Changes in Floods and
Droughts in an
Elevated CO2 Climate
Anthony M. DeAngelis
Dr. Anthony J. Broccoli
Outline of Presentation
Introduction and Motivation for Research
 Model
 Changes in Floods/ Droughts
 Scaling Factor Hypothesis
 Conclusions
 Future Research
 References

Importance of Research
Floods and droughts are major climatic
events that can significantly impact
human life and property.
 Previous research has suggested that the
frequency of these events has changed
over the past century.
 The frequency of floods and droughts may
continue to change in a warmer climate
over the United States.

Projected Changes in Precipitation
Extremes
Frequency of Dry Days
Frequency of 95th percentile events
Anomalies in days/year.
Diffenbaugh et al. 2005, RegCM3, Resolution: 25 km
Our Climate Model
CM2.1
 Developed at NOAA’s Geophysical Fluid
Dynamics Laboratory (GFDL)
 Resolution: 2° latitude by 2.5° longitude.

Our Data
CM2.1U_Control-1860_D4 = Control data.
Coupled (atmosphere + land) and (ocean
+ sea ice) model with forcing agents
consistent with 1860.
 CM2.1U-D4_1PctTo4X_J1 = Elevated CO2
data. Increases CO2 from 1860 levels by
1% per year to quadrupling, then holds
CO2 constant.

Using P-E
Instead of studying precipitation alone, we
study precipitation minus evaporation (PE).
 The negative feedback between soil
moisture and surface evaporation affects
our results.
 As evaporation increases, soil moisture
decreases, and reduces the availability of
water in the soil. Thus, evaporation
increases slow or cease.

Assessing Changes in Extreme Precipitation
Events in Elevated CO2 Climate
Calculate 1st and 99th P-E percentiles for
control and elevated CO2 data for each
location.
 Calculate changes in frequencies of <1st,
and >99th P-E percentile events between
control and elevated CO2 data.
 Calculate changes in 99th P-E percentile
values between control and elevated CO2
data.

Assessing Changes in Extreme Precipitation
Events in Elevated CO2 Climate
We look at changes in >99th percentile P-E
events of period lengths 1 and 7 days to
assess changes in short and long term
floods.
 We look at changes in <1st percentile P-E
events for period lengths 90 and 360 days
to assess changes in short and long term
droughts.

Results: Changes in >99th Percentile
Frequencies (Floods)
Percent Changes in >99th percentile P-E frequencies ranging from -100 (blue) to 100 (red):
Annual, 1 Day:
Summer, 1 Day:
> 99 Percentile Frequency Change (From Control to 4x CO2) (1 Day, Summer)
> 99 Percentile Frequency Change (From Control to 4x CO2) (1 Day, Annual)
14
80
60
60
12
8
0
-20
6
Latitude Index (j)
Latitude Index (j)
20
10
20
8
0
-20
6
4
-60
-80
2
5
mn= -18.3562
10
15
Longitude Index (i)
20
25 % change
mx= 146.0274
10
15
Longitude Index (i)
20
14
0
-20
6
15
Longitude Index (i)
20
5
mn= -21.1921
25 % change
mx= 284.3407
10
15
Longitude Index (i)
20
8
0
-20
6
14
80
60
12
40
10
20
8
0
-20
6
-40
-60
-80
2
5
mn= -81.6327
10
15
Longitude Index (i)
20
25 % change
mx= 254.9669
> 99 Percentile Frequency Change (From Control to 4x CO2) (7 Day, Winter)
20
-60
10
-80
Winter, 7 Day:
10
4
-80
-60
40
-40
5
mn= -32.1429
25 % change
mx= 156.2092
60
12
Latitude Index (j)
Latitude Index (j)
20
2
-20
6
2
80
40
10
0
-40
> 99 Percentile Frequency Change (From Control to 4x CO2) (7 Day, Summer)
60
4
20
8
Summer, 7 Day:
80
8
10
4
-80
5
mn= -59.4771
> 99 Percentile Frequency Change (From Control to 4x CO2) (7 Day, Annual)
12
40
-60
2
Annual, 7 Day:
14
60
-40
-40
4
80
12
40
40
10
14
80
Latitude Index (j)
12
> 99 Percentile Frequency Change (From Control to 4x CO2) (1 Day, Winter)
Latitude Index (j)
14
Winter, 1 Day:
25 % change
mx= 280.9524
-40
4
-60
-80
2
5
mn= 5.5556
10
15
Longitude Index (i)
20
25 % change
mx= 451.3889
Results: Changes in <1st Percentile
Frequencies (Droughts)
Percent Changes in <1st percentile P-E frequencies ranging from -100 (blue) to 100 (red):
Annual, 90 Day:
Summer, 90 Day:
< 1 Percentile Frequency Change (From Control to 4x CO2) (90 Day, Annual)
< 1 Percentile Frequency Change (From Control to 4x CO2) (90 Day, Summer)
14
80
60
12
60
12
8
0
-20
6
10
20
8
0
-20
6
-40
4
-60
-80
2
5
mn= -62.6374
10
15
Longitude Index (i)
20
25 % change
mx= 544.5055
Annual, 360 Day:
< 1 Percentile Frequency Change (From Control to 4x CO2) (360 Day, Annual)
14
80
60
12
Latitude Index (j)
40
10
20
8
0
-20
6
-40
4
-60
-80
2
5
mn= -100
10
15
Longitude Index (i)
20
25 % change
mx= 1191.9668
80
60
12
40
Latitude Index (j)
Latitude Index (j)
20
14
80
40
10
< 1 Percentile Frequency Change (From Control to 4x CO2) (90 Day, Winter)
40
Latitude Index (j)
14
Winter, 90 Day:
10
20
8
0
-20
6
-40
4
-60
-80
2
5
mn= -100
10
15
Longitude Index (i)
20
25 % change
mx= 1080.9524
-40
4
-60
-80
2
5
mn= -100
10
15
Longitude Index (i)
20
25 % change
mx= 832.7869
Results: Comparison of Mean Changes
with Upper Percentile Changes
Mean P-E changes between control and elevated CO2 data: Ranging from -0.5 (blue) to 0.5 (red). 99th
Percentile daily P-E changes: Ranging from -10 (blue) to 10 (red). Units in mm/day.
Mean, Annual:
Mean, Summer:
Mean P-E Change from Control to 4x CO2 (Annual)
Mean P-E Change from Control to 4x CO2 (Summer)
14
0.4
0.3
0.4
0.3
12
10
0.1
8
0
-0.1
6
10
0.1
8
0
-0.1
6
-0.2
4
4
-0.4
10
15
Longitude Index (i)
10
15
Longitude Index (i)
6
0
-2
6
-8
10
15
Longitude Index (i)
20
25 P-E change
mx= 11.6056
-0.4
5
mn= -1.0176
10
15
Longitude Index (i)
20
25 Mean change
mx= 0.76744
(mm/day)
99th, Winter, 1 Day:
99 Percentile Change (From Control to 4x CO2) (1 Day, Winter)
14
8
6
12
4
10
2
8
0
-2
6
4
10
2
8
0
-2
6
-4
-4
-6
-0.3
2
6
12
Latitude Index (j)
Latitude Index (j)
2
5
mn= -1.532
-0.2
8
4
2
-0.1
99 Percentile Change (From Control to 4x CO2) (1 Day, Summer)
10
0
6
20
25 Mean change
mx= 1.2566
(mm/day)
14
8
4
0.1
8
99th, Summer, 1 Day:
99 Percentile Change (From Control to 4x CO2) (1 Day, Annual)
8
10
4
-0.4
5
mn= -0.65062
99th, Annual, 1 Day:
12
0.2
-0.3
2
20
25 Mean change
mx= 0.43137
(mm/day)
14
0.3
12
-0.2
-0.3
2
0.4
0.2
Latitude Index (j)
Latitude Index (j)
0.2
Latitude Index (j)
12
Mean P-E Change from Control to 4x CO2 (Winter)
14
Latitude Index (j)
14
5
mn= -0.42303
Mean, Winter:
4
-6
-8
2
5
mn= -6.4392
10
15
Longitude Index (i)
20
25 P-E change
mx= 23.5532
-4
4
-6
-8
2
5
mn= -3.0113
10
15
Longitude Index (i)
20
25 P-E change
mx= 13.927
Agreement with Previous Research
Diffenbaugh et al. 2005
 RegCM3 model (CO2 from A2 scenario)
 Resolution: 25 km, Entire US
 Increases in annual >95th percentile
precipitation events across east and
northwest US.
 Increases in annual mean precipitation
across eastern US.
 Similar patterns in direction of mean and
precipitation extreme anomalies.

Agreement with Previous Research
Leung et al. 2004
 PCM model (Doubling CO2 from 19952100)
 Resolution: 40 km, Western US
 Increases in winter 95th percentile
precipitation values across parts of the
northwestern US.
 Decreases in winter mean precipitation
across the western US.

Why does extreme precipitation change?
Our hypothesis: An intensification of the
hydrologic cycle only.
 Warmer temperatures  Increased
evaporation  Increased water vapor 
Heavier precipitation in areas and time
periods of convergence  Increased
droughts in areas and time periods of dry
weather.
 Scaling the hydrologic cycle by a constant
factor may explain the changes.

Testing Our Hypothesis
Multiply control data by constant scaling
factor of 1.0581 (globally and time
averaged percent increase in precipitation
and evaporation between control and
quadrupled CO2 climate).
 Perform Kolmogorov-Smirnov (KS) and
Kuiper (KP) statistical tests on
distributions of scaled control and elevated
CO2 data for all locations.

Testing Our Hypothesis

Kolmogorov-Smirnov Test (KS)


Yields D value: The maximum distance
between cumulative distribution functions of
scaled control and elevated CO2 data.
Yields Probability: Ranging from 0 to 1 where
small values show that the cumulative
distribution functions of both data sets are
significantly different.
Testing Our Hypothesis

Kuiper’s Statistic (KP)



Variant on Kolmogorov-Smirnov statistic
Yields V value: Sum of the absolute value of
maximum negative and positive distances
between the cumulative distribution functions
of the scaled control and elevated CO2 data.
Yields Probability: Same as for KS statistic.
KS and KP Statistical Test Results for PE 1 Day Annual Data
Scaled control and elevated CO2 distribution tested. Probability values ranging from 0
(blue) to 1 (red).
KS Test
KP Test
KS Test between Scaled Control and 4x CO2 (1 Day, ALL)
KP Test between Scaled Control and 4x CO2 (1 Day, ALL)
mx= 0.0011965
14
14
0.9
0.8
12
mx= 1.094e-006
0.9
0.8
12
0.7
0.6
8
0.5
0.4
6
Latitude Index (j)
Latitude Index (j)
0.7
10
10
0.6
8
0.5
0.4
6
0.3
0.3
4
0.2
0.1
2
5
10
15
Longitude Index (i)
20
Prob
25
mn= 0
4
0.2
0.1
2
5
10
ALL probabilities near 0
15
Longitude Index (i)
20
Prob
25
mn= 0
Annual Statistical Test Results for All
Period Lengths



The KS test yields an overall lowest D value of
about 0.0085, corresponding to a probability of
0.14.
The KP test yields an overall lowest V value of
above 0.012, corresponding to a probability
below 0.10.
These low probabilities indicate that the
cumulative distribution functions between the
scaled control and elevated CO2 data are different
for all locations and all period lengths (1, 2, 3, 7,
30, 60, 90, 180, 360 days).
Improvements in KS Test D Values and
KP Test V Values After Scaling
Change in D before and after scaling. ∆D values ranging from -0.05 (blue) to 0.05 (red). Positive values (yellow,
orange, red) indicate improvement.
KS, 1 Day:
KS Test Control-Scaled Map (30 Day, Annual)
mx= 0.017479
14
0.04
0.03
12
0.03
12
0
-0.01
6
10
0.01
8
0
-0.01
6
-0.02
4
4
-0.04
5
10
15
Longitude Index (i)
20
14
dD
25
mn= -0.0097808
10
15
Longitude Index (i)
20
KP Test Control-Scaled Map (30 Day, Annual)
mx= 0.019616
14
0.01
0
-0.01
6
-0.03
-0.04
10
15
Longitude Index (i)
20
-0.02
dD
25
mn= -0.013518
-0.03
-0.04
5
dV
25
mn= -0.019644
10
15
Longitude Index (i)
20
KP Test Control-Scaled Map (90 Day, Annual)
mx= 0.035946
14
10
0.01
0
-0.01
6
0.03
12
0.02
10
0.01
8
0
-0.01
6
-0.02
4
-0.03
-0.02
4
-0.03
-0.04
2
-0.04
2
5
10
15
Longitude Index (i)
20
dV
25
mn= -0.016369
mx= 0.054324
0.04
0.02
8
dD
25
mn= -0.022164
KP, 90 Day:
0.03
-0.02
5
-0.01
6
4
0.04
12
Latitude Index (j)
Latitude Index (j)
10
2
0
KP, 30 Day:
0.02
4
0.01
8
2
5
0.03
8
10
-0.04
2
0.04
12
0.02
-0.03
KP, 1 Day:
KP Test Control-Scaled Map (1 Day, Annual)
0.03
12
-0.02
-0.03
2
0.04
0.02
Latitude Index (j)
Latitude Index (j)
0.01
8
mx= 0.060806
14
0.04
0.02
10
KS Test Control-Scaled Map (90 Day, Annual)
mx= 0.037262
Latitude Index (j)
14
KS, 90 Day:
Latitude Index (j)
KS Test Control-Scaled Map (1 Day, Annual)
KS, 30 Day:
5
10
15
Longitude Index (i)
20
dV
25
mn= -0.030321
Comparison of Changes in 99th
Percentile Before and After Scaling
8
6
12
Latitude Index (j)
4
10
2
8
0
-2
6
-4
4
-6
-8
2
5
mn= -1.532
10
15
Longitude Index (i)
20
25 P-E change
mx= 11.6056
99th, Annual, 90 Day:
99 Percentile Change (From Control to 4x CO2) (90 Day, Annual)
14
1.5
12
1
10
0.5
8
0
6
-0.5
-1
4
-1.5
2
5
mn= -1.1809
10
15
Longitude Index (i)
20
25 P-E change
mx= 5.1223
99 Percentile Change (From Scaled to 4x CO2) (1 Day, Annual)
14
8
6
12
4
Latitude Index (j)
14
Latitude Index (j)
Between Control and Elevated CO2
99 Percentile Change (From Control to 4x CO2) (1 Day, Annual)
99th, Annual 1 Day:
10
2
8
0
-2
6
-4
4
-6
-8
2
5
mn= -2.8264
10
15
Longitude Index (i)
20
25 P-E change
mx= 9.7074
99th, Annual, 90 Day:
99 Percentile Change (From Scaled to 4x CO2) (90 Day, Annual)
14
1.5
12
Latitude Index (j)
99th, Annual, 1 Day:
Between Scaled Control and Elevated CO2
Absolute changes in P-E annual data: Ranging from -10 (blue) to 10 (red) in 1 day and from -2 (blue) to 2 (red)
in 90 day. Units in mm/day.
1
10
0.5
8
0
6
-0.5
-1
4
-1.5
2
5
mn= -1.3622
10
15
Longitude Index (i)
20
25 P-E change
mx= 4.8934
Does Using a Higher Scaling Factor
Yield Better Results?
Increasing the scaling factor improves
agreement in cumulative distribution
functions for many locations.
 However, the improvement is not
significant enough to conclude that the
scaled control and elevated CO2
distributions come from the same
population.

Does Scaling Precipitation Alone Yield
Better Results?
Scaling precipitation alone and comparing
its cumulative distribution function with
that of the elevated CO2 data gives higher
probabilities.
 However, these probabilities are still close
to zero, even when scaling factors are
increased beyond 1.0581.

Conclusions
Frequency of floods increases across the
north and east annually and in summer,
and nearly everywhere in winter.
 Frequency of droughts increases in east
annually and in summer, and decreases in
winter.
 With the exception of a few regions, the
direction of mean change is overall similar
to the direction of upper percentile
changes.

Conclusions
Magnitude of mean increases are
significantly smaller than those of upper
percentiles.
 Cumulative Distribution functions between
scaled control and elevated CO2 data are
different for all locations.
 Increasing scaling factors and performing
the analysis on precipitation alone
improves distribution agreement, but not
significantly.

Conclusions

It appears that one reason for the large
differences in cumulative distribution
functions is the inability for the scaling
factor to account for the large absolute
increases in upper P-E percentiles (99th)
between the control and elevated CO2
data.
Future Research
We seek to further understand how the
scaled control distributions differ from the
elevated CO2 distributions.
 If a simple linear scaling of the
hydrological cycle alone cannot explain
changes in extreme precipitation in a
warmer climate, what can?

References


Diffenbaugh NS, Pal JS, Trapp RJ, et al., 2005: Fine-scale
processes regulate the response of extreme events to
global climate change. Proceedings of the National
Academy of Sciences of the United States of America, 102,
15774-15778.
Leung LR, Qian Y, Bian XD, et al., 2004: Mid-century
ensemble regional climate change scenarios for the western
United States. Climatic Change, 62, 75-113.