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ANSWERS-20001


1 This paper is a part of an organized joint effort from within the ASCE, Environmental and Water Resources Institute (EWRI), Water Quality and Drainage Committee under the Task Committee "Non-Point Source Water Quality Models: Their Use and Application"; and the USDA-CSREES Southern Region Research Project S-273 "Development and Application of Comprehensive Agricultural Ecosystems Models".  This paper was originally presented at the 1998 International ASAE Meeting in Orlando, FL as Paper Number 982199.

Theo A. Dillaha, Mary Leigh Wolfe, Adel Shirmohammadi, F. Wes Byne2

Summary:

ANSWERS-2000 is a distributed parameter, physically-based, continuous simulation, farm or watershed scale, upland planning model developed for evaluating the effectiveness of agricultural and urban BMPs in reducing sediment and nutrient delivery to streams in surface runoff and leaching of nitrogen through the root zone. The model is intended for use by planners on ungaged watersheds where data for model calibration is not available. The model divides the area simulated into a uniform grid of square (1 hectare or smaller), within which all properties (surface and subsurface soil properties, vegetation, surface condition, crop management, and climate) are assumed homogeneous. The model uses breakpoint precipitation data and simulates hydrologic processes with a 30-second time step during runoff events and with a daily time step between runoff events. The model simulates interception; surface retention/detention; infiltration; percolation; sediment detachment and transport of mixed particle size classes; crop growth; plant uptake of nutrients; N and P dynamics in the soil; nitrate leaching; and losses of nitrate, ammonium, total Kjeldahl nitrogen, and P in surface runoff as affected by soil, nutrient, cover and hydrologic conditions. The model has an ArcInfo based user interface that facilitates data file creation and manipulation. The model is in the public domain and is available via ftp.

Keywords: Water quality, modeling, erosion, nutrients, watershed

Introduction

This paper was developed as part of the "Project to Evaluate Use and Application of Water Quality Models", which is a component of Southern Regional Research Projects S249, "The Impact of Agricultural Systems on Surface and Groundwater Quality", and S271, "Development and Application of Comprehensive Agricultural Ecosystems Models". The objective of this project is not to validate or compare the accuracy of the various models, but rather to document the intended use/purpose of the models, general model characteristics, verified applications, input/output requirements, known limitations, etc. This paper describes the ANSWERS model portion of this project.

ANSWERS History

Beasley and Huggins (1982) developed the original ANSWERS (Areal Nonpoint Source Watershed Environment Response Simulation) model in the late 1970s. The model was based on one of the first true distributed parameter hydrologic models (Huggins and Monke, 1966). The original ANSWERS was a distributed parameter, event-oriented, planning model developed to evaluate the effects of BMPs on surface runoff and sediment loss from agricultural watersheds. ANSWERS subdivides the watershed into a uniform grid of square cells (Figure 1). Land use, slopes, soil properties, nutrients, crops, and management practices are assumed uniform within each cell. Differences between cells allow the model to consider the heterogeneous nature of watersheds and the site specific effectiveness of individual BMPs. Typical cell sizes range from 0.4 to 1 ha with smaller cells providing more accurate simulations. Ten to twelve parameter values must be provided for each homogeneous cell. Within each cell, the model simulates interception, surface retention/detention, infiltration using Holtan's method (Holtan, 1961), surface runoff, percolation through the infiltration control zone, sediment detachment and sediment transport. Flow was from routed downslope to adjacent overland flow cells or in channel cells. The model could simulate BMPs such as conservation tillage, ponds, grassed waterways, tile drainage (Bottcher et al., 1981) and other practices whose effects on the physically based model input parameters could be described. An original weakness of the ANSWERS model was its erosion model, which was largely empirical and simulated only gross sediment transport. The model was modified in the early 1980s to simulate the particle size distribution of eroded sediment (Dillaha and Beasley, 1983) using Yalin's method (Yalin, 1961) to estimate sediment transport. Rewerts and Engel (1991) developed GIS interfaces for this version of the model. In the late 1980s, phosphorus (Storm et al., 1988) and nitrogen (Dillaha et. al., 1988) transport versions of the event-oriented model were developed. They considered the transport of dissolved and adsorbed orthophosphorus, nitrate and dissolved and adsorbed ammonium and TKN.

The current version of the model, ANSWERS-2000, is a continuous simulation model that was developed in the mid 1990s (Bouraoui and Dillaha, 1996). In this version, the nutrient submodels were overhauled and improved infiltration (Green and Ampt), soil moisture and plant growth components were added to permit long-term continuous simulation. Bouraoui (1994) describes the current version of the model in detail. ANSWERS-2000 simulates transformations and interactions between four nitrogen pools including stable organic N, active organic N, nitrate and ammonium. Transformations of nitrogen include mineralization simulated as a combination of ammonification and nitrification, denitrification, and plant uptake of ammonium and nitrate. The model maintains a dynamic equilibrium between stable and active organic N pools. Four phosphorus pools are simulated: stable mineral P, active mineral P, soil organic P and labile P. Equilibrium is maintained between stable and active mineral P and between active mineral P and labile P. Plant uptake of labile P and mineralization of organic P are also simulated.

The continuous version, ANSWERS-2000, was tested on two watersheds in Watkinsville, Georgia, and performed well in predicting runoff, sediment, nitrate, dissolved ammonium, sediment-bound TKN, and dissolved phosphorus losses from both watersheds (Table 1 and Figures 2 to 8 for the P2 watershed). The model did not predict sediment-bound ammonium losses from either watershed well. The model was also tested on the 1153 ha Owl Run watershed in Virginia. The model performed well for the largest storms, and cumulative predictions of runoff volume, sediment yield, nitrate, ammonium, sediment-bound TKN, and orthophosphorus were within 40% of the measured values (Table 2). In a practical application of ANSWERS-2000, the model was run for eight years on a 225 ha subwatershed in the Nomini Creek watershed in Virginia. Potentially critical source areas were selected, and BMPs (conservation tillage) were then implemented on 10, 20, 30 and 100% of the cropland in the watershed. Targeting was found to significantly increase the efficiency of BMP application with respect to water quality (Table 3). For example, nutrient reductions were 2.4 and 2.1 times as great on a per hectare basis for nitrogen and phosphorus, respectively, when BMPs were targeted to 10% of the cropland with the highest sediment losses as compared to application of BMPs to all cropland. The model also showed that fields that had very high sediment and nutrient yields did not always have large impacts on yields at the watershed level.

To facilitate use of the model, the ANSWERS-2000 NPS decision support system was developed (Wolfe et al. 1995). This ArcInfo based decision support system has a knowledge-based system to advise the user on parameter selection and database creation. The user interface also keeps track of BMP scenarios evaluated and controls model output. The user interface links components and functions of the ANSWERS-2000 modeling system in a manner that is reasonably transparent to the user. A set of menus, prompts, helps, and rule-based functions guide the user, but does not eliminate interaction with the system. Procedures are incorporated to flag problems associated with incorrect data and report when system constraints have been violated and provide appropriate corrective action. The user interface consists of a main menu and secondary menus. The menus allow the user to provide site-specific information for input parameters for the ANSWERS-2000 model. The modeling-related tasks facilitated by the interface include the following: selection of the land area of interest (watershed, farm, or field) from a GIS coverage; automatic access to a soils parameter file with options for replacing general parameter values with site-specific information; developing the grid overlay of the watershed; calculation of topographic characteristics; generating synthetic weather data if desired; assigning crop and tillage parameter values; creation of the ANSWERS-2000 input data file; running the model; displaying model output; applying alternative practices to user-specified land areas; and comparing predicted output values for alternative scenarios. In addition, a help function in the interface includes specific information for the user on how to proceed with the different menu selections.

In a recent development, a groundwater component was added to ANSWERS-2000. This version of the model was validated at the local, field and watershed scales. At the local and field, it accurately predicted drainage below the root zone and evaporation for different vegetative covers. At the watershed scale, it accurately reproduced piezometric levels and trends across the watershed (Bouraoui et al., 1997). It is not known if this version of the model simulates nutrient transport.

Current Developments

Additional work on ANSWERS-2000 is currently being sponsored by the USDA (USDA-NRI project), the Virginia Chesapeake Bay Local Assistance Department, and the Virginia Water Resources Research Center. The principal objectives of these projects are to:

1. Replace the existing empirical sediment detachment submodel with a more reliable and robust physically-based sediment detachment submodel.
2. Add a channel erosion and scour submodel.
3. Improve the existing nitrogen cycle/ammonium submodel to improve predictions of dissolved and adsorbed ammonium transport.
4. Develop new submodels to simulate the effects of buffers, detention facilities, and wetlands on sediment and nutrient loss.
5. Develop new procedures to better simulate nutrient loss from turf areas in urban areas.
6. Develop new procedures or submodels to simulate the effects of urbanization on sediment and nutrient yields and channel stability in rural watersheds.
7. Improve the user interface.

Model Evaluation Criteria for ANSWERS-2000

 

1 Model Use Characteristics
A· Intended Use of the Model
1) Water quality and hydrologic characteristics addressed
Surface runoff (continuous hydrograph at watershed outlets and other designated cells)
Erosion and sediment transport (up to 10 particle size classes). Sediment yield from and or deposition in each cells. Time varying sedigraph for different particle size classes at watershed outlets or designated cells.
Nitrate and adsorbed and dissolved ammonium, TKN, orthophosphorus yields in surface runoff from each cell. Nitrate leaching below the root zone from each cell. Nutrient concentrations versus time at watershed outlets or designated cells.
Processes simulated: spatially varying breakpoint rainfall, interception, surface retention/detention, infiltration, percolation, surface runoff (overland and channel flow), crop growth, evapotranspiration, surface cover, sediment detachment and transport for up to 10 particle size classes, soil nitrogen and phosphorus cycles (organic and inorganic, dissolved and adsorbed nutrient pools, nitrate leaching, nutrient losses in surface runoff
2) Modeling Scale:
Spatial: field, farm (multiple watersheds or parts of multiple watersheds), watershed. Uniform grid of square cells 1 hectare or less in size is required for computational accuracy. Intended for use in medium sized watersheds (500 to 3000 hectares where upland processes dominate the hydrologic cycle.
Temporal: Continuous simulation. 30 second time step during runoff events, daily time step otherwise. Recommended simulation period of 20 or more years.
3) Economics: Not currently simulated.

D· Target Audience
Intended for planners but is currently impractical for use by anyone except experienced modelers and researchers because of lack of documentation and a more user-friendly interface. Currently used primarily by researchers with a strong knowledge of hydrologic, soil and crop processes.

E· Verified Applications
6) Extent of Model Tests
ANSWERS-2000 validation studies have been conducted on the USEPA/USDA Watkinsville, GA small watersheds/fields (Piedmont) and the Owl Run (Piedmont) and Nomini Creek (Coastal Plain) watersheds in Virginia for 14 to 36 month periods. Model predictions of average annual yields with little or no calibration compared favorably (within a factor of two) with observed data except for ammonium. Additional tests are needed with longer-term records and in other regions. See Bouraoui (1995) and Bouraoui and Dillaha (1996).
7) Sensitivity Analysis
Sensitivity analysis was conducted on the data sets developed for the Watkinsville, GA validation runs and are discussed in detail by Bouraoui (1995). The parameters having the biggest impact on model output were the soil clay and silt content because of the impact on infiltration and surface runoff. The most sensitive parameters for the major outputs include:
Runoff volume: silt and clay content, solar radiation.
Sediment yield: clay content
Nitrate in runoff: clay content
Dissolved: sensitive runoff volume parameters
Sediment-bound TKN: clay content, soil N level, active organic N
Sediment-bound P: initial labile P, clay and silt content
Dissolved P: initial labile P, clay and silt content

H· Input/Output
9) Ease of developing input data sets:
Relatively straight forward with the ArcInfo based user interface. Very difficult and time consuming without.
10) Requirements for field measured inputs:
Model was developed as a planning tool and is intended for use on ungaged watersheds. Calibration is beneficial but not required. Most input parameters can be obtained from soil surveys, topographic and landuse maps and the user interface, which aids in the selection of parameters and provides default values.
11) Richness of model output summaries:
Raw output is overwhelming, but the user interface condenses, summarizes and provides graphical output, that is relatively easy to understand and use.
12. Model Characteristics
M· Source and Availability of Model:
ANSWERS-2000 source code (FORTRAN 77) is available via FTP at: ftp://dillaha.ageng.vt.edu/pub/models/answers via anonymous login. The existing ArcInfo interface (Sun Workstation) is still undergoing testing and is being converted to Windows 98/NT ArcInfo, but should be available by January 1999. An ANSWERS home page for model information and distribution is under development and will be available in January 1999.

N· Availability of Continuing Education/Training Opportunities for Model Users:
No training programs have been conducted to date. None are anticipated unless a public or private organization assumes responsibility for model maintenance and distribution.

O· Versions
16) Event Based
a. Documentation: A good users manual is out of print, but available from Theo Dillaha (dillaha@vt.edu)
b. Source Code Availability:
Via Anonymous FTP at: ftp://dillaha.ageng.vt.edu/pub/models/answers
a. Platforms:
Anything with a FORTRAN compiler
2) Continuous Simulation Version
a. Documentation: Very poor. No formal users manual. Best guide is the user interface.
b. Source Code Availability:
Via Anonymous FTP at: ftp://dillaha.ageng.vt.edu/pub/models/answers
b. Platforms: Anything with a FORTRAN compiler. Currently running on a Sun workstation, but other have it running on PCs. Needs a high end PC or workstation with a FORTRAN compiler and ArcInfo

C· Interfaces
4) GIS
GRASS for the event version (Rwerts and Engle, 1991)
ArcInfo for the continuous version (Wolfe et al., 1995)
5) General User Interface
ArcInfo (AML) based user interface called FARMSCALE guides user through data file creation, model execution and interpretation of model output.

F· Input/Output Options
7) Input data sources: soil survey, topographic maps, DEM, landuse maps, user interface
8) Output options: the user interface provides a variety of output options - storm by storm, annual, average annual values, etc.
9) Options for analysis of outputs: user interface can display outputs spatially and temporally

J· Sample Data Sets
Sample input and output sets are at the FTP site.

K· Calibration
Parameters are generally physically-based and calibration is not required. Since the model is intended for use on ungaged upland watersheds, availability of data for calibration is unlikely. If observed data is available, calibration can be used to improve estimates of parameters and model accuracy.

12. Known Limitations and Applicability of the Model
M· Sediment detachment submodel is empirical and out of date. Needs to be replaced with a more physically-based submodel.
N· Predictions of ammonium loss in surface runoff have been poor. This submodel (or submodels influencing it) needs to be updated.
O· Current procedures for simulating fertilizer placement are cumbersome and need to be automated.
P· The currently distributed version of the model does not simulate interflow and groundwater contributions to baseflow. The model is therefore inappropriate for use in watersheds where baseflow is significant. The groundwater version of the model recently developed by Bouraoui et al. (1997) may overcome this limitation.
Q· There is no user's manual for the continuous simulation version of the model.
R· There is very limited user support.
S· The model does not currently simulate nutrient cycles and fate in receiving waters. This limits the use of the model to small upland watersheds.
T· The model does not simulate snow pack and melt and is thus unsuitable for use in areas with significant winter snow accumulation and snowmelt.

21. Publications/Reference List

Event-based Version

Baun, K., M. Bohn, R. Bannerman and J. Konrad. 1986. Application of the ANSWERS model in a nonpoint source program. Final Report, EPA Grant No. R005750-01, Wisconsin Dept. of Natural Resources, Madison, WI.

Beasley, D. B., Huggins, L.F., and Monke, E.J. 1980. ANSWERS: A model for watershed planning. Trans. of the ASAE 23(4):938-944.

Bottcher, A. B., E. J. Monke, and L. F. Huggins. 1981. Nutrient and sediment loadings from a subsurface drainage system. Trans. Of the ASAE 24(5):1221-1226.

Dillaha, T. A. and D. B. Beasley. 1983. Sediment transport from disturbed upland watersheds. Trans. of the ASAE 26(6):1766-1772,1777.

Dillaha, T. A., D. B. Beasley, and L. F. Huggins, 1982. Using the ANSWERS model to estimate sediment yields on construction sites. J. Soil and Water Conservation 37(2):117120.

Holtan, H. N. 1961. A concept for infiltration estimates in watershed engineering. USDA-ARS Bulletin 41-51, Washington, DC. 25 p.

Huggins, L. F. and E.J. Monke. 1966. The mathematical solution of the hydrology of small watersheds. Technical Report No. 1, Water Resources Research Center, Purdue University, West Lafayette, IN. 130 p.

Montas, H.J., C.A. Madramootoo. Using ANSWERS Model to Predict Runoff and Soil Loss in Southwestern Quebec. Transactions of the ASAE 34 4 1991 1752-1762.

Rewerts, C. C., and B. A. Engel, 1991. ANSWERS on GRASS: Integrating a watershed simulation with a GIS. ASAE Paper No. 91-2621, ASAE, St. Joseph, MI.

Storm, D. E., T. A. Dillaha, S. Mostaghimi, and V. O. Shanholtz. 1988. Modeling phosphorus transport in surface runoff. Transactions of the ASAE 31(1):117127.

Wilson, J. P. 1996. GIS-based Land Surface/Subsurface Modeling: New Potential for New Models? In Proceedings, Third International Conference/Workshop on Integrating GIS and Environmental Modeling, Santa Fe, NM, January 21-26, 1996. Santa Barbara, CA: National Center for Geographic Information and Analysis. CD.

Continuous Simulation Version

Bouraoui, F. 1995. Development of a continuous, physically-based, distributed parameter, nonpoint source model. Ph.D. Dissertation. Virginia Polytechnic Institute and State University, Blacksburg, VA. 330 p.

Bouraoui, F. and T. A. Dillaha. 1996. ANSWERS-2000: Runoff and sediment transport model. Journal of Environmental Engineering, ASCE 122(6):493-502.

Bouraoui, F., G. Vachaud, R. Haverkamp and B. Normand. 1997. A distributed physical approach for surface-subsurface water transport modeling in agricultural watersheds. J. of Hydrology 203(1997):79-92.

Paz, J. O., M. L. Wolfe, S. Mostaghimi, and T. A. Dillaha. 1996. Impact of Channel Erosion on Sediment Yield Prediction for Agricultural. ASAE Paper No. 962036, ASAE, St. Joseph, MI.

Wolfe, M. L., T. A. Dillaha, S. Mostaghimi, C.D. Heatwole and W. D. Batchelor. 1995. A farm scale water quality planning system for evaluating best management practices. Final report submitted to the Chesapeake Research Consortium, Inc., under cooperative agreement NPS#1-A. Dept. Of Biological Systems Engineering, Virginia Tech, Blacksburg, VA. 15 p.

Wolfe, M. L., W. D. Batchelor, T. A. Dillaha, C.D. Heatwole and S. Mostaghimi. 1995. Modeling the effects of farm management practices on off-site water quality. Proceedings of the International Symposium on Water Quality Modeling, April, 1995. Kissimmee, Florida.

Yoon, K. S., A. Shirmohammadi, W. J. Rawls. 1995. Application of Continuous, Distributed Watershed/water Quality Model (ANSWERS) on a Mixed Landuse Watershed ASAE Paper No. 952402, ASAE, St. Joseph, MI.


Table 1: Runoff and Pollutant Yields for the Watkinsville, GA P2 and P4 Watersheds

Parameter

P2 Watershed

P4 Watershed

Predicted

Measured

Percent Error1

Predicted

Measured

Percent Error

Runoff, mm

28.8

27.8

-3.6

33.8

21.9

-54.3

Sediment, kg

4420

7420

-40.4

2170

1920

-13.0

NO3-N, g

1400

1920

+27.1

1750

1500

-16.7

NH4-N (Adsorbed), g

138

2680

+94.9

57.3

2190

+97.4

NH4-N (Dissolved), g

1980

2640

+25.0

1500

1290

-16.3

TKN, g

9770

11900

-17.9

6490

4780

-35.8

PO4-P (Dissolved), g

452

413

-9.4

257

477

+46.1

1 100*(Measured-Predicted)/Measured


Table 2: Measured and Predicted Runoff and Pollutant Yields for the Owl Run Watershed

Date

Rainfall

Runoff

Sediment

NO3-N

NH4-N

PO4-P

TKN


(mm)

(mm)

(kg)

(kg)

(kg)

(kg)

(kg)

July 26, 1991








Measured

59

1.2

4610

127

1

33

65

Predicted


0.9

1835

24

2

3

28

% error1


25

60

81

250

91

57

Aug. 9, 1991








Measured

103

18.6

44671

683

16

160

565

Predicted


18.4

73637

566

35

180

998

% error


1

65

17

118

13

77

Sept. 4, 1991








Measured

80

3.8

17346

109

58

50

350

Predicted


2.9

14108

46

32

7

172

% error


24

19

58

45

86

51

Sept. 18, 1991








Measured

61

3.8

17346

97

22

53

217

Predicted


5.9

14108

35

43

17

205

% error


55

19

64

95

68

6

Sept. 24, 1991








Measured

41

3.6

6798

86

4

43

146

Predicted


0.6

1835

11

1

1

27

% error


83

73

87

75

98

82

Cumulative








Measured

344

31.0

90159

1102

101

339

1343

Predicted


28.7

101049

682

113

208

1430

% error


7

12

30

12

39

6

1 100*(Measured-Predicted)/Measured

Table 3: Reductions in Pollutant Yields due to Targeting Conservation Tillage to Critical Fields

Parameter

Scenario Number

(1)

1 (2)

2 (3)

3 (4)

4 (5)

5 (6)

6 (7)

% or cropland changed to conservation tillage


0


8.5


21.5


32.7


32.7


100

Cells or hectares changed

0

6

15

23

23

70

Runoff







Yield, mm/yr

69

68

68

67

68

66

Reduction, %


0.42

1.10

1.70

1.30

4.00

Sediment







Yield, t/yr

1556

1367

1257

1144

1187

700

Reduction, %


12.18

19.20

26.50

23.70

55.00

Reduction cost, $/t-yr


1.58

2.51

2.79

3.12

4.09

Nitrate-N







Yield, kg/yr

22

22

22

21

22

21

Reduction, %


0.60

1.70

2.90

1.70

3.50

Reduction cost, $/kg-yr


2272.73

2005.35

1802.51

3074.87

4545.45

Dissolved ammonium-N







Yield, kg/yr

556

556

552

548

551

544

Reduction, %


0.07

0.65

1.50

0.90

2.20

Reduction cost, $/kg-yr


770.81

207.53

137.89

229.82

286.13

Adsorbed ammonium-N







Yield, kg/yr

74

73

67

61

66

57

Reduction, %


1.14

9.75

17.00

11.00

23.00

Reduction cost, $/kg-yr


355.62

103.95

91.41

141.28

205.64

TKN







Yield, kg/yr

12025

10652

9488

8562

8947

5219

Reduction, %


11.42

21.10

28.80

25.60

56.60

Reduction cost, $/kg-yr


0.22

0.30

0.33

0.37

0.51

Total phosphorus







Yield, kg/yr

1714

1629

1525

1443

1488

1195

Reduction, %


4.95

11.05

15.80

13.20

30.30

Reduction cost, $/kg-yr


3.54

3.96

4.25

5.08

6.74


 

Figure 1: Representation of Processes Simulated by ANSWERS-2000


 

Figure 2: Measured and Predicted Runoff Volume for P2 Watershed

 

Figure 3: Measured and Predicted Sediment Yield for P2 Watershed

 

Figure 4: Measured and Predicted Nitrate Losses for P2 Watershed

 

Figure 5: Measured and Predicted Dissolved Ammonium Losses for P2 Watershed

 

Figure 6: Measured and Predicted Adsorbed Ammonium Losses for P2 Watershed

 

Figure 7: Measured and Predicted Adsorbed TKN Losses for P2 Watershed

 

Figure 8: Measured and Predicted Dissolved Orthophosphorus Losses for P2 Watershed



2 Professor, Biological Systems Engineering Department, Virginia Tech, Blacksburg, VA 24061-0303, Phone: 540-231-6813, Fax: 540-231-3199, E-mail: dillaha@vt.edu ; Associate Professor, Biological Systems Engineering Department, Virginia Tech, Blacksburg, VA 24061-0303, Phone: 540-231-6092, Fax: 540-231-3199, E-mail: mlwolfe@vt.edu; Professor, Biological Resources Engineering Department, University of Maryland, College Park, MD 20742, Phone: 301-405-1185; FAX: 301-314-9023, E-mail: as31@umail.umd.edu; M. S. Student, Biological Systems Engineering Department; Virginia Tech, Blacksburg, VA 24061-0303
 

 

BSE Department

 Maintained by Theo Dillaha, Professor of Biological Systems Engineering,
Virginia Tech, Blacksburg, VA 24061-0303,
Phone: 540-231-6813, Fax: 540-231-3199, E-mail:
dillaha@vt.edu
 copyright ⓒ 2003 Biological Systems Engineering Dept at Virginia Tech. All Rights Reserved.

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