- Email: [email protected]
Incorporation of spatial variability in modeling non-point source groundwater nitrate pollution
~
Pergamon
Wal. Sci. Tech. Vol. 33. No. 4-5. pp. 233-240. 1996. Copynghl © 1996 IA WQ. Published by Elsevier SCIence LId. Printed In Greal Bnta,n. All rights reserved. 0273-1223/96 $15'00 + 0'00
PH: S0273-1223(96)00236-3
INCORPORATION OF SPATIAL VARIABILITY IN MODELING NON-POINT SOURCE GROUNDWATER NITRATE POLLUTION F. S. Goderya, M. F. Dahab, W. E. Woldt and I. Bogardi University of Nebraska - Lincoln. Lincoln. NE 68588-053 J
ABSTRACT A methodology for incorporation of spatial variability in modeling non-point source groundwater nitrate contamination is presented. The methodology combines geostatistical simulation and unsaturated zone modeling for estimating the amount of nitrate loading to groundwater. Three dimensional soil nitrogen variability and 2-dimensional crop yield variability are used in quantifying potential benefits of spatially distributed nitrogen input. This technique. in combination with physical and chemical measurements. is utilized as a means of illustrating how the spatial statistical properties of nitrate leaching can be obtained for different scenarios of fixed and variable rate nitrogen applications. Copyright © 1996 IAWQ. Published by Elsevier Science Ltd.
KEYWORDS Geostatistical simulation; groundwater nitrate contamination; nitrate; nitrogen; non-point source pollution; spatial variability; unsaturated zone; variable application. INTRODUCTION One of the inherent difficulties in reducing agricultural non-point source (NPS) pollution from agricultural land is the relative lack of information relating the effect of agricultural practices on groundwater pollution. Monitoring the concentrations of agrichemicals from all agricultural land would be extremely expensive. and almost impossible. However. communities cannot afford to ignore the potential threat to water supplies from NPS. Computer modeling along with geostatistical simulation has a key role to play in reducing NPS water quality problems. The integration of simulation based on limited spatial data along with transport modeling offers the advantage of utilizing the full information content of spatially distributed data to analyze solute transport on a field scale in three-dimensions. The natural textural and structural variabilities in field soils and hydrologic formations are extensively acknowledged as dominant factors influencing fluid and mass transport through the subsurface zone. In response to this spatial variability, the transport and retention properties of a field scale soil also present spatial variation to inputs such as irrigation, rain, and natural or artificial sources. There are additional sources of variability in soils subject to management and cultural practices. These variabilities also are related to the initial conditions describing the amount of soil chemicals in a typical field. Both sources of 233
F. S. GODERYA et al.
234
variability introduce uncertainty in the modeling process. Numerous efforts have been directed toward quantifying the level of spatial variability in various soil parameters (Jury et at., 1987). Site specific field management is identified as a technology for optimizing net returns from agriculture while reducing or eliminating groundwater contamination. By applying chemicals in a spatially varying manner according to localized needs and yield potentials, fertilizers and pesticides can be applied to the portions of the field that need them the most. It is assumed that such a strategy will carry environmental benefits by minimizing potential leaching offertilizer. Theoretically, it appears that making fertilizer applications more efficiently in tune with localized crop and soil needs would reduce chemical outflows from fields, and hence, water quality problems. However, there is no guarantee that this will always be the case. Furthermore, no concrete evidence has been put forward that shows how much actual reduction in chemicals can be achieved through these practices (Ferguson et at., 1994). This paper focuses on the effects of spatial variability of initial soil nitrogen levels and crop yield within a field. A methodology is presented for incorporating spatial variability in modeling the effects of diffuse pollution of groundwater. This information in combination with simulation and modeling is utilized as a means of illustrating how the spatial statistical properties of leaching can be obtained for different scenarios of fixed and variable rate fertilizer application for a typical field. APPROACH The methodology incorporates 3-D residual soil nitrogen and 2-D yield variability in the modeling process for estimation of leaching of nitrates. This information is useful for quantifying environmental benefits of variable rate application. Geostatistical simulation techniques in combination with multiple-one dimensional transport model runs are utilized as a means of evaluating various scenarios of fixed and variable rate applications. A schematic of major components in the process for a given scenario is illustrated in Fig. 1. Structural analysis of the field data is used to evaluate spatial continuity by calculating a covariance function. Based on the covariance function several realizations of field are generated. For each field realization, multiple runs of a transport model are used to obtain the nitrate loading to groundwater. The procedure is repeated for each scenario with different management controls. Dlftn. SpIUII CDnUnu11y Dr FI.ld Plrlml...
NIIr.t. L Idlng 10 Groundwlter
Figure 1. Primary components of the transport simulation program for one scenario.
Spatial variability in modeling non-point source pollution
235
Nitrogen ReQuirements Nitrogen is the nutrient, most often required for growing crops_ Nearly all crops need some nitrogen fertilizer unless there is abundant nitrogen in the soil. Phosphorus is the second nutrient most likely to be needed. There are some other nutrients like potassium, sulfur, zinc, iron, calcium, magnesium, boron, chlorine, copper, manganese, and molybdenum, which may be needed for growing crop on certain soils. In this research only nitrogen is considered to be the limiting nutrient. The amount of nitrogen needed for growing corn is based on expected yield, the amount of residual soil nitrate-nitrogen and soil organic matter. The following algorithm is recommended by the University of Nebraska for detennining the nitrogen fertilizer application rate to corn (Penas et al., 1994):
NN = 35
+ 1.2*EY - 8*RN - 0.14*EY*OM - ONC
(I)
where NN = nitrogen need (lb/acre); EY = expected yield (busheVacre); RN = average nitrate-nitrogen concentration in the root zone (ppm); OM = percent organic matter; and ONC = other N credits from legumes, manure, and other organic waste products, and irrigation water. yariabJe Rate Auplication Five applications scenarios were developed in the methodology leading to the spatial management technology. All spatial management scenarios were based on appropriate management of nitrogen to meet but not exceed production needs. To ensure that values of the input variables used in the unsaturated zone model were reasonable, the first scenario was based on the traditional farm practices. The results from the principal program were also compared with the well documented program Erosion Productivity Impact Calculator (EPIC) (USDA, 1990, Goderya et at., 1995). This was done to ensure that the results from the application of this scenario were in the reasonable limits of the current problem in the area_ The subsequent scenarios reflects possible advancement in the traditional practice in the framework of spatially variable nitrogen input Each scenario was run for five years of continuous corn cultivation. A simplified illustration of the various scenarios is presented in Fig. 2. The first scenario used unifonn input of nitrogen based on traditional practices. The input rate was also held constant from one year to another. Nitrogen was added once at the beginning of each growing season at an average rate of 200 kglha. The crop received an amount comparable to the historic application rate. This rate was estimated with the expected yield of 9.7 Mglha and the University of Nebraska nitrogen recommendation of fertilizer application. Expected yield is estimated from actual field measurements along with county or state long-tenn records (Meisinger and Randall, 1991). Since no long-tenn averages of yield for the field were available, hence, average yield of the field with a 10 percent increase was used as an estimate in expected yield goal calculation. This scenario and the other following scenarios assumed that the soil has two percent organic matter content. No consideration was given to the initial amount of nitrate• nitrogen present in the root zone. This scenario, therefore, can be regarded as a "worst case" groundwater contamination scenario among the others. Scenario two assumes the same crop and unifonn application, but the amount of application was modified based on one soil sample and yield infonnation from one location in the field. The assumption of one sample can be based on composite average of various soil samples. collected from different parts of the field. The amount of fertilizer application for the first year was calculated based on the available data of yield and residual soil nitrate-nitrogen from a location. However, the amount of fertilizer was varied each year corresponding to previous year yield and the amount of residual soil nitrate-nitrogen before the fertilizer application. The application was unifonn with respect to various locations but variable with respect to time. The third scenario uses variable application based on the spatial variation of parameters. The area was
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divided into four sectors, and the application rate was based according to the measurements of control location in each sector. Hence, the whole field received variable application with respect to position as well as time. The fourth and fifth scenarios were similar to the third scenario except that the field was divided into sixteen (16) and one hundred and twenty (120) sectors, respectively. Each sector received variable rate application with respect to time and location conforming to its control location. Geostatistical Simulation There are several multidimensional simulation techniques described in the literature including matrix models such as the nearest neighbor method used in Smith and Freeze (1979), spectral techniques described in Meija and Rodriguez-Iturbe (1974), and Gaussian related algorithms described in Journel and Huijbregts (1978), and Deutsch and Journel (1992). The simulated quantities are typically used for estimation and interpolation purposes or to drive large-scale simulations involving heterogeneous phenomena. Scenario t
UA-TP
Scenario 4
Scenario 2
Scenario 3
UA-l CP
VA-4 CP
Legends: UAWT-Uniform Application ... r.t Tim. VAWT-Varl,ble Application ...r.l. Tim. UA-TP-Uniform Application, Traditional Practice UA-ICP-Uniform Application, I Control Point
VA-16CP
VA-4 CP-Variabl. Applicatioa, 4 Control Point VA-16 CP-Variabl. Application, 16 Control Poinl
Figure 2. Graphical iUustration of the various application scenarios.
The sequential principle is identified to be the most straightforward algorithm for generating realizations of a multivariate Gaussian field (Deutsch and Journel, 1992). The sequential simulation principle consists of generating a realization of a variable Z(u) from its conditional distribution given the value of the most related covariate at the same location u. The conditioning is extended to include all data available within a neighborhood of u, including the original data and all previously simulated values. The sequential simulation process is independent of the algorithm or model used to establish the sequence of univariate conditional cumulative distribution functions. The algorithm used in this research uses the conditional simulation of a continuous variable z(u) modeled by Gaussian related stationary random function RF Z(u) (Deutsch and Journel, 1992). Structural analysis of the field data is used to evaluate covariance functions. This structural information is then utilized in generating a number of field realizations through conditional simulation. In order to complete three dimensional simulation for residual soil nitrate-nitrogen, structural analysis is completed for both the horizontal-spatial dimension and the vertical dimension. Stochastic fields of corn yield are generated using the two dimensional field measurements.
Spatial variability in modeling non-point source pollution
237
Multiple one-dimensional transport model Studies describing transport through unsaturated soil are concerned with a system in which the vertical plane is small in scale compared with the horizontal plane that defmes a field or even regional area. A common approach employed in describing field scale water and solute movement through unsaturated zone is to view the transport process locally as a vertical, one dimensional flow system. A modified version of this approach is employed in which a multiple one-dimensional system describes the spatial variability in a typical field. A variety of models exist for estimating movement and degradation of agricultural chemicals in the unsaturated zone. Water percolation and nitrate leaching can be simulated using several existing models at various levels of detail. The unsaturated zone model used in this research is similar to CREAMS (Knisel, 1980) except for the water movement algorithm. The model is composed of several subroutines that account for different elements of the nitrate transport process in the unsaturated zone. The hydrology component calculates evapotranspiration, runoff, infiltration, capillary uptake, and deep percolation; whereas the chemical subroutine computes nitrate uptake by plant, mineralization, nitrification, and denitrification. These sub-models are later combined to calculate the daily movement of water and nitrate through the unsaturated zone. To calculate the movement of water through the various soil layers, the model uses a finite difference solution of the one-dimensional unsaturated-zone-flow equation (Bogardi and Bardossy, 1984; Goderya et al., 1995). INITIAL RESULTS The research results are obtained by varying the amount of applied fertilizer based on controlling algorithm recommendations and using the simulation on the basis of measurement data. The management practice of spatially variable application was evaluated on the basis of sustaining production agriCUlture and decreasing the risk of environmental degradation. A comparative evaluation of the effects of five spatial management scenarios on nitrate loading below the root zone was investigated. For all evaluations, effect variables were either averaged or summed for the 5 year simulation period and used in relative comparisons. These results, therefore, represent short-term impacts of the spatial management technology. Figure 3 summarizes the primary nitrogen input. Nitrogen fertilizer input averaged 200 kglha-yr for the traditional practice scenario, which compares favorably with the average com fertilization rate in Nebraska, without any consideration of soil nitrate in the profile (Follet et al., 1991). Fertilizer nitrogen inputs were lower for second scenario because the information from the field including the nitrogen pool were used. The amount of nitrogen fertilizer applied to the crop in the third scenario was reduced by 13 kglha-yr. However, the reductions in nitrogen use in the fourth and fifth scenario over third and fourth were only by 3 and 4 kglha-yr. These reductions may not be sufficient to justify the increased effort of measurements and spatial management of the field. Simulated crop yields were similar under all five spatial management scenarios. The means and the standard deviations of the annual yields from the simulated fields matched very closely with the average expected yields for the site. This research effort was designed with the goal that the production compares well with the traditional baseline output. Hence, although the spatial management scenarios reduced the fertilizer requirements, the yield had little or no effect on these reductions. This suggested that the spatial management scenarios and fertilizer amounts appear to have been modeled appropriately. The amount of nitrate, moved form the soil surface to the bottom of the root zone, was extracted from the number of output variables to compute the sample statistics. The output data were evaluated in terms of field leaching potentials as well as for leaching as a consequence of spatial management practices. Statistical analysis of each scenario simulation for a field, and each node in a field for number of simulations, provided insight into the relative importance of the conditions and modeling of transport processes. Basic statistical parameters including the mean and standard deviation were calculated for different cases.
F. S. GODERY A et al.
238
300
l
-
~ 200
rs
~
-
~
100
]
-
~
C1)
I
o
MRI
MR2
MR3 MR4 Scenarios
MR5
Figure 3. Average annual nitrogen fertilizer inputs for spatial management scenarios.
Figure 4 shows the amounts of nitrogen leaving the root zone. This is the primary factor important to groundwater quality from the geostatistical-transport simulation for five spatial management scenarios. The amount of nitrate leaving the root zone for the first scenario is used as a check. The results of this scenario simulations are consistent with the magnitude of the responses reported from experimental studies in the Midwest (Ferguson et ai., 1994). Comparison of the result from this scenario to nitrate contamination data reported in the area also was used as an indicator of the effectiveness of the subsequent scenario results. Comparing the first and second scenarios, it can be inferred that by considering one measurement from a field, potential nitrate loading to groundwater was reduced by 34%. Similarly, if various sources of information from separate measurements are included in the decision model, then the potential contamination is reduce by 41 % over that of traditional practice. This reduction is 10% when compared to Scenario 2 results. Comparison of the fourth and fifth scenarios with third scenario indicated that nitrate contamination would be reduced by 9.6% and 13% respectively, that is, if one considers 16 and 120 blocks of variable decision input in a sizeable field as opposed to 4 sectors.
1::
600
I
~500
~
~400
~
..S!l300
-e... 200
::z: I
~
t
.:;:
lOO
o
MRl
MR2
MR3 MR4 Scenarios
MR5
Figure 4. Average amount of N03-N leaving root zone spatial scenrios simulations.
Spatial variability in modeling non-point source pollution
239
These results suggest that the application of increased infonnation for different parameters and conditions in a spatial management system may not necessarily result in a substantial decrease in the contamination problem. Therefore. most of the effort associated with spatially variable application would appear to be exces!>ive to justify spatial management and application for the fourth and fifth scenarios. We classify this field as the case of low variability field and hence the degree of variability of controlling parameters may be used as an indicator to evaluate various fields for suitability of spatially variable application technology. This also suggests that available resources should be allocated in a greater proportion toward the assessment of the potential effects of spatial variability in a field than development of variable application technology. Figure 5 shows the average amount of soil nitrate present in the soil profile before and after the simulations. Soil nitrate at the end of 5-yr simulations was slightly higher for traditional practice scenario. but declined under all other management scenarios. For the second scenario. the reduction of nitrate in the soil profile was due to the consideration of realistic yield goal and soil nitrate infonnation. The subsequent spatial management scenarios had smaller effects on the profile nitrogen levels at the end of simulation period. Thus. it seems likely that unifonn application given realistic yield and composite soil samples would achieve results comparable to spatially variable application.
250
.., -~200 :z:;
~ ~ II
I
-.... .., 150 Q.)
~
Q.)
tS C>
0: Q.)
eo Q.)
.:::
100 50
o
Initial MRl
MR2 MR3 Scenarios
MR4
MR5
Figure S. Average amount of soil N03-N in the root zone before and after scenarios simulation.
SUMMARY AND CONCLUSIONS
The methodology presented in this research employs a combination of geostatistical simulation and unsaturated zone transport modeling. The methodology was applied to show how the knowledge about soil parameters related to production system can be organized and presented to concerned parties to predict the environmental impact of production agriculture. The process was shown to be able to give quantitative estimates of the effectiveness of spatially variable application practices. Spatial variation of residual soil nitrates. yield. and hydraulic conductivity in a typical field was used to estimate the nitrate contamination of groundwater. A one dimensional unsaturated zone transport model • TDNIT. was used at a number of locations in the field which resulted in a quasi three-dimensional system. The use of the selected transport model offers the advantage of short computation time and reduced input data demands. The methodology developed in this research was applied to a typical field. The management practice of spatially variable application was evaluated on the basis of sustaining production agriculture and reducing the risk of environmental degradation. Five scenarios of potential spatial management technology were used. These scenarios were evaluated given the spatial distribution of residual soil nitrates. yield. and hydraulic conductivity in the fields. The decision input parameters and fertilizer amount were distinctively different
F. S. GODERYA et al.
240
for the different scenarios as well as spatial locations for the last three scenarios. The initial comparative evaluation of results of various scenarios suggested that an increase of information for related parameters and conditions in a spatial management system may not necessarily result in a substantial decrease in the contamination problem for some fields. We classified this field among various others as one exhibiting low variability. Hence the degree of variability of controlling parameters may be used as an indicator to evaluate various fields for suitability of variable application technology. The results suggested that available resources should be allocated in a suitable proportion towards the assessment of spatial variability. The methodology was demonstrated for estimating nitrate pollution to groundwater. However, the methodology also can be adopted for use in conjunction with many other anthropogenic pollutants in estimating groundwater contamination potential. It should be noted that this paper considered only advective transport with hydraulic conductivity being the only spatially variable hydrogeologic parameter. However, the framework can be used in situations involving advection. dispersion. retardation. and decay. ACKNOWLEDGMENT This paper was supported. in part. by the Center for Infrastructure Research and the Water Center, University of Nebraska-Lincoln. and in part, by the Cooperative State Research Service of the U.S. Department of Agriculture. At the time of the study, F. S. Goderya was a Graduate Research Assistant and M. F. Dahab and I. Bogardi were Professors in the Department of Civil Engineering and W. E. Woldt was an Assistant Professor in the Department of Biological Systems Engineering. University of Nebraska. Lincoln, NE 68588-0531. USA. REFERENCES Bogardi I. and Bardossy A. (1984). Stochastic forecasting of N budget in the unsatumted zone, Proceedings of International Symposium of Recent Investigations in the Zone of Aeration, RIZA. Munich, West Germany. October 1-5. pp. 743-756. Deutsch C. V.• Joumel A. G. (1992). GSUB: Geostatistical software library and Ilser's guide, Oxford University press. Ferguson R. B•• et al., (1994). Managing spatial variability with furrow irrigation to increase nitrogen use efficiency, Proceedings of
the
Second
International
Conference
on
Site-Specific
Management
for
Agricultural
Systems,
BloomingtonlMinneapolis. Minnesota, March. Follet R. F.• Keeney D. R. and Cruse R. M. (1991). Managing nitrogen for groundwater quality andfarm profitability, Soil Science Society of America, Madison. Washington. Goderya F. S.• Dabab M. F.• Woldt W. E.. Bogardi I. (1995). Consideration of Spatial Variability in Nitrate Contamination to Groundwater. Presented at the ASAE International Summer Meetmg. ASAE Paper No. 942092. SL Joseph. M149085. Goderya F. S.• Dabab M. F.• Woldt W. E.• Bogardi I. (1995). Comparison of transport models for predicting nitrate in percolating water. Working paper. Department of Civil Engineering. University of Nebraska-Lincoln. Lincoln, NE 68588-0531. Jones R. L. and Hanks R. J. (1989). Review of unsaturated zone leaching models from a user's perspective. Proceedings of the International Symposium on water quality modeling of Agricultural Non-point Sources. June 19-23. Logan. Utah. Joumel A. G. and Huijhregts Ch. J. (1978). Mining geostatistics. Academic press. Jury W. A.• Russo D.• Sposito G. and Elabd H. (1987). The spatial variability of water and solute transport properties in unsaturated soil; I. Analysis of property variation and spatial structure with statistical models, Hilgardia, 55(4), 1-32. Knisel W. G.• ed. (1980). CREAMS: A field-scale model for chemicals, runoff. and erosion from agricultural management systems. U.S. Department of Agriculture, Conservation research report no. 26. 640 pp. Meija J. and Rodriguez-Itrube 1. (1974). On the synthesis of random fields from the spectrum: An application to the generation of bydrologic spatial processes. Water Res. Res.• 10,705-71 I. Meisinger J. J.. Randall G. W. (1991). Estimating nitrogen budgets for soil-crop systems, In: Managing nitrogen for groundwater quality andfarm profitability. Soil Science Society of America, Madison. Wisconsin Smith L. and Freeze R. A. (1979). Stochastic Analysis of steady state groundwater flow in a bounded domain. 2. Analysis of uncertainty in prediction. Water Res. Res.• 15. 1543-1559. Penas E. J.. Hergert G. W. and Ferguson R. B. (1994). Fertilizer suggestions for corn, NebGuide. G74-174-A. Published by Cooperative Extension. Institute of Agriculture and Natural Resources, University of Nebraska-Lincoln. Lincoln. NE 68583. USDA. U.S. Department of Agriculture, (1990). EPIC-Erosion/Productivity Impact Calculator; I. Model documentation. and User Manual. Technical bulletin no. 1768.
Pergamon
Wal. Sci. Tech. Vol. 33. No. 4-5. pp. 233-240. 1996. Copynghl © 1996 IA WQ. Published by Elsevier SCIence LId. Printed In Greal Bnta,n. All rights reserved. 0273-1223/96 $15'00 + 0'00
PH: S0273-1223(96)00236-3
INCORPORATION OF SPATIAL VARIABILITY IN MODELING NON-POINT SOURCE GROUNDWATER NITRATE POLLUTION F. S. Goderya, M. F. Dahab, W. E. Woldt and I. Bogardi University of Nebraska - Lincoln. Lincoln. NE 68588-053 J
ABSTRACT A methodology for incorporation of spatial variability in modeling non-point source groundwater nitrate contamination is presented. The methodology combines geostatistical simulation and unsaturated zone modeling for estimating the amount of nitrate loading to groundwater. Three dimensional soil nitrogen variability and 2-dimensional crop yield variability are used in quantifying potential benefits of spatially distributed nitrogen input. This technique. in combination with physical and chemical measurements. is utilized as a means of illustrating how the spatial statistical properties of nitrate leaching can be obtained for different scenarios of fixed and variable rate nitrogen applications. Copyright © 1996 IAWQ. Published by Elsevier Science Ltd.
KEYWORDS Geostatistical simulation; groundwater nitrate contamination; nitrate; nitrogen; non-point source pollution; spatial variability; unsaturated zone; variable application. INTRODUCTION One of the inherent difficulties in reducing agricultural non-point source (NPS) pollution from agricultural land is the relative lack of information relating the effect of agricultural practices on groundwater pollution. Monitoring the concentrations of agrichemicals from all agricultural land would be extremely expensive. and almost impossible. However. communities cannot afford to ignore the potential threat to water supplies from NPS. Computer modeling along with geostatistical simulation has a key role to play in reducing NPS water quality problems. The integration of simulation based on limited spatial data along with transport modeling offers the advantage of utilizing the full information content of spatially distributed data to analyze solute transport on a field scale in three-dimensions. The natural textural and structural variabilities in field soils and hydrologic formations are extensively acknowledged as dominant factors influencing fluid and mass transport through the subsurface zone. In response to this spatial variability, the transport and retention properties of a field scale soil also present spatial variation to inputs such as irrigation, rain, and natural or artificial sources. There are additional sources of variability in soils subject to management and cultural practices. These variabilities also are related to the initial conditions describing the amount of soil chemicals in a typical field. Both sources of 233
F. S. GODERYA et al.
234
variability introduce uncertainty in the modeling process. Numerous efforts have been directed toward quantifying the level of spatial variability in various soil parameters (Jury et at., 1987). Site specific field management is identified as a technology for optimizing net returns from agriculture while reducing or eliminating groundwater contamination. By applying chemicals in a spatially varying manner according to localized needs and yield potentials, fertilizers and pesticides can be applied to the portions of the field that need them the most. It is assumed that such a strategy will carry environmental benefits by minimizing potential leaching offertilizer. Theoretically, it appears that making fertilizer applications more efficiently in tune with localized crop and soil needs would reduce chemical outflows from fields, and hence, water quality problems. However, there is no guarantee that this will always be the case. Furthermore, no concrete evidence has been put forward that shows how much actual reduction in chemicals can be achieved through these practices (Ferguson et at., 1994). This paper focuses on the effects of spatial variability of initial soil nitrogen levels and crop yield within a field. A methodology is presented for incorporating spatial variability in modeling the effects of diffuse pollution of groundwater. This information in combination with simulation and modeling is utilized as a means of illustrating how the spatial statistical properties of leaching can be obtained for different scenarios of fixed and variable rate fertilizer application for a typical field. APPROACH The methodology incorporates 3-D residual soil nitrogen and 2-D yield variability in the modeling process for estimation of leaching of nitrates. This information is useful for quantifying environmental benefits of variable rate application. Geostatistical simulation techniques in combination with multiple-one dimensional transport model runs are utilized as a means of evaluating various scenarios of fixed and variable rate applications. A schematic of major components in the process for a given scenario is illustrated in Fig. 1. Structural analysis of the field data is used to evaluate spatial continuity by calculating a covariance function. Based on the covariance function several realizations of field are generated. For each field realization, multiple runs of a transport model are used to obtain the nitrate loading to groundwater. The procedure is repeated for each scenario with different management controls. Dlftn. SpIUII CDnUnu11y Dr FI.ld Plrlml...
NIIr.t. L Idlng 10 Groundwlter
Figure 1. Primary components of the transport simulation program for one scenario.
Spatial variability in modeling non-point source pollution
235
Nitrogen ReQuirements Nitrogen is the nutrient, most often required for growing crops_ Nearly all crops need some nitrogen fertilizer unless there is abundant nitrogen in the soil. Phosphorus is the second nutrient most likely to be needed. There are some other nutrients like potassium, sulfur, zinc, iron, calcium, magnesium, boron, chlorine, copper, manganese, and molybdenum, which may be needed for growing crop on certain soils. In this research only nitrogen is considered to be the limiting nutrient. The amount of nitrogen needed for growing corn is based on expected yield, the amount of residual soil nitrate-nitrogen and soil organic matter. The following algorithm is recommended by the University of Nebraska for detennining the nitrogen fertilizer application rate to corn (Penas et al., 1994):
NN = 35
+ 1.2*EY - 8*RN - 0.14*EY*OM - ONC
(I)
where NN = nitrogen need (lb/acre); EY = expected yield (busheVacre); RN = average nitrate-nitrogen concentration in the root zone (ppm); OM = percent organic matter; and ONC = other N credits from legumes, manure, and other organic waste products, and irrigation water. yariabJe Rate Auplication Five applications scenarios were developed in the methodology leading to the spatial management technology. All spatial management scenarios were based on appropriate management of nitrogen to meet but not exceed production needs. To ensure that values of the input variables used in the unsaturated zone model were reasonable, the first scenario was based on the traditional farm practices. The results from the principal program were also compared with the well documented program Erosion Productivity Impact Calculator (EPIC) (USDA, 1990, Goderya et at., 1995). This was done to ensure that the results from the application of this scenario were in the reasonable limits of the current problem in the area_ The subsequent scenarios reflects possible advancement in the traditional practice in the framework of spatially variable nitrogen input Each scenario was run for five years of continuous corn cultivation. A simplified illustration of the various scenarios is presented in Fig. 2. The first scenario used unifonn input of nitrogen based on traditional practices. The input rate was also held constant from one year to another. Nitrogen was added once at the beginning of each growing season at an average rate of 200 kglha. The crop received an amount comparable to the historic application rate. This rate was estimated with the expected yield of 9.7 Mglha and the University of Nebraska nitrogen recommendation of fertilizer application. Expected yield is estimated from actual field measurements along with county or state long-tenn records (Meisinger and Randall, 1991). Since no long-tenn averages of yield for the field were available, hence, average yield of the field with a 10 percent increase was used as an estimate in expected yield goal calculation. This scenario and the other following scenarios assumed that the soil has two percent organic matter content. No consideration was given to the initial amount of nitrate• nitrogen present in the root zone. This scenario, therefore, can be regarded as a "worst case" groundwater contamination scenario among the others. Scenario two assumes the same crop and unifonn application, but the amount of application was modified based on one soil sample and yield infonnation from one location in the field. The assumption of one sample can be based on composite average of various soil samples. collected from different parts of the field. The amount of fertilizer application for the first year was calculated based on the available data of yield and residual soil nitrate-nitrogen from a location. However, the amount of fertilizer was varied each year corresponding to previous year yield and the amount of residual soil nitrate-nitrogen before the fertilizer application. The application was unifonn with respect to various locations but variable with respect to time. The third scenario uses variable application based on the spatial variation of parameters. The area was
F. S. GODERY A el aL
236
divided into four sectors, and the application rate was based according to the measurements of control location in each sector. Hence, the whole field received variable application with respect to position as well as time. The fourth and fifth scenarios were similar to the third scenario except that the field was divided into sixteen (16) and one hundred and twenty (120) sectors, respectively. Each sector received variable rate application with respect to time and location conforming to its control location. Geostatistical Simulation There are several multidimensional simulation techniques described in the literature including matrix models such as the nearest neighbor method used in Smith and Freeze (1979), spectral techniques described in Meija and Rodriguez-Iturbe (1974), and Gaussian related algorithms described in Journel and Huijbregts (1978), and Deutsch and Journel (1992). The simulated quantities are typically used for estimation and interpolation purposes or to drive large-scale simulations involving heterogeneous phenomena. Scenario t
UA-TP
Scenario 4
Scenario 2
Scenario 3
UA-l CP
VA-4 CP
Legends: UAWT-Uniform Application ... r.t Tim. VAWT-Varl,ble Application ...r.l. Tim. UA-TP-Uniform Application, Traditional Practice UA-ICP-Uniform Application, I Control Point
VA-16CP
VA-4 CP-Variabl. Applicatioa, 4 Control Point VA-16 CP-Variabl. Application, 16 Control Poinl
Figure 2. Graphical iUustration of the various application scenarios.
The sequential principle is identified to be the most straightforward algorithm for generating realizations of a multivariate Gaussian field (Deutsch and Journel, 1992). The sequential simulation principle consists of generating a realization of a variable Z(u) from its conditional distribution given the value of the most related covariate at the same location u. The conditioning is extended to include all data available within a neighborhood of u, including the original data and all previously simulated values. The sequential simulation process is independent of the algorithm or model used to establish the sequence of univariate conditional cumulative distribution functions. The algorithm used in this research uses the conditional simulation of a continuous variable z(u) modeled by Gaussian related stationary random function RF Z(u) (Deutsch and Journel, 1992). Structural analysis of the field data is used to evaluate covariance functions. This structural information is then utilized in generating a number of field realizations through conditional simulation. In order to complete three dimensional simulation for residual soil nitrate-nitrogen, structural analysis is completed for both the horizontal-spatial dimension and the vertical dimension. Stochastic fields of corn yield are generated using the two dimensional field measurements.
Spatial variability in modeling non-point source pollution
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Multiple one-dimensional transport model Studies describing transport through unsaturated soil are concerned with a system in which the vertical plane is small in scale compared with the horizontal plane that defmes a field or even regional area. A common approach employed in describing field scale water and solute movement through unsaturated zone is to view the transport process locally as a vertical, one dimensional flow system. A modified version of this approach is employed in which a multiple one-dimensional system describes the spatial variability in a typical field. A variety of models exist for estimating movement and degradation of agricultural chemicals in the unsaturated zone. Water percolation and nitrate leaching can be simulated using several existing models at various levels of detail. The unsaturated zone model used in this research is similar to CREAMS (Knisel, 1980) except for the water movement algorithm. The model is composed of several subroutines that account for different elements of the nitrate transport process in the unsaturated zone. The hydrology component calculates evapotranspiration, runoff, infiltration, capillary uptake, and deep percolation; whereas the chemical subroutine computes nitrate uptake by plant, mineralization, nitrification, and denitrification. These sub-models are later combined to calculate the daily movement of water and nitrate through the unsaturated zone. To calculate the movement of water through the various soil layers, the model uses a finite difference solution of the one-dimensional unsaturated-zone-flow equation (Bogardi and Bardossy, 1984; Goderya et al., 1995). INITIAL RESULTS The research results are obtained by varying the amount of applied fertilizer based on controlling algorithm recommendations and using the simulation on the basis of measurement data. The management practice of spatially variable application was evaluated on the basis of sustaining production agriCUlture and decreasing the risk of environmental degradation. A comparative evaluation of the effects of five spatial management scenarios on nitrate loading below the root zone was investigated. For all evaluations, effect variables were either averaged or summed for the 5 year simulation period and used in relative comparisons. These results, therefore, represent short-term impacts of the spatial management technology. Figure 3 summarizes the primary nitrogen input. Nitrogen fertilizer input averaged 200 kglha-yr for the traditional practice scenario, which compares favorably with the average com fertilization rate in Nebraska, without any consideration of soil nitrate in the profile (Follet et al., 1991). Fertilizer nitrogen inputs were lower for second scenario because the information from the field including the nitrogen pool were used. The amount of nitrogen fertilizer applied to the crop in the third scenario was reduced by 13 kglha-yr. However, the reductions in nitrogen use in the fourth and fifth scenario over third and fourth were only by 3 and 4 kglha-yr. These reductions may not be sufficient to justify the increased effort of measurements and spatial management of the field. Simulated crop yields were similar under all five spatial management scenarios. The means and the standard deviations of the annual yields from the simulated fields matched very closely with the average expected yields for the site. This research effort was designed with the goal that the production compares well with the traditional baseline output. Hence, although the spatial management scenarios reduced the fertilizer requirements, the yield had little or no effect on these reductions. This suggested that the spatial management scenarios and fertilizer amounts appear to have been modeled appropriately. The amount of nitrate, moved form the soil surface to the bottom of the root zone, was extracted from the number of output variables to compute the sample statistics. The output data were evaluated in terms of field leaching potentials as well as for leaching as a consequence of spatial management practices. Statistical analysis of each scenario simulation for a field, and each node in a field for number of simulations, provided insight into the relative importance of the conditions and modeling of transport processes. Basic statistical parameters including the mean and standard deviation were calculated for different cases.
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Figure 3. Average annual nitrogen fertilizer inputs for spatial management scenarios.
Figure 4 shows the amounts of nitrogen leaving the root zone. This is the primary factor important to groundwater quality from the geostatistical-transport simulation for five spatial management scenarios. The amount of nitrate leaving the root zone for the first scenario is used as a check. The results of this scenario simulations are consistent with the magnitude of the responses reported from experimental studies in the Midwest (Ferguson et ai., 1994). Comparison of the result from this scenario to nitrate contamination data reported in the area also was used as an indicator of the effectiveness of the subsequent scenario results. Comparing the first and second scenarios, it can be inferred that by considering one measurement from a field, potential nitrate loading to groundwater was reduced by 34%. Similarly, if various sources of information from separate measurements are included in the decision model, then the potential contamination is reduce by 41 % over that of traditional practice. This reduction is 10% when compared to Scenario 2 results. Comparison of the fourth and fifth scenarios with third scenario indicated that nitrate contamination would be reduced by 9.6% and 13% respectively, that is, if one considers 16 and 120 blocks of variable decision input in a sizeable field as opposed to 4 sectors.
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Spatial variability in modeling non-point source pollution
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These results suggest that the application of increased infonnation for different parameters and conditions in a spatial management system may not necessarily result in a substantial decrease in the contamination problem. Therefore. most of the effort associated with spatially variable application would appear to be exces!>ive to justify spatial management and application for the fourth and fifth scenarios. We classify this field as the case of low variability field and hence the degree of variability of controlling parameters may be used as an indicator to evaluate various fields for suitability of spatially variable application technology. This also suggests that available resources should be allocated in a greater proportion toward the assessment of the potential effects of spatial variability in a field than development of variable application technology. Figure 5 shows the average amount of soil nitrate present in the soil profile before and after the simulations. Soil nitrate at the end of 5-yr simulations was slightly higher for traditional practice scenario. but declined under all other management scenarios. For the second scenario. the reduction of nitrate in the soil profile was due to the consideration of realistic yield goal and soil nitrate infonnation. The subsequent spatial management scenarios had smaller effects on the profile nitrogen levels at the end of simulation period. Thus. it seems likely that unifonn application given realistic yield and composite soil samples would achieve results comparable to spatially variable application.
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SUMMARY AND CONCLUSIONS
The methodology presented in this research employs a combination of geostatistical simulation and unsaturated zone transport modeling. The methodology was applied to show how the knowledge about soil parameters related to production system can be organized and presented to concerned parties to predict the environmental impact of production agriculture. The process was shown to be able to give quantitative estimates of the effectiveness of spatially variable application practices. Spatial variation of residual soil nitrates. yield. and hydraulic conductivity in a typical field was used to estimate the nitrate contamination of groundwater. A one dimensional unsaturated zone transport model • TDNIT. was used at a number of locations in the field which resulted in a quasi three-dimensional system. The use of the selected transport model offers the advantage of short computation time and reduced input data demands. The methodology developed in this research was applied to a typical field. The management practice of spatially variable application was evaluated on the basis of sustaining production agriculture and reducing the risk of environmental degradation. Five scenarios of potential spatial management technology were used. These scenarios were evaluated given the spatial distribution of residual soil nitrates. yield. and hydraulic conductivity in the fields. The decision input parameters and fertilizer amount were distinctively different
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for the different scenarios as well as spatial locations for the last three scenarios. The initial comparative evaluation of results of various scenarios suggested that an increase of information for related parameters and conditions in a spatial management system may not necessarily result in a substantial decrease in the contamination problem for some fields. We classified this field among various others as one exhibiting low variability. Hence the degree of variability of controlling parameters may be used as an indicator to evaluate various fields for suitability of variable application technology. The results suggested that available resources should be allocated in a suitable proportion towards the assessment of spatial variability. The methodology was demonstrated for estimating nitrate pollution to groundwater. However, the methodology also can be adopted for use in conjunction with many other anthropogenic pollutants in estimating groundwater contamination potential. It should be noted that this paper considered only advective transport with hydraulic conductivity being the only spatially variable hydrogeologic parameter. However, the framework can be used in situations involving advection. dispersion. retardation. and decay. ACKNOWLEDGMENT This paper was supported. in part. by the Center for Infrastructure Research and the Water Center, University of Nebraska-Lincoln. and in part, by the Cooperative State Research Service of the U.S. Department of Agriculture. At the time of the study, F. S. Goderya was a Graduate Research Assistant and M. F. Dahab and I. Bogardi were Professors in the Department of Civil Engineering and W. E. Woldt was an Assistant Professor in the Department of Biological Systems Engineering. University of Nebraska. Lincoln, NE 68588-0531. USA. REFERENCES Bogardi I. and Bardossy A. (1984). Stochastic forecasting of N budget in the unsatumted zone, Proceedings of International Symposium of Recent Investigations in the Zone of Aeration, RIZA. Munich, West Germany. October 1-5. pp. 743-756. Deutsch C. V.• Joumel A. G. (1992). GSUB: Geostatistical software library and Ilser's guide, Oxford University press. Ferguson R. B•• et al., (1994). Managing spatial variability with furrow irrigation to increase nitrogen use efficiency, Proceedings of
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Conference
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BloomingtonlMinneapolis. Minnesota, March. Follet R. F.• Keeney D. R. and Cruse R. M. (1991). Managing nitrogen for groundwater quality andfarm profitability, Soil Science Society of America, Madison. Washington. Goderya F. S.• Dabab M. F.• Woldt W. E.. Bogardi I. (1995). Consideration of Spatial Variability in Nitrate Contamination to Groundwater. Presented at the ASAE International Summer Meetmg. ASAE Paper No. 942092. SL Joseph. M149085. Goderya F. S.• Dabab M. F.• Woldt W. E.• Bogardi I. (1995). Comparison of transport models for predicting nitrate in percolating water. Working paper. Department of Civil Engineering. University of Nebraska-Lincoln. Lincoln, NE 68588-0531. Jones R. L. and Hanks R. J. (1989). Review of unsaturated zone leaching models from a user's perspective. Proceedings of the International Symposium on water quality modeling of Agricultural Non-point Sources. June 19-23. Logan. Utah. Joumel A. G. and Huijhregts Ch. J. (1978). Mining geostatistics. Academic press. Jury W. A.• Russo D.• Sposito G. and Elabd H. (1987). The spatial variability of water and solute transport properties in unsaturated soil; I. Analysis of property variation and spatial structure with statistical models, Hilgardia, 55(4), 1-32. Knisel W. G.• ed. (1980). CREAMS: A field-scale model for chemicals, runoff. and erosion from agricultural management systems. U.S. Department of Agriculture, Conservation research report no. 26. 640 pp. Meija J. and Rodriguez-Itrube 1. (1974). On the synthesis of random fields from the spectrum: An application to the generation of bydrologic spatial processes. Water Res. Res.• 10,705-71 I. Meisinger J. J.. Randall G. W. (1991). Estimating nitrogen budgets for soil-crop systems, In: Managing nitrogen for groundwater quality andfarm profitability. Soil Science Society of America, Madison. Wisconsin Smith L. and Freeze R. A. (1979). Stochastic Analysis of steady state groundwater flow in a bounded domain. 2. Analysis of uncertainty in prediction. Water Res. Res.• 15. 1543-1559. Penas E. J.. Hergert G. W. and Ferguson R. B. (1994). Fertilizer suggestions for corn, NebGuide. G74-174-A. Published by Cooperative Extension. Institute of Agriculture and Natural Resources, University of Nebraska-Lincoln. Lincoln. NE 68583. USDA. U.S. Department of Agriculture, (1990). EPIC-Erosion/Productivity Impact Calculator; I. Model documentation. and User Manual. Technical bulletin no. 1768.