Supplement to “How Much Changes in Precipitation Extremes in a Warming
Climate?”
Definition of Precipitation Intensity
The precipitation intensity is the amount of precipitation in a precipitation event
observed at a station divided by the duration of the event. However, meteorological
stations typically don’t report precipitation by the event, but rather report the amount
of precipitation over a fixed interval of time such as daily or hourly. Climate models
usually provide daily amount of precipitation averaged over the area of a grid point.
The GPCP data used in this work has a low time resolution of 5 days; daily data are
available after 1997. In these cases, the common practice of evaluating the
precipitation intensity is to divide the amount of precipitation by the interval of time,
for example, daily precipitation totals were treated as precipitation events by [Karl
and Knight, 1998]. In this work, we adopt this practice to evaluate the precipitation
intensity. The effect of different time resolution on the change in precipitation
intensity has been discussed by Liu et al. (2009). They found that the change in
precipitation intensity would increase with time resolution, but not by an amount that
would change the major conclusions of this study.
Intensity vs. Frequency
Because the large increase in top 10% heavy precipitation can increase the risk of
floods and mudslides, it is important to know whether the increase is due to frequency
or intensity or both. This question can be addressed by examining Figure S1 below
which shows amounts of precipitation in bins with 2 mm/day resolution for two cases:
one is average values of two coolest years (1984, 1985, blue bars) during the period of
GPCP data (1979-2007), the other being average values of two warmest years (1998,
2005, red bars). Total amounts of precipitation of the two cases differ very little with
the warm case about 2.8% higher. For individual bins the warm case has higher values
for precipitation intensity greater than 12 mm/day, which are compensated to a large
extent by decreases at precipitation intensity lower than 12 mm/day.
It is clear that the overall or average precipitation intensity of the two warm years
is significantly higher than the overall precipitation intensity of the two cool years.
Furthermore it can be seen that red bars reach 0.1 mm (lowest value in the figure) at a
higher intensity than blue bars, specifically blue bars becoming 0.1 mm around 50
mm/day, red bars near 64 mm/day. If one regards any value below 0.1 mm as zero,
then one can claim that heavy precipitation in the warm years breaks the record of the
cool years in the regime of precipitation intensity higher than 50 mm/day. In this case,
there is a clear increase in the intensity of precipitation with the global temperature.
On the other hand, the right side of the peak precipitation (i.e. >4 mm/day) is a
quasi-normal distribution which in theory will have a finite value at precipitation
intensity greater than 50 mm/day, and therefore no record-breaking is possible. In this
case, precipitation with intensity greater than 50 mm/day in the two warm years can
be reached by an increase in frequency of the precipitation from a finite value of the
two cool years. Similarly all increases at precipitation intensity greater than 12
mm/day can be explained by an increase in frequency of the corresponding
precipitation intensity of the two cool years, no change in intensity is needed. For
precipitation intensity less than 12 mm/day, all decreases other than the 2 mm/day can
be explained by a decrease in frequency, no change in intensity is needed.
The above discussion suggests that the changes in Figure S1 can be
accomplished by a change in either frequency or intensity or a combination of them.
This can be easily visualized in Figure S1: moving individual blue bars vertically (i.e.
changing the frequency) can reach the red bars; moving individual blue bars
horizontally (i.e. changing the intensity) can also reach the red bars. So for a
quasi-normal distribution like Figure S1, the overall increase in the precipitation
intensity is a statistical phenomenon which can be interpreted by an increase in either
frequency or intensity or a combination of them. In other words, one can’t distinguish
changes in frequency from those of intensity. Only for a specific precipitation event
can one distinguish changes in frequency from those of intensity.
Precipitation amounts (mm)
100
10
1
0.1
0
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
64
Intensity (mm/day)
Figure S1 Amounts of precipitation vs. precipitation intensity in bins of 2 mm/day
68
bin-width, blue bars being the average values of two coolest years (1984, 1985) in the
GPCP data period (1979-2007), red bars are the average values of two warmest
years (1998, 2005).
Inter-annual Method
Using the GPCP data as an example, all precipitation data for each 2.5o x 2.5o
box within 60oS – 60oN in 1979-2007 are gathered together and sorted into 10 bins of
equal precipitation amount according to their precipitation intensity. Thus, spatial and
temporal variations are included in our ΔP/ΔT ratios, with most of the heavy
precipitation coming from the tropics and the rainy months at mid-latitudes. The
ranges of the 10 bins (the ranges of the 10 bins are 0, 1.75, 2.92, 4.06, 5.28, 6.68, 8.35,
10.48, 13.43, 18.46 mm day-1, and infinite) are determined by this sorting and fixed
throughout the analysis. The precipitation amount within each bin for a given year is
sorted in the same way and then converted into a percentage of the long-term
(1979-2007) mean annual precipitation amount within each bin. The ΔP of each bin in
Figure S2 is the difference in the precipitation amount for each bin between any two
different years within 1979-2007 (including pairs not adjacent to each other, such as
1999 and 2007), and ΔT is the corresponding difference in the observed surface air
temperature and SST from Smith and Reynolds [2005]. However, ΔT for the
reanalysis is from the near-global (60oS-60oN) averaged 2m air temperature of global
models used in the reanalysis.
ΔP/ΔT ratios of the top 10% bin derived from the GPCP data are displayed as a
function of ΔT in Figure S2. Each horizontal bar represents the range in ΔT for a
group of 20 data points. The vertical bars denote 1-standard deviation range for the 20
data points of individual groups. Figure S2 is characterized by an obvious
convergence to an asymptotic value as suggested by the fact that the 1-standard
deviation range decreases with increasing ΔT. In fact, the horizontal line passing
through the mean value of ΔP/ΔT of the group at the largest ΔT near 0.5 oC is well
within the 1-standard deviation ranges of all individual groups. This implies that,
within the 1-standard deviation range, ΔP is practically linearly proportional to ΔT
throughout the entire range of ΔT. Furthermore, mean values of ΔP/ΔT of the groups
with ΔT greater than 0.2 oC are within 30% of the horizontal line. Therefore, in
practice the mean value of ΔP/ΔT of the group at the largest ΔT, with a value of
108.1% K-1 and a relatively small 1-standard deviation range of 9.7% K-1, can be
regarded as the representative of values of the ΔP/ΔT ratio of the top 10% bin derived
from the GPCP data. Similar results can be obtained for other bins of precipitation
intensity, and they are shown in Figure 1 in the main text.
References
Smith, T. M., and R. W. Reynolds (2005), A global merged land–air–sea surface
temperature reconstruction based on historical observations (1880–1997), J. Clim.,
18, 2021–2036, doi:10.1175/JCLI3362.1.
Figure S2 ΔP/ΔT of the top 10% bin of precipitation intensity derived from GPCP
as a function of ΔT. ΔP is the difference between the top 10% bins of any two years in
1979-2007, and ΔT is the difference in global temperatures of the two years. Each
horizontal bar represents the range in ΔT for a group of 20 data points. The vertical
bar denotes the one standard deviation range for the 20 data points of individual
groups.
Results from CMAP Data
Table S1 Comparison between standard and enhanced version of CPC Merged
Analysis of Precipitation (CMAP) pentad data from 1979 to 2007
DP/DT (%/k)
Bin 1
Bin 2
Bin 3
Bin 4
Bin 5
Bin 6
Bin 7
Bin 8
Bin 9
Bin 10
Standard
10.29
4.13
-5.33
-11.50
-13.21
-15.99
-16.64
-12.74
-9.52
31.99
Enhanced
4.37
-2.64
-11.56
-18.63
-20.16
-17.70
-14.86
-4.89
10.61
67.31
1 sigma DP/DT (%/k)
Bin 1
Bin 2
Bin 3
Bin 4
Bin 5
Bin 6
Bin 7
Bin 8
Bin 9
Bin 10
Standard
3.46
5.78
4.71
3.29
3.22
5.47
7.29
7.73
11.03
15.16
Enhanced
2.32
4.03
3.03
3.18
2.73
5.15
5.07
7.50
11.08
13.21
Ranges of Bins for Various Data Sets
Table S2 Ranges of 10 bins for standard and enhanced version of CPC Merged
Analysis of Precipitation (CMAP) pentad data from 1979 to 2007. The unit is in mm
day-1.
Data Sets
Precipitation types
Bin 1
Bin 2
Bin 3
Bin 4
Bin 5
Bin 6
Bin 7
Bin 8
Bin 9
Bin 10
Standard
Total
1.70
2.94
4.27
5.78
7.56
9.74
12.55
16.50
23.30
> 23.30
Enhanced
Total
1.66
2.73
3.86
5.17
6.76
8.76
11.37
15.05
21.51
> 21.51
Table S3 Ranges of 10 bins for total precipitation corresponding to the four data sets
shown in Figure 1 of main text. The unit is in mm day-1.
Data Sets
Precipitation types
Bin 1
Bin 2
Bin 3
Bin 4
Bin 5
Bin 6
Bin 7
Bin 8
Bin 9
Bin 10
NCEP/NCAR R1
Total
2.79
4.63
6.30
7.91
9.57
11.38
13.53
16.49
22.03
> 22.03
ERA-40
Total
2.68
4.71
6.66
8.69
10.91
13.52
16.81
21.80
31.68
> 31.68
GPCP Pentad
Total
1.75
2.92
4.06
5.28
6.68
8.35
10.48
13.43
18.46
> 18.46
Sun et al. (2007)
Total
2.10
3.90
5.60
7.50
9.50
11.90
14.90
19.00
27.00
> 27.00
Table S4 Ranges of 10 bins for convective and stratiform precipitation corresponding
to the two data sets shown in Figure 3 of main text. The unit is in mm day-1.
Data Sets
Precipitation types
Bin 1
Bin 2
Bin 3
Bin 4
Bin 5
Bin 6
Bin 7
Bin 8
Bin 9
Bin 10
Convective
1.85
3.94
5.99
7.95
9.88
11.89
14.14
16.88
21.38
> 21.38
Stratiform
0.79
1.78
3.07
4.58
6.36
8.53
11.31
15.27
22.14
> 22.14
Convective
2.20
3.73
5.18
6.66
8.27
10.13
12.48
15.77
22.08
> 22.08
Stratiform
1.14
2.01
2.93
4.05
5.75
8.66
13.14
20.34
34.41
> 34.41
NCAR CCSM3
ERA-40