Positive Mathematical Programming to Model Regional or Basin-Wide Implications of Producer Adoption of Practices Emerging from Plot-Based Research
Abstract
:1. Introduction
2. Integrating Multidisciplinary Research with Positive Mathematical Programming (PMP)
2.1. From Plot and Field-Level Research to Economic Behavior
2.2. Positive Mathematical Programming
- Use observed county-level data to formulate a constrained linear profit maximization model in which resource and input use and other resource, environmental or policy limitations are represented as constraints and the choice variable is crop acreage;
- Reformulate the problem as a nonlinear constrained optimization problem that calibrates almost exactly to the observed levels;
- Calibrate a quadratic function to capture desired production features (e.g.; water use) not included in the data or modelled explicitly;
- Implement a quadratic program including the estimated cost function as part of the objective function;
- Solve a dynamic model iteratively by updating aquifer levels based on periodic solutions to the quadratic program to produce the optimal land and water use choices.
3. Illustrative Example: Improved Soybean Dryland Yields in Sunflower County, MS
3.1. Sunflower County, MS
3.2. Results and Discussion for an Illustrative Example
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
ARS | USDA Agricultural Research Service |
BMP | Best Management Practice |
bu/a | Bushels per acre |
C2VSim | California Central Valley Groundwater-Surface Water Simulation Model |
CVPM | California Central Valley Production Model |
DREC | Mississippi State University Delta Research and Extension Center |
ECR | Early Career Researcher |
EF | Energy efficiency |
ESMIS | USDA Economics, Statistics and Market Information System |
ft | Feet |
FSA | USDA Farm Service Agency |
GIR | Gross irrigation requirement |
GMD3 | Kansas Groundwater Management District 3 |
GW | Groundwater |
IE | Irrigation water use efficiency |
lb/a | Pounds per acre |
LMRB | Lower Mississippi River Basin |
LP | Linear program |
MDEQ | Mississippi Department of Environmental Quality |
MRVAA | Mississippi River Valley Alluvial Aquifer |
NASS | USDA National Agricultural Statistics Service |
NCAAR | National Center for Alluvial Aquifer Research |
NPV | Net present value |
NRCS | USDA Natural Resources Conservation Service |
PMP | Positive Mathematical Programming |
SW | Surface water |
SWAP | California State-wide Agricultural Production economic model |
TDH | Total dynamic head |
USA | United States of America |
USD | U.S. dollar |
USDA | U.S. Department of Agriculture |
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Component | Parameter | Value |
---|---|---|
Aquifer | Surface elevation (FASL) | 118 |
Initial water table elev. (FASL) | 77.91 | |
Aquifer base elevation (FASL) | −18.49 | |
Net recharge (R, acre-ft) | 231,802 | |
Acres x specific yield () | 89,344 | |
Crop mix | Soybean share | 77% |
Corn share | 12% | |
Rice share | 4% | |
Cotton share | 7% | |
Irrigation | Application efficiency () | 0.54 |
Discount | Rate | 0.03 |
Crop | Irrigation | Min. | Full-Water | Average | Water Use | Cost | Acres |
---|---|---|---|---|---|---|---|
Yield | Yield | Yield | (ft/acre) | (acre) | |||
Corn | Furrow | 114 bu/a | 280 bu/a | 220 bu/a | 0.83 | 680 | 27,857 |
Dryland | 170 bu/a | 585 | 8343 | ||||
Soybean | Furrow | 26 bu/a | 82 bu/a | 77 bu/a | 1.16 | 498 | 158,144 |
Dryland | 57 bu/a | 404 | 76,356 | ||||
Cotton | Furrow | 1090 lb/a | 1800 lb/a | 1479 lb/a | 0.5 | 924 | 16,958 |
Dryland | 1261 lb/a | 833 | 3747 | ||||
Rice | Flood | 99 bu/a | 253 bu/a | 228 bu/a | 2.7 | 817 | 13,830 |
Crop | Irrigation | Acres | Water Use (acre-ft) | Profits (year) | |||
---|---|---|---|---|---|---|---|
Year 1 | Year 20 | Year 1 | Year 20 | Year 1 | Year 20 | ||
Corn/calib. | Furrow | 27,873 | 27,620 | 23,135 | 22,789 | 22.8M | 22.5M |
Dryland | 8343 | 8343 | 0 | 0 | 5.3M | 5.3M | |
Corn/shock | Furrow | 23,752 | 23,775 | 19,715 | 19,757 | 19.4M | 19.4M |
Dryland | 4995 | 4971 | 0 | 0 | 3.19M | 3.18M | |
Soybean/calib. | Furrow | 158,142 | 157,490 | 184,077 | 182,783 | 117.2M | 116.6M |
Dryland | 76,356 | 76,356 | 0 | 0 | 43.8M | 43.8M | |
Soybean/shock | Furrow | 144,668 | 144,707 | 168,393 | 168,536 | 107.2M | 107.3M |
Dryland | 109,167 | 109,094 | 0 | 0 | 83.2M | 83.2M | |
Cotton/calib. | Furrow | 16,913 | 16,592 | 8457 | 8235 | 16.4M | 16.1M |
Dryland | 3747 | 5110 | 0 | 0 | 3.1M | 4.3M | |
Cotton/shock | Furrow | 9811 | 9827 | 4905 | 4920 | 9.5M | 9.5M |
Dryland | ≈0 | ≈0 | 0 | 0 | 0 | 0 | |
Rice/calib. | Flood | 13,859 | 13,723 | 37,420 | 36,799 | 14.9M | 14.8M |
Rice/shock | Flood | 12,841 | 12,861 | 34,670 | 34,772 | 13.9M | 13.9M |
Scenario | Net Present Value | Aggregate | Change in |
---|---|---|---|
of Farm Profits | Water Use (acre-ft) | Aquifer Level (ft) | |
Calibrated scenario | billion | 5 million | 4.5 ft decrease |
Yield shock scenario | billion | 4.6 million | 0.9 ft increase |
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Quintana-Ashwell, N.; Kaur, G.; Singh, G.; Gholson, D.; Delhom, C.; Krutz, L.J.; Hegde, S. Positive Mathematical Programming to Model Regional or Basin-Wide Implications of Producer Adoption of Practices Emerging from Plot-Based Research. Agronomy 2021, 11, 2204. https://doi.org/10.3390/agronomy11112204
Quintana-Ashwell N, Kaur G, Singh G, Gholson D, Delhom C, Krutz LJ, Hegde S. Positive Mathematical Programming to Model Regional or Basin-Wide Implications of Producer Adoption of Practices Emerging from Plot-Based Research. Agronomy. 2021; 11(11):2204. https://doi.org/10.3390/agronomy11112204
Chicago/Turabian StyleQuintana-Ashwell, Nicolas, Gurpreet Kaur, Gurbir Singh, Drew Gholson, Christopher Delhom, L. Jason Krutz, and Shraddha Hegde. 2021. "Positive Mathematical Programming to Model Regional or Basin-Wide Implications of Producer Adoption of Practices Emerging from Plot-Based Research" Agronomy 11, no. 11: 2204. https://doi.org/10.3390/agronomy11112204