Yield response functions and water productivity. Relative yield (YR) reduction due to soil moisture stress is expressed as a percentage of the maximum production achievable in the area under optimal conditions. It can be computed with reference to a single stage of crop cycle or to the whole growing season. The coefficient Ky is a specific yield response factor that describes the reduction in relative yield according to the reduction in relative evapotranspiration. Relative yield due to water stress is generally calculated by using either the standard FAO‐56 method based on a single Ky for all the cropping season (Xxxxx et al., 1998) or a more complex and multiplicative approach as described in Xxx et al. (1988). The latter has been preferred for this application, and it is based on the following formula: Where YR is yield reduction expressed in percentage, Ya and Ym are respectively the actual and the maximum expected crop yield with and without water stress, while ETc_eff and ETc_max are daily crop evapotranspiration with and without water stress. Ky values are crop specific and may vary over the growing season. In general, for field crops the decrease in yield due to water deficit during the vegetative and ripening period is relatively small, while during the flowering and yield formation periods is large (Xxxxx, 1998). To estimate the crop yield (Y) in absolute terms (t ha‐1) for each country, under the given climate and management conditions, crop average values of water productivity (WP, kg m‐3) have been considered. Maximum (potential) yield (Ym) has been computed as follows: while actual yield (Ya) as: In the case of olive trees, because of the lack of reliable Ky coefficients for different development stages, an additional alternative yield response function has been considered, as obtained by Xxxxxxx et al. (2003) and suggested by Xxxxxxx et al. (2012): In the case of field crops, to consider the expected “fertilizing effect” of increasing CO2 levels on crop productivity, an adjusted WP (WP_adj) value has been additionally used under “future” 2050 climate conditions, according to the methodology suggested by Xxxx et al. (2012): where fCO2 is the correction coefficient, estimated as equal to 1.2 under the conditions of our application.
