NHESSNatural Hazards and Earth System SciencesNHESSNat. Hazards Earth Syst. Sci.1684-9981Copernicus PublicationsGöttingen, Germany10.5194/nhess-17-993-2017Simple and approximate estimations of future precipitation return valuesBenestadRasmus E.rasmus.benestad@met.nohttps://orcid.org/0000-0002-5969-4508PardingKajsa M.MezghaniAbdelkaderDyrrdalAnita V.The Norwegian Meteorological Institute, Henrik Mohns Plass 1, Oslo, 0313, NorwayRasmus E. Benestad (rasmus.benestad@met.no)3July2017177993100124June201626July20165April201728May2017This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/This article is available from https://nhess.copernicus.org/articles/17/993/2017/nhess-17-993-2017.htmlThe full text article is available as a PDF file from https://nhess.copernicus.org/articles/17/993/2017/nhess-17-993-2017.pdf
We present estimates of future 20-year return values for 24 h precipitation
based on multi-model ensembles of temperature projections and a crude method
to quantify how warmer conditions may influence precipitation intensity.
Our results suggest an increase by as much as 40–50 % projected for 2100
for a number of locations in Europe, assuming the high Representative
Concentration Pathway (RCP) 8.5 emission scenario. The new strategy was based
on combining physical understandings with the limited information available,
and it utilised the covariance between the mean seasonal variations in
precipitation intensity and the North Atlantic saturation vapour pressure.
Rather than estimating the expected values and interannual variability, we
tried to estimate an “upper bound” for the response in the precipitation
intensity based on the assumption that the seasonal variations in the
precipitation intensity are caused by the seasonal variations in
temperature. Return values were subsequently derived from the estimated
precipitation intensity through a simple and approximate scheme that combined
the 1-year 24 h precipitation return values and downscaled annual wet-day
mean precipitation for a 20-year event. The latter was based on the 95th
percentile of a multi-model ensemble spread of downscaled climate model
results. We found geographical variations in the shape of the seasonal cycle
of the wet-day mean precipitation which suggest that different rain-producing
mechanisms dominate in different regions. These differences indicate that the
simple method used here to estimate the response of precipitation intensity
to temperature was more appropriate for convective precipitation than for
orographic rainfall.
Introduction
Extreme precipitation is associated with flooding and landslides and can have
detrimental effects on infrastructure and society
, as for example during the unusually intense
cloudburst in central Copenhagen on 2 July 2011 which caused massive
flooding, and the 2002 floods in central and eastern Europe
. Return values are commonly used in planning and
design of weather-resilient infrastructure by quantifying the magnitude of a
typical extreme event. However, the return values are not stationary, and
according to the reinsurance company Munich Re ,
there has been an increase in the annual number of loss events related to
weather. Assessments carried out by the Intergovernmental Panel on Climate
Change (IPCC) indicate that heavy precipitation will become more severe in
already wet areas in the future
. These assessments have
largely been based on global climate model (GCM) output and have not made use
of additional local information such as meteorological observations. One of
the difficulties of using observational data is the patchy character of the
information because of missing data and short records. Global climate models
are not designed to represent local precipitation statistics corresponding to
rain gauge data, but are expected to reproduce the nature of large-scale
(regional and global) phenomena and processes seen in the atmosphere and
oceans. Also, some elements are reproduced with higher skill than others. In
other words, GCMs provide a more reliable picture of the temperature
aggregated over larger spatial scales than of grid-box precipitation
estimates , and their ability to simulate
large-scale features can be utilised for inferring changes to local
precipitation through downscaling
. This caveat also applies to
regional climate models (RCMs), which also have a minimum skillful scale
and have a limited ability to reproduce
the observed precipitation statistics
. Nevertheless, RCMs
have been used to study precipitation extremes
e.g., although the heavy computational demands
have limited analysis to a small number of GCMs which means that the
ensembles do not provide a realistic range of possible outcomes associated
with natural variability and model uncertainty
.
Traditional methods of estimating return values that make use of extreme
value theory (EVT) are sensitive to sampling fluctuations and require long
data records to avoid extrapolation of extreme characteristics
. Extreme precipitation
modelled through EVT usually describes amounts that are far out in the tail of
the distribution and associated with low probability, and the estimates may
change when new extremes are sampled. Most uses of EVT also assume
stationarity, although there are ways to account for trends
.
Local precipitation has been notoriously difficult to predict
;
one reason may be that it has involved quantities such as the monthly mean
precipitation that are calculated from a blend of different (both dry- and
wet-day) conditions and phenomena without accounting for these differences.
There are many different types of phenomena that generate precipitation, e.g.
the formation of nimbostratus, mid-latitude
cyclones, fronts, atmospheric rivers, convection and warm and cold initiation
of rain
.
Some of these have a stronger presence in certain regions and seasons. For
instance, convective precipitation is typically a summer phenomenon at
mid-to-high latitudes, whereas mid-latitude cyclones are more pronounced in
autumn, winter and spring. Another reason for the limited success may be the
small sample size in calculations of the mean precipitation for locations and
seasons where it rains rarely. For example, if it rains less than 30 % of
the total number of days in a month, the monthly average precipitation is
based on less than 10 values. The quantification of future extreme
precipitation is associated with uncertainties from a number of sources (e.g.
model imperfections, sparsity of data, sensitivity to random variations in
small samples constituting the tail of the distribution, non-stationarity and
the representation of natural variability). Large multi-model ensembles can
be used to explore the natural variability of the climate system, although
the range of the ensembles also includes other sources of uncertainty and
variability, and some ensemble members may be inter-dependent
.
Moderate extremes in 24 h precipitation amounts
(X) can be approximated with an
exponential distribution
,
which is described with one parameter – the wet-day mean μ – and its
percentile (qp) can be estimated as qp=-ln(1-p)μ. The exponential distribution can be used to estimate changes
in the moderate upper tail of the statistical distribution, assuming that
these follow changes in the bulk characteristics where the probability adds
up to unity . This approximation has been
tested against daily rain-gauge records from around the world, confirming
that the exponential distribution (qp=-ln(1-p)μ) predicts
the observed precipitation percentiles with high accuracy for
low-to-moderately heavy precipitation amounts (Fig. S1 in the Supplement).
This means that μ is useful for risk analysis to estimate upper
percentiles of 24 h precipitation amounts because the 95th percentile
q95 is expected to change proportionally with μ.
A comparison between the mean seasonal cycle in the saturation
vapour pressure (x axis) and the wet-day mean (y axis) for the site
Velikie Luki, Russia. The error bars indicate 2 standard deviations of the
year-to-year variations in the two variables. An inset shows the standardised
seasonal cycles, both variables peaking in July–August (red line =es, blue line =μ).
Data and methods
Our objective was to get estimates of future extreme precipitation that were
robust to outliers in situations when local observations are limited and to
avoid some of the caveats described above. We therefore explored a method of
extracting information about extreme precipitation from the multitude of data
sources available while reducing the uncertainty associated with small sample
sizes and blended conditions. Our analysis drew on available and relevant
information concerning precipitation, for instance geographical variations,
seasonal variations, ensemble spread and different physical processes
present during wet and dry days.
The estimated precipitation change was based on the change in temperature and
did not explicitly take atmospheric circulation changes or feedback processes
into consideration. This change can, for all intents and purposes, be
interpreted as a zeroth-order measure of an “upper bound” of change in
precipitation intensity associated with increased temperature, rather than
the most likely value. Attributing all of the seasonal variations in the
precipitation intensity to its covariance with temperature may inflate the
role of the temperature, as other factors exhibit a similar mean seasonal
cycle and may have an influence on the precipitation intensity. For this
reason, we use the terms upper bound and potential sensitivity. It is
also true that other unaccounted-for processes possibly may influence
precipitation intensity in a nonlinear fashion and possibly result in even
higher intensities if they also change in the future. However, as long as (a) such
factors have an approximately linear dependency on the temperature and
(b) the temperature may be taken as a proxy for climate change, then this
simple assumption may provide a reasonable figure. This simple method
differs from traditional methods in that rather than attempting to specify
the most likely value, it estimates a kind of upper bound
of the systematic response of extreme precipitation to changes in
temperature. We henceforth describe this relation as the potential
sensitivity (PS) since the calibration used the covariance of the mean
annual variation that may exaggerate the effect of the temperature. This is
described in more details below.
Our approach was based on empirical–statistical downscaling (ESD) applied to
a large multi-model ensemble to provide estimates of return values for heavy
precipitation, and is an alternative to EVT-based approaches. It provided an
estimate that was more approximate and crude, but less sensitive to outliers
because a larger portion of the data sample is used.
The Supplement provides more details and explanations of the strategy, as
well as the R scripts used to perform the analysis. The calculations and
graphics were produced with the open-source R package “esd”
. The data used in this analysis are available from
the reference provided in .
Data
Precipitation observations were obtained from the daily European Climate
Assessment, ECA&D, data set for 1032
stations in northern Europe with data available for the time period
1961–2014 (Fig. ). Surface temperature data from the National
Centers for Environmental Prediction/National Center for Atmospheric Research
(NCEP/NCAR) Reanalysis 1 over a selected North
Atlantic domain
(100∘ W–30∘ E/0∘ N–40∘ N; see Fig. S2)
were used to calculate the predictors for the downscaling, and corresponding
projections from the CMIP5 ensembles of GCMs assuming the Representative
Concentration Pathway (RCP) 2.6, 4.5 and 8.5 scenarios
were used for the projections of future change
(Table 1). We used the NCEP/NCAR Reanalysis 1 because the data covered the
1961–2014 period and because it provided a representation for the surface
temperature that was comparable to that of the CMIP5 GCMs.
The weights for the two leading principal components (a, b)
of the seasonal cycle of the wet-day mean precipitation μ in the 1032
rain gauge records. The colour of the symbols indicates how strongly the
shape is present in the local seasonal cycle, and the size reflects R2
from the regression analysis between es and μ (see Fig. S5).
Filled circles were used for locations with R2>0.6, hollow circles for 0.6≥R2>0.4 and crosses indicate locations with
R2<0.4. The shape of the seasonal cycle principal component for μ is
shown in the inset (top left of each panel).
Summary of the CMIP5 experiments. RCP4.5 was used as default
here, whereas RCP2.6 and 8.5 were taken as lower and upper limits based on
different emission scenarios.
A traditional approach for modelling and analysing precipitation typically
involves the monthly mean precipitation (X‾), but in this study,
we instead downscaled the wet-day mean, μ. In this analysis we used
μ to represent the wet-day mean precipitation in general, reflecting both
the annual wet-day mean precipitation and the mean seasonal variations in the
wet-day mean precipitation estimated for the 12 calendar months. The mean
precipitation was not the optimal quantity for describing precipitation
statistics because in most places it does not rain every day, and the
proportion of wet days to total number of days in a monthly sample can have
implications for the estimation of the statistical parameters describing the
distribution. The mean precipitation can be expressed as the product of the
wet-day frequency (fw) and μ according to X‾=fwμ. A comparison between the seasonal dependence of
X‾, μ and wet-day frequency fw indicated a
stronger seasonal cycle in μ than in fw and X‾
(see Fig. S3). The weaker seasonal cycle in X‾ was due to the
blending of different types of weather conditions in the mean precipitation.
The strong seasonal cycle of μ indicated a sensitivity to climatological
variations, which is an important requirement for the statistical downscaling
strategy proposed here.
Predictor: the saturation vapour pressure
We assumed that the vapour saturation pressure, es, is more linearly
related to the atmospheric water content and precipitation than the
temperature, and hence we used es as a predictor in the downscaling of the
annual wet-day mean precipitation μ.
The saturation vapour pressure was estimated from the surface temperature
(0.995 σ level), T.
es=10(11.40-2353/T)
This approximation was based on integration of the Clausius–Clapeyron
equation, assuming a constant latent heat of vaporisation (see Eq. 2.89 in
). The mean seasonal variations in the
regional average es over the North Atlantic domain was used as
predictor for μ, based on its mean seasonal variation (Fig. 1); our
reasoning was that it can be considered as the source region for humidity in
Europe. The domain was set after some trials for a few test stations, but no
systematic study or tuning of the predictor domain was conducted. The
predictor index was calculated from gridded temperature data from reanalyses
and global climate models (GCMs) and was then spatially and temporally
aggregated where monthly gridded es values were estimated
according to Eq. (1) and surface temperatures from the multi-model ensemble,
and were used to downscale an ensemble of local results of annual wet-day
mean precipitation μ^ (here μ^ is used for predicted
annual mean).
The empirical–statistical model
A model for predicting the annual wet-day mean precipitation μ^
can be constructed as a sum of a constant, β0, a term
depending on the saturation vapour pressure, βTes, and a Gaussian
noise term, N(0,σ), assuming that factors other than temperature that
are affecting wet-day precipitation are stochastic and stationary:
μ^=β0+βTes+N(0,σ).
The assumptions about other factors being stationary and stochastic is
partly based on the heuristic notion of physical interdependencies between
various aspects of the planetary atmosphere in general and that the
temperature is a proxy for such influences. One example may be the cloud top
height which is expected to be influenced by the convective available
potential energy (CAPE) that is sensitive to temperatures. We used the
observed standard deviation of μ in the month with the highest
interannual variability as an estimate of the standard deviation σ of
the noise term N, which in this case was August. We calculated the
coefficients β0 and βT using linear regression analysis between the mean
seasonal cycle of the observed monthly mean μ and the corresponding
seasonal cycle of the regionally averaged es calculated from reanalysis
temperature data from the Atlantic domain, as described in
Sect. . The coefficient βT is the scaling ratio
which we refer to as the potential sensitivity.
Annual mean time series of μ^ were then derived by applying the
downscaling models to annual mean es time series obtained from reanalysis
or GCM temperature data from the same domain. The GCM results were not
bias-adjusted; however, the use of large-scale
(100∘ W–30∘ E/0–40∘ N) spatially and annually
aggregated mean helped mitigating the effects from systematic model biases.
The model represented an approximation of the systematic effect that
temperature changes can have on μ, rather than a most likely value. It is
possible that other factors that play a role in precipitation also exhibit a
seasonal cycle and interfere with the regression analysis so that the
coefficient is weaker or stronger than the true influence of temperature on
precipitation.
A 90 % uncertainty range for μ^ was estimated for the
projections based on the ensembles of downscaled results, taken as the limit
between the 5th and 95th percentiles (see, e.g., Fig. S4). This interval
included the noise term N(0,σ), and captured the observed year-to-year
variations as well as model differences . We
assumed that the multi-model ensemble spread for any given year could
approximately represent the typical year-to-year variance, which meant that
the 95th percentile for μ^, which we henceforth refer to as
μ^95, could be used as a proxy for the value to be exceeded once
in 20 years (the 20-year event has a
probability of 0.05 (1/20) of occurring in a given year, and the 95th
percentile represents a limit that only 5 % (1 in 20) of the distribution
exceeds).
Return value probabilities
To estimate future return values based on the downscaled μ^, we
again assumed that the wet-day precipitation amount was exponentially
distributed and that the probability for 24 h precipitation exceeding a
critical threshold x could be calculated as follows:
Pr(X>x)≈fwe-x/μ,
where fw was the wet-day frequency
. Previous analysis suggest that the
exponential distribution gives a reasonable description of the probabilities
for moderate precipitation events such as the 95-percentile, but is not
expected to be suitable for rare extremes much beyond the 20-year return
level .
The probability associated with the 1-year return value of 24 h
precipitation is approximately Pr(X>x)=1/365.25, and the corresponding threshold value was approximated
according to
x1year≈μln(365.25fw).
Previous comparison between the return values based on Eq. () and
general extreme value theory, has suggested that they give roughly similar
results . A test of Eq. ()
indicated that the return values scale with μ: values of
x1year that were associated with high percentiles and low
values of μ^ approximately corresponded to x1year
with low percentiles and high values of μ^ (Fig. S1). Based on
Eq. (), we made a rough estimate of the 20-year return value for
the 24 h precipitation amount (x20year) by replacing μ
with the 20-year return value of the annual wet-day mean. The estimate for
x^20year was calculated based on the downscaled annual
wet-day mean precipitation, using the 95th percentile μ^95 as a
proxy for the 20-year return values:
x^20year=μ^95ln(365.25fw).
In calculating future return values, we neglected changes in fw and simply
assumed that it will remain constant. Previous analysis has indicated that
the wet-day frequency is strongly influenced by circulation patterns
, and that it is closely connected to slow
natural variations such as the North Atlantic Oscillation (NAO)
. Such natural variations are difficult to
predict and there is little evidence of a systematic shift in the frequency
of different circulation patterns.
Principle component analysis of the seasonal cycle
Principal component analysis (PCA) was used to extract the most dominant
shapes of the seasonal cycle in μ amongst the observation sites
(Fig. ). The mean seasonal cycle was estimated for each site
and used to construct a data matrix X with 12 columns (one for
each month) and n rows (one for each site). Singular value decomposition
(SVD) was then used to compute the principal components: UΣVT=X, where U is the left inverse, V the
right inverse and Σ is a diagonal matrix holding the
eigenvalues . The procedure
deconstructed the data into a set of shapes of the seasonal cycle,
corresponding eigenvalues that described the explained variance and a spatial
matrix that described the relative strength of each shape at the different
locations.
Results and discussionPotential sensitivity and the seasonal cycles in μ and es
The mean seasonal cycles of μ at many European locations co-varied with
the mean seasonal cycle of es in the North Atlantic domain. This
can be seen as a validation of the assumptions underlying the empirical
model, because the downscaling models were based on the regression between
the seasonal cycles of es and μ (Eq. ).
Figure provides an example of a scatter plot between the mean
seasonal variations in es (x axis) and the corresponding cycle
in μ (y axis) for one location (Velikie Luki, Russia). The example in
Fig. was not unique: there was a high and statistically
significant correlation (R2>0.6; Fig. S5) between the seasonal cycle of
these two quantities for many of the rain gauge records (612 of the 1032
stations). The majority of the locations with a poor fit (R2<0.6) were
found along the western coast of Norway and south-east of the Alps, while inland
sites and locations in central Europe had higher R2 values (see
Fig. where the size of the markers is proportional to R2).
This indicated that a linear relationship between μ and es
could not be expected in regions where orographic precipitation was dominant.
Downscaled projections were carried out only for the locations with a good
fit (R2>0.6).
It was also evident that there were pronounced year-to-year variations in the
wet-day mean (vertical error bars in Fig. ) which were not
related to the temperature, suggesting that factors other than temperature
also played a role in precipitation variations. The downscaling strategy
adopted here was designed to evaluate the maximum potential effect of
temperature changes on the wet-day mean precipitation, and the scaling factor
between the two is described as the potential sensitivity. Since other
processes also influenced precipitation, the method could not be expected to
reproduce past interannual variability, but it could be used to obtain a
rough estimate of the effect of temperature changes on precipitation.
Figure presents maps showing the two major components of the
mean seasonal cycle in μ, which together accounted for 94 % of the
variability for the 1032 locations examined. The spatial patterns in the
principle components (PC) revealed different seasonal cycles of precipitation
along the mountainous western coast of Norway and close to the Alps compared
to the rest of Europe, probably related to orographic effects. There was a
gradient in the shape of the mean seasonal cycle in μ with the distance
from the coast that was particularly visible over the Netherlands. Inland
sites indicated higher precipitation intensities during July and August,
which could be associated with convective rainfall. We found a positive
correlation between the spatial vector of the leading PCs and R2 of the
seasonal cycles of es and μ: 0.82 (with a 90 % uncertainty range of
0.80, 0.84), but negative correlation for mode 2 (-0.84; -0.86, -0.82) and no
significant correlation for mode 3 (0.00; -0.06, 0.06). This indicated that
the dominant shapes of the seasonal cycle of μ in Europe were associated
with a strong connection to the North Atlantic temperature.
Projections of future precipitation
Projected values of the annual mean wet-day mean, μ^, based on the
downscaling model (Eq. ) applied to the CMIP5 ensemble, are
shown in Fig. . The downscaled results suggested an increase
of up to 13 % in the wet-day mean from 2010 to 2100, assuming the RCP4.5
emission scenario , and as much as 38 % at
many of the locations given the high emission scenario RCP8.5. The most
extreme estimate was an 85 % increase at Sihccajavri (Norway). Since the
wet-day precipitation amount approximately followed an exponential
distribution, the proportional change in any percentile was the same as for
μ. The inset in Fig. shows estimated changes for the
emission scenarios RCP4.5, 2.6 and 8.5 for both the
ensemble mean and 95th percentile.
An analysis of historical observations provided some indication of skill of
the downscaling models in terms of predicting trends of μ based on the
North Atlantic temperature (Fig. S6). The historical trends exhibited a more
pronounced scatter than the predicted trends, suggesting that factors other
than the sea-surface temperature also had influenced the long-term changes.
For most locations, there was an increase in μ between 1961 and 2014,
typically 0.1 mm day-1 per decade (Fig. S6–S7).
Estimates of future 20-year return values (Eq. ) based on
μ^95 and assuming a constant value of the wet-day frequency,
fw, are shown in Table . Based on downscaling of the RCP4.5
scenario, the 20-year return values may increase by between 7 and 28 %
by 2100 (ensemble median: 11 %), or assuming the high emission scenario
RCP8.5, between 22 and 85 % (ensemble median: 33 %). Nevertheless,
changes in fw may also influence return values, and an increase in the
number of rainy days would imply an even stronger change in return values.
Summary of the projected change from 2010 to 2100 in the 20-year
return value for 24 h precipitation under the assumption of stationary
wet-day frequency. The sample comprises the 615 locations shown in
Fig. . The numbers represent the change in percentage with
respect to year 2010.
Projected local change from 2010 to 2100 in the ensemble mean and
95th percentile annual mean μ for the RCP4.5 emission scenario. The
colour of the inner part of the symbols indicates changes in the ensemble mean
and the outer part the 95th percentile in terms of percentages since 2010.
The inset shows a boxplot of the projected change in μ, both for the
ensemble mean (left) and the 95th percentile (right) of emission scenarios
RCP4.5, 2.6 and 8.5.
The historical fw trends at the stations tend to cluster roughly
around zero (Fig. S8). However, studying the geographical pattern of trends,
we saw a general increase in southern Scandinavia and the Netherlands for the
period 1961–2014, but a less coherent pattern elsewhere (Fig. S9). This
implied that factors other than the North Atlantic temperature may also have
played a role in past trends and future precipitation changes. The wet-day
frequency was strongly influenced by the circulation patterns
and could potentially be predicted based on
the mean sea-level pressure, but here we have focused on the influence of
temperature changes on the precipitation.
Validation of results
In order to assess the veracity of our results, we performed an independent
test to examine the dependency of μ on temperature, consisting of a
regression analysis comparing the spatial variations of the mean of μ and
es calculated from local temperature measurements
(see Figs. S10–S11). The test was limited to
locations where both temperature and precipitation observations were
available and did not involve the regionally averaged temperature of the
North Atlantic domain. The geographical variations in the relationship
between μ and es were consistent with the regression
coefficients from the downscaling models (Eq. ,
Fig. ) within the range of estimated error margins (Fig. S11).
An exception was seen in stations located in western Norway and
south-east of the Alps, where the
seasonal cycle regression also showed a weak relationship between μ and
es. The fact that the link between μ and es was
found in both time and space provided a stronger indicator of a physical link
than if it were limited to only the time dimension.
Summary and conclusions
We have proposed a novel and simple method for obtaining an approximate
estimate of changes in the return values for 24 h precipitation caused by a
temperature change, taking all precipitation relevant processes into account.
This method made use of the information embedded in the seasonal cycle,
physical conditions and multi-model ensembles to provide a rough estimate of
the potential sensitivity of precipitation intensity to temperature. The
results suggested that the zeroth-order estimate for an upper bound of the
20-year return value for many European locations increases by 40–50 % by
2100 for the RCP8.5 scenario, rather than the exact or most likely value.
One of the benefits of the proposed strategy for downscaling μ is that
the description of the seasonal cycle does not require long data records and
hence may provide a means for estimating a zeroth-order value for the
potential sensitivity and an upper bound
to the change in rainfall statistics in regions with limited observations.
This strategy can be used for other mid-latitude locations, but further
analysis is needed to see if it is applicable to the monsoon regions where
the temperature is at maximum before the rains start. An alternative approach
could be to estimate future changes in μ based on downscaled local
temperature from GCMs and a similar regression model as used in the test
described above.
The approach was based on a set of assumptions: (a) the maximum seasonal mean
response of the wet-day mean precipitation to the seasonal variations in
temperature is represented by a proportional change, (b) the 95th
percentile of the annual wet-day mean precipitation from large multi-model
ensembles (e.g. CMIP5) can be used to represent a 20-year event and (c) the
wet-day frequency is stationary. On the one hand, this new strategy is less
rigorous than traditional extreme value statistics; on the other hand, it
is more robust to outliers even in cases when the available information is
limited.
Another potential weakness of the study is the use of the multi-model
ensembles as a representation of natural climate variability. These
“ensembles of opportunity” involve non-independent members and cannot really
be considered a random data sample .
However, internal variability dominates the variance on regional and local
scales and gives a spread that is comparable to the observed variations even
in single-model ensembles .
Data used in this analysis are available from figshare
(10.6084/m9.figshare.5047789; see ). The analysis
was based on the esd package (10.5281/zenodo.29385; see
).
The Supplement related to this article is available online at https://doi.org/10.5194/nhess-17-993-2017-supplement.
The authors declare that they have no conflict of
interest.
Acknowledgements
The methods and results produced for this paper were connected to research
carried out for the H2020 EU-Circle (GA no. 653824), Nordforsk eSACP. The
work was supported by the Norwegian Meteorological Institute. Edited by: Thorsten Wagener Reviewed by: Reik
Donner and two anonymous referees
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