## Formal Statistical Approach

The Tebaldi and Lobell (2008) paper is meant to be a methodological study. As the title suggests it proposes an approach towards a formal and rigorous quantification of the uncertainties that, from multiple sources, affect the estimates of climate change impacts in the agricultural sector.

A Bayesian hierarchical model is used to synthesize the joint projections of temperature and precipitation change from a multi-model ensemble, for a given SRES scenario. The output of this step of the analysis are bivariate probability distribution functions of future changes in temperature and precipitation, for the regions of the world where a given crop is cultivated, and tailored to an optimally defined crop-specific growing season. The next step of the method consists of sampling from these distributions pairs of change factors that are input to the statistical crop model (Lobell and Field 2007), similarly to what was done in Lobell et al. (2008) but substituting now a posterior distribution of climate changes to the empirical distribution of the CMIP3 models. The statistical treatment estimates the joint posterior probabilities by bringing to bear estimates of systematic biases in the models' simulations, estimates of the overall correlation of temperature and precipitation in the region and season analyzed, and observed trends in the two climate parameters and their degree of similarity to the simulated trends.

Like in any statistical modeling, assumptions on the data distributions are made and influence the final results, together with our assessment of the initial uncertainty in the quantities we want to estimate. This last point is a function of adopting the Bayesian paradigm, which updates a priori estimates of uncertainty through the information contained in the observed and simulated data. Nonetheless, the procedure provides a transparent and computationally efficient way of integrating the uncertainties at each step to make probabilistic statements about impacts, such as that by 2030 there is "larger than 80% chance that net losses for maize will exceed 10%" (Tebaldi and Lobell 2008).

## Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

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