Optimization:

Mathematics for Sustainable Agriculture

Since attending a Sustainability workshop at The American Institute of Mathematics, we have been focusing on understanding farming strategies to help reduce water usage. This research was motivated by the berry farming industry in the Pajaro Valley, CA. The water intensive irrigation of crops paired with droughts has further contributed to salt-water intrusion along the coast. Current focus is on investigating ways to recharge rainwater into the aquifer and crop rotation strategies that use less water.

The National Science Foundation has supported and highlighted this work. See Strawberries With a Thirst: Mathematicians help California drought-weary berry growers address water issues

We also contributed to a blog for the Mathematics of Planet Earth 2013 Initiative: Raspberry Fields Forever

Some of this work has been using a virtual farming tool, implemented in MATLAB, which accounts for water usage, varying water and sales prices, and an optimization framework that seeks to understand the trade-offs in maximizing profit, meeting the market demand, and minmizing water usage. See for example,

K.R. Fowler, E.W. Jenkins, M. Parno, J.C. Chrispell, A. Rivas, and R.T. Hanson, Development and Use of Mathematical Models and Software Frameworks for Integrated Analysis of Agricultural Systems and Associated Water Use Impacts, Accepted to Agriculture and Food, May 2016.

K.R. Fowler, C. Ostrove, M.D. Parno, J.C. Chrispell, M.W. Farthing, and E.W. Jenkins, A Decision Making Framework with MODFLOW-FMP2 via Optimization: Determining Trade-off s in Crop Selection, Environmental Modeling and Software, December 2014.

J. Bokhiria, K.R. Fowler, E.W. Jenkins, Modeling and Optimization for Crop Portfolio Management Under Limited Irrigation Strategies , Journal of Agriculture and Environmental Sciences, 2(1), 01-31, 2014.

J.C. Chrispell, S.E. Howington, K.R. Fowler, E.W. Jenkins, M.J. Minick, T. Sendova, Mathematical Modeling, Simulation, and Optimal Design for Agridultural Management, Water Resources Conference, Columbia, SC, 2012.

$Description: C:\Users\kfowler\Documents\public_html\research_files\starburst.gif$ To facilitate future studies involving simulation-based optimization for agricultural water management, we are providing a framework using python. This file contains the necessary data files, objective functions, and wrappers for the example provided in "A Decision Making Framework with MODFLOW-FMP2 via Optimization: Determining Trade-offs in Crop Selection", currently submitted for publication (link coming soon). The details of the underlying hydrological setting can be found in Technical Report TR2014_8 (Department of Mathematical Sciences, Clemson University).

You will need the DAKOTA software package for optimization which can be obtained here. You will need to install the MODFLOW-FMP2 simulator which can be obtained here. For this implementation we used MODFLOW-2005 and DAKOTA version 5.4.

$Description: C:\Users\kfowler\Documents\public_html\research_files\starburst.gif$ Mark Minick won the SIGMAA EM Award at Mathfest, which recognizes exceptional presentations that involve work on problems arising from environmental sources for our 2010
summer research project with Ruby Fu (now at MIT), Optimizing Aquifer Water Consumption and Maximizing Profit for Strawberry Farmers. This approach used constrained linear programming and was the focus of this Honor's thesis.