HESSHydrology and Earth System SciencesHESSHydrol. Earth Syst. Sci.1607-7938Copernicus GmbHGöttingen, Germany10.5194/hess-19-877-2015Global trends in extreme precipitation: climate models versus observationsAsadiehB.basadie00@citymail.cuny.eduhttps://orcid.org/0000-0002-3606-2575KrakauerN. Y.https://orcid.org/0000-0002-4926-5427Civil Engineering Department and NOAA-CREST, The City College of New York, City University of New York, New York, USAB. Asadieh (basadie00@citymail.cuny.edu)12February20151928778915September201415October2014–9January2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://www.hydrol-earth-syst-sci.net/19/877/2015/hess-19-877-2015.htmlThe full text article is available as a PDF file from https://www.hydrol-earth-syst-sci.net/19/877/2015/hess-19-877-2015.pdf
Precipitation events are expected to become substantially more intense under
global warming, but few global comparisons of observations and climate model
simulations are available to constrain predictions of future changes in
precipitation extremes. We present a systematic global-scale comparison of
changes in historical (1901–2010) annual-maximum daily precipitation between
station observations (compiled in HadEX2) and the suite of global climate
models contributing to the fifth phase of the Coupled Model Intercomparison
Project (CMIP5). We use both parametric and non-parametric methods to
quantify the strength of trends in extreme precipitation in observations and
models, taking care to sample them spatially and temporally in comparable
ways. We find that both observations and models show generally increasing
trends in extreme precipitation since 1901, with the largest changes in the
deep tropics. Annual-maximum daily precipitation (Rx1day) has increased
faster in the observations than in most of the CMIP5 models. On a global
scale, the observational annual-maximum daily precipitation has increased by
an average of 5.73 mm over the last 110 years, or 8.5 % in relative terms.
This corresponds to an increase of 10 % K-1 in global warming since
1901, which is larger than the average of climate models, with
8.3 % K-1. The average rate of increase in extreme precipitation per
K of warming in both models and observations is higher than the rate of
increase in atmospheric water vapor content per K of warming expected from
the Clausius–Clapeyron equation. We expect our findings to help inform
assessments of precipitation-related hazards such as flooding, droughts and
storms.
Introduction
Trends in extreme meteorological events have received considerable attention
in recent years due to the numerous extreme events such as hurricanes,
droughts and floods observed (Easterling et al., 2000). Changes in global
climate and alteration of Earth's hydrological cycle (Allen and Ingram, 2002;
Held and Soden, 2006; Wentz et al., 2007) have resulted in increased heavy
precipitation with consequent increased surface runoff and flooding risk
(Trenberth, 1999, 2011), which is likely to continue in the future (Dankers
et al., 2013). Anthropogenic climate change is expected to change the
distribution, frequency and intensity of precipitation and result in
increased intensity and frequency of floods and droughts, with damaging
effects on the environment and society (Dankers et al., 2013; Field, 2012;
Min et al., 2011; O'Gorman and Schneider, 2009; Solomon et al., 2007;
Trenberth, 2011; Trenberth et al., 2003).
As a result of greenhouse gas (GHG) build-up in the atmosphere, global mean
near-surface temperature shows an increasing trend since the beginning of the
twentieth century (Angeles et al., 2007; Campbell et al., 2011; Singh, 1997;
Solomon et al., 2007; Taylor et al., 2007), with greater increases in mean
minimum temperature than in mean maximum temperature (Alexander et al., 2006;
Peterson, 2002). The Fifth Assessment Report of the Inter-Governmental Panel
on Climate Change (IPCC) indicates that, globally, near-surface air
temperature has increased by approximately 0.78 ∘C (0.72 to 0.85)
since 1900, with a greater trend slope in recent decades (Stocker et al.,
2013).
As a result of global warming, climate models and satellite observations both
indicate that atmospheric water vapor content has increased at a rate of
approximately 7 % K-1 warming (Allen and Ingram, 2002; Held and
Soden, 2006; Trenberth et al., 2005; Wentz et al., 2007), as expected from
the Clausius–Clapeyron equation under stable relative humidity (Held and
Soden, 2006; Pall et al., 2006). Increasing availability of moisture in the
atmosphere can be expected to result in increased intensity of extreme
precipitation (Allan and Soden, 2008; Allen and Ingram, 2002; O'Gorman and
Schneider, 2009; Trenberth, 2011; Trenberth et al., 2003), with a
proportionally greater impact than for mean precipitation (Lambert et al.,
2008; Pall et al., 2006). An increase in the frequency and intensity of
extreme precipitation has already been identified in observations (Alexander
et al., 2006; Min et al., 2011; Solomon et al., 2007; Westra et al., 2013) as
well as in simulations of climate models (Kharin et al., 2013; Scoccimarro et
al., 2013; Toreti et al., 2013). Climate models also indicate that further
increases in extreme precipitation would be expected over the next decades
(Kharin et al., 2007, 2013; O'Gorman and Schneider, 2009; Pall et al., 2006;
Toreti et al., 2013), while in terms of mean precipitation, moist regions
become wetter and dry regions drier (Allan and Soden, 2008; Chou and Neelin,
2004; Wentz et al., 2007; Zhang et al., 2007).
Although climate models generally indicate an increase in precipitation and
its extremes, the rate of this increase seems to be underestimated (Allan and
Soden, 2008; Allen and Ingram, 2002; Min et al., 2011; O'Gorman and
Schneider, 2009; Sillmann et al., 2013; Wan et al., 2013; Wentz et al., 2007;
Zhang et al., 2007), which implies that future projections of changes in
precipitation extremes may also be underpredicted (Allan and Soden, 2008).
This underestimation can be a result of differences in scale between climate
model grids and observational data (Chen and Knutson, 2008; Sillmann et al.,
2013; Toreti et al., 2013; Wan et al., 2013; Zhang et al., 2011) and/or
limitations in moist convection or other parameterizations in the models
(O'Gorman and Schneider, 2009; Wilcox and Donner, 2007). Assessments of
climate models also reveal that the rate of increase in precipitation
extremes varies greatly among models, especially in tropical zones (Kharin et
al., 2007; O'Gorman and Schneider, 2009), which makes it especially important
to compare modeled trends with those identified in observations. However, few
global comparisons of observations and climate model simulations are
available to constrain predictions of future changes in precipitation
extremes. Of the available global-scale studies, some use older versions of
climate models or observations and/or use only one or a few climate models
(Allan and Soden, 2008; Min et al., 2011; O'Gorman and Schneider, 2009; Wentz
et al., 2007; Zhang et al., 2007). Spatial and temporal differences in data
coverage between climate models and observations also challenge comparisons.
In this paper, we present a systematic comparison of changes in
annual-maximum daily precipitation in weather station observations (compiled
in HadEX2) with 15 models from the suite of global climate models
contributing to the latest phase of the Coupled Model Intercomparison Project
(CMIP5) (Taylor et al., 2012), as the largest and most recent set of global
climate model runs. Both parametric (linear regression) and non-parametric
methods – Mann–Kendall (Appendix A1) as well as Sen's slope estimator
(Appendix A2) – are utilized to quantify the strength of trends in extreme
precipitation in observations and models, taking care to sample them
spatially and temporally in comparable ways. We also calculate the rate of
change in the defined extreme precipitation index per K of global warming in
both observations and models to investigate the relation between global
warming and precipitation extremes. Climate models and observation data sets
do not provide the same spatial and temporal coverage for precipitation data,
leading to some uncertainties in the comparison of the results. In the
present study, precipitation data for years/grids of climate models that do
not have corresponding observational data are excluded, resulting in a
comparable sampling approach for both data sets.
Data and methodology
Precipitation data in the Hadley Centre global land-based gridded climate
extremes data set (HadEX2) is based on daily observations from about
11 600 precipitation stations gridded on a
2.54∘× 3.75∘ grid from 1901 to 2010 (Donat et al.,
2013). Here, gridded HadEX2 annual maximum 1-day precipitation data (Rx1day)
are analyzed as the observation data set. The Rx1day extreme precipitation
index is defined as the annual-maximum daily precipitation, in which the
maximum 1-day precipitation amount is selected for each year. The same index
is also obtained for the climate model simulations. Daily precipitation
amounts from simulations with 15 models (overall 19 runs) with complete
temporal data coverage have been retrieved from the fifth phase of the
Coupled Model Intercomparison Project (CMIP5) (Taylor et al., 2012), as the
largest and most recent set of global climate model (GCM) runs. The
historical data for projections from 1901 to 2005 and the high radiative
forcing path scenario (representative concentration pathway, RCP) RCP8.5
(Moss et al., 2010) for projections from 2006 to 2010 are selected. The
aforementioned 15 CMIP5 models, provided by the IRI/LDEO Climate Data
Library, are BCC-CSM1-1, CMCC-CM, CMCC-CMS, CNRM-CM5, GFDL-CM3, GFDL-ESM2G,
HadGEM2-CC, IPSL-CM5A-LR, IPSL-CM5A-MR, IPSL-CM5B-LR, MIROC5 (three runs),
MPI-ESM-LR (three runs), MPI-ESM-MR, MRI-CGCM3 and NorESM1-M.
(a) Global averaged extreme precipitation and
(b) linear regression trend slope averaged over HadEX2 grid cells
with a different minimum number of years with extreme precipitation data
available. (c) Map of the number of annual extreme precipitation
records in HadEX2 (1901–2010). (d) Minimum number of years with
extreme precipitation data available versus the percentage of the grid cells
with corresponding coverage.
Climate models produce simulated precipitation fields for all years of a
specified time interval, covering all coordinates of the globe thoroughly,
even the oceans and polar zones. This is completely different from the
spatial and temporal coverage of station observation data sets, such as
HadEX2, where usually cover only a certain part of the continents, with
missing data for a considerable number of years. This difference in coverage
results in some difficulties in comparison of the two data sets.
As a solution for this issue, a new subsampled data set is created for each
of the 19 CMIP5 climate models in which each of the HadEX2 grid cells take
the GCM precipitation data of the grid cell in which its geo-referenced
coordinates fit. The new data set is created with the same resolution and the
same data availability pattern of HadEX2, which means that only data of the
grids/years will be assigned to the new data set for which HadEX2 has
recorded precipitation data for that year for the corresponding grid cell.
The newly created data set is called the subsampled CMIP5 data set.
As stated above, most grid cells in HadEX2 do not have recorded precipitation
data for most of the years. A sensitivity analysis of global averaged maximum
precipitation and trend slopes to the minimum number of years with
precipitation data required for a grid cell to be considered shows that these
values do not change drastically (Fig. 1a and b). Selection of only stations
with longer records may strengthen the confidence with which trends are
quantified, but limits the calculations to smaller spatial coverage of the
globe, which is not in line with the scope of this study to evaluate global
changes in precipitation. We chose to use the grid cells with at least 30
years of available precipitation data over the last 110 years, which includes
more than 90 % of the 766 HadEX2 grid cells that had any Rx1day data
(Fig. 1c and d).
Tests for trend detection in time series can be classified as parametric and
non-parametric methods. Parametric trend tests require independence and a
particular distribution in the data, while non-parametric trend tests require
only that the data be independent. The trend slope (b) obtained from the
linear regression method, which assumes that the data variability follows a
normal distribution, is utilized for trend strength analysis and comparison
of the data sets. The relative change in extreme precipitation is defined as
the trend slope divided by the average extreme precipitation of the grid
cell (b/P). The relative change in extreme precipitation per K of warming
is also calculated as an index for the relation between changes in
precipitation extremes of each grid cell with global mean near-surface
temperature, which indicates the percentage change in extreme precipitation
per K global warming. Linear regression is utilized to calculate this
parameter, in which global annual mean near-surface temperature obtained from
NASA-GISS (Hansen et al., 2010) is selected as the predictor and the natural
logarithm of extreme precipitation time series is chosen as the response.
Statistics of variation of global average extreme precipitation for
HadEX2 and the 19 subsampled CMIP5 model runs from 1901 to 2010. The 19
climate model runs give 19 global averages, of which the minimum, maximum,
median, mean, and standard deviation are presented.
The Z score (Z) obtained from the Mann–Kendall test (Kendall, 1975;
Mann, 1945) and the Q median (Qmed) from Sen's slope estimator
(Sen, 1968) are also applied in order to support the results of linear
regression using non-parametric trend detection approaches. It is important
to compare the non-parametric trend estimates with those obtained from linear
regression, since the extreme precipitation time series need not follow the
normal distribution but may instead be better represented by, for example,
the generalized extreme value distribution (Katz, 1999; Westra et al., 2013).
The trend tests are applied for each grid cell's extreme precipitation time
series. The obtained values are averaged globally as well as by continent in
order to present the general trend of precipitation extremes in different
regions. Continents studied comprise Africa, Asia, Europe, North America,
South America and Oceania. The subcontinent of India has results shown
separately and is also included in Asia. Results are also averaged by
latitude to investigate changes in the tropics versus the northern/southern
mid-latitudes.
The statistical significance of the trends, presented in the text as well as
the figures, at the 95 % confidence level is based on p values less
than 0.05 from the linear regression. The statistical significance of trends
estimated from the Mann–Kendall and Sen methods is evaluated differently
(Appendix A).
Results
Linear regression indicates that 66.2 % of the studied grid cells show a
positive trend in annual-maximum daily precipitation during the past
110 years, including 18 % that are statistically significant at the 95 %
confidence level. On the other hand, 33.8 % of the studied grids show a
negative trend, including only 4 % that are statistically significant at
the 95 % confidence level. The results are very similar to those found by
Westra et al. (2013) for the same HadEX2 data set (64 % positive and 36 %
negative). Thus, the global record of extreme precipitation shows a
meaningful increase over the last century. This increase is expected to
continue over the next decades, based on physical arguments and modeling
(Kharin et al., 2007, 2013; O'Gorman and Schneider, 2009; Pall et al., 2006;
Toreti et al., 2013).
Boxplots of CMIP5 model run averaged results (minimum,
25th percentile, median, 75th percentile and maximum of the 19 model runs) as
well as the average of HadEX2 observational data (shown as blue circles) for
1901–2010 extreme precipitation data on global and continental scales –
(a) annual-maximum daily precipitation (mm day-1),
(b) relative change in annual-maximum daily precipitation
(% yr-1), (c) linear regression slope of change in
annual-maximum extreme precipitation (mm day-1 yr-1), and
(d) trend slope from the Sen test (Qmed)
(mm day-1 yr-1). The red markers outside the boxes represent
model outliers.
Table 1 presents the statistics of global averaged trend parameters of
annual-maximum daily precipitation for HadEX2 and 19 subsampled CMIP5 model
runs (from 15 models) from 1901 to 2010. Observation is only one data set;
hence, it has one global average for each parameter. The 19 climate model
runs give 19 global averages, of which we present the minimum, maximum,
median, mean, and standard deviation in Table 1. Figure 2 illustrates the
results presented in Table 1 as boxplots of trend parameters and average
precipitation for annual-maximum daily precipitation for all 19 subsampled
data sets of CMIP5 on global as well as continental scales, showing
observations (HadEX2) as blue circles. The boxplots show the minimum,
25th percentile, median, 75th percentile and maximum values obtained from the
climate models. As seen in Fig. 2a., the global average of extreme
precipitation data shows a higher value than the largest value obtained from
the climate models, which indicates that all of the climate models
underestimate the annual-maximum daily precipitation. This underestimation
can be seen in continental scale averages as well, and is expected given the
difference in spatial scale between GCMs and station precipitation gauges.
The mean linear regression slope (b) for HadEX2 observation data globally
shows a positive trend of 0.052 mm day-1 per year in extreme
precipitation over the last 110 years (Table 1). This positive trend is
captured by the climate models but is significantly underestimated, since
HadEX2 shows a greater mean value of b than all but one of the values
obtained from CMIP5 models. This underestimation is seen particularly in the
continents of America, Europe and Oceania as well as the subcontinent of
India. The global average of relative change in precipitation (b/P) for
HadEX2 is close to the 75th percentile of the GCMs, which indicates that
approximately 75 % of the CMIP5 models have underestimated the relative
change in extreme precipitation, but is close to the average value of the
CMIP5 models. This substantial difference between the CMIP5 average and
median value can be linked to the large and positive skew scatter among the
results obtained from the models and the large inter-model standard deviation
(Table 1). The observational relative changes in extreme precipitation for
North America and Europe are higher than the values obtained from any of the
CMIP5 climate models but, for South America, Oceania, Asia and Africa, are
lower than the median of the CMIP5 models, suggesting that there may be
coherent spatial patterns in the model bias (Fig. 2) analogous to those seen
for changes in mean precipitation (Krakauer and Fekete, 2014).
Similar to the linear regression slope (b), Qmed from Sen's
test shows the direction and magnitude of the trend in a time series, having
the advantage of using a non-parametric method for the trend test. The global
average of Qmed for observations is 0.050 mm day-1 per
year (Table 1), very close to the average value of b obtained from the
linear regression, which further supports increasing trends in observational
annual-maximum daily precipitation. Considering the similar trend magnitudes
from parametric and non-parametric methods, similar values for the relative
change in annual-maximum daily precipitation are also expected from the two
methods. As seen in Fig. 2, the boxplots of the distribution of b and
Qmed over the climate models show very similar results on global
and continental scales (Fig. 2c and d, respectively).
HadEX2 observational data versus CMIP5 averaged results of global
extreme precipitation in 1901–2010 – annual-maximum daily precipitation map
(mm day-1) for (a) HadEX2 and (b) the average of
CMIP5 model runs.
HadEX2 observational data versus CMIP5 averaged results of global
extreme precipitation in 1901–2010 – linear regression slope of change in
annual-maximum daily precipitation map (mm day-1 yr-1) for
(a) HadEX2 and (b) the average of CMIP5 model runs.
Stippling indicates significance of the calculated trend at the 95 %
confidence level. In cases of CMIP5 average maps, filled/empty stippling
indicates a positive/negative trend on average. The larger marker size means
a larger number of models agreeing on the presented trend, with the largest
one indicating only 7 out of 19 model runs agreeing on the presented trend
significance, which also implies the discrepancy in the trend significance
between the climate models.
HadEX2 observational data versus CMIP5 averaged results of global
extreme precipitation in 1901–2010 – relative change in annual-maximum
daily precipitation (% yr-1) map for (a) HadEX2 and
(b) the average of CMIP5 model runs. Stippling indicates
significance of the calculated trend at the 95 % confidence level. In cases
of CMIP5 average maps, filled/empty stippling indicates a positive/negative
trend on average. The larger marker size means a larger number of models
agreeing on the presented trend, with the largest one indicating only 7 out
of 19 model runs agreeing on the presented trend significance.
Average parameter value at each 2.5∘ latitudinal window –
(a) annual-maximum daily precipitation (mm day-1) for HadEX2
and average CMIP5, (b) slope of change in annual-maximum daily
extreme precipitation (mm day-1 yr-1) for HadEX2 and average
CMIP5, and (c) relative change in extreme precipitation
(% yr-1) for HadEX2 and average CMIP5. Values for the climate models
are averages of the 19 runs and the dashed lines are the medians of the
models plus/minus the standard deviation of the models. The gap in the
tropics indicates the lack of grid cells with more than 30 years of
precipitation data available in those zones.
Relative change in extreme precipitation per K of global warming
(% K-1) maps for 1901–2010 for (a) HadEX2 observations and
(b) the average of CMIP5 model runs.
The last column of Table 1 presents a relative change in extreme
precipitation per K of global warming (% K-1). On a global scale, the
observed annual-maximum daily precipitation has increased by an average of
10 % K-1 of global warming since 1901, which is larger than the
average of climate models, with 8.3 % K-1. The Clausius–Clapeyron
equation under stable relative humidity indicates that atmospheric water
vapor content will increase at a rate of approximately 7 % K-1
warming (Held and Soden, 2006; Pall et al., 2006). The rates of increase in
extreme precipitation per K warming in both models and observations are
higher than the rate of increase in atmospheric water vapor content per K
warming expected from the Clausius–Clapeyron equation. Observational
relative change in extreme precipitation with respect to global warming is
also higher than all of the modeled values for North America and Europe, and
is higher than the model median for South America, Africa and India, but is
lower than the median of the models for Asia and Oceania (Fig. 8a).
Values of the Z score index obtained from the Mann–Kendall method shows
the non-parametric confidence level of statistical significance in the
identified trends in the data. The expectation might be that observational
data would have a lower confidence level in the identified trends due to
higher levels of noise in observations compared to climate model simulations.
However, Table 1 shows that the global average value of the Z score for
HadEX2 is higher than the largest value obtained from the climate models,
indicating that the CMIP5 climate models' simulations generally show lower
level of confidence in the trends compared to the HadEX2 observations. This
interesting finding that the level of internal variability in climate models
appears to be too high compared to observations warrants further
investigation.
Figure 3 depicts the global maps of the average of annual-maximum daily
precipitation (P) for HadEX2 (Fig. 3a) as well as the average of CMIP5
model runs (Fig. 3b). Figure 4 shows the linear regression slope (b) for
HadEX2 (Fig. 4a) and the average of CMIP5 model runs (Fig. 4b). Relative
change in extreme precipitation (b/P) for HadEX2 as well as the average of
CMIP5 model runs are illustrated in Fig. 5a and b, respectively. Stippling in
Figs. 4 and 5 means that the grid cell has a significant trend at the 95 %
confidence level. In cases of CMIP5 average maps, filled/empty stippling
indicates a positive/negative trend on average. While a larger marker size
means a larger number of models agreeing on the presented trend, the largest
marker size shown indicates only 7 out of 19 model simulations agreeing on
the presented trend significance, which also illustrates the discrepancy in
the trend significance between the climate models.
Figure 6 shows the average values of extreme precipitation (P), linear
regression trend slope (b) and relative change in extreme
precipitation (b/P) at each 2.5∘ latitudinal window (Fig. 6a–c).
The figure presents the result of the HadEX2 data set with the average result
of CMIP5 data sets as well as their mean ± SD. As seen in Fig. 6a, average extreme precipitation observed and
simulated in the Northern Hemisphere (NH) is lower than in the Southern
Hemisphere (SH), and the underestimation of extreme precipitation by the
climate models can also be seen. Figure 6b and c depict the fact that the SH
shows larger percentage changes in extreme precipitation than the NH.
Tropical zones of the globe show much higher ranges of fluctuations in both
observed and simulated extreme precipitation trends compared to
mid-latitudes, as well as a larger discrepancy between the observations and
simulations (Fig. 6). There is larger uncertainty regarding the results in
the tropics, due to fewer numbers of cells with observational data in these
regions. The failure of climate models to capture changes in tropical zones
has been reported by previous studies as well (Kharin et al., 2007; O'Gorman
and Schneider, 2009).
Figure 7 depicts the relative change in extreme precipitation per K of global
warming maps for HadEX2 observations (Fig. 7a) and the grid average of CMIP5
model runs (Fig. 7b). Boxplots of CMIP5 model run results as well as HadEX2
observational data (shown as blue circles) for relative change in extreme
precipitation per K of global warming on global and continental scales are
shown in Fig. 8a. Figure 8b shows the relative change in extreme
precipitation per K of global warming at each 2.5∘ latitudinal window.
As seen in Fig. 8b, the Southern Hemisphere shows higher ranges of relative
changes in extreme precipitation per K global warming than the Northern
Hemisphere. Similar behavior in fluctuations in observational extreme
precipitation per K warming can also be seen in Westra et al. (2013) in the
HadEX2 data set for 1900–2009, although the aforementioned study presents
the results as the median of the trends across grid cells instead of the
average.
Discussion
Results show that both observations and climate models show generally
increasing trends in extreme precipitation intensity since 1901. Although the
climate models reproduce the direction of observational trends on global and
continental scales, the rate of change seems to be underestimated in most
models, though the observations fall within the range of inter-model
variability for at least the global mean relative change (b/P). Similar
discrepancies between observations and climate models have also been reported
in earlier studies (Allan and Soden, 2008; Allen and Ingram, 2002; Min et
al., 2011; O'Gorman and Schneider, 2009; Sillmann et al., 2013; Wan et al.,
2013; Wentz et al., 2007; Zhang et al., 2007).
The global average of trends from the non-parametric method (Qmed
from Sen's slope estimator) show similar values to those obtained from the
parametric method (b from the linear regression) in observations,
confirming the results of the parametric method, which further supports an
increasing trend in observational annual-maximum daily precipitation (Table 1
and Fig. 2c and d). Also, the boxplots of b and Qmed for
climate models are very similar on global and continental scales for
different percentiles (Fig. 2c and d, respectively).
Tropical latitudes show higher ranges of fluctuations observed and simulated
for extreme precipitation trends compared to mid-latitudes, as well as a
larger discrepancy between the observations and simulations (Fig. 6). The
high variation of the results for observations as well as models might be due
to the small number of data available for those regions, given that the
models are sub-sampled the same way as the available observations. However,
the larger discrepancy between observations and models in tropics might also
be a result of inaccuracy of the climate models in simulation of tropical
climate and of precipitation generated by deep convection, as reported by
previous studies (O'Gorman and Schneider, 2009). The continents of North
America, Europe and Asia, respectively, contain about 22, 18 and 34 % of
total global data grid cells (Fig. 1c). The trend results averaged for the
continents of North America and Europe are generally in line with global
averaged results. The subcontinent of India generally shows different results
from the Asia average, in both observations and models (Figs. 2 and 8a).
The Clausius–Clapeyron equation indicates that atmospheric water vapor
content increases at a rate of 7 % K-1 of warming (Held and Soden,
2006; Pall et al., 2006). Although a change in global-mean precipitation with
respect to warming does not scale with the Clausius–Clapeyron equation and
from energy balance consideration, the rate of increase might be expected to
be around 2 % K-1 (Held and Soden, 2006). The impact of global
warming on extreme precipitation is expected to be close to the
Clausius–Clapeyron slope (Pall et al., 2006). The results of the present
study show that, on average, extreme precipitation since 1901 has increased
by 10 % K-1 of global warming in observations and 8.3 % K-1
in climate models over land areas with available station observations
(Table 1). North and South America as well as Europe show an even stronger
increase in extreme precipitation with respect to global warming (Fig. 8a).
These numbers are considerably larger than the 7 % K-1 of the
Clausius–Clapeyron equation, which further emphasizes the impact of changes
in the Earth's global temperature on precipitation extremes.
Relative change in extreme precipitation per K of global warming
(% K-1) in 1901–2010 – (a) boxplots of CMIP5 model run
averaged results (minimum, 25th percentile, median, 75th percentile and
maximum of the 19 model runs) as well as the average of HadEX2 observational
data (shown as blue circles) on global and continental scales and
(b) average changes at each 2.5∘ latitudinal window.
As stated earlier, increased availability of moisture in the atmosphere is
expected to result in a greater increase in intensity of extreme
precipitation than for mean precipitation (Lambert et al., 2008; Pall et al.,
2006). Faster change in extreme precipitation than mean precipitation implies
a change in precipitation pattern, where the climate shifts to fewer rainy
days and more intense precipitation. This can affect the availability of
fresh water resources throughout the year. Such changes in precipitation
pattern can affect the capability of reservoirs to capture excessive surface
run-off and result in increased flooding events. Failure of the available
reservoirs to capture the designed amount of annual surface run-off might
also result in a lower total annual amount of water stored in the reservoir,
and hence fewer available fresh water resources. The design of newly
constructed reservoirs strongly depends on the appropriate prediction of
future climate and precipitation extremes, but the available climate models
seem to underestimate those for at least some regions. The consequences of
changes in both mean and extreme precipitation for water resource system
reliability deserve to be investigated further.
Conclusions
This study presented a systematic global-scale comparison of changes in
historical annual-maximum daily precipitation between the HadEX2
observational records and a CMIP5 ensemble of global climate models. The
climate models were spatially and temporally subsampled like the
observations, and trends were analyzed for grid cells with at least 30 years
of extreme precipitation data over the past 110 years. Both parametric and
non-parametric methods were used to quantify the strength of trends in
extreme precipitation as well as the confidence level of the identified
trends. Results from both parametric and non-parametric tests show that both
observations and climate models show generally increasing trends in extreme
precipitation since 1901, with larger changes in tropical zones, although
annual-maximum daily precipitation has increased faster in the observations
than in most of the CMIP5 models. Observations indicate that approximately
one-fifth of the global data-covered land area had significant increasing
maximum precipitation recorded during the last century. This is more than 4
times larger than the areas with a significant decreasing record, which
indicates that the global record of extreme precipitation shows a meaningful
increase over the last century. On a global scale, the observational
annual-maximum daily precipitation has increased by an average of
5.73 mm day-1 over the last 110 years, or 8.53 % in relative terms.
The observational annual-maximum daily precipitation has also increased by an
average of 10 % K-1 of global warming since 1901, which is larger
than the average of climate models, with 8.3 % K-1. The rates of
increase in extreme precipitation per K of warming in both models and
observations are higher than the rate of increase in atmospheric water vapor
content per K of warming expected from the Clausius–Clapeyron equation,
which is approximately 7 % K-1, which highlights the importance of
extreme precipitation trends for water resource planning.
Non-parametric trend testsMann–Kendall trend test
The MK test is a non-parametric rank-based test (Kendall, 1975; Mann, 1945).
The Mann–Kendall test statistic S is calculated as
S=∑i=1n-1∑j=i+1nsgnxj-xi,
where n is the number of data points, xi and xj are the data
values in time series i and j (j>i), respectively, and
sgn(xj-xi) is the sign function
sgnxj-xi=+1ifxj-xi>00,ifxj-xi=0-1ifxj-xi<0.
The variance is computed using the equation below:
Var(S)=n(n-1)(2n+5)-∑i=1mtiti-12ti+518,
where n is the number of data points, m is the number of tied groups and
ti is the number of ties of extent i. A tied group is a set of sample
data having the same value. In cases where the sample size n is greater
than 10, the standard normal test statistic ZS is computed as
ZS=S-1Var(S),ifS>00,ifS=0S+1Var(S),ifS<0.
The sign of ZS indicates the trend in the data series, where
positive values of ZS mean an increasing trend, while negative
ZS values show decreasing trends. For the tests at a specific
α significance level, if |ZS|>Z1-α/2,
the null hypothesis is rejected and the time series has a statistically
significant trend.
Z1-α/2 is obtained from the standard normal distribution table,
where, at the 5 % significance level (α= 0.05), the trend is
statistically significant if |ZS|> 1.96 and, at the 1 %
significance level (α= 0.01), the trend is statistically
significant if |ZS|> 2.576.
Sen's slope estimator
The non-parametric procedure for estimating the slope of the trend in the
sample of N pairs of data was developed by Sen (1968) as
Qi=xj-xkj-kfori=1,…,N,
where xj and xk are the data values at times j and k
(j>k), respectively. N is defined as n(n-1)2, where
n is the number of time periods.
If the N values of Qi are ranked from smallest to largest, the
parameter Qmed is computed as the median of the Qi
vector. The Qmed sign reflects the direction of trend, while its
value indicates the magnitude of the trend. To determine whether the median
slope is statistically different than zero, the confidence interval of
Qmed at a specific probability should be computed as follows
(Gilbert, 1987; Hollander and Wolfe, 1973):
Cα=Z1-α/2Var(S),
where Var(S) is defined before and Z1-α/2 is obtained from the
standard normal distribution table. Then,
M1=N-Cα2 and
M2=N+Cα2 are computed. The lower and upper
limits of the confidence interval, Qmin and Qmax, are
the M1th largest and the (M2+ 1)th largest of the N ordered
slope estimates (Gilbert, 1987). The slope Qmed is statistically
different than zero if the two limits Qmin and Qmax
have the same sign.
Acknowledgements
The authors gratefully acknowledge support from NOAA under grants NA11SEC4810004
and NA12OAR4310084. All statements made are the views of the
authors and not the opinions of the funding agency or the US government.
Edited by: P. Gentine
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