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Mathematical simulation of nitrogen interactions in soils
Mathematics North-Holland
and Computers
in Simulation
MATHEMATICAL
XXV (1983) 241-248
SIMULATION
241
OF NITROGEN
INTERACTIONS
IN SOILS
H.M. SELIM Louisiana Agrrcultural
Experiment
Station, Louisiana State University, Baton Rouge, LA 70803, U.S.A.
M. MEHRAN D’Appolonia
Consulting Engineers, Inc., Irvine, CA 92714, U.S.A.
K.K. TANJI Department
of Lund, Air and Water Resources,
Unrversity of California, Davis, CA 95616, U.S.A.
I.K. ISKANDAR U.S. Army Cold Regions Research and Engineering
Laboratory,
Hanover, NH 03755, U.S.A.
Four mathematical models were evaluated for their ability to describe the fate of nitrogen (N) in the soil environment. The first model is a general one which accounts for convective-dispersive N transport under transient water flow conditions with Model II considers N transport to be only of the active N uptake by plants. In convective type, whereas model III considers N uptake as a passive process. contrast, model IV considers N transport under conditions of steady water flow in the Experimental data from lysimeter studies for two soils showed that the soil. convective model (II) and the steady state model (IV) are inferior in describing N transport in comparison to models I and III. It is concluded that transient water flow in the soil system as well as the convective dispersive transport mechanisms must be considered for reliable simulation of N behavior in the soil environment. INTRODUCTION The need to simulate the interactions of nitrogen (N) in the soil environment is essential for the proper management of N in agricultural lands as well as in land disposal Nitrogen is present in of municipal wastes. the soil environment in various organic and These forms inorganic forms (Keeney, 1981). are in a dynamic condition and governed by various chemical and microbiological processes of reversible and irreversible transformations Water soluble N forms, in the soil matrix. extent and to a lesser N03-N such as NH -N, are susceptible to leaching in the soI 1 profile. The movement of N below the root zone not only presents the potential hazard of groundwater contamination but also reduces the amount of N available for plant uptake. several decade, Over the past mathematical models have been developed to describe N transport and transformations in For a review of the the soil profile. available models the reader may refer to Tanji (1982), Iskandar (1981), Frissel and van Veen (1981), and Nielsen and MacDonald (1978). several models consider only N transformation processes (Mehran and Tanji. 1974), whereas others deal with the simultaneous transport and transformations of N species in the soil system. Most models consider N trans-
0378-4754/83/$3.00
0 1983, IMACS/Elsevier
flow formations under steady state water conditions (Cho, 1971; Misra et al., 1974; Wagenet et al., 1977). Recently, a number of models have been developed that consider N transformations in water-unsaturated soils under transient flow conditions (Davidson et al., 1977; Tanji and Mehran. 1979; Selim and Iskandar. 1981). The purpose of this paper is evaluate applicability of four to the simulation models to a greenhouse lysimeter The models presented vary in experiments. their degree of complexity as well as the method of solution. WATER FLOW EQUATION To simulate N transport under transient conditions in an flow unsaturated soil profile, one must solve Richards' water flow equation prior to the N transport and transformation equations. This is necessary in order to predict the fate of N under field conditions of water infiltration (rainfall and/or redistribution. irrigation) and Richards' flow equation with a plant water uptake (sink) term may be expressed as C(O) ah/at = (a/as)
(K(h) ah/az) -
aK(h)/az - A(z,h)
SciencePublishers B.V. (North-Holland)
(1)
H.M. S&n
242
et al. / Mathematical
where h=
K(h) = soil hydraulic conductivity (cm hr-1), hr
-1
NITROGEN TRANSPORT AND TRANSFORMATION EQUATIONS
c(C) = soil-water capacity (cm-l), D= soil-water content (cm3 cm-3 ), z=
distance in soil, positive downward
t=
time (hr).
(cm),
In equation (l), the term c(O) represents unique relations between 0 and h for each soil horizon encountered in the soil profile. The plant water uptake (sink) term A(z.h) was described using a macroscopic approach (Molz and Remson. 1970) which accounts for the root distribution with time and depth (capacity term) and the hydraulic conductivity of the soil A(z,h)
= T R(z,t)
K(h)$R(z,t)K(h)
of nitrogen interactions in soils
solved using an explicitconditions was implicit finite difference method. A Gaussian elimination technique was used to solve the system of equations since the associated matrix was tridiagorial. In addition, the stability and convergence criteria were satisfied at all times.
soil water pressure head (cm),
A(z,h) = rate of extraction (cm3 -3 cm ).
simulation
dz
where T is the evapotranspiration rate (cmlhr) and t is the maximum depth of root penetration in the soil profile. The term R(z,h) is the root distributio (or length) per unit volume %3 of soil (cm cm ). For further details on the use of the water uptake term see Selim and Iskandar (1980). To solve Richards' flow equation the and initial boundary must be conditions described. The initial condition considered was that of a soil profile having a nonuniform C or h distribution at some assumed (starting) time. Boundary conditions at the soil surface commonly used are water flux or pressure head type boundaries. In this study a flux type boundary was chosen:
In this study four N simulation models are presented. Three models (I, II and III) consider N transport and transformations under transient water flow conditions in unsaturated Ln contrast, model IV deals with the soils. fate of N under conditions of steady-state It should be water flow in the soil profile. (convectivethat model I emphasized dispersive) is considered as a generalized N model, whereas models II (purely convective) and III (passive uptake) may be regarded as simplified versions of model I for transient water flow conditions. Model I (Convective-Dispersive) The N transformation processes considered in this model were nitrification of NH -N to NO -N! In and denitrification of NO -N ada ition, it was assumed that NH4-a in the soil solution Is in equilibrium with that It was sorbed on the ion exchange complex. and further assumed that N mineralization immobilization processes are slow and therefore need not be incorporated in these models. convective-dispersive equation for The NO -N and NH -N in the soil system (Selim ana Iskandar, k 981) may be written as a(ox)/at
= (alaz) a (qx)laz
= -K(h)
ah/a2
+ K(h),
at
z=O
+ Q,
-
- uX
(4)
and = (a/az)
a(ou)/at q,(t)
(SD axiaz)
(2)
(CD ay/az)
-
a(qf)/az
Q
Y - UY
+ (5)
where where qo(t) is the flux as a function of time (q t and accounts for water infiltration positive) as well as evaporation (q negative). The second boundary condition at some depth L below the surface was considered as h=O
?z=L
t>o
x=
concentration of NH4-N in soil
Y=
concentration of N03-N in soil
solution (pg cmm3),
solution (up cme3), (3)
which describes the presence of a water table at depth L. The model presented here is not limited to these boundary conditions; others may be easily incorporated. For a discussion on the various types of boundary conditions for water flow in the soil profile the reader may refer to Selim and Iskandar (1980).
D=
solute dispersion coefficient
q=
soil water flux (cm hr-l),
(cm2 hr-l),
Ux and U
Y
= rate of plant uptake of NH4-N and N03-N per unit soil volume (ug cm-3 hr-l),
Richards' flow equation (1) subject the appropriate boundary and initial
to
respectively,
H.M. Selim et al. / Mathematical
Qx =** Qy= rate
qxo= -
soil
qYo
volume (!Jgcm -3 hr-l),
and (4) and (5) the terms U the rate of N uptake w fereas transOafndN imz;nsQy "fz them fife N03-N, and The 4 nitrification respectively. denitrification processes were considered as kinetic the ion first-order type whereas considered of the exchange of NHL-N was Freundich type (Instantaneous or equilibrium). Therefore, the rate of transformation Q, and can be expressed as QY 9,
equations refer to
= -
QY =
kl
P KD ax/at
-
kl 0 X
(6)
OX-k20Y
(7)
where p is the soil bulk density ,(g/cm3), the distribution coefficient (cm /g) for ion exchange process, and kl and first-order kinetic coefficients nitrification denitrification and processes, respectively. The rate coefficients
such as pH, SOil factors influence of content on N and SOil water temperature transformation processes (Hagin and Amberger, 1974; Iskandar, 1981). where kl
= x1
of nitrogen rnteractions in soils
of NH -N and 4 N03-N transformations per unit
respectively. In
simulation
fl
and
k2 = A
2
f2
(8)
where X and X are maximum rate coefficients and f (constaAs) an2 f are dimensionless 2 zero to unity. The functions varyinglfrom and f dependence of f on h and B were described by Se&n and iskandar (1980). In equations (4) and (5) the plant uptake terms and U U were described by a macroscopic &de1 wheX the Michaelis-Menten approach was used (Claassen and Barber, 1976); = I R(z,t) X/[K, + (X + Y)] (9) Ux (10) = I R(z,t) Y/[K U + (X + Y)] m Y where I is the maximum rate of N uptake per root length unit when the (vg/hr-cm) concentration of nitrogen in the soil solution The is extremely high. term K is the Michaelis constant (up cme3) which Represents the concentration of N at 0.5 I. The surface boundary conditions for the N equations (4) and (5) were those of the third type:
0
D aX/az
= - 0 D aY/az
+ qC
243
, z=O,
+ qY,
t > T
(11)
z=o , t > T
(12)
where q = q(t), the flux of water (rainfall or irrigation) at the soil surface. X and Y the concentrations of NH -N an8 NO -NY respectively, in the infiltra4 ion water, ax?d T is the duration of water infiltration. During evaporation and water redistribution, i.e. following water infiltration, the surface boundary conditions are ax/a2
=
0
and
ay/az
=
0,
z=o,
t >T
(13)
The boundary conditions at some depth L in the soil profile are (Dankwerts, 1953) ax/a2
=
0
and
ay/az
=
0,
z=o,
t>
T
(14)
For multilayered soil profiles, it is necessary to include the boundary conditions at the interface between SOil layers. These boundaries were such that h. X and Y are continuous functions across the interlayers (Selim, 1978). In addition, initial conditions required to solve the N equations are the distribution of the various N species with depth in the soil at some starting (or initial) time. transport The N and transformation equations (4) and (5) are nonlinear partial differential equations and were thus solved using numerical analysis techniques. The method used was the explicit-implicit finite difference method similar to that used in solving Richards' water flow equation (1). This method was successfully used by Selim (1978) for steady as well as transient water and solute transport in layered soils. ShCS from equations (4) and (5) N transport is dependent on 8 and q, Richards' flow equation (1) was solved prior to the N equations (4) and (5). Therefore, for any time step n + 1, where all variables are assumed known at time step n, equations (I), (4) and (5) were sequentially solved for any desired time t. Model II (Convective) This model is a transient flow model where Richards' flow equation was used in a similar fashion to model I. Moreover, the transformation processes and boundary and initial conditions were also similar to those described in model I. The complexity of model however, WSS simplified without I, compromising the transient flow aspect of N transport in the SO-i1 system. Two simplifications WS?X made. First, the dispersion term of N transport in equations (4) and (5) was ignored. Second, the method of solution of the N equations was the fully
244
H.M.
Selim et al. / Mathematical
explicit-finite difference method. Therefore, the N equations for the convective model (II) were (15)
aoYfat
(16)
+ Q, - uy
were above equations further The two rearranged, utilizing the continuity equation for water flow, as 0 ax/at = - 4 0 au/at
ax/a2
= - q aYfas
- Q,
- ux
- 9, - uy
(18)
Model III (Passive Uptake) This model is a transient flow model, where above two models, similar to the Richards' water flow equation was utilized. three model this developing However, in First, simplifying assumptions were made. plant uptake of NH4-N and N05-N forms was NH4-N Second, passive. considered nitrification to NO -N "as considered as the dominant transforma 2ion process and other N NH4-N, exchange of ion processes (i.e. therefore, were, etc.) denitrification, ignored. Third, the nitrification process "as considered of the first kinetic type, with the The rate coefficient considered constant. for equations transport and transformation NH -N and NO -N were similar to those of However, the MoLdel I (eque?tions 4 and 5). transformation and uptake terms, based on the above assumptions, were expressed as
Q,
=
-
x2
0
x
0 Y
X A(z,h)
(21) (27.)
= Y A(z,h) Y
In equations (19) and_l(20) the term X is the rate coefficient (hr ) for the nitr i?f ication process. The N uptake equations (21) and (22) assume the uptake of N to be proportional to the rate of water uptake and NH4-N and NO.,-N concentrations in the soil solution.
(17)
justification for ignoring the The dispersion term of the convective-dispersive equations (4) and (5) "as based on the fact that during water infiltration, the mass flow or convection term is far more dominant than the influencing term in the dispersion In transport of solutes in porous media. addition, the dispersion coefficient D has been shown to be dependent on the pore water velocity (q/O). As a result, during periods of water redistribution where the flow velocity is small, the value of D becomes extremely small. It should be emphasized here, however, that the influence of the dispersion term on the shape of the solute distribution curve and to a lesser extent on the advance of a solute front miscible flow water steady under (or documented (Brenner, is well displacement) In solving equations (17) and (18) 1962). using the explicit schemes, the need for matrix inversion was avoided, which resulted not only in considerable simplification of the computer program but also in saving in computer time.
Qx = - x1
ux= U
aoxlat = - aqx/az - Qx - ux = - aqYfaz
simulation of nitrogen interactions in soils
(19) (20)
It is obvious from equations (19) to (22) that this model represents drastic simplifications over model I. The fact that N uptake "as passive and only the nitrification process, with a constant rate coefficient, "as considered are obvious simplifications. However, the introduction of N uptake as a passive process results in an additional simplification. Unlike passive uptake, when N uptake is considered active (such as in models I and II) it is necessary to maintain solute balance in the soil system, since water and N uptake were treated as independent processes (see equations (14) and (15) in Selim and Iskandar, 1981). Moreover, the numerical method used in solving the N transport and transformation equations "as the explicitimplicit finite difference technique. For further details of model III, which "as originally developed as part of an integrated study of nitrate leaching losses from irrigated lands, the reader may refer to Tanji and Mehran (1979). Model IV (Steady State) In contrast to all the above models, this model "as developed to describe the fate of N under conditions of steady water flow in the soil profile. Obviously, such a steady-state model may not adequately describe the fate of N in the top portion of the soil surface or root where infiltration the zone, and redistribution cause the flow conditions to be strictly transient. On the other hand, such models may be adequate under conditions where a somewhat continuous and steady flux is dominant, such as the case in land treatment of wastewater as well as at soil depths beyond the root zone, where quasi-steady state may be assumed. The N equations for steady-state water flow (Misra et al., 1974) are ax/at
= D a2X/az2 (Qx
aY/at
+
= D a2Y/az2 (Q,
+
- v ax/a2
-
ux)/w
Uy)/w
(23)
- v ax/a2
(24)
where v is the pore water velocity and w is an average water content and both parameters were considered constant for each soil layer.
H.M.
&lint et al. / Maihematical
simulation of nitrogen interactions in soils
It is obvious that several assumptions must be made in order to arrive at appropriate parameters (especially v and w) necessary for the solution of the above equations. These assumptions were (i) steady-state water flow, (ii) constant' water content or suction with time for each soil layer, (iii) amount of water infiltration equal to that applied minus evapotranspiration, and (iv) input pulses continuous and constant within each water irrigation or infiltration event. In addition to these assumptions, this model does not the allow incorporation of the N transformation processes as a function of soil water content or suction. This is crucial when describing the nitrification as well as denitrification processes which are highly dependent on the degree of soil saturation. The method of solution used for model IV was the explicit-implicit method. The solution was stable and a mass balance was maintained as a check on the numerical results.
24s
.*
-150 .
t/
I
l
.l:*‘*@
’
-100
0
.
Z5 cm
.
I
-Jy , ,wiyg;i; , (
1.0
2.0
3.0
4.0
MODEL VALIDATIONS The scarcity of comprehensive field data makes extensive evaluation of the above models difficult. Moreover, critical evaluation of these models requires that necessary input parameters (e.g. o, R(h), I$,, etc.) for an indivi&ual soil be vali"x fork2' a wide range of conditions. In this paper the data base was that from greenhouse experiments using soil lysimeters which received frequent applications of wastewater as a source of nitrogen. Two soils were used, a Windsor sandy loam and a Charlton silt loam. Each soil consisted of three layers 15, 30 and 105 cm in thickness. A mixture of grasses was both Secondary-treated grown on soils. wastewater was applied every 3-4 days at a rate of 3.83 cm application. The per wastewater varied in nitrogen concentrations from 17 to 45 ug/ml for NH&-N and zero to 29 pg/ml for N03-N. The lysimeters were intensively monitored for soil water pressure head h, NH4-N and N03-N concentrations, Eh, pR, temperature and root distribution with soil depth. In addition, the volume of applied effluent and leachate was measured and analyzed. N uptake by plants was measured several times by frequent cuttings and analysis of the grass. The details of the lysimeter set-up and may be construction found in Iskandar and Nakano (1978). In order to fully evaluate the transient N models (I, II and III) it is essential to validate Richards' water flow equation prior to incorporation into the nitrogen equations. Good model predictions were obtained for pressure head with time and soil depth (Fig. 1) as well as water content (based on gravimetric sampling) and depth (figure not shown). The predictions and the soil water
0
I.o
4.0
I
0
I
1.0 Time After
Fig.1
I
I
I
2.0
1
,
3.0
Application
4.0
(days)
Soil water pressure head vs time at three depths in Windsor soil.
CHARLTON .
20
Fig.2
40
GO TIME
80 , days
WINDSOR
loo
120
Measured and predicted N uptake for Windsor and Charlton soils.
140
246
H.M. S&n
et al. / Mathematical
simulation of nitrogen interactions in soils
NO;-N,
t I&
00
‘0 _____,20
30 :
A
3o
$
60
’
40 ” “’
l. l
/*.*
50 ..’ ‘... .I
.
,/’
/.“*
150 IT-Model
I
-
m-
Fig.
3
Experimental and calculated nitrate (NO3 - N) concentrations in soil solution vs depth for days 17, 21, 24, and 29 for Windsor soil.
NO;-N,
Nglml
b
Model
I III-
Fig.
4
II _--N
- .___.. _. .
EXP
.
Experimental and calculated nitrate (NO3 - N) concentrations in soil solution vs. depth for days 87, 91, 94, and 98 for Windsor soil.
H.M. Selim et al. / Mathematical
simulation
parameters for individual layers as well as the root distribution function are given by It should be Iskandar and Selim (1981). emphasized here that such results are not surprising since there is ample evidence in the literature of the validity of Richards' flow equation under various boundary and initial conditions. Model predictions of N uptake by plants for Windsor and Charlton soils are shown in Fig. 2. P&ant upta:? P-Y ameters used were I of 5 x 10 ng hr cm of root and K of -3 1.0 ng cm . It is interesting to note ?hat for all four models the cumulative plant uptake was similar for both soils. Moreover, plant uptake predictions were linear, which indicate high N concentrations in the soil root zone. In contrast, nonlinear plant uptake behavior was measured experimentally after 60 days (Fig. 2) for both soils. It is surprising that closer agreements were obtained using the steady water flow model IV than the transient models. This is due primarily to the fact that in order to simulate a continuous steady-state feed condition, the concentrations of applied N Such adjustments resulted in were adjusted. lower NH4-N and NO -N concentration in the 0 to 15 cm soil depta and affected the rate of uptake in comparison to the transient flow models. It should be noted also that the uptake (model III) assumption of passive resulted in better agreement with measured data in comparison to active uptake (models I and II). Experimental and simulated results of N03-N concentration distributions with depth for Windsor soil for selected times are shown in Figs. 3 and 4. It is obvious that transient models I and III are far superior to models II and IV. For all models, deviations of simulated results from experimental data were pronounced in the soil surface zone (0 to 30 cm). Such deviations are crucial since this soil zone is the most active in the soil profile and directly affects plant uptake of N. It is apparent from Figs. 3 and 4 that the purely convective model II predicted lcG?er N03-N peak concentrations whereas the opposite was true for the steady-state model IV for the selected times shown. To obtain the predicted results shown in Figs. 3 a d 4 wz;e I$ = 1.5 cm' g-l f~~rP~cZZt~rsI,Us~~ . The nitrification ratelcoefficient was chosen as 0.050 hr for tllf s h$eady-state model IV whereas a 0.075 hr value was chosen for the transient models I, II and III. Such a A value was chosen since it provided the best' agreement using model I (Iskandar and Selim, 1981). In addition, for the transient models I and II, fl of equation (8) was considered variable depending on soil water suction. .In contrast, a constant was
of nitrogen interactions in soils
247
considered (i.e. f (see Iskandar and ) was
chosen for model value
of
IV
0.01
As mentioned processes were % = x2 = 0).
ignored
for model ,111
(i.e.
For a more complete assessment of the predictive capabilities of the models, the NO -N results are presented with time for se1ected soil depths in Rig. 5. The depths selected were those where NO -N measurements were made. It is obvious tI? at none of the models provided close agreement with measured data for all depths and times. More crucial is the inability of all models to predict NO concentration peaks which occurred at di?ferent times for the different soil depths. However, the transient models I and III
Model
n ---
I -
TIME, Fig. 5
-
days
Measured and predicted NO -N concentration vs. time at selec 2ed soil depths for Windsor soil.
H.M. Selim et al. / Mathematical
248
overall agreement with provided the best experimental data. In contrast, the purely (II) provided less than convective model showed adequate overall predictions and several peak concentrations with time for all obtain improved Attempts to depths. predictions by use of several values for kD did not result in better predictions and k using&ode1 II. Therefore, it can be concluded that purely convective transport provides poor the incorporation of prediction, and the dispersion term is necessary to describe N transport in soils. The steady state model IV consistently predicted higher than measured for all depths. with time concentrations However, it can be regarded as a superior model than model II, which is a transient model. In summary, four models which describe the fate of N in the soil profile have been Three models are of the transient evaluated. water flow type, whereas one is for steady The results indicated water flow conditions. the II where flow model transient that dispersion term was ignored, provided less prediction of overall adequate than In addition, convective experimental data. dispersive transient models proved superior to the steady state model.
simulation of nitrogen interactions in soils
t91
[lOI
illI
1121
t131
[I41
[I51
LITERATURE CITED [Ml 1962. The diffusion model of longitudinal mixing in beds of finite length, numerical values. Chem. Eng. Sci. 17:229-243. Cho, C. M. 1971. Convective transport of t2 ammonium with nitrification in soil. Can. J. Soil Sci. 51:339-350. 13 Claassen, N. and S. A. Barber. 1976. Simulation model for nutrient uptake from soil by a growing plant root system. Agron. J. 68:961-966. 143 Dankwerts, P. W. 1953. Continuous flow systems; Distribution of residence time. Chem. Eng. Sci. 2: 1-13. [51 Davidson, J. M., P. S. C. Rao and H. M. Selim. 1977. Simulation of nitrogen movement, transformations and plant uptake in the root zone. Proc. Nat. Conf. Irrigated Return Flow, Ft. Collins, Cola. pp. 9-18. Frissel, M. J. and J. A. van Veen (eds.). Nitrogen behavior 1981. Simulation of of soil-plant systems. Pudoc, Wageningen. Hagin, J. and A. Amberger. 1974. Contri[71 bution of fertilizer and manures to the Nand P-load of waters; A computer simulation. Final Rept. to Deutsche Forschungs Gemeinschaft from Technion. Haifa, Israel (123 p). 1’31 Iskandar, I. K. (ed.). 1981. Modeling Wastewater Renovation, Land Treatment. Wiley-Interscience.
111 Brenner, H.
[17 ‘1
t18 ;I
[I91
[7-01
12 -1
Iskandar, I. K. and Y. Nakano. 1978. Soil lysimeters for validation models of wastewater renovation by land application: Construction, operation and performance. CRREL Spec. Rpt. 78-12, U.S. Army CRREL, Hanover, NH. Iskandar, I. K. and H. M. Selim. 1981. Modeling nitrogen transport and transformations in soils; 2. Validation. Soil Sci. 131:303-312. Keeney, D. R. 1981. Soil Nitrogen Chemistry and biochemistry. Ip I. K. Iskandar (ed) Modeling Wastewater Renovation, Land Treatment. pp. 259-276. Wiley-Interscience. Mehran, M. and K. K. Tanji. 1974. Computer modeling of nitrogen transformations in soils. J. Environ. Qual. 3:391-396. Misra, C., D. R. Nielsen and J. W. Biggar. 1974. Nitrogen transformation in soil during leaching: I, II and III. Soil Sci. Sot. Am. Proc. 38:289-304. Molz, F. J., and I. Remson. 1970. Extraction term models of soil moisture use by transpiring plants. Water Resources Res. 6:1346-1356. Nielsen, D. R.. and J. G. MacDonald. (eds.). 1978. Nitrogen in the Environment. Vol. 1. Nitrogen behavior in field soils. Academic Press. 526 p. Selim, H. M. 1978. Transport of reactive solutes during transient unsaturated water flow in multilayered soils. Soil sci. 126:127-135. Selim, H. M. and I. K. Iskandar. 1980. Simplified model for prediction of nitrogen behavior in land treatment of wastewater. CRREL Rept. 80-12, U.S. Army CRREL, Hanover, N.H. Selim, H. M. and I. K. Iskandar. 1981. Modeling nitrogen transport and transformations in soils; 1. Theoretical considerations. Soil sci. 131:233-241. Tanji, K. K. 1982. Modeling of the soil nitrogen cycle. Ch. 19, &r Nitrogen in Agricultural Soils, F. J. Stevenson (ea.), Agron. Mon. 22 (pp 721-772) Am. Sot. Agron., Madison, Wisconsin. Tanji, K. K., and M. Mehran. 1979. Conceptual and dynamic models for nitrogen in irrigated croplands. p. 555-646. & P. F. Pratt, Nitrate in effluents from irrigated lands. Final Rept. to Nato Sci. Found., Univ. Calif., Riverside. Wagenet, R. J., J. W. Biggar, and D. R. Nielsen. 1977. Tracing the transformations of urea fertilizer during leaching. Soil Sci. Sot. Am. Proc. 41:896-902.
ACKNOWLEDGEMENT The authors gratefully acknowledge Mrs. Pam Latimer for her efforts in the preparation of this manuscript.
and Computers
in Simulation
MATHEMATICAL
XXV (1983) 241-248
SIMULATION
241
OF NITROGEN
INTERACTIONS
IN SOILS
H.M. SELIM Louisiana Agrrcultural
Experiment
Station, Louisiana State University, Baton Rouge, LA 70803, U.S.A.
M. MEHRAN D’Appolonia
Consulting Engineers, Inc., Irvine, CA 92714, U.S.A.
K.K. TANJI Department
of Lund, Air and Water Resources,
Unrversity of California, Davis, CA 95616, U.S.A.
I.K. ISKANDAR U.S. Army Cold Regions Research and Engineering
Laboratory,
Hanover, NH 03755, U.S.A.
Four mathematical models were evaluated for their ability to describe the fate of nitrogen (N) in the soil environment. The first model is a general one which accounts for convective-dispersive N transport under transient water flow conditions with Model II considers N transport to be only of the active N uptake by plants. In convective type, whereas model III considers N uptake as a passive process. contrast, model IV considers N transport under conditions of steady water flow in the Experimental data from lysimeter studies for two soils showed that the soil. convective model (II) and the steady state model (IV) are inferior in describing N transport in comparison to models I and III. It is concluded that transient water flow in the soil system as well as the convective dispersive transport mechanisms must be considered for reliable simulation of N behavior in the soil environment. INTRODUCTION The need to simulate the interactions of nitrogen (N) in the soil environment is essential for the proper management of N in agricultural lands as well as in land disposal Nitrogen is present in of municipal wastes. the soil environment in various organic and These forms inorganic forms (Keeney, 1981). are in a dynamic condition and governed by various chemical and microbiological processes of reversible and irreversible transformations Water soluble N forms, in the soil matrix. extent and to a lesser N03-N such as NH -N, are susceptible to leaching in the soI 1 profile. The movement of N below the root zone not only presents the potential hazard of groundwater contamination but also reduces the amount of N available for plant uptake. several decade, Over the past mathematical models have been developed to describe N transport and transformations in For a review of the the soil profile. available models the reader may refer to Tanji (1982), Iskandar (1981), Frissel and van Veen (1981), and Nielsen and MacDonald (1978). several models consider only N transformation processes (Mehran and Tanji. 1974), whereas others deal with the simultaneous transport and transformations of N species in the soil system. Most models consider N trans-
0378-4754/83/$3.00
0 1983, IMACS/Elsevier
flow formations under steady state water conditions (Cho, 1971; Misra et al., 1974; Wagenet et al., 1977). Recently, a number of models have been developed that consider N transformations in water-unsaturated soils under transient flow conditions (Davidson et al., 1977; Tanji and Mehran. 1979; Selim and Iskandar. 1981). The purpose of this paper is evaluate applicability of four to the simulation models to a greenhouse lysimeter The models presented vary in experiments. their degree of complexity as well as the method of solution. WATER FLOW EQUATION To simulate N transport under transient conditions in an flow unsaturated soil profile, one must solve Richards' water flow equation prior to the N transport and transformation equations. This is necessary in order to predict the fate of N under field conditions of water infiltration (rainfall and/or redistribution. irrigation) and Richards' flow equation with a plant water uptake (sink) term may be expressed as C(O) ah/at = (a/as)
(K(h) ah/az) -
aK(h)/az - A(z,h)
SciencePublishers B.V. (North-Holland)
(1)
H.M. S&n
242
et al. / Mathematical
where h=
K(h) = soil hydraulic conductivity (cm hr-1), hr
-1
NITROGEN TRANSPORT AND TRANSFORMATION EQUATIONS
c(C) = soil-water capacity (cm-l), D= soil-water content (cm3 cm-3 ), z=
distance in soil, positive downward
t=
time (hr).
(cm),
In equation (l), the term c(O) represents unique relations between 0 and h for each soil horizon encountered in the soil profile. The plant water uptake (sink) term A(z.h) was described using a macroscopic approach (Molz and Remson. 1970) which accounts for the root distribution with time and depth (capacity term) and the hydraulic conductivity of the soil A(z,h)
= T R(z,t)
K(h)$R(z,t)K(h)
of nitrogen interactions in soils
solved using an explicitconditions was implicit finite difference method. A Gaussian elimination technique was used to solve the system of equations since the associated matrix was tridiagorial. In addition, the stability and convergence criteria were satisfied at all times.
soil water pressure head (cm),
A(z,h) = rate of extraction (cm3 -3 cm ).
simulation
dz
where T is the evapotranspiration rate (cmlhr) and t is the maximum depth of root penetration in the soil profile. The term R(z,h) is the root distributio (or length) per unit volume %3 of soil (cm cm ). For further details on the use of the water uptake term see Selim and Iskandar (1980). To solve Richards' flow equation the and initial boundary must be conditions described. The initial condition considered was that of a soil profile having a nonuniform C or h distribution at some assumed (starting) time. Boundary conditions at the soil surface commonly used are water flux or pressure head type boundaries. In this study a flux type boundary was chosen:
In this study four N simulation models are presented. Three models (I, II and III) consider N transport and transformations under transient water flow conditions in unsaturated Ln contrast, model IV deals with the soils. fate of N under conditions of steady-state It should be water flow in the soil profile. (convectivethat model I emphasized dispersive) is considered as a generalized N model, whereas models II (purely convective) and III (passive uptake) may be regarded as simplified versions of model I for transient water flow conditions. Model I (Convective-Dispersive) The N transformation processes considered in this model were nitrification of NH -N to NO -N! In and denitrification of NO -N ada ition, it was assumed that NH4-a in the soil solution Is in equilibrium with that It was sorbed on the ion exchange complex. and further assumed that N mineralization immobilization processes are slow and therefore need not be incorporated in these models. convective-dispersive equation for The NO -N and NH -N in the soil system (Selim ana Iskandar, k 981) may be written as a(ox)/at
= (alaz) a (qx)laz
= -K(h)
ah/a2
+ K(h),
at
z=O
+ Q,
-
- uX
(4)
and = (a/az)
a(ou)/at q,(t)
(SD axiaz)
(2)
(CD ay/az)
-
a(qf)/az
Q
Y - UY
+ (5)
where where qo(t) is the flux as a function of time (q t and accounts for water infiltration positive) as well as evaporation (q negative). The second boundary condition at some depth L below the surface was considered as h=O
?z=L
t>o
x=
concentration of NH4-N in soil
Y=
concentration of N03-N in soil
solution (pg cmm3),
solution (up cme3), (3)
which describes the presence of a water table at depth L. The model presented here is not limited to these boundary conditions; others may be easily incorporated. For a discussion on the various types of boundary conditions for water flow in the soil profile the reader may refer to Selim and Iskandar (1980).
D=
solute dispersion coefficient
q=
soil water flux (cm hr-l),
(cm2 hr-l),
Ux and U
Y
= rate of plant uptake of NH4-N and N03-N per unit soil volume (ug cm-3 hr-l),
Richards' flow equation (1) subject the appropriate boundary and initial
to
respectively,
H.M. Selim et al. / Mathematical
Qx =** Qy= rate
qxo= -
soil
qYo
volume (!Jgcm -3 hr-l),
and (4) and (5) the terms U the rate of N uptake w fereas transOafndN imz;nsQy "fz them fife N03-N, and The 4 nitrification respectively. denitrification processes were considered as kinetic the ion first-order type whereas considered of the exchange of NHL-N was Freundich type (Instantaneous or equilibrium). Therefore, the rate of transformation Q, and can be expressed as QY 9,
equations refer to
= -
QY =
kl
P KD ax/at
-
kl 0 X
(6)
OX-k20Y
(7)
where p is the soil bulk density ,(g/cm3), the distribution coefficient (cm /g) for ion exchange process, and kl and first-order kinetic coefficients nitrification denitrification and processes, respectively. The rate coefficients
such as pH, SOil factors influence of content on N and SOil water temperature transformation processes (Hagin and Amberger, 1974; Iskandar, 1981). where kl
= x1
of nitrogen rnteractions in soils
of NH -N and 4 N03-N transformations per unit
respectively. In
simulation
fl
and
k2 = A
2
f2
(8)
where X and X are maximum rate coefficients and f (constaAs) an2 f are dimensionless 2 zero to unity. The functions varyinglfrom and f dependence of f on h and B were described by Se&n and iskandar (1980). In equations (4) and (5) the plant uptake terms and U U were described by a macroscopic &de1 wheX the Michaelis-Menten approach was used (Claassen and Barber, 1976); = I R(z,t) X/[K, + (X + Y)] (9) Ux (10) = I R(z,t) Y/[K U + (X + Y)] m Y where I is the maximum rate of N uptake per root length unit when the (vg/hr-cm) concentration of nitrogen in the soil solution The is extremely high. term K is the Michaelis constant (up cme3) which Represents the concentration of N at 0.5 I. The surface boundary conditions for the N equations (4) and (5) were those of the third type:
0
D aX/az
= - 0 D aY/az
+ qC
243
, z=O,
+ qY,
t > T
(11)
z=o , t > T
(12)
where q = q(t), the flux of water (rainfall or irrigation) at the soil surface. X and Y the concentrations of NH -N an8 NO -NY respectively, in the infiltra4 ion water, ax?d T is the duration of water infiltration. During evaporation and water redistribution, i.e. following water infiltration, the surface boundary conditions are ax/a2
=
0
and
ay/az
=
0,
z=o,
t >T
(13)
The boundary conditions at some depth L in the soil profile are (Dankwerts, 1953) ax/a2
=
0
and
ay/az
=
0,
z=o,
t>
T
(14)
For multilayered soil profiles, it is necessary to include the boundary conditions at the interface between SOil layers. These boundaries were such that h. X and Y are continuous functions across the interlayers (Selim, 1978). In addition, initial conditions required to solve the N equations are the distribution of the various N species with depth in the soil at some starting (or initial) time. transport The N and transformation equations (4) and (5) are nonlinear partial differential equations and were thus solved using numerical analysis techniques. The method used was the explicit-implicit finite difference method similar to that used in solving Richards' water flow equation (1). This method was successfully used by Selim (1978) for steady as well as transient water and solute transport in layered soils. ShCS from equations (4) and (5) N transport is dependent on 8 and q, Richards' flow equation (1) was solved prior to the N equations (4) and (5). Therefore, for any time step n + 1, where all variables are assumed known at time step n, equations (I), (4) and (5) were sequentially solved for any desired time t. Model II (Convective) This model is a transient flow model where Richards' flow equation was used in a similar fashion to model I. Moreover, the transformation processes and boundary and initial conditions were also similar to those described in model I. The complexity of model however, WSS simplified without I, compromising the transient flow aspect of N transport in the SO-i1 system. Two simplifications WS?X made. First, the dispersion term of N transport in equations (4) and (5) was ignored. Second, the method of solution of the N equations was the fully
244
H.M.
Selim et al. / Mathematical
explicit-finite difference method. Therefore, the N equations for the convective model (II) were (15)
aoYfat
(16)
+ Q, - uy
were above equations further The two rearranged, utilizing the continuity equation for water flow, as 0 ax/at = - 4 0 au/at
ax/a2
= - q aYfas
- Q,
- ux
- 9, - uy
(18)
Model III (Passive Uptake) This model is a transient flow model, where above two models, similar to the Richards' water flow equation was utilized. three model this developing However, in First, simplifying assumptions were made. plant uptake of NH4-N and N05-N forms was NH4-N Second, passive. considered nitrification to NO -N "as considered as the dominant transforma 2ion process and other N NH4-N, exchange of ion processes (i.e. therefore, were, etc.) denitrification, ignored. Third, the nitrification process "as considered of the first kinetic type, with the The rate coefficient considered constant. for equations transport and transformation NH -N and NO -N were similar to those of However, the MoLdel I (eque?tions 4 and 5). transformation and uptake terms, based on the above assumptions, were expressed as
Q,
=
-
x2
0
x
0 Y
X A(z,h)
(21) (27.)
= Y A(z,h) Y
In equations (19) and_l(20) the term X is the rate coefficient (hr ) for the nitr i?f ication process. The N uptake equations (21) and (22) assume the uptake of N to be proportional to the rate of water uptake and NH4-N and NO.,-N concentrations in the soil solution.
(17)
justification for ignoring the The dispersion term of the convective-dispersive equations (4) and (5) "as based on the fact that during water infiltration, the mass flow or convection term is far more dominant than the influencing term in the dispersion In transport of solutes in porous media. addition, the dispersion coefficient D has been shown to be dependent on the pore water velocity (q/O). As a result, during periods of water redistribution where the flow velocity is small, the value of D becomes extremely small. It should be emphasized here, however, that the influence of the dispersion term on the shape of the solute distribution curve and to a lesser extent on the advance of a solute front miscible flow water steady under (or documented (Brenner, is well displacement) In solving equations (17) and (18) 1962). using the explicit schemes, the need for matrix inversion was avoided, which resulted not only in considerable simplification of the computer program but also in saving in computer time.
Qx = - x1
ux= U
aoxlat = - aqx/az - Qx - ux = - aqYfaz
simulation of nitrogen interactions in soils
(19) (20)
It is obvious from equations (19) to (22) that this model represents drastic simplifications over model I. The fact that N uptake "as passive and only the nitrification process, with a constant rate coefficient, "as considered are obvious simplifications. However, the introduction of N uptake as a passive process results in an additional simplification. Unlike passive uptake, when N uptake is considered active (such as in models I and II) it is necessary to maintain solute balance in the soil system, since water and N uptake were treated as independent processes (see equations (14) and (15) in Selim and Iskandar, 1981). Moreover, the numerical method used in solving the N transport and transformation equations "as the explicitimplicit finite difference technique. For further details of model III, which "as originally developed as part of an integrated study of nitrate leaching losses from irrigated lands, the reader may refer to Tanji and Mehran (1979). Model IV (Steady State) In contrast to all the above models, this model "as developed to describe the fate of N under conditions of steady water flow in the soil profile. Obviously, such a steady-state model may not adequately describe the fate of N in the top portion of the soil surface or root where infiltration the zone, and redistribution cause the flow conditions to be strictly transient. On the other hand, such models may be adequate under conditions where a somewhat continuous and steady flux is dominant, such as the case in land treatment of wastewater as well as at soil depths beyond the root zone, where quasi-steady state may be assumed. The N equations for steady-state water flow (Misra et al., 1974) are ax/at
= D a2X/az2 (Qx
aY/at
+
= D a2Y/az2 (Q,
+
- v ax/a2
-
ux)/w
Uy)/w
(23)
- v ax/a2
(24)
where v is the pore water velocity and w is an average water content and both parameters were considered constant for each soil layer.
H.M.
&lint et al. / Maihematical
simulation of nitrogen interactions in soils
It is obvious that several assumptions must be made in order to arrive at appropriate parameters (especially v and w) necessary for the solution of the above equations. These assumptions were (i) steady-state water flow, (ii) constant' water content or suction with time for each soil layer, (iii) amount of water infiltration equal to that applied minus evapotranspiration, and (iv) input pulses continuous and constant within each water irrigation or infiltration event. In addition to these assumptions, this model does not the allow incorporation of the N transformation processes as a function of soil water content or suction. This is crucial when describing the nitrification as well as denitrification processes which are highly dependent on the degree of soil saturation. The method of solution used for model IV was the explicit-implicit method. The solution was stable and a mass balance was maintained as a check on the numerical results.
24s
.*
-150 .
t/
I
l
.l:*‘*@
’
-100
0
.
Z5 cm
.
I
-Jy , ,wiyg;i; , (
1.0
2.0
3.0
4.0
MODEL VALIDATIONS The scarcity of comprehensive field data makes extensive evaluation of the above models difficult. Moreover, critical evaluation of these models requires that necessary input parameters (e.g. o, R(h), I$,, etc.) for an indivi&ual soil be vali"x fork2' a wide range of conditions. In this paper the data base was that from greenhouse experiments using soil lysimeters which received frequent applications of wastewater as a source of nitrogen. Two soils were used, a Windsor sandy loam and a Charlton silt loam. Each soil consisted of three layers 15, 30 and 105 cm in thickness. A mixture of grasses was both Secondary-treated grown on soils. wastewater was applied every 3-4 days at a rate of 3.83 cm application. The per wastewater varied in nitrogen concentrations from 17 to 45 ug/ml for NH&-N and zero to 29 pg/ml for N03-N. The lysimeters were intensively monitored for soil water pressure head h, NH4-N and N03-N concentrations, Eh, pR, temperature and root distribution with soil depth. In addition, the volume of applied effluent and leachate was measured and analyzed. N uptake by plants was measured several times by frequent cuttings and analysis of the grass. The details of the lysimeter set-up and may be construction found in Iskandar and Nakano (1978). In order to fully evaluate the transient N models (I, II and III) it is essential to validate Richards' water flow equation prior to incorporation into the nitrogen equations. Good model predictions were obtained for pressure head with time and soil depth (Fig. 1) as well as water content (based on gravimetric sampling) and depth (figure not shown). The predictions and the soil water
0
I.o
4.0
I
0
I
1.0 Time After
Fig.1
I
I
I
2.0
1
,
3.0
Application
4.0
(days)
Soil water pressure head vs time at three depths in Windsor soil.
CHARLTON .
20
Fig.2
40
GO TIME
80 , days
WINDSOR
loo
120
Measured and predicted N uptake for Windsor and Charlton soils.
140
246
H.M. S&n
et al. / Mathematical
simulation of nitrogen interactions in soils
NO;-N,
t I&
00
‘0 _____,20
30 :
A
3o
$
60
’
40 ” “’
l. l
/*.*
50 ..’ ‘... .I
.
,/’
/.“*
150 IT-Model
I
-
m-
Fig.
3
Experimental and calculated nitrate (NO3 - N) concentrations in soil solution vs depth for days 17, 21, 24, and 29 for Windsor soil.
NO;-N,
Nglml
b
Model
I III-
Fig.
4
II _--N
- .___.. _. .
EXP
.
Experimental and calculated nitrate (NO3 - N) concentrations in soil solution vs. depth for days 87, 91, 94, and 98 for Windsor soil.
H.M. Selim et al. / Mathematical
simulation
parameters for individual layers as well as the root distribution function are given by It should be Iskandar and Selim (1981). emphasized here that such results are not surprising since there is ample evidence in the literature of the validity of Richards' flow equation under various boundary and initial conditions. Model predictions of N uptake by plants for Windsor and Charlton soils are shown in Fig. 2. P&ant upta:? P-Y ameters used were I of 5 x 10 ng hr cm of root and K of -3 1.0 ng cm . It is interesting to note ?hat for all four models the cumulative plant uptake was similar for both soils. Moreover, plant uptake predictions were linear, which indicate high N concentrations in the soil root zone. In contrast, nonlinear plant uptake behavior was measured experimentally after 60 days (Fig. 2) for both soils. It is surprising that closer agreements were obtained using the steady water flow model IV than the transient models. This is due primarily to the fact that in order to simulate a continuous steady-state feed condition, the concentrations of applied N Such adjustments resulted in were adjusted. lower NH4-N and NO -N concentration in the 0 to 15 cm soil depta and affected the rate of uptake in comparison to the transient flow models. It should be noted also that the uptake (model III) assumption of passive resulted in better agreement with measured data in comparison to active uptake (models I and II). Experimental and simulated results of N03-N concentration distributions with depth for Windsor soil for selected times are shown in Figs. 3 and 4. It is obvious that transient models I and III are far superior to models II and IV. For all models, deviations of simulated results from experimental data were pronounced in the soil surface zone (0 to 30 cm). Such deviations are crucial since this soil zone is the most active in the soil profile and directly affects plant uptake of N. It is apparent from Figs. 3 and 4 that the purely convective model II predicted lcG?er N03-N peak concentrations whereas the opposite was true for the steady-state model IV for the selected times shown. To obtain the predicted results shown in Figs. 3 a d 4 wz;e I$ = 1.5 cm' g-l f~~rP~cZZt~rsI,Us~~ . The nitrification ratelcoefficient was chosen as 0.050 hr for tllf s h$eady-state model IV whereas a 0.075 hr value was chosen for the transient models I, II and III. Such a A value was chosen since it provided the best' agreement using model I (Iskandar and Selim, 1981). In addition, for the transient models I and II, fl of equation (8) was considered variable depending on soil water suction. .In contrast, a constant was
of nitrogen interactions in soils
247
considered (i.e. f (see Iskandar and ) was
chosen for model value
of
IV
0.01
As mentioned processes were % = x2 = 0).
ignored
for model ,111
(i.e.
For a more complete assessment of the predictive capabilities of the models, the NO -N results are presented with time for se1ected soil depths in Rig. 5. The depths selected were those where NO -N measurements were made. It is obvious tI? at none of the models provided close agreement with measured data for all depths and times. More crucial is the inability of all models to predict NO concentration peaks which occurred at di?ferent times for the different soil depths. However, the transient models I and III
Model
n ---
I -
TIME, Fig. 5
-
days
Measured and predicted NO -N concentration vs. time at selec 2ed soil depths for Windsor soil.
H.M. Selim et al. / Mathematical
248
overall agreement with provided the best experimental data. In contrast, the purely (II) provided less than convective model showed adequate overall predictions and several peak concentrations with time for all obtain improved Attempts to depths. predictions by use of several values for kD did not result in better predictions and k using&ode1 II. Therefore, it can be concluded that purely convective transport provides poor the incorporation of prediction, and the dispersion term is necessary to describe N transport in soils. The steady state model IV consistently predicted higher than measured for all depths. with time concentrations However, it can be regarded as a superior model than model II, which is a transient model. In summary, four models which describe the fate of N in the soil profile have been Three models are of the transient evaluated. water flow type, whereas one is for steady The results indicated water flow conditions. the II where flow model transient that dispersion term was ignored, provided less prediction of overall adequate than In addition, convective experimental data. dispersive transient models proved superior to the steady state model.
simulation of nitrogen interactions in soils
t91
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illI
1121
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LITERATURE CITED [Ml 1962. The diffusion model of longitudinal mixing in beds of finite length, numerical values. Chem. Eng. Sci. 17:229-243. Cho, C. M. 1971. Convective transport of t2 ammonium with nitrification in soil. Can. J. Soil Sci. 51:339-350. 13 Claassen, N. and S. A. Barber. 1976. Simulation model for nutrient uptake from soil by a growing plant root system. Agron. J. 68:961-966. 143 Dankwerts, P. W. 1953. Continuous flow systems; Distribution of residence time. Chem. Eng. Sci. 2: 1-13. [51 Davidson, J. M., P. S. C. Rao and H. M. Selim. 1977. Simulation of nitrogen movement, transformations and plant uptake in the root zone. Proc. Nat. Conf. Irrigated Return Flow, Ft. Collins, Cola. pp. 9-18. Frissel, M. J. and J. A. van Veen (eds.). Nitrogen behavior 1981. Simulation of of soil-plant systems. Pudoc, Wageningen. Hagin, J. and A. Amberger. 1974. Contri[71 bution of fertilizer and manures to the Nand P-load of waters; A computer simulation. Final Rept. to Deutsche Forschungs Gemeinschaft from Technion. Haifa, Israel (123 p). 1’31 Iskandar, I. K. (ed.). 1981. Modeling Wastewater Renovation, Land Treatment. Wiley-Interscience.
111 Brenner, H.
[17 ‘1
t18 ;I
[I91
[7-01
12 -1
Iskandar, I. K. and Y. Nakano. 1978. Soil lysimeters for validation models of wastewater renovation by land application: Construction, operation and performance. CRREL Spec. Rpt. 78-12, U.S. Army CRREL, Hanover, NH. Iskandar, I. K. and H. M. Selim. 1981. Modeling nitrogen transport and transformations in soils; 2. Validation. Soil Sci. 131:303-312. Keeney, D. R. 1981. Soil Nitrogen Chemistry and biochemistry. Ip I. K. Iskandar (ed) Modeling Wastewater Renovation, Land Treatment. pp. 259-276. Wiley-Interscience. Mehran, M. and K. K. Tanji. 1974. Computer modeling of nitrogen transformations in soils. J. Environ. Qual. 3:391-396. Misra, C., D. R. Nielsen and J. W. Biggar. 1974. Nitrogen transformation in soil during leaching: I, II and III. Soil Sci. Sot. Am. Proc. 38:289-304. Molz, F. J., and I. Remson. 1970. Extraction term models of soil moisture use by transpiring plants. Water Resources Res. 6:1346-1356. Nielsen, D. R.. and J. G. MacDonald. (eds.). 1978. Nitrogen in the Environment. Vol. 1. Nitrogen behavior in field soils. Academic Press. 526 p. Selim, H. M. 1978. Transport of reactive solutes during transient unsaturated water flow in multilayered soils. Soil sci. 126:127-135. Selim, H. M. and I. K. Iskandar. 1980. Simplified model for prediction of nitrogen behavior in land treatment of wastewater. CRREL Rept. 80-12, U.S. Army CRREL, Hanover, N.H. Selim, H. M. and I. K. Iskandar. 1981. Modeling nitrogen transport and transformations in soils; 1. Theoretical considerations. Soil sci. 131:233-241. Tanji, K. K. 1982. Modeling of the soil nitrogen cycle. Ch. 19, &r Nitrogen in Agricultural Soils, F. J. Stevenson (ea.), Agron. Mon. 22 (pp 721-772) Am. Sot. Agron., Madison, Wisconsin. Tanji, K. K., and M. Mehran. 1979. Conceptual and dynamic models for nitrogen in irrigated croplands. p. 555-646. & P. F. Pratt, Nitrate in effluents from irrigated lands. Final Rept. to Nato Sci. Found., Univ. Calif., Riverside. Wagenet, R. J., J. W. Biggar, and D. R. Nielsen. 1977. Tracing the transformations of urea fertilizer during leaching. Soil Sci. Sot. Am. Proc. 41:896-902.
ACKNOWLEDGEMENT The authors gratefully acknowledge Mrs. Pam Latimer for her efforts in the preparation of this manuscript.