Soil Science Society of America Journal 67:1-11 (2003)
© 2003 Soil Science Society of America
DIVISION S-1—SOIL PHYSICS
Modeling Ammonia Volatilization from Surface-Applied Swine Effluent
J. Wu,
D. L. Nofziger*,
J. G. Warren and
J. A. Hattey
Department of Plant and Soil Sciences, Oklahoma State University, Stillwater, OK 74078
* Corresponding author (dln{at}okstate.edu)
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ABSTRACT
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Ammonia volatilization is an important issue in agricultural production and environmental protection. Experimental methods and numerical models exist to estimate the rate and amount of ammonia volatilization from commercial fertilizers and animal manures applied to a field. The existing models imposed assumptions on water movement in a soil profile that were judged to be inadequate for surface-applied swine (Sus Domesticus) effluent. In this research, a computer model was developed to estimate short-term ammonia volatilization from swine effluent applied to a field by flood or sprinkler irrigation. The model simulates simultaneous water flow, heat flow, and the transport and transformation of ammoniacal N in a soil profile using the finite difference method. Submodels were developed to evaluate concentrations of ammoniacal N in the infiltration pond of a flood irrigation event and in the droplets of sprinkler irrigation. The governing equations for the water flow, heat flow, and chemical transport modules and the irrigation submodules were derived from mass balance and energy balance employing constitutive laws established empirically. The model was tested against data from field experiments using parameters obtained from independent sources. The simulation results were in excellent agreement with experimental data in three out of six experiments. In the other three experiments, the predicted cumulative volatilization exceeded the measured amount by 5 to 30 kg ha-1 at the end of 1 wk. The differences were primarily in the first sampling period after the application. The simulated cumulative volatilization was most sensitive to temperature, pH of the soil system, and pH of the effluent applied.
Abbreviations: E.C.E.T.O.C., European Centre for Ecotoxicology and Toxicology of Chemicals • IHF, integrated horizontal flux
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INTRODUCTION
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AMMONIA VOLATILIZATION from applied N fertilizer and animal manure significantly reduces the amount of ammoniacal N available for crop use. In calcareous soils, over 50% of ammoniacal N from ammonium nitrate (NH4NO3) incorporated into the topsoils may be lost to ammonia volatilization (Fenn and Escarzaga, 1977). Ammonia volatilization is also one of the largest sources of atmospheric ammonia that contributes to soil acidification and water eutrophication (Asman and van Jarrsveld, 1992; European Centre for Ecotoxicology and Toxicology of Chemicals [E.C.E.T.O.C.], 1994; Sutton et al., 1995). Therefore, enormous effort has been made to quantify ammonia volatilization from the soil surface. In the 1970s and 1980s, laboratory and field experiments were conducted to measure ammonia volatilization from urea incorporated in a soil profile (Fenn and Escarzaga, 1977; Khengre and Savant, 1977; McInnes et al., 1985; Reynolds et al., 1985). In the 1990s the integrated horizontal flux method and micrometerological methods were used to measure ammonia volatilization from slurry and swine effluent applied to land surface (Genermont and Cellier, 1997; Schjoerring et al., 1992; Zupancic et al., 1999). Mathematical models were developed to extend experimental results to different climate–soil management conditions (Genermont and Cellier, 1997; Rachhpal-Singh and Nye, 1986; Kirk and Nye, 1991). Genermont and Cellier's model was developed for estimating ammonia volatilization from surface-applied slurry while Rachhpal-Singh and Nye's and Kirk and Nye's models were for estimating ammonia volatilization from urea incorporated in a soil profile. In the model developed by Genermont and Cellier (1997), Darcy's law was employed to evaluate the flux density of vertical water flow. But no transient flow conditions were considered in the model. Kirk and Nye (1991) expanded Rachhpal-Singh and Nye's (1986) model to account for the effects of transient-state water evaporation, but the model cannot simulate water flow during infiltration. Since none of the above-mentioned models could simulate the infiltration process at the soil surface, they were considered inadequate for simulating transport and transformation of ammoniacal N in a soil profile under swine-effluent irrigation.
The main objective of this research was to develop a mechanistic model to predict short-term (such as a week) ammonia volatilization from swine effluent applied to a field during and after a flood or sprinkler irrigation event. The case of flood irrigation was included to simulate field experiments. The main body of the model developed in this research simulates simultaneous water flow, heat flow, and the transport and transformation of ammoniacal N in a soil profile using finite difference methods. Submodels were also developed to estimate the concentrations of ammoniacal N in the infiltration pond of a flood irrigation event or the droplets of a sprinkler irrigation event.
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General Description of the Model
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The mechanistic ammonia volatilization model consists of modules simulating water infiltration and ammonia volatilization during an irrigation event, water evaporation, and ammonia volatilization from the soil surface after an irrigation event, and transport and transformation of ammoniacal N in a soil profile during and after an irrigation event. The ammonia volatilization model incorporates the effect of the major factors illuminated by previous investigations. These include soil and effluent pH, soil and air temperature, wind speed, application rate of the source of ammoniacal N, soil wetness and soil hydraulic properties (Ismail et al., 1991). The transport-and-transformation module is the main body of the model. It is made up of three submodules simulating water flow, heat flow, and the transport and transformation of ammoniacal N in a soil profile. The water flow and heat flow modules were included to provide information on soil wetness and soil temperature, which were needed for the computation of the parameters in the transport-and-transformation module. The transport-and-transformation module produces concentrations of ammoniacal N at different depths in a soil profile. The rate of ammonia volatilization from soil surface was determined from the concentration of ammoniacal N at the soil surface. The governing equations of all the modules were derived from mass and energy balances. Constitutive relationships such as Darcy's law, Fourier's law, and Fick's law were employed to specify the fluxes of water, heat, and ammoniacal N. Henry's law, the equilibrium constant of the NH+4
NH3 reaction, and linear adsorption-desorption isotherms were used to quantify the transformation among the component ammoniacal N species in a soil system.
The governing equations for water flow and heat flow are well established in the literature (Hillel, 1998; Scott, 2000). The focus of this research is the transport and transformation of ammoniacal N in a soil system. Because of the complexity of the processes involved, the following simplifications were introduced in the derivation of the governing equation for the transport-and-transformation model: (i) soil pH is not affected by the current application of swine effluent; (ii) the transformation reactions among the component species of ammoniacal N reach equilibrium instantaneously; (iii) contribution of ammoniacal N from mineralization of soil organic matter and loss of ammoniacal N through immobilization and nitrification are insignificant compared with volatilization loss for the small time of interest in this research; (iv) adsorption-desorption reactions of ammoniacal N species in soil follow linear equilibrium isotherms; (v) convective movement of soil air is insignificant and transport of gas-phase ammonia in soil is controlled by diffusion; (vi) transport of liquid-phase ammoniacal N is controlled by the convection-dispersion process.
A submodel for ponded infiltration was developed to estimate ammoniacal N concentration in the ponding layer of a flood-irrigation event. The concentration is needed to specify the upper boundary condition of the transport-and-transformation model during a flood irrigation event. Concentration of ammoniacal N in the ponding layer is also needed for evaluating ammonia volatilization rate during a flood-irrigation event. Equations in the ponded-infiltration submodel were derived from mass balance of water and ammoniacal N. The following simplifications were introduced in this submodel: (i) swine effluent was surface applied instantaneously in a flood irrigation event; (ii) distribution of ammoniacal N is uniform in the ponding layer.
Another submodel for droplet volatilization was developed to estimate ammoniacal N concentration of a droplet when it hits the ground. Droplet ammonium concentration at the soil surface is needed to specify the upper boundary condition of the transport-and-transformation model during a sprinkler-irrigation event. The droplet-volatilization submodel also evaluates the loss of ammoniacal N from a droplet during its exposure time in the air. Equations of the droplet volatilization submodel were derived from mass and energy balance in a droplet. Distributions of ammoniacal N and liquid temperature inside a droplet were assumed uniform in the derivation.
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Development of the Transport-and-Transformation Model
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Mass Balance of Ammoniacal Nitrogen in Soils
Transport of ammoniacal N in a soil system is a multiphase, multispecies process. There are ammonium ions (NH4+[aq]) and dissolved ammonia (NH3[aq]) in soil solution, gaseous ammonia (NH3[g]) in soil air, adsorbed NH4+(ad) and NH3(ad) at the solid–liquid interface, and adsorbed NH3(ad) at the solid–air interface. The total concentration of ammoniacal N in a soil system is the sum of the concentrations of all the component species in the three phases of the soil system
 | [1] |
where Ct is the total concentration of ammoniacal N in a soil system, which is defined as the amount of ammoniacal N in unit bulk volume of soil (kg m-3 bulk soil); SNH+4 is the concentration of ammoniacal N in the form of adsorbed ammonium ion at the solid–liquid interface (kg kg-1 dry soil); SNH3 is the concentration of ammoniacal N in the form of adsorbed ammonia at the solid–liquid interface (kg kg-1 dry soil); SNH3
is the concentration of ammoniacal N in the form of adsorbed ammonia at the solid–air interface (kg kg-1 dry soil); CNH+4 is the concentration of ammoniacal N in the form of ammonium ion in soil solution (kg m-3 solution); CNH3 is the concentration of ammoniacal N in the form of dissolved ammonia in soil solution (kg m-3 solution); CNH3 is the concentration of ammoniacal N in the form of gaseous ammonia in soil air (kg m-3 soil air); 
b is the bulk density of the soil (kg m-3); 
s is the porosity of the soil (m3 m-3); and is the water content of the soil (m3 m-3).
The total flux of ammoniacal N crossing a horizontal plane is the sum of the dispersive and convective fluxes for aqueous ammonium ion and ammonia in soil solution and the diffusive flux for gaseous ammonia in soil air. Mathematically the total flux can be expressed as
 | [2] |
where Jt the total flux of ammoniacal N crossing a horizontal plane (kg m-2 s-1); DNH+4 is the dispersion coefficient of ammonium ion in soil solution (m2 s-1); DNH3 is the dispersion coefficient of dissolved ammonia in soil solution (m2 s-1); DNH3 is the diffusion coefficient of gaseous ammonia in soil air (m2 s-1); q is the flux density of soil solution (m s-1); t is time (s); and z is the vertical coordinate starting from the soil surface and positive downward (m).
Within a relatively short period (such as a week) during and after a swine-effluent-irrigation event, the contribution of ammoniacal N from mineralization of soil organic matter and the loss of ammoniacal N because of immobilization (such as plant uptake) and nitrification are expected to be negligible compared with ammonia volatilization from soil surface. Neglecting the effect of mineralization, immobilization, and nitrification, the mass balance of ammoniacal N in a soil system can be expressed as
 | [3] |
Transformation of Ammoniacal Nitrogen in Soils
Ammoniacal N in swine effluent exists mainly in two species: NH+4 and NH3(aq). Upon entering a soil system, the two component species are distributed into the three phases of the soil system through adsorption–desorption reactions at the solid–liquid and solid–air interfaces, and the transformation of NH3(aq) into NH3(g) at the liquid–air interface. Assuming a linear equilibrium isotherm for the adsorption–desorption reactions, concentrations of the adsorbed species are related to those of their corresponding reactants by the following system of equations:
 | [4] |
where KNH+4 is the partition coefficient for liquid-phase ammonium ion (m3 kg-1), KNH3 is the partition coefficient for liquid-phase ammonia (m3 kg-1), and KNH3 is the partition coefficient for gas-phase ammonia (m3 kg-1). The concentrations of ammonium ion and dissolved ammonia in soil solution are related to each other by
 | [5] |
where Ka is an equilibrium constant for the following Bronstead acid-base reaction in soil solution:
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CH3O+ is the molar concentration of hydronium ion in soil solution (mol L-1) and is related to soil pH by
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Assuming instantaneous equilibrium between gas-phase and liquid-phase ammonia, we have
 | [8] |
where KH is Henry's constant for the dissolution of ammonia in soil solution.
Equations [4], [5], and [8] reveal that under equilibrium conditions the concentrations of all the component species of ammoniacal N in a soil system are related to each other. Given the concentration of any of the component species, the concentrations of all other component species and the total concentration of ammoniacal N in the soils system can be evaluated from the known concentration.
Governing Equation and Parameter Specification
Substituting the total concentration and total flux of ammoniacal N in Eq. [1] and [2] into Eq. [3] of mass balance gives
 | [9] |
Selecting the concentration of ammonium ion in solution as a dependent variable, plugging in the relationships between concentrations of the component species in the Eq. [4], [5], and [8] into Eq. [9], and rearranging yield the following governing equation for ammoniacal N transport in a soil profile
 | [10] |
where
 | [11] |
and
 | [12] |
The dispersion coefficients, DNH+4, and DNH3, and diffusion coefficient, DNH3 in a soil system are related to the corresponding coefficients in water and air by (Marshall and Holmes, 1988; Moldrup et al., 1997; Olesen et al., 1999)
 | [13] |
where 
L is the dispersivity of the soil medium (m), DNH+4,water is the diffusion coefficient of ammonium ion in water (m2 s-1), DNH3,water is the diffusion coefficient of dissolved ammonia in water (m2 s-1), 
w() is the impedance factor of water flow path in the soil medium at a water content , DNH3,air is the diffusion coefficient of ammonia in free air (m2 s-1), a() is the impedance factor of the air flow path in the soil medium at a water content . The dependence of the impedance factors on soil-water content can be expressed as (Moldrup et al., 1997; Olesen et al., 1999)
 | [14] |
where 0.022b equals the threshold soil water content at which solute diffusion ceases because of disconnection of the continuous water films, b is a pore-size distribution parameter which is estimated from the percentages of clay and fine sand particles using the equation (Moldrup et al., 1997; Williams et al., 1992)
 | [15] |
where fclay and fFS are the mass percentages of clay (<0.002 mm in diameter) and fine sand (0.02–0.2 mm in diameter) particles, respectively.
Temperature Dependence of Transformation and Transport Parameters
The equilibrium constant Ka, Henry's constant KH, and diffusion coefficients DNH+4,water, DNH3,water, and DNH3,air vary with temperature. The following empirical formulas were used to describe the dependence of these parameters on temperature (Beutier and Renon, 1978; Genermont and Cellier, 1997):
 | [16] |
where T (K) is the temperature of the fluids in which the acid-base reaction, liquid-gas transformation, and aqueous and gaseous diffusion occur, and R is the universal gas constant (0.008315 kJ mol-1 K-1). In this model we assume that the temperature of the soil solution is the same as that of the bulk soil. During ponding infiltration, we assume that the temperature of the ponding layer is the same as the temperature of the ambient air. DRefNH+4,water, DRefNH3,water, and DRefNH3,air (m2 s-1) are the diffusion coefficients at a reference temperature, TRef (K). At 25°C, the diffusion coefficients of aqueous ammonium ion and gaseous ammonia were taken as 1.96 x 10-9 m2 s-1 (Kemper, 1986) and 2.8 x 10-5 m2 s-1 (Incropera and DeWitt, 1990), respectively. The diffusion coefficient of dissolved ammonia was also taken as 1.96 x 10-9 m2 s-1.
Boundary Conditions for the Transport of Ammoniacal Nitrogen in a Soil Profile
Upper Boundary.
Transport and transformation of ammoniacal N at the upper boundary of a soil profile under swine-effluent irrigation is dependent on the way the effluent is delivered to soil surface. During a flood-irrigation event, the total flux of ammoniacal N into a soil profile equals the flux entering the soil profile with the infiltrating water. That is
 | [17] |
where Jt|z=0 is the total flux of ammoniacal N into a soil profile (m s-1 g L-1); K0a is the equilibrium constant of the NH+4NH3 reaction in the ponding layer of the irrigated effluent; pH0 is the pH value of the swine effluent in the ponding layer; C0NH+4 (g L-1) is the average concentration of ammoniacal N in the form of ammonium ion in the ponding layer; q0 (m d-1) is the infiltration flux of swine effluent into the soil profile from the ponding layer. C0NH+4 is evaluated in the submodule for flood irrigation. q0 is evaluated in the submodule for water flow.
During a sprinkler-irrigation event, the net flux of ammoniacal N into a soil profile equals the flux entering the soil profile with the infiltrating water minus the volatilization flux from soil surface. That is
 | [18] |
where Kdropa is the equilibrium constant of the NH+4 NH3 reaction in a droplet of a sprinkler-irrigation event; pHdrop is the pH value of the swine effluent in the droplet; ir is the effective intensity of the sprinkler irrigation event (m s-1); CdropNH+4 (g L-1) is the average concentration of ammoniacal N in the form of ammonium ion in the droplet; CNH3(g)|z=0 is the concentration of ammoniacal N in the form of gaseous ammonia at the soil surface (g L-1); CairNH3 is the background concentration of ammoniacal N in the form of ammonia in the air (g L-1); 0 is soil water content at the surface, and hm (m s-1) is the average mass transfer coefficient for ammonia transport across an ammonia concentration boundary layer at the soil surface of an irrigated strip. Because of ammonia volatilization from droplet surfaces, the ammoniacal N concentration of a droplet at the time it hits the ground may be different from the concentration of the source effluent. The ammoniacal N concentration in Eq. [18] is the average concentration of all the droplets of a sprinkler system at the time the droplets hit the ground. The average droplet concentration, CdropNH+4, is estimated in a droplet-volatilization submodule (Wu et al., 2002). The average mass transfer coefficient, hm, is estimated using the following empirical equation established for mass transfer across a turbulent-flow-dominated concentration boundary layer on a hydraulically smooth flat plate in a parallel flow of a binary fluid mixture (Genermont and Cellier, 1997; Incropera and DeWitt, 1990; Schlichting, 1968)
 | [19] |
where L is the width of the irrigated strip in the wind direction (m); u
is the wind speed across the irrigated strip (m s-1); 
is the kinematic viscosity of the air (m2 s-1). The kinematic viscosity is dependent on temperature and values of at different air temperatures were obtained through linear interpolation using the base points given by Incropera and DeWitt (1990).
The upper boundary condition for ammoniacal N transport in a soil profile after an irrigation event can be expressed as
 | [20] |
The gas-phase ammonia concentration at the soil surface is dependent on the concentration of ammonium ion in soil solution
 | [21] |
Lower Boundary.
The lower boundary for ammoniacal N transport in the soil profile can be set at a depth deep enough that the ammoniacal N from the manure application never reaches that depth, therefore
 | [22] |
where ZN is the depth set as the lower boundary for the transport of ammoniacal N (m).
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Development of the Ponded-Infiltration Submodel
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Assuming that the concentration of ammoniacal N in the infiltration pond is uniformly distributed, the mass balance of ammoniacal N in an infiltrating pond surrounded by an elevated border can be expressed as
 | [23] |
where C0NH3 (g L-1) is the concentration of ammoniacal N in the form of aqueous ammonia in the infiltration pond; C0NH3 (g L-1) is the concentration of ammoniacal N in the form of gaseous ammonia at the liquid-air interface of the infiltration pond; h0(t) is the thickness of the ponding layer (m); C0NH+4, CairNH3, q0, and hm are defined in the Eq. [17] and [18].
Applying Eq. [5] to [8] to the transformation of ammoniacal N in the infiltration pond, we obtain
 | [24] |
where C0H3O+ is the molar concentration of hydronium ion in the infiltrating pond (mol L-1); K0H is the Henry's constant for the dissolution of ammonia in the infiltrating pond; K0a and pH0 are defined in Eq. [17].
Expanding Eq. [23], substituting Eq. [24] into the expanded equation, and taking into account the fact that 
= -q0 yields
 | [25] |
Introducing 
= 1 + 
, ß = 
, and y = C0NH+4
, and rearranging Eq. [25], we obtain
 | [26] |
Solving Eq. [26] using the variation-of-parameter method (Loomis, 1982) and replacing y with C0NH+4 yields
 | [27] |
where (0) is the value of at time zero; C0NH+4 (0) is the initial concentration of ammoniacal N in the form of ammonium ion in the irrigated-swine effluent (g L-1). Variations of and ß are caused by the temperature dependence of the equilibrium constant K0a and the Henry's constant K0H, and the fluctuation of air temperature with time.
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Coupling the Component Modules
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Distributions of soil-water content and soil temperature in a profile are needed to evaluate the coefficients in the governing equation of ammoniacal N transport. Soil-water contents and soil temperatures in a profile are obtained by solving the water flow and heat flow equations. Since the volumetric heat capacity and thermal conductivity of a soil system are dependent on soil-water content (Hillel, 1998; Scott, 2000; Wu and Nofziger, 1999), the water flow equation must be solved before the heat flow equation. Because of the nonlinearity in the governing equation of water flow and the complexity in the expressions of the coefficients in all the governing equations and boundary conditions, numerical methods are employed to solve the problems. Temporal variations of the concentrations of ammoniacal N in a soil profile and the amount and rate of ammonia volatilization from soil surface are obtained by solving the initial-boundary problems of N transport, water flow, and heat flow in a stepwise manner. At each time step, the model evaluates the concentrations of ammoniacal N, soil-water potentials, and soil temperatures in a profile at the end of the time interval from those at the beginning of the interval. The water flow problem was solved first at a time step to determine water contents and Darcy velocities in the profile. Then the heat flow problem was solved for soil temperatures in the profile using the volumetric heat capacity and thermal conductivity calculated from water contents obtained in the solution of the water-flow problem (Farouki, 1986; Hillel, 1998; Wu and Nofziger, 1999). Measured data of hourly air temperature were used as the surface-soil temperature at the upper boundary of the heat-flow problem. The lower boundary was set at a location deep enough that soil temperature at such a depth is not significantly affected by temperature fluctuations at the soil surface. Since the lower boundary of the heat-flow problem was at a much deeper location than that of the water-flow and transport problems, mesh points used to solve the heat-flow problem are different from those used to solve the water-flow and transport problems. Linear interpolation was employed to evaluate soil temperatures at the mesh points of the water-flow and transport problems. Water contents at the mesh points of the heat-flow problem were also evaluated by interpolation. At locations below the lower boundary of the water-flow and transport problems, water contents at the mesh points of the heat-flow problem were set at the water content of the mesh point at the lower boundary of the water-flow and transport problem. Finally the N transport problem was solved for concentrations of ammoniacal N in the soil profile using the storage and transport parameters calculated from the water contents, Darcy velocities, and soil temperatures obtained in the solutions of water-flow and heat-flow problems.
During the infiltration phase of an irrigation event, a submodel is invoked at each time step to evaluate the concentration of ammoniacal N entering the soil profile. The submodel invoked is dependent on the irrigation method used. In the case of flood irrigation, Eq. [27] is used to calculate concentration of ammoniacal N entering the soil profile. For a sprinkler-irrigation event, the droplet volatilization model (Wu et al., 2002) is invoked to evaluate the average droplet concentration of ammoniacal N at the soil surface. The droplet volatilization model also calculates the amount of droplet volatilization of ammoniacal N from the sprinkler system.
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Evaluating Rate and Amount of Ammonia Volatilization
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A major objective of this model is to estimate the rate and amount of ammonia volatilization from surface-applied swine effluent. Like the specification of the upper boundary condition for the transport of ammoniacal N in a soil profile, the method for evaluating the rate and amount of ammonia volatilization is dependent on the irrigation method used to deliver swine effluent to a soil surface. During the infiltration phase of a flood-irrigation event, ammonia volatilization occurs at the liquid–air interface of the ponding layer instead of the soil surface. The volatilization rate during that time was calculated using the equation
 | [28] |
where Jvola(t) is the vertical flux of ammoniacal N at time t (kg ha-1 s-1).
During a sprinkler-irrigation event, ammonia volatilization loss includes droplet volatilization loss, wind drift loss, and volatilization loss from soil surface. Losses from wind drift and droplet volatilization may be estimated using the efficiency-coefficient method developed by irrigation engineers for estimating water losses from wind drift and droplet evaporation (Wu et al., 2002). The soil-surface-volatilization rate during a sprinkler-irrigation event was calculated using the following equation
 | [29] |
Equation [29] can also be used to evaluate soil-surface-volatilization rate during the redistribution phase after an irrigation event.
The cumulative volatilization up to time t for all the upper-boundary scenarios described above can be expressed as
 | [30] |
where mNH3 is the cumulative amount of ammoniacal N volatilized from unit area of soil surface and the surface of the ponding layer in flood irrigation (kg ha-1).
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Model Testing
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The partial differential equations for ammoniacal N transport, water flow, and heat flow in a soil profile were solved numerically using implicit finite difference schemes (Allen et al., 1988; Haverkamp et al., 1977). Explicit linearization was used to estimate the nonlinear coefficients in the water flow equation (Haverkamp et al., 1977; Nofziger et al., 1989). The numerical model was implemented in MATLAB on a PC and the computer model was tested against six sets of data from field experiments conducted in different seasons of the year (Warren, 2001; Zupancic et al., 1999).
The field experiments were conducted at the Oklahoma State University Panhandle Research Station located in Goodwell, OK (36° 36' 6'' N lat., 101° 36' 5'' W long.) in May, July, and September of 1998, July of 1999, and March and July of 2000. The swine effluent was applied to a bare soil of a Richfield clayey loam (fine, smectitic, mesic Aridic Argiustolls) by flood irrigation. The integrated horizontal flux (IHF) method (McInnes et al., 1985; Schjoerring et al., 1992) was employed to measure the volatilization rate from a circular area of 15.24 m in diameter. Detailed information on the experiments was given by Warren (2001) and Zupancic (1999).
Figure 1
and Fig. 2
show the comparison of the measured and simulated volatilization rate and cumulative amount of ammonia volatilized. The data points of different symbols in a graph represent measured data in different replicate plots of an experiment. The solid line represents simulation results. Simulated volatilization rates in Fig. 1 are average rates over different experimental sampling periods. Input data of management-related parameters for swine-effluent irrigation events are summarized in Table 1. Input data of climate-related parameters including hourly averages of air temperature, wind speed, precipitation, and solar radiation were taken from Mesonet observations. Air temperatures and wind speeds were measured at a height of 1.5 and 2 m, respectively. The Mesonet station was within 50 m of the experimental plots. The saturated hydraulic conductivity of the soil was estimated from observed ponding duration of a swine-effluent irrigation experiment (Warren, 2001). All other soil hydraulic properties were extracted from the UNSODA unsaturated soil hydraulic database based on soil texture (Leij et al., 1996). Flow and transport parameters of the soil medium used in model testing are summarized in Table 2.
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Fig. 1. Comparison of predicted average rate of ammonia volatilization loss with field data measured in different seasons. Symbols represent measured data of different replicates, and solid lines are simulation results.
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Fig. 2. Comparison of predicted cumulative ammonia volatilization loss with field data measured in different seasons. Symbols represent measured data of different replicates, and solid lines are simulation results.
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Both the experimental data and simulation results revealed large seasonal changes in percentage of volatilization loss of ammoniacal N from surface-applied swine effluent primarily because of changes in air temperature and wind speed. About 50% of ammoniacal N was lost at the end of 1 wk after a swine-effluent-irrigation event on 28 May 1998. The loss was <20% when swine effluent was applied on 28 Mar. 2000. The simulated volatilization rate in Fig. 1(a) to 1(f) matched well with the measured data. However, significant discrepancies between the simulation results and the measured data occurred in three of the cumulative volatilization curves (see Fig. 2b, 2d, and 2f). Examining the volatilization-rate curves in Fig. 1d and 1f revealed that the discrepancies in the cumulative curves were caused mainly by the differences of the volatilization rate in the first sampling period of the experiments. Starting from the end of the first sampling period, the curves of the simulated cumulative volatilization losses in Fig. 2d and 2f are basically parallel to the measured data. In Fig. 2b, the significant discrepancy between the simulated and measured cumulative volatilization loss began at the end of the third sampling period. The simulated volatilization rate in Fig. 1b basically went through the upper limits of the measured data points. Starting from the end of the third sampling period, the curve of the simulated cumulative volatilization loss in Fig. 2b also runs parallel to the measured data. The averages of the air temperature and wind speed for the whole week and during the first sampling period for the field experiments are summarized in Table 3.
In the IHF method, the volatilization rate was determined by integrating horizontal fluxes measured at different sampling heights. This method may underestimate the volatilization rate during the early period of an experiment when the concentration boundary layer is not fully developed. Before the top of the concentration boundary layer reached the first horizontal-flux sampler at the bottom of a sampling mast, the samplers would not catch any of the volatilized ammonia. This underestimation is expected to increase with the increase in wind speed, temperature, and the height of the first horizontal-flux sampler. The average wind speeds and air temperatures of the three experiments performed in July of 1998, 1999, and 2000 were among the highest observed (Table 3). This might explain why the measured volatilization rates in the first sampling period of these three experiments were lower than the simulated rates.
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Sensitivity Analysis
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The input parameters of the mechanistic model may be divided into groups of soil-related parameters, weather-related parameters, and management-related parameters. Soil-related parameters include soil hydraulic properties, transport and reaction properties of ammoniacal N in a soil medium, and particle-size distribution of the soil medium. Weather-related parameters include wind speed, air temperature, solar radiation, and relative humidity. Management-related parameters include the amount of swine effluent applied, concentration of ammoniacal N in the effluent, effluent pH, and width in the wind direction of the field where swine effluent is applied. Figure 3
demonstrate the sensitivity of cumulative ammonia volatilization loss to soil texture, soil pH, air temperature, and wind speed. Clay-loam-textured soil, Mesonet weather data at Goodwell, OK between 28 May 1998 and 4 June 1998, and the management-related parameters from the experiment starting on 28 May 1998 were used in the simulations of sensitivity analysis if not indicated otherwise.
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Fig. 3. Sensitivity of cumulative ammonia volatilization loss to soil texture, soil pH, air temperature, and wind speed. Time started from the beginning of simulated irrigation events.
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The difference in simulated cumulative volatilization loss at the end of 1 wk after an irrigation event between a clay-loam textured soil and a silt-loam-textured soil is <5%. The hydraulic parameters of the clay-loam and silt-loam textured soils are shown in Table 4. A 0.2-unit decrease in soil pH from 8.1 caused an 8% decrease in simulated cumulative volatilization loss. The 0.2-unit is the expected deviation of lab-measured pH value of an individual soil sample (Dr. Hailin Zhang, personal communication, 2000). The difference in simulated volatilization loss caused by a change in soil texture from clay loam to silt loam is less than that caused by the uncertainty in lab-measured pH value of a soil sample. Changes in air temperature also resulted in considerable change in simulated cumulative volatilization loss. Raising the set of temperatures measured between 28 May 1998 and 4 June 1998 by 5°C caused a 13% increase in the simulated cumulative volatilization loss while lowering the temperatures by 5°C caused a 16% decrease in the simulated cumulative volatilization loss. The sensitivity of the simulated cumulative volatilization loss to changes in wind speed varies with the magnitude of the wind speed. Reducing the set of wind speeds measured between 28 May 1998 and 4 June 1998 by 50% caused a 13% decrease in simulated cumulative volatilization loss at the end of 1 wk while increasing the wind speeds by 50% caused a 6% increase in the simulated cumulative volatilization loss.
To aid decision-making in swine-effluent irrigation, we need to predict ammonia-volatilization loss under future weather conditions. Since future weather is unknown, historical weather data of the same season is often used for making simulations. Under such conditions, variation in weather conditions of the same season over different years largely determines the quality of the predicted results. Figure 4
shows the comparison of simulated cumulative ammonia volatilization losses from swine effluent applied to the soil surface on 28 May of 1998, 1999, and 2000 respectively. Again, hourly average Mesonet weather data were used in the simulations. Average air temperatures of the simulated period in 1998, 1999, and 2000 are 26.1, 20.8, and 25.2°C. Average wind speeds of the simulated period are 3.74, 3.85, and 5.94 m s-1 for 1998, 1999, and 2000, respectively. The simulated volatilization loss in 1999 was <80% of that in 2000. The difference in volatilization loss between 1999 and 2000 was caused by a difference of 4.4°C in average air temperature, and a difference of 2.08 m s-1 in average wind speed during the simulated period. Uncertainty of the simulated ammonia volatilization loss because of unknown future weather conditions at the time of application must be considered when using this model in a decision support system.
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Fig. 4. Comparison of simulated cumulative ammonia volatilization loss from swine effluent applied to the soil surface on 28 May of 1998, 1999, and 2000. Hourly average Mesonet weather data were used in the simulations.
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SUMMARY AND CONCLUSIONS
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A mechanistic model was developed to predict the rate and amount of ammonia volatilization from surface-applied swine effluents. The process-based model couples water flow, heat flow, and multiphase, multispecies ammoniacal N transport in a soil profile. A submodel was developed to predict concentrations of ammoniacal N in the infiltrating water of a flood-irrigation event and to estimate the rate and amount of ammonia volatilization from the surface of the infiltration pond. The infiltration submodel was integrated into the transport-and-transformation model to specify the upper boundary condition for the chemical transport model. The governing equations of water flow, heat flow, and the transport-and-transformation models were derived from mass and energy balances employing well-established constitutive relationships. The equations of the mechanistic model were solved numerically. The computer model was tested against the field experiments of ammonia volatilization from swine effluent applied to a field of Richfield clay loam by flood irrigation. The input parameters for the simulations were determined independently. The simulated average volatilization rate matched very well with the measured data with a few exceptions. The exceptions occurred mainly in the first sampling period of the experiments, which might be because of experimental underestimation of the vertical flux in the early stage of experiments with high wind speeds. Preliminary sensitivity analysis of the model revealed significant effect of temperature fluctuation and pH variation on the simulated amount of ammonia volatilized. Variations in flow- and transport-related input parameters (except saturated hydraulic conductivity) caused relatively little change in the simulated cumulative volatilization. Further testing of the model is needed to determine if the discrepancies between simulated and measured volatilization rates arise from problems in the model or from the experimental methods employed.
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NOTES
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This research was supported in part by funds from the Oklahoma Agricultural Experiment Station.
Received for publication June 26, 2001.
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