There are at least three types of uncertainty associated with most LC studies. The first has to do with modeling inputs. Although many LCA practitioners utilize a single average value for modeling inputs, all parameters generally exhibit a range of values in the real world and all measurements are subject to some unknown error. Key examples of algae modeling parameters that may have wide ranges of values or unknown measurement errors include algae yield; algae lipid content; conversion efficiency; and even life cycle impact factors (energy use, GWP, etc.) for material inputs such as electricity from the US grid, etc. The second type of uncertainty is associated with spatial and temporal differences in systems operation. These sys­tematic differences in time and location can have important effects on LCA results; (e. g., it is reasonable to expect higher algae yields in sunnier parts of the country). The third and final type of uncertainty arises from extrapolation of bench-scale data to hypothetical full-scale systems. This type of uncertainty is largely unavoidable at present, in the absence of many full-scale algae-to-energy systems that have been in operation for any appreciable length of time.

Stochastic tools have become increasingly important for bounding uncertainty in LCA over the last few years (Fig. 4). Monte Carlo analysis is one of the common stochastic tools used by practitioners [30]. This method is useful for quantifying a range of probable output values from a series of input variables which have been assigned empirical or theoretical distributions. These distributions make it possible to encapsulate the three types of uncertainty referenced in the previous paragraph. Repeated sampling from the input distributions creates distributions of output val­ues, which can be parameterized to give empirical estimates of mean or median. Empirical uncertainty for output parameters can also be quantified using standard deviations, standard errors, or percentiles [10]. Most life cycle software (e. g., SimaPro and GaBi) now include stochastic toolkits to perform Monte Carlo and related analyses. For LC practitioners using spreadsheet-based models, a number of commercial add-ins (e. g., Crystal Ball® and @Risk®) allow for flexible management of input and output distributions in models. It should be noted that few of the life

cycle studies published to date have included uncertainty, largely because data availability is a limiting factor and the computational complexities are nontrivial. Moving forward, it will be necessary for algae life cycle models to address this uncertainty in a systematic fashion.