional) cumulative probabilities beyond the largest cutoff were extrapolated linearly to a chosen maximum (Table 6).

View this table: [in this window] [in a new window]   Table 6. Minima, maxima, and exponent () of power function used to extrapolate beyond the lower and upper tail of conditional cumulative distribution function of Cd. When = 1, the power function is equivalent to linear extrapolation.

1. Draw 100 values of SOM, clay, and pH values by Latin hypercube sampling (LHS) (McKay et al., 1979; Stein, 1987) from the respective cdfs of SOM, clay, and pH; this results in 100 triples of SOM, clay, and pH;
   
2. Calculate the critical threshold, Q_soil,crit, from the first triple of SOM, clay, and pH;
   
3. Determine the ccdf of Cd from SOM and clay of the first triple, and from the land use according to LGN3⁺;
   
4. Draw 100 Cd values from this ccdf by LHS sampling;
   
5. Compare the 100 Cd values of Step 3 with the Q_soil,crit value of Step 2, and count the number of times the Cd value is larger than Q_soil,crit value;
   
6. Repeat Steps 2 to 5 for Triples 2–100, and sum the number of times Q_soil,crit is exceeded;
   
7. Estimate the probability by the total number of times Q_soil,crit is exceeded, divided by 10000.
   

At each node we thus obtained 100 drawn values for the critical threshold of Cd in soil and 10000 drawn values for the actual Cd concentration in soil. We used the median of these values as estimates of the critical and actual Cd concentrations in soil to make maps.

In Step 1, SOM, clay, and pH values were drawn independently, that is, we assumed that these properties were independent. To check the validity of this assumption we calculated correlation coefficients between these three properties in intersections of the SOM, clay, and pH subregions. It appeared that the correlation was generally weak.

	RESULTS AND DISCUSSION

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

 
Actual Cadmium Concentrations in Soil
The geographical pattern with estimated Cd concentrations resembles, more or less, the pattern with clustered units of the Soil Map of the Netherlands 1:50 000 (Fig. 2) . In broad outlines, peat soils have the largest concentrations of Cd, fluvial and marine clay soils have intermediate concentrations, and sandy soils have the smallest concentrations. This illustrates the effect of clay and SOM on the actual Cd concentration. Sandy, cultivated areas have somewhat larger concentrations than their uncultivated counterparts, such as the ice-pushed ridges covered with forest and heath in the center of the Netherlands (Veluwe and Utrechtse Heuvelrug), and the coastal dunes. However, we cannot conclude from this that the Cd concentrations in agricultural soils are increased by the input of agrochemicals, because the natural background values of the cultivated sandy soils can also be relatively large (high weathering potential), and because less Cd may have been leached due to relatively high pH values in cultivated areas.

View larger version (61K): [in this window] [in a new window]   Fig. 2. Estimated Cd concentration (mg kg-1) in the topsoil. Median of 10 000 values simulated with the updated conditional distribution functions of Cd are taken as estimates. The class boundaries are chosen such that the number of cells in each class is approximately equal.

View larger version (69K): [in this window] [in a new window]   Fig. 3. Difference between updated Cd concentration (Fig. 2) and a priori Cd concentration (mg kg-1) in the topsoil.

View larger version (13K): [in this window] [in a new window]   Fig. 4. Cumulative frequency distributions of estimated critical threshold for Cd concentrations in soils (mg kg-1) (A) and of estimated probability of exceeding this critical threshold (B). For grassland the probability of exceeding the critical threshold for Cd concentrations in soil is 0.0 nearly everywhere, when the quality standard for Cd in kidney (2.5 mg kg-1) or in grass (1.0 mg kg-1) is used to calculate the critical threshold for Cd in soils.

View larger version (61K): [in this window] [in a new window]   Fig. 5. Estimated critical threshold for Cd (mg kg-1) in soils for the actual land use. For arable soils the reference crop is sugar beet. The class boundaries are chosen such that the number of cells in each class is approximately equal.

Two remarks must be made. First, for all crops the regression models must be extrapolated for many nodes to derive the critical threshold for Cd in soil from the quality standards for the crops. For grass, maize, wheat, and sugar beet this was the case for 42, 33, 33, and 41% of the nodes, respectively (see Appendix). These large percentages imply that we are rather uncertain about the critical threshold for Cd in soils in considerable parts of the agricultural area. The second remark concerns the model for Cd in the kidney of cattle. We are rather confident of the model for the uptake of Cd in soil by grass, but we need more data on the transfer of Cd in soil and in grass to the kidney of cattle. Therefore, the critical thresholds for Cd in grassland soils derived from the quality standard for Cd in kidney are tentative only. On the other hand, we believe that the estimated critical thresholds are safe because we assumed that the transfer coefficient from soil to animal equals that of grass to animal, whereas it is probably smaller (Eq. [7]).

Probability of Exceeding the Critical Threshold for Cadmium Concentrations in Soil
The probability that the actual concentrations of Cd exceed the critical threshold in soil are negligibly small for the entire grassland area. For 98% of the grassland area the probability that the critical threshold for Cd in soil is exceeded is less then 0.1% using the critical threshold in grassland soils derived from the quality standard for kidneys of cattle. The probabilities of exceeding the thresholds are negligible for the peat and clay soils in the "Groene Hart" with estimated Cd concentrations in soil up to 2.7 mg kg^-1 (Fig. 6) . The large Cd concentrations in these soils are compensated by the large critical thresholds here. For maize land the probabilities of exceeding the critical threshold for Cd in soils are also small: only 3% of the present maize land area has a probability larger than 5%. However, for arable soils, these probabilities are much larger. For example, with sugar beet as a reference crop, 75% of these soils have probabilities larger than 5%, and 38% of the soils have a probability larger than 50%. For wheat as the reference crop, 82% of these soils have probabilities larger than 5%, and 12% have a probability larger than 50%. For the arable soils where the regression model was not extrapolated to derive critical thresholds, 57% have probabilities larger than 5%, and 7% has probabilities larger than 50% when sugar beet is the reference crop. Thus, based on the area where the regression model need not be extrapolated, the estimated areal percentages with exceedence probabilities larger then 5 or 50% are considerably reduced. For wheat as the reference crop, these areal percentages are reduced to 80% with a probability of exceeding the threshold of >5% and 5% with a probability of exceeding the threshold of >50%.

View larger version (65K): [in this window] [in a new window]   Fig. 6. Estimated probability of exceeding critical threshold for Cd in soils. For arable soils the reference crop is sugar beet.

	SUMMARY AND CONCLUSIONS

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

For grassland the probability of exceeding the critical threshold for Cd in soils is negligible (<0.1%) everywhere, even in areas with high baseline concentrations of Cd in soil. For maize land the probabilities are small (<5%) almost everywhere. For arable soils, however, these probabilities are usually greater than 5% when sugar beet or wheat is taken as a reference crop, and locally exceed 50%.

To derive the critical thresholds for Cd in soils from the quality standards for Cd in grass, maize, wheat, and sugar beet, or the kidney of cattle, the regression models must be extrapolated in large parts of the Netherlands. For arable soils where the regression models need not be extrapolated, the areal percentages with high exceedence probabilities are much smaller than for the total area with arable soils.

Extrapolation with Regression Model
To determine whether the regression model is suitable for predicting the Cd concentration in the crop at a given prediction point (node), we might evaluate if all predictors individually fall within the range of the values at the original data points used to fit the model. However, for multiple regression models this method is inappropriate because there can be prediction points that satisfy the individual condition, but still fall outside the multidimensional cloud of original data. Therefore it is proposed to calculate, for all prediction points, the quantity h₀ defined as (Montgomery and Peck, 1992):

[A1]

where x₀' is the p vector with values of the predictors at the prediction point (p is the number of regression coefficients), and X is the (n x p) matrix with values of the predictors at the n data points used to fit the model. When h₀ > 2p/n, the model must be extrapolated, and the predictions and prediction variances are not reliable.

If we insert the estimated critical threshold for Cd in the soil at a given node in vector x₀ of Eq. [A1], and h₀ 2p/n, then we can safely derive the critical threshold for Cd in soil from the quality standard for Cd in the crop at this node.

	ACKNOWLEDGMENTS

 
We are very grateful to the authorities of the provinces of Groningen, Friesland, Drenthe, Flevoland, Gelderland, Noord-Holland, Zuid-Holland, Utrecht, Zeeland, and Noord-Brabant for giving permission to use the data of the Provincial Soil Quality Monitoring Networks.

	REFERENCES

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

 

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