Fewer large waves projected for eastern Australia due to decreasing storminess

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1 SUPPLEMENTARY INFORMATION DOI: 0.08/NCLIMATE Fewer large waves projected for eastern Australia due to decreasing storminess Details of the wave observations The locations of the five buoys used in this study are shown in Supplementary Figure. Of the 690 days making up the 9-year period of available data, there are only days for which wave data are not available for at least one of the five buoys. Missing data are therefore not likely to influence the conclusions of this study, partly because of the low number of days for which data are not available, as well as due to the wave height data showing considerable similarities between individual sites, particularly for adjacent locations (Supplementary Table ). Details of the diagnostic method The diagnostic region used to produce the wave projections covers an area of degrees in longitude and 0. degrees in latitude, extending about 000 km offshore from the east coast of Australia (Figure ). When applied to ERA-Interim reanalyses, the diagnostic region is from 8. E to 6. E and 6.0 S to. S, with the closest area to this being used for each GCM (based on the spatial resolution of each individual GCM). This region corresponds to the region of strong curvature in the 00 hpa geopotential height field for days on which large wave heights are observed (e.g. from Figure a), noting that the specific location selected for the diagnostic region is robust to some variation in its position as indicated by the spatial extent of the region of strong curvature in the geopotential height fields. The diagnostic method used here has previously been found to be a better indicator of storm occurrence in this region than other potential diagnostic quantities, including baroclinicity measures such as Eady Growth Rate in the mid-troposphere and other vorticity measures such as isentropic potential vorticity in the upper-troposphere,. NATURE CLIMATE CHANGE

2 Fewer large waves projected for eastern Australia due to decreasing storminess The diagnostic method can identify storms within the diagnostic region, as well as storms that have centres outside of this region, as long as the region of strong vorticity surrounding the storm centre has at least one point of overlap with the diagnostic region (noting that the strong vorticity region in the upper troposphere can be of the order of 000 km wide, ). Consequently, the diagnostic can identify large waves generated by storm centres that may be up to about 000 km away (accounting for the size of the diagnostic region as well as the size of the strong vorticity region in the upper troposphere associated with these storms). Although it may be possible that some swell-waves reaching the coastal study region might be generated by storms that are so far away that their surrounding region of strong vorticity does not overlap the diagnostic region, Figures and show that this is not a significant limitation of the method, with the diagnostic providing a good indication of the likelihood of occurrence of large waves in this coastal region (noting that the wave height data from the buoys consists of the superposition of both near-field waves and far-field swell waves). To provide further details regarding the relationship between wave height and Diagnostic Event Days (in addition to Figures and ), the Cumulative Distribution Function (CDF) of Diagnostic Event Days is shown in Supplementary Figure a, calculated as the fraction of the total number of Diagnostic Event Days that occur for wave heights equal to or lower than a given value. This is shown for various different time lags of the diagnostic with respect to the wave height observations: from -7 hours to +8 hours at 6-hourly intervals (based on the 6-hourly temporal resolution of the ERA-Interim reanalyses used to calculated the Diagnostic Event Days). If a diagnostic method has little or no skill, the values shown in Supplementary Figure a would be close to a line of slope equal to passing through the origin, whereas a skillful diagnostic method for identifying large wave events would have values lower than this line (such that the area under the CDF, i.e. its summation, would be less than 0.). For the various different time lags examined here,

3 Fewer large waves projected for eastern Australia due to decreasing storminess the best skill is obtained when the diagnostic lags the wave observations by -6 hours (shown in red in Supplementary Figure a), corresponding to the smallest area under the CDF (shown in Supplementary Figure b), while noting that the method is robust to some variation in this time lag. Consequently, the diagnostic is produced throughout this study using a lag of -6 hours with respect to the timing of the wave data. Supplementary Figure b also shows results based on mean sea level pressure (MSLP) fields, using the same technique as used for the diagnostic method of this study (with the only difference being that MSLP fields are used instead of 00 hpa geopotential height fields). The results based on MSLP are broadly similar to those based on geopotential height, apart from some small differences such as the optimal time lag for MSLP being slightly later than for 00 hpa geopotential height. This difference in the optimal time lag between the study method (i.e. based on 00 hpa geopotential height) and the alternative method (i.e. based on MSLP) is consistent with the conceptual model that the surface intensification of these storms is driven by baroclinic processes associated with uppertropospheric forcing,. Supplementary Figure shows the number of Diagnostic Event Days per year based on ERA- Interim reanalyses from 979 to 00. Although a linear fit to these data shows some indication of a long-term change in the climate towards fewer Diagnostic Event Days (based on minimizing the Chisquare error statistic), the magnitude of this change is difficult to estimate with a high degree of confidence given the period of available reanalyses. In contrast to the reanalyses, the longer time period of the GCM simulations (i.e. 0 years) allows the long-term change in the climate to be shown with greater clarity, noting that a 0-year moving average is applied to the GCM values in Figure to show the climate signal rather than the short-term variability.

4 Fewer large waves projected for eastern Australia due to decreasing storminess The diagnostic method was originally designed to indicate the risk of occurrence of intense extratropical cyclones that occur in the vicinity of the east coast of Australia. These storms, known as East Coast Lows in this region, often have a low-level thermal asymmetry such that the strongest pressure gradients (and therefore winds) occur on the poleward side of the storm, leading to strong onshore winds and waves along the central east coast of Australia. In spite of this low-level thermal asymmetry, these systems are fully baroclinic, developing in response to deep tropospheric potential vorticity advection,. The sound dynamic link between upper-tropospheric vorticity and surface cyclogenesis suggests that such a technique may be more widely applicable in other subtropical regions. GCM application of the diagnostic The diagnostic method was previously shown to be suitable for application to GCMs from detailed comparisons between results based on a variety of different GCMs and reanalyses,. In addition to the 8 GCMs used in this study, there were four other GCMs that had archived the required fields (i.e. daily geopotential height at 00 hpa) but were found to be not suitable for the application of the diagnostic method. One of these four GCMs (HadGem-ES) did not have data available for the entire historical period (i.e. from 90-00) as used for all of the other GCMs, and so this model was not used to avoid inconsistencies between different GCMs. Two models (CCSM and CMCC-CM) were not suitable for the application of our method due to local maxima in the geopotential height climatology that are not similar to the observed climatology (e.g. from reanalyses ), with a likely explanation for these maxima being that they are artefacts resulting from vertical interpolation schemes applied in post-processing. A fourth GCM was excluded (MIROC-ESM) due to a discontinuity in the number of Diagnostic Event Days that coincides with the change between the historical and future projections, indicating a likely issue with the future projected data (not seen in the

5 Fewer large waves projected for eastern Australia due to decreasing storminess historical data) that results in too few cases of strong geostrophic vorticity at 00 hpa in this region, given that such a discontinuity has not occurred in recent years as indicated by reanalyses (e.g. Supplementary Figure ) and does not occur for any of the other GCMs at any time during the 0 year period examined here. The 8 GCMs used for this study are listed in Supplementary Table. Model grid spacing is listed for each GCM, as well as the diagnostic threshold (i.e. the 90 th percentile of cyclonic geostrophic vorticity during the historical period from 90 to 00). There is some indication of a relationship between the diagnostic threshold and the grid spacing of the GCMs, with finer (coarser) resolution GCMs tending to have higher (lower) diagnostic thresholds, which is perhaps the intuitive expectation. There is still, however, some considerable unexplained variance: reasons for this are likely manifold, but the precise numerical formulations of the models may have some influence. A wide variety of downscaling methods are currently available for application to GCM climate simulations. The downscaling method applied here can be considered to be a stochastic statistical method in that it is based on relating the frequency of occurrence of Diagnostic Event Days to wave heights, while noting that the method is based on sound physical arguments (i.e. the dynamic link between upper-tropospheric vorticity and surface cyclogenesis). Intercomparisons between statistical downscaling methods show that methods which explicitly represent the stochastic component can produce results that are comparable to, and sometimes better than, results produced by methods that take a more deterministic approach 6,7. References. Dee, D. P., et al. The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Q. J. R. Meteorol. Soc. 7(66), -97 (0).

6 Fewer large waves projected for eastern Australia due to decreasing storminess Eady, E. T. Long waves and cyclones waves. Tellus, - (99).. Dowdy, A. J., Mills, G. A. & Timbal, B. Large-scale diagnostics of extratropical cyclogenesis in eastern Australia. Int. J. Climatol. (0), 8-7, doi: 0.00/joc.99 (0).. Dowdy, A. J., Mills, G. A. Timbal, B. & Wang, Y. Changes in the risk of extratropical cyclones in eastern Australia. J. Clim. 6, 0-7, doi: 0.7/JCLI-D (0).. Mills, G. A., et al. The Pasha Bulker east coast low of 8 June 007. Centre for Australian Weather and Climate Research, Australia, CAWCR Technical Report (00). 6. Frost, A. J., et al. A comparison of multi-site daily rainfall downscaling techniques under Australian conditions. J. Hydrology 08, -8 doi: 0.06/j.jhydrol (0). 7. Benestad, R. E. Downscaling Precipitation Extremes: Correction of Analog Models through PDF Predictions. Theor. & Appl. Clim. 00, -, doi: 0.007/s (00).

7 Fewer large waves projected for eastern Australia due to decreasing storminess 7 Supplementary Table Cross-correlation coefficients between wave heights for each of the five buoys. Coffs Harbour Crowdy Head Sydney Port Kembla Eden Coffs Harbour Crowdy Head Sydney Port Kembla Eden

8 Fewer large waves projected for eastern Australia due to decreasing storminess 8 Supplementary Table Details of the 8 GCMs used in this study: model name is shown, as well as diagnostic threshold and spatial resolution (longitudinal and latitudinal, significant figures). Model name Diagnostic threshold (-0 - s - ) Latitudinal resolution (degrees) Longitudinal resolution (degrees) ACCESS BCC-CSM BCC-CSM.(m)... BNU-ESM CanESM CMCC-CMS..9.9 CNRM-CM GFDL-ESMM...0 HadGEM-CC.0.9. IPSL-CMA-LR IPSL-CMA-MR 0.9..

9 Fewer large waves projected for eastern Australia due to decreasing storminess 9 IPSL-CMB-LR MIROC... MIROC-ESM-CHEM MPI-ESM-LR..9.8 MPI-ESM-MR..9.9 MRI-CGCM.0.. NorESM-M

10 Fewer large waves projected for eastern Australia due to decreasing storminess 0 Supplementary Figure Locations of the five buoys used in this study. Latitude, longitude and topography are shown.

11 Fewer large waves projected for eastern Australia due to decreasing storminess Supplementary Figure Diagnostic skill as indicated by the Cumulative Distribution Function (CDF) of Diagnostic Event Days for increasing wave heights. a, CDFs for various different time lags of the diagnostic with respect to the timing of the wave observations (at 6-hourly intervals from -

12 Fewer large waves projected for eastern Australia due to decreasing storminess 7 hours to +8 hours), with the best diagnostic skill corresponding to a time lag of -6 hours (highlighted in red). b, The area under the CDF as a function of diagnostic time lag (solid black line), with an alternative method shown for comparison based on mean sea level pressure (dashed black line). The time lag corresponding to the best diagnostic skill is shown for the study methodology (solid red line) and for the alternative method based on mean sea level pressure (dashed red line).

13 Fewer large waves projected for eastern Australia due to decreasing storminess Supplementary Figure The number of Diagnostic Event Days per year during the time period from 979 to 00 based on ERA-Interim reanalyses. A linear fit to the data is shown (dashed line).