Distributional Assumptions in Chance-Constrained Programming Models of Stochastic Water Pollution

Abstract

In the water management literature both the normal and log-normal distribution are commonly used to model stochastic water pollution. The normality assumption is usually motivated by the central limit theorem, while the log-normality assumption is often motivated by the need to avoid the possibility of negative pollution loads. We utilize the truncated normal distribution as an alternative to these distributions. Using probabilistic constraints in a cost-minimization model for the Baltic Sea, we show that the distribution assumption bias is between 1% and 60%. Simulations show that a greater difference is to be expected for data with a higher degree of truncation. Using the normal distribution instead of the truncated normal distribution leads to an underestimation of the true cost. On the contrary, the difference in cost when using the normal versus the lognormal can be positive as well as negative.

Does Divergence of Nutrient Load Measurements Matter for Successful Mitigation of Marine Eutrophication?

“…For such statistically/scenario-quantifiable uncertainty, previous studies have addressed how the uncertainty propagates further into the problem of minimum costs for abating nutrient loads to international waters by comparing the sensitivity of minimum cost results to different assumptions in, and/or to quantifiable randomness around a single basic modelling approach to expected nutrient loads (e.g. Elofsson 2003Elofsson , 2006Bayramoglu 2006;Gren 2008b;Fernandez 2009;Kataria et al 2010). This study considers instead the problem of how divergent results of different, independent nutrient load reports, based on different nutrient load modelling approaches, propagate into both minimum cost and fairness outcomes.…”

Combating eutrophication in coastal areas at risk for oil spills

“…Several deterministic studies have proposed least-cost or optimal solutions for nutrient abatement measures for the entire Baltic or some of its sub-basins (Byström 2000, Brady 2003, Gren 2001, Ollikainen and Honkatukia 2001, Elofsson 2003, Hart and Brady 2002, Laukkanen and Huhtala 2008. The analyses of Gren et al (2000), Elofsson (2003), Gren (2008) and Kataria et al (2010) have incorporated stochastic pollutant transports and agricultural loads, but the management of eutrophication in waters subject to other environmental threats, such as major oil spills, would require additional stochastic elements in the policy analysis. To our knowledge, the impacts of a potential oil spill on the profitability of nutrient abatement measures have not been examined in an economic analysis before.…”

Economic-environmental trade-offs and the conservativeness of the upper partial moment

“…Alternative abatement strategies and/or policy instruments are compared on the basis of the alternative that achieves an environmental goal with the least impact on the economic indicator. A complicating factor is that environmental emissions are inherently stochastic as a result of a variety of environmental conditions (Horan 2001;Kampas and White 2004;Kataria et al 2010). Consequently, pollutioncontrol strategies should be aimed at improving the distribution of outcomes rather than some scalar value (McSweeny and Shortle 1990).…”

“…A modeling alternative to incorporate the variability of environmental outcomes while quantifying economic-environmental trade-offs is chance-constrained programming (CCP) (Li et al 2014b;Kataria et al 2010;Kampas and White 2003). The application of CCP requires the specification of a functional form for the distribution of the environmental variable (Qiu et al 2001).…”

“…The application of CCP requires the specification of a functional form for the distribution of the environmental variable (Qiu et al 2001). Various researchers have shown that the distributional assumptions employed in CCP models have a significant impact on the estimated trade-offs (Zhu et al 1994;Qiu et al 2001;Kampas and White 2003;Kataria et al 2010) and may not hold for all situations as a result of the site-specific nature of agricultural NPS pollution (Wang et al 2016;Qiu et al 2001). To overcome the problem, techniques like the Environmental Target-MOTAD model (Teague et al 1995) were developed to estimate economic-environmental tradeoffs while making use of empirical distributions.…”