Ammonia Volatilization, Animal Waste, Irrigation, Swine Effluent, Target MOTAD, Production Economics, Resource /Energy Economics and Policy,

Hattey, Jeffory A.

Park, Seong Cheol

Phetcharat, Chaowana

Stoecker, Arthur L.

English

Research Papers in Economics

Optimal Application of Swine Effluent under Stochastic Weather Conditions in the 
Texas and Oklahoma Panhandles 
 
 
Seong C. Park 
Texas AgriLife Research and Extension Center 
P.O.Box 1658, Vernon, TX 76385 
Email: scpark@ag.tamu.edu 
 
Chaowana Phetcharat 
Department of Agricultural Economics, Oklahoma State University  
423 Ag. Hall, Stillwater, OK 74078-6026 
Email: phetcha@okstate.edu 
 
Art Stoecker 
Department of Agricultural Economics, Oklahoma State University  
312 Ag. Hall, Stillwater, OK 74078-6026 
Email: art.stoecker@okstate.edu 
 
Jeffory A. Hattey 
Department of Plant and Soil Sciences, Oklahoma State University 
170 Ag. Hall, Stillwater, OK 74078-6026 
Email: jeff.hattey@okstate.edu 
 
Support for this research was provided by USDA grant for Comprehensive Animal Waste 
Systems in Semiarid Ecosystems.  Copyright 2010 by Seong Cheol Park, Chaowana 
Phetcharat, Art Stoecker, and Jeffory A. Hattey. All rights reserved. Readers may make 
verbatim copies of this document for non commercial purposes by any means, provided 
that this copyright notice appears on all such copies. 
 
A target MOTAD model was used to determine optimal application strategies for swine 
effluent. The most efficient timing occurs at night with low wind speed and with high 
relative humidity. Significant nitrogen loss can be prevented and potential benefits in 
terms of crop yield and net return can be obtained by switching to efficient irrigation 
timing practices.  
 
Key words 
 
Ammonia Volatilization, Animal Waste, Irrigation, Swine Effluent, Target MOTAD  
Producers in the Southern High Plains, especially in the Texas and Oklahoma 
Panhandle areas apply swine effluent through irrigation systems because it is the most 
economical way to dispose of swine effluent.  However, if inadequately managed, swine 
manure can impose a critical threat to the quality of air and water close to disposal lands. 
Much of the nitrogen in anaerobically digested swine effluent is in the ammonium form 
(NH4-N), which can convert to ammonia (NH3) gas and volatilize during or after field 
application (Liu et al., 1997).  A significant portion of nitrogen is lost as volatilized 
ammonia before the effluent reaches the ground. Ammonia volatilization is indirectly 
related with soil acidification and water eutrophication as a major source of atmospheric 
ammonia (Sutton et al 1995). Ammonia loss from agriculture is now considered a threat 
to the global environment and is a challenge for agri-environmental policy.   
Nitrogen losses take place via ammonia volatilization, leaching, denitrification, 
and plant uptake and removal in the harvested portion of the crop.   Ammonia 
volatilization commonly happens in all ammonium type fertilizers like anhydrous 
ammonia, urea and swine effluent and is affected by various soil characteristics and 
weather conditions following application.   Generally, ammonia volatilization increases 
in high soil pH, temperature, crop residue, and soil moisture content and decreases when 
nitrogen fertilizers move below the soil surface through tillage incorporation and 
movement by irrigation and rain (Jones et al., 2007).  Al-Kaiser et al. (2002) found that 
the percent of N lost through volatilization is not greatly affected by N concentration in 
effluent but that air temperature and wind speed are important factors for N loss.  
Swine effluent can be a good source of crop nutrients if properly managed. Many 
efforts have been conducted to quantify amount of ammonia volatilization of swine effluent from the soil source for the better nutrient management. A recent field 
experiment at the Oklahoma State University Research Station in Goodwell, OK showed 
that 37 to 90 percent of applied nitrogen in the form of ammonia can volatilize to the 
atmosphere as ammonium (NH4) within a few days following swine effluent application 
to a Richfield clay loam soil, a calcareous type of soil in the Oklahoma Panhandle 
(Zupanic et al. 1999 and Warren 2001). The level of volatilization depends on the 
climatic conditions following application.  The high volatilization occurred during hot, 
dry weather conditions with low relative humidity, and brisk wind speeds (Zupancic 
1999). A mechanistic model was developed using parameters from field experiments with 
flood and sprinkler irrigation (Wu et al. 2003). This model was designed to predict 
ammonia volatilization rate and cumulative volatilization from liquid and soil surfaces 
and the simulated ammonia volatilization rate and cumulative volatilization closely 
matched data from field irrigation experiments.  
Management of animal wastes from animal confinement facilities has been one of the 
important issues in swine and poultry farming. Moreover, ammonia loss from agriculture 
is now considered a threat to the global environment and is a challenge for agri-
environmental policy. However, previous analyses of nitrogen losses have mainly 
focused on water pollution from nonpoint sources and little economic study of nitrogen 
loss through ammonia volatilization has been conducted.  
The objectives of this study are 1) to determine efficient choices of irrigation timing 
with swine effluent in the pre-plant season to minimize nitrogen loss based on historical 
weather (wind and temperature) data 2) to compare nutrient loss (i.e. nitrogen) between 
the optimal application schedule and conventional application timing; and 3) calculate economic benefits from adopting the optimal irrigation timing with application of swine 
effluent.  
 
Data and Method 
Hourly weather data of first two weeks in April between 1998 and 2005 such as 
temperature, precipitation, relative humidity, wind speed, and solar radiation were 
collected from Mesonet in the Oklahoma Panhandle. The cumulative amount of nitrogen 
lost via ammonia volatilization for each six-hour time block was calculated for a pre-
plant season (e.g. April) using a mechanical model developed by Wu et al (2003). Initial 
conditions and other important factors in simulating ammonia volatilization are shown in 
Table 1.  
The timing commonly adopted in the region for application of swine effluent to 
corn field is at approximately the 6-leaf (V6) corn growth stage, which typically occurs 
about 3 weeks after seedling emergence. This stage varies from late April to early June 
but actual timings when swine effluent was applied in the experiment station were 
considered the conventional timing of application in this research. The economic 
profitability of alternative strategies of applying swine effluent was calculated as the 
return (corn price times yield) above specified costs. The recent three-year average price 
of corn (2006-2008), US $126.11 Mg
-1 was used. Fertilizer application cost of swine 
effluent is presented in Table 2.  Method 
Target MOTAD  
Efficient irrigation timing is determined in the target MOTAD programming model that 
minimizes total expected nitrogen loss with constraints that require nitrogen loss to not 
exceed a target level. A target level is flexible because the average annual deviations 
from a target level of N loss are incorporated.  The objective of this model is to determine 
the optimal irrigation timing that will minimize expected ammonia loss rate (ALR) with 
respect to the target ammonia volatilization rate. The target MOTAD model in this 
research can be written 
(1)
j
j
j X X CMEAN EALR
j ∑
=
=
1
min
 
s.t   b X a j
j
j ≤ ∑
=1   
  ,
1
ALR TGT Y X C t j
j
tj ≤ + ∑
=  
  λ = ∑ t
t
t ob Y Pr  
where  j CMEAN is expected ammonia loss rate (ALR) from time block j,  j X is time block 
j,  t Y  is value of any deviation in ALR below the target in state of nature t,  tj C is ALR 
from timing block j in state of nature t,  ALR TGT  is target ALR,  t ob Pr  is probability of 
a state of nature t, and λ is allowable average deviation from the target ALR.   
 
Expected Net Return Optimal irrigation strategy is compared with the conventional irrigation timing in terms 
of expected profits of two strategies based on estimated crop response functions Expected 
profit function of a farmer can be written 
(2)  TVC NA r p − ⋅ − ⋅ = ) E(Y π  
), , ( pH TAN f Y =  
, ) 1 ( SN Nloss NA TAN + − =  
 
where Y is corn response function,  p  is the price of corn, r  is the price  of nitrogen 
fertilizer, TAN is total available nitrogen for plant,  NAis the amount of nitrogen fertilizer, 
pH is soil pH level, TVC  is total variable cost of all inputs except fertilizer,  Nloss is a 
nitrogen loss rate via ammonia volatilization and SN  is the soil nitrate-nitrogen level. 
We are only interested in major plant nutrients such as nitrogen and soil pH levels 
in this study. Therefore, the functional form for corn yield used in this study is a modified 
quadratic function, thus,  
 
(3)  t t t t t t u pH TAN TAN Y ε κ ρ β α + + + + + =
2 ) ( ,   
where  t Y  is a corn yield at year  , t   κ ρ β α and   , ,  are the parameters to be estimated, 
t TAN  is  the total available nitrogen in year  , t   t pH is the soil pH level at year  , t   t u is 
random year effects,  ( )
2 , 0 ~
u t N u σ , and  t ε is an error term,  ( )
2 , 0 ~
ε σ ε N t .  
Parameter estimates are presented in Table 3.   
Results  
Results of the target MOTAD programming model in Table 4 show the most efficient 
timing is expected with low wind speed and with high relative humidity at night. 
Assuming that three times of effluent application were required, the best application 
timing is a time block from midnight to 6:00 am on April 7, April 11 and April 12. The 
expected ALR from the model is 0.15, which is much lower compared to 0.46, an 
averaged level of actual ALR between 1998 and 2005. Two application strategies were 
compared in terms of crop yield and net return (Table 4)  Switching to efficient irrigation 
timing practices resulted in higher yield (162 Kg/ha) and net return ($20.40).   
 
Conclusion and Discussion 
A target MOTAD model was used to determine efficient application strategies of 
swine effluent. As predicted, results showed that the most efficient timing occurs at night 
with low wind speed and with high relative humidity. Significant nitrogen loss can be 
prevented by switching to efficient irrigation timing practices. In addition, potential 
benefits in terms of crop yield and net return can be obtained.  Therefore, this new 
approach to irrigation timing has the potential to both reduce environmental impact and 
increase producer income.   
However, some caution should be taken in interpreting results.  The adoption of a 
mechanical model is only appropriate in the Texas and Oklahoma Panhandle area 
because the calcareous nature of soil in the region increases risks associated with N losses 
due to ammonia volatilization that occurs under increased pH levels found in Gruver soils. Further research is necessary to address more realistic application strategies under 
stochastic weather condition because the application of swine effluent at night can create 
nuisance problems (i.e. odor) among communities near disposal land.  
 
 Reference 
Al-Kaisi, M. and R.M. Waskom. 2002. “Estimating Ammonia Loss from Sprinkler- 
Applied Swine Effluent.” Agronomy Journal 94:1156-1162.  
 
Jones, C. A., R. T. Koenig, J. W. Ellsworth, B. D. Brown, and G. D. Jackson. 2007  
“Management of Urea Fertilizer to Minimize Volatilization.” the Ag/Extension 
Communications Coordinator, Communications Services, 416 Culbertson Hall, 
Montana State University-Bozeman, Bozeman, MT 59717.   
 
Lie, F., C.C. Mitchell, J.W. Odom, D.T. Hill, and E.W. Rochester.  1997. “Swine 
Effluent Disposal by Overland Flow: Effect on Forage Production and Uptake of 
Nitrogen and Phosphorus.” Agronomy Journal 89:90-904. 
 
Sutton, M.A., J.K. Schjoerring, and G.P. Wyers. 1995. “Plantatmosphere Exchange of 
Ammonia.” Philosophical Transactions of the Royal Society of London, Series A: 
251:261–278. 
 
Warren, J.G. 2001. “Ammonia volatilization from applied swine effluent in the southern 
Great Plains”. M.S. thesis. Department of Plant and Soil Sciences, Oklahoma State 
University, Stillwater, OK. 
 
Wu, J., D.L. Nofziger, J. Warren, and J.Hattey. 2003. “Estimating Ammonia 
Volatilization from Swine-Effluent Droplets in Sprinkler Irrigation.” Soil Science 
Society of America Journal 67:1352-1360.  
 
Zupancic, K.S., 1999. “Determination of Ammonia Flux from Swine Effluent Applied to 
Calcareous Soils.” Unpublished M. S. Thesis, Oklahoma State University, 
Stillwater, May 1999.  
 
Zupancic, K.S., J.A. Hattey, R. Mikkelsen, H.A. Zhang, D. Hamilton, and M. Kizer. 1999. 
“Determination of ammonia flux from swine effluent applications in the Southern 
Great Plains.” p. 411–414. In Havenstein (ed.) Proc. 1999 NC State University 
Animal Waste Management Symposium. NCSU Animal Waste Management Field 
Day Committee, College of Agriculture and Life Sciences, North Carolina State 
University, Raleigh, NC.  
 
 
 
 
aPump costs include only the pumping costs of SE from the lagoon to the center pivot. Operating and fixed 
costs of applying irrigation water are not included  
bFixed costs for tractor and irrigation equipment are not included in application cost calculations since they 
are not exclusively required for fertilizer operations.   
cTotal variable costs (TVCs) per hectare are assumed to be $200.  
 
Table 1. Factors and Condition in Simulating Ammonia Volatilization 
Factor   Values  Unit 
Ammoniacal N Concentration in swine effluent  1.1605  g/L 
Soil pH  7.75   
Effluent pH  7.5   
a target application rate of nitrogen  168  Kg/ha 
Soil nitrogen in top 15 cm  90.5  Kg/ha 
Pre-Plant Application Date  April 1 to April 14 
Table 2. Fertilizer Application Costs of  Swine Effluent (SE) (kg ha
-1) 
Item  56  168  504 
Operating Costs          
    Tractor          
    Fuel and lube  0  0  0 
    Labor  0  0  0 
    Repair  0  0  0 
  Pump
a          
    Fuel and lube  11.86  25.45  65.49 
    Labor  6.25  7.3  8.11 
    Repair  0.24  0.24  0.24 
Fixed Costs
b            
   Pump and Pipe          
    Depreciation  6.73  6.73  6.73 
    Interest  3.65  3.65  3.65 
    Insurance  1.06  1.06  1.06 
Total  29.79  44.43  85.28  
Table 3. Maximum Likelihood Parameter Estimates of Irrigated Corn Yield Function for 
Swine Effluent (kg/ha/year) 
Variables  Symbol  Parameter 
Estimates 
Standard 
Errors 
Intercept  α        -3,509  7.43 
TAN  β   9.30  3.10 
TAN squared  ρ   -0.015  0.001 
Soil pH  κ   1,304  61.62 
Variance of random year effect 
2
u σ   517,439  0.0004 
Variance of  error term 
2
ε σ   1,544,913  0.04 
Note: all parameters are significant at the 5 % level.  
 
 
 
Table 4. Results of a Target MOTAD and Benefits by Adopting Optimum Strategy 
  Ammonia Loss Rate  Expected Yield 
(Kg/ha) 
Expected Net Return 
($/ha) 
Optimal timing  0.15  7952  758.43 
Ordinary timing  0.46  7790  738.02 
Difference  -0.31  162  20.40 
 
 
 
 
 
 
 

Ammonia volatilization from applied swine effluent in the southern Great Plains”.

Determination of ammonia flux from swine effluent applications in the Southern Great Plains.”

Determination of Ammonia Flux from Swine Effluent Applied to Calcareous Soils.” Unpublished

Estimating Ammonia Loss from SprinklerApplied Swine Effluent.”

Estimating Ammonia Volatilization from Swine-Effluent Droplets in

Swine Effluent Disposal by Overland Flow:

Optimal Application of Swine Effluent under Stochastic Weather Conditions in the Texas and Oklahoma Panhandles

Optimal Application of Swine Effluent under Stochastic Weather Conditions in the Texas and Oklahoma Panhandles

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