Impacts of rainfall extremes on wheat yield in semi-arid cropping systems in eastern Australia

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1 Supplementary material for Supplementary material for Feng et al, Climatic Change Impacts of rainfall extremes on wheat yield in semi-arid cropping systems in eastern Australia Puyu Feng Bin Wang De Li Liu Hongtao Xing Fei Ji Ian Macadam Hongyan Ruan Qiang Yu Corresponding Author: Qiang Yu State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Northwest A&F University, Yangling , Shaanxi, China College of Resources and Environment, University of Chinese Academy of Science, Beijing , China School of Life Sciences, Faculty of Science, University of Technology Sydney, PO Box 123, Broadway, NSW 2007, Australia T: E: S1 Multicollinearity diagnostics of input variables VIF (variance inflation factor) is a widely used index for multicollinearity detection (Dormann et al., 2013; Graham, 2003; Mansfield and Helms, 1982), which measures the inflation in the variances of the parameter estimates due to collinearities that exist among the predictors. Small VIF values indicate high independence of input variables. Generally, a VIF value of less than 10 is considered to be acceptable in climate related studies (Doetterl et al., 2015; Laubhann et al., 2009; Scheller and Mladenoff, 2008). Before model fitting, high multicollinearity amongst the independent variables was reduced by computing the VIF and iteratively removing variables with >10 VIF values, until only variables with VIF < 10 remained (Table S1). Table S1 Multicollinearity diagnostics of input variables. VIF Region I Region II Region III Whole region SPI MAM SPI JJA SPI SON SPI DJF CDD CWD R99pTOT Rx1day Rx5day SDII S2 Seasonal rainfall cycle over the study region Fig. S1 illustrates the seasonal rainfall cycle over 3 sub-regions and the whole New South Wales wheat belt during Frequent and severe ups and downs of rainfall amount existed in all seasons, with summer had the largest fluctuation range, nearly 400 mm. Spring and winter rainfall also fluctuated severely. Region I had relatively more rainfall during spring and winter. Region II had had a summer-dominant rainfall pattern. All the study regions had similar rainfall amount during autumn. 1

2 Fig. S1 Seasonal rainfall in 3 sub-regions and the whole New South Wales wheat belt during S3 Temporal trends of rainfall extremes indices Temporal trends of rainfall extremes indices in three sub-regions and the whole New South Wales wheat belt during are shown in Fig. S3. Nearly all rainfall extremes indices had frequent and severe ups and downs or maintained a high level in all study regions during the study period. For example, consecutive dry days (CDD) often exceeded 50 days in region II. Specially in Fig. S3(h-j), there were obvious variations between multi-annual wet and dry periods, indicating the great inter-annual variability of rainfall in the New South Wales wheat. 2

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4 Fig. S2 Temporal trends of rainfall extreme indices in three sub-regions and the whole New South Wales wheat belt during The three sub-regions consist of 20, 12, and 34 shires respectively, so they occupy different widths in (h-j). In (a-g), blue points represent values for each shire and red lines are shire-averaged values for each region. 4

5 Supplementary references Doetterl S, Stevens A, Six J, Merckx R, Oost KV, Pinto MC, Casanovakatny A, Muñoz C, Boudin M, Venegas EZ (2015) Soil carbon storage controlled by interactions between geochemistry and climate. Nature Geoscience 8. Dormann CF, Elith J, Bacher S, Buchmann C, Carl G, Carré G, Marquéz JRG, Gruber B, Lafourcade B, Leitão PJ (2013) Collinearity: a review of methods to deal with it and a simulation study evaluating their performance. Ecography 36: Graham MH (2003) Confronting multicollinearity in ecological multiple regression. Ecology 84: Laubhann D, Sterba H, Reinds GJ, Vries WD, Vries WD (2009) The impact of atmospheric deposition and climate on forest growth in European monitoring plots: an individual tree growth model. Forest Ecology & Management 258: Mansfield ER, Helms BP (1982) Detecting multicollinearity. The American Statistician 36: Scheller RM, Mladenoff DJ (2008) Simulated effects of climate change, fragmentation, and interspecific competition on tree species migration in northern Wisconsin, USA. Climate Research 36: