Soil Science Society of America Journal 64:533-542 (2000)
© 2000 Soil Science Society of America
DIVISION S-1-SOIL PHYSICS
Inverse Estimation of Parameters in a Nitrogen Model Using Field Data
Barbara Schmied,
Karim Abbaspour and
Rainer Schulin
Swiss Federal Institute of Technology, Dep. of Soil Protection, Grabenstrasse 3, 8952 Schlieren, Switzerland
barbara.schmied{at}ito.umnw.ethz.ch
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ABSTRACT
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An important step in numerical modeling is the determination of model parameters. Because of practical limitations, as well as time and financial constraints, inverse algorithms have in recent years presented an attractive alternative to direct methods of parameter estimation. In this study we linked the inverse algorithm of SUFI with the simulation program LEACHM to study N turnover of an agricultural field. Addressing the inherent modeling uncertainties, we introduce the concept of conditioned parameter distributions as being a more appropriate alternative to best-fit parameters. Conditioned parameter distributions are quantified within uncertainty domains, and the task of an inverse model then is to reduce or condition this domain through minimization of an appropriate objective function. Propagating the uncertainty in the conditioned parameter distributions will result in simulations where most of the measurements are respected or fall within the 95% confidence interval of the Bayesian distribution (95PCIBD). In this study we used measured pressure heads and NO3 concentrations to estimate 12 hydraulic parameters and up to 14 N turnover–related parameters. Most of the measurements in three soil layers fell within the 95PCIBD. Exceptions were some observed pressure heads corresponding to intense rainfall events and periods of soil freezing, as well as some high NO3 concentrations in the subsoil between 40- and 70-cm depth. We attributed the discrepancies to processes that were not addressed by the simulation model such as freezing and short-circuiting due to macropore flow.
Abbreviations: 95PCIBD, the 95% confidence interval of the Bayesian distribution
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INTRODUCTION
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INTENSIFICATION OF AGRICULTURE has led to an increased input of N into agricultural soil–plant systems that greatly increased crop output, but also at the same time increased N losses to the environment. To balance the supply of N for optimal plant performance and minimal losses to the environment, various simulation models differing in representation of processes, numerical algorithms, complexity, and scale have been developed. Comparing earlier (Frissel and Van Veen, 1981) and more recent (Groot et al., 1991; Thomasson et al., 1991) approaches reveals that although numerical models in general have become more comprehensive, but still limitations exist as the result of inadequate description of simultaneous processes of N turnover (Hansen et al., 1995; Diekkrüger et al., 1995), and the incomplete definition and collection of model input parameters (De Willigen, 1991).
Serious problems in modeling N transfer through soil–crop systems are currently posed by the lack of understanding of soil biological processes (Otter-Nacke and Kuhlmann, 1991; De Willigen, 1991), the influence of physical soil factors (Van Veen and Kuikman, 1990; Verberne et al., 1990; Ladd et al., 1993), and the nature of decomposing substrates (Amato and Ladd, 1992; Jensen, 1994; Motavalli et al., 1995). The more exactly a model tries to describe the processes involved, the more complex it gets and, hence, the more difficult it becomes to use. Greater model complexity also means introduction of more parameters. Model parameters are generally unknown and difficult to measure, especially for field problems.
To estimate model parameters of a field study, inverse modeling offers sometimes the only viable choice because of time, expenses, practical limitations and inadequacy of laboratory methods. Since N turnover is strongly affected by microenvironmental conditions, additional difficulties arise from the heterogeneity of soil properties, even on very small geographical scales (Becket and Webster, 1971). Neglecting spatial variability can lead to unsatisfactory and often erroneous prediction results (Addiscott et al., 1991; Finke, 1993; Huwe and Totsche, 1995; Abbaspour et al., 1998).
We found relatively few publications that described inverse estimation of hydraulic and transport properties using data from field experiments (Feddes et al., 1993; Romano, 1993; Zijlstra and Dane, 1996; Lehmann and Ackerer, 1997, Simunek et al., 1998). Abbaspour et al. (1999) estimated hydraulic, transport, and plant parameters from a lysimeter experiment. To our knowledge only one study was performed to estimate N turnover rates from a soil column leaching experiment by inverse modeling (Yamaguchi et al., 1992).
The objectives of this paper were to investigate the applicability of inverse estimation of parameters to a complex soil–plant system in the field, and to obtain model parameters that would describe our field observations of pressure head and nitrate (NO3) concentration. To estimate the unknown parameters we linked the N turnover model LEACHM (Hutson and Wagenet, 1992) with the sequential uncertainty-fitting algorithm SUFI proposed by Abbaspour et al. (1997).
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Materials and methods
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The database used in this paper is from a field experiment in which we studied N fluxes (net mineralization, drainage losses, and plant uptake) and pools (ammonia and NO3) in a formerly wetland area in the Canton Zurich, Switzerland. Schmied (2000) gives a detailed description of the project's context and results including sampling strategies and chemical analysis of the different N species. Here, we will give only a brief overview of the experiment.
The following data were collected from March through December 1996 on a 1.6-ha field planted with sugarbeet (Beta vulgaris L. cv. Riposte). The soil mineral N pool was sampled every 14 to 21 d at 0- to 20-cm, 20- to 40-cm, and 40- to 70-cm depths. These samples were taken systematically in a distance of 15.7 m on 12 sampling points along a diagonal transect. At each point, we took one soil sample per depth and bulked every four neighboring samples for a total of three composite samples per sampling time. Chemical analyses of soil NO3 and ammonium were made in 0.01 M CaCl2 extracts according to the Swiss Reference Methods (Eidgenössische Forschungsanstalten, 1996) using an Autoanalyser (Alliance Instruments Nanterre, France). We determined NO3 by the hydrazine reduction method resulting in a colored azo dye that was measured spectrophotometrically at 540 nm. Ammonia was determined using the modified Berthelot reaction and spectrophotometry at 660 nm. To estimate plant N uptake, plant samples were collected from randomly selected plants at each soil sampling point. As for the soil samples, the plant samples were also pooled for every four neighboring samples. After drying (at 60°C) and grinding, total N content of subsamples of 1 to 2 mg plant materials were determined by a CHNS-Analyser (CHNS-932, Leco Instrumente GmbH, Kirchheim, Germany). An overview of the sampling schedule along with the measured soil NO3 and plant N contents is given in Table 1
.
Relevant soil properties are presented in Table 2
. Air temperature, humidity, radiation, wind speed, and precipitation were recorded hourly at a nearby meteorological station. A data logger connected to a piezometer monitored the groundwater table continuously. Pressure heads at 5-, 15-, 30-, and 60-cm depths were recorded on a weekly basis with tensiometers installed on three different plots with three replications per plot.
Management data were obtained from the farmer's management control sheets. Crops were rotated as: winter wheat (Triticum aestivum L.)–sunflower (Helianthus annuus L.)(catch crop)–sugarbeet–winter wheat. After harvesting the winter wheat, sunflower was sown in August 1995 as a catch crop. After the first frost was over, the soil was plowed in mid-December 1995, burying the plant residues in the top 20 cm of soil. The field was left fallow until 28 Mar. 1996, when the sugarbeet was sown.
The sugarbeet harvest lasted about 6 wk, from mid-September to the end of October 1996, followed by the seeding of winter wheat in November.
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Simulation techniques
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Model Description
The program LEACHM (Hutson and Wagenet, 1992) consists of several submodels. In the present study, we used the submodels LEACHW and LEACHN. LEACHW simulates soil water regime on the basis of a numerical solution of the Richards equation:
 | (1) |
where 
is volumetric water content (L3 L-3), H is total hydraulic head (L), K is hydraulic conductivity (L T-1), t is time (T), z is depth (L), positive downwards, and U is a sink term representing water lost by transpiration (T-1).
Soil water retention functions are parameterized according to the model of Hutson and Cass (1987), and the hydraulic conductivity function is according to Campbell (1974). See Appendix 1 for details of the equations.
The upper boundary condition was assigned as atmospheric with rainfall and evapotranspiration, and for the lower boundary condition the hydraulic head was prescribed according to the measured moving water table.
Potential evapotranspiration was calculated from the recorded climate data according to the model of Allen et al. (1994). A crop cover fraction was used to partition potential evapotranspiration into potential evaporation and transpiration. It was assumed that evapotranspiration started at 0.3 d and ended at 0.8 d, and that during this period potential evapotranspiration flux density varied sinusoidally. A factor representing the ratio of maximum actual to potential transpiration (RT) allowed an increased transpiration to compensate for reduced surface evaporation under dry conditions (Hutson and Wagenet, 1992).
Solute transport is simulated by a numerical solution to the following form of the convection–dispersion equation:
 | (2) |
where c is solute concentration in the solution (M L-3), 
is soil bulk density (M L-3), Kd is the solute partition coefficient between the liquid and solid phases (L3 M-1), 
is the gas-filled soil porosity, K*H is a modified Henry's law constant, q is the Darcian flux (L T-1), D (,q) is the dispersion coefficient (L2 T-1), z is the soil depth (L), and 
indicates the source or sink term (M L-3 T-1).
Nitrogen transformation in LEACHN follows the concept of Johnsson et al. (1987). The different organic and mineral N pools and the fluxes between the pools are illustrated in Fig. 1
. In general, organic matter turnover processes are described by first-order kinetics of the following form:
 | (3) |
where ki (T-1) is the constant basic reaction rate for the organic C pool Ci (M), e and eT are two correction functions accounting for the influence of water content and temperature, respectively. The latter dependence is considered as a Q10-type function.
Nitrogen mineralization is assumed to follow the rate of organic matter decomposition and the C/N ratios of three different pools described as litter, easily degradable manure, and relatively stables humus according to the equations given in Appendix 1. An overview of the main input data required by LEACHM is also given in Appendix 2.
Inverse Parameter Estimation by SUFI
The simulation model described above contains several unknown parameters that were estimated by the inverse program SUFI (Abbaspour et al., 1997). An important feature of the SUFI program is that it is forward and repeatedly invokes the simulation program. Also, SUFI provides opportunities which prevent falling into local minima (Abbaspour et al., 1997; Abbaspour et al., 2000).
The essential steps carried out by SUFI for parameter identification can be shortly described as follows. First, each parameter pi (i = 1, ..., n) is depicted as an uncertain variable defined within a domain of uncertainty based on prior information. Then an objective function, quantifying the deviation of simulated from observed values, is minimized. The following steps are carried out repeatedly:
- For every single parameter pi the uncertainty domain is divided into a number mpi of user-specified strata of equal width. Parameter values are defined by the first moment of each stratum.
- For every possible combination of parameter values, M = mp1, mp2 ... mpn, the simulation model is run, and the value of the objective function is calculated for each run. Using the M simulations, the 95% confidence interval of the Bayesian distribution (Benjamin and Cornell, 1970) of the objective function as well as any desired model variable such as water content or pressure head are calculated.
- The user identifies a critical value of the objective function, and all the parameter combinations producing values of the objective function below the critical value are recorded as successful. Parameter strata not meeting the critical condition are eliminated resulting in updated, narrower uncertainty domains for each parameter.
- The above steps are repeated again with the updated parameter domains of step 3 until no further improvements to the objective function are achieved.
The number of iterations depends on the stratification strategy, which is problem-dependent. As the number of strata becomes larger, the program converges faster, but the computational cost increases Estimated parameter domains are independent of the stratification strategy. For inverse analysis, SUFI can be combined with different simulation programs. In the present study we linked SUFI with LEACHW and LEACHN to estimate the unknown hydraulic, chemical, and biological parameters.
Conditioned Parameter Distribution vs. Fitted Parameters
The first iteration of SUFI is based on a prior estimate of the uncertainty domain of the model parameters and therefore, because of the often large initial uncertainties, the 95% confidence interval of the Bayesian distribution (95PCIBD) of any model variable is large. This is shown by the space within the example curves `a' in Fig. 2
that is used to demonstrate this concept. As iterations proceed, the uncertainty domain of the parameters become smaller as they are more and more conditioned on the measurements of the variable(s) used in the objective function. Thus, `conditioned parameter distributions' in the context of this study refer to parameter distributions such that, when propagated stochastically through a simulation program, the 95PCIBD of the simulated variable would contain all, or most of the measured points (i.e., curves `c' in Fig. 2). In SUFI, the iterations can be continued until the upper and the lower limits of the 95PCIBD coincide to a single curve. This curve is produced by a set of single-valued parameters generally referred to as best-fit parameters (curve `d' in Fig. 2). However, as illustrated by curve d in Fig. 2, fitted parameters produce simulations that often miss most of the measured points. In our opinion, fitted parameters are inadequate for analysis of environmental problems if used without the uncertainty associated with them. In least square optimization programs, the covariance of the parameter matrix and hence the 95% confidence interval associated with each parameter are based on linear regression analysis. The problem, therefore, with the calculated parameter uncertainties are that they hold only approximately for the nonlinear analysis (Kool and Parker, 1988). Instead, we suggest obtaining conditioned parameter distributions, where most of the data points are respected within the 95PCIBD.
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Fig. 2 Simulations based on the conditioned parameter distribution concept vs. the best-fit parameters. Best-fit parameters produce simulations which usually miss most of the measurements, that is, curve d. Whereas conditioned parameter distributions produce simulations that respect most of the measurements, that is, curves c
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Results and discussion
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The data on climate variables and management practices used as input in the simulations with LEACHW and LEACHN, are shown in Fig. 3
. It can be seen that the groundwater table responded quickly to precipitation events. Measured soil NO3 and plant N contents are listed in Table 1.
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Fig. 3 Measured data from August 1995 to December 1996. (a) Field management data. (b) Mean daily temperature. (c) Water fluxes: daily precipitation, cumulative precipitation, and evapotranspiration. (d) Groundwater table measured as distance below surface
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Estimation of Parameters Related to the Water Regime
In LEACHW, parameters describing the hydraulic properties of a soil are given by a, b, and Ks in Eq. [A1.1] to [A1.5]. These parameters were treated as unknown random variables. To take into account plant water uptake we had three more unknown parameters, that is, the crop cover at maturity (CC), the relative root depth (RD), and the ratio of maximum actual to potential transpiration (RT). Other crop parameters were estimated from literature data (see Appendix 2). Since the simulated profile was divided into three different layers, there were 12 unknown parameters to estimate. The objective function g(h) for LEACHW was expressed as
 | (4) |
where hm is the measured pressure head, hp is the simulated pressure head, 
is the number of measurements over time, s is the number of measurements over space, and n is the total number of measurements ( x s).
Parameter estimation was performed using the pressure head data measured for the period of March to December 1996. The initial uncertainty domains for the unknown parameters, the final uncertainty domains (conditioned parameter distributions), and the estimated best fits are given in Table 3
. For lack of information, the initial distribution of each parameter was assumed to be uniform within its uncertainty domain. Figure 4
shows the simulation results for three depths along with the measured data. The 95PCIBD for the pressure head contains most but not all of the measured data points. Some of the fast system responses, especially after intensive rainfall events, could not be captured regardless of how much the uncertainties of the parameters were increased.
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Table 3 LEACHW input parameters estimated by inverse analysis; initial uncertainty domains, final uncertainty domains (conditioned parameters), and best-fit parameter values
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Fig. 4 LEACHW calibration (March 1996–December 1996). Simulation of pressure head with conditional hydraulic and plant parameters showing the 95% confidence interval of the Bayesian distribution for the pressure head (curves). Symbols represent the measured data ± one standard deviation
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The parameter distributions conditioned on the measured data from March to December 1996 were then validated by simulating pressure heads for the period of August 1995 to March 1996. This means that the conditional parameters (Table 3) were propagated by a Monte Carlo procedure using the August 1995 to March 1996 climate, groundwater, and agricultural data. The validation results for the three depths are shown in Fig. 5
. In the context of the conditioned parameter distributions, a validation is considered successful if all of the measured data points would fall within the 95PCIBD. In Fig. 5, the validation result shows that most of the measurements fell within the 95PCIBD, with the exception of a freezing period in January 1996 and after an intensive rainfall event in August 1995. The discrepancies between the measured and the simulated pressure heads in this case may at least have two causes; inadequate inversely estimated parameters and inadequate characterization of hydraulic processes in the simulation model.
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Fig. 5 LEACHW validation (August 1995–March 1996). Simulation of pressure head with conditional hydraulic and plant parameters determined based on observations of March 1996–December 1996 time period. Curves are the 95% confidence interval of the Bayesian distribution of the simulated pressure heads. Symbols represent the measurements ± one standard deviation
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For the case of the inversely measured parameters, the program SUFI, being a forward model, is always stable. However, given the large number of parameters in this study there is a good chance that the parameters at the absolute minimum of the objective function were not obtained, albeit by employing procedures such as tunneling (see Abbaspour et al., 2000). To check if the discrepancies, observed in both the calibration and the validation data sets, were caused by inadequate parameters we increased the uncertainty of all parameters by a large interval and propagating the uncertainties through the LEACHW model. The 95PCIBD still could not account for some observations in the June, July, and August of 1996 (Fig. 4) in the calibration data set and January of 1996 and August of 1995 (Fig. 5) in the validation data set. Since LEACHW assumes water flow to occur in a homogenous single-region porous medium, we decided that the discrepancies were caused by the inadequate accounting of the hydraulic processes such as preferential flow and freezing, the latter occurring in January of 1996. Preferential flow may have been triggered by intensive rainfall events that occurred during 1995 and 1996.
In inverse modeling, it is important to realize that we are only adjusting the unknown parameters to obtain a good fit, where as often certain hydraulic or chemical processes can only account for some observations. In field situations especially, non-uniform hydraulic and chemical processes may influence much of the observations, and it would be futile to try to account for them by adjusting parameters of a model that applies to homogenous and uniform conditions. For this reason care should be taken in identifying the existing hydraulic and chemical processes at work and using appropriate models. Hydraulic processes (see Kätterer et al., 2000) and the soil profile system (see Abbaspour et al., 2000) can also be treated as unknown random variables by invoking different models which handle different processes. We are planning further modeling work with the program MACRO-N (Larsson and Jarvis, 1999) which accounts for macropore flow and soil freezing. An interesting experience of the authors with inverse modeling of field problems is that so far it was not possible to obtain good fits by the force of parameter fitting alone if important hydraulic, chemical, or system dependent processes were neglected (Abbaspour et al., 1999, 2000). We consider this to be an important and positive aspect of inverse modeling, one that could make inverse modeling a tool for the analyses of the system and the processes as well as a parameter estimation routine.
Estimation of Parameters Related to Nitrogen Turnover
After conditioning the hydraulic parameters for LEACHW, we used SUFI to estimate the parameters of the N submodel LEACHN. To assess the importance of different processes in soil N dynamics several scenarios of different complexity were considered. Scenario S1 represents the simplest scenario involving only one organic matter pool (i.e., measured soil organic C and N were considered to belong to the humus pool) and ignoring any water and temperature dependence of the reaction rates (e and eT in Eq. [3]). In the other scenarios, adding a fast decomposing litter pool (scenario S2), plus adjusting the reaction rates for water and temperature effects (scenario S3) included further processes. The objective function used in these scenarios was expressed as
 | (5) |
where superscripts m and p stand for measured and simulated variables, is the number of measurements over time, s is the number of measurements over space, and n is the total number of measurements ( x s).
Finally, in scenario S4 we investigated the effect of including plant N uptake as a second variable in the objective function on parameter estimates, using the following objective function:
 | (6) |
where Nup is the plant N uptake, and s are the number of measured NO3 over time and space, respectively, ' and s' are the number of measured Nup over time and space, respectively,
, and
. The above multiplicative form of the objective function was first tested by Abbaspour et al. (1999) and found to produce reasonable results without the need for calculating any weights for different variables.
The final results of parameter estimation are given in Table 4 . Simulated and measured NO3 data are compared in Fig. 6 and 7 . Note that the measured data are averages of three data points per depth. In general, simulations with best-fit parameters (Fig. 6) were almost always within the range of measurements ± one standard deviation in the first and second layers. All scenarios underestimated the NO3 concentration in the subsoil indicating that, as discussed before, either the model assumptions were inadequate, or given the large number of parameters to estimate we did not achieve the global minimum of the objective functions.
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Fig. 6 LEACHN calibration (March 1996–December 1996). Simulations of NO3 concentrations are based on the fitted parameters for Scenarios S1, S2, and S3. Symbols represent the measurements ± one standard deviation
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Fig. 7 Simulations of NO3 using the conditional parameters in Table 4 for scenarios S1 and S2. Symbols represent the measurements ± one standard deviation
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Scenario S1 (without litter pool) resulted in a final parameter combination with unreasonably high values for the nitrification rate constant Knit and the soil solution distribution coefficient KdNH4. The value of the objective function for scenario S1 was 0.92 (kg N ha-1). A major improvement was achieved in scenario S2 with the addition of a fast decomposing litter pool. In this scenario, the value of the objective function decreased to 0.80 (kg N ha-1) and simulated NO3 values were closer to the measured averages. Since in scenario S3 the various N turnover rate coefficients were made dependent on temperature and soil water content, the simulation results were expected to be further improved. The new value of the objective function was 0.67 (kgN ha-1) due to a higher nitrification rate indicating better estimates of the measured points in the period of litter mineralization. However, estimates of the other parameters in S2 and S3 were fairly close to each other.
The 95PCIBD for scenarios S1 and S2 are shown in Fig. 7. Propagating the final uncertainty domains in the parameters related to litter mineralization to the simulation outputs resulted in a 95PCIBD that respected most of the measurements in the period when the litter pool was relevant (spring–early summer). But regardless of any increases in the uncertainty domains of N turnover and the hydraulic parameters, the observed high NO3 averages in the 40- to 70 cm-depth could not be matched. This emphasizes the point we made earlier with respect to hydraulic parameters, meaning that the discrepancies are probably process rather than parameter dependent.
We used the parameter set obtained in S3 (litter pool plus environmental adjustments) to simulate the total plant N uptake (Fig. 8)
. Simulation results underestimated total plant N content by about 100 kgN ha-1. Since plant uptake is a major sink for mineral N, it was expected that scenario S4, which included Nup in the objective function, would perform better than S3 in predicting total plant N uptake. For scenario S4, the root mean square error between the measured and simulated NO3 increased from 0.67 (in scenario S3) to 0.76 (Table 4). As expected, the estimate of the total plant N content showed a significant improvement, and the difference between simulated and measured total Nup decreased from 100 (in scenario S3) to 10 kg N ha-1 (Fig. 8). Although during the vegetation period, the observed dynamics of Nup was still not very well described.
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Fig. 8 Simulation of plant N uptake using parameters in scenarios S3 and S4. Measurements of the plant total N pool are mean values ± one standard deviation. Simulation results are represented as the 95% confidential interval of the Bayesian distribution for plant uptake
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A comparison of the parameter estimates obtained in S4 with those of S3 (Table 4) shows that incorporation of Nup into the objective function forced a better match of plant N uptake by approximately doubling the nitrification rate, while at the same time the soil solution distribution coefficient reduced by more than half. Otherwise, the parameter estimates of S3 and S4 obtained by means of the SUFI algorithm are fairly similar to each other and also in close agreement with values reported in the literature (Table 4). The results above illustrate the conditionality of the estimated parameters on the formulation of the objective function and, thus, the importance of choosing it carefully (see also Abbaspour et al., 1999).
Sensitivity Analysis
Sensitivity of fitted parameters is a routine output of the SUFI program. The analysis is performed by varying the parameters one by one from their optimal values by ±50%. Figure 9 shows the results of this analysis for the six most sensitive parameters in scenario S4. It can be seen that the parameters related to the litter pool and its mineralization (i.e., N–pool, C–pool, fe, fh, and klit) and the denitrification rate (kden) are the most sensitive. Other sensitive parameters (not shown in Fig. 9) were found to be the humus mineralization rate and the Q10 factor that accounts for the temperature dependence of the rate coefficients. The hydraulic and crop parameters, with the exception of the Cambell's exponent in the uppermost layer b–1 and the relative root depth factor RD, were not found to be sensitive relative to the soil NO3 and plant uptake.
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Conclusions
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The inverse parameter estimation algorithm of SUFI was linked with LEACHW and LEACHN to estimate, respectively, hydraulic and N turnover parameters of an agricultural field. The conditioned parameter distributions led to good descriptions for both the observed pressure heads and the NO3 concentrations in the soil solution at different layers in the top 70 cm of the field soil under study. The exceptions, however, were some pressure heads corresponding to intense rainfall events and periods of soil freezing, and some high NO3 concentrations at 40- to 70-cm depth. These deviations, we concluded, were process rather than parameter dependent. Future studies are being designed with a N model that takes preferential flow and soil freezing into account.
In this paper we introduced the concept of conditioned parameter distributions vs. best-fit parameters. We maintain that conditioned parameter distributions are more appropriate than best-fit parameters for describing environmental processes, because of the inherent uncertainty associated with the quantification of the parameters and because parameter distributions expressed in conditioned form allow for probabilistic interpretation as demanded in the framework of risk analyses.Davidson Graetz Rao Selim 1978; Eidgenössische Forschungsanstalten 1996; Nimah Hanks 1973; Tillotson Robbins Wagenet Hanks 1980; Watts Hanks 1978
Received for publication March 22, 1999.
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Appendix 1
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Soil water retention functions according to the model of Hutson and Cass (1987):
 | (A1.1) |
 | (A1.2) |
where a and b are constants, h is the pressure head (L), s is the saturated water content (L3 L-3), and (hc, c) is the intersection point calculated according to
 | (A1.3) |
 | (A1.4) |
Soil hydraulic conductivity function according to Campbell (1974),
 | (A1.5) |
where Ks is the saturated hydraulic conductivity (L T-1).
Equations describing N mineralization are expressed as
 | (A1.6) |
 | (A1.7) |
 | (A1.8) |
where N and C are the concentration of N and C, respectively, k is the reaction rate for C mineralization for the three different organic matter pools assigned by the subscripts lit (litter), man (manure), and hum (humus), fe is the fraction of organic C that is converted to humus and biomass, fh is the humification factor, and ro is the C/N ratio of humus and microbial biomass.
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Appendix 2. Input parameters of LEACHM
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Model-Compartment Properties
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Specification
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Code
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Unit
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Source
|
Value
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|
| Driving Variables |
|
|
|
|
|
| Weekly weather data |
Evapotranspiration |
ET |
mm |
calc |
drivar |
|
Groundwater table below surface |
GWT |
mm |
meas |
drivar |
|
Mean air temperature |
T |
°C |
meas |
drivar |
|
Amplitude |
AMP |
°C |
meas |
drivar |
| Rainfall or irrigation |
Amount per event |
PRE |
mm |
meas |
drivar |
|
Surface flux density |
SFD |
mm d-1 |
calc |
drivar |
| Managment Data |
|
|
|
|
|
|
Fertilizer applications |
|
kgN ha-1 |
mfs |
|
|
Date of crop planting, emergence, |
|
mmddyy |
mfs |
|
|
maturity and harvesting |
|
|
|
|
| LEACHW-SOIL |
|
|
|
|
|
| Physical properties |
Texture 1 (clay)§ |
CLAY |
% |
meas |
Tab. 2 |
|
Texture 2 (silt) |
SILT |
% |
meas |
Tab. 2 |
|
Texture 3 (Organic matter) |
OM |
% |
meas |
Tab. 2 |
|
Bulk density |
rB |
g cm-1 |
meas |
Tab. 2 |
|
Particle density 1 (clay) |
dp1 |
g cm-1 |
lit |
2.65 |
|
Particle density 2 (silt) |
dp2 |
g cm-1 |
lit |
2.65 |
|
Particle density 3 (org.matter) |
dp3 |
g cm-1 |
lit |
1.10 |
|
Porosity (calculated) |
E |
% |
calc |
|
| Hydraulic properties |
Campbell's constant (Air entry value) |
a |
kPa |
est |
Tab. 3 |
|
Campbell's exponent |
b |
– |
est |
Tab. 3 |
|
Hydr. conduct. at saturation |
KS |
mm d-1 |
est |
Tab. 3 |
|
Pore interaction parameter |
p |
– |
lit |
1.0 |
| Transport parameter |
Dispersivity |
D |
mm |
lit |
100 |
| LEACHW-CROP |
|
|
|
|
|
| Plant water uptake |
Crop cover at maturity |
CC |
– |
est |
Tab. 3 |
|
Relative root depth |
RD |
– |
est |
Tab. 3 |
|
Wilting point (soil) |
WP |
kPa |
lit |
-1500 |
|
Minimum root water potential |
HRoot |
kPa |
lit |
-3000 |
|
Ratio of maximal actual to potential transpiration |
RT |
– |
est |
Tab. 3 |
|
Root resistance coefficient |
1 + RC |
– |
lit |
1.05 |
| LEACHN-SOIL |
|
|
|
|
|
| Transport parameters |
Molecular diffusion coefficient |
DL |
mm2 d-1 |
lit |
120 |
|
Bresler's equation adjustment a |
ABRES |
– |
lit |
0.001 |
|
Bresler's equation adjustment b |
BBRES |
– |
lit |
10 |
| Chemical properties |
Distr. coeff. soil/solution NH4 |
KdNH4 |
dm3 kg-2 |
est |
Tab. 4 |
|
Distr. coeff. soil/solution NO3 |
KdNO3 |
dm3 kg-1 |
lit |
0.0 |
| LEACHN-CROP |
|
|
|
|
|
| Plant N uptake |
Potential N uptake |
PNU |
kgN ha-1 |
meas |
305 |
| LEACHN-NITROGEN TRANSFORMATIONS |
|
|
|
|
|
| Reaction rates |
Nitrification |
knit |
d-1 |
est |
Tab. 4 |
|
Denitrification |
kden |
d-1 |
est |
Tab. 4 |
|
Mineralisation LITTER pool |
klit |
d-1 |
est |
Tab. 4 |
|
Mineralisation HUMUS pool |
khum |
d-1 |
est |
Tab. 4 |
|
Vilatilisation NH+3 |
kvolat |
d-1 |
lit |
0.4 |
| Constants |
Initial ration N-litter/N-humus |
N_pool |
– |
est |
Tab. 4 |
|
Initial ration C-litter/C-humus |
C_pool |
– |
est |
Tab. 4 |
|
Synthesis efficiency |
fe |
– |
est |
Tab. 4 |
|
Humification factor |
fh |
– |
est |
Tab. 4 |
|
Denitrification half saturation |
csat |
mg l-1 |
lit |
10 |
|
Max. NO3/NH4 ratio nitrification |
rmas |
– |
lit |
8 |
| Correction functions |
Base temperature |
tbase |
°C |
lit |
20 |
|
Q10-factor |
Q10 |
– |
est |
Tab. 4 |
|
High end of opt. wat. cont. range |
HEopt |
% |
est |
Tab. 4 |
|
Low end of opt. wat. cont. range |
LEopt |
kPa |
est |
Tab. 4 |
|
Min. matric potential |
LEmin |
kPa |
est |
Tab. 4 |
|
Relative transformation rate at saturation
|
trSAT
|
–
|
est
|
Tab. 4
|
|
calc = calculated; mfs = management fact sheet; meas = measured; lit = literature; est = parameter estimation by inverse analysis.
drivar = driving variables for LEACHM program; Tab. 3 and Tab. 4 = see respective Tables.
§ Texture classes according to USDA classification.
|
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|
|---|
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ABSTRACT
INTRODUCTION
