13. Heavy Metal (Cd, Cu & Zn) Dynamics

The concentration of the metals Cu, Zn, and Cd in the topsoil and subsoil is determined by a mass-balance equation that describes the inputs, outputs, and accumulation in each layer.

13.1. Crop uptake

As with all other nutrients, Cd, Cu and Zn uptake is calculated by multiplying the crop yield with the metal content in crops. For Cu, the crop Cu content is assumed to be independent of soil conditions. For Cd and Zn, the metal concentration in the plant is derived by a non-linear relationship with the metal concentration in the topsoil (layer 0-30 cm), accounting for the impact of soil properties that control the (bio)availability of metals in soils for Cd and Zn (Adams et al., 2004; Brus et al., 2002; De Vries et al., 2008).

Equation 13.1

where:

is the metal (Cd or Zn) concentration in plant (mg kg^–1).

is the total metal (Cd or Zn) concentration in soil (mg kg^–1).

is a coefficient describing the non-linear relationship between the metal concentration in plant and in soil (unitless).

Crop	Cd	Zn
Grass	1.22	0.41
Maize	1.08	0.64
Potatoes	0.81	0.68
Sugar beet	0.62	1.13
SprintBarley	1.08	0.67
Wheat & Other crops	0.62	0.45

is a function of pH, soil organic matter content, and clay according to:

where:

is the KCl-extracted pH of the soil (unitless).

is the percentage of organic matter content in the soil (%).

is the percentage of clay content in the soil (%).

are regression coefficients derived for different metal elements and crops (unitless).

Metal	Crop
Cd	Grass	1.45	-0.38	0	0
	Maize	0.9	-0.21	0	-0.32
	Potato	0.97	-0.21	-0.41	-0.2
	Sugar beet	1.33	-0.22	0	-0.13
	Sprint barley	0.9	-0.21	0	-0.32
	Wheat & Other crops	0.22	-0.12	-0.33	-0.04
Zn	Grass	2.06	-0.09	1.09	-1.05
	Maize	3.05	-0.31	0	-0.61
	Potato	0	-0.09	-0.64	0.41
	Sugar beet	2.69	-0.41	-0.71	-0.37
	Sprint barley	3.05	-0.31	0	-0.61
	Wheat & Other crops	1.32	-0.06	0	-0.24

The uptake of metal elements by crops is calculated by multiplying the plant metal concentration with the crop yield (Y):

Equation 13.2

where:

	is the amount of metal uptake by crops (mg ha^–1).
	is the metal concentration in the plant (mg kg^–1 DM).
	is the crop yield (kg DM ha^–1).

13.2. Runoff & leaching

The reactive soil metal concentration is derived from total metal concentration by accounting for the variation in organic matter and clay content, according to Römkens et al. (2004):

Equation 13.3

where:

is the reactive metal concentration in the soil (mg kg^–1).

is the percentage of organic matter content in the soil (%).

is the percentage of clay content in the soil (%).

is the total metal concentration in the soil (mg kg^–1).

are regression coefficients derived for different metal elements (unitless).

Metal
Cd	-0.089	0.022	-0.062	1.08
Cu	-0.331	0.023	-0.171	1.15
Zn	-0.703	0.183	-0.298	1.24

The dissolved metal concentration is related to the reactive soil metal concentration according to a Freundlich equation (De Vries et al., 2008b).

Equation 13.4

where:

is the metal concentration in the soil solution (mmol L^–1).

is the reactive metal concentration in the soil (mol kg^–1). See Equation 13.3.

To convert from mg kg^–1 to mol kg^–1:

where is the molar mass of the respective metal element (g mol^–1).

is a non-linear relationship coefficient (unitless).

0.54

0.47

0.74

is a Freundlich coefficient as a function of pH, soil organic matter content, and clay:

where:

is the pH determined in water (unitless).

is the percentage of organic matter content in the soil (%).

is the percentage of clay content in the soil (%).

are regression coefficients derived for different metal elements (unitless).

Metal
Cd	-4.85	0.58	0.28	0.27
Cu	-3.55	0.48	0.18	0.16
Zn	-4.51	0.39	0.35	0.45

Finally, the runoff and leaching rates from the topsoil are calculated by multiplying the dissolved metal concentration with the runoff or leaching water fluxes.

Equation 13.5

where

	is the metal element loss via surface runoff (mol ha^–1).
	is the metal element loss via leaching below the root zone (mol ha^–1).
	is the metal concentration in the soil solution (mmol L^–1). See Equation 13.4.
	is the annual interflow (surface runoff) (m³ ha^–1).
	is the annual leaching effluent to groundwater (m³ ha^–1).