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. The overall system dynamics depend on pasture growth, soil water infiltration, evaporation, transpiration and runoff, soil organic matter and inorganic nutrient dynamics, animal intake, metabolism and nutrient returns through dung and urine. These components are all interrelated: over-grazing may cause a reduction in pasture growth which in turn will impact on the flux of carbon into the soil pool through reduced root growth and senescence. Similarly, nutrient losses through leaching, denitrification and volatilization may impact plant available nutrients and plant growth.[r1]

To plan GHG mitigation strategies, which aim to reduce emissions from pastures, we needconfidence 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 data dynamic interactions through simulation. Furthermore, many GHG emission estimates are based on simple conversion coefficients emission factors– ; for example, in most estimates of emissions over the landscape, denitrification is assumed to be a fixed fraction of nitrogen inputs (Rich, refDCCEE 2010). The model may help us to assess the accuracy of these emissionsfactorsestimates, or better still, provide a means of developing Tier 3 emissions estimates. Furthermore, because of high climate variability is a fact of life for in Australian grazing systems, experimental programmes, generally conducted over a short time periods, between a season to a few years (although there are rare exceptions), 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 (see Fig 5, 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. For example, a model describing soil organic matter dynamics will provide valuable insight into the behaviour of that particular component but, since it is driven primarily by inputs from dead plant material, the results will be dependent on the accuracy of the estimates of these inputs and are applicable only in a limited sense.

In this paper we use the SGS Pasture [r2]Model model to study 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. The advantage of using a process-based model, rather than an empirical model, is that it is generally applicable and not specific to any one region. The physiological model structure describing the growth of perennial ryegrass or kikuyu, for example, in response to environmental conditions has been seen to operate with confidence under different circumstances. If long-term climate data is available, the model can be applied at any location. Apart from climate, the only local information required is knowledge of soil physical properties, plant species and stock enterprise.[r3]

Model structure[r4][r5]

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[r6] 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.

Figure 1. Overview of the model structure. The red lines indicate interactions.

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, m water d-1 is given by

(1)

where m3(water) m-3(soil) the volumetric soil water content, the saturated water content, m d-1 is the saturated hydraulic conductivity, which is the value of when , and is a flux coefficient. is calculated from the soil bulk density, kg m-3(soil) according to the standard equation

(2)

where is the particle density taken to be 2,650 kg m-3. In order to calculate , a drainage point is defined with corresponding prescribed flux so that is given by

(3)

In the model, the value

m d-1(4)

which is equivalent to 0.1 mm d-1is used so that, for example, if = 0.1 m d-1, = 1,400 kg m-1, = 0.4, then = 0.47 and = 41.9. Equation (1) is illustrated in Fig. 2 with these parameters.

Figure [IH7]2. Water flux, , 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 time-step 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)(ref), CENTURY (Parton et al. 1998).(ref), 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 measurement techniquesrecommended measureable soil carbon pools (Skjemstad et al. 2004) ref to Baldock stuff). The general approach is to define organic matter decay of pool kg C m-3 as where , d-1, is a decay coefficient. Decay occurs with efficiency so that kg C m-3 is retained and respired. It is assumed that the retained carbon for both fast and slow pool decay is transferred to the fast pool.

Figure 3. Overview of the soil carbon dynamics.

Denoting the carbon mass in the fast and slow turn-over pools by and kg C m-3 respectively, their dynamics are described by

(5)

(6)

where and (d-1) are the decay rates for the fast and slow pools, (d-1) is the transfer coefficient for movement from the fast to slow pool, and are the dimensionless efficiencies of fast and slow organic matter decay, and (kg C m-3 d-1)is the rate of carbon input, and (d) is time. The corresponding respiration is

(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 , kg N (kg C)-1 which is taken to be a fixed quantity, and the corresponding N fractions for the pools as and , which will be variables that depend on the inputs and decay parameters, the nitrogen dynamics corresponding to eqns (5) and (6) are

(8)

(9)

The associated N mineralization rate, which is the flux of N from the soil organic matter into the ammonium pool, is

(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 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 , , are defined by

(11)

where and are dimensionless water and temperature functions respectively, and 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 , the generic function for is illustrated in Fig. 4. A similar equation is used for , 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 the wilting point and drainage point are be prescribed for different regions in the soil profile, and for the minimum and optimum temperatures can also be adjusted.