Changes in Floods and Droughts in a Warmer Climate
Anthony M. DeAngelis
Summer 2007
Introduction:
In a future climate with elevated CO2 concentrations, many studies have indicated that
the frequency and intensity of precipitation extremes and precipitation in general may change.
While a change in mean precipitation may not impose an immediate threat on human life and
property, changes in extreme precipitation can cause potentially serious problems. Floods and
droughts are major climatic events that can quickly alter and destroy many aspects of human
existence. In this study, we take interest in these events and study their potential changes in a
warmer climate.
Previous research has shed light on trends in precipitation and precipitation extremes over
the past. Groisman et al. 2004 references earlier papers showing a century long increase in mean
precipitation over much of the United States during the 20th century. They further show that the
increases in heavy and very heavy precipitation were more extreme than the mean increases, that
the contribution of extreme events to total precipitation has increased, and that these trends are
most notable in the eastern two-thirds of the country in the summer. A later study, Groisman et
al. 2005 finds statistically significant increases by 20% in the frequency of very heavy daily
precipitation events (> 99th percentile), all of which have occurred in the last third of the 20th
century. They further attribute these changes to an increase in atmospheric water vapor in a
warming climate, manifesting itself in increased cumulonimbus clouds and thunderstorm
activity.
Here, we study projected changes in mean and extreme precipitation following a global
increase of CO2 concentrations in the future. We look at the United States and analyze how and
by what degree the frequency and intensity of these precipitation characteristics will change. We
look at events of different time scales and during annual, summer, and winter periods. In
addition, we attempt to answer the question of why the climate will change in such a way.
Our hypothesis streams from the scientific concept that a warmer climate will give rise to
the intensification of the hydrologic cycle. The intensification of the hydrologic cycle would
lead to an increase in the intensity of evaporation, allowing for more water vapor in the air, and
ultimately more intense precipitation when the moister air converges. Emori and Brown 2005
and Meehl et al. 2005 show that in mid latitudes, both thermodynamic and dynamic effects
contribute to changes in mean and extreme precipitation. Our hypothesis rejects this and tests
the idea that changes in the hydrologic cycle alone can explain changes in precipitation
distribution in a warmer climate. We test that multiplying the control data by a constant scaling
factor will be enough to explain the changes in precipitation distribution brought on by elevated
CO2.
Materials and Methods
The climate model predominantly used in this study is called the GFDL CM2.1. The first
simulation we utilized is the CM2.1U_Control-1860_D4 experiment. This simulation is used as
our control data and consists of a coupled atmosphere + land and ocean + sea ice model with
forcing agents consistent with the year 1860 and given a 220 year adjustment period. The data
presented is daily and we use 100 years of the precipitation and evaporation output variables.
The second simulation is called the CM2.1U-D4_1PctTo4X_J1 experiment and is used as our
elevated CO2 data. This simulation increases CO2 levels at a rate of 1% per year for 140 years or
to the point of quadrupling. All non-CO2 forcing agents are held constant throughout the entire
experiment, and from years 141 through 300, CO2 is held constant. Here we look at the output
variables precipitation and evaporation (in daily form) for the last 100 years of this experiment
(201-300).
Although the GFDL CM2.1 model simulations produce data for the entire globe, we only
consider a portion of the data including the contiguous United States. Parts of southern Canada
and northern Mexico lie on the borders of our boundary and are included in some of the analyses.
Also, we combine the precipitation and evaporation data by subtracting evaporation from
precipitation (P-E), and using this quantity for a majority of the project. In the end, the two main
data sets utilized are a 36500x15x27 control matrix and a 36500x15x27 elevated CO2 matrix.
Essentially, there are 27 units of longitude, 15 units of latitude, and 36500 P-E values for each
location in time order.
We choose P-E because it gives one variable that combines the influence of precipitation
and evaporation for 1 day. High values of P-E in the 1 day data represent flash flooding events
for a particular location. With the use of Matlab 7.0, an elaborate calculating and graphing tool,
we combine the 1 day data into 2, 3, 7, 30, 60, 90, 180, and 360 day period lengths by taking
rolling averages of the date ordered data with length corresponding to the period length. High PE values in the 2, 3, 7, and 30 day data represent flood events of the corresponding period
lengths. Similarly, low P-E values in the 30, 60, 90, 180, and 360 day data represent drought
events of the corresponding period lengths. We also look at annual, summer, and winter data.
Annual data is simply the entire data set, summer data is obtained by pulling out data points
congruent with the months May through September, and winter data is obtaining by pulling out
data points corresponding to November through March.
One aspect of our research involves using the data to represent how extreme precipitation
(floods and droughts) is changing between the control and elevated CO2 climate over the region.
We produce maps that show the change in frequency in extreme precipitation events between the
different climate types. The primary method of doing this is to order the P-E data from lowest to
highest and discover the values of fundamental percentiles in the control data. The percentiles
we use are the 1st, 2nd, 5th, 95th, 98th, and 99th. We then calculate the frequency of events that lie
<1st, <2nd, <5th, >95th, >98th, and >99th percentiles for each point for both the control and elevated
CO2 data while keeping the percentile values constant (obtained from the control data). Finally,
we calculate the percent change in frequency for each percentile range between the control and
elevated CO2 data, and plot these numbers on a map. This procedure is done for the higher
percentiles in lower period lengths (1, 2, 3, 7, and 30 day) to represent flood events, and for the
lower percentiles in higher period lengths (30, 60, 90, and 180 day) to represent droughts. In the
summer and winter analysis, the 180 and 360 day period lengths are omitted.
We also look at how the intensity of precipitation extremes changes between the different
climates in a similar fashion. After ordering the data from lowest to highest, we obtain the
values of the same percentiles as above for both the control and elevated CO2 data (but also
include the median in the annual analysis) and calculate the absolute change in the percentile
values between the control and elevated CO2 climate for each location. These numbers are then
mapped.
Next, we pick locations that show distinct frequency change trends between the control
and elevated CO2 climate for annual, summer, and winter seasons. These trends are increased
floods and increased droughts, increased floods and decreased droughts, decreased floods and
increased droughts, and decreased floods and decreased droughts. We then develop histograms
using bins that are consistent with the unique control percentile values for each location. The
percentile values used are the minimum, 1st, 2nd, 5th through 95th in increments of 5, 98th, 99th,
and the maximum. By holding the bins constant and changing the data, we produce different
histograms using different data sets. One outcome is a histogram showing the frequency changes
in the percentile bins between the control and elevated CO2 climate. The information obtained is
similar to that in the percentile frequency change map analysis, but uses more bins and covers all
period lengths, making it more detailed.
Another facet of our research is to attempt to explain why the observed changes in
precipitation extremes are happening as a result of the changing level of CO2. As described in
the introduction, our hypothesis is that simply scaling the control data by a constant factor will
be enough to explain the change in distribution of P-E seen in the elevated CO2 data. To
determine the scaling factor, we use the CM2.1U_Control-1860_D4 and CM2.1UD4_1PctTo4X_J1 experiments model data to calculate the globally and time averaged ratio of
precipitation and evaporation between the control and elevated CO2 climate for the same years as
the daily data. We obtain a ratio of 1.0581 for both precipitation and evaporation, which is used
as our scaling factor.
To quantitatively test our hypothesis, we use two statistical tests. The first is the
Kolmogorov-Smirnov Test which returns D, the absolute maximum distance between the plotted
distributions (percentage of data to the left of a value vs. data) and the probability that the
distributions are the same. Values of D closer to zero and probabilities closer to 1 indicate better
distribution correlation. The other test is a variant of the first entitled Kuiper’s Test, which
returns V (similar to D but the sum of the maximum positive and negative distance) and the
probability that the distributions are the same.
We perform these tests to the scaled control (control data multiplied by 1.0581) and the
elevated CO2 data for each location and map the results. The procedure is applied to all period
lengths for annual data only. Additionally, we look at only half the data set (where P-E < 0) to
see if the results are better. We also apply the tests to the unchanged control and elevated CO2
data as a method of assessing the improvements in distribution correlation after scaling the
control data, and also to assess the differences in distribution between the control and elevated
CO2 data. This is done for all period lengths for annual, summer, and winter seasons. The
absolute percentile change maps can also be used to more specifically show how the P-E
distributions change between the control and elevated CO2 climate for the region.
When looking at the same individual locations discussed above, we produce a histogram
where scaled control data is used. We also produce QQ-plots, where the elevated CO2 data is
plotted against the control data, and where the elevated CO2 data is plotted against the scaled
control data. The purpose is to assess if and how the distribution is improving after scaling the
control data, and where the distributions differ most before and after scaling. Also, certain
locations that show distribution correlation improvement after scaling for both tests are put under
a detailed analysis where we try higher scaling factors. Furthermore, we perform the statistical
tests on precipitation alone for a few locations.
Results
Changes in floods and droughts in an elevated CO2 climate.
The percentile frequency change charts showing the change in extreme precipitation in an
elevated CO2 climate at the annual level show a general increase in the frequency of floods
across the much of the northern part of the United States, including the northern Rockies and a
majority of the east coast. Elsewhere, there is little or no distinct trend (see Figure 1). Longer
period lengths show a more intense frequency increase and a spreading of positive values. Also,
frequency increases are more intense and widespread in bins that are narrower and closer to the
maximum, such as the >98th and >99th percentile bins, indicated a greater increase in the more
extreme floods.
Figure 1: Frequency changes in 1 day flood events in an elevated CO2 climate.
> 99 Percentile Frequency Change (From Control to 4x CO2) (1 Day, Annual)
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The percentile frequency change charts for droughts at the annual level show an increase
in the frequencies of droughts across many parts of the northern and eastern sections of the
region, with no change or decreases near the central US/ Canadian border. This pattern more or
less holds for period lengths up to 90 days. For long period droughts of 360 days, parts of the
east show frequency decreases as well as parts of the northwest, which is mainly due to a
decrease in droughts in winter for these areas. Figure 2 (next page) contrasts short and long
period droughts. For all period lengths, the relative pattern of change in less extreme droughts
holds but positive and negative values become more intense as the droughts become more
extreme (<2nd and <1st percentile). The southwestern parts of the region and some coastal points
have been omitted from this analysis. We discuss the reason for this later.
The percentile frequency change charts for winter and summer show some regions with
different patterns in the change of floods and droughts from the annual. The pattern of increases
in the frequency of floods is confined further north in the summer and areas in the southwest
show frequency decreases. In the winter, the pattern of increases extends further south than the
annual, and the southwest sees frequency increases. The pattern of droughts between the annual
and summer data is very similar, except for changes in magnitude. In winter, the north and east
see frequency decreases in droughts and in the summer these regions show frequency increases.
Figure 2: Contrast between projected changes in short and long period droughts.
< 1 Percentile Frequency Change (From Control to 4x CO2) (90 Day, Annual)
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< 1 Percentile Frequency Change (From Control to 4x CO2) (360 Day, Annual)
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Figure 2: Left: Frequency change of <1st percentile 90 day droughts in elevated CO2 climate. Right: Same but for
360 day droughts.
The absolute percentile change maps generally agree with the trends shown in the
percentile frequency change maps for floods. Areas that see an increase in the frequency of
floods between the control and elevated CO2 climate also see an increase in the intensity of the
95th, 98th, and 99th percentiles. This is true for annual, summer, and winter seasons. For
droughts, the changes in the 1st, 2nd, and 5th percentile values are very little compared to changes
in the upper percentiles, therefore there is not much similarity between frequency changes and
absolute percentile changes for droughts. Another apparent trend with the absolute percentile
change maps is that the median changes very little if at all between the control and elevated CO2
data for all period lengths in the annual analysis.
An analysis of the mean P-E change between the control and elevated CO2 climate for
annual, summer, and winter seasons shows that in many parts of the north and east, the direction
of change in the mean is consistent with that of the upper percentiles. However, the magnitude
of the mean change is much smaller than that of the upper percentiles. Elsewhere, changes in
mean P-E aren’t as consistent in direction with changes in upper or lower percentiles. For
instance, in summer, the upper northeast shows decreases in the mean but increases in upper
percentiles, which is also true in winter in the southwest.
In the individual location analyses, the elevated CO2 histogram (with bins being the
control data percentile values) generally show the same pattern of frequency changes of flood
and drought events as is indicated by the percentile frequency change maps. On the flip side,
some locations show a different trend in droughts for period lengths that are shorter than is
typical for a drought event. For example, south-central Canada, southeast-central Canada, and
southeast Canada all show an increase in the frequency of floods and a decrease in the frequency
of droughts in an elevated CO2 climate for annual, summer, and winter seasons respectively. In
the full histograms, all three locations show an increase in the frequencies of extreme
evaporation events for short period lengths, but a decrease in these events for long period
lengths. Similarly, in winter north-central Mexico shows a decrease in floods and an increase in
droughts in an elevated CO2 climate, but shows a decrease in extreme evaporation events for
short period lengths.
Comparing scaled control climate with elevated CO2 climate.
In this part of the analysis, we test the idea that scaling the control data will do enough to
match the distribution of the elevated CO2 data. The Kolmogorov-Smirnov (KS) and Kuiper
(KP) statistical test maps for annual data show that the distributions between the scaled control
and elevated CO2 data are very different for all locations in the region. The overall lowest D
value across all period lengths in the KS test is 0.014247 corresponding to a probability of
0.0012. The overall lowest V value in the KP test is 0.022164 corresponding to a probability of
1.0946e-006. In the KS test, parts of the Rockies and the northeast show an increase in D values
as the period length grows to 360 days, while other regions see less significant changes. The KP
test shows the same geographic pattern of increasing V values with increasing period length.
Despite the lack of distribution correlation between the scaled control and elevated CO2
data, many areas show improvement in distribution correlation after scaling. More specifically, a
large region stretching from the east and northeast into the northwest shows lower D values (and
thus higher probabilities) after scaling the control data in the KS test. The KP test results also
show improvements in the same geographic areas. For both tests, the magnitude of drop in D
and V values is more significant in longer period lengths. Other regions show little change or
minor increases in D and V values. The most apparent occurrence of worsening distribution
correlation is along the west coast in longer period lengths.
The unanticipated results obtained from this part of the analysis indicate that scaling the
control data is not enough to explain the changes in distribution seen in the elevated CO2 data.
Looking back to the results from the absolute percentile change analysis between the scaled
control and elevated CO2 climate, we see that a reason for the lack of distribution correlation is
that lower percentiles are not changing or are decreasing slightly and higher percentiles are
increasing more dramatically in areas that show improvement in distribution correlation after
scaling. This is true for all period lengths. Figure 3 (next page) shows this trend.
Streaming from this conclusion, we test to see if the lower half of the P-E distribution
responds better to the statistical tests, as the overall changes in the lower half of the distribution
aren’t dramatic. We only look at P-E < 0 and apply the test to the entire region for all period
lengths in the annual data. The results show that overall, the results here are similar to those
obtained for the full P-E data set for both tests. The magnitudes of D and V are similar or
slightly worse where P-E < 0 and geographic regions that show increases in D and V values with
increasing period length are roughly the same. The 180 and 360 day maps are omitted from this
analysis because some locations contain all positive P-E values. These results show that scaling
the negative portion of the control P-E distribution does not show a better correlation with the
elevated CO2 distribution than the full P-E distribution analysis.
In this analysis, the lowest D value in the KS test obtained at a non-coastal location was
approximately 0.009, corresponding to a probability of about 0.10. This is the highest
probability obtained in all statistical test analyses performed in this research, but is still close to
zero and would indicate that the distribution correlations are different. For the KP test, there
were no con-coastal V values that were below 0.012, indicating that all probabilities were at or
below 0.10. Some coastal points in the P-E < 0 analysis show probabilities close to 1, but this
data has to be eliminated for reasons discussed later.
Figure 3: Contrast in changes in lower and higher percentile values.
1 Percentile Change (From Scaled to 4x CO2) (1 Day, Annual)
99 Percentile Change (From Scaled to 4x CO2) (1 Day, Annual)
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Figure 3: Left: 1st percentile change between scaled control and elevated CO2 climate for 1 day annual data. Right:
Same but for the 99th percentile.
Figure 4: Comparing statistical test results between the full P-E and P-E < 0 data.
KS Test Scaled Control Map (1 Day, Annual)
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Figure 4: Upper Left: KS statistical test results for full P-E data set in 1 day annual analysis. Upper Right: Same as
upper left but for P-E < 0 analysis. Bottom Left: Changes in D values before and after scaling (positive values
indicate smaller D values after scaling) for full P-E data set in 1 day annual analysis. Bottom Right: Same as bottom
left but for P-E < 0 analysis.
The statistical test maps showing changes in D and V values show areas where D and V
become lower in a broad region in the northeast stretching into the northwest. With longer
period lengths, the magnitude of these differences is slightly larger. This trend is similar to what
is seen in the full P-E analysis. In the 1 day analysis, the improvements are somewhat greater in
the P-E < 0 data set (shown in Figure 4), but this trend diminishes in longer period lengths.
Also, longer period lengths in the P-E < 0 analysis show an area near the US/ Canadian border
where D and V values become higher after scaling. This finding is inconsistent with the full P-E
analysis. Figure 4 (previous page) compares KS statistical test results for 90 day data between
the full P-E and P-E < 0 analysis.
Finally, we look at individual locations that show improvements in distribution
correlation after scaling the full P-E data set and test if increasing the scaling factor shows
probabilities that approach 1. The locations put under the analysis are northern Maine (1 day,
annual), south-central Canada (1 and 90 day, annual), southwest Michigan (90 day, summer),
southeast-central Canada (1 day, summer), central Utah (1 day, winter), southwest-central
Canada (1 day, winter), southeast Canada (1 and 90 day, winter), Maryland (1 and 90 day,
annual), and the Carolinas (1 and 90 day, annual).
Overall, the results show that there are no locations where the probability exceeds
0.0071612 for either the KS or KP test. In general, increasing the scaling factor improves the
probabilities to a certain extent, with each location having a unique optimum scaling factor
ranging from 1.055 in The Carolinas for the KP test to 2.675 in southwest-central Canada for the
KS test. On average, the optimum scaling factor for all locations and both tests is 1.435.
Furthermore, we look at QQ plots plotting the elevated CO2 data versus the scaled control data
using the optimum KS test scaling factor for each location. All QQ plots show that the greatest
difference in magnitude between the scaled control and elevated CO2 data occurs to the right of
the median. In some instances, differences in distribution correlation occur only to the right of
the median, and in others both the left and right sides of the distributions show similar
differences, with differences appearing greater in magnitude to the right of the median. This
trend agrees with what is seen in the absolute percentile change maps between the scaled control
and elevated CO2 climate. Figure 5 (next page) contrasts three general types of best scaled QQ
plots seen in this analysis.
We also look at precipitation alone for Maryland and the Carolinas in 1 day annual data
and perform the statistical tests analysis using the original scaling factor of 1.0581 and increased
scaling factors. We find that probabilities are better than in the P-E analysis for both locations
but are still quite low. The highest probability obtained in this analysis is 0.03962 in the
Carolinas in the KS test with a scaling factor of 1.036. Overall, increasing the scaling factors in
this analysis does not prove to be helpful, as the average optimum scaling factor for both
locations and both tests is 1.0475, less than our original scaling factor of 1.0581.
The cumulative results testing our hypothesis that scaling the control data will be enough
to explain distribution changes in the elevated CO2 data is disproved. Clearly, there are
mechanisms more complicated than a simple scaling of the hydrologic cycle that are contributing
to the change in climate between the 1860 and quadrupled CO2 climate.
Figure 5: Contrast in appearance of best scaled QQ plots.
Plot of 4X CO2 versus Best Scaled Control P-E for 93.8W, 49.5N (90 Day, Annual)
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4X CO2 P-E (mm/day)
Plot of 4X CO2 versus Best Scaled Control P-E for 68.8W, 47.5N (1 Day, Annual)
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Figure 5: Upper Left: Best scaled QQ plot for northern Maine in 1 day annual analysis. Upper Right: Same but for
south-central Canada in 90 day annual analysis. Bottom Left: Same but for Maryland in 1 day annual analysis.
Solid red lines indicate the median for both data sets.
Discussion
Shortcomings:
In our first climate change analysis we omit the southwest region of the land mass from
the percentile frequency change discussion for droughts. The results for short term droughts and
summer droughts show a decrease in the frequency of extremely low P-E events between the
control and elevated CO2 climate, which is atypical of a dry and desert like region (Diffenbaugh
et al. 2006). Because we look at evaporation rather than potential evaporation, the amount of
soil moisture greatly affects the magnitude of surface evaporation that contributes to P-E. There
is a negative feedback between the level of soil moisture and the amount of evaporation over the
soil. As evaporation increases, soil moisture decreases, and the amount of water available to
evaporate decreases. Soon, a lack of soil moisture leads to little or no evaporation and
evaporation quantities contributing to P-E approach zero. We believe this is happening in our
data in the southwest United States. As the climate warms, evaporation increases initially,
drying out the soil, and eventually causing surface evaporation to decrease and P-E values to
rise. An analysis of soil moisture changes between the control and elevated CO2 climate
collected from GFDL CM2.1 model data shows that soil moisture is decreasing in the southwest
United States.
Similarly, the use of evaporation rather that potential evaporation has an impact on
coastal points that are partially water. With an unlimited amount of water that is available to
evaporate, there is no limit to how high surface evaporation can be, nor a limit to how low P-E
values can become. For many coastal locations in the drought frequency change analysis, we see
significant increases in the frequency of droughts that are discontinuous with surrounding
regions along some coastal points. For this reason we cannot make meaningful conclusions from
these points. We also see the effect of coastal points on the statistical test analysis where P-E < 0
along the west coast. The partially water characteristics of these points allow P-E to extend very
low in an elevated CO2 climate, ultimately causing the scaled control data to have a better
distribution correlation with the elevated CO2 data. Again, we have omitted the results obtained
from these points in this analysis.
Comparison of flood/drought change results with previous research
Diffenbaugh et al. 2006 find increases in the frequency of >95th percentile daily
precipitation across parts of the Pacific Northwest in an elevated CO2 climate. Though our
results do not converge on the areas of most intense increase, we also find increases in the same
measure across the same general region. In a more extended study of the entire United States,
Diffenbaugh et al. 2005 find increases in >95th percentile events across the east and northwest,
and statistically significant patterns in anomalies of mean and extreme precipitation to be similar.
Our results generally agree on both findings.
Leung et al. 2004 find increases in 95th percentile values across parts of the northwestern
United States. Our results show the same trend. Bell 2004 finds decreases in the frequency of
extreme precipitation events across much of the state of California. Our results show decreases
in the central and southern parts of the state, and little or no change elsewhere, which is similar
to this finding. Finally, Tebaldi et al. 2006 find increases in the contribution of >95th percentile
precipitation events to total precipitation for parts of the northeastern and northwestern United
States, and little or no change elsewhere. Our results show increases in >95th percentile events
and 95th percentile values in the same areas, and small changes or decreases elsewhere, which
would make sense with their findings.
Shifting our attention to mean precipitation, Diffenbaugh et al. 2005 find increases in
annual mean precipitation across the eastern US, which is consistent with our findings. Leung et
al. 2004 find increases in mean daily summer precipitation and decreases in mean daily winter
precipitation across the western US. Our results converge better on the finding of decreases in
mean daily winter precipitation in this region. Finally, Bell 2004 finds little change in mean
daily annual precipitation across much of the state of California. Our results show overall
decreases in this measure over California, which is inconsistent with this study.
Comparison of hypothesis results with previous studies
As discussed in the introduction, previous research has contributed both thermodynamic
and dynamic effects to changes in precipitation in a warmer climate. Thermodynamic effects
include changes in atmospheric moisture, and contribute to changes in precipitation when a
change in atmospheric moisture is carried to areas of mean moisture convergence (Meehl et al.
2005). Dynamic effects contribute to changes in atmospheric circulation. Emori and Brown
2005 find that in middle and high latitudes, both thermodynamic and dynamic effects contribute
to changes in mean and extreme precipitation. Furthermore, Meehl et al. 2005 find that
advective effects, indicated by sea level pressure changes, contribute to greatest precipitation
intensity increases over northeastern and northwestern North America. Since our region covers
mid-latitudes as well as the same regions in North America, our finding that the scaling of the
hydrologic cycle alone does not explain changes in extreme precipitation, is consistent with these
studies.
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