1
Auxiliary Material
2
Attributing intensification of precipitation extremes to human influence
3
Xuebin Zhang1, Hui Wan1, Francis W. Zwiers2, Gabriele C. Hegerl3, Seung-Ki Min4
4
1. Observational data
5
We use gridded annual maximum 1-day (RX1day) and 5-day (RX5day) precipitation
6
amounts available from the HadEX2 [Donat et al., 2013]. This dataset covers the period
7
1901-2010. A previous detection and attribution study on extreme precipitation [Min et
8
al., 2011] used RX1day and RX5day from HadEX [Alexander et al., 2006], which covers
9
1951-2003. Compared with HadEX, HadEX2 includes almost twice as many
10
precipitation stations and substantial improvements in spatial coverage (see Figure S1).
11
We conduct our detection and attribution analysis on the longest time period for which
12
there is good spatial coverage so that large area spatial averaging will reduce noise
13
from internal variability. Since observations started to become abundant in the 1950s
14
but significantly reduced around 2005, and most model simulations end in 2005, we
15
conduct our analysis over the period 1951-2005. To avoid possible data
16
inhomogeneities caused by changes in data availability, we only use long-term data.
17
Data from a grid box are not used if there are more than 10 missing years during 1951-
18
2005. Figure S1 shows the map of grid box locations of these long-term data.
1
Climate Research Division, Environment Canada, Toronto, Ontario M3H 5T4, Canada.
Pacific Climate Impacts Consortium, University of Victoria, Victoria, British Columbia V8W2Y2, Canada.
3
School of GeoSciences, University of Edinburgh, Edinburgh #H93JW, UK.
4
School of Environmental Science and Engineering, Pohang University of Science and Technology, Pohang,
Gyungbuk, 790-784 Korea.
2
1
19
The availability of Russian daily precipitation data was limited to the late 1990s at the
20
time of HadEX2 construction. As a result, HadEX2 has few grid boxes over Russia that
21
meet our missing data criterion. As Russia represents a large fraction of the Northern
22
Hemisphere mid-latitude land area, we augment HadEX2 with extreme precipitation
23
extracted from daily precipitation data that have become available recently from the
24
Russian Met Service via their website
25
(http://www.meteo.ru/English/climate/d_temp.php).
26
We used daily precipitation amounts observed at 600 stations covering time period
27
1874-2011 from this source. In 1966-67, the Hydrometeorological Services of the former
28
Soviet Union initiated an effort to account for light precipitation “to the last drop” and
29
introduced a wetting correction to each nonzero precipitation measurement (0.2mm for
30
liquid and 0.1mm for frozen precipitation) when at least one drop was extracted from the
31
gauge. This resulted in a substantial increase in the number of precipitation days and
32
affected annual total precipitation [Groisman and Rankova, 2001]. However, this
33
practice does not affect measurements of extreme precipitation. Gauge under-catch due
34
to wind, and changes in the use of instruments also affect precipitation measurement.
35
However, again, extreme precipitation measurements are mostly unaffected by such
36
data inhomogeneity issues [Groisman et al., 2013].
37
RX1day is extracted from Russian station daily data if there are no more than 15
38
missing values in the daily amount of precipitation for each year. We compute 5-day
39
precipitation accumulations if there are at least 4 daily values within a given 5-day
40
window (if only 4 daily values are available within a given 5-day window, the value for
41
the missing day is set to zero). RX5day is extracted if no more than 15 values are
2
42
missing from all possible overlapping 5-consecutive days. Stations with less than 10-yr
43
missing during 1951-2005 in RX1day or RX5day are retained for the analysis. A total of
44
433 stations for RX1day and 427 stations for RX5day meet this requirement. The
45
RX1day and RX5day values at individual stations are then averaged within the
46
2.5x3.75° grid boxes, consistent with the approach used by Donat et al. [2013]. Grid box
47
values are converted into PI to replace the PI values from the original HadEX2. This
48
merged dataset forms our observational dataset. We also computed PI values from
49
station data and then averaged these PI values from individual stations within the
50
2.5x3.75° grid boxes. The resulting regional series are essentially the same (not
51
shown). The addition of Russian data improves data spatial coverage substantially
52
(Figure S1).
53
Area-averaged PI from the merged dataset differs from that calculated from HadEX2
54
(Figure S2), but differences in 5-year mean values are much smaller than for annual
55
values. The long-term trends remain in the merged dataset though the trend is smaller.
56
Wan et al. [2013] showed that the bias of northern hemispheric annual precipitation
57
anomalies tend to be smaller when spatial averages are calculated over networks with
58
greater spatial coverage. Analogously, we expect smaller bias in the spatial averages
59
calculated from the merged HadEX2 plus Russian data than in corresponding spatial
60
averages from HadEX2. Figure S3 displays 5-yr PI averages computed from different
61
datasets. Averages from the merged HadEX2+Russian data have a weaker trend due to
62
the increased spatial coverage over Russia, which includes many more northern Asian
63
locations with weak trends. When masked by the HadEX data availability, averages
64
from the merged HadEX2+Russian data yield a trend that is almost identical to that of
3
65
HadEX due to similar spatial coverage. In contrast, when HadEX2 alone is masked by
66
HadEX data availability, coverage is lower than in HadEX due to the lack of Russian
67
data, and a stronger trend results than estimated from HadEX.
68
2. Model data processing
69
Model simulated RX1day and RX5day under historical forcing (ALL) were extracted
70
from the Coupled Model Intercomparison Project Phase 5 (CMIP5) archive [Sillmann et
71
al., 2013]. At the time of analyses, 54 historical simulations from 14 coupled climate
72
models (GCMs) and 34 historical natural forcing (NAT) simulations from 9 GCMs were
73
available. The simulations in general start in the late 19th century and finish in the early
74
21th century. Many modelling centers do not provide ALL and NAT forcing simulations
75
beyond 2005. Over 15000 model-years of pre-industrial control (CTL) simulations
76
conducted with 31 GCMs are also available. We extracted all of the available simulated
77
daily precipitation data from NAT and CTL simulations through the PCMDI CMIP5
78
website and computed RX1day and RX5day. Since different GCMs have different
79
spatial resolutions we interpolated model indices to the HadEX2 grid at 2.5°x3.75°
80
resolution using distance weighting average remapping implemented in the Climate
81
Data Operators (https://code.zmaw.de/projects/cdo) for the subsequent analysis.
82
Model simulated indices for 1951-2005 for each of the available ALL and NAT runs are
83
masked using the merged dataset to mimic the availability of observational data. They
84
are then converted to PI (see main paper). Figure S5 shows PI trends from
85
observations and model simulations. Overall, there is a spatially consistent increasing
86
trend over North America and Europe. Russia does not show spatially consistent
87
positive or negative trends, as is also the case in annual total precipitation [Min et al.,
4
88
2008]. This explains the smaller trend in PI averages when Russian data are included
89
(Figure S2). Multi-model simulated ALL trend is in general, positive almost everywhere.
90
The model-simulated NAT trend is mixed with regions of positive and negative changes,
91
but overall, it is weakly negative.
92
Note that averaging of multi-model PI trends substantially reduces the spatial variability
93
in trends that is induced by internal climate variability, and thus the multi-model mean
94
trends should not be expected to be of similar magnitude to observed trends on the
95
grid-box scale. Spatially smoothing the observed trends (e.g., by applying a 9 grid-box
96
spatial moving average to the observed trends) dampens internal variability
97
considerably and produces observational maps that are more directly comparable to the
98
multi-model maps (Fig. S5). It should also be noted, however, that the smoothed
99
observational map contains regional features that may be related to the specific
100
realization of internal variation that we are experiencing. Individual model simulations
101
also have features of similar scale, but since these are of natural internal origin, they are
102
filtered out when multi-model PI- trends are averaged. Note that the model maps are
103
spatially very homogenous, as expected (see discussion in the main paper, and also
104
Hegerl et al., 2004), limiting the prospects for the separation of signals based on the
105
expected spatial features of the responses to forcing.
106
Model PIs are spatially averaged to produce NH or regional series. For the same forcing
107
group, signals are estimated by first computing single-model ensemble means and then
108
averaging the model-means. Model simulated indices for 1896-1950 are also used for
109
internal variability estimation. For this purpose, each of the available ALL and NAT runs
110
is masked using the merged dataset for 1951-2005 in a way such that the data
5
111
availability from the model year (e.g., 1896) is the same as that from the corresponding
112
observation year (e.g., 1951). These model-simulated segments are then converted to
113
PI and averaged across the space to produce regional series. Ensemble means from
114
individual GCMs are removed. The available control simulations from each model are
115
divided into 55-yr chunks. These are then masked using the merged observational
116
dataset such that the data availability in each model year of each 55-yr chunk is the
117
same as that from the corresponding observation year over the 55-yr period. Data from
118
CTL simulations are converted to PI by fitting a GEV distribution at each grid box to
119
RX1day and RX5day series representing the entire length of the control simulation.
120
Regional averaged PIs are split into an equal number of 55-yr chunks from each
121
model’s CTL run and 0.5 (the mean probability) is subtracted. We use control
122
simulations and the inter-ensemble differences from ALL and NAT simulations to
123
construct two independent noise datasets N1 and N2 . N1 includes inter-ensemble
124
differences for 1896-1950 and half of the control simulations while N2 includes inter-
125
ensemble differences for 1951-2005 and the remaining half of the control simulations.
126
They are used to produce two independent estimates of internal variability covariance
127


( C N 1 and C N 2 ) respectively. In total, there are 142, 54, and 34 55-yr chunks respectively
128
from CTL, ALL, and NAT simulations for the estimation of each covariance matrix.
129
3. Single-signal non-optimized analysis.
130
We also conducted the single-signal analyses using the non-optimized analysis method
131
of Polson et al. [2013]. In a nutshell, model-simulated signals are fitted to observation
132
via the TLS method without pre-whitening residuals as in the optimal generalized TLS
133
approach of Allan and Stott [2003]. Since the distribution of the scaling factors cannot
6
134
be determined analytically in this case without making the unrealistic assumption that
135
the residuals are independent and identically distributed, confidence intervals for the
136
scaling factors are estimated with a resampling scheme that takes the covariance
137
structure of the residuals into account. This is done by adding model simulated noise to
138
the best-fit reconstruction of the signal with a bootstrap procedure. Details of the
139
method are described in Polson et al. [2013].
140
Figure S6 shows scaling factor best estimates and their 90% confidence intervals for
141
ALL, ANT and NAT based on single-signal analyses of 5-yr mean PI. Results are
142
essentially the same as those obtained with the optimized analyses: the 90%
143
confidence intervals for scaling factors from the non-optimized analyses are in general
144
wider (but not to a large extent). It appears that there is not a great advantage to use
145
the optimized method in this case.
146
4. Detection and attribution results for annual mean PI
147
Compared with multi-year mean PI, the annual mean PI series has higher temporal
148
resolution and thus more data points. This requires the estimation of a much larger
149
covariance matrix that may no longer be of full rank given limited model data. In this
150
case, dimension reduction is required so that estimated covariance matrix will be of full
151
rank and thus be invertible. Also, importantly, dimension reduction may be necessary to
152
ensure that the analysis is performed at temporal and spatial scales at which the GCMs
153
represent internal variability well, avoiding small scales at which variability may be
154
underestimated [Hegerl et al., 1997, Allen and Tett, 1999]. Thus it is important to
155
evaluate whether the variability in the regression residual is consistent with model
156
simulated variability. A typical approach in such cases is to reduce data dimension by
7
157
projecting both observations and model simulations onto the leading Empirical
158
Orthogonal Functions (EOFs) estimated from model simulated internal variability. The
159
maximum number of EOFs that can be retained is often determined by a residual
160
consistency test [Allen and Stott, 2003] such that model simulated variability is not
161
smaller than the variability in the regression residual. We use the formula of Ribes and
162
Terray [2013] to compute critical values for this statistic. Figure S7 displays residual
163
consistency test results for Northern Hemisphere land area averages for single-signal
164
analyses. In general, model simulated variability becomes smaller than that of
165
regression residual only when a large number (>40) of EOFs are retained in the
166
truncation. The scaling factor and its 90% confidence interval vary only slowly in relation
167
to the number of EOFs retained in the analysis (Figure S8). Figure S9 shows results
168
from 2-signal analysis, corresponding to EOF truncations under which model simulated
169
variability is consistent with that of residuals. For NH or ML and TR two-region
170
combined, the effect of anthropogenic forcings can be detected in extreme precipitation
171
observations when simultaneously estimating anthropogenic and naturally forced
172
changes while the effect of natural forcings is not detectable. This conclusion is robust
173
across a wide range of EOF truncations. Model simulated variability is also consistent
174
with that of the residuals corresponding to these EOF truncations. However, for the
175
NA+EU+AS three region analysis, ANT and NAT cannot be jointly detected and ANT
176
cannot be separately detected. Overall, optimal detection analysis on annual series
177
does not provide much more information than that of 5-year analysis since the annual PI
178
analysis can only be conducted on a reduced dimension that is not much larger than
179
that of 5-yr mean analysis.
8
180
181
5. Sensitivity of detection and attribution results to different time period and
GCMs used
182
To examine whether the detection and attribution results presented in the main text are
183
sensitive to the time period used in the analysis, we also conducted an analysis for
184
the1951-2000 period that was used in Min et al. [2011] for NH, ML+TR, and
185
NA+EU+AS. Figure S10 displays scaling factors from single-signal analyses and Figure
186
S11 shows results for two-signal analyses. Overall, results are very similar to those for
187
1951-2005 described in the main text.
188
We also examined if the two-signal detection results are sensitive to the differences
189
among the GCMs being used in the estimate of ALL and NAT signals by estimating ALL
190
and NAT signals from simulations of the 7 GCMs for which both ALL and NAT
191
simulations are available. Figure S12 shows results from two-signal analyses for 5-yr
192
mean PI series for NH, ML+TR, and NA+EU+AS over period 1951-2005. These results
193
are also similar to those in Fig. 3 of the main paper.
194
195
Additional References:
196
Groisman, P. Y.and E. Y. Rankova (2001), Precipitation trends over the Russian
197
permafrost-free zone: removing the artifacts of pre-processing. Int. J. Climatol., 21, 657-
198
678 .
199
Groisman, P.Ya., R.W. Knight and O.G. Zolina (2013), Recent trends in regional and
200
global extreme precipitation patterns. Chapter 5.03 in Pielke, R. Sr., Hossain F., et al.
9
201
(eds) Water Encyclopedia (Elsevier Sciences) Climate Vulnerability: Understanding and
202
Addressing Threats to Essential Resources. Elsevier Publishing House, in press.
203
204
10
205
Table S1. List of coupled model simulations available at the time of analysis and used in
206
this study, ‫ ٭‬marks GCMs from which both ALL and ANT simulations are available.
Model
Bcc-csm1-1
CanESM2‫٭‬
CCSM4
CNRM-CM5‫٭‬
CSIRO_Mk3-6-0‫٭‬
FGOALS-s2
GFDL-CM3‫٭‬
HadGEM2-ES‫٭‬
IPSL-CM5A-LR‫٭‬
IPSL-CM5A-MR
MIROC5
MIROC-ESM‫٭‬
MPI-ESM-LR
MPI-ESM-MR
MRI-CGCM3-p1
NorESM1-M
ACCESS1-0
ACCESS1-3
Bcc-csm1-1-m
BNU-ESM
CESM1-BGC
CMCC-CM
CMCC-CMS
EC-EARTH
GFDL-ESM2G
GFDL-ESM2M
HadGEM2-CC
Inmcm4
IPSL-CM5B-LR
MIROC-ESM-CHEM
MPI-ESM-P
ALL 1896-2005
NAT 1896-2005
Pre-industrial control (CTL)
[# of runs/# of 55-yr
[# of runs/# of 55-
simulations
chunks]
yr chunks]
[# of 55-yr chunks]
3
5
5
5
3
5
4
5
4
3
3
3
3
3
14 GCMs
5
4
5
5
3
3
3
3
3
9 GCMs
8
18
2
14
8
8
8
10
18
4
12
8
18
18
8
8
4
8
6
10
8
6
8
8
8
8
4
8
4
4
20
31 GCMs
54 runs/108 chunks
34 runs/68 chunks
284 chunks
Sum
207
11
208
209
210
211
212
213
214
215
Table S2. Estimated attributable changes in PI (δPI, in percent), in percentage of annual
extreme precipitation, and return periods in 2000s for a 20-yr event in the 1950s in
RX1day and RX5day due to anthropogenic forcing. The second column indicates spatial
domains used in the detection and attribution analyses for one (NH), two (ML+TR) and
three (NA+EU+AS) dimensions. The third column indicates the results for single-signal
(ANT) or two-signal (ANT+NAT) analysis. The first, second, third columns under
RX1day and RX5day correspond to results for the lower 5%, the median, and the upper
95% of changes, respectively.
RX1day
NH
δPI (%)
ML+TR
NA+EU+AS
NH
Changes in annual extreme precipitation
(%)
ML+TR
NA+EU+AS
Return period in 2000s for a 20-yr event
in 1950s (year)
NH
ML+TR
RX5day
2signal
1.544
3.923
6.333
2.396
4.743
7.158
ANT
1.685
4.049
6.463
2.839
5.112
7.486
2signal
1.569
4.069
6.614
1.926
4.396
6.946
ANT
1.776
4.250
6.790
2.527
4.893
7.366
2signal
1.353
3.541
5.774
2.354
4.650
7.039
ANT
1.383
3.506
5.664
2.550
4.708
6.950
2signal
1.249
3.243
5.356
1.910
3.859
5.958
ANT
1.365
3.351
5.474
2.272
4.174
6.250
2signal
1.270
3.369
5.610
1.529
3.566
5.770
ANT
1.439
3.524
5.769
2.016
3.987
6.143
2signal
1.093
2.917
4.858
1.875
3.781
5.852
ANT
1.117
2.887
4.760
2.035
3.830
5.773
2signal
18
15
12
16
14
11
ANT
18
15
12
16
13
11
2-
18
15
12
17
14
12
12
signal
NA+EU+AS
ANT
17
14
12
16
14
11
2signal
18
15
13
16
14
12
ANT
18
15
13
16
14
12
216
13
217
218
219
220
221
Figure S1. Locations of long-term grids for RX1day from HadEX and HadEX2. A grid is
222
considered as a long-term grid if there are no more than 10 missing years during 1951-
223
2003 for HadEX or during 1951-2005 for HadEX2. Note that because of missing values
224
in the more recent years, some Russian grid boxes that were considered to have
225
sufficient records in HadEX (up to 2003) do not meet the selection criteria for HadEX2
226
(up to 2005). Black dots, green circles, and red circles indicate HadEX, HadEX2, and
227
merged HadEX2+Russian data points, respectively. The horizontal dashed black line
228
shows the division between the tropics and middle-latitude regions, while the vertical
229
blue lines delineate the three west-east regions used in the analyses.
230
231
14
232
233
234
235
236
237
238
239
240
241
Figure S2. Time series of annual (thin lines) and non-overlapping 5-yr mean (thick
lines) area-averaged PI over Northern Hemisphere land during 1951-2005. a,
RX1day, b, RX5day. For each panel, red lines represent averages obtained from
HadEX2 data while blue lines from merged HadEX2/Russian data.
242
15
243
244
245
246
247
248
249
250
251
252
Figure S3. 5-yr average of PI for RX1Day based on different datasets: HadEX, HadEX2,
and HadEX2+Russia are averages from their respective long-term grids;
HadEX2+HadEXmask and HadEX2+Russia+HadEXmask are averages from HadEX2
and the merged HadEX2+Russian data but masked by the availability of HadEX longterm grids.
16
253
254
255
256
257
258
259
260
261
Figure S4. 5-yr average PI for RX5day over Northern Hemispheric land based on
merged HadEX2 and Russia data computed by (1) fitting GEV distributions to individual
grids (GEV), and (2) by using a ranking based method (ranking) where PIt=(nt0.31)/(N+0.38)*100. Here N is the number of years in the record while nt is the rank of
the data value in year t.
17
262
263
264
265
266
267
268
269
270
271
272
273
RX1day, OBS
RX5day, OBS
RX1day, OBS, Smoothed
RX5day, OBS, Smoothed
RX1day, ALL
RX5day, ALL
RX1day, NAT
RX5day, NAT
Figure S5. Linear trends of extreme precipitation indices (PI) during 1951-2005 in
observations (OBS, first row; and OBS with 9-point spatial smoothing, second row),
in model simulations with combined anthropogenic and natural forcing (ALL, third
row), in model simulations with natural forcing (NAT, fourth row). For each pair of
panels, results are shown for annual maximum one-day (RX1day) and five-day
(RX5day) precipitation amounts. For model simulations, ensemble means of trends
from individual simulations are displayed. Units: probability (in percent) over 55 year
period.
274
275
18
276
277
278
279
280
281
282
283
284
285
286
Figure S6. Results from single-signal non-optimized detection analyses of extreme
precipitation indices for RX1day (upper panel) and RX5day (lower panel). Best
estimates (data points) and 5-95% confidence intervals (error bars) of the scaling
factors are displayed for ALL, ANT and NAT, when using five-year mean PI averaged
over mid-latitude (ML), northern tropics (TR), western Hemisphere land (NA), western
East Hemisphere land (EU), and eastern East Hemisphere land (AS), Northern
Hemisphere (NH), and when using two regional averages (ML+TR) or three regional
averages (NA+EU+AS).
287
19
288
All
Ant
NH
ML+TR
NA+EU+AS
289
290
291
292
Figure S7. Residual consistency statistics for RX1day and RX5day annual mean PI


as a function of number of EOFs retained when covariance matrices. C N 1 and C N 2
293
294
295
are estimated with independent noise data N1 and N2, respectively. The pink and
blue curves depict the 5%-95% acceptance region for the test of consistency
between model-simulated and residual-observed variance.
296
20
297
ALL
ANT
NH
ML+TR
NA+EU+AS
298
299
300
301
302
303
304
305
Figure S8. Estimated scaling factors and their 90% confidence intervals from singlesignal analyses for annual series corresponding to different number of EOFs
retained in the analyses for NH (upper panel), ML+TR (middle panel), and
NA+EU+AS (lower panel).
306
21
307
RX1day
RX5day
NH
ML+TR
NA+EU+AS
308
309
310
311
312
313
Figure S9. Estimated scaling factors and their 90% marginal confidence intervals
and 90% joint confidence region from two-signal analyses for annual series
corresponding to different number of EOFs returned in the analyses for NH (upper
panel), ML+TR (middle panel), and NA+EU+AS (lower panel).
22
314
315
Figure S10: Results from single-signal optimal detection analyses of extreme
316
precipitation indices for RX1day and RX5day for time period 1951-2000. Best estimates
317
(data points) and 5-95% confidence intervals (error bars) of the scaling factors are
318
displayed for ALL (red), ANT (green) and NAT (blue), when using five-year mean PI
319
averaged over Northern Hemisphere (NH), and when using two regional averages
320
(ML+TR) or three regional averages (NA+EU+AS).
321
23
322
323
324
325
326
327
328
329
330
331
332
a: RX1day, NH
b: RX1day, ML+TR
c: RX1day, NA+EU+AS
d: RX5day, NH
e: RX5day, ML+TR
f: RX5day, NA+EU+AS
Figure S11: Results from two-signal optimal detection analyses of extreme
precipitation indices. a, b, c, for RX1day, and d, e, f, for RX5day for time period
1951-2000. Data points of the crossing between two error bars represent best
estimates of the scaling factors for ANT and NAT. The 5-95% marginal confidence
intervals of the scaling factors are displayed as error bars. The 5-95% joint
confidence regions are represented by ellipses. The left, central, and right panels
are for results when using five-year mean PI averaged over Northern Hemisphere
(NH), when using two regional averages combined (ML+TR), and using three
regions combined (NA+EU+AS).
333
24
334
335
336
a: RX1day, NH
b: RX1day, ML+TR
c: RX1day, NA+EU+AS
d: RX5day, NH
e: RX5day, ML+TR
f: RX5day, NA+EU+AS
Figure S12: Same as in Fig. S11 but for 1951-2005 using GCM simulations from the
7 GCMs for which both ALL and NAT runs are available.
337
25
338
339
340
341
342
343
344
345
346
a: RX1day, NH
b: RX1day, ML+TR
c: RX5day, NH
d: RX5day, ML+TR
Figure S13: Results from two-signal optimal detection analyses of extreme precipitation
indices. a and b for RX1day, and c and d for RX5day. The intersections of the two error
bars represent best estimates of the scaling factors for ANT and NAT. The 5-95%
marginal confidence intervals of the scaling factors are displayed as error bars. The 595% joint confidence regions are represented by ellipses. The left and right panels are
for results when using five-year mean PI averaged over Northern Hemisphere (NH), and
when using two (ML+TR) regional averages.
347
26