SUPPLEMENTARY INFORMATION

Transcription

1 SUPPLEMENTARY INFORMATION DOI: 1.138/NCLIMATE1327 Lack of uniform trends but increasing spatial variability in observed Indian rainfall extremes SI Guide Supplementary Information Title of the file: Supplementary Information Contents: Supplementary Methods, Supplementary Discussion, Supplementary Note on Datasets, Supplementary Figures S1-S9 and References. Size: 2 Pages Supplementary Files (732 KB in compressed zipped format) Readme Document (3 pages): Description of codes, data and results Codes (described in the Readme document) Data and Results (described in the Readme document) NATURE CLIMATE CHANGE Macmillan Publishers Limited. All rights reserved.

2 Supplementary Information Lack of uniform trends but increasing spatial variability in observed Indian rainfall extremes Subimal Ghosh 1, Debasish Das 2, Shih-Chieh Kao 3, Auroop R Ganguly* 4 1 Indian Institute of Technology Bombay, Mumbai 476, India 2 Temple University, Philadelphia, PA 19122, USA 3 Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA 4 Northeastern University, Boston, MA 2115, USA Supplementary Information Supplementary Methods Statistical approach for rainfall extremes trends The gridded observed daily rainfall time series from 1951 to 23 at each grid are examined using 3-year overlapping moving windows. The 3-year and 1-year return levels are calculated by fitting a Generalized Extreme Value (GEV) distribution to the series of 3 annual maxima extracted from each of the 3-year moving windows. The goodness-of-fit is estimated using the Kolmogorov-Smirnov (KS) test, and if the test fails an empirical distribution is fit instead of a GEV. However, for the gridded datasets, all 3-year windows within each 1-degree spatial grid pass the KS tests at a 1% level of significance. The fitted GEV parameters were used to calculate the return levels for each of the 3-year moving windows and their linear temporal trend was computed at each grid-point. For each 3-year window, the spatial variance was 211 Macmillan Publishers Limited. All rights reserved.

3 calculated by considering all available grid-points. This resulted in a set of 24 values of spatial variance for the period from The linear temporal trend in the spatial variance and its significance were calculated by linear regression methods fitted to the set of 24 values. Data quality issues are potentially important for application of extreme value theory because of the relatively limited data size (3 annual maxima for each moving window) to which the GEV distribution is fitted. The Q-Q plots for two points picked at random from each of the five meteorologically-homogeneous regions (other than the Hilly Region which is thought to be less reliable because of limited measurement coverage) for the window of years suggest that (Supplementary Figure 3) the data are relatively well-behaved (as seen from the quantiles). However, as the Q-Q plots suggest, the fit of the GEV is not equally good for all meteorologically-homogeneous regions for rainfall. Fitting probability distributions, for example the GEV, makes assumptions of stationarity and homogeneity within the time period of the fit. Our implementation based on moving windows requires a weaker assumption. Temporal homogeneity, which may be impacted by changes in instrumentation or measurement locations, needs to be valid only for the 3-year windows. While we do not have direct access to each instrument locations or records, based on the documentation, we have no reason to believe that there was significant non-homogeneity in the records for the time period of our analysis. The stationarity of the time series, which is required for the purposes of GEV applicability, needs to apply to each of the 3-year moving windows as well. In addition, Supplementary Figure 4 shows the Q-Q plots for the first 3-year (years ) and the last 3-year window ( ) for two randomly selected points in the meteorologically-homogeneous regions over India. When taken together with Supplementary Figure 3, which shows the Q-Q plots for the middle 3-years ( ) at those points, there 211 Macmillan Publishers Limited. All rights reserved.

4 is no evidence of any systematic difference in the goodness-of-fit over time. However, there are differences in the Q-Q plots across the different regions, which may be expected. The use of time as a covariate, where the parameters of the GEV distribution are assumed to be functions of time, has been developed as a way to deal with the issue of non-stationarity S1-S3. However, the method requires apriori prescription of a form for the functional relations with the covariates, which in turn has often been assumed to be linear with time (e.g., location and shape parameters of the GEV as linear functions of time elapsed) in the literature. Supplementary Figure 5 examines the degree to which a linear regression may be able to characterize changes in GEV parameters by examining the parameter values at each of the 3-year windows. In general, the linearity assumption does not seem to explain much of the trends, and hence covariates are not used in this present study. Supplementary Figure 6 depicts the changes in each of the three GEV parameters over time based on the 3-year moving windows for randomly selected grids in the meteorologically homogeneous regions over India. Upon visual inspection, the trends do not appear to follow a simple linear trend and there appears to be no uniform functional form that describes the trends for all parameters and regions. The spatial covariates are avoided because of complicated topography, atmospheric wind patterns during the monsoon, heterogeneity in regional to local weather patterns and features like vegetation and land use. The uncertainties associated with the estimates of GEV parameters are computed using bootstrapping, similar to Kharin et al. 23, by sub-sampling (with repetition) 3 annual maxima within each 3-year block 1 times. The 4 th and 6 th percentile values out of this set of 1 estimates of GEV parameters are reported as lower and upper confidence bounds around most likely values of the parameters. The confidence bounds of the parameters for the last 3-year window at each grid are shown in Supplementary Figure 7. The temporal trends for the 211 Macmillan Publishers Limited. All rights reserved.

5 confidence bounds of the three GEV parameters are shown in Supplementary Figure 8. The uncertainties are not large enough to impact the validity of our overall conclusions. Following the approach adopted by Kharin and Zwiers S13, the change in GEV parameters, between the first and the last 3-year windows, are presented in Supplementary Figure 9a, at a 2 percent significance level considering the uncertainties, as estimated using bootstrapping. Similarly, the changes computed for return levels, at 2 percent significance level, are presented in Supplementary Figure 9b. The changes are reported for a parameter or a return level at 2 percent significance level, when, the 6 percent confidence interval (2 to 8 percentile) of parameter estimates from first and last 3-year windows are non-overlapping. Grid-points with overlapping confidence intervals (i.e. not significant) are marked white. The results show spatially heterogeneous changing patterns of return levels and parameters. This provides an estimate of spatial variability of significant change in extremes parameters over time. One important discussion point is the possible influence of outliers on our results. As shown in the box-plots of Figure 3 and Supplementary Figure 2, the boxes exhibit a tendency to widen over time, and the fences of the boxes are by definition robust to outliers. Thus, our conclusion regarding trends in spatial heterogeneity does not appear to be tainted by outliers. The bootstrap confidence bounds Figure 3 further support this consideration. The bootstrap procedure essentially attempts to sample outliers in proportion to their observed occurrence; it assumes that the empirical distribution (the given sample) approximates the population distribution. If the observed trend in spatial variability were a consequence of chance, the bootstrap-based confidence bounds should reflect that via sampling variability and may tend to encompass a flat or even a negative trend. 211 Macmillan Publishers Limited. All rights reserved.

6 Supplementary Discussion Physical interpretations, future projections and policy implications The present section discusses the possible reasons for trends in rainfall extremes, including its association with anthropogenic activities as discussed in literature, and the possible interpretation and explanation of spatial heterogeneity of trends in Indian extreme rainfall events. Anthropogenic warming and implications for rainfall extremes over India The trends found in the present study may be viewed in the context of anticipated future changes in extreme monsoon precipitation as a consequence of anthropogenic changes in greenhouse gas forcing encapsulated by change scenarios S4-S6. Recent literature 25-26, S7-S9 suggests an overall increase in precipitation extremes trends as a consequence of atmospheric or oceanic warming. A recent study 2 attributed world-wide growing trends in precipitation extremes to global warming. However, the credibility of the projections of increasing precipitation trends is in general higher for the extra-tropical regions but lower for the tropics. For the Indian monsoon specifically, global warming has been shown to decrease the predictability of Indian monsoon weather 6. Two studies S1-S11 suggested that global climate models used by the IPCC can be split into two groups depending on their projections of extreme monsoon rainfall events: those in which the projected changes are directly predictable based on local surface warming and the corresponding effect on moisture availability (i.e., the Clausius-Clapeyron relation) versus those in which the increasing trends significantly exceeds predictions based on local warming alone. The growing trends in geographical heterogeneity of rainfall extremes concurrent with a lack of spatially uniform trends shown in our paper suggest local influences (e.g., urban heat island effects) may be at least as dominant as global influences (e.g., global warming). 211 Macmillan Publishers Limited. All rights reserved.

7 Topography, vegetation and other regional influences on changes in extremes Indian monsoon rainfall is largely a function of topography, which results in significant spatial heterogeneity. The western coast of India receives most of its rainfall because of prevailing westerly winds which are perpendicular to Western Ghats and subsequent orographic precipitation. Similarly, high orographic precipitation also occurs in the North-East India, at windward side. Deccan plateau, being at the leeward side of Western Ghats, receives less rainfall. This spatial heterogeneity of Indian rainfall is also reflected in Fig. 2(a) and 2(b). One possible reason for spatial heterogeneity in trends (Fig. 2(d) and 2(e)) may be due to the combined impacts of changes in climatic variables (e.g., increases in SST 1 ). The other reasons could be related to local changes and urbanization, as reported in literature 7. The mean state of Indian monsoon rainfall has also been reported to be affected by agricultural intensification S12 ; however, such a relation for extreme rainfall has not been investigated. Because of nonavailability of finer resolution data before 1981, we do not attempt such an analysis. A modelbased approach to testing the influence of such factors that may contribute to the trends in regional rainfall extremes may be considered in future work. 211 Macmillan Publishers Limited. All rights reserved.

8 Supplementary Note on datasets 1 latitude X 1 longitude gridded rainfall data 22 is used for analyzing the trend of extreme rainfall events in India. A total of 6329 stations are maintained by the IMD and individual state governments of India, out of which 183 stations were used in developing the gridded product. These 183 stations have at least 9% data availability for the period and thus are used to minimize temporal inconsistencies. The data product is known as product No. 1/25, which may be purchased from the India Meteorological Department (IMD) for a processing fee. Station data were interpolated to 1 latitude X 1 longitude grids using a weighted sum, which was a variant of a method adopted by the Global Precipitation Climatology Project. The density of stations is not uniform throughout India. Density is the highest over the south peninsula and poorer over the northern plains of India (Uttar Pradesh, for example) and eastern parts of Central India. Overall, while rainfall data quality and availability are relatively uniform within each meteorologically-consistent region over India, they may differ across regions. Our understanding is that the data, used here for our rainfall extremes analysis, were made temporally consistent to the extent possible within each region. 211 Macmillan Publishers Limited. All rights reserved.

9 Supplementary Figures Figure S1: Coefficient of determination for grid-based 3-year moving trends in rainfall extremes return levels The coefficient of determination (r-squared) values for trends in 3-year (a) and 1-year return levels (b) calculated on each one-degree spatial grid. The values can be compared with the trends shown in Figure 2 ((c)-(d)) of the main text for an understanding of the confidence associated with the trends. The values of r-squared are spatially heterogeneous and do not exhibit obvious visual trends. 211 Macmillan Publishers Limited. All rights reserved.

10 Figure S2: Trends in annual maximum rainfall and their spatial variability for the six regions within in India considered homogeneous in terms of rainfall patterns Overall trends in annual maximum rainfall and their spatial variability for the six regions in India considered be to homogeneous in terms of rainfall (the corresponding maps are available from the Indian Institute of Tropical Meteorology): Peninsular India, North-West India, North-East India, West-Central India, Central North East India and Hilly Region. The trends in each of these regions appear visually different. Within the six regions, increasing trends in spatial variability are statistically significant in North-West India and Central North-East India, marginally significant for Peninsular India and North-East India and not significant for West- Central India and Hilly Region. The trend lines are shown in bold lines with their confidence intervals in dotted lines. 211 Macmillan Publishers Limited. All rights reserved.

11 Figure S3: Quantile-Quantile (Q-Q) plots for the middle 3-year window ( ) at two randomly selected points in Indian meteorologically-homogeneous regions other than the Hilly Region The Q-Q plots are for the following five meteorologically-homogeneous regions (listed from top to bottom): Peninsular India, North-West India, North-East India, West-Central India, and Central-North East India. Each row represents two randomly selected points in the region. 211 Macmillan Publishers Limited. All rights reserved.

12 (a) (b) Figure S4: Temporal homogeneity of the Q-Q plots shown for the beginning ( ) and ending 3-year windows ( ) at the two randomly selected points (same as in Fig. S4) per region Fig. S4a shows the Q-Q plots for the beginning 3-year time windows while Fig. S4b shows the ending 3-year. The two points per region are the same as in Fig. S Macmillan Publishers Limited. All rights reserved.

13 (a) (b) (c) Figure S5: Temporal linear trends and regression r-squared for each of the three GEV parameters for each grid-cell Figs. S5a, b and c show the gradients and goodness of linear fit for the scale, shape and location parameters of the GEV parameters respectively at each grid-cell over India. 211 Macmillan Publishers Limited. All rights reserved.

14 1 GEV paramters at a point from Central Northeast region 1 GEV paramters at a point from Central Northeast region Shape Parameter x 1 Location Parameter Scale Paramter Shape Parameter x 1 Location Parameter Scale Paramter Starting year of 3-yr window Starting year of 3-yr window GEV paramters at a point from Northwest region Shape Parameter x 1 Location Parameter Scale Paramter GEV paramters at a point from Northwest region Shape Parameter x 1 Location Parameter Scale Paramter Starting year of 3-yr window Starting year of 3-yr window GEV paramters at a point from Northeast region GEV paramters at a point from Northeast region Shape Parameter x 1 Location Parameter Scale Paramter Shape Parameter x 1 Location Parameter Scale Paramter Starting year of 3-yr window Starting year of 3-yr window FIGURE S6a 211 Macmillan Publishers Limited. All rights reserved.

15 1 9 8 GEV paramters at a point from Peninsular Region region Shape Parameter x 1 Location Parameter Scale Paramter GEV paramters at a point from Peninsular Region region Shape Parameter x 1 Location Parameter Scale Paramter Starting year of 3-yr window Starting year of 3-yr window GEV paramters at a point from West Central region Shape Parameter x 1 Location Parameter Scale Paramter GEV paramters at a point from West Central region Shape Parameter x 1 Location Parameter Scale Paramter Starting year of 3-yr window Starting year of 3-yr window FIGURE S6b 211 Macmillan Publishers Limited. All rights reserved.

16 .6 Shape parameters at different geographically homogenous region.6 Shape parameters at different geographically homogenous region Peninsular Region -.4 Central Northeast -.6 Northwest -.6 West Central Northeast Starting year of 3-yr window Peninsular Region Central Northeast Northwest West Central Northeast Starting year of 3-yr window FIGURE S6c Figure S6: Trends in the three Generalized Extreme Value (GEV) parameters at two randomly selected points (same as in Figs. S4 and S5) per meteorologically-homogeneous region Figures S6a and b show trends in the GEV parameters based on the parameters calculated over each 3-year moving window. The trends show significant disparity ranging from uniform and linear to cyclical and relatively erratic. The shape parameter values are very small compared to scale and location parameters; hence they were scaled up by a factor of 1 in Figs. S6(a) and S6(b) for visual clarity. The variations are visually prominent in Fig. S6(c), which plots just the shape parameters: The left plot shows all 1 shape parameters (both randomly selected points in the five regions) while the right plot shows one point from each of the five regions. 211 Macmillan Publishers Limited. All rights reserved.

17 Shape( ) - Most Likely 4 N Shape( ) - Lower Bound 4 N Shape( ) - Upper Bound 4 N 3 N.5 3 N.5 3 N.5 2 N 2 N 2 N 1 N N N E 8 E 9 E 1 E 7 E 8 E 9 E 1 E 7 E 8 E 9 E 1 E Scale( ) - Most Likely 4 N 6 Scale( ) - Lower Bound 4 N 6 Scale( ) - Upper Bound 4 N 6 3 N 2 N 1 N N 2 N 1 N N 2 N 1 N E 8 E 9 E 1 E 7 E 8 E 9 E 1 E 7 E 8 E 9 E 1 E Location( ) - Most Likely 4 N Location( ) - Lower Bound 4 N Location( ) - Upper Bound 4 N 3 N 15 3 N 15 3 N 15 2 N 1 2 N 1 2 N 1 1 N 5 1 N 5 1 N 5 7 E 8 E 9 E 1 E 7 E 8 E 9 E 1 E 7 E 8 E 9 E 1 E Figure S7: Uncertainty in the GEV parameters at each grid-cell for the last 3-year window The most likely projections, lower bounds, and upper bounds the three GEV parameters are shown for the last 3-year window ( ). Specifically, the location, scale and shape parameters are shown from top to bottom, while most likely, lower bounds and upper bounds are shown from left to right. 211 Macmillan Publishers Limited. All rights reserved.

18 4 N Shape - Mean Trend 4 N Shape - Lower Bound 4 N Shape - Upper Bound 3 N.2 3 N.2 3 N.2 2 N 2 N 2 N 1 N N N E 8 E 9 E 1 E 7 E 8 E 9 E 1 E 7 E 8 E 9 E 1 E 4 N 3 N Scale - Mean Trend N 3 N Scale - Lower Bound N 3 N Scale - Upper Bound N 2 N 2 N 1 N N N E 8 E 9 E 1 E 7 E 8 E 9 E 1 E 7 E 8 E 9 E 1 E 4 N 3 N Location - Mean Trend 1 4 N 3 N Location - Lower Bound 1 4 N 3 N Location - Upper Bound 1 2 N -1 2 N -1 2 N -1 1 N -2 1 N -2 1 N -2 7 E 8 E 9 E 1 E 7 E 8 E 9 E 1 E 7 E 8 E 9 E 1 E Figure S8: Uncertainty in the trends of the GEV parameters at each grid-cell The most likely projections, lower bounds, and upper bounds of the trends in the three GEV parameters are shown. Specifically, the location, scale and shape parameters are shown from top to bottom, while most likely, lower bounds and upper bounds are shown from left to right. The uncertainty in the trends of the GEV parameters does not appear significant enough to change our overall spatially aggregate conclusions. 211 Macmillan Publishers Limited. All rights reserved.

19 (a) (b) Figure S9: Changes in GEV parameters and return levels Following the approach adopted by Kharin and Zwiers S13, the changes of GEV parameters and return levels from the first 3-year window ( ) to the last 3-year window ( ) are estimated at 2 percent significance level. Grid points without significant change are not colored. While this figure cannot be directly compared with Figure 4, together they may convey a holistic impression of the trends and variability in rainfall extremes as well as their uncertainties. Had all or perhaps most locations exhibited insignificant changes in return values, the resampling confidence bounds would have very likely suggested that the observed trend in spatial variability 211 Macmillan Publishers Limited. All rights reserved.

20 was a product of statistical chance. In fact, a number of grid points show changes at levels more significant than 2%. If most of these grid points in the figure were to, for instance, show a significantly increase over the two 3-year windows, then these may have contributed to an increase in the overall regional magnitude (i.e., spatially uniform increase) rather than spatial heterogeneity. However, in the absence of such uniform increase and in view of the robustness of the resampling results, this figure suggests an increase in spatial heterogeneity. 211 Macmillan Publishers Limited. All rights reserved.

21 References S1. Smith, R.L., Statist. Sci. 4(4), (1989) S2. Towler, E. et al., Water Resour. Res. 46, W1154. (21) S3. Katz, R.W., Climatic Change, 1, (21) S4Dairaku K., and Emori S., Geophys. Res. Lett. 33,doi: 1.129/25GL (26) S5. May W., Clim. Dyn. 22, (24) S6. Turner AG, Slingo JM, Atmos. Sci. Let. 1, (29) S7. O Gorman, P. A., and Schneider, T., J. Clim. 22, (29) S8. Allan, R.P. and Soden, B.J., Science 321(5895), (28). S9.Allan, R.P., Soden, B.J., John, V.O., Ingram, W., and Good, P., Environ. Res. Lett. 5,2525. (21). S1. Turner, A.G., and Slingo, J.M., Q. J. R. Meterol. Soc., 133: (29) S11. Turner A.G., and Slingo J.M., Atmos. Sci. Lett., 1: (29) S12. Niyogi et al., Water. Resour. Res., 46, W3533. (21) S13. Kharin, V.V., and Zwiers, F.W., J. Clim. 18, (25) 211 Macmillan Publishers Limited. All rights reserved.