14. Base Cation Dynamics

In this chapter, mol_e is defined as one mole of positive or negative electric charge.

14.1. Base cation accumulation

The base cation (BC) accumulation is simply calculated as the difference of input minus output:

Equation 14.1

where:

	is the accumulation of base cation charges in soil solution (mol_e ha^–1).
	is the total external input of BC charges by fertilizer, manure, and deposition (not including weathering) (mol_e ha^–1). See Equation 14.2.
	is the total uptake of BC charges by plants (mol_e ha^–1). See Equation 14.3.
	is the losses of BC charges via runoff from soil (mol_e ha^–1). See Equation 14.4.
	is the losses of BC charges via leaching from soil (mol_e ha^–1). See Equation 14.4.

Input and uptake terms are usually expressed in kg ha^–1.

To convert between kg ha^–1 and mol_e ha^–1:

where:

is the molar mass per charge of the cation (g mol_e^–1), being 20 for Ca²⁺ (40/2), 12 for Mg²⁺ (24/2), 39 for K⁺ and 23 for Na⁺.

Soil acidification due to the release of base cations (BC, defined as the sum of Ca²⁺, Mg²⁺ K⁺, and Na⁺) occurs when the sum of leaching and uptake exceeds the external input by fertilizer, manure, and deposition. This is generally the case since the loss of nitrate from the soil is accompanied by base cations.

Input and uptake

The input of BCs by fertilizer and manure is determined by their application rates and composition.

Equation 14.2

where:

	is the BC input from fertilizer, manure, and deposition (kg BC ha^–1).
	is the annual application rate of the input material (kg N or total weight ha^–1), be it a fertiliser, manure, or deposition.
	is the fraction of a BC in the input material, relative to the N content or total weight (kg BC kg^–1 N or material).

The BC removal by crop harvesting is determined by crop yields and BC concentrations in crop products.

Equation 14.3

where:

	is the BC uptake by crops (kg BC ha^–1).
	is the annual yield of the crop (kg DM or fresh weight ha^–1).
	is the fraction of a BC in the harvested crop product, relative to the dry or fresh weight (kg BC kg^–1 DM or fresh weight).

Runoff and leaching

BC losses by runoff and leaching are calculated by multiplying the water flux with BC concentrations.

Equation 14.4

where:

	is the loss of BC charges via surface runoff (mol_e ha^–1).
	is the loss of BC charges via leaching below the root zone (mol_e ha^–1).
	is the concentration of respective BC charges in soil solution (mol_e L^–1).
	is the annual interflow (surface runoff) ([.unit][m³ ha^–1]).
	is the annual leaching effluent to groundwater (m³ ha^–1).

These concentrations are calculated by assuming charge balance, i.e., the sum of cation charge is equal to the sum of anion charge. The cations include Ca²⁺, Mg²⁺, K⁺, and Na⁺ (assuming that other cations, such as ammonium, aluminium, and iron, are negligible), and anions consist of SO₄^2–, NO₃^–, Cl^– and HCO₃^– (assuming that other anions, such as phosphate and organic anions, are negligible):

Equation 14.5

The subscript e denotes that these concentrations are expressed as concentrations of electric charges.

All terms are given in mol_e L^–1.

The fractions of Ca²⁺, Mg²⁺, K⁺, and Na⁺ charges in total BC charge concentration are set to fixed values based on soil calcareousity.

Table 14.1: Fractions of cation in total base cations.

Non-calcareous soil	0.7	0.2	0.1	0
Calcareous soil	1.0	0	0	0

Fractions are given as the electric charge concentration of respective cation relative to the total BC charge concentration.

Below we give the calculation of the charge concentrations of anions:

The calculation of SO₄^2– and NO₃^– concentrations is given in 12.5. Runoff & leaching and N leaching, respectively.

The SO₄^2– concnetration (mol L^–1) must be multiplied by 2 to give the charge concentration of SO₄^2– (mol_e L^–1).
The Cl^– concentration in leaching/runoff is calculated by assuming no interaction with the soil (tracer behaviour), i.e., the output is equal to the input minus crop removal without accumulation.
The HCO₃^– concentration is calculated based on the calcareousity of the soil, according to De Vries and Breeuwsma (1986):
- A soil is considered as calcareous when soil CaCO₃ content > 3 g kg^–1, and soil pH > 7.
- In non-calcareous soils, the HCO₃^– concentration is calculated by assuming equilibrium with the soil CO₂ pressure and soil pH.
- In calcareous soils, the HCO₃^– concentration is calculated by assuming equilibrium with the CO₂ pressure in the soil only.
Equation 14.6

where:

is the concentration of HCO₃^– charges (mol_e L^–1).

is the soil CO₂ pressure (bar), which is set to 0.02 bar (20 mbar).

is the soil pH determined in water (unitless).

Note

For non-calcareous soils, the original equation is given as:

In calcareous soils, base saturation is set to 100%, and the change in base saturation is assumed negligible since the acid production rate is fully counteracted by the dissolution of CaCO₃. The initial pH is assumed to stay constant. The change in BCexchangeable is thus proportioned over Ca, Mg, K and Naexchangeable with the initial fractions on the adsorption complex being derived from data and assumed to stay equal over time.

14.2. Base cation weathering

A first approximation of weathering rates can be determined by a combination of soil texture class (determined by clay and sand content), and parent material (classified into acidic, intermediate, basic, or organic based on soil type), as given below (De Vries et al., 1994a; UNECE Mapping Manual, 2004).

Table 14.2: Relationships between BC weathering rates (mol_e ha^–1 m^–1 yr^–1) and combinations of parent material class and texture class.
Parent material class	Texture class
Parent material class	Coarse	Coarse/Medium	Coarse/Fine	Medium	Medium/Fine	Fine
Acidic	250	750		1250	1750
Intermediate	750	1250	1750	1750	2250	2750
Basic	750	1250		2250	2750

Determination of texture classes

Texture class	Clay content (%)
Coarse	≤ 18
Medium	(18, 35]
Fine	> 35

Texture class

Clay content (%)

Coarse

≤ 18

Medium

(18, 35]

Fine

> 35

Two texture classes may occur within the same mapping unit.

Determination of parent material class

Class	Parent material
Acidic	Sand (stone), gravel, granite, quartzite, gneiss (schist, shale, greywacke, glacial till)
Intermediate	Granodiorite, loess, fluvial, and marine sediment (schist, shale, greywacke, glacial till)
Basic	Gabbro, basalt, dolomite, and volcanic deposits

Class

Parent material

Acidic

Sand (stone), gravel, granite, quartzite, gneiss (schist, shale, greywacke, glacial till)

Intermediate

Granodiorite, loess, fluvial, and marine sediment (schist, shale, greywacke, glacial till)

Basic

Gabbro, basalt, dolomite, and volcanic deposits

Schist, shale, greywacke, and glacial till are put in brackets since soil types containing these parent materials can be classified as either acidic or intermediate, depending on the other parent materials available.

The weathering rates derived from Table 14.2 must be further corrected for the effect of temperature according to (Sverdrup, 1990; De Vries et al., 1994a):

Equation 14.7

where

is the corrected weathering rate (mol_e ha^–1 m^–1 yr^–1) at a local mean annual temperature (K);

is the average weathering rate (mol_e ha^–1 m^–1 yr^–1) defined in Table 14.2 at a reference temperature (K) (De Vries et al., 1994a);

Texture class	Coarse	Coarse/Medium	Coarse/Fine	Medium	Medium/Fine	Fine
T₀ (in °C)	4.3	2.6	6.5	8.3	8.5	8.8

is the base for natural logarithms, approximately 2.71828.

is a pre-exponential temperature factor (K), with a default value of 3600 K (Sverdrup, 1990).

To convert temperature between Kelvin (K) and Celsius (°C),n:

14.3. Changes in base saturation, pH, and CEC

The dynamics of base cations (BC, defined as the sum of Ca²⁺, Mg²⁺ K⁺, and Na⁺) in the soil is characterised by the change in exchangeable BCs, which consists of BC accumulation and BC release from weathering:

Equation 14.8

where:

	is the change in exchangeable BC charges (mol_e ha^–1 yr^–1).
	is the annual accumulation of BC charges (mol_e ha^–1 yr^–1). See Equation 14.1.
	is the annual release of BC charges from weathering under local temperature (mol_e ha^–1 m^–1 yr^–1). See Equation 14.7.
	is soil thickness (m).

The change in base saturation can be derived as:

Equation 14.9

where:

	is the change in base saturation (%).
	is the change in exchangeable BC charges (mol_e ha^–1 yr^–1). See Equation 14.8.
	is cation exchange capacity (mmol_e kg^–1). See Equation 14.12.
	is bulk density of the soil (g cm^–3).
	is soil thickness (cm).

The base saturation (BS) is then calculated as the initial BS plus the change:

Equation 14.10

where:

	is base saturation (%).
	is the initial base saturation at the beginning of the period (%). It can be derived from Equation 14.11 for non-calcareous soils. For calcareous soils, it is set to 100%.
	is the change in base saturation (%). See Equation 14.9.

BS should not be lower than 20%.

The calculated BS can be higher than 100%, which indicate the extra "buffer" BC pool.

For calcareous soils, we assume soil pH remained unchanged during the entire period. For non-calcareous soils, we assume a linear relationship between pH 4.5 and pH 6.5 with a base saturation varying from 20-100%, according to:

Equation 14.11

where:

is base saturation (%). See Equation 14.10.

The calculated pH is constrained to .

When the calculated pH < 4.5: pH is reset to 4.5, and BS to 20%.
When the calculated pH > 6.5: pH is reset to 6.5, and BS remains unchanged.

Cation exchange capacity (CEC) can be determined as:

Equation 14.12

where:

	is cation exchange capacity (mmol_e kg^–1).
	is the soil pH determined in water (unitless]). See Equation 14.11.
	is the percentage of clay in the soil (%).
	is the percentage of soil organic carbon in the soil (%).

	is the concentration of HCO₃^– charges (mol_e L^–1).
	is the soil CO₂ pressure (bar), which is set to 0.02 bar (20 mbar).
	is the soil pH determined in water (unitless).