Bradley L. Barnhart

Spatial Targeting of Agri-Environmental Policy Using Bilevel Evolutionary Optimization

In this study we describe the optimal designation of agri-environmental policy as a bilevel optimization problem and propose an integrated solution method using a hybrid genetic algorithm. The problem is characterized by a single leader, the agency, that establishes a policy with the goal of optimizing its own objectives, and multiple followers, the producers, who respond by complying with the policy in a way that maximizes their own objectives. We assume that the leader has perfect knowledge of policy outcomes for all parameterizations of agri-environmental policy. We use a hybrid genetic algorithm to simulate perfect knowledge of all policy outcomes in a bilevel optimization. Our hybrid genetic algorithm integrates a biophysical model (Soil and Water Assessment Tool; SWAT) with an economic model (profit maximization; DEA). The Soil and Water Assessment Tool (SWAT) is included to specify agency environmental objectives, and Data Envelopment Analysis (DEA) is used to model producer behavior in response to agri-environmental policy. We applied the resulting integrated modeling system to the analysis of an input tax on fertilizer in the Calapooia watershed in Oregon, USA. Application of the incentive policy at different geographical resolutions showed that bilevel optimization is effective for calculating optimal spatial targeting of agri-environmental policy. Surprisingly, the presented algorithm found multiple different policy configurations that achieved nearly identical results for the upper level (agency) objectives. This observation raises the possibility that additional objectives could incorporate equity, equality of outcome, and policy initiatives such as support for small farms at no additional cost.

Cost of areal reduction of gulf hypoxia through agricultural practice

A major share of the area of hypoxic growth in the Northern Gulf of Mexico has been attributed to nutrient run-off from agricultural fields, but no estimate is available for the cost of reducing Gulf hypoxic area using agricultural conservation practices. We apply the Soil and Water Assessment Tool using observed daily weather to simulate the reduction in nitrogen loading in the Upper Mississippi River Basin (UMRB) that would result from enrolling all row crop acreage in the Conservation Reserve Program (CRP). Nitrogen loadings at the outlet of the UMRB are used to predict Gulf hypoxic area, and net cash farm rent is used as the price for participation in the CRP. Over the course of the 42 year simulation, direct CRP costs total more than

Incorporating Data Envelopment Analysis solution methods into bilevel multi-objective optimization

388 billion, and the Inter-Governmental Task Force goal of hypoxic area less than 5000 square kilometers is met in only two years.

Handling practicalities in agricultural policy optimization for water quality improvements

This study illustrates the use of Data Envelopment Analysis (DEA) solution methods in bilevel optimization problems. Here, we show that DEA and bilevel optimization can also be used together as part of an integrated solution framework. We work with a policy-oriented problem in which the regulators multi-objective optimization problem at the upper level is constrained by the profit-maximizing decisions of individual firms at the lower level. Each firms response to the policy is a prori unknown to the regulator, and depends on the underlying production technology. Rather than assuming a common production relationship across firms, DEA allows us to model each firms response to the policy without imposing a functional form on the production technology. We use DEA to estimate the technology facing each producer, based on observed practices of other producers. Doing so endogenizes the cost of responding to prospective policies at the lower level, providing a more realistic solution set at the upper level. Our application addresses the design of a policy to reduce fertilizer runoff from agriculture, an important problem in environmental economics. We employ a multi-objective bilevel evolutionary algorithm to solve for the approximate optimal frontier.

MOESHA: A Genetic Algorithm for Automatic Calibration and Estimation of Parameter Uncertainty and Sensitivity of Hydrologic Models

Bilevel and multi-objective optimization methods are often useful to spatially target agri-environmental policy throughout a watershed. This type of problem is complex and is comprised of a number of practicalities: (i) a large number of decision variables, (ii) at least two inter-dependent levels of optimization between policy makers and policy followers, and (iii) uncertainty in decision variables and problem parameters. Given agricultural and economic data from the Raccoon watershed in central Iowa, we formulate a bilevel multi-objective optimization problem that accommodates objectives of both policy makers and farmers. The solution procedure then explicitly accounts for the nested nature of farm-level management decisions in response to agri-environmental policy incentives constructed by policy makers. We specifically examine the spatial targeting of a fertilizer-reduction incentive policy while seeking to maximize farm-level productivity while generating mandated water quality improvements using this framework. We test three different evolutionary optimization algorithms - m-BLEAQ, NSGA-II, and SPEA2 - and show that m-BLEAQ is well suited for handling the bilevel optimization problems and the considered practicalities.

Valuing Water Quality Tradeoffs at the Farm Level: An Integrated Approach

Characterization of the uncertainty and sensitivity of model parameters is an essential facet of hydrologic modeling. This article introduces the multi-objective evolutionary sensitivity handling algorithm (MOESHA) that combines input parameter uncertainty and sensitivity analyses with a genetic algorithm calibration routine to dynamically sample the parameter space. This novel algorithm serves as an alternative to traditional static space-sampling methods, such as stratified sampling or Latin hypercube sampling. In addition to calibrating model parameters to a hydrologic model, MOESHA determines the optimal distribution of model parameters that maximizes model robustness and minimizes error, and the results provide an estimate for model uncertainty due to the uncertainty in model parameters. Subsequently, we compare the model parameter distributions to the distribution of a dummy variable (i.e., a variable that does not affect model output) to differentiate between impactful (i.e., sensitive) and non-impactful parameters. In this way, an optimally calibrated model is produced, and estimations of model uncertainty as well as the relative impact of model parameters on model output (i.e., sensitivity) are determined. A case study using a single-cell hydrologic model (EXP-HYDRO) is used to test the method using river discharge data from the Dee River catchment in Wales. We compare the results of MOESHA with Sobols global sensitivity analysis method and demonstrate that the algorithm is able to pinpoint non-impactful parameters, demonstrate the uncertainty of model results with respect to uncertainties in model parameters, and achieve excellent calibration results. A major drawback of the algorithm is that it is computationally expensive; therefore, parallelized methods should be used to reduce the computational burden.

Improved Soil Temperature Modeling Using Spatially Explicit Solar Energy Drivers

This study evaluates the tradeoff between agricultural production and water quality for individual producers using an integrated economic-biophysical hybrid genetic algorithm. We apply a multi-input, multi-output profit maximization model to detailed farm-level production data from the Oregon Willamette Valley to predict each producers response to a targeted fertilizer tax policy. Their resulting production decisions are included in a biophysical model of basin-level soil and water quality. We use a hybrid genetic algorithm to integrate the economic and biophysical models into one multi-objective optimization problem, the joint maximization of farm profits and minimization of Nitrate runoff resulting from fertilizer usage. We then measure the tradeoffs between maximum profit and Nitrogen loading for individual farms, subject to the fertilizer tax policy. We find considerable variation in tradeoff values across the basin, which could be used to better target incentives for reducing Nitrogen loading to agricultural producers.

SWAT hydrologic model parameter uncertainty and its implications for hydroclimatic projections in snowmelt-dependent watersheds

Modeling the spatial and temporal dynamics of soil temperature is deterministically complex due to the wide variability of several influential environmental variables, including soil column composition, soil moisture, air temperature, and solar energy. Landscape incident solar radiation is a significant environmental driver that affects both air temperature and ground-level soil energy loading; therefore, inclusion of solar energy is important for generating accurate representations of soil temperature. We used the U.S. Environmental Protection Agency’s Oregon Crest-to-Coast (O’CCMoN) Environmental Monitoring Transect dataset to develop and test the inclusion of ground-level solar energy driver data within an existing soil temperature model currently utilized within an ecohydrology model called Visualizing Ecosystem Land Management Assessments (VELMA). The O’CCMoN site data elucidate how localized ground-level solar energy between open and forested landscapes greatly influence the resulting soil temperature. We demonstrate how the inclusion of local ground-level solar energy significantly improves the ability to deterministically model soil temperature at two depths. These results suggest that landscape and watershed-scale models should incorporate spatially distributed solar energy to improve spatial and temporal simulations of soil temperature.