Equation Chapter 1 Section 1Modelling greenhouse gas
dynamics in Australian pastures
Ian R Johnson, Richard J Eckard
*Melbourne School of Land and Environment, University of Melbourne, Vic 3010, Australia.
Abstract
Introduction
The amount of greenhouse gases emitted from pasture systems depends on the many complex biophysical
interactions between the soil, plant, animal and climate. Experimental programmes have successfully measured
emissions but are necessarily short-term, except in a few exceptions, and may not capture the effect of longer
term variability in climate such as drought or a wet la nina cycle. Models offer a way of exploring such complex
systems over longer time periods and with greater environmental variability. The model described here (Johnson
et al. 2003; Johnson et al. 2008) is based on the underlying biophysical processes of the pasture system and gives
a balanced description of each component at a similar level of complexity. This mechanistic biophysical model is
used to explore the greenhouse gas dynamics of pasture systems in Australia.
Greenhouse gas (GHG) dynamics in pastures are a combination of the flux of carbon to and from the soil, nitrous
oxide (N2O) emissions from the soil and methane (CH4) emissions from grazing ruminants. .
To plan GHG mitigation strategies, which aim to reduce emissions from pastures, we need confidence in our
assessment of current and possible future emissions, information which is not wholly available through
experiment. A mechanistic model can provide a close approximation of these dynamic interactions through
simulation. Furthermore, many GHG emission estimates are based on simple emission factors; for example, in
most estimates of emissions over the landscape, denitrification is assumed to be a fixed fraction of nitrogen
inputs (DCCEE 2010). The model may help us to assess the accuracy of these emissions estimates, or better still,
provide a means of developing Tier 3 emissions estimates. Furthermore, because of high climate variability in
Australian grazing systems, experimental programmes, generally conducted over short time periods, are unlikely
to capture the long-term fluctuations in system dynamics (Eckard at al. 2005). Extended wet or dry periods may
persist for several years yet not occur within the experimental time period. However, Lodge and Johnson (2008)
were able to describe these events using the SGS Pasture Model in a long-term simulation study (Lodge and
Johnson, 2008).
Methods
The model used in this paper is the SGS (Sustainable Grazing Systems) Pasture Model (Johnson et al., 2003)
developed over a number of years in Australia. The model has been applied to a range of research questions, and
compared with experimental data from different geographical locations for a range of pasture species (Cullen et
al., 2008; Johnson et al., 2003). It has been used to explore climate variability and drought (Lodge and Johnson,
2008a, b; Chapman et al, 2009), business risk (Chapman et al., 2008a, b), and the impacts of climate change
(Cullen et al., 2009; Lodge et al., 2009; Perring et al., 2010). The biophysical structure of the model means it can
be further adapted to explore new management strategies or plant characteristics, environmental impacts of
climate change scenarios, and the analysis of GHG dynamics in pastures. While there are several models of
varying degrees of complexity for describing and studying individual components of the system, we are unaware
of any other biophysical grazing systems model that studies the integrated plant, animal, water and nutrient
system. In this paper model the fluctuations in GHG dynamics, including soil carbon, N2O and CH4 emissions for a
range of locations across Australia from winter rainfall dominant temperate regions in southern Australia to
summer rainfall dominant arid regions of northern Australia. The analysis uses long-term SILO daily climate data
(Jeffrey, 2001) from the period 1901 to 2011 inclusive.
1
Model structure
The SGS Pasture Model is a daily time-step model that includes pasture growth and utilization by grazing animals,
animal metabolism and growth, water and nutrient dynamics, and options for pasture management, irrigation
and fertilizer application.






The pasture growth module includes calculations of light interception and photosynthesis; growth and
maintenance respiration, nutrient uptake and nitrogen fixation, partitioning of new growth into the
various plant parts, development, tissue turnover and senescence, and the influence of atmospheric CO2
on growth. The model allows up to five pasture species in any simulation, which can be annual or
perennial, C3 or C4, as well as legumes.
The water module accounts for rainfall and irrigation inputs that can be intercepted by the canopy,
surface litter or soil. The required hydraulic soil parameters are saturated hydraulic conductivity, bulk
density, saturated water content, field capacity or drained upper limit, wilting point and air-dry water
content.
Different soil physical properties can be defined through the soil profile. The nitrogen module
incorporates the dynamics of NO3 and NH4, including leaching, and soil organic matter. Gaseous losses of
nitrogen through volatilization and denitrification are included.
The animal module has a sound treatment of animal intake and metabolism including growth,
maintenance, pregnancy and lactation. There are options to select sheep (wethers or ewes with lambs),
cattle (steers or beef cows with calves), and dairy cows. Methane emissions are included.
The farm management module describes the movement of stock around the paddocks as well as the
strategies for conserving forage, and incorporates a wide range of rotational grazing management
strategies that are used in practice. There are options for single- and multi-paddock simulations that can
each be defined independently to represent spatial variation in soil types, nutrient status, pasture
species, fertilizer and irrigation management.
The model has a complete description of the system carbon dynamics as well as non-CO2 (methane and
nitrous oxide) emissions.
Note that the model has the same underlying biophysical structure as DairyMod (Johnson et al., 2008) which has
been developed to address questions relevant to the dairy industry.
A key characteristic of the model is the interaction between the individual modules as illustrated in Fig. 1.
Climate
Pasture
Climate
Soil water
Animal
Climate
Soil
OM/nutrients
Climate
Figure 1. Overview of the model structure. The red lines indicate interactions.
2
As with most biophysical simulation models, this model is subject to continual review and refinement in light of
assessment of on-going model application. A brief description of the modules is therefore presented, and a
complete mathematical description is given by Johnson (2012). Note that SI units are used throughout the
analysis although results will be presented on a per ha basis.
A fundamental objective in the development of the SGS Pasture Model has been to ensure that model
parameters have an underlying biophysical interpretation and that the parameter values defining biophysical
processes are generic and not specific to individual sites. For example, with a pasture species such as phalaris,
the same set of physiological parameters can be applied at any location and, though different varieties may have
different physiological characteristics, key parameters can be modified with knowledge of the characteristics of
each variety. This approach has been applied, for example, by Cullen et al. (2008) who, with the knowledge that
later varieties had better growth at low temperatures, were able to model both old and more recent varieties of
perennial ryegrass. Furthermore, all model parameters are directly accessible from the model interface so that it
is quite straightforward for model users to adjust parameter values and explore the corresponding responses.
Pasture growth
The pasture growth model is driven by photosynthesis, with canopy photosynthesis and respiration described
according Johnson et al. (2010). According to this model, leaf gross photosynthesis in response to photosynthetic
photon flux (PPF) is described using the non-rectangular hyperbola, with the parameters of this equation being
related to temperature and plant nitrogen status. Growth and maintenance respiration components are
included. Different respiratory costs for synthesising cell wall material and protein, and maintenance respiration
depends on plant protein concentration. The tissue turnover dynamics are based on the model structure of
Johnson and Thornley (1983) which has been widely used, and developed, both for the present model and other
models, such as the Hurley Pasture Model (Thornley, 1998). For multiple species, light interception is described
according to Johnson et al. (1989). Carbon partitioning to the roots is influenced by soil water status and nitrogen
concentration.
Soil hydrology and evapotranspiration
Soil water infiltration is defined using a capacitance multi-layer approach. The top 4 layers are each 5 cm and
subsequent layers 10 cm. The flux of water, 𝑞 m water d-1 is given by

  
q  K sat 

  sat 
(1)
where 𝜃 m3(water) m-3(soil) the volumetric soil water content, 𝜃𝑠𝑎𝑡 the saturated water content, 𝐾𝑠𝑎𝑡 m d-1 is the
saturated hydraulic conductivity, which is the value of 𝑞 when 𝜃 = 𝜃𝑠𝑎𝑡 , and 𝜎 is a flux coefficient. 𝜃𝑠𝑎𝑡 is
calculated from the soil bulk density, 𝜌𝑏 kg m-3(soil) according to the standard equation
 sat  1 
b
p
(2)
where 𝜌𝑝 is the particle density taken to be 2,650 kg m-3. In order to calculate 𝜎, a drainage point 𝜃𝑑𝑝 is defined
with corresponding prescribed flux 𝑞𝑑𝑝 so that 𝜎 is given by


ln dp

 sat 
ln qdp K sat
(3)
In the model, the value
qdp  104 m d-1
(4)
which is equivalent to 0.1 mm d-1 is used so that, for example, if 𝐾𝑠𝑎𝑡 = 0.1 m d-1, 𝜌𝑏 = 1,400 kg m-1, 𝜃𝑑𝑝 = 0.4,
then 𝜃𝑠𝑎𝑡 = 0.47 and 𝜎 = 41.9. Equation (1) is illustrated in Fig. 2 with these parameters.
3
8.0
6.0
4.0
2.0
0.0
0.00 0.10 0.20 0.30 0.40 0.50
Soil water content, %vol
Log [ flux ( cm / day ) ]
Flux, cm / day
10.0
1.0
0.0
0.00 0.10 0.20 0.30 0.40 0.50
-1.0
-2.0
Soil water content, %vol
Figure 2. Water flux, 𝑞, in relation to soil water content as linear (right) and log (left) plot. See text
for parameter values.
Soil water infiltration is calculated using eqn (1) at each layer in the soil. This involves selecting a sub-daily timestep to ensure the solution is stable and smooth. Details and examples are presented in Johnson (2012). This
approach is simple to work with and provides a realistic distribution of water through the profile for different
locations and soil types (eg Lodge and Johnson, 2008a).
Transpiration and evaporation are calculated using the Penman-Monteith equation: the precise formulation is
given in Johnson (2012). Transpiration demand is related to the fraction of light interception by the green
canopy. Soil evaporation demand is related to the bare soil fraction and also litter cover. The actual transpiration
and evaporation are then calculated from demand, available soil water and, for transpiration, the root
distribution.
Soil organic matter and nutrient dynamics
Soil organic matter dynamics are generally modelled by using pools of organic matter with different turnover
rates. Early models of this type were developed by Van Veen & Paul (1981) and Van Veen et al. (1984, 1985),
McCaskill and Blair (1988), Parton et al. (1988). Since then, the multi-pool approach has been extensively applied
with well-known models being APSIM (Probert et al. 1998), RothC(Jenkinson 1990), CENTURY (Parton et al. 1998),
and SOCRATES (Grace et al., 2006). While these models have provided insight into underlying processes and
interactions of soil organic matter dynamics, they are generally quite complex with a large number of parameters
that are difficult to estimate. An added challenge with soil carbon models comprising several pools is that it is
possible to get similar overall carbon dynamics with different rates of input and turnover and so we must
continually assess all aspects of the soil carbon dynamics in the model including the description of plant growth
and senescence as it feeds into the soil carbon.
Our approach has been to simplify the description of soil organic matter dynamics to include dynamic fast and
slow turn-over pools, plus an inert component. The fast and slow pools are sometimes referred to as particulate
organic matter and humus soil carbon. The inert carbon pool, which is essentially charcoal, is not subject to
turnover. Keeping the model relatively simple avoids having to define a large number of parameters that are
likely to have strong interactions and are difficult to estimate. The only parameters required are the decay rate
constants for the fast and slow pools (proportion that decays per unit time), their efficiency of decay (proportion
of carbon respired during decay), and the transfer rate from the fast to slow pool. The nutritional status of the
inputs are also required as well as for the organisms during organic matter breakdown. The soil carbon dynamics
are also affected by temperature and soil water status. Soil carbon dynamics are driven by inputs from the plant
material, and its digestibility.
The model is illustrated in Fig. 3, and model variables and parameters are listed in Table 1. Note that restricting
our analysis to these three pools is consistent with current recommended measureable soil carbon pools
(Skjemstad et al. 2004) ). The general approach is to define organic matter decay of pool 𝑊𝐶 kg C m-3 as 𝑘𝑊𝐶
where 𝑘, d-1, is a decay coefficient. Decay occurs with efficiency 𝑌 so that 𝑌𝑘𝑊𝐶 kg C m-3 is retained and
(1 − 𝑌)𝑘𝑊𝐶 respired. It is assumed that the retained carbon for both fast and slow pool decay is transferred to
the fast pool.
4
Figure 3. Overview of the soil carbon dynamics.
Denoting the carbon mass in the fast and slow turn-over pools by 𝑊𝐹,𝐶 and 𝑊𝑆,𝐶 kg C m-3 respectively, their
dynamics are described by
dWF ,C
dt
dWS ,C
dt
 IC  kFS WF ,C  kF 1  YF WF ,C  YS kS WS ,C
(5)
 kFS WF ,C  kS WS ,C
(6)
where 𝑘𝐹 and 𝑘𝑆 (d-1) are the decay rates for the fast and slow pools, 𝑘𝐹𝑆 (d-1) is the transfer coefficient for
movement from the fast to slow pool, 𝑌𝐹 and 𝑌𝑆 are the dimensionless efficiencies of fast and slow organic matter
decay, and 𝐼𝐶 (kg C m-3 d-1) is the rate of carbon input, and 𝑡 (d) is time. The corresponding respiration is
R  1  YF  kF WF ,C  1  YS  kS WS ,C
(7)
Now consider the associated nitrogen dynamics. (Other nutrients can be treated similarly.) The decay of organic
matter is assumed to be through digestion by biomass. The biomass pool is not modelled explicitly, and is taken
to be part of the fast pool. Defining the N fraction of the biomass as 𝑓𝐵,𝑁 , kg N (kg C)-1 which is taken to be a fixed
quantity, and the corresponding N fractions for the pools as 𝑓𝐹,𝑁 and 𝑓𝑆,𝑁 , which will be variables that depend on
the inputs and decay parameters, the nitrogen dynamics corresponding to eqns (5) and (6) are
dWF ,N
dt
dWS ,N
dt

f
 IN  kFS WF ,N  kF WF ,N  1  YF B ,N

f F ,N


f B ,N
  YS kS
f S ,N

 kFS WF ,N  kS WS ,N
(8)
(9)
The associated N mineralization rate, which is the flux of N from the soil organic matter into the ammonium pool,
is

f
MN  kF WF ,N  1  YF B ,N

f F ,N



f B ,N
  kS WS ,N  1  YS
f S ,N





(10)
If this is negative then immobilization of inorganic nitrogen occurs and it is assumed that this nitrogen can be
supplied either from the NH4 or NO3 pools.
These relatively simple equations completely define the soil organic matter dynamics, including carbon
assimilation and respiration as well as nitrogen mineralization or immobilization. We have used nitrogen
fractions of organic matter and biomass rather than C:N ratios which are more common. The analysis is clearer to
work with using fractions, although the C:N ratio is the inverse of the N fraction. Thus, the default value for 𝑓𝐵,𝑁
5
is taken to be 1/8 which is equivalent to a C:N ratio in biomass of 8 (does this come from Kikby? He shows C:N in
humus is 12:1, but that is not the biomass). In the simulations that follow, results will be shown as C:N ratios.
Organic matter dynamics are influenced by soil water status and temperature (Davidson et al., 2000). The rate
constants 𝑘𝐹𝑆 , 𝑘𝐹 , 𝑘𝑆 are defined by
k  HT kref
(11)
Soil water function
Soil w ater response function
1.00
0.80
0.60
0.40
0.20
0.00
0.00 0.10 0.20 0.30 0.40 0.50
Temperature function
where 𝜙𝐻 and 𝜙 𝑇 are dimensionless water and temperature functions respectively, and 𝑘𝑟𝑒𝑓 is a reference value
for each of the rate constants defined at non-limiting soil water conditions and 20°C. Estimating these responses
from experimental data is difficult owing to variation in the data. We have assumed that soil biological processes
are unrestricted by available water at water potentials above -100kPa which, using the Campbell water retention
function to relate water potential to content, can be shown to occur at the average of the drainage point and
wilting point in the soil (Johnson, 2012). Denoting this by 𝜃100 , the generic function for 𝜙𝐻 is illustrated in Fig. 4.
A similar equation is used for 𝜙 𝑇 , which is also illustrated in Fig. 4. The mathematical details of these equations
are described by Johnson (2012). In the model, users can adjust the curvature of both these curves and. For 𝜙𝐻
the wilting point and drainage point are be prescribed for different regions in the soil profile, and for 𝜙 𝑇 the
minimum and optimum temperatures can also be adjusted.
Soil water content
Temperature response function
1.00
0.80
0.60
0.40
0.20
0.00
0
10
20
30
Temperature
Figure 4. Soil water (left) and temperature (right) response functions, 𝜙𝐻 and 𝜙 𝑇 respectively.
Now consider the influence of the quality of organic matter inputs through plant and root senescence on organic
matter dynamics. For each plant species, the digestibility of both the live and dead plant tissue is prescribed. The
value for the dead material is taken to influence both the decay coefficient, 𝑘𝐹 , and efficiency of breakdown, 𝑌𝐹 ,
of the fast pool. This is done on a pro-rata basis, so that the decay coefficient on day 𝑡 is related to the value on
day 𝑡-1 by



kF ,t  kF ,ref WC ,in in  kF ,t 1WF ,C 
 ref


WF ,C  WC ,in 
(12)
where 𝑊𝐹,𝐶 is the initial mass of carbon in the fast pool, Δ𝑊𝐶,𝑖𝑛 is the carbon input with digestibility 𝛿𝑖𝑛 , 𝛿𝑟𝑒𝑓 is a
reference digestibility (taken to be 0.4), and 𝑘𝑟𝑒𝑓 is the reference decay rate for material with digestibility 𝛿𝑟𝑒𝑓 .
The efficiency is then calculated according to
YF  YF ,ref
kF
kF ,ref
(13)
It is assumed that the decay rates for the fast and slow pools are independent of soil type, whereas the transfer
from the fast to slow pool is taken to be related to the soil clay fraction. Thus,
kFS  kFS ,ref

 ref
(14)
where 𝛾 is the clay fraction and 𝛾𝑟𝑒𝑓 is a reference value so that 𝑘𝐹𝑆 = 𝑘𝐹𝑆,𝑟𝑒𝑓 when 𝛾 = 𝛾𝑟𝑒𝑓 . By default,
𝛾𝑟𝑒𝑓 =0.5.
This completely defines the soil organic matter dynamics including carbon accumulation and respiration, N
mineralization and immobilization, and the influence of soil water, temperature, and quality of inputs. In general,
6
the decay rate will decline as the soil dries below -100 kPa and 20°C. Both the rate and efficiency of decay of the
fast turnover pool will decline with decreasing quality of organic matter inputs, as defined by digestibility.
Animal intake, metabolism, growth and nutrient returns
The animal model is described in Johnson et al (2012). The model includes protein, water and fat components of
body composition, and energy is utilized for growth of new tissue, resynthesis of degraded protein, and the
energy required for physical activity. Pregnancy and lactation are also incorporated where relevant. For the
present analysis, all simulations are for set-stocking and so, to keep the management options as simple as
possible, we do not include animal growth, but assume the animal is always at a fixed mature weight, so that
energy requirement is then calculated in relation to mature body weight. Dry matter intake requirement is then
determined by energy requirement and pasture digestibility. Actual intake then depends on available pasture
and potential intake which, in turn, declines with digestibility.
Since, for the present simulations, the animal weight is taken to be fixed, all carbon intake, after CH4 and CO2
emissions through fermentation and respiration respectively, is assumed to be excreted as dung. It is further
assumed that there is no net change in animal N content so that all N intake is excreted. Dung is taken to have a
fixed N concentration with all excess N excreted in urine (Whitehead 1995). If C and N outputs do not meet this
fixed concentration, then the N concentration in dung is reduced and there is no N in urine.
Methane emissions are assumed to be a fixed proportion of animal intake on an energy basis which, for pasture,
is taken to be 6% of the gross energy intake is emitted as methane. Taking the IPCC value of 18.45 MJ kg-1 for
gross energy content of plant dry weight, and 55.65 MJ kg-1 for methane (IPCC 2006), this corresponds to 19.9 g
CH4 (kg d.wt forage intake)-1.
GHG dynamics in pasture systems
The complete carbon balance in the system, Δ𝐶, can be defined as:
C  Pnet  Rlitter  Rdung  Rsoil  Ranimal
(15)
where 𝑃𝑛𝑒𝑡 is the rate of net photosynthesis and the 𝑅 terms are respiration or fermentation with associated
subscripts. All terms have units of mass of C per unit area per unit time. Note that 𝑅𝑎𝑛𝑖𝑚𝑎𝑙 includes both carbon
emission as CO2 through animal respiration and CH4 through fermentation, both expressed in carbon units. In
practice, annual dynamics in t C ha-1 yr-1 are used: in the SGS model all calculations are made on a daily basis
which are then aggregated to give monthly or annual totals.
For GHG analyses, CO2e dynamics, Δ𝐶𝑂2 𝑒 (with units CO2e per time), are calculated, as defined by:
CO2e 
44
C soil   CH4 Ranimal ,CH4   N2O DN2O
12
(16)
where the ΔC𝑠𝑜𝑖𝑙 is the change in soil organic carbon, 𝑅𝑎𝑛𝑖𝑚𝑎𝑙,𝐶𝐻4 is the animal CH4 emission, 𝐷𝑁2𝑂 is the rate of
denitrification as N2O, the fraction 44/12 converts carbon to CO2 and the 𝛾 coefficients are the CO2e conversion
coefficients for methane and nitrous oxide. These are taken to be 21 and 310 respectively, as in the IPCC Second
Assessment Report. These coefficients are under continual review and it is straightforward to change them in the
model. Note that eqn (16) does not include plant, litter or dung carbon dynamics directly, although these will
affect the soil carbon dynamics. It is therefore not a true mass balance, but captures the net impact of the
pasture system on the GHG emissions.
This description of the GHG dynamics for the paddock, through the calculation of Δ𝐶𝑂2 𝑒, does not include
estimates of off-site impacts through denitrification that may occur from N losses through leaching or
volatilization (indirect N2O emissions; IPCC 2007), although both leaching and volatilization are calculated in the
model. The aim here is to focus on the paddock dynamics, but the model includes these other losses that can be
used to estimate off-site impacts.
7
Simulations
The sites and simulation details are presented in Table 2. These have been selected to represent a range of
climatic characteristics around Australia. There are two native pasture systems and four improved, with the
improved pastures including a legume. For the native pasture systems these are generic C3 and C4 species,
representing a mixed species sward. For all simulations, with the exception of Kidman Springs (NT), there is no
product removal and so the only N losses are through leaching, volatilization and denitrification. At Kidman
Springs, a fire is simulated on 30 June every third year. The slope at each site is set to 3% so that runoff may
occur, which can influence the simulation results. The SGS Pasture Model is a daily time-step model and daily
climate data are from the SILO data-drill database (Jeffrey, 2001), which are interpolated data from available
records. The model uses rainfall, maximum and minimum temperature, solar radiation, vapour pressure, as well
as site latitude and elevation. All simulations use a fixed 2 m s-1 wind speed and 380 ppm atmospheric CO2
concentration. Although animal growth is included in the model, in this analysis a non-growing animal was used;
that is, it was assumed that the grazing animal is always at its normal mature weight. . Animal daily energy
requirement therefore remains constant which, combined with the energy density of the pasture, defines the
daily animal pasture intake requirement. Any reduction in intake is due to lack of available pasture. Intake by
grazing animals influences pasture growth through its effect on green dry matter and canopy photosynthesis. No
fertilizer inputs are incorporated with the objective being to analyse the long-term carbon dynamics based on
nutrient cycling alone. It is assumed that atmospheric N inputs are 3 kg N ha-1 yr-1; although a small value, as will
be seen, this is sufficient to offset N losses in the native systems while, for the improved systems, N inputs are
dominated by N fixation.
The initial amount, and nitrogen composition, of the soil organic matter can have a marked impact on simulation
results. These are difficult to prescribe accurately and so we use a common starting point for all simulations, run
three simulations without re-initializing the system state variables, and use the output from the third of these for
analysis. This means that the simulations are run for 222 years (using 111 years of climate data twice) before a
third run of 111 years for analysis. The initial soil carbon distribution is shown in Fig. 5, which is equivalent to 44 t
C ha-1 in the top 30 cm. The initial C:N ratios for the fast, slow and inert pools are 12, 15, 15 respectively (we will
need a reference here for where these came from – Skjemstad/ Kirkby). For all sites, the simulations reached a
dynamic equilibrium where subsequent simulations no longer changed SOM pools, indicating that our original
choice of soil organic matter content and C:N ratio was not influencing the results.
Soil organic matter dynamics are directly influenced by inputs from senescent plant material and so estimating
these inputs are central to the model. These inputs are related to pasture growth rate, and so we first consider
some aspects of plant carbon dynamics. Pasture growth rate is often estimated by using exclusion cages whereby
a section of the pasture is cut to a prescribed height or weight, animals are prevented from grazing this area, the
pasture is cut again after a period of time – say 3 to 4 weeks – and the accumulated dry matter divided by the
regrowth period is taken as an estimate of growth rate. There is no doubt that this provides useful information
regarding growth rate, and may be of direct application for some rotational grazing systems, but it does not
include direct interactions between the stock and pasture which have been shown to be significant (eg Parsons,
1988). Three aspects of the shoot carbon dynamics are shown in Fig. 5 for the Hamilton and Moree locations that
represent contrasting pasture systems. These are the long-term averages of:



Rate of net photosynthesis for the whole sward, 𝑃𝑛𝑒𝑡 . This is the difference between carbon fixed by
photosynthesis and respiration, including the roots, and is the net carbon inputs into the system.
Flux of carbon into the soil, ∆𝐶𝑠𝑜𝑖𝑙,𝑖𝑛 . This includes dead roots and leaf litter.
Growth rate estimated under a simulated cutting trial where the pasture is cut to 1 t ha-1 (d.wt, assumed
to be 45% carbon) on the last day of the month and the harvested dry matter is used to calculate the
mean monthly growth rate. If the d.wt at the end of the month is less than the target cutting residual of 1
t ha-1, no pasture is harvested and the net growth rate is calculated as zero, so that this system will not
produce negative growth rates. The individual daily growth rate is then calculated by linear interpolation.
***The cutting trial simulations are run for non-limiting nitrogen, since the harvested dry matter represents a
removal of nutrients from the system. The grazing simulations include nitrogen dynamics, although there was no
direct product removal and these systems both had adequate nitrogen. 𝑃𝑛𝑒𝑡 and ∆𝐶𝑠𝑜𝑖𝑙,𝑖𝑛 are calculated daily
8
and the illustration in Fig. 5 shows the daily averages over the simulation period 1901 to 2011. The growth rate
under cutting is calculated monthly and the long-term averages are presented.
The illustrations in Fig. 5 highlight several features. The contrasting growth characteristics for the improved
Hamilton pasture, with winter dominant rainfall, and native pasture at Moree with highly variable summer
dominant rainfall, show that growth is generally higher in spring and early summer at Hamilton while this occurs
in summer for Moree. Also, 𝑃𝑛𝑒𝑡 is greater at Hamilton indicating that there is a greater total carbon input to the
system. In both cases ∆𝐶𝑠𝑜𝑖𝑙,𝑖𝑛 lags 𝑃𝑛𝑒𝑡 , which is to be expected. Of interest is the fact that the cut growth rate
is substantially less than 𝑃𝑛𝑒𝑡 , due to carbon being partitioned to the roots and also being transferred to litter
from standing dead, which is accelerated at higher stock density. It is apparent from these illustrations that cut
growth rate alone is not a direct indicator of either 𝑃𝑛𝑒𝑡 or ∆𝐶𝑠𝑜𝑖𝑙,𝑖𝑛 .
For the grazing simulations in Fig. 5 it can be seen that increasing stock density causes a reduction in both 𝑃𝑛𝑒𝑡
and hence ∆𝐶𝑠𝑜𝑖𝑙,𝑖𝑛 . This is because increasing stock numbers results in a greater removal of leaf dry weight so
that there is less leaf area for photosynthesis. For Hamilton at 10, 15, 20 wethers ha-1, the percent carbon fixed
thorough photosynthesis that is transferred to the soil, that is ∆𝐶𝑠𝑜𝑖𝑙,𝑖𝑛 ⁄𝑃𝑛𝑒𝑡 expressed as a percentage, is 88%,
81%, 74% respectively, with the remainder being grazed. The corresponding values for Moree at 1, 3, 6 wethers
ha-1 are 96%, 81%, 77%. Using the conventional method that defines pasture utilization efficiency (PUE) as the
ratio of intake to growth under cutting, the PUE values for Hamilton were 27%, 39%, 47% and for Moree 8%, 18%,
26%. In practice, PUE can be increased by management, but we are not addressing management strategies in the
present analysis.
20
Hamilton
80
18
70
16
Moree
14
60
SD10
50
SD15
40
SD20
30
Cut
20
kg C ha-1 d-1
kg C ha-1 d-1
90
12
SD1
10
SD3
8
SD6
6
Cut
4
10
2
0
0
1/1
1/3
1/5
1/7
1/9
1/11
1/1
1/1
1/3
1/5
1/7
1/9
1/11
1/1
Figure 5. Long-term average daily net photosynthetic rate (𝑃𝑛𝑒𝑡 ) solid lines, daily carbon flux into the
soil (including litter) (∆𝐶𝑠𝑜𝑖𝑙,𝑖𝑛 ), dashed lines, and monthly cut growth rate (◊). 𝑃𝑛𝑒𝑡 and ∆𝐶𝑠𝑜𝑖𝑙,𝑖𝑛 for
different DSE as indicated
Note the different scales.
It is clear from the illustrations in Figs 5 that the interactions between the carbon dynamics are complex. We
have not attempted any systematic analysis of the proportion of 𝑃𝑛𝑒𝑡 that is transferred to the soil since ∆𝐶𝑠𝑜𝑖𝑙,𝑖𝑛
is calculated daily in the model. Furthermore, these illustrations are for long-term averages, which may not give a
direct estimate of the daily dynamics. As a final illustration of pasture growth characteristics, Fig. 6 shows the
variability in the monthly cut growth rate is shown for Hamilton and Moree, demonstrating that while analysis of
averages is of value, variability in growth as a result of climate fluctuations means that average patterns may be
of limited predictive value. Furthermore, it can be seen that the median growth rate for Moree is zero, or close to
zero, for each month. This reflects the high variability in the rainfall. If conditions are good, then growth can be
substantial. The variation in these results is consistent with drought analysis by Lodge and Johnson (2008a, b).
9
100
80
Hamilton
80
70
60
50
Mean
40
Median
30
20
10
0
Cut growth rate, kg ha-1 d-1
Cut growth rate, kg ha-1 d-1
90
Wagga Wagga
70
60
50
40
Mean
30
Median
20
10
0
J F M A M J J A S O N D
J F M A M J J A S O N D
Figure 6. Long-term cut growth rate: Hamilton (left) and Moree (right). The mean and median are
indicate; the box shows the 25 to 75 percentile range; the whiskers are the 10 and 90 percentiles.
Note the different scales.
We now turn our attention to the overall carbon and GHG dynamics at each of the sites in Table 2. Recall that all
simulations were close to dynamic equilibrium, so that there was little change in the net soil carbon over the
simulation period of 111 years. However, fluctuations between years do occur. Figure 7 shows the annual carbon
fixed at each site and the corresponding change in soil carbon is shown in Fig. 8. It is apparent that carbon
fixation potential varies throughout the simulation at all sites, and that the sites have markedly different amounts
of carbon fixed. The most variable location is Moree where annual net photosynthesis can be extremely low,
while in some years it is close to 10 t C ha-1 yr-1. The highest 𝑃𝑛𝑒𝑡 values occurred at Woodstock, which is a
summer dominant tropical rainfall region, although here the carbon dynamics are also highly variable, with
several years having very low 𝑃𝑛𝑒𝑡 . For all sites, there were fluctuations in soil carbon of several t C ha-1 yr-1 which
were due entirely to climate variation. The CO2e dynamics, as defined by eqn (16), are illustrated in Fig. 10,
where negative values indicate a net flux into the system. Once again, the fluctuations are apparent, in spite of
the stock density being fixed at each location.
The fluctuations apparent in Figs 8-10 also occur in the individual CH4 and N2O emissions. These are not
presented for all sites, but just for Wagga Wagga in Fig. 11, which also shows the annual N fixation and highlights
potential variation in these N inputs. While the magnitudes of emissions differ between sites, the characteristic
variability is common to all sites.
10
𝑃𝑛𝑒𝑡, t C ha-1 yr-1
20
Hamilton
15
10
5
0
𝑃𝑛𝑒𝑡, t C ha-1 yr-1
20
Wagga Wagga
15
10
5
0
𝑃𝑛𝑒𝑡, t C ha-1 yr-1
12
Moree
10
8
6
4
2
0
𝑃𝑛𝑒𝑡, t C ha-1 yr-1
8
Kidman Springs
6
4
2
0
𝑃𝑛𝑒𝑡, t C ha-1 yr-1
40
Woodstock
30
20
10
0
𝑃𝑛𝑒𝑡, t C ha-1 yr-1
25
Mt Barker
20
15
10
5
0
1901
1911
1921
1931
1941
1951
1961
1971
1981
1991
2001
2011
Figure 8. Annual net photosynthesis, 𝑃𝑛𝑒𝑡 t C ha-1 yr-1 for the sites described in Table 2.
The solid lines are 10 year trailing means.
11
∆𝐶𝑠𝑜𝑖𝑙,𝑖𝑛, t C ha-1 yr-1
∆𝐶𝑠𝑜𝑖𝑙,𝑖𝑛, t C ha-1 yr-1
∆𝐶𝑠𝑜𝑖𝑙,𝑖𝑛, t C ha-1 yr-1
∆𝐶𝑠𝑜𝑖𝑙,𝑖𝑛, t C ha-1 yr-1
∆𝐶𝑠𝑜𝑖𝑙,𝑖𝑛, t C ha-1 yr-1
∆𝐶𝑠𝑜𝑖𝑙,𝑖𝑛, t C ha-1 yr-1
6
Hamilton
4
2
0
-2
-4
6
Wagga Wagga
4
2
0
-2
-4
4
Moree
2
0
-2
-4
3
Kidman Springs
2
1
0
-1
-2
10
Woodstock
5
0
-5
-10
3
Mt Barker
2
1
0
-1
-2
-3
1901
1911
1921
1931
1941
1951
1961
1971
1981
1991
2001
2011
Figure 9. Annual carbon flux into the soil, ∆𝐶𝑠𝑜𝑖𝑙,𝑖𝑛 t C ha-1 yr-1, corresponding to Fig. 8.
The solid lines are 10 year trailing means.
12
CO2e, t ha-1 yr-1
15
Hamilton
10
5
0
-5
-10
-15
CO2e, t ha-1 yr-1
20
Wagga Wagga
10
0
-10
-20
1901
1911
1921
1931
1941
CO2e, t ha-1 yr-1
10
1951
1961
1971
1981
1991
2001
2011
1971
1981
1991
2001
2011
Moree
5
0
-5
-10
-15
CO2e, t ha-1 yr-1
10
Kidman Springs
5
0
-5
-10
CO2e, t ha-1 yr-1
30
Woodstock
20
10
0
-10
-20
-30
CO2e, t ha-1 yr-1
15
Mt Barker
10
5
0
-5
-10
1901
1911
1921
1931
1941
1951
1961
Figure 10. Annual CO2e emissions, ∆CO2e t C ha-1 yr-1, corresponding to Fig. 8.
The solid lines are 10 year trailing means.
13
CH4, kg CO2e ha-1 yr-1
3
Wagga Wagga
2.5
2
1.5
1
0.5
N2O, kg CO2e ha-1 yr-1
0
1.4
Wagga Wagga
1.2
1
0.8
0.6
0.4
0.2
0
Nfix, kg N ha-1 yr-1
200
Wagga Wagga
150
100
50
0
1901
1911
1921
1931
1941
1951
1961
1971
1981
1991
2001
2011
Figure 11. Annual CH4 (top) and N2O (middle) emissions at Wagga Wagga expressed as CO2e,
∆CO2e t C ha-1 yr-1, corresponding to Fig. 8. Also shown (bottom) is the annual N fixation.
The solid lines are 10 year trailing means.
The illustrations in Figs 8, 9, 10, show the annual variation in flux of carbon into the system, into the soil, and net
GHG emissions. We now look at aspects of the long-term average behaviour. Soil carbon dynamics are of
interest in GHG analyses due to the potential to accumulate carbon. The analysis presented here has focused on
long-term simulations that have been run for 300 years to achieve dynamic-equilibrium and so there is negligible
net change in soil carbon. However, it is instructive to examine the soil carbon status at the different sites. Figure
12 shows the soil organic matter in the top 30 cm of the soil profile at the end of the simulation for each site,
including the breakdown into the fast and slow turn-over pools as well as the inert component, along with the
corresponding C:N ratio. It is apparent that there is substantial variation in soil carbon between the sites which
generally coincides with the level of productivity at each site. These results may be of value in assessing the
potential to sequester carbon for regions that are not currently under pasture. It should be noted that the fast
turnover pool can fluctuate considerably due to climate variability and that most of the variation in soil carbon
apparent in Fig. 9 occurs in the fast pool. Similarly, the C:N ratio varies across sites, which is primarily a result of
the different quality of the pastures, both through their N content and digestibility. In practice, soil carbon and its
composition will depend on the long-term history of sites which is often difficult to quantify. Nevertheless, the
general characteristics of the illustrations in Fig. 12 are in broad agreement with variation in soil organic matter
across the country (ref)
14
25
100
20
80
Fast
60
Slow
15
C:N
Soil organic matter (30 cm), t C ha-1
120
10
Inert
40
5
20
0
0
H
WW
W
MB
M
KS
H
WW
W
MB
M
KS
Figure 12. Soil organic matter in the top 30 cm (left) and corresponding C:N ratio (right) at the end of
the simulations. The sites are indicated by their first letter.
The soil carbon content is affected not only by the carbon input but also the decay rates for each pool. As
discussed earlier, these are not fixed but depend on soil water content, temperature and, for the fast turn-over
pool, the organic matter quality (defined through its digestibility). The average half-lives for the fast and slow
turnover pools are illustrated in Fig. 13 where considerable variation can be seen. It is interesting to note that
these simulations use the same underlying biophysical parameter sets for soil organic matter dynamics.
70
Fast
1.2
60
1
50
Half-life, yrs
Half-life, yrs
1.4
0.8
0.6
0.4
40
30
20
0.2
10
0
0
H
WW
W
MB
M
Slow
KS
H
WW
W
MB
M
KS
Figure 12. Half-lives for the fast and slow turnover soil organic matter pools corresponding to Fig. 11.
The long-term average CO2e emissions are presented in Fig. 14, which also shows the breakdown between soil
carbon, methane and nitrous oxide components. These emissions vary markedly between sites as a direct result
of the pasture production potential at the sites. While emissions per ha are extremely small at Kidman Springs
(NT), grazing enterprises in this region tend to cover much larger area that the other locations.
CO2e emission, t CO2e ha-1 yr-1
5
4
3
N2O
2
CH4
Soil OM
1
0
H
WW
W
MB
M
KS
-1
15
Figure 13. Long-term average CO2e emissions and the breakdown into N2O, CH4 and soil carbon
emissions. All sites are in approximate long-term soil carbon equilibrium, and negative values
indicate a flux of carbon into the soil.
120
7
100
6
80
Fast
60
Slow
Inert
40
20
0
H
WW
W
MB
M
KS
CO2e emission, t CO2e ha-1 yr-1
Soil organic matter (30 cm), t C ha-1
The illustrations presented here, with the exception of the pasture carbon dynamics in Fig. 5, have been run for
one stock density appropriate for each site (Table 2). However, the characteristics of the overall system dynamics
will depend on stock density. In general, overstocking will reduce photosynthetic inputs and therefore the
transfer of carbon to the soil. In addition, while intake per ha may increase, it is likely that intake per animal will
fall and so the system will not be viable. To illustrate this, all simulations have been run with double the stock
density in Table 2. We do not suggest these stock numbers would be viable, but use the simulations to
demonstrate the general impact of over stocking. The soil organic matter at the end of the simulations and longterm average CO2e emissions corresponding to Figs. 11 and 13 are shown in Fig. 14 and it can be seen that soil
carbon is generally lower (cf Fig 11) for all sites except Woodstock, where there is a slight increase in soil carbon.
Woodstock is an interesting location in that when climatic conditions are good, pasture production can be very
high, so that the system seems resilient to high stock density. However, it must be noted that, although not
presented here, animal intake was significantly below requirement. CO2e emissions increased noticeably at
Hamilton, Wagga Wagga and Mt Barker as a result of increased CH4 emissions due to greater animal intake. At
Wagga Wagga, the higher stock density reduced pasture production to the extent that intake significantly
declined and CH4 emissions fell.
5
4
N2O
3
CH4
2
Soil OM
1
0
-1
H
WW
W
MB
M
KS
Figure 14. Soil organic matter in the top 30 cm (left) at the end of the simulations, and the long-term
average CO2e emissions (right) for double the stock densities given in Table 2.
The sites are indicated by their first letter.
Variation in all aspects of system behaviour at all sites was apparent although not all details are presented here.
Discussion
We have described some recent developments to the SGS Pasture Model and have presented long-term
simulation analysis of GHG dynamics for 6 characteristic grazing locations around Australia. The model
incorporates pasture growth and utilization by grazing animals, animal metabolism and growth, water and
nutrient dynamics, with each component described at a similar level of complexity. The C and N dynamics in
pastures are complex, with interactions throughout the system. For example, while the source of N for
denitrification is N2O, this is affected by pasture growth, leaching, organic matter turnover and nitrification of
NH4, as well as the effect of soil water dynamics on the soil water content. There are various other interactions
between the components that impact the overall system behaviour and so the model can provide insights that
may not be apparent when studying a specific component in isolation. Of course, understanding gained from
these detailed analyses of the components provides important information for the present model development.
Since is a mechanistic, process based model, and most model parameters have a direct biophysical interpretation,
the model can be applied at a wide variety of locations with parameter values selected according to
understanding of the underlying system. For example, pasture growth is defined through canopy photosynthesis,
dry matter production, tissue turnover and senescence, according to established modelling techniques that have
16
been applied for about 30 years (eg Johnson and Thornley, 1983; Parsons et al, 1988a, b; .Parsons et al., 1991;
Johnson et al., 2003, 2008).
The simulations for the contrasting sites and pasture types presented here demonstrate the inherent variability in
system dynamics of Australian pastures. This suggests caution should be applied when extrapolating from shortterm experimental data to long-term trends. The simulations were run twice over the simulation period to allow
the soil carbon to reach close to dynamic equilibrium and for all sites there was minimal net change in soil carbon
over the 111 year simulation period. However, within that time period there was significant variation in soil
organic matter which is due entirely to variation in climatic conditions. Again, this suggests that caution should
be applied when interpreting the impact of management on short-term changes in soil organic matter. For
example, a strategy that may result in increases over time-periods of decades may show declines in an
experiment.
One of the challenges of working with a whole-system model is attempting to compare the model results with
experimental data. For such systems it is not possible to ‘validate’ the models in the sense of proving them to be
a true representation of the physical system, as discussed by Oreskes et al. (1994), Johnson (2011) and many
others. These systems are described by Oreskes et al as ‘open’ systems in that all possible causes of system
behaviour cannot be included in experimental programmes, nor included in models. The present model has been
built on sound understanding of the underlying biophysics and has been shown to display the expected
characteristics of pasture systems for a wide variety of locations in Australia and New Zealand (eg Cullen et al.,
2008). The treatment of soil organic matter dynamics has been revised for the present work and the amounts
and C:N ratio of soil organic matter predicted by the model are plausible for all locations considered here. This
component of the model is simpler that other widely used models, although it is at a similar level of complexity as
the other modules. A fundamental aspect of soil carbon dynamics is the flux of carbon into the soil pools, and this
is related to pasture production in response to climatic conditions and also the impact of animal grazing. We are
unaware of detailed long-term experimental measurements of these dynamics and, as far as we are aware, this is
the only mechanistic daily time-step model incorporating these processes to have been applied widely to
Australian grazing systems.
The simulations demonstrate the power of using the SGS Pasture Model for the study of GHG dynamics in
pastures at a wide range of sites. We have focused on direct emissions form the paddock but, since the model
also calculates N leaching and volatilization, it can also be used to estimate indirect N2O emissions according to
the methods of (xxx – Rich) Since it is a process based mechanistic model, all parameters have been prescribed
through an understanding of the basic processes. These simulations are not definitive, but demonstrate the
potential of the model to be used for analysis of GHG emissions in Australian pastures. Future work will explore
possible mitigation strategies aimed at reducing emissions.
Acknowledgements
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sandy loam and a clay soil incubated with C-14 glucose and N-15 ammonium sulfate under different moisture
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Whitehead DC (1995) 'Grassland nitrogen.' (CAB International: Wallingford, UK)
19
Table 1. Model variables and parameters for the soil organic matter dynamics module.
Variables
SOM refers to soil organic matter
𝑓𝐹,𝑁 , 𝑓𝑆,𝑁
N fractions of fast and slow turn-over SOM pools
kg N (kg C)-1
𝑓𝐵,𝑁
N fraction of soil biomass
kg N (kg C)-1
𝐼𝐶 , 𝐼𝑁
Daily C and N inputs to SOM
kg m-3 d-1
𝑘𝐹 , 𝑘𝑆
Decay rates for fast and slow turn-over SOM pools.
d-1
𝑘𝐹𝑆
𝑀𝑁
𝑡
Transfer rate from fast to slow SOM pool.
Rate of N mineralization
Time
d-1
kg N m-3 d-1
d
𝑊𝐹,𝐶 , 𝑊𝑆,𝐶
Fast and slow turn-over SOM pools.
kg C m-3
𝑊𝐹,𝑁 , 𝑊𝑆,𝑁
Nitrogen content of fast and slow turn-over SOM pools.
kg N m-3
𝑌𝐹
𝜙𝐻 , 𝜙 𝑇
Efficiency of decay of fast SOM pool
Water and temperature functions affecting 𝑘𝐹 , 𝑘𝑆 , 𝑘𝐹𝑆
-
Parameters
𝑘𝐹,𝑟𝑒𝑓
Value of 𝑘𝐹 at 20°C and non-limiting water.
0.8 %d-1
𝑘𝑆,𝑟𝑒𝑓
Value of 𝑘𝑆 at 20°C and non-limiting water.
0.008 %d-1
𝑘𝐹𝑆,𝑟𝑒𝑓
Value of 𝑘𝐹𝑆 at 20°C and non-limiting water.
0.04 %d-1
𝑌𝐹,𝑟𝑒𝑓
Efficiency of decay of fast SOM pool at 𝑘𝐹,𝑟𝑒𝑓
0.6
𝑌𝑆
Efficiency of decay of slow SOM pool
0.4
𝛾
Soil clay fraction
0.5
𝛾𝑟𝑒𝑓
Reference soil clay fraction
0.5
20
Table 3. Site simulation details. Climate data are from SILO (Jeffrey, 2001) for the prescribed decimal coordinates.
Animal weights for wethers and steers are 50 kg and 450 kg with daily ME requirements of 6.8 and 63.3 MJ d-1
respectively. Annual rainfall calculated from 1901 to 2011 inclusive. For the Kidman Springs simulations, all above
ground dry matter was removed through fire on 30 June every 3rd year.
Mean rainfall
mm yr-1
Pasture composition
Soil type
Site
lat /long
(decimal)
Stock
Hamilton, Vic
-37.75, 142
676
Phalaris / white clover
15 wethers ha-1
Wagga Wagga, NSW
-35.1, 147.4
530
Phalaris / sub-clover
10 wethers ha-1
Moree, NSW
-29.45, 149.9
499
Native C3/C4
3 wethers ha-1
Kidman Springs, NT
-16.1, 130.95
476
Native C4
0.05 steers ha-1
Woodstock, Qld
-19.6, 146.85
950
Rhodes grass / stylo
1.5 steers ha-1
Mt Barker, WA
-34.65, 117.65
708
Kikuyu / sub-clover
15 wethers ha-1
21
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