Supplementary Materials

Transcription

1 1 Supplementary Materials 2 Philippe Roy* Patrick Grenier Evelyne Barriault Travis Logan Anne Blondlot Gaétan Bourgeois Diane Chaumont 3 February 14,

2 4 A Supplementary material Occurrence year For DDB10 (Figure A.1), the minimum seasonal growing degree days (DD) needed to sustain vine growing is approximately 900 C. From Figure A.1a, we see that most of the southern already receives sucient DD for sustainable vine growing (light green color). Using this threshold can also inform us on where and when new regions with current low climatic suitability for winemaking could potentially become productive. Perhaps more interesting is the OY of higher DD thresholds where the Estrie region results show that new grape varieties requiring increased DD thresholds could become viable within the next few decades (see Figure A.1). Results show OY of approximately 2020 (1000 DD), 2030 (1100 DD) and 2050 (1250 DD). Results for this region also indicate a general east-west gradient around Sherbrooke with sooner OY in the western part where the elevation is lower. For the 4 CNFD thresholds (Figure A.2), the St-Lawrence valley shows sooner OY than for inland regions, highlighting the eect of water masses thermal inertia over coastal regions. The Estrie region shows that around 2050, one can expect a probability of 0.8 of having 166 consecutive days without frost, which is approximately the minimum for early ripening Vitis vinifera species such as Gamay and Pinot Noir (Jones, 2012). For AWMT (Figure A.3), one can expect a disappearance of very cold temperatures (lower than -30 C) by 2040 in southern, as shown in Figure A.3a-b. On the other hand the warmest temperature threshold (i.e. -24 C) is rarely exceeded even at the end of the time period (i.e. 2070). The -27 C threshold is exceeded between for limited locations: for example the southern part of the province, along the St-Lawrence river and in the Gaspésie peninsula. 2

3 a) 900 degree days b) 1000 degree days c) 1100 degree days d) 1250 degree days Year km Figure A.1: Year of occurrence of probabilities over 0.8 for DDB10 higher than a) 900 degree-day, b) 1000 degree-day, c) 1100 degree-day and d) 1250 degree-day thresholds. The Estrie sub-region is shown with a black contour (south of the agricultural region). Occurrence year before the year 2020 is shown in light green. Dashed lines indicate that the occurrence year does not emerge before

4 a) 150 days b) 156 days c) 166 days d) 180 days Year km Figure A.2: Year of occurrence of probabilities over 0.8 for CNFD higher than a) 150 days, b) 156 days, c) 166 days and d) 180 days thresholds. The Estrie subregion is shown with a black contour (south of the agricultural region). Occurrence year before the year 2020 is shown in light green. Dashed lines indicate that the occurrence year does not emerge before

5 a) -34 Celsius b) -30 Celsius c) -27 Celsius d) -22 Celsius Year km Figure A.3: Year of occurrence of probabilities over 0.8 for AWMT higher than a) -34 C, b) -30 C, c) -27 C and d) -22 C thresholds. The Estrie sub-region is shown with a black contour (south of the agricultural region). Occurrence year before the year 2020 is shown in light green. Dashed lines indicate that the occurrence year does not emerge before

6 a) 5 days b) 10 days c) 20 days d) 30 days Year km Figure A.4: Year of occurrence of probabilities over 0.8 for ANVCD lower than a) 5 days, b) 10 days, c) 20 days and d) 30 days thresholds. The Estrie sub-region is shown with a black contour (south of the agricultural region). Occurrence year before the year 2020 is shown in light green. Dashed lines indicate that the occurrence year does not emerge before Late-spring frost probability One important limiting factor to growing vines is the risk of late-spring frost conditions during the budbreak period, approximately once there is about 55 degree days accumulated. To estimate this risk, we calculate the probability of having a minimum temperature lower than 2 C. As shown in Figure A.5, the probability is constant in time. This is explained by the fact that although there apppear to be a general shift towards early spring conditions, the length of the transition period between winter conditions (temperature < 0 C) and spring conditions (temperature > 0 C) where there is a potential for frost damage does not seem to change greatly. 6

7 1 Late spring frost probability after budbreak Model : 20 Scenarios : Probability Year Figure A.5: Time series of probabilities over the Estrie sub-region for Late-Spring Frost Risk. Probabilities are calculated for each grid points of the sub-region and then spatially averaged, using RCP 4.5 and RCP Performance of PCS against classical approach Dierent approach can be used to estimate the probability of exceeding a given threshold. We compare four methods in Figure A.6. Classical approachs for the calculation of probabilities (dened in Table A.1) are mostly encompassed in the calculation of the number of occurrences divided by the length of the observation time series. These approaches are compared to a theoretical probability given by the use of the whole ensemble through the PCS method. Our aim here is not to compare classical method to observations but to quantify the dierence in estimated probabilities. As shown in Figure A.6, the classical approachs underestimate the probability for most of the common time period. As expected, the climate change signal is introduced in the sample (i.e. increase of the probability value, consistent with a warming climate) with a signicant lag for the three methods. When we include all possible years, the underestimation of the probability is important and begin to signicantly diverge from the other two methods around This is explained by the fact that climate change is not signicant in the period and begin to be important later. The best classical approach would be to include only the last 30 years, a compromise between the exclusion of data that is not inuenced by climate change and the inclusion of a maximum of years 7

8 into the sample. With Figure A.6 we argue that the PCS approach is the one that avoids the use of data not inuenced by climate change by considering the only year of interest, in phase with the anthropogenic forcing. This simple thought experiment highlights the benet of using a large-ensemble for the time-dependent probabilities. Name Denition Example: Estimation of P (X > x) for year 2003 Ocial Normals Use the normal period (i.e and ) data Last 30 years Use the last 30 years of data data All years Use the whole dataset data PCS method Use all simulation for year t 2003 simulated index values (i.e. 90 simulations) Table A.1: Denition of classical approach used for the calculation of probabilities and the denition used for each method 8

9 Figure A.6: Comparison of three classical method for the calculation of probability against the PCS approach for a) DDB10 and b) CNFD Statistical adjustment considerations One of the possible drawback of using statistical adjustment is the inuence of such adjustment on raw variable trends. To measure such inuence, the linear trends of each simulation has been estimated for the annual mean, maximum and minimum values of daily minimum and maximum temperature. Scatter plots of non-corrected vs corrected simulations are shown in Figure A.7. Trends of mean annual values are rather robust with respect to the statistical adjustment used in the study. However, trends of extremum annual values are inuenced by the statistical adjustment, as shown by the linear regression (blue and black lines), especially the maximum annual values (for Tasmin and Tasmax) and the minimum annual values of Tasmin. Clearly, the inuence of the statistical adjustment on an- 9

10 75 76 nual minimum values of Tasmin will have an impact on the estimated probability of AnnTasmin. Figure A.7: Eect of statistical adjustment on trends of Tasmin (rst row) and Tasmax (second row) for the annual mean (rst panels), the annual minimum (middle panels) and annual maximum (right panels) Probability convergence Robust estimation of a given quantity is directly proportional to sampling size. Estimation of the sample mean is termed standard error and decrease as the square root of the sample size. In this study, the estimated quantity is the probability to exceed specied threshold. The robustness of this estimation is also related to sampling size. The relevent question is again : Which simulations ensemble size is needed for a robust estimation? Through a bootstrapping approach, we estimated sampling error associated with a given ensemble size. For each sample size N between 15 and 90, the probability of exceeding 1100 DD is estimated for a given grid point and a given year by resampling the CMIP5 ensemble (2000 times for each sample size N). This gives a distribution of 2000 estimations for sample size N and the estimation spread can thus be estimated. Figure A.8 shows the sampling error with respect to the sampling size. As expected, the sampling error decrease as the sample size N 10

11 increase (red solid line). The uncertainty continue to decrease between sample size 80 to 90, suggesting that the robustness of the probabiilty estimation can still be improved with bigger ensemble, assuming sucient independence between climate models (Knutti et al., 2013). Perhaps more interesting is to know that the decrease of the uncertainty as the sample size increase is slower than the theoretical standard error decrease with sample size (red dashed line), a clear indication of the lack of independence across GCMs (Knutti et al., 2013; Bishop and Abramowitz, 2013). Probability Sampling influence on probability estimation for grid point #900 for year 2010 Bootstrap iteration = Sampling error Spread of sampling error 0.9 Standard error for Normal distributions Sampling size Figure A.8: Speed of convergence with respect to the number of simulations used. Bootstrap with 2000 iterations References Bishop, C. and G. Abramowitz (2013). Climate model dependence and the replicate Earth paradigm. Climate Dynamics 41 (3-4),

12 Jones, N. K. (2012, apr). The inuence of recent climate change on wine regions in Quebec, Canada. Journal of Wine Research 23 (2), Knutti, R., D. Masson, and A. Gettelman (2013, mar). Climate model genealogy: Generation CMIP5 and how we got there. Geophysical Research Letters 40 (6),