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Appendix 1 Ammonia emission processes M.R. Theobald, A.G. Williams and M.A. Sutton General Principles The general mass transfer equation Mathematical models of ammonia emissions from livestock housing, stored slurries and solid manures and the land application of manures and fertilisers have the potential to improve the accuracy, sensitivity and applicability of the UK national emissions inventory. In principle, mechanistic models should achieve better results than empirical models because they address the key factors that affect emissions, e.g. temperature, moisture content, pH, wind speed, movement of material etc. Despite differences associated with their intended areas of application (e.g. solids vs liquids), all existing mechanistic models deal with the same fundamental process of ammonia volatilisation from aqueous solutions, via a physical interface between the source material and air. Hence, all use the following first order differential equation to describe this aspect of the process (Haslam et al, 1924): dM/dt = A K (P NH3liquid -P NH3air ) Eqn 1 The term dM/dt is the rate of NH 3 emission in terms of mass per unit time; A is the exposed surface area, K is a mass transfer coefficient (with units of velocity, e.g. m s -1 ) and P NH3liquid and P NH3air are the partial pressures of NH 3 in the bulk of the emitting aqueous solution and in the air above respectively. is a coefficient that relates the partial pressure of NH 3 to the concentration of free NH 3 in solution (C NH3liquid ), such as the Henry’s Law coefficient, where C NH3liquid = P NH3liquid . The emission process is driven by the difference between P NH3liquid and P NH3air . Significance of terms in the general mass transfer equation Each term in Eqn 1 has particular significance within this mechanistic model that can relate directly to physical systems. The simplest example is the term, A, which expresses the direct proportionality between emission rate and exposed surface area, (Anderson et al 1987; Scotford and Williams, 2001; Williams et al.1998). The mass transfer coefficient, K, quantifies the combined properties of the emitting surface that can limit the movement of gas molecules. Experimental studies have shown that it increases with temperature, air speed and liquid movement and generally reduces as liquid viscosity and/or solids content increase (e.g. Zhang, 1992; Olesen and Sommer, 1993; Zhang, et al 1994; Cumby, et al 1995). Some studies have related the value of K to fundamental material properties such as diffusivity and liquid turbulence (Higbie, 1935; Danckwerts, 1951; Dobbins, 1962), whilst others have examined the separate contributions of resistances to mass transfer on both the liquid Process modelling of NH 3 emissions Appendix 1 Page 1 of 4

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Page 1: 1randd.defra.gov.uk/Document.aspx?Document=AM0130_3695... · Web viewAmmonia emission processes M.R. Theobald, A.G. Williams and M.A. Sutton General Principles The general mass transfer

Appendix 1Ammonia emission processesM.R. Theobald, A.G. Williams and M.A. Sutton

General PrinciplesThe general mass transfer equationMathematical models of ammonia emissions from livestock housing, stored slurries and solid manures and the land application of manures and fertilisers have the potential to improve the accuracy, sensitivity and applicability of the UK national emissions inventory. In principle, mechanistic models should achieve better results than empirical models because they address the key factors that affect emissions, e.g. temperature, moisture content, pH, wind speed, movement of material etc. Despite differences associated with their intended areas of application (e.g. solids vs liquids), all existing mechanistic models deal with the same fundamental process of ammonia volatilisation from aqueous solutions, via a physical interface between the source material and air. Hence, all use the following first order differential equation to describe this aspect of the process (Haslam et al, 1924):

dM/dt = A K (PNH3liquid-PNH3air) Eqn 1

The term dM/dt is the rate of NH3 emission in terms of mass per unit time; A is the exposed surface area, K is a mass transfer coefficient (with units of velocity, e.g. m s-1) and PNH3liquid and PNH3air are the partial pressures of NH3 in the bulk of the emitting aqueous solution and in the air above respectively. is a coefficient that relates the partial pressure of NH3 to the concentration of free NH3 in solution (CNH3liquid), such as the Henry’s Law coefficient, where CNH3liquid = PNH3liquid. The emission process is driven by the difference between PNH3liquid and PNH3air.

Significance of terms in the general mass transfer equationEach term in Eqn 1 has particular significance within this mechanistic model that can relate directly to physical systems. The simplest example is the term, A, which expresses the direct proportionality between emission rate and exposed surface area, (Anderson et al 1987; Scotford and Williams, 2001; Williams et al.1998). The mass transfer coefficient, K, quantifies the combined properties of the emitting surface that can limit the movement of gas molecules. Experimental studies have shown that it increases with temperature, air speed and liquid movement and generally reduces as liquid viscosity and/or solids content increase (e.g. Zhang, 1992; Olesen and Sommer, 1993; Zhang, et al 1994; Cumby, et al 1995). Some studies have related the value of K to fundamental material properties such as diffusivity and liquid turbulence (Higbie, 1935; Danckwerts, 1951; Dobbins, 1962), whilst others have examined the separate contributions of resistances to mass transfer on both the liquid side and gas side of the interface (Lewis and Whitman, 1924). However, such studies have been largely confined to relatively simple materials, and the complexities of emissions from biological sources such as slurries and/or solid manures have meant that empirical determination of K has remained the most pragmatic approach for modelling farm-scale emissions.

The pressure difference term, (PNH3liquid-PNH3air), is affected by several factors. For example, outdoors, the ambient partial pressure of ammonia (PNH3air) is usually negligible, but this is not the case within the headspace of covered stores, or in some buildings. Hence, the value of (PNH3air) can be used to represent these situations. The pressure exerted by ammonia at the emitting surface (PNH3surface) depends on the (CNH3liquid), as given by , which itself depends on temperature. In turn, (CNH3liquid) depends on the total ammoniacal-N (TAN) concentration and the partition between ammonium-N and ammonia-N, which is governed by pH and the dissociation constant, which also depends on temperature (Bates and Pinching, 1950; Hashimoto, 1972; Zhang, 1992; Srinath and Loehr, 1974, Sutton et al., 1994; Nemitz et al., 2001).

Process modelling of NH3 emissions Appendix 1 Page 1 of 4

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Application of the general PrinciplesInteractions Although Eqn 1 is relatively simple, the terms contained within it represent several factors, including some interacting effects, for example:

Increasing air speed will increase mass transfer, but may also increase evaporation and hence cool the emitting surface, so decreasing K.

Volatilisation of ammonia will decrease surface pH, but nevertheless, surface pH values have been observed in stored slurries that are higher than the bulk pH, due to the simultaneous volatilisation of carbon dioxide (Ni, et al, 2000; Williams et al, 2000). The net effects of such changes affect the value of (PNH3liquid).

Increasing temperature and air speed will (in addition to the effect to decrease K), will increase the concentration of TAN in the liquid, so increasing (PNH3liquid).

Spatial and temporal variabilityFurther complexities derive from the effects of scale. For example, as ammonia volatilises from a slurry surface, it will deplete the local concentration of ammoniacal-N, unless it can be replaced by diffusion from lower layers. Most farm-scale slurry stores are mixed only before emptying, and so during most of the storage period (e.g. up to 120 days), stratification occurs. This creates gradients of TAN, pH and temperature within the slurry, which some studies have shown to be the rate-limiting step in the overall process of ammonia volatilisation (Muck and Steenhuis, 1982; Ruxton, 1995). When applying manures to land, the effects of infiltration into the soil need to be taken into account. These processes can be very complex, depending on the weather and soil characteristics, with factors promoting infiltration leading to reduced ammonia emissions.

Solid manures present additional challenges, e.g. what is the effective surface area for ammonia emissions, including the large-scale effects of heap geometry and the smaller-scale influences of the porous structure of the material? Similarly, external airflows may be measured or estimated independently, but gases also pass through the manure due to pressure and/or concentration gradients. Biological activity (composting) may also create thermal gradients. Nevertheless, within limits, it has been shown that the mechanistic approaches described above can be applied to such processes (Olesen and Sommer,1993; Cronjé, et al 2005).

Weather conditions will affect ammonia emissions substantially. Changes in air temperature, humidity, air speed and solar radiation mean that the terms in Eqn 1 seldom have steady values. Due to the great complexities involved, none of the models studied have attempted to represent these effects via full dynamic simulations, although some have proved suitable for iterative calculations involving time steps down to 1 hour (Olesen and Sommer,1993; Cronjé, et al 2005).

Bi-directional fluxes and competition between sources and sinksThe above examples primarily focus on the simple case of emission from an ammonia rich surface, such as manure or slurry. In principle, however, it can be seen in Eqn. (1) that if PNH3liquid < PNH3air then deposition rather than emission will occur. This introduces the possibility for bi-directional fluxes, such at one time a surface may be a source, while at another time it acts as a sink. Such bi-directional exchange is very important for sources where PNH3liquid is not so large, such as in grazed fields and fertilized croplands. The net flux with a surface as measured by field experiments is thus the sum of the upward and downward fluxes occurring over the period of measurement. For example, Milford et al. (2001) showed that the sum of half hourly upward fluxes over 18 months for fertilised grassland was ~5 kg N ha-1 year-1, while the net emission (including bi-directional exchange was less than half of this value.

Process modelling of NH3 emissions Appendix 1 Page 2 of 4

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The instantaneous net flux with a surface can also be conceptually decomposed into the upward and downward components acting at any one time. Thus Eqn (1) represents the instantaneous net flux, but with the component upward and downward fluxes being:

dM/dt (upward component) = A K (PNH3liquid-0) Eqn 1

dM/dt (downward component) = A K (0-PNH3air) Eqn 1

Such a separation can be useful in models to interpret manipulation studies using 15NH3, where 15N is present in significant quantities only in one of the terms (e.g. PNH3liquid), or in mathematical dispersion models (e.g. fluid particle models), where production and destruction are treated as separate terms (e.g. Loubet et al., 2001).

Finally, it should be noted that in field contexts the net exchange with the atmosphere is actually the balance between several competing sources and sinks. A clear example of this is the exchange of ammonia between grasslands and croplands and the atmosphere. In these cases PNH3air is the atmospheric potential compared with several potentials for: a) ammonia in the apoplast in the sub-stomatal cavity, PNH3stomata, b) ammonia at the soil surface, decomposing leaf litter or fertiliser residue, PNH3ground, c) ammonia on the leaf surface, resulting from the balance of adsorption or desorption of previous deposits, PNH3cuticle. A whole series of models have been developed to handle the trade-offs between these competing processes, in particular dealing with the controls on the PNH3stomata often termed the ‘stomatal compensation point’ and its distinction from the overall ‘canopy compensation point’ (Sutton et al., 1995; Nemitz et al., 2001), as well as issues of leaf surface adsorption/desorption (Sutton et al., 1998; Flechard et al. 1999), and the link to grassland C-N cycling (Reido et al. 2002).

ReferencesAnderson, G.A., Smith ,R.J., Bundy, D.S. and Hammond, E.G. (1987) Model to predict gaseous

contaminants in swine confinement buildings. Journal of Agricultural Engineering Research 37, 235-253.

Bates, R.G., Pinching G.D. (1950) Dissociation constant of aqueous ammonia at 0 to 50°C from e.m.f. studies of the ammonium salt of a weak acid. Journal of the American Chemical Society 72, 1393-1396.

Cronjé , A. L. (2004) Ammonia emissions and pathogens inactivation during controlled composting of pig manure, PhD Thesis, Birmingham: University of Birmingham.

Cumby, T. R., Moses, B. S. O. and Nigro, E. (1995) Gases from livestock slurries: emission kinetics. ROSS, C. C. 230-240. 1995. St Joseph, Michigan, USA: ASAE. 18-6-1995.

Danckwerts, P. V. (1951) Significance of liquid-film coefficients in gas absorption. Industrial and Engineering Chemistry, 43 (6) 1460-1467

Dobbins, W. E. (1962) Mechanism of gas absorption by turbulent liquids. In: Advances in Water Pollution Research, Proceedings of an International Conference, Eckenfelder Jr, W W (Ed.) Vol 2 Pergamon Press London 61 – 96.

Flechard C., Fowler D., Sutton M.A. and Cape J.N. (1999) Modelling of ammonia and sulphur dioxide exchange over moorland vegetation. Quart. J. Royal Meteor. Soc. 125, 2611-2641.

Hashimoto A G. (1972) Ammonia desorption from concentrated chicken manure slurries. Cornell University, Ithaca, NY..

Haslam R T, Hershey R L and Keen R H (1924) Effect of gas velocity and temperature on rate of absorption. Industrial and Engineering Chemistry 16, 1224-1230.

Higbie, R (1935) The rate of absorption of a pure gas into a still liquid during short periods of exposure. Transactions of the American Institute of Chemical Engineers 31, 365 - 389

Lewis, W.K. and W.G. Whitman. (1924). Principles of gas absorption. Industrial and Engineering Chemistry, 16 pp 215 - 220.

Loubet B., Milford C., Sutton M.A. and Cellier P. (2001) Investigation of the interaction between sources and sinks of atmospheric ammonia in an upland landscape using a simplified dispersion-exchange model. J. geophys Res. (Atmospheres) 106, 24,183-24,195.

Milford C., Theobald M.R., Nemitz E. and Sutton M.A. (2001) Dynamics of ammonia exchange in response to cutting and fertilizing in an intensively-managed grassland. Water, Air and Soil Pollution: Focus, 1, 167-176.

Muck R.E. and Steenhuis T.S. (1982) Nitrogen losses from manure storages. Agricultural Wastes 4, 41-54.

Process modelling of NH3 emissions Appendix 1 Page 3 of 4

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Nemitz E., Milford C. and Sutton M.A. (2001) A two-layer canopy compensation point model for describing bi-directional biosphere/atmosphere exchange of ammonia. Q. J. Roy. Meteor. Soc. 127, 815-833.

Ni, J.Q., Hendriks,J., Vinckier,C. and Coenegrachts,J. (2000) Development and validation of a dynamic mathematical model of ammonia release in pig house. Environment International 26, 105-115.

Olesen, J.E. and Sommer, S.G. (1993) Modelling effects of wind-speed and surface cover on ammonia volatilization from stored pig slurry. Atmospheric Environment Part A-General Topics 27, 2567-2574.

Riedo, M., Milford, C., Schmid, M. and Sutton, M.A. (2002) Coupling soil-plant-atmosphere exchange of ammonia with ecosystem functioning in grasslands. Ecological Modelling 158, 83-110.

Ruxton ,G.D. (1995) Mathematical modelling of ammonia volatilization from slurry stores and its effect on cryptosporidium oocyst viability. Journal of Agricultural Science 124, 55-60.

Scotford, I.M. and Williams, A.G. (2001) Practicalities, costs and effectiveness of a floating plastic cover to reduce ammonia emissions from a pig slurry lagoon. Journal of Agricultural Engineering Research 80, 273-281.

Srinath E G and Loehr R C (1974) Ammonia desorption by diffused aeration. Journal of Water Pollution Control Federation 46, 1939-1957.

Sutton M.A., Asman W.A.H. and Schjørring J.K. (1994) Dry deposition of reduced nitrogen.Tellus 46B, 255-273.

Sutton M.A., Schjørring J.K. and Wyers G.P. (1995) Plant - atmosphere exchange of ammonia. Phil. Trans. Roy. Soc., London. Series A. 351, 261-275.

Sutton M.A., Burkhardt J.K., Guerin D., Nemitz E. and Fowler D. (1998) Development of resistance models to describe measurements of bi-directional ammonia surface atmosphere exchange. Atmospheric Environment 32 (3), 473-480.

Williams A G, Nigro, E., Scotford I M and Cumby, T. R. (1998) Improving the conservation of nitrogen during the storage of slurries and manures. NT1403, 1-18. 1998. Silsoe, SRI. Final Report to MAFF.

Williams A G. The effects of covering slurry stores on emissions of ammonia, methane and nitrous oxide. WA0625, 1-20. 2000. Silsoe Research Institute. 2000.

Zhang R. (1992) Degradation of swine manure and a computer model for predicting the desorption rate of ammonia from an under-floor pit. PhD Thesis, 112 pages. University of Illinois at Urbana-Champaign.

Zhang, R.H., Day, D.L., Christianson, .L. and Jepson, W.P. (1994) A computer-model for predicting ammonia release rates from swine manure pits. Journal of Agricultural Engineering Research 58, 223-229.

Process modelling of NH3 emissions Appendix 1 Page 4 of 4

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Appendix 2Summary of ammonia emission abatement techniques

M.R. Theobald, A.G. Williams, J. Rosnoblet, C. Campbell, B.Gabrielle, B. Loubet, S. Génermont, E. Le Cadre and P. Cellier.

The following tables summarise the wide range of ammonia emission abatement techniques, noting how these may give benefits for several forms of nitrogen pollution and a reduction in several types of environmental impact. Conversely, key limitations or draw backs are also noted.

Table 1: Methods of ammonia emission abatement for livestock housing (adapted from Angus et al., 2003).

Abatement technique

Pollutants abated Environmental impacts reduced

Possible drawbacks of the technique

Maintain dry litter in housing sheds through water and ventilation management

NH3, Odour Acidification, Eutrophication Litter must not be too dry or there will be dust generation.

Optimal amount of bedding material

NH3, N2O, NO AcidificationEutrophicationGlobal WarmingOzone depletion

Supplementing the bedding material with additives

NH3 AcidificationEutrophication

Currently very uncertain. May increase N2O, NO emission.

Dietary manipulation NH3, NO3-, N2O, Global warming, Acidification,

Eutrophication of soils and water

Will increase costs to producer if quality of product is compromised. Higher costs of feed.

Low emission removal of waste/cleaning

NH3 Methods need investigation to deal with emission pulse. E.g. minimum disturbance & air filtering systems. Washing down with dilute organic acid.

Further study is necessary to refine techniques and quantify benefits

Dust filter on ventilation

Dust, NH3, NO, NO3-,

N2OEutrophication, Acidification

Biofilters/scrubbers All airborne pollutants

Acidification, Eutrophication and global warming

Ammonia scrubbers on air vents

NH3 Acidification, Eutrophication, Odour

Ammonia filters Dust, NH3 Acidification, Eutrophication

Farm building design – top or side air outlet.

NH3 A side air outlet may actually lead to more NH3 recapture by immediate vegetation, reducing that available for deposition to nature areas.

Process Modelling of NH3 emissions Appendix 2 Page 1 of 4

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Table 2: Methods of ammonia emission abatement for manure storage

Abatement method

Application to slurry stores

Relevant terms in Eqn 1

Application to solid manure

stores

Relevant terms in NH3 transfer

Equation (Appendix 1)Fixed Covers Includes rigid

structures and supported fabric canopies.

Emission rates from the liquid surface are affected by the increased headspace concentration of ammonia, i.e. PNH3air. Reduced wind effects also reduce K.

Storage in enclosed building.

Emission rates from the solid surface are affected by the increased concentration of ammonia in the building, i.e. PNH3air. Reduced wind effects also reduce K.

Floating Covers

Includes floating impermeable sheets, floating particles and floating organic matt (e.g. crusts, straw).

As above, plus possible reduction in A .

Plastic sheets or tarpaulins.

As above, plus possible reduction in A.

Wind speed reduction - shelters

Example: Shelter belts of trees around slurry stores.

Reduced wind effects also reduce K.

Example: Shelter belts of trees around solid manure stores.

Reduced wind effects also reduce K

Acidification and/or surfactants

Example: Chemical sprays above the surface of stored slurries to reduce surface pH.

Reduced value of PNH3liquid . Increased surface crusting also reduces K

Example: Chemical spraying of solid manure heaps to reduce surface pH.

Reduced value of PNH3liquid. Possibly some reduction of K

Addition of ammonia sinks

Example: zeolite filters on the exhaust ducts from covered slurry stores.

Not addressed by Eqn 1, since it concerns the removal of ammonia from the air after release from the slurry.

Example: zeolite particle sprinkled on the surface of solid manure stores.

Reduced value of PNH3liquid. Possibly some reduction of K

Drying Not applicable. Not applicable. Only for relatively high dry matter material such as poultry manure.

Reduced value of PNH3liquid. Possibly some reduction of K

Compression Not applicable. Not applicable. Compaction of solid manures to increase density minimise aerobic activity.

Reduced value of PNH3liquid. Possibly some reduction of K

Process Modelling of NH3 emissions Appendix 2 Page 2 of 4

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Table 3: Methods of ammonia emission abatement for land application of manures and fertilisers

Abatement method * Manures(FYM, slurry)

Mineral fertilisers

Comments

Fertiliser characteristicsAcidification (i.e. lower pH-value) yes yes Chemical equilibrium.Dilution yes Yes (UAN)Chemical formulation no Yes

(granules or prills)

See Le Cadre, 2004.

Application practicesSoil injection / increased injection depth

slurry only no Decrease of the soil’s Nitrogen concentration.

Soil cultivation or incorporation after spreading / shortest delay between spreading and incorporation

yes yes Decrease of the soil’s Nitrogen concentration.

Band spreading yes noApplication under vegetation cover slurry only yes Lower soil surface temperature.

Lower atmospheric exchanges.Irrigation after application or “washing” / shortest delay between application and irrigation, highest irrigation depth

yes yes Infiltration of the surface ammonium.

Application during rainfall yes yes Infiltration of the surface ammonium.Combination of climate effects : low air temperature & low wind speed

yes yes A decreased ammonia volatilisation is created by :- a decrease of the wind speed, which decreases the atmospheric diffusion ;- a decrease of the air temperature, which decreases the soil surface ammonia concentration.But the 2 conditions are antagonist, as a decrease of the wind speed increases the soil surface temperature, which increases volatilisation.

Delay of several 10-15 days between cutting of grass sward and mineral fertilization

no yes Such a delay (rather than immediate fertilisation) allows the sward to recover and recycle cutting induced N excess more effectively, reducing overall emissions (Milford 2004).

Application on low pH-value soils yes yesChoice of the fertiliser type yes yes* The cited conditions decrease ammonia volatilisation during and/or after fertiliser application

Abating emissions from grazed systems

Ammonia emissions from grazed systems originate from two sources: 1) from the TAN excreted directly onto the field by the livestock and 2) from the TAN applied to the field in the form of mineral and organic fertilisers. Measures to abate the emissions from the applied TAN are similar to those for abating emissions from land-applied manures and fertilisers (Table 3). Incorporation of applied manures is not an option for grazed land since this would destroy the grass sward. An additional measure for grazed systems is to increase the coverage of legumes (i.e. clovers) within the sward, which will fix atmospheric N thus reducing the demand for fertiliser N.

Process Modelling of NH3 emissions Appendix 2 Page 3 of 4

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For excreted TAN, the main options for abating NH3 are:

1) Reducing the stocking densityThis will therefore reduce the amount of TAN available for emission. This will result in a decrease in the number livestock (unless they are grazed elsewhere or housed – thus moving the emissions) which may not be a viable option.

2) Shorten the grazing periodThis will reduce the grazing emission period but will also increase the total housing and manure storage emissions and may therefore increase total emissions.

References

Angus A.J., Hodge I.D., McNally S. and Sutton M.A. (2003), The setting of standards for agricultural nitrogen emissions: a case study of the Delphi technique, J. Env. Management 69 (4): 323-337.

Le Cadre, E., 2004. Modélisation de la volatilisation d'ammoniac en intéraction avec les processus chimiques et biologiques du sol. Le modèle VOLT'AIR. Thèse CIFRE de Doctorat de l'Institut National Agronomique Paris-Grignon: p. 1-211.

Milford C. (2004) Dynamics of atmospheric ammonia exchange with intensively-managed grassland. Ph.D. thesis. University of Edinburgh, 219 pp.

Process Modelling of NH3 emissions Appendix 2 Page 4 of 4

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Appendix 3Critical analysis of livestock housing ammonia emission models

A.G. Williams, T.G.M. Demmers, T.R. Cumby and D.J. Parsons

Six models were assessed: Anderson et al (1987), Groot Koerkamp (1998), Monteny (2000), Ni et al. (2000), Sun et al. (2002), Zhang et al. (1994). These included aspects of cattle, pig and poultry housing and all were in mechanically ventilated houses. Summary assessments follow:

Anderson, G.A., Smith, R.J., Bundy, D.S. and Hammond, E.G. (1987) Model to predict gaseous contaminants in swine confinement buildings. Journal of Agricultural Engineering Research 37, 235-253.

Comments Has simple model of ammonia release, based on simplified mass transfer and mass transfer coefficient derived from Haslam et al. (1924)

Groot Koerkamp, P.W.G. (1998) Ammonia emission from aviary housing systems for laying hens. PhD Thesis, Wageningen University IBSN 90-5485-885-0 [pp 73-86, Degradation of nitrogenous components and volatilisation of ammonia from litter]

Comments It is very useful for calculating ammonia production from litter, concentrating on managerially influenced conditions, but it does not properly deal with mass transfer to be called a model of ammonia emissions. It is a good research tool, with some potential for abatement. It has a limited capacity for use in NARSES, but perhaps shows the likely scope of emissions.

Monteny, G. J. (2000) Modelling of ammonia emissions from dairy cow houses. Thesis, Wageningen University

Comments Good, mainly mechanistic model, which is certainly very useful for experimental work and for assessing some approaches to abatement. The high level of detail required may mean that it is not too suitable for use in NARSES.

Ni,J.Q., Hendriks,J., Vinckier,C. and Coenegrachts,J. (2000) Development and validation of a dynamic mathematical model of ammonia release in pig house. Environment International 26, 105-115.

Comments It is a useful, largely mechanistic model for mechanically ventilated houses, but limited by need for very detailed data and need to estimate empirical factors for the partition of well mixed and unmixed air. Emissions from a house are also limited to slurry channels and not floors of walls. It makes a good, novel contribution in the effect of CO2 emissions on surface pH. It has potential for abatement processes, but the mathematical solution used seems naïve compared with the description.

Sun, H., Stowell, R.R., Keener, H.M. and Michel, F.C. (2002) Two-dimensional computational fluid dynamics (CFD) modeling of air velocity and ammonia distribution in a High-Rise (TM) hog building. Transactions of the ASAE 45, 1559-1568.

Comments Does not calculate ammonia volatilisation, but used a concentration values as an input and used CFD to calculate the distribution of ammonia within a building. This approach is of some use in calculating velocities at emitting surfaces, but is not without difficulty. Not really a model of ammonia emissions.

Process Modelling of NH3 emissions Appendix 3 Page 1 of 8

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Zhang, R.H., Day, D.L., Christianson, L.L. and Jepson, W.P. (1994) A computer-model for predicting ammonia release rates from swine manure pits. Journal of Agricultural Engineering Research 58, 223-229.

Comments This is a useful, largely mechanistic model, but with limitations. It uses 2-film theory of mass transfer (widely respected in the world of chemical engineering) and deals with diffusion though accumulating slurry. It is limited by: using an arbitrary ammonia generation rate, limited knowledge of air velocities around channels, no account of pH profiles and proper effects of mixing. Emissions from a house are also limited to slurry channels and not floors of walls.

Three models were thus considered to suitable for further examination (Table 4). Groot Koerkamp’s model was recognised as having limitations, but was included as it was the only model dealing with poultry (Table 5).

Table 4: Decisions on what to do with livestock housing models

Authors FutureAnderson. et al. (1987) Do not consider furtherGroot Koerkamp (1998) Examine further Monteny (2000) Examine further.

Ni et al. (2000) Examine further.

Sun et al. (2002) Do not consider furtherZhang et al. (1994) Do not consider further

Table 5: Coverage of species and stages by housing models

Pigs Poultry CattleSolid Liquid Solid Liquid Solid Liquid

HousingGeneration (Monteny) GK Monteny

Emission Ni(Monteny)

Monteny(Ni)

Key: Ni Ni et al. (2000) GK

Groot Koerkamp

(1998)Monteny Monteny (2000)

(Brackets) indicate that a model has not been validated for a species, but might be extended to it

Table 6: Detailed model assessments that follow

Livestock housing modelsGroot Koerkamp (1998)Monteny (2000) Ni et al. (2000) Zhang et al. (1994)

Process Modelling of NH3 emissions Appendix 3 Page 2 of 8

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Evaluation of model of Groot Koerkamp (1998)

Model AssessorGroot Koerkamp, P.W.G. (1998) Ammonia emission from aviary housing systems for laying hens. PhD Thesis, Wageningen University IBSN 90-5485-885-0 [pp 73-86, Degradation of nitrogenous components sand volatilisation of ammonia from litter]

Adrian Williams (SRI)

Comments

a Common processes TAN chemistry, microbial reaction modelling, basic mass transfer, mass balance.

b Parameters that need measuring or estimating

Temperature, water content, pH, TAN of litter, mass transfer coefficient (all derived in the paper)

c Limits in application and extrapolationIt does not predict emissions from the building as such. There is no term for substrate limitation or end product inhibition, but these may not be major.

d Strengths of parts or whole Useful for predicting TAN prodn rates in range on managerially influenced environments.

e

Weaknesses of parts or whole (e.g. the multiple linear regression equation developed by Zhang et al., 1994 can suggest very misleading relationships between air speed and temperature that were otherwise mechanistically sound)

No attempt to include environmental factors affecting the mass transfer coefficient.

f How mechanistic and empirical it isLargely Mechanistic, although I suppose it does not try to model the microbial processes explicitly, but as though they were chemical reactions.

g Ability to deal with abatement processes Yes, in terms of litter management.

h Potential for use in a geo-spatial National Ammonia Inventory (e.g. NARSES)

Yes, but with the big caveat of the lack of terms dealing with emissions from the house.

iPotential to improve the current estimates in the National Ammonia Inventory

As above

jPotential for use in national and international ammonia emission and deposition models

As above

k Level of detail required in input data Needs main properties of litter: TAN conc., pH, temp, water content, density

lAvailability of suitable input data in terms of variable type together with spatial and temporal resolution

Not sure

m

Ability to use readily available geo-spatial data (e.g. 30 year met. data means, soil textures, vegetation classes on 5 km2 grids)

Possibly, but I suspect limited by model linking ambient conditions with litter conditions (e.g. temperature)

nInclusion of supplementary environmental information (e.g. calculation of nitrate leaching)

No

Process Modelling of NH3 emissions Appendix 3 Page 3 of 8

Effects of litter pH, water content and temperature on TAN production rate in poultry litter - Groot Koerkamp (1998)

5

10

15

20

25

30

35

40

45

100 120 140 160 180 200 220 240 260 280 300

Org N degradation Rate (TAN production rate)

Litt

er te

mpe

ratu

re, °

C o

r w

ater

con

tent

, %

7

7.5

8

8.5

9

9.5

10

pH

TWaterpH

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Process Modelling of NH3 emissions Appendix 3 Page 4 of 8

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Evaluation of model of Monteny (2000)

Model Name Monteny, G.J. (2000) Modelling of ammonia emissions from dairy cow houses. Thesis, Wageningen University

Assessor Theo Demmers, SRI

Criteria Evaluation

a What is the model for? Estimating ammonia emissions from mechanically or naturally ventilated dairy/beef houses

b Common processes mass transfer liquid air interfaceair exchange through slatsHenry’s lawCarbon dioxide effects (although not modelled)

c Parameters that need measuring or estimating

Parameters: 2-3Henry’s constant (H)Mass transfer coefficient slurry to air (k)correction constants (A, B & C) for pH surface layerfraction of free ammonia (f)urease activity

Input variables:Urine and faeces productionUrination behaviourTemperature of emitting liquid, Temperature of slatssurface area emitting surfaces (slurry & slats separate)Ventilation rate building (air exchange rate), pH of emitting liquid,Total Ammonia concentration (TAN) in emitting liquidair velocity in the pit

d Limits in application and extrapolation

not tested on other species

e Strengths of parts or whole appears to be very useful validated modelHas been validated using data set from other two sites

f Weaknesses of parts or whole (e.g. the multiple linear regression equation developed by Zhang et al., 1994 can suggest very misleading relationships between air speed and temperature that were otherwise mechanistically sound)

does use a empirical relation to adjust the surface pH, which has a big impact on emission raterequires ventilation rate to be measured independently

g How mechanistic and empirical it is

mechanistic with some empirically derived constants (factors) in it

h Ability to deal with abatement processes

tested with good results on dietary abatement processes. Might work on some changes to building layout.

i Potential for use in a geo-spatial National Ammonia Inventory (e.g. NARSES)

Don’t know (we have the code)

j Potential to improve the current estimates in the National Ammonia Inventory

Reasonable

k Potential for use in national and international ammonia emission and deposition models

Reasonable

l Level of detail required in input data

high level of detail required

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m Availability of suitable input data in terms of variable type together with spatial and temporal resolution

I might have a data set that is partially suitable, but the model does require high detail in temperature measurement which we do not generally have.

n Ability to use readily available geo-spatial data (e.g. 30 year met. data means, soil textures, vegetation classes on 5 km2 grids)

o Inclusion of supplementary environmental information (e.g. calculation of nitrate leaching)

None

p Usefulness in future experimental work

This model should definitely be considered

Evaluation of model of Ni et al. (2000)

Model Name J.-Q. Ni, J. Hendriks, C. Vinckier, J. Coenegrachts. (2000) A new concept of carbon dioxide accelerated ammonia release from liquid manure in pig house Environment International 26, 97-104J.-Q. Ni, J. Hendriks, C. Vinckier, J. Coenegrachts. (2000) Development and validation of a dynamic mathematical model of ammonia release in pig house Environment International 26, 105-115

Assessor Theo Demmers, SRI

Criteria Evaluation

a What is the model for? Estimating ammonia emissions from mechanically ventilated livestock houses

b Common processes mass transfer liquid air interfaceHenry’s lawCarbon dioxide effects

c Parameters that need measuring or estimating

Parameters: 2-3the convection mass transfer coefficient (estimated from data set)the proportionality coefficient (fraction of NH4 over total ammoniacal N)Factor to describe a well mixed area

Input variables:Temperature of emitting liquid, Surface area of emitting liquid, pH of emitting liquid,Ammonia concentration in emitting liquidAir flow velocity over surface of emitting liquid,

d Limits in application and extrapolation

not suitable for straw based or naturally ventilated buildings

e Strengths of parts or whole appears to be very useful validated modelHowever it has been validated using data set with abrupt changes in ammonia concentration and or pH (as modellers do) that will not normally occur.

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f Weaknesses of parts or whole (e.g. the multiple linear regression equation developed by Zhang et al., 1994 can suggest very misleading relationships between air speed and temperature that were otherwise mechanistically sound)

Did not spot an obvious one

g How mechanistic and empirical it is

mechanistic with some empirically derived constants (factors) in it

h Ability to deal with abatement processes

Not suitable

i Potential for use in a geo-spatial National Ammonia Inventory (e.g. NARSES)

Don’t know (we do not have the code at the moment)

j Potential to improve the current estimates in the National Ammonia Inventory

reasonable

k Potential for use in national and international ammonia emission and deposition models

not rated very high

l Level of detail required in input data

high level of detail required

m Availability of suitable input data in terms of variable type together with spatial and temporal resolution

I might have a data set that is suitable, but the model does require a high quality data set of which there won’t be many around.

n Ability to use readily available geo-spatial data (e.g. 30 year met. data means, soil textures, vegetation classes on 5 km2 grids)

only predicts emission

o Inclusion of supplementary environmental information (e.g. calculation of nitrate leaching)

None

p Usefulness in future experimental work

This model should definitely be considered

Evaluation of model of Zhang et al 1994

Model Name Zhang,R.H., Day,D.L., Christianson,L.L. and Jepson,W.P. (1994) A computer-model for predicting ammonia release rates from swine manure pits. Journal of Agricultural Engineering Research 58, 223-229.

Assessor Trevor Cumby, SRI

Criteria Evaluationa What is the model for? Prediction of ammonia emissions from slurries in under-floor

pits and similar storesb Common processes Ammonia diffusion through slurry layers.

Generation of ammonia n slurry during storageHenry’s law is used to estimate the partial pressure of gaseous ammonia created by that dissolved in the slurryEquilibrium between ammonia and ammonium according to temperature and pHTwo-film theory of mass transfer, with main resistance to

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emissions due to the gas filmAdditions of fresh slurry to the store are treated as though they fully mix with the existing store contents – their effect is modelled as equal increase in the thickness of each slurry layer

c Parameters that need measuring or estimating

Parameters: Rate coefficient for generation of ammonia – values were determined experimentally by the authorsCoefficients for ammonia and ammonium diffusivities as functions of slurry temperature - the authors used an arithmetic average value determined from the diffusivities of dissolved ammonia and ammonium ions, each as predicted by previous authors for dilute aqueous solutions, with each as a function of temperature. Equilibrium coefficients for equilibrium between ammonia and ammonium – the authors measured their own value of this coefficient at 21 oC and combined this with results from previous authors to determine the effect of other temperaturesMass transfer coefficient (KL) - the authors measured their own values as functions of air velocity and temperaturesNumber of slurry layers, - the authors used 10Time step for solution – the authors used 1 hour for ammonia release and 10 days for slurry additionInput variables:Slurry temperature, Slurry depth, Slurry surface area, Initial pH of surface slurry, Ammonia concentration in fresh slurry, including that already present at the start of the simulation, and in each new volume added.Air flow velocity over surface of slurry, Ambient ammonia concentration

d Limits in application and extrapolation

Does not take account of air velocity profiles in practical installationsApplies only to stored slurry, not to floors and wallsDoes not apply to solid manures Does not take account of changes of surface pH with time due to loss of carbon dioxide, although changes due to loss of ammonia are included.Considers only systems where fresh slurry is fully mixed into the bulk, although the diffusion of ammonia is modelled as discrete layers

e Strengths of parts or whole Simple computation (finite element methods)Readily adapted to consider effects of additions of fresh slurry to accumulated matterTwo-film approach is widely accepted in chemical engineering applicationsShow effects of different stead temperatures , and could be adapted to cope with conditions of changing temperaturesModels effects of different pH values in the fresh slurryAllows effects of different ambient ammonia concentrations to be modelled

f Weaknesses of parts or whole (e.g. the multiple linear regression equation developed by Zhang et al., 1994 can suggest very misleading relationships between air speed and temperature that were otherwise mechanistically

Simplistic model of ammonia generationDoes not take account of surface renewal effects in the slurry (e.g. achieved by mixing)Multiple regression (as listed in previous column)Does not include spatial variability except for changing ammonia profiles with depth in slurryAssumes that fresh slurry is fully mixed with the existing store contents whilst the diffusion of ammonia is modelled as

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sound) discrete layers. g How mechanistic and empirical

it isMechanistic concepts, but subject to empirical evaluation of parameters

h Ability to deal with abatement processes

Well-suited to modelling abatement measures based on reduced exposure of slurry surface area. Could be adapted to show effects of low protein diets (by changing values of initial ammonia concentration and generation parameter) and floating barriers to mass transfer (by changing KL)

i Potential for use in a geo-spatial National Ammonia Inventory (e.g. NARSES)

Limited by: Lack of knowledge of air velocities distributions and slurry propertiesExclusion of walls and floors

j Potential to improve the current estimates in the National Ammonia Inventory

Ditto

k Potential for use in national and international ammonia emission and deposition models

Ditto

l Level of detail required in input data

Acceptable if empirical parameters are used

m Availability of suitable input data in terms of variable type together with spatial and temporal resolution

Simple: physical dimensions of slurry stores Moderate: temperatures, slurry pH, Difficult: ammonia generation coefficient, local air velocities

n Ability to use readily available geo-spatial data (e.g. 30 year met. data means, soil textures, vegetation classes on 5 km2 grids)

Not appropriate

o Inclusion of supplementary environmental information (e.g. calculation of nitrate leaching)

None

p Usefulness in future experimental work

Useful for interpreting emission data obtained from laboratory-scale and pilot-scale experiments, leading to evaluation of parameters that are widely used by other models.

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Appendix 4Critical analysis of manure storage ammonia emission models

A.G. Williams, T.G.M. Demmers, T.R.. Cumby and D.J. Parsons

Seven models were assessed:

Cronjé (2004), Cumby et al. (1995), Muck and Steenhuis (1982), Olesen and Sommer (1993), Ruxton (1995), Scotford and Williams (2001) and Williams et al. (1998). These included aspects of cattle, pig slurry storage and pig FYM storage. There appeared to be no poultry manure storage models (although much of Groot Koerkamp’s science could be applied to poultry litter storage). Summary assessments follow.

Cronjé A L (2004) Ammonia emissions and pathogen inactivation during controlled composting of pig manure. PhD Thesis, University of Birmingham.

Comments This is a largely mechanistic model of composting solid manure, including ammonia emissions. It was designed for in-vessel composting with known air supply, rather than uncontrolled composting of a field heap and so does not represent mainstream practice especially well. Nonetheless, it is the only model to address this major source of ammonia emission.

Cumby, T. R., Moses, B. S. O. and Nigro, E. Gases from livestock slurries: emission kinetics. ROSS, C. C. 230-240. 1995. St Joseph, Michigan, USA: ASAE. 18-6-1995.

Comments They used the two film theory to produce equations for convective mass transfer and described how mass transfer coefficients could be measured in unsteady state, together with the equilibrium gas concentrations. It has great value in evaluating parts of the emission process and some abatement processes (and is not limited to ammonia). There are plenty of data available.

Muck R.E. and Steenhuis T.S. (1982) Nitrogen losses from manure storages. Agricultural Wastes 4, 41-54.

Comments It uses diffusion through layers and convective mass transfer from upper layer, but assumes no microbial generation of ammonia. It uses Haslam’s mass transfer relationship for U and T on KL, which has arguably been superseded by other approaches. It was limited to top filling of stores and so assumed a layer of almost completely fresh slurry at the top and does not allow for mixing – mechanical or by convection. Has some potential for studying abatement processes, but not non-contact covering.

Olesen, J.E. and Sommer, S.G. (1993) Modeling effects of wind-speed and surface cover on ammonia volatilization from stored pig slurry. Atmospheric Environment Part A-General Topics 27, 2567-2574.

Comments This is a largely mechanistic model derived from one for land spreading. The method for calculating the mass transfer coefficient is more suitable and flexible than that used by Muck & Steenhuis or Ruxton, but there may be some doubts about the details of airflow over and around a store. It has diffusion through layers, but does not address mixing, surface pH effects or generation of ammonia from organic N.

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Ruxton ,G.D. (1995) Mathematical modelling of ammonia volatilization from slurry stores and its effect on cryptosporidium oocyst viability. Journal of Agricultural Science 124, 55-60.

Comments Based almost entirely on Muck and Steenhuis (1982). Includes microbial generation of ammonia from urea. Uses Haslam’s relationship for U and T on KL. Diffusion equation solved by finite difference. He included ammonia generation from urea, but not other organic N.

Scotford, I.M. and Williams, A.G. (2001) Practicalities, costs and effectiveness of a floating plastic cover to reduce ammonia emissions from a pig slurry lagoon. Journal of Agricultural Engineering Research 80, 273-281.

Comments They dealt with the geometry of lagoons as they fill and are subject to evaporation and rainfall and hence produce a changing surface area for emission. Only deals with limited part of ammonia emission process, but useful for inventory work and mechanistic models with non-uniform cross sections.

Williams A G, Nigro, E., Scotford I M and Cumby, T. R. Improving the conservation of nitrogen during the storage of slurries and manures. NT1403, 1-18. 1998. Silsoe, SRI. Final Report to MAFF.

Comments Pig farm yard manure storage. First order equation with little sophistication.

Four models were thus considered to suitable for further examination (Table 7). Cronjé’s model was included as being the only one dealing with solid manure (Table 8)., but it was developed for forced ventilation, rather than normal storage. The Ruxton model was included partly to contrast it with Olesen and Sommer’s model, but also as obtaining the model code was thought to be easier than the earlier model of Muck and Steenhuis. Scotford and Williams’s model applied only to the geometry of a lagoon and so was not considered suitable for analysis beyond sensitivity.

Table 7: Decisions on what to do with manure storage models

Authors FutureCronjé (2004) Examine further *** Cumby et al. (1995) Do not consider furtherMuck and Steenhuis (1982) Do not consider furtherOlesen and Sommer (1993) Examine furtherRuxton (1995) Examine further Scotford and Williams (2001) Include in sensitivity analysis, but no more.Williams et al. (1998) Do not consider further

Table 8: Coverage of species and stages by housing models

Pigs Poultry CattleStorage Solid Liquid Solid Liquid Solid Liquid

Generation (Ruxton) GK Ruxton

Emission Cronjé Olesen (Cronjé) (Olesen)(Ruxton) RuxtonScotford Scotford

Cronjé Cronjé (2004) Ruxton Ruxton (1995)Olesen Olesen & Sommer (1993) Scotford Scotford & Williams (2001)(Brackets) indicate that a model has not been validated for a species, but might be extended to it

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Table 9: Detailed model assessments that follow

Storage of manures and dirty waterCronjé (2004) Cumby et al. (1995)Muck and Steenhuis (1982) Olesen and Sommer (1993) Ruxton (1995) Scotford and Williams (2001) Williams et al. (1998)

Evaluation of model of Cronjé (2004)

Model Name AssessorCronjé, Angela. L., Ammonia emissions and pathogen inactivation during controlled composting of pig manure. PhD Thesis, 2004 (Adrian’s student)

Adrian Williams

a Purpose of modelTo predict temperature changes, mass loss, ammonia emissions and pathogen from composting pig farm yard manure.

b Common processes NH3 - NH4+ equilibrium, NH3 mass transfer

coefficient, convective NH3 emission equation

c Parameters that need measuring or estimating

ParametersReaction rate coefficient (fitted eqn from expts with various temperatures)Biodegradability coefficientCoefficients for non-optimal activity associated with pH, oxygen and water content.Surface area of porous mediumRespiratory quotientHeat evolution coefficientThermal conductivity and heap capacity of manureReactor surface heat loss coefficientOrg-N synthesis rate coefficientInitial TAN concentrationInitial pHInitial dry matter contentC & N contentsBulk densityCompost temperatureInput variablesAmbient temperature and rhAir flow rate options

d Limits in application and extrapolation

Limited to core of heap, not full spatial variation, does not model mineralization of org-N or long term maturation processes. Models forced air flow, not natural ventilation, no interaction with the wider environment (e.g. wind speed)

e Strengths of parts or whole Good mechanistic basis of much of the process from chemical and physical properties and principles. Models initial part of composting well. Allows predictions to be made from manure of different compositions and with some different management options.

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f Weaknesses of parts or whole

Assumes all N lost as NH3-N. Does not deal with de-nitrification, does not model pH change during composting, assumes microbial population operates like chemical reaction, limited capacity to deal with C:N ratio, temperature changes are very dependent on water evaporation, which is modelled rather empirically.

g How mechanistic and empirical it is

Generally mechanistic, but some features are empirical (e.g. evaporation of water). Main part on organic matter degradation could be more closely based on microbial kinetics. pH changes are empirical.

h Ability to deal with abatement processes Some scope for composting, but much less for unmanaged FYM stores.

i Potential for use in a geo-spatial National Ammonia Inventory (e.g. NARSES) Limited without further development

jPotential to improve the current estimates in the National Ammonia Inventory

A little

kPotential for use in national and international ammonia emission and deposition models

A little

l Level of detail required in input dataHigh, including what is needed to estimate some parameters, such as reaction rate as affected by temperature

mAvailability of suitable input data in terms of variable type together with spatial and temporal resolution

Little

n

Ability to use readily available geo-spatial data (e.g. 30 year met. data means, soil textures, vegetation classes on 5 km2 grids)

Not really

oInclusion of supplementary environmental information (e.g. calculation of nitrate leaching)

Pathogen inactivation via an empirical relationship.

p Usefulness in future experimental work Very useful for highlighting what measurements and parameter estimates are needed.

Evaluation of model of Cumby et al 1995

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Model Name Cumby, T. R., Moses, B. S. O. and Nigro, E. Gases from livestock slurries: emission kinetics. ROSS, C. C. 230-240. 1995. St Joseph, Michigan, USA: ASAE. 18-6-1995..

Assessor Trevor Cumby, SRI

Criteria Evaluation

a What is the model for? Analysis of data from ammonia emission experiments in closed-circuit and open-circuit wind tunnels. It is not specific to ammonia emission from slurries. It is not a predictive model in itself for ammonia emissions, but enables evaluation of parameters to be included in others’ models (e.g. Muck and Steenhuis 1982; Zhang et al., 1994)

b Common processes Henry’s law is used to estimate the partial pressure of gaseous ammonia created by the ammonia dissolved in the slurryEquilibrium between ammonia and ammonium according to temperature and pHTwo-film theory of mass transfer, with main resistance to emissions due to the gas filmAccumulation of ammonia in the headspace – i.e. ambient ammonia concentration changes with time as a function of the emission process and ventilation rateEffects of liquid mixing on ammonia emissions

c Parameters that need measuring or estimating

Parameters: Equilibrium coefficients for equilibrium between ammonia and ammonium – the authors used results from previous authors to determine the effects of temperatureMass transfer coefficient (KL) - the authors measured their own values as functions of air velocity and temperatures, and degree of liquid mixing, and compared these with various previous authorsInput variables:Temperature of emitting liquid, Surface area of emitting liquid, pH of emitting liquid,Ammonia concentration in emitting liquidAir flow velocity over surface of emitting liquid, Initial ammonia concentration in the headspace

d Limits in application and extrapolation

This is not a complete model to predict ammonia emissions from stored slurriesDoes not take account of air velocity profiles in practical installationsApplies only to stored liquids, although the approach could be adapted for other emitting systems, including solids Does not take account of changes of surface pH with time

e Strengths of parts or whole Two-film approach is widely accepted in chemical engineering applicationsShows effects of different steady temperatures , and could be adapted to cope with conditions of changing temperaturesAllows effects of different ambient ammonia concentrations to be modelled, including changes with timeEnables evaluation of the mass transfer coefficient, KL in unsteady state conditions, which provide large changes in the concentration of gaseous ammonia, thus improving the signal-to-noise ratio of the measurements.Includes the effects of liquid mixingApplies complete mass-balance to the emitting liquid and to the headspace, as an integrated system

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f Weaknesses of parts or whole (e.g. the multiple linear regression equation developed by Zhang et al., 1994 can suggest very misleading relationships between air speed and temperature that were otherwise mechanistically sound)

In itself, does not predict ammonia emissions from stored slurries, but assists other models (e.g. Muck and Steenhuis 1982; Zhang et al., 1994)Does not include ammonia generationDoes not include spatial variability in slurry, except for effects at the surface

g How mechanistic and empirical it is

Mechanistic concepts, but subject to empirical evaluation of parameters

h Ability to deal with abatement processes

Facilitates pilot-scale experimental determination of the effectiveness of several abatement measures (e.g. reduced exposure of slurry surface area; low protein diets and floating barriers.

i Potential for use in a geo-spatial National Ammonia Inventory (e.g. NARSES)

Only possible through combination with other models

j Potential to improve the current estimates in the National Ammonia Inventory

As above

k Potential for use in national and international ammonia emission and deposition models

As above

l Level of detail required in input data

Acceptable in the context of supporting experiments

m Availability of suitable input data in terms of variable type together with spatial and temporal resolution

Simple: physical dimensions of emitting systems and associated ventilated headspaces Moderate: temperatures, liquid pH, Difficult: ammonia and ammonium concentrations in the emitting liquid , air velocities at surface of slurry

n Ability to use readily available geo-spatial data (e.g. 30 year met. data means, soil textures, vegetation classes on 5 km2 grids)

Not appropriate

o Inclusion of supplementary environmental information (e.g. calculation of nitrate leaching)

None

p Usefulness in future experimental work

Useful for interpreting emission data obtained from laboratory-scale up to full-scale experiments in enclosed systems, such as buildings or covered slurry stores. These would evaluate parameters that are widely used by other models. The model is reversible, an enables measurement of key parameters for both absorption and desorption

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Evaluation of model of Muck and Steenhuis, 1982

Model Name Muck R.E. and Steenhuis T.S. (1982) Nitrogen losses from manure storages. Agricultural Wastes 4, 41-54.

Assessor Trevor Cumby, SRI

Criteria Evaluation

a What is the model for? Prediction of ammonia emissions from slurries in under-floor pits and other stores, including those with bottom-filling

b Common processes Ammonia diffusion through slurry layers.Equilibrium between ammonia and ammonium according to temperature and pHHenry’s law is used to estimate the partial pressure of gaseous ammonia created by that dissolved in the slurryTwo-film theory of mass transfer, with main resistance to emissions due to the gas filmAdditions of fresh slurry to the store are treated as though they do not mix with the existing store contents – their effect is modelled as a new layer

c Parameters that need measuring or estimating

Parameters: Coefficient for ammonia diffusivity in slurry – the authors used a value for ammonia in water at 25oC, obtained from a standard reference source (American Institute of Physics, 1957) Equilibrium coefficients for equilibrium between ammonia and ammonium – the authors used a value from Hashimoto (1972)Mass transfer coefficient (KL) – the authors used the relationship for effect of U and T on KL from Haslam et al (1924)Depth of each slurry layer – the authors used 1 cmTime step for solution – the authors used 1 hourInput variables:Slurry temperature, Slurry depth, Slurry surface area, Initial pH of bulk slurry, Initial ammonia concentration in each layer of slurry, including the layers already present at the start of the simulation, and in each new layer added.Air flow velocity over surface of slurry,

d Limits in application and extrapolation

Does not take account of air velocity profiles in practical installationsApplies only to stored slurry, not to floors and wallsDoes not apply to solid manures Does not take account of changes of surface or bulk pH with time (e.g. due to loss of carbon dioxide) Changes in the ambient ammonia concentration in the air are ignored, so the model is not valid for use in buildings with ammonia concentration gradients, or in covered stores Additions of fresh slurry are limited to an incremental step size that is equal to the assumed depth of each slurry layer (authors used 1 cm)Although top and bottom filling are considered, the model does not enable intermediate filling levels.Not applicable for slurry storage systems with mixing

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e Strengths of parts or whole Simple computation (finite difference methods)Consider effects of additions of fresh slurry to accumulated matter and distinguishes between top-filled and bottom-filled stores – as illustrated by the authorsTwo-film approach is widely accepted in chemical engineering applicationsModels changing temperatures – as illustrated by the authorsModels effects of different pH values in the bulk of the slurrySome attempt made at validation using data from three separate full-scale systems

f Weaknesses of parts or whole (e.g. the multiple linear regression equation developed by Zhang et al., 1994 can suggest very misleading relationships between air speed and temperature that were otherwise mechanistically sound)

No model of ammonia generation – assumed to be zero (i.e. biological activity is ignored)It is assumed that bulk and surface pH values are similar and that these do not change with timeDoes not take account of surface renewal effects in the slurry (e.g. achieved by mixing). This could be important where natural thermal mixing is likely (e.g. dark-coloured, above-ground steel stores in strong sunlight)Does not include spatial variability except for changing ammonia profiles with depth in slurryDoes not take account of changes in the ambient ammonia concentration – this is assumed to be zero at all timesThe assumed validity of the model of Haslam et al (1924) for KL is questionable.The authors note that their model was no well-validated for top-loaded stores.

g How mechanistic and empirical it is

Mechanistic concepts, but subject to empirical evaluation of parameters, including the assumption that parameter values reported by previous authors were valid

h Ability to deal with abatement processes

Well-suited to modelling abatement measures based on reduced exposure of slurry surface area or bottom filling. Could be adapted to show effects of low protein diets, but only by changing values of initial ammonia concentration. The model is limited because biological generation of ammonia is ignored. Potentially, the model could consider the effects of floating barriers to mass transfer (e.g. by changing KL)

i Potential for use in a geo-spatial National Ammonia Inventory (e.g. NARSES)

Limited by: Lack of knowledge of air velocities distributions and slurry propertiesExclusion of walls and floorsLack of term for generation of ammonia

j Potential to improve the current estimates in the National Ammonia Inventory

As above

k Potential for use in national and international ammonia emission and deposition models

As above

l Level of detail required in input data

Acceptable if parameter values from the previous studies are accepted

m Availability of suitable input data in terms of variable type together with spatial and temporal resolution

Simple: physical dimensions of slurry stores Moderate: temperatures, slurry pH, Difficult: local air velocities

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n Ability to use readily available geo-spatial data (e.g. 30 year met. data means, soil textures, vegetation classes on 5 km2 grids)

Not appropriate

o Inclusion of supplementary environmental information (e.g. calculation of nitrate leaching)

None

p Usefulness in future experimental work

Useful for interpreting emission data obtained from pilot-scale and full-scale slurry storage experiments where top or bottom filling methods need to be compared. However, if there is a discrepancy between the model predictions and measured ammonia emissions, there is only limited capacity to improve the predictions by using better parameter values.

Evaluation of model Olesen and Sommer (1993)

Model Name

Olesen, J.E. and Sommer, S.G. (1993) Modeling effects of wind-speed and surface cover on ammonia volatilization from stored pig slurry. Atmospheric Environment Part A-General Topics 27, 2567-2574.

a Purpose of model To calculate ammonia emissions from stored slurry.

b Common processes

Convective volatilisation equation with a mass transfer coefficient. Equilibrium of TAN, NH3 and NH4

+

Henry’s LawMass transfer coefficient sum of reciprocal resistances (turbulent air, laminar air and slurry cover [or surface resistance I think])Turbulent resistance from z0, k and U*Wind profile by standard Monteith & Unsworth eqn with uz, u*, k, and ln (z/z0)Movement of ammonia by diffusion through slurry

c Parameters that need measuring or estimating

ParametersSurface resistance, diffusion coefficient, friction velocity, U* (I think), roughness lengthInput variablesAir temperatureSlurry depth & areaTAN, pHWind velocity and aspects of profile

d Limits in application and extrapolation No effects of radiation on temperature or convective cooling - so perhaps not suitable for long term use as it is. Not suitable outside neutral atmospheric conditions & the assumption of the wind profile being as described is somewhat doubtful. Not designed for fully mixed slurry, but that could be an easy step. Allowing for mixing by natural convection would be much more difficult to include. Numerical solution seems limited to steady environmental conditions. Not for solid manures.

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Does not account for change in pH with time or TAN generation from organic N.

e Strengths of parts or wholeA useful model. Calculates mass transfer coefficient from basic principles, mechanistic approach, should deal with all slurries. It does model ammonia from slurry right into atmosphere.

f Weaknesses of parts or wholeAs c. Also, I am not sure not how suitable the assumptions are in the model about the velocity profile and hence movement of ammonia to the upper atmosphere are.

g How mechanistic and empirical it isIt is largely mechanistic, with some empirical relationships for equilibrium and Henry’s Law coefficients and, to some degree, the mass transfer coefficient.

h Ability to deal with abatement processes Yes, it should deal with changes in, wind speed, TAN, pH, area, depth and surface cover.

i Potential for use in a geo-spatial National Ammonia Inventory (e.g. NARSES)

Yes, e.g. response to regional wind and temperature

j Potential to improve the current estimates in the National Ammonia Inventory Yes (as above)

kPotential for use in national and international ammonia emission and deposition models

Yes, the emission side

l Level of detail required in input data They used hourly data, but it could probably be used with daily weather means.

mAvailability of suitable input data in terms of variable type together with spatial and temporal resolution

Some should be readily available, i.e. wind and temperatures. Details of store geometry may be more difficult or ability to estimate surface resistance from 1st principles. TAN and pH may be difficult.

n

Ability to use readily available geo-spatial data (e.g. 30 year met. data means, soil textures, vegetation classes on 5 km2 grids)

Yes

oInclusion of supplementary environmental information (e.g. calculation of nitrate leaching)

No

p Usefulness in future experimental work Useful - shows need to characterise air flow around stores and surface resistance.

Evaluation of model of Ruxton (1995)

Model G.D. Ruxton. Mathematical modelling of ammonia volatilization from slurry stores and its effect on Cryptosporidium oocysts. Journal of Agricultural Science, Cambridge (1995), 124, 55–60

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Assessor David Parsons, SRICriteria Evaluation

a What is the model for? Simulating ammonia emissions from stores and (but not relevant) effect of ammonia on Cryptosporidium oocysts. Based on Muck and Steenhuis with some simplifications and one added mechanism.

b Common processes Diffusion (1-d); mineralization of urea; volatilizationc Parameters that need

measuring or estimating[I’m including variables]Paper says: Store depth; initial NH3-N conc; pH; temperature; wind speed.The last 3 are converted by empirical relationships to mass transfer coef; fraction of unionized NH3-N; Henry’s law const. This is OK if we trust these relationships.Also, the diffusion coef is given a fixed value. Might need to be estimated.Likewise rate constant for urea mineralization.

d Limits in application and extrapolation

For liquid slurries only, but validation included cattle and pig slurry, so possibly a reasonably wide range of TS, TAN, etc., but don’t know how far it could stretch. Fairly simple assumptions about geometry, initial and boundary conditions, but these could be relaxed. Empirical relationships noted above would need testing if extrapolated.

e Strengths of parts or whole Simple, but appears to work adequately.f Weaknesses of parts or whole

(e.g. the multiple linear regression equation developed by Zhang et al., 1994 can suggest very misleading relationships between air speed and temperature that were otherwise mechanistically sound)

Those empirical relationships again.There is a philosophical contradiction between the boundary condition (concentration = 0 at the surface) and the volatilization rate (proportional to concentration), which is concealed by the fact that Ruxton switches from continua to thin layers as soon as he has dealt with diffusion. (Volatilization takes place from the whole of a discrete layer, rather than the surface.)

g How mechanistic and empirical it is

Largely empirical.

h Ability to deal with abatement processes

Limited. Maybe manipulation of TAN, pH and wind speed, but not covering etc., because it ignores NH3 concentration.

i Potential for use in a geo-spatial National Ammonia Inventory (e.g. NARSES)

Limited by: Lack of knowledge of air speed distributions and slurry propertiesExclusion of walls and floorsLimited modelling of generation of ammonia

j Potential to improve the current estimates in the National Ammonia Inventory

As above

k Potential for use in national and international ammonia emission and deposition models

As above

l Level of detail required in input data

Low

m Availability of suitable input data in terms of variable type together with spatial and temporal resolution

Climatic: Temperature probably no problem, but wind speed at the slurry surface is unknown.Farm: Need slurry store dimensions (probably OK) and slurry characteristics (harder)

n Ability to use readily available geo-spatial data (e.g. 30 year met. data means, soil textures, vegetation classes on 5 km2 grids)

Not appropriate

o Inclusion of supplementary None, unless you interested in Cryptosporidium

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environmental information (e.g. calculation of nitrate leaching)

p Usefulness in future experimental work

Limited

Evaluation of model of Scotford and Williams (2001)

Model AssessorScotford, I.M. and Williams, A.G. (2001) Practicalities, costs and effectiveness of a floating plastic cover to reduce ammonia emissions from a pig slurry lagoon. Journal of Agricultural Engineering Research 80, 273-281.

Adrian Williams

CommentsThose to calculate evaporation using the Penman equation.

a Purpose of modelTo calculate a changing surface area for emission from lagoons as they fill or empty and are subject to evaporation and rainfall. It was originally more to do with water evaportion than ammonia.

b Common processes

c Parameters that need measuring or estimating

3 of:: Angle of elevation of lagoon wall, length and width of lagoon base at top or bottom or the depth. Daily inflow of slurry, storage time. Need evaporation rates from met data or those parameters needed to calculate evaporation using the Penman equation.

d Limits in application and extrapolation Was designed for lagoons with shape of truncated pyramid as an approximation of the real shape

e Strengths of parts or whole Gives estimate of emitting surface area for slurry stores with sloping sides.

f

Weaknesses of parts or whole (e.g. the multiple linear regression equation developed by Zhang et al., 1994 can suggest very misleading relationships between air speed and temperature that were otherwise mechanistically sound)

Simplifies the geometry

g How mechanistic and empirical it is The calculation of surface area is mechanistic, but it uses empirical data to drive it.

h Ability to deal with abatement processes It can be used with floating lagoon covers

i Potential for use in a geo-spatial National Ammonia Inventory (e.g. NARSES)

Yes as it could be used to give a better estimate of emitting area

j Potential to improve the current estimates in the National Ammonia Inventory Yes, for reason given above.

k Potential for use in national and international ammonia emission and deposition models Some

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l Level of detail required in input dataDaily weather data for evaporation and rainfall, slurry storage time(s) and typical volumes of slurry flowing in each day.

mAvailability of suitable input data in terms of variable type together with spatial and temporal resolution

Should be fairly straightforward to get evaporation and rainfall data. Farm activity data may be more elusive.

nAbility to use readily available geo-spatial data (e.g. 30 year met. data means, soil textures, vegetation classes on 5 km2 grids)

as above (rain is certainly easy - I have it)

oInclusion of supplementary environmental information (e.g. calculation of nitrate leaching)

not applicable

p Usefulness in future experimental workUseful in cases where store cross section is non-uniform. It is really an “add on” to an emission model.

Evaluation of model of Williams et al (1998)

  Model Name

Williams A G, Nigro, E., Scotford I M and Cumby, T. R. Improving the conservation of nitrogen during the storage of slurries and manures. NT1403, 1-18. 1998. Silsoe, SRI. Final Report to MAFF.

a Purpose of modelTo describe ammonia emissions and hence N loss from stored pig farm yard manure. First order equation with little sophistication.

b Common processes First order rate loss

c Parameters that need measuring or estimating

Rate constant, initial TAN concentration, storage time

d Limits in application and extrapolation Not affected by environment or the geometry of a heap. May not apply to manure for other species

e Strengths of parts or whole Simplicity!

f

Weaknesses of parts or whole (e.g. the multiple linear regression equation developed by Zhang et al., 1994 can suggest very misleading relationships between air speed and temperature that were otherwise mechanistically sound)

Assumes all N lost as NH3-N. Does not deal with composting processes

g How mechanistic and empirical it is Uses one mechanistic equation in a fairly empirical way.

h Ability to deal with abatement processes Very limited

i Potential for use in a geo-spatial National Ammonia Inventory (e.g. NARSES) Some

j Potential to improve the current estimates in the National Ammonia Inventory A little

kPotential for use in national and international ammonia emission and deposition models

Little

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l Level of detail required in input data Low level

mAvailability of suitable input data in terms of variable type together with spatial and temporal resolution

Some

n

Ability to use readily available geo-spatial data (e.g. 30 year met. data means, soil textures, vegetation classes on 5 km2 grids)

No

oInclusion of supplementary environmental information (e.g. calculation of nitrate leaching)

No

p Usefulness in future experimental work Limited, but at least suggests when sampling is needed.

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Appendix 5Critical analysis of land application ammonia emission models

J. Rosnoblet, B.Gabrielle, B. Loubet, S. Génermont, E. Le Cadre and P. Cellier

Introduction

There are three main types of model: empirical models (E), mechanistic models (M) and intermediates models (EM).

Table 10 shows the main models of volatilisation described in the literature, their type (E, M, EM), the conditions under which they were obtained and/or validated, and the level of explicit description of the («soil» and «atmosphere») compartments involved in volatilisation. Models have been developed for the application of organic (manures) and synthetic fertilisers.

Empirical models The empirical models are essentially based on experimentation and the reproducible observation of a phenomenon. These models establish statistical correlations between the variable investigated and the factors thought to influence it. There are two main groups of empirical models for calculating the volatilisation of ammonia. They can be divided on the basis of the purpose for which they are intended: cognitive or predictive.

The first group of empirical models consists of models which are primarily intended to predict the total ammonia losses after the application of synthetic (Fenn and Kissel, 1973-1976) or organic fertilisers (Menzi et al. 1998). The second group of empirical models consists of models that predict both the total losses and the dynamics of the cumulative flux. To do this, dynamic models (logistical, exponential) are used. The parameters of the equations are adjusted as a function of the fluxes measured (Stevens et al. 1989; Sommer and Ersboll, 1994; Demeyer 1995). The need for specific calibration is therefore very important, since it means that these models cannot be applied to another type of fertiliser or extrapolated to other conditions due to the small number of explanatory variables used in the equations. In particular, models that do not take into account the amount applied are scarcely credible. Ismail et al. (1991) have established a logarithmic multiple regression for a period of two weeks on the basis of 4 explanatory variables (pH of the soil, moisture content expressed in terms of the weight of the soil before application, the amount applied, and the air temperature) after the application of urea under controlled conditions. This model has more explanatory variables than in the other models of this type, but they do not take into account all the factors that influence volatilisation, such as wind speed, the cation exchange capacity and the nitrification rate. The most developed of these models, the ALFAM model (Sogaard et al., 2002) links the parameters of Michaelis kinetics to the cumulative losses by volatilisation after applying slurry. The parameters Nmax (or total cumulative losses) and Km (the time at which the losses are equal to one half of the total losses) are calculated using different modules. These modules use several linear functions that combine the explanatory variables. This model was devised and validated on the basis of a large number of datasets obtained Europe-wide.

Although the empirical models integrate an increasingly large numbers of factors that influence ammonia volatilisation, the complexity of the agro-pedo-climatic processes means that they do not constitute a sufficiently reliable tool for predicting volatilisation for a wide variety of soils or climates (Sommer and Hutchings, 2001).

Semi-mechanistic or semi-empirical models Intermediate models propose a compromise between the mechanistic and empirical models (Génermont, 1996) which is acceptable for several purposes. In models of this type, either both the «soil» and «atmosphere» compartments are described partially (English et al.,

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1980), or the description of the «soil» compartment (Sherlock et al., 1984 – 1985) is given priority over the «atmosphere» compartment (Hengrium et al., 1999). However, the intermediate models available are too tainted by empiricism and inadequately validated to be used over a wide range of pedo-climatic conditions.

Mechanistic modelsMechanistic models are complex models based on an understanding of the processes and mechanism of action of the factors of influence. They make use of the laws of physics, chemistry, biology and mathematics. Mechanistic models have always been devised for a cognitive purpose, and are sometimes also predictive. They require more input variables than the empirical models, but are more readily generalized or even generic in nature. Mechanistic models are viewed as the basis for devising predictive models (van der Molen et al., 1990a, b). All mechanistic models are based on the same general outline (Ni, 1999; Sommer et al., 2003). They consist of a central equation that constitutes the core of the model:

Flux of NH3 = K (C surface-Cair)

Csurface is the concentration of ammonia gas on the surface of the soil, and Cair, the concentration of ammonia in the atmosphere. K is the mass transfer coefficient for transfer into the atmosphere.

Each of the different modules of the models calculates each of the terms in the equation. The mechanistic models propose virtually the same description of the «soil» compartment in which only the following aspects differ: (1) the parameterisation of the adsorption equilibrium, (2) the parameterisation of the acid/base and Henry constants as a function of temperature and (3) the method of calculating the transfer of the various ammoniacal species.

When an adsorption isotherm (linear, Freundlich, Langmuir) is chosen, the coefficients are determined experimentally (Wu et al., 2003; Rachhpal-Singh and Nye, 1984 -1988; Kirk and Nye, 1991a, b) and are sometimes also used by other models (Génermont, 1996) or required as input variables (van der Molen, 1990a, b). The exchange isotherm is rarely taken into account except in the model of Fleischer et al. (1987). The two major parameterisations of the dissociation and Henry constants as a function of temperature are those of Hales and Drewes (1979) used by van der Molen and of Beutier and Renon, used by Génermont and Cellier (1997), Sommer and Olesen (2000) and Wu et al. (2003). It should be noted that the formulation of Hales and Drewes (1979) is now considered to be quantitatively inaccurate (Sutton et al. 1994). The distinctive feature of the models of Racchpal Singh and Nye (1986-1988) and also of Fleischer et al. (1987)- the only models designed on the basis of laboratory experimentation for inorganic fertilisers – is that they do not propose any correction for the acidity constant as a function of the temperature, which makes them unusable, as they stand, for field studies.

The transfer of the different ammoniacal species is based on the convection-dispersion model. Transfer is assumed to be entirely vertical (van der Molen et al., 1990a, b; Génermont and Cellier, 1997) between two layers of the soil by van der Molen et al. (1990a, b, the first is involved in volatilisation, and the second acts as a reservoir) or explicitly between several soil layers down to a depth of 1 m in the model of Génermont and Cellier (1997). In contrast, the model of Wu et al. (2003) takes into consideration both the horizontal transportation and vertical transfer of the ammoniacal species. Sometimes the transportation of the ammoniacal species within the soil as a result of the flow of water is ignored as done by Fleisher et al. (1987), which makes this model unreliable if rain or irrigation occurs during the volatilisation episode.

Despite these differences, the description of the «soil» compartment is relatively similar in the different mechanistic models, but this is not the case for the «atmosphere» compartment. The way the transfer term in the core equation is calculated is specific to each model. It is calculated from the wind speed and a coefficient of penetration (Fleischer et al. 1987;

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Rachhpal-Singh and Nye, 1986; Wu et al. 2003). This parameterisation is the one most similar to the empirical models. The transfer term can also be calculated from the sum of the different types of resistance (resistance in boundary layer of the soil surface, resistance of the boundary layer of the atmosphere and resistance of the soil) to the transfer of ammonia (van der Molen, 1990a, b; Sommer and Olesen, 2000). This approach has the advantage of taking into account the stability of the atmosphere, but two of the types of resistance involved (atmospheric and soil limit layers) are calculated empirically.

The third approach adopted by Génermont and Cellier (1997) differs somewhat from the ones described above, because it does not calculate a vertical transfer of the ammonia into the atmosphere, but estimates the flow using an advection model (Itier and Perrier, 1976). The ammonia fluxes are obtained by comparison with an upwind area. The range of models available makes it possible to use them for areas ranging from a few m2 to several hectares, making it possible to simulate both experimental and field conditions.

The diurnal kinetics of volatilisation are highly dependent on temperature changes on the surface of the soil (Sharpe and Harper, 1995) which depends on the time of day; it is greatest at midday and lowest in the evening, morning and during the night. In most of the other mechanistic models, the temperature used to calculate the equilibria is sometimes the air temperature (Sommer and Olesen, 2000; Wu et al., 2003 ), or no temperature correction is indicated at all (Fleisher et al., 1987; Rachhpal-Singh and Nye 1986-1988). Only the model of Génermont and Cellier (1997) calculates the surface temperature from meteorological data using a simplified module for assessing the surface energy.

Changes in the pH during the volatilisation episode are not taken into account by the mechanistic models, except in those of Sommer and Olesen (2000) for slurries, and of Rachhpal-Singh and Nye (1986-1988) for urea. These modules cannot be used as they stand for all synthetic fertilisers, and do not take into account the other biological processes that influence the pH, such as nitrification, for instance.

Finally, when these models are resolved implicitly (as in the model of Rachhpal-Singh and Nye, for instance), they cannot be easily adapted to keep pace with new discoveries. A modular approach and explicit resolution (e.g. the model of Génermont and Cellier) makes it possible to investigate the influence of the factors on volatilisation separately, as well as to investigate the interactions between them, and this means that they can quickly be adjusted after adding other modules.

ConclusionsThere are about 17 models available for calculating the volatilisation of ammonia after fertiliser application. There are equal numbers of empirical and mechanistic models (7 of each), but fewer semi-mechanistic models (3). Of the 17 models described, the synthetic fertilisers are covered by 7 models (4 empirical models, 1 intermediate and 2 mechanistic models). The synthetic fertiliser modelled is usually urea (5, including 1 mechanistic model), followed by ammonium salts (3 models, 2 of them empirical) and nitrogenous solutions (1 empirical model). This means that they are severely under-represented compared to the organic fertilisers (mainly slurries). There is no mechanistic or empirical model that is applicable to both synthetic and organic fertilisers, except VOLT’AIR.

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Table 10: Summary of principal ammonia volatilisation models for the land application of manures and fertilisers (E: Empirical, EM: Intermediate, M: Mechanistic, B.S.: Bare Soil, F.C., Field Conditions, L.C., Laboratory Condition, AS : Ammonium Sulphate, AN : Ammonium Nitrate, DAP : DiAmmonium Phosphate)

Type Authors Model Conditions Fertiliser Soil Air Validation Objective

E Fenn et Kissel (1973-1976)

B.S. + L.C. AS, DAP, AN - - yes Predictive

E Stevens et al. (1989)

Logistic model. dynamic

B.S. + L.C urea - - no Cognitive + predictive. Treatment comparison in laboratory

E Ismail et al. (1991)

Logarithmic model. dynamic

B.S. + L.C urea - - yes Cognitive + predictive.

E Sommer et Ersbøll (1994)

Dynamic B.S. + F.C. slurry - - Cognitive + predictive. Sol practice comparisons

E Demeyer et al. (1995)

Logistic model. dynamic

B.S. + L.C. AS, AN, urea, N solutions.

- - yes Cognitive. Fertiliser comparison in laboratory conditions

E Menzi et al. (1998)

Grassland + F.C.

slurry - - no Predictive. Comparison of experiments

E Søgaard et al. (2002)

Michaelis- Menten kinetics. Dynamic. Conceived from a EU data base

slurry - - no Predictive

EM English et al. (1980)

Dynamic B.S. sewage sludge * * incomplete Cognitive.

EM Sherlock and Goh

(1984-1985)

Dynamic Pasture. + F.C.

urea/urine * incomplete Predictive

EM Hengnirum et al. (1999)

Sub-model of MANIMEA (Hengnirum et al., 1995)

B.S. + slurry

F.C.

slurry - * yes Predictive.

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M Fleisher et al. (1987)

Dynamic B.S. + L.C. (NH4+)aYb * yes Predictive

M van der Molen et al. (1989-1990)

Dynamic B.S. + F.C. slurry yes Cognitive + predictive

M Racchpal-Singh and Nye (1986a, b, c) ; Kirk and Nye (1991a, b)

Dynamic B.S. + L.C.

B.S. +F.C.

urea

urea

-

*

yes

no

Predictive (laboratory)

Predictive (field)

M Olesen and Sommer (1993)

Dynamic B.S. +wheat straw +F.C.

slurry yes Cognitive

M Génermont and Cellier (1997)

Dynamic B.S. + F.C. slurry yes Cognitive + predictive

M Sommer and Olesen (2000)

Dynamic BS + crops + F.C.

slurry Cognitive + predictive

M Wu et al. (2003)

Dynamic B.S. + F.C. swine slurry yes Cognitive + predictive.

The following section contains detailed critical analyses of the following models:

Model Type Reference

PLÖCHL Empirical Plöchl (2001)

ALFAM Empirical Sogaard et al. (2002)

Volt’Air Mechanistic XX

STAL Mechanistic Morvan (1999)

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Evaluation of PLOCHL

Critical Analysis Criteria PLÖCHL (Plöchl, 2001)a) What is the model for? Developed for simulating ammonia volatilisation after manure

application.Ammonia fluxes are calculated from Michaelis-Menten kinetics whose parameters (Nmax, maximal ammonia losses and Km, time at N=Nmax/2) are calculated from a neural network approach. The neural network was trained with 51 experimental EU datasets of ammonia emission time courses and 15 driving parameters.

b) Common processes No common processes with other models (VOLT’AIR, PASIM, Olesen & Sommer) because the model is empirical.

c) Parameters that need measuring or estimating

None.The 2 model parameters were nevertheless calculated from 51 experimental dataset of 15 driving parameters :manure characteristics : dry matter, pH-value, TAN, applied Ammoniumvegetation type (bare soil, grassland, shoots or residue)daily climates at 1st day and at 2nd day : minimum and maximum temperature, precipitation, wind speed, solar radiation

d) Limits in application and extrapolation

The soil is poorly detailed (pH-value, initial water content, hydrodynamical parameters).

e) Strengths of parts or whole

Varied experimental databases are represented (many sites and authors).

f) Weaknesses of parts or whole

No specificity.No submodel equations are given to calculate the Michaelis-Menten parameters. Any improvement can only be made by training and testing the neural network with new datasets.

g) How mechanistic and empirical it is

Empirical only.

h) Ability to deal with abatement processes

Abatement measure

Comments

Reduction in fertiliser application rate

yesSummer application of N in wet periods

yes (wet periods can be expressed by rainfall, not by soil water content)

Irrigation after fertilizer application

yes (irrigation may be treated as precipitation)

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Critical Analysis Criteria PLÖCHL (Plöchl, 2001)Abatement measure

Can be modelled?

Use of an urease inhibitor to reduce NH3 volatilisation from applied urea (from NZ Ministry of Agric. and Forestry)

no

Applying manure and slurries at night (colder temperatures and lower wind speeds)

no

Applying manure and slurries in winter (colder temperatures)

yes

Reducing water content of slurries

yes by increasing the dry matter content

Applying slurry/manure after canopy has grown to reduce wind speed at emitting surface

no (the neural network was not trained in this situation)

Applying slurry/manure during rainfall

no (daily variables)Soil management before application

yes (bare soil, grassland, shoots, or residue)

Incorporation after surface application

noBand spreading/slurry injection application method

no

Acidification before application

yes

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Evaluation of ALFAM

Critical Analysis Criteria ALFAM

Søgaard H.T., Sommer S.G., Hutchings N.J., Hujismans J.F.M., Bussink D.W., Nicholson F.

a) What is the model for?

Developed for simulating ammonia volatilisation after slurry (different types and pre-treatment) applicationAmmonia fluxes are calculated from a Michaelis-Menten kinetics whose parameters (Nmax, maximal ammonia losses and Km, time at N=Nmax/2) are calculated from a regression model. The regression model was conceived from an EU database. 10 parameters are included to calculate the Michaelis-Menten parameters. 10 submodels were performed to estimate each parameter, then used to calculate the Michaleis Menten parameters

b) Common processes

No common processes with others models (VOLTAIR, PASIM, Olesen et Sommer), because. Alfam is an empirical model

c) Parameters that need measuring or estimating

none

d) Limits in application and extrapolation

pH value of the slurry is not taken into account when calculating the michaelis menten parameters

e) Strengths of parts or whole

Lot of application methods modelled: 1) band spred/trailing hose and 2) open slot injection, closed slot injection, pressurised injection (vs. Broadcast spreading).Different types of ammonia measurement techniques (wind tunnel, micromet., Lennart boxes –dynamic chambers)

f) Weaknesses of parts or whole

slurry pH not taken into accountNo significance of the slurry application techniquesNo significance of the incorporation of slurry (vs. Shallow cultivation)Min. T°C can be –6°C but specificities of frozen soils are not modelled

g) How mechanistic and empirical it is

Empirical only

h) Ability to deal with abatement processes

Abatement measure Can be modelled?Reduction in fertiliser application rate

yes

Summer application of N in wet periods

Yes

Irrigation after fertiliser application no

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Critical Analysis Criteria ALFAM

Søgaard H.T., Sommer S.G., Hutchings N.J., Hujismans J.F.M., Bussink D.W., Nicholson F.Use of an urease inhibitor to reduce NH3 volatilisation from applied urea(from NZ Ministry of Agric and Forestry)

no

Applying manure and slurries at night (colder temperatures and lower wind speeds)

yes

Applying manure and slurries in winter (colder temperatures)

yes

Reducing water content of slurries yes by the % dry matterApplying slurry/manure after canopy has grown to reduce wind speed at emitting surface

Applying slurry/manure during rainfall

no

Soil management before application noIncorporation after surface application

yes

Band spreading/slurry injection application method

yes

Acidification before application no

Evaluation of Volt’Air

Critical Analysis Criteria

Volt’Air

a) What is the model for?

Developed for simulating ammonia volatilisation after liquid organic waste and synthetic fertilizer application on arable land.Deals with the chemical and physical equilibria between the various species of ammoniacal N in the soil, the transfer of heat, water and ammoniacal N within the soil, and the transfers of ammonia, heat and evaporation between the topsoil and the lower atmosphere.Processes are simulated with short time intervals over several days, or several weeks following the application of ammoniacal nitrogen in the field. The model is composed of several sub-models:

1. description of the effect of agricultural practices on water and ammoniacal N repartition in the soil (includes 3 agricultural practices: fertilization, incorporation after surface application and irrigation, and takes into account the effect of the structural degradation of the soil surface layers on water infiltration after surface spreading of liquid organic wastes)

2. nitrification3. physical and chemical equilibria in the soil,4. pH evolution due to synthetic fertilizer application5. dissolution of pellets and discontinuity of ammoniacal-N sources

and pH6. urea hydrolysis7. soil transfers sub-models8. water transfer through the soil

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Critical Analysis Criteria

Volt’Air

9. aqueous and gaseous ammoniacal N transfers through the soil10. heat transfer in the soil11. energy budget, water and heat exchange between the topsoil and

the atmosphere (energy fluxes modelled are net radiation, sensible, latent and soil heat fluxes)

12. gaseous ammonia transfer from the soil to the atmosphere.b) Common

processesVOLT’AIR and STALGaseous ammonia transfer from the soil to the atmosphere thanks to an advection sub-modelPhysical and chemical equilibria (except adsorption for STAL)Infiltration (Volt’Air : mechanistic; STAL: empirical functions)Nitrification (not the same formalism)

c) Parameters that need measuring or estimating

Input driving variables needed on a hourly time step are:In the case of utilisation in the field:Global radiation or net radiation (W m-2) Precipitation rate (mm)Air temperature (°C)Water vapour pressure (mPa)Wind speed (m s-1)Surface NH3 concentration of the up-wind plot (g N-NH3 m-3)NH3 flux of the up-wind plot (g N-NH3 m-2 s-1)If available: Soil surface temperature (°C)Number of soil temperature measurementsDepth of soil temperature measurements (m)Soil temperatures (°C)In the case of utilization for wind-tunnel data:Air temperature (°C)Soil evaporation (mm)Wind speed (m s-1)NH3 concentration of the air entering the wind-tunnel (g N-NH3 m-3)NH3 flux of the up-wind plot (g N-NH3 m-2 s-1)Soil surface temperature (°C)If available: Number of soil temperature measurementsDepth of soil temperature measurements (m)Soil temperatures (°C)

Management variables needed for the simulation period:Fertilisation Day and hour of the fertiliser application (decimal day of year, the sun is at the highest position at the middle of the day)Type of fertiliser (liquid organic manure, ammonium nitrate pellet, prilled urea, ammonium nitrate urea solution)In case of liquid organic fertiliser: Theoretical amount of liquid organic manure applied (m3 ha-1)NH4-N (kg m-3)Dry matter content (% weight basis)pHIn case of ammonium nitrate pellets:Theoretical amount of Nitrogen applied (kg N ha-1)Fraction of N in form of NH4-NFraction of N in form of NO3-N

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Critical Analysis Criteria

Volt’Air

In case of prilled urea: Theoretical amount of Nitrogen applied (kg N ha-1)In case of ammonium nitrate urea solution:Theoretical amount of Nitrogen applied (kg N ha-1)Fraction of N in form of NH4-NFraction of N in form of NO3-NFraction of N in form of urea-NIncorporation for liquid organic manure or liquid fertiliserDay and hour of the fertiliser incorporation (decimal day of year, the sun is at the highest position at the middle of the day)Depth of incorporation (m)Proportion of the liquid really incorporated (no more in contact with air) ([0-1])IrrigationsNumber of irrigationsDay and hour of the irrigations (decimal day of year, the sun is at the highest position at the middle of the day)Amount of water (mm)

Information for the runDay of the beginning of the run (day of year)Day of the end of the run (day of year)Time step of the model (hour)Number of soil layers of the model Depth of the soil layers of the model (mm)

Site-specific parameters:Latitude (°)Reference height above soil surface for wind speed (m) Reference height above soil surface for air temperature (m) Reference height above soil surface for water vapour pressure (m) Albedo (proposition of tabulated values)Soil surface roughness length (m) (proposition of tabulated values)Infiltrability coefficient for spreading of liquid organic waste Fetch (m)And for each soil layer:Clay content (g kg-1)Parameter a for soil NH4

+ partitioning Parameter b for NH4

+ partitioningType of soil (obtained thanks to the texture among 11 types of soils) which allows for the proposition of tabulated values of hydraulic properties of the soilIf available: Bulk density (kg m-3)Soil porosity or saturated soil water content (m3/m3) Saturated head pressure (m) Saturated hydraulic conductivity (10-6 m s-1) Parameter b (acts on field capacity)

Initial conditions for each soil layer:soil ammonium (mol m-2) soil nitrate (mol m-2) soil pH soil water content (m3/m3) soil calcareous content (cmoles kg-1)

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Critical Analysis Criteria

Volt’Air

CEC (cobaltihexamine) (cmoles kg-1) organic Carbon (g kg-1)

d) Limits in application and extrapolation

The modelis valid for an abrupt change in surface concentration but with no roughness changedoes not account for competition between different ammonia volatilization processes, such as the mineralisation of organic matter, the immobilization of ammoniacal nitrogen, uptake by plants or oxidationdoes not simulate the changes of soil pH after slurry application over timedoes not allow for changes in the physical properties of the soil after the application of fertilizer, irrigation, or slurry incorporationdoes not take into account the effect of a crop canopy on the soil surface and therefore on the volatilization, or the possible reabsorption of the ammonia gas emittedhas only been tested by comparison to two experimental dataset comprising the first one : two treatments: slurry that was or was not incorporated after surface application the second one: five types of fertilisers ((1) ammonium nitrate pellets, (2) liquid ammonium nitrate, (3) prilled urea, (4) liquid urea, (5) liquid ammonium nitrate urea) with or without irrigation just before fertilisationCould be overcome thanks to the modular structure of the model

e) Strengths of parts or whole

In theory:the energy budget, together with heat transfer sub-model, makes the model operational as it allows calculation of soil temperatures from readily available meteorological data and soil descriptions. the advection sub-model makes it possible to account for local advection and makes the model suitable for field scale applications as well as experimental applications. It has been parameterised for wind-tunnel applicationsThe model takes account of the temperature of the surface of the soil (and not of the air) on a sufficiently small time scale (hourly or less) to be able to reproduce the true pattern of ammonia volatilisation and its diurnal kineticsMost of the sub-models have been validated separately before inclusion in the whole model

Readily observed:Volt’Air is able to simulate either high ammonia fluxes after liquid manure application or small ammonia fluxes after synthetic fertiliser application, with a relatively nice description of the dynamic of ammonia fluxes at a hourly time step, and a good one at a daily time step (excepted for the first day)

f) Weaknesses of parts or whole

The coefficients of the adsorption isotherm were empirically determined from measurements of a tropical soil, and may not be appropriate for European soils under temperate conditionsThe diffusion coefficient of ammoniacal N in water is taken to be the same for ammonia and ammonium ionsThe effect of the ionic strength is not taken into account, and solute activities are assumed to be equal to their molar concentrationspH for synthetic fertilizers: inadequate only in the context of the application of urea to alkaline soilsHigh in determination of the time lag for nitrification, no parameterisation

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Critical Analysis Criteria

Volt’Air

the transfers of water and solutes must be reworked:in the case of liquid manure applied in great amount: it does not simulate liquid manure pooling at the soil surface. The water and aqueous ammoniacal N infiltrate too fast. Consequently, ammoniacal N availability at the surface decrease too fast, and ammonia fluxes are underestimated, especially for the first day. One problem is that the water supplied with the slurry is added to the uppermost soil layer in the model. But, in fact, the aqueous phase of the slurry remains above the soil surface for several hours before actually entering the soil.In the case of synthetic fertilisers applied without or with very small amount of water: to deal with the first centimetre of soil as a separate entity so as to be better able to take into account the influence of the water content of the surface layer on the dissolution of the solid fertilizers and the hydrolysis of the urea.

g) How mechanistic and empirical it is

Mechanistic bases for each sub-model, with some empirical parameterisations Time and space have been discretised so as to provide a good compromise between computing time and model precision. The topsoil is divided into several layers, whose limits between layers increased quasi-geometrically: 2, 5, 10, 20, 50 and 100 cm. They can be changed to any depth progression. The physical and chemical properties within each soil layer are considered to be uniform. The time scale of each module is adapted to the mechanism described. It must be large enough to allow the physical and chemical equilibria to be established, but short enough to describe the rapid changes in surface fluxes, surface temperature and water transfers in the soil. The compromise between these constraints has resulted in a time step of 15 minutes, but this can be increased to several hours, as long as it is less than one day. The equations are solved either using an iterative scheme or numerical solutions.

h) Ability to deal with abatement processes

Abatement measure Volt’Air suitabilityReduction in fertiliser application rate

Yes through variation of input variable:Dose_theorique (slurry amount applied: kg m-2 or fertiliser ammonium applied: kg N m-2)In input file: (tech_cult.txt)

Summer application of N in wet periods

Yes through input variable:day and hour of fertiliser application(tech_cult.txt)

Irrigation after fertilizer application

Yes through input information:Nb_irrigation, day and hour of irrigation(s), quantity of water applied (mm)(tech_cult.txt)

Use of an urease inhibitor to reduce NH3 volatilisation from applied urea(from NZ Ministry of Agric and Forestry)

Possibly by integrating a parameterization of the effect of the inhibitor

Applying manure and slurries at night (colder temperatures and lower wind speeds)

Yes through input variable:day and hour of fertiliser application(tech_cult.txt)

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Critical Analysis Criteria

Volt’Air

Applying manure and slurries in winter (colder temperatures)

Yes through input variable:day and hour of fertiliser application(tech_cult.txt)

Reducing water content of slurries

Yes through variation of input variable:%DM of slurry In input file: (slurry.txt)

Applying slurry/manure after canopy has grown to reduce wind speed at emitting surface

Don’t think so

Applying slurry/manure during rainfall

Yes through input variable:day and hour of fertiliser application(tech_cult.txt)

Soil management before application

Not for the moment

Incorporation after surface application

Yes through input variables:day and hour of incorporation, depth of incorporation, effectiveness of incorporation(tech_cult.txt)

Band spreading/slurry injection application method

Not for the moment, but could be integrated during this project by improving the “agricultural practices“ sub-model

Acidification before application Yes through variation of input variable:By fixing soil or slurry pH(soil.txt or slurry.txt)

i) Small improvements which could be operated during the DEFRA project

Improvement of the parameterisation of the model for making it suitable the extrapolation for wind-tunnel experimentsImprovements of the “agricultural practices“ sub-modelAbility to deal with injection, band spreading…Ability to deal with several soil management practices during one run, before and/or after applicationAbility to simulate ammonia volatilisation during application, depending on the type of application technique (splash plate, sprinkler application).

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Evaluation of STAL

Critical Analysis Criteria

STAL

a) What is the model for?

Developed for simulating ammonia volatilisation after liquid organic waste application on arable land, in order to quantify the N fertilising value of slurries, and to calculate environmental risks due to slurry applicationsThe model is composed of 2 coupled sub-models Volatilisation-Biotransformations and simulates:volatilisationnitrificationgross immobilisationgross mineralisation

b) Common processes

VOLT’AIR and STALGaseous ammonia transfer from the soil to the atmosphere thanks to an advection sub-modelPhysical and chemical equilibria (except adsorption for STAL)Infiltration (Volt’Air : mechanistic; STAL: empirical functions)Nitrification (not the same formalism)

c) Parameters that need measuring or estimating

Input driving variables needed on a hourly time step are:Precipitation rate (mm)Air temperature (°C)Wind speed (m s-1)

Management variables needed for the simulation period:Slurry application Day and hour of the fertiliser applicationOrganic C brought by the slurry (g C g-1 soil or kg C ha-1)Organic N brought by the slurry (g N g-1 soil or kg N ha-1)Ammoniacal N brought by the slurry (g N g-1 soil or kg N ha-1)Dry matter content (% weight basis)pH of the soil surface after slurry applicationSoil surface status/porosityAmmoniacal N in the first cm of the soil (kg N ha-1)Parameter for the depth of contribution to ammonia volatilisationIncorporation Day and hour of the incorporationA parameter for the incorporation

Site-specific parameters:Latitude (°)Friction velocity u* (m s-1)Soil surface roughness length (m) (proposition of tabulated values)Fetch (m)

Soil / slurry parameters:C org ini / N org iniC/N for both compartmentYield of C assimilationi/Cmin ratio ( µg N µg-1 C)Decomposition constant for both compartmentsGrowth rate of nitrifying biomass (cellules µg-1 N)Mickaëlis constant (µg N g-1 soil or kg N ha-1)

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Critical Analysis Criteria

STAL

d) Limits in application and extrapolation

The modelOnly valid for the conditions for which the empirical functions have been established; acid loamy soils of Western North of France

e) Strengths of parts or whole

In theory:parameters and variables quite easy to obtain the advection sub-model makes it possible to account for local advection and makes the model suitable for field scale applications as well as experimental applications.accounts for competition between different ammonia volatilization processes, such as the mineralisation of organic matter, the immobilization of ammoniacal nitrogen

f) Weaknesses of parts or whole Empirical functions for transfer into the soil and for pH determination of

soil-slurry complex: parameterisation

g) How mechanistic and empirical it is

The sub-model “volatilisation” of STAL is based on a simplified description of the physical and chemical processes implied in ammonia volatilisation and on an empirical approach of infiltration of ammoniacal N into the soil and of pH increase within the soil due to slurry application.

h) Ability to deal with abatement processes

Abatement measure STAL suitabilityReduction in fertiliser application rate

Yes through variation of input variable

Summer application of N in wet periods

Yes through input variable

Irrigation after fertilizer application YesUse of an urease inhibitor to reduce NH3 volatilisation from applied urea(from NZ Ministry of Agric and Forestry)

Possibly

Applying manure and slurries at night (colder temperatures and lower wind speeds)

Yes through input variable:day and hour of fertiliser application

Applying manure and slurries in winter (colder temperatures)

Yes through input variable:day and hour of fertiliser application

Reducing water content of slurries Yes through variation of input variable:%DM of slurry and increasing infiltration (function of infiltration due to rainfall)

Applying slurry/manure after canopy has grown to reduce wind speed at emitting surface

Yes

Applying slurry/manure during rainfall

Yes through input variable:day and hour of fertiliser applicationand use of function of infiltration due to rainfall

Soil management before application

Yes through input variable:ES

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Critical Analysis Criteria

STAL

Incorporation after surface application

Yes through input variable:Enf

Band spreading/slurry injection application method

Not for the moment, but could be integrated during this project by improving the “agricultural practices“ sub-model

Acidification before application Yes through variation of input variable:pH of soil slurry pH after surface application

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Kirk G.J.D., Nye P.H., 1991a. A model of ammonia volatilization from applied urea. V. The effect of steady-state drainage and evaporation. J. Soil Sci., 42, 1, 103-113.

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Menzi H., Katz P.E., Fahmi M., Netfel A., Frick R., 1998. A simple empirical model based on regression analysis to estimate ammonia emissions after manure application. Atmos. Environ., 32, 301-307.

Morvan T., 1999. Quantification et modélisation des flux d’azote résultant de l’épandage de lisier. Thèse université Paris 6, 146 p.

Ni J.Q., 1999. Mechanistic models of ammonia release from liquid manure, a review. J. Agric. Eng. Res., 72, 1-7.

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Olesen J.E., Sommer S.G., 1993. Modelling effects of wind speed and surface cover on ammonia volatilization from stored pig slurry. Atmos. Environ., Part A, 27, 16, 2567-2574.

Plöchl, M., 2001. Neural network approach for modelling ammonia emission after manure application on the field. Atmosph. Envir. (35): p. 5833-5841.

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Rachhpal-Singh, Nye P.H., 1988. A model of ammonia volatilization from applied urea. IV. Effect of method of urea application. J. Soil Sci., 39, 9-14.

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van der Molen J., Beljaars A.C.M., Chardon W.J., Jury W.A., van Faassen H.G., 1990b. Ammonia volatilization from arable land after application of cattle slurry. 1. Derivation of a transfer model. J. Agric. Sci., 38, 239-254.

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