Credibility of Statistical Downscaling under Nonstationary Climate
Kaustubh Salvi1, Subimal Ghosh1,2,*, AuroopR. Ganguly2,3
1
Department of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai400 076, India
2
Interdisciplinary Program in Climate Studies, Indian Institute of Technology Bombay, Powai, Mumbai, 400
076, India
3
Sustainability and Data Sciences Laboratory, Civil and Environmental Engineering,
NortheasternUniversity,Boston, MA 02115, USA
*
Corresponding Author: Department of Civil Engineering, Indian Institute of Technology Bombay, Powai,
Mumbai – 400 076, India, Email: subimal@civil.iitb.ac.in, Phone: +91 22 2576 7319, Fax: +91 22 2576 7302
Supplementary Figure 1 (SF1): Correlation contours, obtained with coefficient of correlation between
spatially averaged rainfall time series and different predictors such as surface level specific humidity (a),
specific humidity at 850hPa (b), specific humidity at 500hPa (c), specific humidity at 300hPa (d), mean sea
level pressure (e), geopotential height at 850hPa (f), geopotential height at 500hPa (g), geopotential height at
250hPa (h), surface air temperature (i), air temperature at 850hPa (j), air temperature at 500hPa (k), air
temperature at 250hPa (l), surface level zonal wind (m), zonal wind at 850hPa (n), zonal wind 500hPa (o), zonal
wind at 250hPa(p), surface meridional wind(q), meridional wind at 850hPa(r), meridional wind at 500hPa(s),
and meridional wind at 250hPa(t) at each grid, for identification of zone of predictors (yellow rectangle) for
WCI zone (location shown with black boundary) for WCI region in India.
Supplementary Figure 2 (SF2): Correlation contours, obtained with coefficient of correlation between
spatially averaged rainfall time series with different predictors such as surface level specific humidity (a),
specific humidity at 500hPa (b), mean sea level pressure (c), surface air temperature (d), air temperature at
500hPa (e), zonal wind at 500hPa (f), surface level zonal wind (g), meridional wind 500hPa (h), surface
meridional wind (i), geopotential height at 500hPa (j) at each grid, for identification of zone of predictors
(yellow rectangle) for Region 3 in NEUS.
Supplementary Figure 3 (SF3):Identification of regions where assumption of stationarity does not hold
good for individual predictors using the approach developed by Duan et al. (2012).
Grid wise trends of regression coefficients (obtained by selecting a 30 year moving window 1951-1980,19521981...as training period and computing regression coefficients for each 30-year window) different predictors,
viz., Surface level specific humidity (a), mean sea level pressure (b), surface temperature (c), surface U wind
(d), surface V wind(e), specific humidity at 500hPa (k), geopotential height at 500hPa (l), temperature at 500
hPa(m), U wind at 500hPa (n), and V wind at 500hPa (o). The statistical significance levels of the trends for
each predictor are also displayed in the form of grid wise probability values. Figure SF3(f-j) show significance
level for all surface level predictors and Figure SF3(p-t) show significance level for all pressure level predictors
(order remains the same as mentioned above). The grids, showing 10% significance level, are marked with
different color and these are the locations where the downscaling model suffers from lack of stationarity.
Supplementary Figure 4 (SF4): Identification of regions where assumption of stationarity does not hold
good for individual predictors using the approach developed by Hertig and Jacobeit(2013).
Plots a-d1 show RMSE obtained for the simulations with different model calibration periods (with 31 year
moving window) e.g. 1951-1981, 1952-1982....
Supplementary Figure 5 (SF5): Comparison between outcomes of‘Reverse climate change scenario’
experiments (TR-H-TE-C, and TR-EN-TE-nonEN)and base experiment (TR-RAN-TE-RAN) over India
and NEUS, in terms of magnitude and spatial distribution of RMSE.
For India,(a) RMSE of experiment TR-RAN-TE-RAN,(b) RMSE of experiment TR-H-TE-C, (c) grid-wise
absolute percentage difference between (a) and (b) with (a) as reference, (d) Comparison between RMSE of TRRAN-TE-RAN and TR-H-TE-C, represented as PDFs, (e) RMSE of experiment TR-EN-TE-nonEN, (f) gridwise absolute percentage difference between (a) and (e) with (a) as reference, (g) Comparison between RMSE
of TR-RAN-TE-RAN and TR-EN-TE-nonEN, represented as PDFs.
For NEUS, (h) RMSE of experiment TR-RAN-TE-RAN,(i) RMSE of experiment TR-H-TE-C, (j) grid-wise
absolute percentage difference between (h) and (i) with (h) as reference, (k) Comparison between RMSE of TRRAN-TE-RAN and TR-H-TE-C, represented as PDFs, (l) RMSE of experiment TR-EN-TE-nonEN, (m) gridwise absolute percentage difference between (h) and (l) with (h) as reference, (n) Comparison between RMSE
of TR-RAN-TE-RAN and TR-EN-TE-nonEN, represented as PDFs.
Supplementary Figure 6 (SF6):PDF comparison analysisand results of experiment series 2: Signature
based approach SB-AP-PI and SB-AP-RCP85, obtained using MIROC-ESM GCM
Plots a-j show PDF comparison plots of different predictors viz. (a) specific humidity at 500hPa (b) surface
level specific humidity (c) geopotential height at 500hPa (d) mean sea level pressure (e) air temperature at
500hPa (f) surface air temperature (g) zonal wind at 500hPa (h) zonal wind at surface level (i) meridional wind
at 500hPa (j) meridional wind at surface level, obtained over historic period (1981-2005) and strongest future
radiative forcing (RCP8.5, 2071-2100).
Plots k-p show results of experiment series 2: Signature based approach SB-AP-PI and SB-AP-RCP85, obtained
using MIROC-ESM GCM; (k)Mean of observed rainfall for years close to centroid of Pre-industrial scenario,
(m)mean of observed rainfall for years close to centroid of RCP8.5 scenario, (o) difference in mean rainfall for
observed data, (l) mean of projected rainfall for years close to centroid of Pre-industrial scenario, (n) mean of
projected rainfall for years close to centroid of RCP8.5 scenario, (p) difference in mean rainfall for projected
rainfall for India.
Supplementary Figure 7 (SF7):Probability Density Function comparison of surface and different pressure
level predictors, specific humidity at 500hPa (a), specific humidity at 850hPa (b), surface level specific
humidity (c), geopotential height at 250 hPa (d), geopotential height at 500 hPa (e), geopotential height at 850
hPa (f), mean sea level pressure (g), air temperature at 250hPa (h), air temperature at 500hPa (i), air temperature
at 850hPa (j), surface level air temperature (k), zonal 'U' wind at 250hPa (l), zonal 'U' wind at 500hPa (m), zonal
'U' wind at 850hPa (n), surface level zonal 'U' wind (o), meridional 'V' wind at 250hPa (p), meridional 'V' wind
at 500hPa (q), meridional 'V' wind at 850hPa (r), surface level meridional 'V' wind (s), simulated for 'Historical'
and 'RCP8.5' scenarios over India.
Supplementary Figure 8 (SF8):Partial correlation (PC) between predictor and predictand over WCI
region in India
PC between observed rainfall, obtained over years that show ACC-PI Signatures and ACC-RCP85 Signatures,
with specific humidity at 300hPa (a1-a2), specific humidity at 500hPa (b1-b2), specific humidity at 850hPa (c1c2), surface level specific humidity (d1-d2), mean sea level pressure (e1-e2), air temperature at 250hPa (f1-f2),
air temperature at 500hPa (g1-g2), air temperature at 850hPa (h1-h2), surface level air temperature (i1-i2), U
wind at 250hPa (j1-j2), U wind at 500hPa (k1-k2), U wind at 850hPa (l1-l2), surface level U wind (m1-m2), V
wind at 500hPa (n1-n2), V wind at 850hPa (o1-o2), surface level V wind (p1-p2), Geopotential height at 250hPa
(q1-q2), Geopotential height at 500hPa (r1-r2), Geopotential height at 850hPa (s1-s2),
Supplementary Figure 9 (SF9):Partial correlation (PC) between predictor and predictand over CNI
region in India
PC between observed rainfall, obtained over years that show ACC-PI Signatures and ACC-RCP85 Signatures,
with specific humidity at 300hPa (a1-a2), specific humidity at 500hPa (b1-b2), specific humidity at 850hPa (c1c2), surface level specific humidity (d1-d2), mean sea level pressure (e1-e2), air temperature at 250hPa (f1-f2),
air temperature at 500hPa (g1-g2), air temperature at 850hPa (h1-h2), surface level air temperature (i1-i2), U
wind at 250hPa (j1-j2), U wind at 500hPa (k1-k2), U wind at 850hPa (l1-l2), surface level U wind (m1-m2), V
wind at 500hPa (n1-n2), V wind at 850hPa (o1-o2), surface level V wind (p1-p2), Geopotential height at 250hPa
(q1-q2), Geopotential height at 500hPa (r1-r2), Geopotential height at 850hPa (s1-s2),