Simulation-optimization approach for trading point and non-point source nutrient permits

Abstract

Excess nutrients in surface water systems cause many environmental problems. Some governments restrict nutrient overloading through nutrient permits. Economic theory states that the best allocation of such permits is made via trading. However, nutrient permit trading is complicated by two factors associated especially with non-point sources: (1) time lags between loading and appearance in a water body and (2) differences between the load and the quantity transported to a water body. In a nutrient permit market, the prices and allocations depend heavily on these hydro-geological factors, so they should be incorporated into the trading system. Nutrient trading programs to date fail to include all factors simultaneously. We present a new system for trading point and non-point source nitrate permits. The methodology of trading is based on a simulation-optimization approach which is similar to the simulation-optimization approaches used in other non-market based nutrient management programs. Simulations are used to incorporate the hydro-geological impacts and a simple optimization technique is used to clear the market. The system consists of four components. First, a farm simulation model estimates the nutrient leaching from farm practices. Second, a nutrient transport model simulates the fate of leached nutrients in the catchment. Third, traders bid to buy and offer to sell in a centralized online auction. Finally, a linear program finds optimal trades based on the bids and water quality standards. Using a simple example, we show how this system facilitates trade among point and non-point sources. The illustration is for nitrates, but the concept applies to other contaminants such as phosphates. The example addresses the common case in which nitrates enter a river from both groundwater and direct point sources. The permits specify the maximum allowed nitrate loading into the aquifer for non-point sources and into the river directly for point sources. The results suggest that trade among point and non-point sources is desirable only under some hydrological and economic conditions. If nitrate transport in groundwater is sufficiently fast that a significant amount of nitrates leached from non-point sources reach the receiving surface water body within a year or few, the opportunities for trade between point and non-point sources are high. We investigated trading under two market rules. First, the market allows trade in permits valid for a single year only (year-1 permits, permits for next year) and second, the market allows trade in different permits valid for distinct future years (year-1, year-2, ..., year-5 permits, permits for next five years). We found that the latter provides more opportunities for trade between point and non-point sources, because the non-point source bids for recent permits have to compete with the point source bids for future permits. Therefore, point and non-point source nutrient trading is most suitable when nutrient flow in the catchment is relatively fast and/or point sources are willing to buy future permits. The price assigned to each source reflects all its spatiotemporal impacts, transaction costs are negligible as the sources buy permits from a centralized auction without having to find sellers, and water quality standards are always maintained. However, in trading loading-based permits, the problem of resource allocation over time arises as nutrients loaded into the aquifer from distinct non-point sources may reach a surface water body gradually over many years. Defining permits based on the water quality constraints is a solution, but the sources will have to purchase a portfolio of permits to match their impacts on the constraints defined over time and the set of receptors. Linear Programming is applicable if the underlying assumptions hold; mainly, the relationship between the quantity of nitrates loaded and the quantity transported to a receptor is linear.