Assessment of uncertainty in emergy evaluations using Monte Carlo simulations

Emergy evaluations most often rely on point estimates for important energy, material and solar transformity (or more generally unit emergy values, UEVs) parameters. For emergy science to continue its advancement as a tool for assessing energy and environmental sustainability, it needs to include estimates of uncertainty surrounding emergy budgets so that statistical confidence can be assessed. Here, Monte Carlo simulation was used to analyze the effect of uncertainty in the estimates of energy, material and UEVs of system-sources (e.g., sunlight, evapotranspiration, fuel, fertilizer) on the uncertainty of the UEV of the system-yield. Eight unique corn and wheat production systems, reported in the literature, provided the statistical properties (e.g., means, standard deviations, minima) of the energy, material and UEVs of the system-sources, but the probability distribution functions were assumed to be normal, lognormal, or uniform. Uncertainty from system-sources was partitioned into energy/material and UEV. The contribution that a system-source made to total emergy flow was strongly indicative of the amount of uncertainty it contributed. Out of 22 parameters (11 energy/mass and their 11 UEVs), four of them contributed more than 86% of the uncertainty to the UEV of the crop yield. The UEV of nitrogen fertilizer contributed the most uncertainty (19%), followed by the rate of soil erosion (11%), application rate of nitrogen fertilizer (4%), and labor requirements (5%). When uncertainty from all 22 parameters was included, the expected UEV of the crop yield was 118,000 sej/J with a total level of uncertainty (95% confidence interval) of ±106,000 sej/J (±90% of the mean), indicating that uncertainty was vast. However, ±50% was due to energy/mass uncertainty, while ±40% was due to UEV uncertainty, of which all but ±2% was due to the UEV of nitrogen fertilizer, indicating that little uncertainty (±12,600 sej/J) was derived from non-nitrogen fertilizer UEVs. Most of the uncertainty came from the energy/mass, rather than UEVs, indicating that as much care should be given to estimating energy and material use as to selecting or estimating UEVs. Our simulation ignored any multicollinearity that may have existed among the energy/mass use of the system-sources, which likely meant that we overestimated uncertainty. Future investigation should build in the correlations that exist among the system-sources (e.g., nitrogen fertilizer is related to water availability) to better quantify uncertainty. The simulations suggested that uncertainty from UEVs may be hierarchically organized with a few system-sources contributing a majority and most contributing little, indicating that management of uncertainty can be focused on a few parameters.