By Kathleen Kavanagh, Lea Jenkins, and Shawn Matott
Resource management, like most things in life, is an optimization problem. When resources grow particularly scarce, their allocation becomes part of national and global news. Efficient water use is increasingly vital as periods of sustained drought, increased activity in previously-undeveloped regions, and overuse of water supplies place long-term water availability in peril. Recent examples include water shortages in the agriculturally-intense states of California and Kansas, where underlying aquifers could be pumped completely dry in our lifetime.
The crises are heightened when there are disparate uses for the resource. In agricultural regions, for instance, farmers, residents, and native environments all compete for access to the same shared water source. Our efforts are intended to help solve challenging resource allocation problems through meaningful dialogue. This requires us to be mindful of all perspectives, and to help resource managers model and balance these perspectives—using trusted, validated solution components—for synergistic, sustainable solutions. As world populations continue to grow, we constantly need to do more with less; our ability to support existing and future populations is dependent on our ability to sustain, and even supplement, available resources. Local governments, including water development boards, are required to set policy to govern the efficient use of resources. As decision-makers, their recommendations must be supported by quantitative analysis that attempts to balance the interests of the competing users.
Addressing these resource crises requires significant collaboration between applied mathematicians with expertise in computer simulation, optimization, and uncertainty; hydrologists; economists; computer scientists; members of the farming community; and water control boards that can define and simulate the relevant problems. We have taken advantage of the workshop program available through the American Institute of Mathematics (AIM) to gather researchers with expertise in different aspects of water resource issues. Funding through the AIM in 2015 allowed us to connect researchers from these disciplines for a week-long discussion of these issues. We aim to model and simulate water resource problems in agricultural sectors of California by developing a user-friendly and open-source software framework to facilitate rational stakeholder decisions in agricultural settings where water availability is of concern (see Figure 1).
Our goal is to develop and make easily available an integrated modeling system for exploring water policy alternatives using a linked set of existing models of farming economics and the hydrologic cycle. We chose to meet this objective by making extensive use of existing software tools, in part because repeated studies by a wide range of users have validated these tools. We use the MODFLOW One Water Hydrologic Model (MF-OWHM), created by the United States Geological Survey, to model water resource management and agricultural production in our regions of interest, and we use the Dakota software suite1 developed at Sandia National Laboratories to handle the optimization.
Our initial attempt, along with farmers from Reiter Affiliated Companies, to address concerns about water usage in the Pajaro Valley berry-growing region of California generated multiple competing objectives. Preliminary results from an optimization study that did not use an underlying simulation tool have already yielded changes in farming techniques [1, 4]. The ability to represent the farming cycle’s impact on water resources and the environment with state-of-the art modeling software will further advance sustainable farming practices.
Researchers have developed, enhanced, and implemented MF-OWHM over decades as an industrial simulation tool meant to fully analyze water usage in a large-scale region and provide reliable representations for decision-makers. It incorporates every major component of the water cycle, including subsurface flow, precipitation events, streamflow routing, surface-water routing, seawater intrusion, and riparian evapotranspiration. This allows for accurate tracking of the water balance throughout the domain of interest. Such accounting is especially useful when applying the model to regions that are subject to water rights, usage restrictions, and other regulatory controls. Ultimately, the MF-OWHM model has the potential to be a key linkage point for agricultural economic modeling if paired with the appropriate computational models within that regime. For example, shifts in the supply and demand of water within the economic model will trigger changes in the water balance within the MF-OWHM model.
Dakota is a widely-used and well-supported optimization suite; it contains a variety of derivative-free optimization methods and is thus well suited to handle “black box” simulation-based problems. Optimization algorithms in Dakota allow us to consider single- and multi-objective formulations of the problem, meaning that we can acknowledge competing viewpoints of different members of the community. Our team wrote Python wrappers to connect the I/O streams between Dakota and OWHM. The wrappers write the appropriate input (i.e., decision variables) to Dakota-formatted data files, read the output from an OWHM simulation, and compute the associated values for the objective functions and constraints required by the optimization algorithm in Dakota. Thus, we can consider any model parameter in OWHM as a decision variable and use any output from OWHM to define an objective function that captures the priorities of the various stakeholders in a given agricultural region. This flexible approach, using well-trusted software tools, lets us focus our efforts on defining appropriate objective functions, constraints, and design spaces.
The complexity of coupled modeling frameworks like Dakota/MF-OWHM presents challenges of usability and computational cost. In this regard, several recent efforts have attempted to link these types of modeling frameworks with user-friendly graphical interfaces and high-performance computing resources. For example, Michael Fienen and Randall Hunt describe an open-source appliance (HTCondor) that runs on a remote cluster of distributed computers and is readily adapted to support wide-ranging environmental applications . The underlying software stack is capable of supporting a variety of simulation-based optimization and model assessment (e.g., parameter estimation and sensitivity and uncertainty analysis) approaches. Additional customizable frameworks for providing web-based parallel computing portals include AWESIM and HubZero. For instance, the Virtual Infrastructure for Data Intensive Analysis (VIDIA) project customizes the HubZero framework to provide access to HPC-enabled data analytics software like R/RStudio , RapidMiner, and Orange. One could similarly adapt HubZero to support water resources management and the aforementioned Dakota/MF-OWHM decision tool.
Ultimately, the success of our efforts will be measured by our ability to build on our existing collaborations to develop and deploy a truly interactive modeling framework that is useful for and used by real, existing stakeholders in a region – and not just in academics. To achieve this, we rely on our fellow researchers in modeling, simulation, and optimization, and on the software and computational tools they have developed and already applied to a wide range of challenging, real problems. We have been fortunate to work with experts who are generous with their time and knowledge. Our team’s success is attributable in part to effective communication and open collaboration. In addition, we believe that using existing open-source software frameworks—coupled through user-friendly, accessible interfaces—is the path forward for resolving these difficult problems.
1 Read about the Dakota software suite’s features in the corresponding article, "Dakota Software: Explore and Predict with Confidence."
 Bokhiria, J., Fowler, K., & Jenkins, E. (2014). Modeling and optimization for crop portfolio management under limited irrigation strategies. Journal of Agriculture and Environmental Sciences, 2, 1-13.
 Fienen, M.N., & Hunt, R.J. (2015). High-Throughput Computing versus High-Performance Computing for Groundwater Applications. Groundwater, 53(2), 180-184.
 Ihaka, R., & Gentleman, R. (1996). R: A Language for Data Analysis and Graphics. Journal of Computational and Graphical Statistics, 5(3), 299-314.
 Kupec, I.F. (2014, July 1). Strawberries with a thirst. National Science Foundation. Retrieved from https://www.nsf.gov/discoveries/disc_summ.jsp?org=NSF&cntn_id=131827.
 Adams, B., Bauman, L., Bohnho, W., Dalbey, K., Ebeida, M., Eddy, J.,…Vigil, D. (2009). Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 5.4 User’s Manual. Technical Report SAND2010-2183. Albuquerque, N.M.: Sandia National Laboratories.
 Hanson, R.T., Boyce, S.E., Schmid, W., Hughes, J.D., Mehl, S.M., Leake, S.A.,…Niswonger, R.G. (2014). One-Water Hydrologic Flow Model (MODFLOW–OWHM). Techniques and Methods 6-A51, U.S. Geological Survey. Retrieved from http://dx.doi.org/10.3133/tm6A51.
Kathleen Kavanagh is a professor of mathematics at Clarkson University. Lea Jenkins is an associate professor in the Department of Mathematical Sciences at Clemson University. Shawn Matott has a B.S. in computer engineering and a Ph.D. in environmental engineering. He is a computational scientist at the Center for Computational Research at the University at Buffalo, where he also serves as industry outreach coordinator.