Interpretation of the probability results
Actors in the agricultural industry often use historical-occurrence frequencies as a form of probability, working with the formulation “X years out of Y.” This formulation might give the wrong picture in a context of non-stationary climate, where historical occurrence does not reflect future climate regime. In this sub-section, we discuss how these concepts (“X years out of Y” and the PCS approach) can be merged.
Figure 7 shows two ways to see the probability for a given year. Each filled square corresponds to a year (along the x axis) and a given simulation (along the y axis). The filled squares indicate that the given simulation exceeds the prescribed threshold for a given year (the first line [grey squares] represent the NRCAN observation-based product). When the threshold is exceeded, the colour saturation indicates the intensity of the excess (normalized to the maximum of the excess magnitude of the whole ensemble and time period). Each line (i.e., scenario) is a possible climate trajectory. The natural variability of the climate ensures that the actual trajectory will be different than the PCS estimation or any climate trajectory. However, given a number of realizations large enough for the observed climate (which is impossible to do outside of a thought experiment), the observed probability would plausibly converge towards P(X > x, t).
The first approach is the one where the user looks at a single simulation over a given period of years and answers such questions as “How many exceedances do I have over 10 years?” The second approach, represented by the black line, is the method proposed in this article: the proportion of scenarios exceeding a prescribed threshold for a given year, effectively reducing the information of the ensemble scenario for that year.
To see how we can reconcile the concept of “X years out of Y” and the PCS approach, we take the year 2010 (other years — 2030, 2050 and 2060 — have been tested and show the same behaviour — not shown). The black line from Fig. 7 shows that the probability estimation for 2010 (the PCS approach) is approximately 50% (which means that about half of the scenarios for 2010 give values over 1100 DD). We compare this estimation with each simulation between 2006—2015 to see the possible trajectory that the climate could have taken (i.e., each simulation being a possible trajectory that southern Québec could see), as shown in Fig. 8 which indicates the number of years (between 2006—2015) where DDB10 is over 1100 DD. The spread of the distribution highlights the fact that even though the best estimate is close to 50% (PCS estimation and the scenario’s distribution mean), the possible trajectories for the individual scenarios are numerous and range from 1 to 10. Interestingly, the mean value of the possible trajectory is similar to the ensemble estimation. This is caused by a compensation of the influence of climate change on the data. In other words, by using 2006—2015 to estimate the mean trajectory for 2010, we have years after 2010 that are (usually) warmer than 2010 and years before 2010 are usually colder than 2010. It is important to emphasize that in reality, we will see a single realization and the “X years out of Y” for any given decade will be different than the PCS estimation, mainly due to natural climate variability.
These results suggest that the PCS approach gives results close to the usual user formulation (“X years out of Y”) and that users could use the estimated PCS probabilities and associate them with their standard formulation, without much loss of generality. This also means that the PCS approach gives a good estimate of the climatological probabilities of exceeding a given threshold, in phase with the background climate change forcing, which is not the case with historical observations. However, this result indicates that natural variability creates a rather large distribution of possible trajectories for any given decade. We note that this possible difference between the estimated PCS probability and the actual climate trajectory probability for a given decade also applies to most, if not all, climatological statistics.
Uncertainties and limitations
Along with the RCP-related assumptions discussed in Section 2, one important limitation of the PCS approach is that the ensemble used might have common biases (e.g., processes unknown to climatologists). Hence, the ensemble is not guaranteed to represent the real climate system, meaning that estimated probabilities can have an associated bias. Moreover, our results represent only probabilities from a given “opportunity ensemble” (Tebaldi and Knutti 2007). The inclusion of other models and/or members will have an effect on the estimated probabilities. The potential extent of this effect is partially evaluated (see Supplementary Material). It must be noted that these biases represent a fundamental limitation in climate assessment from the use of climate models, and are not specific to the PCS approach presented here.
Refining the climate indices is also something that could be examined. Current research indicates that periods of very high temperatures are unfavourable for crops in general (White et al. 2006; Schlenker and Roberts 2009) and may affect vines as well. Our indices of degree-days are calculated by naively adding temperature units over a given threshold and do not account for potential damage caused by very high temperatures. Since we can expect higher extreme temperatures in the coming century (IPCC 2012), this effect, as well as other extremes such as wind gusts and heavy rains, should potentially be considered in future assessments.
This study did not look at future precipitation regimes for Québec. At the end of the viticulture season, grapes benefit from dry conditions (helping sugar concentration). Historical precipitation conditions are not a limiting/helping factor in Québec. However, future climate scenarios show an increase of precipitation over the eastern part of North America. This should be documented, whether or not this increase limits viticulture.
An important protection measure against harsh cold is snow cover. Projections from climate models show a possible reduction in snow cover in southern Québec, combined with annual winter temperatures below the critical threshold for V. vinifera of − 17 ∘C. This means that growers will face another challenge and incur additional costs associated with alternative winter thermal protection.
Finally, even though sunshine hours are currently higher than in other traditional viticultural regions such as Bordeaux and New Zealand (Jones 2012), it is unclear how cloud cover will affect future sunshine hours in southern Québec. Cloud physics in climate models being mostly associated with sub-grid parameterizations, a rigorous assessment of future cloud cover is beyond the scope of this article and remains a challenging topic in climate research (Bony et al. 2015).