12. Soil S Dynamics

SO4 adsorption-desorption

SO4 accumulation or release is limited to an adsorption-desorption isotherm that governs the flux of SO4 between dissolved and sorbed phases. Unlike P, no distinction is made in stable and labile pools, thus not including a rate limited flux from a stable to a labile pool. SO4 adsorption-desorption is described by an extended Freundlich equation, with the inclusion of pH impacts on adsorption constant, according to Martinson et al.(2003), and Gustafsson et al. (2015):

Equation 12.1

where

is the amount of adsorbed SO4 (mol kg–1).

is the Freundlich SO4 adsorption coefficient, with a default value of 2.

is the total dissolved SO4 concentration (mol L–1).

pH measured in MgCl2 or CaCl2.

is the total dissolved proton (mol L–1).

are Freundlich equation parameters, with a default value of m = 0.2 and n = 1.7.

Initialization

The initial SO4 concentration in soil solution is calculated by assuming equilibrium with the historic S input and uptake in soils in the past:

Equation 12.2

where

is the initial concentration of SO4 in soil solution (mol L–1).

is the historic average combined S input from all sources (kg ha–1yr–1).

is the historic average S uptake (kg ha–1 yr–1).

is the annual interflow (subsurface runoff) (m3 ha–1 yr–1).

is the annual leaching effluent to groundwater (m3 ha–1 yr–1).

is the molar mass of S (32 g mol–1).
For calculations of and , refer to 5. Water Fluxes.

The initial amount of adsorbed SO4 is calculated from Equation 12.1 using .

Pool dynamics

The SO4 concentration in the soil is determined by input, uptake, and accumulation using a mass-balance equation. The change in adsorbed SO4 pools is described as:

Equation 12.3

where

are the size of the adsorbed S pool at time and time , respectively (mol kg–1 ).

is the SO4 accumulation in soil (mol kg–1 yr–1), which is assumed to be only adsorbed SO4.

is the length of the time step (1 year).

S accumulation

Soil SO4 accumulation is calculated as the balance of S input and S losses via different pathways:

Equation 12.4

where

is the combined S input by fertilizer, manure, and atmospheric deposition.

is the S uptake by plants.

is the S leaching from the soil layer.

is the surface runoff of S.

All S flux terms are in kg ha–1 yr–1.

To convert S flux terms from kg ha–1 to mol kg–1:

where

is the thickness of the soil layer (cm).

the bulk density of the soil (g cm–3).

is the molar mass of S (32 g mol–1).

Runoff & leaching

Equation 12.5

where

is the concentration of SO4 in soil solution (mol L–1).

is the annual interflow (surface runoff) (m3 ha–1 yr–1).

is the annual leaching effluent to groundwater (m3 ha–1 yr–1).