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Mathematical modelling of nitrous oxide evolution during nitrification
Soil Eiol. Biochem. Vol. 27. No. 9. DI). I 117-I 125. 1995 Copyright 0 1995 ‘Fkevier Science Ltd Printed in Great Britain. All rights reserved 0038-0717(95)ooo38-0 0038-0717/95 $9.50 + 0.00
MATHEMATICAL MODELLING OF NITROUS OXIDE EVOLUTION DURING NITRIFICATION R. F. GRANT Department
of Soil Science,
University
of Alberta,
Edmonton,
Alberta,
Canada
T6G 2E3
(Accepted 23 February 1995) Summary-There is a need for a process-based model of N,O evolution during nitrification as part of larger models used to study trace gas exchange between terrestrial ecosystems and the atmosphere. The model proposed here for N,O evolution is based on the hypothesis that NO; is used as an alternative acceptor for electrons not accepted by 0, during C oxidation for growth by NH, oxidizers. Rates of N,O evolution simulated using this hypothesis are thereby sensitive to any physical or biological attribute of such as substrate the soil that controls the demand for, or the supply of, 0, during nitrification, concentration, temperature (T) or water content (0). These rates were compared under a common range of T (10, 20 and 30°C) and 0 (0.10, 0.20 and 0.30m3 me3) to ones reported in the literature that were measured during incubation of an NH: amended soil. Simulated rates of N,O evolution reproduced a sensitivity to T and 0 that increased with both T and 0, although these rates were overestimated at 0 = 0.20 m3 nl-j. This overestimation is probably caused by uncertainty in parameterizing the model equation in which rates of gas transfer between gaseous and aqueous phases are calculated. Ratios of simulated N,O evolution to NO; + NO, production increased with both T and tJ through a range of l-5 x 10-3p,g N,O-N,LL~-’ NO; + NOT-N in a way that was consistent with ratios of measured evolution to production reported from the NH: amended soil as well as with those reported from other soils and pure cultures. As part of the larger ecosystem model ecosys, this model hypothesis will make a useful contribution towards the estimation of NZO evolution from terrestrial ecosystems under different climates and fertilizer managements.
INTRODUCTION
Nitrification has become recognized as an important source of N,O in global N,O budgets (Robertson, 1993). Because nitrification, and hence N,O evolution, is increased by the use of ammonium fertilizers (Bremner and Blackmer, 1978; Eichner, 1990), there is a need to underst,and how N,O evolution is related to nitrification so t:hat such use may avoid as much as possible the damaging effects of N,O in the atmosphere (Crutzen and Ehalt, 1977). The evolution of N,O by nitrifying bacteria occurs under aerobic conditions (Yoshida and Alexander, 1970; Ritchie and Nicholas, 1972), but increases with decreasing O2 concentration (Goreau et al., 1980). Ritchie and Nicholas (1972) demonstrated that Nitrosomonas europaea produces nitrite reductase which would allow the use of NO; as an electron acceptor in place of O2 during NH: oxidation. Such use was confirmed in 15N labelling studies by Poth and Focht (1985). Hydrologic and thermal conditions will therefore control rates of N,O evolution during nitrification through their control both of nitrification rates and of nitrification product ratios (Firestone and Davidson, 1989). Mathematical modelling of gas transport and exchange in soil-plant systems is an important method
of formulating and testing complex hypotheses concerning physical and biological controls on gas exchange between terrestrial ecosystems and the atmosphere. However, current models of trace gas fluxes are largely empirical rather than mechanistic or process-based (Whitman and Rogers, 1991). Nitrous oxide fluxes from nitrification have been modelled as simple dimensionless functions of relative water content and NH: concentrations (Mosier et al., 1983), but a more comprehensive, mechanistic modelling approach has not yet been undertaken. As part of the ecosys simulation model, Grant (1994) modelled nitrification from basic kinetics of NH, oxidation, CO, reduction and microbial growth as controlled by heat and 0, transfer. To make ecosys more comprehensive in its simulation of soil-atmosphere gas exchange, the simulation of nitrification has since been extended to include NzO evolution. Simulated N,O evolution during nitrification is based on the hypothesis that NO, is used as an alternative electron acceptor by NH, oxidizers for electrons not accepted by 0, due to diffusion constraints, as proposed by Poth and Focht (1985). This hypothesis is tested with data for NO; + NO, production and N,O evolution under different temperatures and water contents reported by Goodroad and Keeney (1984).
1117
R. F. Grant
1118 MODEL DEVELOPMENT
Aerobic oxidation-reduction
reactions
Definitions of all variables and subscripts used in the equations below are listed in the Appendix and relationships among these equations are represented in Fig. 1. In this simulation model, nitrification is assumed to be entirely autotrophic, with CO,(,, as the sole substrate for microbial growth, and NH,(,, as the sole source for microbial energy. In a development on the model of Grant (1994), potential oxidation rates (X’) of NHJcSj to NO; by ammonia oxidizers, and of NO, to NO; by nitrite oxidizers, are calculated:
(1993b). A pH-dependent equilibrium is maintained among [CO& [HCO;] and [CO:-], and between [NH,(,,] and [NH:] in the soil solution. Equilibrium is also maintained between [NH,,,,] and [NH,(,,] through volatilization, and between [NH:] and exchangeable NH: through a Ca*+-NH: Capon selectivity coefficient as part of a solution chemistry sub-model (Grant, 1995) based on that of Robbins et al. (1980). The value of Xh,, from equation (1) is used to calculate the potential reduction of CO,(,, (Rho,) by M iWI,o,
X’NH, = ftxfw~(NH,MNH,a,c{[COZ(s)l/(Kco2+ [CO,,&) x UNH,WI/(KW GoI
= ftxfwpNo2M~o2o.r WO,,,,I/(Kco, x UNO,I/(K,o,
(1)
+ [NH&}
+ [NOzl)J
+ [CO,,,,l)) (2)
where f,, , f, , Kc,, and KNHl are the same as those in equation (1) of Grant (1994). The value of ft, is calculated from an Arrhenius equation based on the energy of activation for N mineralization reported by Addiscott (1983) and used by Grant and Rochette (1994). The values of [CO,(,,] and [NH,,,,] in equations (1) and (2) are also controlled by the mineralization of organic substrates by heterotrophic microbial communities as described in Grant et al.
R;‘02-NHI= XLH,rc02-NH,
(3)
R;1oZ.No2= So,
(4)
rco2-N02
are taken from where values of rCo2_NH,and rcOZ_N02 Belser (1984). The values of RLco,,from equations (3) and (4) are used to calculate the potential oxidation of reduced C (X&o,) for growth and maintenance processes by each microbial population under nonlimiting [O,(,,]: X&oz-NH,= R&NH, ( 1 - Eo,1
(5)
X&W,,
(6)
= R;oz-~o> (1 - EoZ).
The values of XhH, and X&, from equations (1) and (2) and of X&o,,,, and Xko2_No1from equations (5)
WATER
SOIL Fig. 1. Flow diagram names and equation
showing oxidation-reduction reactions in nitrification model. See text for variable numbers. Dashed lines represent transfers between aqueous and gaseous phases. Stippled lines represent transfers of information.
AIR
Nitrous oxide evolution
1119
and (6) are used to calculate the potential reduction
x W%s,I/Wco, + Wd)~
of 01(S)(Ro,) under non-limiting
x {[NO; I/&,,, + [NO; I)>
Rb2-NHJ =
r02-NH3 &H3
, R02-N02
rOi-NOzX~02
=
+ +
[O,,,,]:
r02.C02&02-NH3 r02-C02X&02-N02.
(7) (8)
Actual reduction of O,(,, under ambient [O,J (R,,) is calculated from coupled equations for spherical diffusion to, and active uptake at, microbial microsites for both MIqHja.rand MNOla.c.These equations are solved by convergence to a value of [O,(,,] at the microsites ([O,,,,]) at which diffusion [equations (9a) and (lOa)] = uptalce [equations (9b) and (lob)] (Grant, 1991; Grant and Rochette, 1994): Ro~-NH,
=
47t n MNn,u.cDo2s(d, d, /(d, - d, )) x (PqsJ -
[Q)-NH,
I)
= R~,-NH,[C’,(,,-NH,~/([~,(,,-NH,I
+ &,I
x (]“,,~,] -
(104
[02(m)-N0$
= Rb,-N0~~C’Z(m,-N0~~/~~02(m)-N0~~
+
KoJ
(lob)
The oxidation of NH,(,) and NO; (X), and the reduction of CO,,,) @CO,) by MNH,o,r and MNO~~.~ under ambient [O,(,,] is then calculated from the ratio of actual [equations (9) and (lo)] to potential [equations (7) and (8)] reduction of 02($,: XNH3
=’ Xk4H3 R02-NH3 /Rb2-NH3
(11)
&02
== %o,Ro~-No~
(12)
/%No~
RC02-NH~
=
XNH3rC02-NH3
(13)
RC02-N02
=
XN02
(14)
rCOI-NOZ
so that rates of NH,(,) oxidation and hence C02(,, reduction are coupled to rates of O,,,, diffusion and uptake. Each mole of XNHl [equation (1 1)] causes 2 mol of H+ to enter the soil solution, one from the oxidation of NH,(,, and another from the re-equilibration between PiH,,,,] and [NH:]. Following the re-equilibration of [H+] with other ions in the soil solution, the change in [H+ ] from XNHl causes a change in the ratio between [NH,J and [NH:], and hence a change in XhHI [equation (1)] and XNHl [equation (1 l)]. Oxidation of reduced C for growth and maintenance processes (Xco,) under ambient [O,(,,] is calculated as: XC02-N,,,
=
Rco2-NH,
(1
-
Eo* 1
(15)
XCO>-N02
=
RCO~NO~
(1
-
Eo,).
(16)
Anaerobic oxidation-reduction
on the assumption that O,,,, is a required electron acceptor for XhHI in equation (7) so that XNH, does not contribute to RNOrNH,.The value of rNo2-02 is calculated from the number of electrons accepted per g of NO, vs that per g of O,(,,. This approach to calculating RNo2_NuIis the same as that used to calculate dissimilatory reduction of NO; by facultative heterotrophs in ecosys (Grant et al., 1993a). The sensitivity of MNH,a.rcatabolism to [CO,J is assumed to be independent of the electron acceptor, so that the value of Kco2 is retained from equation (1). RN02_NH, is assumed to drive the reduction of COz(S)by MNu,a,c (Rcol) on the assumption that MNH,o.cis entirely autotrophic:
WI
R 02-NO2 = 4x n M~o2a.cDoZs(d, d, /(d, - d, ))
reactions
The reduction of NO; by MNHla.<(RNo,) is hypothesized to be driven by the demand for electron acceptors for X&OZ_NHj [equation (5)] that was unmet by OZtSj[from equation (15)j:
(17)
R CO*-NHJ
=
(18)
~o~-No~~No~-NH~.
R N02_NH, from equation (17) is not currently coupled in the model to an oxidation reaction, and in the absence of further information, rC02_N02 is assumed equal to rc02_N02[equations (4) and (14)]. The oxidation of C (Xco,) that is reduced through RN02_NH, is calculated as: XC02-NH3
=
RCOI-NH~ c1 -
ENO> )
(19)
where Eo2 [equations (15) and (16)] and ENo2 [equation (19)] reflect growth efficiencies of bacteria when O,,,, or NO, is the electron acceptor (Koike and Hattori, 1975). Growth of nitrifiers
Growth of MNHjo,
=
RCO~NH~
+
-XCO~-NH~
RCO~NH,
-
i ,=I
-
XC02-NH3
{ftmXjMNH,a.c
+ ftxDjMNH3a.c I AM No2a.c /At =
Rco~-NO~
-
iKmX,M j=l
-
(20)
XCOz-NO>
N02a.r +
ftxDjMNoja.rj. (21)
Immobilization-mineralization of mineral N and P during growth and decay of MNH,o,cand MN02a.ris calculated in the same manner as that for the heterotrophic microbial populations in ecosys (Grant et aI., 1993b). Products from the decomposition of MNH,a.c and M~0~u.c are partitioned among microbial residue
R. F. Grant
1120 Table 1. Properties of the Piano silt loam used in ecosw to simulate N,O evolution (data from Goodroad and Keenev. 1984) 1.61 0.164 I5 41 31 50 I9 - I.6 -0.005 0.18 0.54 67
Organic C (%) Total N (%) Initial NH:-N (pgg ‘) Initial NO;-N (pgp ‘) Sand (%) Silt Clay II/, (MPa) at 0 = 0.1 m3 m ’ I//, (MPa) at 0 = 0.3 m’ II+ WFP* at 0 =O.l m’)m-’ WFP’ at 0 = 0.3 m3 mm’ PH *Water-filled
porosity.
pools that are substrates bial populations (Grant
for the heterotrophic et al., 1993b).
micro-
Gas exchange
The exchange of OZcsj and CO,(,, between both M NH,~.~ and MNO~.< and the soil solution [Ro2 from equations (9) and (lo)], Rco, from equations (13) and (14) and Rco2 from equation (18) is coupled to the convective-dispersive transfer of 0, and CO, through, and volatilization-solubilization transfer between, the aqueous and gaseous phases of the soil. The simulation of these transfers is described in equations (12)<16) of Grant (1994), equations (27)<35) of Grant (1993) and equations (18H22) of Grant et al. (1993a). Values of [O,,,,] in equations (9) and (10) and of [CO,(,,] in equations (l), (2) and (17) are also influenced by the exchange of 0, and CO, between heterotrophic microbial populations (Grant et al., 1993b; Grant and Rochette, 1994), root systems (Grant, 1993) and the aqueous phase of the soil (Fig. 1). MODEL TESTING
Initial and boundary conditions used in model testing were set to reproduce those used by Goodroad
and Keeney (1984) to study N,O production in a Plano silt loam (Typic Argiudoll) at different soil temperatures (T) and water contents (0) following NH: amendment. Simulated soil profiles were established from the soil properties reported by Goodroad and Keeney (1984) (Table 1) with a depth of 0.04 m to reproduce that in the Erlenmeyer flasks in which their experiment was conducted. The simulated profiles were resolved into 4 x 0.01 m layers to improve model resolution. These profiles were incubated for 5 d at T = IO,20 or 30°C and 8 = 0.10 m3 mm3 before being irrigated to 0 = 0.10, 0.20, 0.30, 0.40 or 0.50 m3 m-3, amended with 100 pg g-’ of NH:, and then completely mixed by a simulated tillage. Soil NO, + NO, and total surface fluxes of N,O were compared to values reported by Goodroad and Keeney (1984) 5 d after NH: amendment, except those at 0 = 0.40 and 0.50 m3 mm3 which were not included in their experiment. For this study, a time step of 60 s was selected for the calculation of all physical transfers of mass and energy through the layers of the simulated soil profiles. A standard time step of 1 h was used for the calculation of all biological transformations within each layer of the profiles. RESULTS
Total NO; + NO; production measured and simulated 5d after NH: amendment increased with both T and 0 [Table 2(a)]. Simulated production rates increased more with T than did measured ones such that NO, + NO, production was overestimated by about 30% at T = 30°C. The effect of reduced surface-to-volume ratios in the Erlenmeyer flasks on gas exchange in the measured results was not accounted for in the simulated results. In the model, increased production with increased T arises from the combined effects of increased f,,, [CO,(,,] and [NH,{,,] on Xko* [equations (1) and (2)]. Increased Xf.lH1 and
Table 2. (a) NO; + NO< production (FgN gg’ soil), (b) N,O evolution (ng N g-’ soil) and (c) N,O evolution/NO; + NO; production (pgpg-’ x 103) measured and simulated in a Piano silt loam after 5 d at different water contents (0) and temperatures (measured data from Goodroad and Keeney, 1984) IO’C 0 (m’rv’)
Measured
20 c
Simulated
Measured
30°C
Simulated
Measured
Simulated
(a) 0.10
0.20 0.30 0.40 0.50 (b) 0.10 0.20 0.30 0.40 0.50
Cc) 0.10 0.20 0.30 0.40 0.50
9 I6 I6
6 I3 I3 13 I4
14 26 30
I4 42 43 42 34
24 49 56
20 63 79 80 3
9 I2 I6
7 I7 I9 21 24
I3 25 I81
23 95 96 IO1 410
23 49 318
45 214 280 320 9396
1.o
I.1 1.3 I.5 I.6 1.7
0.9 1.0 6.0
1.6 2.2 2.3 2.4 Il.9
I.0 I.0 5.7
2.2 3.4 3.6 4.0
0.8 I .o
Nitrous oxide evolution [CO,J and [NH,(,,] are caused by the effect of increased f,, on heterotrophic mineralization of C and N (Grant and Roclhette, 1994), so that X’ is sensitive to simulated heterotrophic microbial activity. This activity is controlled in ecosys by many soil attributes [e.g. concentration and quality of organic substrates (Grant et al., 1993b), concentrations of mineral N and P (Grant et (zl., 1993b), T and 0 (Grant and Rochette, 1994), bulk density (Grant, 1993), and others]. Therefore the sensitivity of NO, + NO, production to T in ecosys is not a unique function, but is affected by any soil condition that affects heterotrophic or autotrophic microbial activity. Also, because these results represent total product accumulations over a defined period of time, the sensitivity to T of NO; + NO, production in Table 2(a) includes that of the lag phase immediately following amendment when MNHla,( and MN02a.care growing, as well as that of maximum nitrification rates achieved after MNHlo.
1121
consumption rates (Grant and Rochette, 1994), and by decreased Ozcsj solubility as described above. Decreased [O,(,,] causes decreased R02_NHI/Rb2_NH, [equation (9X RC02-NHx [equation (1311, XCO~.NH~ [equation (15)] and hence increased RNOTNHI [equation (17)]. Evolution of N,O under higher T is further increased by increased autotrophic O,(,, consumption rates [equations (7)-(10)] driven by increased XhH2 [equation (I)] through increased f,,, [CO,J and [NH,,,,] as described above. Increased XL,, causes increased RcOrNHI [equation (3)], XL,,,,, [equation (5)] and RN02_NHj [equation (17)]. Evolution of N,O under higher T is further increased by the effects of T on heterotrophic activity and hence on [CO,J and RN02_NHI [equation (17)]. These combined effects cause [N,O(,,] and hence N,O evolution to be very sensitive to T, although there is no unique function relating evolution to T in the model. Both measured and simulated N,O evolution increased markedly with 0, especially at higher T [Table 2(b)]. Simulated evolution increased more than did measured when 8 = 0.20 vs 0.10m3mm3 at all T and was consequently overestimated in that irrigation treatment. In the model, increased evolution with increased 0 is caused by increased d, [equation (9)] and hence decreased porosity and gaseous diffusivity (Millington, 1959), causing decreased R02_NH,/R&NH, [equation (9)] and hence in[equation (17)] through increased creased RN02_NHj RC02_NH,[equation (13)] and XC02_NH,[equation (15)]. Evolution is further increased by reduced Ro*_NOZ [equation (lo)] and hence XNo2 [equation (12)] which causes increased [NO, ] [equation (17)], although this increase will be offset by reduced R02_NH,[equation (9)] and hence XNH, [equation (ll)]. The processes affected by increased 0 through which these increases in N,O evolution are effected interact with processes affected by increased T so that evolution becomes increasingly sensitive to both 0 and T as both increase. At 0 = 0.50 m3 me3 and T = 20 or 3O”C, the dominant source of N,O in the model was heterotrophic NO; reduction through the pathway NO; -*NO; -+ N,O (Grant, 1991; Grant et al., 1993a). Measured and simulated ratios of N,O evolution to NO, + NO, production (pg pg-‘) increased with both 0 and T from 1 x lo-’ when 0 = 0.10 m3 m-3 and T = 10°C to 4-5 x 10m3 when 0 = 0.30 m3 me3 and T = 30°C [Table 2(c)]. Measured ratios showed little sensitivity to 0 and T when f? < 0.3 m3 mm3 and T < 20°C although simulated ratios showed a continuous sensitivity through the entire range of experimental conditions. An example of hourly model output at 0 = 0.30 m3 mm3 and T = 30°C is shown in Fig. 2 for the 0.034.04 m layer of the simulated soil profile.The rapid reduction of O2,s, driven by nitrification [equations (8) and (9)] caused [O,,,,] to decline below pre-amendment values [Fig. 2(a)], which reflected only heterotrophic reduction of O,,,,. However, the
1122
R. F. t3rant 8.0],
-
a
(6.0
7.5 5.5 I
7.0
0.
5.0 6.5
0”
J .,. ,,,,...,.,.
(a)
6.0 0
20
40
60
60
100
4.5
120
Hour
r
‘c 4.Oe-3
-
’9
autotrophic helwotrophk
-4.Oe-3
7 P
3.Oe-3-
-3.Oe-3
2.Oe-3 -
-2.Oe-3
9 E .; s v t
N. The decline in pH eventually caused a decline in [NH,(,,], and hence one in XNH, that allowed [O,(,,] to recover slightly during the final day of the simulated experiment. During the simulated experiment, the ratio of O,(,, reduced from C oxidation (ro~co2X,o,+,,,) to that reduced from [NH,(,,] oxidation (r02_NHIXNHJ) by M NH,W remained at 0.02 for all treatments, indicating that [NH,{,,] oxidation is the dominant cause of O,(,, reduction during nitrification in the model. The value of this ratio is defined by rCOI_NH,[equation (S)] and Eo, [equation (5)]. This ratio partially determines ratios of N,O evolution to NO; + NO; production [Table 2(c)] because it represents the relationship between Xc02.NHIand XE&, and because Xc02_NHjsets the upper limit to autotrophic NO; reduction [R,,, NH, in equation (17)]. The oxidation of fixed C by M NHpv is coupled to the reduction of O,(,, [equation (9)] as XCOZ_NH, through equations (1 1), (13) and (1 S), and to the reduction of NO, [equation (17)] as through equations (17), (18) and (19). At XC02-NH3 B = 0.30 m3 mm3 and T = 3O”C, XCo2_NH,remained between two and three orders of magnitude larger than XC02_NH, [Fig. 2(b)], although the latter increased comparatively more rapidly during the simulated incubation as [O,J declined. Both oxidation rates declined as X,,, became constrained by [NH,,,,] later during the experiment. In ecosys, NO; reduction may be driven by either autotrophic [equation (17)] or heterotrophic (Grant al., 1993a) processes. At Grant et 1991; 0 = 0.30 m3 mm3 and T = 3O”C, the former was the dominant process [Fig. 2(c)] through which 0.8 of all N,O was evolved from the soil layer during the simulated experiment. However this ratio declined as fl increased such that heterotrophic reduction became dominant at 0 = 0.50 m3 me3 [Table 2(b)]. At 0 = 0.3 m3 mm3 and T = 3O”C, the values of pNH, [equation (l)], [email protected]) [equation (l3)] and rco2_No2 [equation (18)] used to calculate XCoZ_NH) and Xco2_NH, [Fig. 2(b)] allowed MNHJa,< to maintain a specific growth rate of 0.03 h-’ and a specific NH,(,) oxidation rate of 0.02 pmol cell-’ h-’ which is close to maximum rates measured for NH,(,, oxidizers by Belser and Schmidt (1980b) and by Goreau et al. (1980). DISCUSSION
Fig. 2. (a) Concentration of soluble 0, and pH, (b) rates of C oxidation from 0, and NO; reduction by autotrophic NH: oxidizers, and (c) rates of NO; reduction by autotrophic NH: oxidizers and by heterotrophic denitrifiers during the simulated experiment at 0 = 0.30 m3 m-3 and T = 30°C. Initial changes in (a) represent effects of irrigation and NH: amendment.
release of H+ with X NH,also caused soil pH to decline helow pre-amendment values, which reflected only heterotrophic oxidation of C and mineralization of
The development and testing of process-based models are an important research goal in understanding and eventually predicting trace gas exchange between terrestrial ecosystems and the atmosphere (Whitman and Rogers, 1991). The model proposed here for N,O evolution during nitrification is based on the simple hypothesis that NO; is used as an alternative acceptor for electrons not accepted by OZcsj during C oxidation for growth by NH,(,, oxidizers [equation (17)]. Although alternative hypotheses are not excluded by this modelling study, this hypothesis is useful because it reproduces the behaviour of N,O
Nitrous oxide evolution evolution during mtrification that has been measured experimentally under different 0 and T. Ratios of N,O evolution to NO; + NO; production simulated using this hypothesis (l-5 x IO-‘) are within the range reported by Goodroad and Keeney (1984) for the same soil under the same range of 0 and T. These ratios are also consistent with values measured from pure cultures of lnarine Nitrosomonas by Goreau et al. (1980) that increased exponentially from 3 to 100 x 10m3 when [O,,,,] was reduced from 7.0 to 0.35 /*grnl-‘. The larger increases with T of N,O evolution than of NO; production simulated with this hypothesis (Table 2) have been found experimentally for N. europaea by Yoshida and Alexander (1970). These remain a number of uncertainties in the formulation and testing of the hypothesis used in this study. One of the uncertainties to which the model is sensitive are the rates of heterotrophic CO, production and NH.: mineralization. In the model, [CO,(,,] approached equilibrium values within 24 h of NH: amendment and irrigation indicating that the rate of nitrifier reduction minus oxidation of CO, [Rco> - Xco, from equations (13) to (16)] was close to the rate of heterotrophic production minus escape of CO, to the atmosphere. Competition between Rcoz and CO2 escape is partially determined in the model by KCo2 [equations (1) and (2)], the value of which (0. I5 pg C ml-‘) was derived from measurements of CO, fixation by RuBP carboxylase in plants (Jordan and Ogren, 1981). However, halving or doubling this value increased or decreased NO; + NO< production by 5 and 20% and N,O evolution by 10 a.nd 25% respectively after 5 d at 0 = 0.3 m3 mm3 and T = 3O”C, suggesting that model performance was not strongly sensitive to Kco2. Performance was more sensitive to heterotrophic NH: mineralization before the amendment which determined the values of MNHlo,< and MN020,r at the time of the amendment. Thus the addition or removal of organic matter from the soil increased or decreased NO, + NO; production in the simulated experiment. In future studies of nitrification rates following NH: amendment, the reporting of CO1 evolution from amended vs unamended soils, by providing an indication of heterotrophic activity, would provide a more rigorous test of model hypotheses. Competition between NO; oxidation [x,,, from equation (12)] an’d reduction [RNo, from equation (17)] is partially determined in the model by KNOl vs K RNO1,values for neither of which were found in the literature. The values used in this study (3.5 and 7.0 pg N ml-‘) were estimated from those of similar oxidation and reduction reactions. Halving or doubling KRNOl did not affect NO; + NO; production and increased or decreased N,O evolution by 3 and 5% respectively after 5 d at 8 = 0.30 m3 mm3 and T = 3O”C, suggesting that model performance was . not strongly sensltlve to KRN02.Nonetheless indepen-
1123
dently measured values for KNOz and KRNol would improve confidence in the model. Competition between NO; oxidation and reduction is also controlled in the model by [O,(,,] [equations (9x17)] which is in turn controlled by O2 transfers within, and between, aqueous and gaseous phases in the soil. Although the parameterization of algorithms for these transfers within each phase is well described, that for transfers between these phases is not. The algorithm used in ecosys is based on that of Skopp (1985), values for some of the parameters of which can only be estimated. Uncertainty in these values may have led to the overestimation of N,O evolution at 0 = 0.20 m3 mm3 [Table 2(b)]. Further testing of this algorithm is needed to improve confidence in model performance. The mechanisms for C reduction (RcOZ_NH,)during NO; reduction by NH3(,) oxidizers [equation (18)] remains unclear. Such reduction is suggested by the ability of Nitrosomonas sp. to grow at low [O2(s)] (Goreau et al., 1980) but a value for rC02.N02in equation (18) could not be estimated from the literature. There are therefore several areas in which the scientific basis for the model hypothesis could be more firmly established. The hypothesis tested here will contribute towards estimates of N20 evolution under different climates and managements as part of the larger ecosys model in which it is coupled to activities of other microbial communities, and to transfers of heat, water and gases. The high sensitivity of simulated evolution to CO, production when 0 8, T and heterotrophic and/or T are high would suggest that under these conditions comparatively small temporal and spatial variation in 0 and T would account for the comparatively large temporal and spatial variation in N,O evolution commonly reported in field studies (e.g. Grant et al., 1993~). Acknowledgements-This research was carried out as part of the Global Change and Terrestrial Ecosystems project in the International Geosphere-Biosphere Program. Development of the ecosys model was partially supported by a grant from the National Science Foundation for use of the CONVEX 3880 facility of the National Center for Supercomputing Applications at the University of Illinois in Urbana-Champaign. Model results were generated on an IBM model 560 workstation located at the University of Alberta.
REFERENCES
Addiscott T. M. (1983) Kinetics and temperature relationships of mineralization and nitrification in Rothamsted soils with differing histories. Journal of Soil Science 34, 343-353. Belser L. W. (1977) Nitrate reduction to nitrite, a possible source of nitrite for growth of nitrite-oxidizing bacteria. Applied and Environmental Microbiology 34, 403410.
Belser L. W. (1984) Bicarbonate uptake by nitrifiers: effects of growth rate, pH, substrate concentration, andmetabolic inhibitors. Applied and Environmental Microbiology 48, 1IO&l 104.
1124
R. F. Grant
Belser L. W. and Schmidt E. L. (1980a) Growth and oxidation kinetics of the three genera of ammonia oxidizers. FEMS Microbiology Letters 7, 213-216. Belser L. W. and Schmidt. E. L. (1980b) The specific inhibition of nitrite oxidation by chlorate and its use in assessing nitrification in soils and sediments. Applied Environmental Microbiology 39, 505-S IO. Bremner J. M. and Blackmer A. M. (1978) . , Nitrous oxide emission from soils during nitrification of fertilizer nitrogen. Science 199, 2955296. Crutzen P. J. and Ehalt D. H. (1977) Effects of nitrogen fertilizers and combustion on the stratospheric ozone layer. Ambio 6, 112-I 17. Eichner M. J. (1990) Nitrous oxide emission from fertilized soils: summary of available data. Journal of Environmentat Quality 19, 2722280. Firestone M. K. and Davidson E. A. (1989) Microbiological basis of NO and N,O production and consumption in soil. In Exchange qf Trace Gases Between Terrestrial Ecosystems and the Atmosphere (M. 0. Andreae and D. S. Schimel, Eds), pp. 7-21. Wiley, Chichester. Focht D. D. and Verstraete W. (1977) Biochemical ecology of nitrification and denitrification. Advances in Microbial Ecology 1, 1355214. Gilmour J. T. (1984) The effects of soil properties on nitrification and nitrification inhibition. Soil Science Society of America Journal 48, 1262-1266. Goodroad L. L. and Keeney D. R. (1984) Nitrous oxide production in aerobic soils under varying pH, temperature and water content. Soil Biology & Biochemistry 16, 3943. Goreau T. J., Kaplan W. A., Wofsy S. C., McElroy M. B.. Valois F. W. and Watson S. W. (1980) Production of NO; and N,O by nitrifying bacteria at reduced concentrations of oxygen. Applied & Environmental Microbiology 40, 526-532. Grant R. F. (1991) A technique for estimating denitrification rates at different soil temperatures, water contents and nitrate concentrations. Soil Science 152, 41-52. Grant R. F. (1993) Simulation model of soil compaction and root growth. I. Model structure. Plant and Soil 150, I-14. Grant R. F. (1994) Simulation of ecological controls on nitrification. Soil Biology & Biochemistry 26, 305-3 15. Grant R. F. (1995) Salinity, water use and yield of maize: testing of the mathematical model ecosys. Plant and Soil. In press. Grant R. F., Nyborg M. and Laidlaw J. W. (1993a) Evolution of nitrous oxide from soil. I. Model development. Soil Science 156, 259-265. Grant R. F., Juma N. G. and McGill W. B. (1993b) Simulation of carbon and nitrogen transformations in soils. 1. Mineralization. Soil Biology & Biochemistry 25, 1331-1338. Grant R. F., Nyborg M. and Laidlaw J. (1993) Evolution of nitrous oxide from soil: II. Experimental results and model testing. Soil Science 156, 266277. Grant R. F. and Rochette P. (1994) Soil microbial respiration at different temperatures and water potentials: theory and mathematical modelling. Soil Science Sociery of America Journal. 58, I68 1-I 690 Jordan D. B. and Ogren W. L. (1981) Species variation in the specificity of ribulose biphosphate carboxylase/ oxygenase. Nature 291, 513-515. Juma N. G. and Mcgill W. B. (1986) Decomposition and nutrient cycling in agro-ecosystems. In MicroJoral and Fauna1 Interactions in Naturaland Agro-ecosystems (M. J. Mitchell and J. P. Nakas, Eds), pp. 74-136. Nijhoff/Junk, The Netherlands. Kemper W. D. and Rollins J. B. (1966) Osmotic efficiency coefficients across compacted clays. Soil Science Society of America Proceedings 30, 529-534.
Koike I. and Hattori A. (1975) Growth yield of a denitrifying bacterium, Pseudomonas denitrt$cans, under aerobic and denitrifying conditions. Journal of General Microbiology 88, l-10. Millington R. J. (1959) Gas diffusion in porous media. Science 130, 100-102. Mosier A. R., Parton W. J. and Hutchison G. L. (1983) Modeling nitrous oxide evolution from cropped and native soils. In Environmental Biogeochemistry (R. Hallberg, Ed.), pp. 2299241. Ecological Bulletins Publishing House No. 35. Stockholm. Pirt S. J. (1975) Principles of Microbe and Cell Cultivation. Blackwell Scientific, Oxford. Poth M. and Focht D. D. (1985) “N kinetic analysis of N,O production by Nitrosomonas europaea: an examination of nitrifier denitrification. Applied and Environmental Microbiology 49, I1341141. Ritchie G. A. F. and Nicholas D. J. D. (1972) Identification of the sources of nitrous oxide produced by oxidative and reductive processes in Nitrosomonas europaea. Biochemistry Journal 126, 1181-1191. Robbins C. W., Wagenet R. J. and Jurinak J. J. (1980) A combined salt transportchemical equilibrium model for calcareous and gypsiferous soils. Soil Science Society of America Journal 44, 1191-l 194. Robertson G. P. (1993) Fluxes of nitrous oxide and other nitrogen trace gases from intensively managed landscapes: a global perspective. In Agriculatural Ecosystem Effects on Trace Gases and Global Climate Change, pp. 95-108. American Society of Agronomy, Special Publication No. 55. Madison. Shields J. A., Paul E. A., Lowe W. E. and Parkinson D. (1973) Turnover of microbial tissue in soil under field conditions. Soil Biology & Biochemistry 5, 753-764. Skopp J. (1985) Oxygen uptake and transfer in soils: analysis of the air-water interfacial area. Soil Science Society of America Journal 49, 1327-l 33 1. Suzuki I., Dular U. and Kwok S. C. (1974) Ammonia or ammonium ion as substrate for oxidation by Nifrosomonas europaea cells and extracts. Journal of Bacteriology 120, 556-558. Whitman W. B. and Rogers J. E. (1991) Research needs in the microbial production and consumption of radiatively important trace gases. In Microbial Production and Consumption of Greenhouse Gases: Methane, Nitrogen Oxides and Halomethanes (J. E. Rogers and W. B. Whitman, Eds), pp. 2877291. American Society of Microbiology, Washington. Wilhelm E., Battino R. and Wilcock R. J. (1977) Low-pressure solubility of gases in liquid water. Chemical Reviews 77, 2 199262. Wuhrmann K. (1963) Effects of oxygen tension on biochemical reactions in sewage purification plants. In Biological Waste Treatment Processes (W. W. Eckenfelder and J. McCabe, Eds), pp. 27738. Third Conference on Biological Waste Treatment. Pergamon Press, New York. Yoshida T. and Alexander M. (1970) Nitrous oxide formation by Nitrosomonas europaea and heterotrophic microorganisms. Soil Science Society of America Proceedings 34, 880-882.
APPENDIX Subscripts a c j
active component of M (Grant er al., 1993b) dry matter (DM) fraction of active component of M (Grant et al., 1993b) kinetic components of a,r soluble gaseous
Nitrous
oxide evolution
Variables (Roman)
w,,,,1
D,
liOI_NOZunder ambient IO,,,,] (pg g-’ h-‘) (14,16,21) actual rate of NOT reduction by MN”?,,,, under ambient (02(S,] (pg g-’ h-l) (17,18) potential rate of O,,,, reduction by MNH,,,,, under non-limiting [O,(,,] (pgg-’ h-‘) (7.9.1 I) potential rate of O,,, reduction by MNOZL,,‘ under non-limiting [O,,,,] (pg g-’ h-l) (8,10.12) actual rate of O,(,, reduction by MN”,<,,
CO, concentration in soil solution (fig ml-‘) (I ,2, I ?) specific decomposition (g reduced Cg M,;'h-‘) (Juma and McGill, 1986)
PO,2 1) D 02s 4
4
E O? E NO? fUIl
ftx
fW K CO?
K RN@ K NH, K NO? Ko>
diffusivity of 02(rj at ambient temperature and water content (cm’h-‘) (9,lO) radius of microbial microsite for M,,,,,,, and M NO,,,, (cm) (9,10)* rad& of d, + water film (Kemper and Rollins, 1966) at current water content (cm) (9.10) growth efficiency of M,,,,,, and MNo_,,< using O,,,, (5.6.15.16)* _l.,(I’ . CRC’ - ) growth efficiency of MLHlr,,< using NO, (g C g C-‘) (Koike and Hattori, 1975) (l9)* temperature function for maintenance with a value of I at 30°C (dimensionless) (Grant et al., 1993b) (20,21)* temperature function for oxidation with a value Iof 1 at 30°C (dimensionless) (Addiscott, 1983; Gilmour, 1984) (1,2,20,21)* water function for oxidation (dimensionless) (Pirt, 1975) (1,2)* Michaelis-Menten constant for reduction of by Mw,,, and MNOla.r (pg ml-‘) ;2?7)* Michaelis-Menten constant for reduction of NO; [pgml-‘) (17) Michael&Menten constant for oxidation of NH,(,, (pgml-‘) (Suzuki et al., 1974) (l)* Michaelis-Menten constant for oxidation of NO; (PgmlF’) (2)* Michaelis-Menten constant for reduction of
MNH,~.~
rO?-NH, rO*-NOS Xk~?-~~~
Xk~~~~~ Xco~-~~~ XCO~-NHI
% by MNH,,,and M I
M NHID.< M No*“,< [NH,,,,1
PQI n
and Verstraet;, 1977) $$~gml~‘) (Focht DM of active NH,(,, ’oxidizers (pgg-‘) (1,9,20) DM of active NO, oxidizers (pgg-‘) (2,lO,Z!l) NH, concentration in soil solution (pg ml-‘) (1) NO, concentration in soil solution (pg ml-‘) (2717) number of active MNHlo,( or MNOZ,,,I(pg-‘) (9,lO) 0, concentration at MN,,,,, microsite (rgml-‘) (9) 0, concentration at MNO_,( microsite (pg ml-‘) (10) 0, concentration in soil solution (pg ml-‘) (9,lO) potential rate of COZ(S, reduction by MN,,,,.< under non-limiting [O,,,,] (pg gg’ h-‘) (3,5) potential rate of CO,(,, reduction by MNOZs,< under non-limiting [O,(,,] (pgg-’ h-‘) (4,6) actual rate of CO,,,, reduction by MN”,,,,, from under ambient [O+,] (pgg-’ h-‘)
R CO?-NH,
actual rate of CO,,,, reduction by under ambient [02($,]
R C&N02
actual rate of COZ,r, reduction
from h-‘)
by MNO1e.cfrom
1125
x CO!-NO> x / x, NH,
xho~
X NH, X NO>
d)
(I@*
ratio of NO, reduced to 0, reduced by M NO>rr.r (g g-‘1 (17)* ratio of O,(,, reduced to C oxidized by MN”,,,< and MNO,,., k g-‘1 (7,8,17)* ratio of O,(,, reduced to NH,,,, oxidized by 2(Sjreduced to NH,(,, oxidized by M NOx,,< kg-‘) c8)* potential rate of C oxidation by MNHlo,‘under non-limiting [O,(,,] (pg g-’ h-l) (5,7,17) potential rate of C oxidation by M,oz,,, under non-limiting [O,J (pgg-’ h-l) (6,s) actual rate of C oxidation by MNH,“,< from O,(,, reduction (pgg-‘h-l) (15,17,20) actual rate of C oxidation by M,,,,,, from NO, reduction (pg gg’ h-l) (19,20) actual rate of C oxidation by MNO?o,l from O,,,, reduction (pgg-‘h-l) (16,21) specific maintenance respiration (g reduced C g M,;’ h-‘) (Shields et al., 1973) (20,21) potential rate of NH, oxidation by M,,,., under non-limiting [O,,,,] (pg g-’ h-l) (1,3,7,11) potential rate of NO, oxidation by MNO?,,,‘ under non-limiting [OZcS,] (pg g-’ h-‘) (2,4,8,12) actual rate of NH, oxidation by M,,,,,,, under ambient [O,,,,] (pgg-‘h-l) (ll,l3) actual rate of NO; oxidation by MNOlo,c under ambient [02J (pgg-‘h-‘) (12,14)
Variables (Greek) PNH,
PNO2
specific oxidation rate of NH,,,, by MNHlu,< (g NH,-N g-’ mNHla.‘h-‘) at 30°C under nonlimiting conditions (Belser and Schmidt, 1980a) (I)* specific oxidation rate of NO; by MNO_,,( (g NO;-N g-’ MN02B.1. h-’ ) at 30°C under non-limiting conditions (Belser, 1977) (2)*
*Indicates values recorded at the experimental site or taken from the literature and provided to the ecosystem model. Numbers in parentheses refer to equations in which the variable is used.
MATHEMATICAL MODELLING OF NITROUS OXIDE EVOLUTION DURING NITRIFICATION R. F. GRANT Department
of Soil Science,
University
of Alberta,
Edmonton,
Alberta,
Canada
T6G 2E3
(Accepted 23 February 1995) Summary-There is a need for a process-based model of N,O evolution during nitrification as part of larger models used to study trace gas exchange between terrestrial ecosystems and the atmosphere. The model proposed here for N,O evolution is based on the hypothesis that NO; is used as an alternative acceptor for electrons not accepted by 0, during C oxidation for growth by NH, oxidizers. Rates of N,O evolution simulated using this hypothesis are thereby sensitive to any physical or biological attribute of such as substrate the soil that controls the demand for, or the supply of, 0, during nitrification, concentration, temperature (T) or water content (0). These rates were compared under a common range of T (10, 20 and 30°C) and 0 (0.10, 0.20 and 0.30m3 me3) to ones reported in the literature that were measured during incubation of an NH: amended soil. Simulated rates of N,O evolution reproduced a sensitivity to T and 0 that increased with both T and 0, although these rates were overestimated at 0 = 0.20 m3 nl-j. This overestimation is probably caused by uncertainty in parameterizing the model equation in which rates of gas transfer between gaseous and aqueous phases are calculated. Ratios of simulated N,O evolution to NO; + NO, production increased with both T and tJ through a range of l-5 x 10-3p,g N,O-N,LL~-’ NO; + NOT-N in a way that was consistent with ratios of measured evolution to production reported from the NH: amended soil as well as with those reported from other soils and pure cultures. As part of the larger ecosystem model ecosys, this model hypothesis will make a useful contribution towards the estimation of NZO evolution from terrestrial ecosystems under different climates and fertilizer managements.
INTRODUCTION
Nitrification has become recognized as an important source of N,O in global N,O budgets (Robertson, 1993). Because nitrification, and hence N,O evolution, is increased by the use of ammonium fertilizers (Bremner and Blackmer, 1978; Eichner, 1990), there is a need to underst,and how N,O evolution is related to nitrification so t:hat such use may avoid as much as possible the damaging effects of N,O in the atmosphere (Crutzen and Ehalt, 1977). The evolution of N,O by nitrifying bacteria occurs under aerobic conditions (Yoshida and Alexander, 1970; Ritchie and Nicholas, 1972), but increases with decreasing O2 concentration (Goreau et al., 1980). Ritchie and Nicholas (1972) demonstrated that Nitrosomonas europaea produces nitrite reductase which would allow the use of NO; as an electron acceptor in place of O2 during NH: oxidation. Such use was confirmed in 15N labelling studies by Poth and Focht (1985). Hydrologic and thermal conditions will therefore control rates of N,O evolution during nitrification through their control both of nitrification rates and of nitrification product ratios (Firestone and Davidson, 1989). Mathematical modelling of gas transport and exchange in soil-plant systems is an important method
of formulating and testing complex hypotheses concerning physical and biological controls on gas exchange between terrestrial ecosystems and the atmosphere. However, current models of trace gas fluxes are largely empirical rather than mechanistic or process-based (Whitman and Rogers, 1991). Nitrous oxide fluxes from nitrification have been modelled as simple dimensionless functions of relative water content and NH: concentrations (Mosier et al., 1983), but a more comprehensive, mechanistic modelling approach has not yet been undertaken. As part of the ecosys simulation model, Grant (1994) modelled nitrification from basic kinetics of NH, oxidation, CO, reduction and microbial growth as controlled by heat and 0, transfer. To make ecosys more comprehensive in its simulation of soil-atmosphere gas exchange, the simulation of nitrification has since been extended to include NzO evolution. Simulated N,O evolution during nitrification is based on the hypothesis that NO, is used as an alternative electron acceptor by NH, oxidizers for electrons not accepted by 0, due to diffusion constraints, as proposed by Poth and Focht (1985). This hypothesis is tested with data for NO; + NO, production and N,O evolution under different temperatures and water contents reported by Goodroad and Keeney (1984).
1117
R. F. Grant
1118 MODEL DEVELOPMENT
Aerobic oxidation-reduction
reactions
Definitions of all variables and subscripts used in the equations below are listed in the Appendix and relationships among these equations are represented in Fig. 1. In this simulation model, nitrification is assumed to be entirely autotrophic, with CO,(,, as the sole substrate for microbial growth, and NH,(,, as the sole source for microbial energy. In a development on the model of Grant (1994), potential oxidation rates (X’) of NHJcSj to NO; by ammonia oxidizers, and of NO, to NO; by nitrite oxidizers, are calculated:
(1993b). A pH-dependent equilibrium is maintained among [CO& [HCO;] and [CO:-], and between [NH,(,,] and [NH:] in the soil solution. Equilibrium is also maintained between [NH,,,,] and [NH,(,,] through volatilization, and between [NH:] and exchangeable NH: through a Ca*+-NH: Capon selectivity coefficient as part of a solution chemistry sub-model (Grant, 1995) based on that of Robbins et al. (1980). The value of Xh,, from equation (1) is used to calculate the potential reduction of CO,(,, (Rho,) by M iWI,o,
X’NH, = ftxfw~(NH,MNH,a,c{[COZ(s)l/(Kco2+ [CO,,&) x UNH,WI/(KW GoI
= ftxfwpNo2M~o2o.r WO,,,,I/(Kco, x UNO,I/(K,o,
(1)
+ [NH&}
+ [NOzl)J
+ [CO,,,,l)) (2)
where f,, , f, , Kc,, and KNHl are the same as those in equation (1) of Grant (1994). The value of ft, is calculated from an Arrhenius equation based on the energy of activation for N mineralization reported by Addiscott (1983) and used by Grant and Rochette (1994). The values of [CO,(,,] and [NH,,,,] in equations (1) and (2) are also controlled by the mineralization of organic substrates by heterotrophic microbial communities as described in Grant et al.
R;‘02-NHI= XLH,rc02-NH,
(3)
R;1oZ.No2= So,
(4)
rco2-N02
are taken from where values of rCo2_NH,and rcOZ_N02 Belser (1984). The values of RLco,,from equations (3) and (4) are used to calculate the potential oxidation of reduced C (X&o,) for growth and maintenance processes by each microbial population under nonlimiting [O,(,,]: X&oz-NH,= R&NH, ( 1 - Eo,1
(5)
X&W,,
(6)
= R;oz-~o> (1 - EoZ).
The values of XhH, and X&, from equations (1) and (2) and of X&o,,,, and Xko2_No1from equations (5)
WATER
SOIL Fig. 1. Flow diagram names and equation
showing oxidation-reduction reactions in nitrification model. See text for variable numbers. Dashed lines represent transfers between aqueous and gaseous phases. Stippled lines represent transfers of information.
AIR
Nitrous oxide evolution
1119
and (6) are used to calculate the potential reduction
x W%s,I/Wco, + Wd)~
of 01(S)(Ro,) under non-limiting
x {[NO; I/&,,, + [NO; I)>
Rb2-NHJ =
r02-NH3 &H3
, R02-N02
rOi-NOzX~02
=
+ +
[O,,,,]:
r02.C02&02-NH3 r02-C02X&02-N02.
(7) (8)
Actual reduction of O,(,, under ambient [O,J (R,,) is calculated from coupled equations for spherical diffusion to, and active uptake at, microbial microsites for both MIqHja.rand MNOla.c.These equations are solved by convergence to a value of [O,(,,] at the microsites ([O,,,,]) at which diffusion [equations (9a) and (lOa)] = uptalce [equations (9b) and (lob)] (Grant, 1991; Grant and Rochette, 1994): Ro~-NH,
=
47t n MNn,u.cDo2s(d, d, /(d, - d, )) x (PqsJ -
[Q)-NH,
I)
= R~,-NH,[C’,(,,-NH,~/([~,(,,-NH,I
+ &,I
x (]“,,~,] -
(104
[02(m)-N0$
= Rb,-N0~~C’Z(m,-N0~~/~~02(m)-N0~~
+
KoJ
(lob)
The oxidation of NH,(,) and NO; (X), and the reduction of CO,,,) @CO,) by MNH,o,r and MNO~~.~ under ambient [O,(,,] is then calculated from the ratio of actual [equations (9) and (lo)] to potential [equations (7) and (8)] reduction of 02($,: XNH3
=’ Xk4H3 R02-NH3 /Rb2-NH3
(11)
&02
== %o,Ro~-No~
(12)
/%No~
RC02-NH~
=
XNH3rC02-NH3
(13)
RC02-N02
=
XN02
(14)
rCOI-NOZ
so that rates of NH,(,) oxidation and hence C02(,, reduction are coupled to rates of O,,,, diffusion and uptake. Each mole of XNHl [equation (1 1)] causes 2 mol of H+ to enter the soil solution, one from the oxidation of NH,(,, and another from the re-equilibration between PiH,,,,] and [NH:]. Following the re-equilibration of [H+] with other ions in the soil solution, the change in [H+ ] from XNHl causes a change in the ratio between [NH,J and [NH:], and hence a change in XhHI [equation (1)] and XNHl [equation (1 l)]. Oxidation of reduced C for growth and maintenance processes (Xco,) under ambient [O,(,,] is calculated as: XC02-N,,,
=
Rco2-NH,
(1
-
Eo* 1
(15)
XCO>-N02
=
RCO~NO~
(1
-
Eo,).
(16)
Anaerobic oxidation-reduction
on the assumption that O,,,, is a required electron acceptor for XhHI in equation (7) so that XNH, does not contribute to RNOrNH,.The value of rNo2-02 is calculated from the number of electrons accepted per g of NO, vs that per g of O,(,,. This approach to calculating RNo2_NuIis the same as that used to calculate dissimilatory reduction of NO; by facultative heterotrophs in ecosys (Grant et al., 1993a). The sensitivity of MNH,a.rcatabolism to [CO,J is assumed to be independent of the electron acceptor, so that the value of Kco2 is retained from equation (1). RN02_NH, is assumed to drive the reduction of COz(S)by MNu,a,c (Rcol) on the assumption that MNH,o.cis entirely autotrophic:
WI
R 02-NO2 = 4x n M~o2a.cDoZs(d, d, /(d, - d, ))
reactions
The reduction of NO; by MNHla.<(RNo,) is hypothesized to be driven by the demand for electron acceptors for X&OZ_NHj [equation (5)] that was unmet by OZtSj[from equation (15)j:
(17)
R CO*-NHJ
=
(18)
~o~-No~~No~-NH~.
R N02_NH, from equation (17) is not currently coupled in the model to an oxidation reaction, and in the absence of further information, rC02_N02 is assumed equal to rc02_N02[equations (4) and (14)]. The oxidation of C (Xco,) that is reduced through RN02_NH, is calculated as: XC02-NH3
=
RCOI-NH~ c1 -
ENO> )
(19)
where Eo2 [equations (15) and (16)] and ENo2 [equation (19)] reflect growth efficiencies of bacteria when O,,,, or NO, is the electron acceptor (Koike and Hattori, 1975). Growth of nitrifiers
Growth of MNHjo,
=
RCO~NH~
+
-XCO~-NH~
RCO~NH,
-
i ,=I
-
XC02-NH3
{ftmXjMNH,a.c
+ ftxDjMNH3a.c I AM No2a.c /At =
Rco~-NO~
-
iKmX,M j=l
-
(20)
XCOz-NO>
N02a.r +
ftxDjMNoja.rj. (21)
Immobilization-mineralization of mineral N and P during growth and decay of MNH,o,cand MN02a.ris calculated in the same manner as that for the heterotrophic microbial populations in ecosys (Grant et aI., 1993b). Products from the decomposition of MNH,a.c and M~0~u.c are partitioned among microbial residue
R. F. Grant
1120 Table 1. Properties of the Piano silt loam used in ecosw to simulate N,O evolution (data from Goodroad and Keenev. 1984) 1.61 0.164 I5 41 31 50 I9 - I.6 -0.005 0.18 0.54 67
Organic C (%) Total N (%) Initial NH:-N (pgg ‘) Initial NO;-N (pgp ‘) Sand (%) Silt Clay II/, (MPa) at 0 = 0.1 m3 m ’ I//, (MPa) at 0 = 0.3 m’ II+ WFP* at 0 =O.l m’)m-’ WFP’ at 0 = 0.3 m3 mm’ PH *Water-filled
porosity.
pools that are substrates bial populations (Grant
for the heterotrophic et al., 1993b).
micro-
Gas exchange
The exchange of OZcsj and CO,(,, between both M NH,~.~ and MNO~.< and the soil solution [Ro2 from equations (9) and (lo)], Rco, from equations (13) and (14) and Rco2 from equation (18) is coupled to the convective-dispersive transfer of 0, and CO, through, and volatilization-solubilization transfer between, the aqueous and gaseous phases of the soil. The simulation of these transfers is described in equations (12)<16) of Grant (1994), equations (27)<35) of Grant (1993) and equations (18H22) of Grant et al. (1993a). Values of [O,,,,] in equations (9) and (10) and of [CO,(,,] in equations (l), (2) and (17) are also influenced by the exchange of 0, and CO, between heterotrophic microbial populations (Grant et al., 1993b; Grant and Rochette, 1994), root systems (Grant, 1993) and the aqueous phase of the soil (Fig. 1). MODEL TESTING
Initial and boundary conditions used in model testing were set to reproduce those used by Goodroad
and Keeney (1984) to study N,O production in a Plano silt loam (Typic Argiudoll) at different soil temperatures (T) and water contents (0) following NH: amendment. Simulated soil profiles were established from the soil properties reported by Goodroad and Keeney (1984) (Table 1) with a depth of 0.04 m to reproduce that in the Erlenmeyer flasks in which their experiment was conducted. The simulated profiles were resolved into 4 x 0.01 m layers to improve model resolution. These profiles were incubated for 5 d at T = IO,20 or 30°C and 8 = 0.10 m3 mm3 before being irrigated to 0 = 0.10, 0.20, 0.30, 0.40 or 0.50 m3 m-3, amended with 100 pg g-’ of NH:, and then completely mixed by a simulated tillage. Soil NO, + NO, and total surface fluxes of N,O were compared to values reported by Goodroad and Keeney (1984) 5 d after NH: amendment, except those at 0 = 0.40 and 0.50 m3 mm3 which were not included in their experiment. For this study, a time step of 60 s was selected for the calculation of all physical transfers of mass and energy through the layers of the simulated soil profiles. A standard time step of 1 h was used for the calculation of all biological transformations within each layer of the profiles. RESULTS
Total NO; + NO; production measured and simulated 5d after NH: amendment increased with both T and 0 [Table 2(a)]. Simulated production rates increased more with T than did measured ones such that NO, + NO, production was overestimated by about 30% at T = 30°C. The effect of reduced surface-to-volume ratios in the Erlenmeyer flasks on gas exchange in the measured results was not accounted for in the simulated results. In the model, increased production with increased T arises from the combined effects of increased f,,, [CO,(,,] and [NH,{,,] on Xko* [equations (1) and (2)]. Increased Xf.lH1 and
Table 2. (a) NO; + NO< production (FgN gg’ soil), (b) N,O evolution (ng N g-’ soil) and (c) N,O evolution/NO; + NO; production (pgpg-’ x 103) measured and simulated in a Piano silt loam after 5 d at different water contents (0) and temperatures (measured data from Goodroad and Keeney, 1984) IO’C 0 (m’rv’)
Measured
20 c
Simulated
Measured
30°C
Simulated
Measured
Simulated
(a) 0.10
0.20 0.30 0.40 0.50 (b) 0.10 0.20 0.30 0.40 0.50
Cc) 0.10 0.20 0.30 0.40 0.50
9 I6 I6
6 I3 I3 13 I4
14 26 30
I4 42 43 42 34
24 49 56
20 63 79 80 3
9 I2 I6
7 I7 I9 21 24
I3 25 I81
23 95 96 IO1 410
23 49 318
45 214 280 320 9396
1.o
I.1 1.3 I.5 I.6 1.7
0.9 1.0 6.0
1.6 2.2 2.3 2.4 Il.9
I.0 I.0 5.7
2.2 3.4 3.6 4.0
0.8 I .o
Nitrous oxide evolution [CO,J and [NH,(,,] are caused by the effect of increased f,, on heterotrophic mineralization of C and N (Grant and Roclhette, 1994), so that X’ is sensitive to simulated heterotrophic microbial activity. This activity is controlled in ecosys by many soil attributes [e.g. concentration and quality of organic substrates (Grant et al., 1993b), concentrations of mineral N and P (Grant et (zl., 1993b), T and 0 (Grant and Rochette, 1994), bulk density (Grant, 1993), and others]. Therefore the sensitivity of NO, + NO, production to T in ecosys is not a unique function, but is affected by any soil condition that affects heterotrophic or autotrophic microbial activity. Also, because these results represent total product accumulations over a defined period of time, the sensitivity to T of NO; + NO, production in Table 2(a) includes that of the lag phase immediately following amendment when MNHla,( and MN02a.care growing, as well as that of maximum nitrification rates achieved after MNHlo.
1121
consumption rates (Grant and Rochette, 1994), and by decreased Ozcsj solubility as described above. Decreased [O,(,,] causes decreased R02_NHI/Rb2_NH, [equation (9X RC02-NHx [equation (1311, XCO~.NH~ [equation (15)] and hence increased RNOTNHI [equation (17)]. Evolution of N,O under higher T is further increased by increased autotrophic O,(,, consumption rates [equations (7)-(10)] driven by increased XhH2 [equation (I)] through increased f,,, [CO,J and [NH,,,,] as described above. Increased XL,, causes increased RcOrNHI [equation (3)], XL,,,,, [equation (5)] and RN02_NHj [equation (17)]. Evolution of N,O under higher T is further increased by the effects of T on heterotrophic activity and hence on [CO,J and RN02_NHI [equation (17)]. These combined effects cause [N,O(,,] and hence N,O evolution to be very sensitive to T, although there is no unique function relating evolution to T in the model. Both measured and simulated N,O evolution increased markedly with 0, especially at higher T [Table 2(b)]. Simulated evolution increased more than did measured when 8 = 0.20 vs 0.10m3mm3 at all T and was consequently overestimated in that irrigation treatment. In the model, increased evolution with increased 0 is caused by increased d, [equation (9)] and hence decreased porosity and gaseous diffusivity (Millington, 1959), causing decreased R02_NH,/R&NH, [equation (9)] and hence in[equation (17)] through increased creased RN02_NHj RC02_NH,[equation (13)] and XC02_NH,[equation (15)]. Evolution is further increased by reduced Ro*_NOZ [equation (lo)] and hence XNo2 [equation (12)] which causes increased [NO, ] [equation (17)], although this increase will be offset by reduced R02_NH,[equation (9)] and hence XNH, [equation (ll)]. The processes affected by increased 0 through which these increases in N,O evolution are effected interact with processes affected by increased T so that evolution becomes increasingly sensitive to both 0 and T as both increase. At 0 = 0.50 m3 me3 and T = 20 or 3O”C, the dominant source of N,O in the model was heterotrophic NO; reduction through the pathway NO; -*NO; -+ N,O (Grant, 1991; Grant et al., 1993a). Measured and simulated ratios of N,O evolution to NO, + NO, production (pg pg-‘) increased with both 0 and T from 1 x lo-’ when 0 = 0.10 m3 m-3 and T = 10°C to 4-5 x 10m3 when 0 = 0.30 m3 me3 and T = 30°C [Table 2(c)]. Measured ratios showed little sensitivity to 0 and T when f? < 0.3 m3 mm3 and T < 20°C although simulated ratios showed a continuous sensitivity through the entire range of experimental conditions. An example of hourly model output at 0 = 0.30 m3 mm3 and T = 30°C is shown in Fig. 2 for the 0.034.04 m layer of the simulated soil profile.The rapid reduction of O2,s, driven by nitrification [equations (8) and (9)] caused [O,,,,] to decline below pre-amendment values [Fig. 2(a)], which reflected only heterotrophic reduction of O,,,,. However, the
1122
R. F. t3rant 8.0],
-
a
(6.0
7.5 5.5 I
7.0
0.
5.0 6.5
0”
J .,. ,,,,...,.,.
(a)
6.0 0
20
40
60
60
100
4.5
120
Hour
r
‘c 4.Oe-3
-
’9
autotrophic helwotrophk
-4.Oe-3
7 P
3.Oe-3-
-3.Oe-3
2.Oe-3 -
-2.Oe-3
9 E .; s v t
N. The decline in pH eventually caused a decline in [NH,(,,], and hence one in XNH, that allowed [O,(,,] to recover slightly during the final day of the simulated experiment. During the simulated experiment, the ratio of O,(,, reduced from C oxidation (ro~co2X,o,+,,,) to that reduced from [NH,(,,] oxidation (r02_NHIXNHJ) by M NH,W remained at 0.02 for all treatments, indicating that [NH,{,,] oxidation is the dominant cause of O,(,, reduction during nitrification in the model. The value of this ratio is defined by rCOI_NH,[equation (S)] and Eo, [equation (5)]. This ratio partially determines ratios of N,O evolution to NO; + NO; production [Table 2(c)] because it represents the relationship between Xc02.NHIand XE&, and because Xc02_NHjsets the upper limit to autotrophic NO; reduction [R,,, NH, in equation (17)]. The oxidation of fixed C by M NHpv is coupled to the reduction of O,(,, [equation (9)] as XCOZ_NH, through equations (1 1), (13) and (1 S), and to the reduction of NO, [equation (17)] as through equations (17), (18) and (19). At XC02-NH3 B = 0.30 m3 mm3 and T = 3O”C, XCo2_NH,remained between two and three orders of magnitude larger than XC02_NH, [Fig. 2(b)], although the latter increased comparatively more rapidly during the simulated incubation as [O,J declined. Both oxidation rates declined as X,,, became constrained by [NH,,,,] later during the experiment. In ecosys, NO; reduction may be driven by either autotrophic [equation (17)] or heterotrophic (Grant al., 1993a) processes. At Grant et 1991; 0 = 0.30 m3 mm3 and T = 3O”C, the former was the dominant process [Fig. 2(c)] through which 0.8 of all N,O was evolved from the soil layer during the simulated experiment. However this ratio declined as fl increased such that heterotrophic reduction became dominant at 0 = 0.50 m3 me3 [Table 2(b)]. At 0 = 0.3 m3 mm3 and T = 3O”C, the values of pNH, [equation (l)], [email protected]) [equation (l3)] and rco2_No2 [equation (18)] used to calculate XCoZ_NH) and Xco2_NH, [Fig. 2(b)] allowed MNHJa,< to maintain a specific growth rate of 0.03 h-’ and a specific NH,(,) oxidation rate of 0.02 pmol cell-’ h-’ which is close to maximum rates measured for NH,(,, oxidizers by Belser and Schmidt (1980b) and by Goreau et al. (1980). DISCUSSION
Fig. 2. (a) Concentration of soluble 0, and pH, (b) rates of C oxidation from 0, and NO; reduction by autotrophic NH: oxidizers, and (c) rates of NO; reduction by autotrophic NH: oxidizers and by heterotrophic denitrifiers during the simulated experiment at 0 = 0.30 m3 m-3 and T = 30°C. Initial changes in (a) represent effects of irrigation and NH: amendment.
release of H+ with X NH,also caused soil pH to decline helow pre-amendment values, which reflected only heterotrophic oxidation of C and mineralization of
The development and testing of process-based models are an important research goal in understanding and eventually predicting trace gas exchange between terrestrial ecosystems and the atmosphere (Whitman and Rogers, 1991). The model proposed here for N,O evolution during nitrification is based on the simple hypothesis that NO; is used as an alternative acceptor for electrons not accepted by OZcsj during C oxidation for growth by NH,(,, oxidizers [equation (17)]. Although alternative hypotheses are not excluded by this modelling study, this hypothesis is useful because it reproduces the behaviour of N,O
Nitrous oxide evolution evolution during mtrification that has been measured experimentally under different 0 and T. Ratios of N,O evolution to NO; + NO; production simulated using this hypothesis (l-5 x IO-‘) are within the range reported by Goodroad and Keeney (1984) for the same soil under the same range of 0 and T. These ratios are also consistent with values measured from pure cultures of lnarine Nitrosomonas by Goreau et al. (1980) that increased exponentially from 3 to 100 x 10m3 when [O,,,,] was reduced from 7.0 to 0.35 /*grnl-‘. The larger increases with T of N,O evolution than of NO; production simulated with this hypothesis (Table 2) have been found experimentally for N. europaea by Yoshida and Alexander (1970). These remain a number of uncertainties in the formulation and testing of the hypothesis used in this study. One of the uncertainties to which the model is sensitive are the rates of heterotrophic CO, production and NH.: mineralization. In the model, [CO,(,,] approached equilibrium values within 24 h of NH: amendment and irrigation indicating that the rate of nitrifier reduction minus oxidation of CO, [Rco> - Xco, from equations (13) to (16)] was close to the rate of heterotrophic production minus escape of CO, to the atmosphere. Competition between Rcoz and CO2 escape is partially determined in the model by KCo2 [equations (1) and (2)], the value of which (0. I5 pg C ml-‘) was derived from measurements of CO, fixation by RuBP carboxylase in plants (Jordan and Ogren, 1981). However, halving or doubling this value increased or decreased NO; + NO< production by 5 and 20% and N,O evolution by 10 a.nd 25% respectively after 5 d at 0 = 0.3 m3 mm3 and T = 3O”C, suggesting that model performance was not strongly sensitive to Kco2. Performance was more sensitive to heterotrophic NH: mineralization before the amendment which determined the values of MNHlo,< and MN020,r at the time of the amendment. Thus the addition or removal of organic matter from the soil increased or decreased NO, + NO; production in the simulated experiment. In future studies of nitrification rates following NH: amendment, the reporting of CO1 evolution from amended vs unamended soils, by providing an indication of heterotrophic activity, would provide a more rigorous test of model hypotheses. Competition between NO; oxidation [x,,, from equation (12)] an’d reduction [RNo, from equation (17)] is partially determined in the model by KNOl vs K RNO1,values for neither of which were found in the literature. The values used in this study (3.5 and 7.0 pg N ml-‘) were estimated from those of similar oxidation and reduction reactions. Halving or doubling KRNOl did not affect NO; + NO; production and increased or decreased N,O evolution by 3 and 5% respectively after 5 d at 8 = 0.30 m3 mm3 and T = 3O”C, suggesting that model performance was . not strongly sensltlve to KRN02.Nonetheless indepen-
1123
dently measured values for KNOz and KRNol would improve confidence in the model. Competition between NO; oxidation and reduction is also controlled in the model by [O,(,,] [equations (9x17)] which is in turn controlled by O2 transfers within, and between, aqueous and gaseous phases in the soil. Although the parameterization of algorithms for these transfers within each phase is well described, that for transfers between these phases is not. The algorithm used in ecosys is based on that of Skopp (1985), values for some of the parameters of which can only be estimated. Uncertainty in these values may have led to the overestimation of N,O evolution at 0 = 0.20 m3 mm3 [Table 2(b)]. Further testing of this algorithm is needed to improve confidence in model performance. The mechanisms for C reduction (RcOZ_NH,)during NO; reduction by NH3(,) oxidizers [equation (18)] remains unclear. Such reduction is suggested by the ability of Nitrosomonas sp. to grow at low [O2(s)] (Goreau et al., 1980) but a value for rC02.N02in equation (18) could not be estimated from the literature. There are therefore several areas in which the scientific basis for the model hypothesis could be more firmly established. The hypothesis tested here will contribute towards estimates of N20 evolution under different climates and managements as part of the larger ecosys model in which it is coupled to activities of other microbial communities, and to transfers of heat, water and gases. The high sensitivity of simulated evolution to CO, production when 0 8, T and heterotrophic and/or T are high would suggest that under these conditions comparatively small temporal and spatial variation in 0 and T would account for the comparatively large temporal and spatial variation in N,O evolution commonly reported in field studies (e.g. Grant et al., 1993~). Acknowledgements-This research was carried out as part of the Global Change and Terrestrial Ecosystems project in the International Geosphere-Biosphere Program. Development of the ecosys model was partially supported by a grant from the National Science Foundation for use of the CONVEX 3880 facility of the National Center for Supercomputing Applications at the University of Illinois in Urbana-Champaign. Model results were generated on an IBM model 560 workstation located at the University of Alberta.
REFERENCES
Addiscott T. M. (1983) Kinetics and temperature relationships of mineralization and nitrification in Rothamsted soils with differing histories. Journal of Soil Science 34, 343-353. Belser L. W. (1977) Nitrate reduction to nitrite, a possible source of nitrite for growth of nitrite-oxidizing bacteria. Applied and Environmental Microbiology 34, 403410.
Belser L. W. (1984) Bicarbonate uptake by nitrifiers: effects of growth rate, pH, substrate concentration, andmetabolic inhibitors. Applied and Environmental Microbiology 48, 1IO&l 104.
1124
R. F. Grant
Belser L. W. and Schmidt E. L. (1980a) Growth and oxidation kinetics of the three genera of ammonia oxidizers. FEMS Microbiology Letters 7, 213-216. Belser L. W. and Schmidt. E. L. (1980b) The specific inhibition of nitrite oxidation by chlorate and its use in assessing nitrification in soils and sediments. Applied Environmental Microbiology 39, 505-S IO. Bremner J. M. and Blackmer A. M. (1978) . , Nitrous oxide emission from soils during nitrification of fertilizer nitrogen. Science 199, 2955296. Crutzen P. J. and Ehalt D. H. (1977) Effects of nitrogen fertilizers and combustion on the stratospheric ozone layer. Ambio 6, 112-I 17. Eichner M. J. (1990) Nitrous oxide emission from fertilized soils: summary of available data. Journal of Environmentat Quality 19, 2722280. Firestone M. K. and Davidson E. A. (1989) Microbiological basis of NO and N,O production and consumption in soil. In Exchange qf Trace Gases Between Terrestrial Ecosystems and the Atmosphere (M. 0. Andreae and D. S. Schimel, Eds), pp. 7-21. Wiley, Chichester. Focht D. D. and Verstraete W. (1977) Biochemical ecology of nitrification and denitrification. Advances in Microbial Ecology 1, 1355214. Gilmour J. T. (1984) The effects of soil properties on nitrification and nitrification inhibition. Soil Science Society of America Journal 48, 1262-1266. Goodroad L. L. and Keeney D. R. (1984) Nitrous oxide production in aerobic soils under varying pH, temperature and water content. Soil Biology & Biochemistry 16, 3943. Goreau T. J., Kaplan W. A., Wofsy S. C., McElroy M. B.. Valois F. W. and Watson S. W. (1980) Production of NO; and N,O by nitrifying bacteria at reduced concentrations of oxygen. Applied & Environmental Microbiology 40, 526-532. Grant R. F. (1991) A technique for estimating denitrification rates at different soil temperatures, water contents and nitrate concentrations. Soil Science 152, 41-52. Grant R. F. (1993) Simulation model of soil compaction and root growth. I. Model structure. Plant and Soil 150, I-14. Grant R. F. (1994) Simulation of ecological controls on nitrification. Soil Biology & Biochemistry 26, 305-3 15. Grant R. F. (1995) Salinity, water use and yield of maize: testing of the mathematical model ecosys. Plant and Soil. In press. Grant R. F., Nyborg M. and Laidlaw J. W. (1993a) Evolution of nitrous oxide from soil. I. Model development. Soil Science 156, 259-265. Grant R. F., Juma N. G. and McGill W. B. (1993b) Simulation of carbon and nitrogen transformations in soils. 1. Mineralization. Soil Biology & Biochemistry 25, 1331-1338. Grant R. F., Nyborg M. and Laidlaw J. (1993) Evolution of nitrous oxide from soil: II. Experimental results and model testing. Soil Science 156, 266277. Grant R. F. and Rochette P. (1994) Soil microbial respiration at different temperatures and water potentials: theory and mathematical modelling. Soil Science Sociery of America Journal. 58, I68 1-I 690 Jordan D. B. and Ogren W. L. (1981) Species variation in the specificity of ribulose biphosphate carboxylase/ oxygenase. Nature 291, 513-515. Juma N. G. and Mcgill W. B. (1986) Decomposition and nutrient cycling in agro-ecosystems. In MicroJoral and Fauna1 Interactions in Naturaland Agro-ecosystems (M. J. Mitchell and J. P. Nakas, Eds), pp. 74-136. Nijhoff/Junk, The Netherlands. Kemper W. D. and Rollins J. B. (1966) Osmotic efficiency coefficients across compacted clays. Soil Science Society of America Proceedings 30, 529-534.
Koike I. and Hattori A. (1975) Growth yield of a denitrifying bacterium, Pseudomonas denitrt$cans, under aerobic and denitrifying conditions. Journal of General Microbiology 88, l-10. Millington R. J. (1959) Gas diffusion in porous media. Science 130, 100-102. Mosier A. R., Parton W. J. and Hutchison G. L. (1983) Modeling nitrous oxide evolution from cropped and native soils. In Environmental Biogeochemistry (R. Hallberg, Ed.), pp. 2299241. Ecological Bulletins Publishing House No. 35. Stockholm. Pirt S. J. (1975) Principles of Microbe and Cell Cultivation. Blackwell Scientific, Oxford. Poth M. and Focht D. D. (1985) “N kinetic analysis of N,O production by Nitrosomonas europaea: an examination of nitrifier denitrification. Applied and Environmental Microbiology 49, I1341141. Ritchie G. A. F. and Nicholas D. J. D. (1972) Identification of the sources of nitrous oxide produced by oxidative and reductive processes in Nitrosomonas europaea. Biochemistry Journal 126, 1181-1191. Robbins C. W., Wagenet R. J. and Jurinak J. J. (1980) A combined salt transportchemical equilibrium model for calcareous and gypsiferous soils. Soil Science Society of America Journal 44, 1191-l 194. Robertson G. P. (1993) Fluxes of nitrous oxide and other nitrogen trace gases from intensively managed landscapes: a global perspective. In Agriculatural Ecosystem Effects on Trace Gases and Global Climate Change, pp. 95-108. American Society of Agronomy, Special Publication No. 55. Madison. Shields J. A., Paul E. A., Lowe W. E. and Parkinson D. (1973) Turnover of microbial tissue in soil under field conditions. Soil Biology & Biochemistry 5, 753-764. Skopp J. (1985) Oxygen uptake and transfer in soils: analysis of the air-water interfacial area. Soil Science Society of America Journal 49, 1327-l 33 1. Suzuki I., Dular U. and Kwok S. C. (1974) Ammonia or ammonium ion as substrate for oxidation by Nifrosomonas europaea cells and extracts. Journal of Bacteriology 120, 556-558. Whitman W. B. and Rogers J. E. (1991) Research needs in the microbial production and consumption of radiatively important trace gases. In Microbial Production and Consumption of Greenhouse Gases: Methane, Nitrogen Oxides and Halomethanes (J. E. Rogers and W. B. Whitman, Eds), pp. 2877291. American Society of Microbiology, Washington. Wilhelm E., Battino R. and Wilcock R. J. (1977) Low-pressure solubility of gases in liquid water. Chemical Reviews 77, 2 199262. Wuhrmann K. (1963) Effects of oxygen tension on biochemical reactions in sewage purification plants. In Biological Waste Treatment Processes (W. W. Eckenfelder and J. McCabe, Eds), pp. 27738. Third Conference on Biological Waste Treatment. Pergamon Press, New York. Yoshida T. and Alexander M. (1970) Nitrous oxide formation by Nitrosomonas europaea and heterotrophic microorganisms. Soil Science Society of America Proceedings 34, 880-882.
APPENDIX Subscripts a c j
active component of M (Grant er al., 1993b) dry matter (DM) fraction of active component of M (Grant et al., 1993b) kinetic components of a,r soluble gaseous
Nitrous
oxide evolution
Variables (Roman)
w,,,,1
D,
liOI_NOZunder ambient IO,,,,] (pg g-’ h-‘) (14,16,21) actual rate of NOT reduction by MN”?,,,, under ambient (02(S,] (pg g-’ h-l) (17,18) potential rate of O,,,, reduction by MNH,,,,, under non-limiting [O,(,,] (pgg-’ h-‘) (7.9.1 I) potential rate of O,,, reduction by MNOZL,,‘ under non-limiting [O,,,,] (pg g-’ h-l) (8,10.12) actual rate of O,(,, reduction by MN”,<,,
CO, concentration in soil solution (fig ml-‘) (I ,2, I ?) specific decomposition (g reduced Cg M,;'h-‘) (Juma and McGill, 1986)
PO,2 1) D 02s 4
4
E O? E NO? fUIl
ftx
fW K CO?
K RN@ K NH, K NO? Ko>
diffusivity of 02(rj at ambient temperature and water content (cm’h-‘) (9,lO) radius of microbial microsite for M,,,,,,, and M NO,,,, (cm) (9,10)* rad& of d, + water film (Kemper and Rollins, 1966) at current water content (cm) (9.10) growth efficiency of M,,,,,, and MNo_,,< using O,,,, (5.6.15.16)* _l.,(I’ . CRC’ - ) growth efficiency of MLHlr,,< using NO, (g C g C-‘) (Koike and Hattori, 1975) (l9)* temperature function for maintenance with a value of I at 30°C (dimensionless) (Grant et al., 1993b) (20,21)* temperature function for oxidation with a value Iof 1 at 30°C (dimensionless) (Addiscott, 1983; Gilmour, 1984) (1,2,20,21)* water function for oxidation (dimensionless) (Pirt, 1975) (1,2)* Michaelis-Menten constant for reduction of by Mw,,, and MNOla.r (pg ml-‘) ;2?7)* Michaelis-Menten constant for reduction of NO; [pgml-‘) (17) Michael&Menten constant for oxidation of NH,(,, (pgml-‘) (Suzuki et al., 1974) (l)* Michaelis-Menten constant for oxidation of NO; (PgmlF’) (2)* Michaelis-Menten constant for reduction of
MNH,~.~
rO?-NH, rO*-NOS Xk~?-~~~
Xk~~~~~ Xco~-~~~ XCO~-NHI
% by MNH,,,and M I
M NHID.< M No*“,< [NH,,,,1
PQI n
and Verstraet;, 1977) $$~gml~‘) (Focht DM of active NH,(,, ’oxidizers (pgg-‘) (1,9,20) DM of active NO, oxidizers (pgg-‘) (2,lO,Z!l) NH, concentration in soil solution (pg ml-‘) (1) NO, concentration in soil solution (pg ml-‘) (2717) number of active MNHlo,( or MNOZ,,,I(pg-‘) (9,lO) 0, concentration at MN,,,,, microsite (rgml-‘) (9) 0, concentration at MNO_,( microsite (pg ml-‘) (10) 0, concentration in soil solution (pg ml-‘) (9,lO) potential rate of COZ(S, reduction by MN,,,,.< under non-limiting [O,,,,] (pg gg’ h-‘) (3,5) potential rate of CO,(,, reduction by MNOZs,< under non-limiting [O,(,,] (pgg-’ h-‘) (4,6) actual rate of CO,,,, reduction by MN”,,,,, from under ambient [O+,] (pgg-’ h-‘)
R CO?-NH,
actual rate of CO,,,, reduction by under ambient [02($,]
R C&N02
actual rate of COZ,r, reduction
from h-‘)
by MNO1e.cfrom
1125
x CO!-NO> x / x, NH,
xho~
X NH, X NO>
d)
(I@*
ratio of NO, reduced to 0, reduced by M NO>rr.r (g g-‘1 (17)* ratio of O,(,, reduced to C oxidized by MN”,,,< and MNO,,., k g-‘1 (7,8,17)* ratio of O,(,, reduced to NH,,,, oxidized by 2(Sjreduced to NH,(,, oxidized by M NOx,,< kg-‘) c8)* potential rate of C oxidation by MNHlo,‘under non-limiting [O,(,,] (pg g-’ h-l) (5,7,17) potential rate of C oxidation by M,oz,,, under non-limiting [O,J (pgg-’ h-l) (6,s) actual rate of C oxidation by MNH,“,< from O,(,, reduction (pgg-‘h-l) (15,17,20) actual rate of C oxidation by M,,,,,, from NO, reduction (pg gg’ h-l) (19,20) actual rate of C oxidation by MNO?o,l from O,,,, reduction (pgg-‘h-l) (16,21) specific maintenance respiration (g reduced C g M,;’ h-‘) (Shields et al., 1973) (20,21) potential rate of NH, oxidation by M,,,., under non-limiting [O,,,,] (pg g-’ h-l) (1,3,7,11) potential rate of NO, oxidation by MNO?,,,‘ under non-limiting [OZcS,] (pg g-’ h-‘) (2,4,8,12) actual rate of NH, oxidation by M,,,,,,, under ambient [O,,,,] (pgg-‘h-l) (ll,l3) actual rate of NO; oxidation by MNOlo,c under ambient [02J (pgg-‘h-‘) (12,14)
Variables (Greek) PNH,
PNO2
specific oxidation rate of NH,,,, by MNHlu,< (g NH,-N g-’ mNHla.‘h-‘) at 30°C under nonlimiting conditions (Belser and Schmidt, 1980a) (I)* specific oxidation rate of NO; by MNO_,,( (g NO;-N g-’ MN02B.1. h-’ ) at 30°C under non-limiting conditions (Belser, 1977) (2)*
*Indicates values recorded at the experimental site or taken from the literature and provided to the ecosystem model. Numbers in parentheses refer to equations in which the variable is used.