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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

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

View larger version (35K): [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 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.

View larger version (32K): [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).

View larger version (35K): [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).

View larger version (23K): [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 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).