HESSHydrology and Earth System SciencesHESSHydrol. Earth Syst. Sci.1607-7938Copernicus PublicationsGöttingen, Germany10.5194/hess-22-4183-2018A classification algorithm for selective dynamical downscaling of precipitation extremesSelective dynamical downscalingMeredithEdmund P.edmund.meredith@met.fu-berlin.dehttps://orcid.org/0000-0001-7555-0005RustHenning W.https://orcid.org/0000-0003-0763-3954UlbrichUwehttps://orcid.org/0000-0001-7558-6622Institut für Meteorologie, Freie Universität Berlin, Carl-Heinrich-Becker-Weg 6–10, 12165 Berlin, GermanyEdmund P. Meredith (edmund.meredith@met.fu-berlin.de)7August2018228418342007November20177December20173May201812July2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://hess.copernicus.org/articles/22/4183/2018/hess-22-4183-2018.htmlThe full text article is available as a PDF file from https://hess.copernicus.org/articles/22/4183/2018/hess-22-4183-2018.pdf
High-resolution climate data O(1 km) at the catchment scale can be of
great value to both hydrological modellers and end users, in particular for
the study of extreme precipitation. While dynamical downscaling with
convection-permitting models is a valuable approach for producing quality
high-resolution O(1 km) data, its added value can often not be
realized due to the prohibitive computational expense. Here we present a
novel and flexible classification algorithm for discriminating between days
with an elevated potential for extreme precipitation over a catchment and
days without, so that dynamical downscaling to convection-permitting
resolution can be selectively performed on high-risk days only, drastically
reducing total computational expense compared to continuous simulations; the
classification method can be applied to climate model data or reanalyses.
Using observed precipitation and the corresponding synoptic-scale circulation
patterns from reanalysis, characteristic extremal circulation patterns are
identified for the catchment via a clustering algorithm. These extremal
patterns serve as references against which days can be classified as
potentially extreme, subject to additional tests of relevant meteorological
predictors in the vicinity of the catchment. Applying the classification
algorithm to reanalysis, the set of potential extreme days (PEDs) contains
well below 10 % of all days, though it includes essentially all extreme days;
applying the algorithm to reanalysis-driven regional climate simulations over
Europe (12 km resolution) shows similar performance, and the subsequently
dynamically downscaled simulations (2 km resolution) well reproduce the
observed precipitation statistics of the PEDs from the training period. Additional tests on continuous 12 km resolution historical and future (RCP8.5)
climate simulations, downscaled in 2 km resolution time slices, show
the algorithm again reducing the number of days to simulate by over 90 % and
performing consistently across climate regimes. The downscaling framework we
propose represents a computationally inexpensive means of producing
high-resolution climate data, focused on extreme precipitation, at the
catchment scale, while still retaining the advantages of
convection-permitting dynamical downscaling.
Introduction
Hydrological modellers and regional decision-makers benefit greatly from high
spatial O(1 km) and temporal resolution climate data to both drive
their catchment-scale hydrological models and design regional planning
strategies. These high-resolution data are necessary as standard-resolution
model data O(10–100 km) suffer from many deficiencies, most noticeably
both “averaging” and “scale-interaction” effects whereby (i) area
averaging over large grid cell areas smooths out fine-scale detail and
(ii) feedbacks from small to large scales are not represented
; these deleterious effects are amplified towards
the tails of the distribution . Despite their
desirability, suitably high-resolution datasets are rarely available, either
due to the computational expenses associated with running climate models at
such high spatial resolutions or, in the case of observations, due to
insufficiently dense observational networks. To bridge this gap, both
statistical and dynamical downscaling techniques have been developed for
precipitation and other variables.
Statistical downscaling, encompassing a range of approaches
in which empirical relationships between
large scales and local weather (i.e. observations) are developed, allows
large ensembles of high-resolution climate data to be produced from
coarse-resolution models at minimal computational expense and tailored to
specific end-user needs. Such relationships can, however, only be developed in
the presence of both appropriate local weather data (typically observations)
and corresponding large-scale data (reanalysis or observational data), which
are often unavailable at sub-daily and sub-hourly temporal resolutions and/or
are spatially too sparse. Dynamical downscaling with regional climate models (RCMs),
O(10 km), provides an alternative to the statistical approach,
which is, however, computationally far more expensive. Issues of computational
expense aside, both methods have their own strengths and (sometimes common)
weaknesses. The representation of large scales in the parent general
circulation model (GCM) can be a limiting factor, the so-called “garbage in,
garbage out” problem . If the large scales are
not skilfully represented, then downscaling techniques cannot add value
as errors in the large scales will not be
corrected; isolated examples of value being added via RCMs correcting
large-scale errors have, however, been reported e.g..
The assumption of stationarity – that predictor–predictand relationships will
remain unchanged in a future climate – in RCM parametrizations and
statistical downscaling methods may also not be valid
, lowering confidence in projections.
Statistical and dynamical downscaling both produce climate change signals
that are, to varying degrees, influenced by the climate change signal of the
parent GCM. If the GCM has an incorrect climate-change signal this may be
inherited without meaningful modification.
further discuss different facets of the statistical and dynamical downscaling
approaches, additionally explaining that the approaches are complementary and
can be combined, rather than being treated as mutually exclusive alternatives.
In general, high-resolution RCMs (∼10 km) add value to coarser GCMs for
multiple variables . This added value (AV) is
primarily achieved through better representation of surface forcings and
mesoscale processes and is thus most evident in the presence of complex
topography or strong land–sea contrasts
. For example, recent studies have shown cases in
which high-resolution RCMs can not only modify but even reverse the
mean-precipitation climate-change signal in their parent GCM
, which is attributable to their representation of complex
topography and ability to hence simulate increased convective activity at
higher elevations in a warmer climate. Precipitation, due to its high spatial
and temporal variability, is perhaps the variable for which high-resolution
RCMs exhibit the most AV. The strongest manifestations of AV for
precipitation are found at short temporal scales, in the warm season, and in
regions of complex topography regardless of temporal scale and season
; AV is most evident for the extremes
. Importantly, this AV should not simply be understood as
representing increased small-scale detail, but rather AV at the spatial scale
of the driving GCM due to more processes being represented .
As input for impact and hydrological models, dynamical downscaling can
provide a large set of physically consistent variables
, meaning that, for example, changes in cloud cover will
be reflected in appropriate knock-on effects on other input variables such as
radiation, temperature, humidity, surface pressure, etc.
Despite their relatively high resolution, typical RCMs O(10 km) still
cannot resolve many precipitation-causing processes such as convection, which
must instead be parametrized. As a result, models with parametrized
convection tend to misrepresent heavy precipitation events, causing them to
be too temporally persistent, too spatially widespread and not
intense enough locally ; further issues are too much drizzle
and a temporally displaced diurnal convective
cycle . Increasing horizontal resolution below
about 4 km, convection-permitting models (CPMs) can explicitly simulate
deep-convective processes and improve on many of these shortcomings
. The explicit representation of convective dynamics
in CPMs produces more realistic convective features
, more accurate local precipitation intensities
, and an improved representation of the
diurnal convective cycle . With respect to the accuracy
of precipitation totals, the main AV of CPMs can be expected to be found in
area averages over, for example, a river catchment
. Importantly, the AV of CPMs is not restricted
to improved present-climate precipitation statistics
e.g., but may also extend to the climate change
signal. Recent studies show that sub-daily convective extremes in CPMs
exhibit an amplified response to enhanced boundary forcings compared to that
found in their coarser parametrized-convection parent models
, which can be highly non-linear
. The explicit simulation of physical process
chains in CPMs, which can be highly localized, gives more confidence in their
projections than those derived from models using convective parametrizations.
Coarse-resolution model extreme precipitation is a poor predictor of extreme
precipitation in both observations and high-resolution simulations. Plots
show the rate at which extreme precipitation events in a coarse model are
temporally and spatially coincident with extreme precipitation events in
(a, b) observations and (c, d) further downscaled
high-resolution simulations. (a) For summer extreme
precipitation (1979–2015), the percentage of 99th percentile days in
ERA-Interim for which the corresponding day in observations
REGNIE; exceeds the observed
99th percentile; percentiles are over all days. A value of 100 % would mean
that, for a given grid cell, all “extreme” dates in ERA-Interim were also
“extreme” dates in REGNIE. (b) As in (a), except for
winter (1980–2015). (c, d) As in (a), except between the
0.11 and 0.02∘ CLM simulations discussed in Sect. 2 for the
(c) historical (1970–1999) and (d) RCP8.5 (2070–2099)
periods. Values in the bottom-left of each panel show the area average over
all data points, while values in the bottom right show area averages over the
Wupper catchment in western Germany (marked; see also Sect. 2).
CPMs provide a reliable and state-of-the-art means of downscaling
coarse-model output to the high spatial-resolutions (with fine-scale
variability) needed by hydrologists and end users for many applications,
particularly the study of extremes. A serious limitation of CPMs, however, is
the considerable computational expense incurred when carrying out
convection-permitting simulations on multi-year timescales, making them an
infeasible option for many; an approach for limiting these costs must be
sought. For users interested in studying the impact of heavy or extreme
precipitation events on their catchment, at least 90 % of the days in any
continuous simulation will be of little interest and could be viewed as
wasted computational time. In an ideal procedure, dynamically downscaling to
convection-permitting resolution might be skipped on these redundant days and
only be carried out when there is a significant chance of the catchment
experiencing heavy precipitation. Similarly, some users are more interested
in assessing the catchment-scale impacts of a selection of
physically plausible extremes from a present or future climate, without being
focused on precise probabilities derived from continuous CPM simulations
; examples of this include design situations for
hydraulic infrastructure, process-oriented case studies, and stress testing.
The identification of which days to downscale, however, is a non-trivial
task. Coarse model precipitation on its own is a poor predictor of extreme
precipitation events in both observations and CPMs, especially in the summer,
when precipitation extremes tend to be of short duration and of a convective
nature (Fig. 1).
With the aim of slashing computational time and expense, we develop a
transferable methodology to discriminate between days with an increased
likelihood of extreme precipitation – potential extreme days (PEDs) – and
redundant days so that dynamical downscaling to convection-permitting
resolution can be performed over a catchment only when a day has been
identified as a PED. In Sect. 2 we set out in detail our methodology and
validation approach, with the subsequent sections containing results,
discussion and conclusions.
Methodology and data
To identify for dynamical downscaling days with an increased likelihood of
extreme precipitation – “potential extreme days” (PEDs) – over the region
of interest, we develop a two-step classification method based on (1) the
synoptic-scale circulation pattern and (2) local-scale (modelled)
meteorological predictors in the coarser-resolution parent model. This
requires the identification of synoptic-scale circulation patterns that
typically accompany extreme precipitation events in our catchment and the
careful selection of meteorological predictors that, when a defined threshold is exceeded in the vicinity of
the catchment, are conducive to the development of intense precipitation.
Our study catchment is that of the River Wupper in western Germany (Fig. 2).
The Wupper catchment, home to some 950 000 inhabitants, has an area of
813 km2, contains about 2300 km of streams and rivers, and drains into
the River Rhine. The Wupper basin is vulnerable to winter flooding and
summertime flash-flooding from mesoscale convective events; we thus focus on
these two seasons.
Identification of synoptic-scale extremal circulation patterns
The REGNIE gridded daily precipitation dataset ,
developed by the German weather service specifically for hydrological
applications and with a grid spacing of roughly 1 km, is used to compute
separate time series of observed daily precipitation area-averaged over the
Wupper catchment (Fig. 2) for each full winter and summer in the period 1979–2015.
From these time series the 99th precipitation
percentiles of all days are computed separately for each season, and all days
above their seasonal 99th percentile are defined as “extreme”.
The areal extent of the Wupper catchment contains 753 REGNIE grid cells;
precipitation-recording stations of the German weather service are marked in
Fig. 2. An advantage of the REGNIE dataset is that measured totals are
conserved, so that observed events (dry or wet) can be found preserved in the
gridded field, which is in contrast to other methods on coarser grids, which
use smoothing . Despite this, the usual warnings
about using gridded observations to study heavy precipitation events must be
recalled. In the absence of a sufficiently dense rain-gauge network in and
around the catchment, the spatial variability and local intensity maxima of
heavy precipitation events will not be captured in the gridded product,
leading to precipitation extremes that are both underestimated and too
spatially homogeneous, in particular in areas of complex topography and for
convective events e.g..
The rain-gauge network underlying the gridded dataset must thus be
sufficiently dense so that catchment-relevant extremes are acceptably
captured. Alternatively, individual station(s) known to be broadly
representative could be used for small- to medium-sized catchments.
The Wupper catchment (black outline) with main tributaries and
lakes, and the River Rhine running north-northwestwards. Shading represents
the regional orography as represented in the 0.02∘ CCLM model used in
the simulations (see Sect. 2.3). Note that this is not the full
0.02∘ simulation domain, but rather a close-up of the Wupper
catchment; the full spatial extent of the CPM domain and the exact region
covered by this map are marked in the inner box of the top-left panels in
Figs. 3 and 4. Magenta-coloured circles mark the precipitation-recording stations
of the German weather service, as listed here
https://www.dwd.de/DE/leistungen/klimadatendeutschland/statliste/statlex_html.html?view=nasPublication&nn=16102.html
(last access: 25 July 2018). Note that some stations do not
cover the entire 1979–2015 period.
To identify the large-scale circulation patterns associated with the heavy
rainfall days, the corresponding 500 hPa geopotential height (Z500) anomalies
are extracted from the ERA-Interim reanalysis . REGNIE
precipitation has a measurement period of 07:30–07:30 LT (local time), equating to
05:30–05:30 UTC in summer and 06:30–06:30 UTC in winter. Z500 anomalies are thus
averaged over the timesteps 12:00, 18:00 and 00:00 UTC, i.e. the middle of the
accumulation period, and are relative to their 1979–2015 seasonal means.
500 hPa geopotential height anomalies (shading) of extremal
circulation patterns identified for the Wupper catchment in winter, via the
clustering algorithm, and one outlier; the zero line is marked in black.
White contours represent the accompanying sea level pressure patterns. The
grey box centred over western Germany is the 0.02∘ simulation domain
(Sect. 2.3).
The extracted Z500 anomaly patterns next undergo a cluster analysis via the
simulated annealing and diversified randomization (SANDRA) method
. SANDRA has been shown to overcome many of the
limitations of standard k-means clustering algorithms, greatly reducing the
role of stochastic effects in the final cluster partitions and thus providing
clusters much closer to the “global optimum” . It is
also less numerically costly than model-based clustering algorithms such as
Gaussian mixture models e.g.. Relevant
software for meteorological applications has been developed in the EU COST
Action 733 , and we use this software in our
study. Geopotential height is a standard variable for cluster analyses of
atmospheric circulation patterns e.g..
Following , the spatial extent of the
clustering domain is subjectively chosen such that the typical synoptic
patterns associated with extreme precipitation in the Wupper catchment can be
captured within the domain when present (Figs. 3 and 4), which is easily
identifiable from historical extremes. Prior to the cluster analyses,
outliers that would have little chance of being assigned to an appropriate
cluster are removed from the datasets. Outliers are identified by computing,
for each day, the Pearson pattern correlation of each Z500 anomaly pattern
with that on all other extreme days; any day whose maximum pattern
correlation (i.e. across all days) is more than 2 standard deviations below
the sample mean of the same is excluded from the cluster analysis. In our
case, this results in just 1 day being removed from each of the winter and
summer input data, leaving 31 and 33 days respectively. As a stability
criterion, the number of clusters K is increased until the minimum
intra-cluster pattern correlation – that is, the Z500-anomaly pattern
correlation between each cluster member and its own cluster mean – is not
less than 0.5. This way all days are assigned to a cluster with which they
have genuine similarities, rather than simply the error-minimized “least
bad”
cluster, as is typically the case in clustering large datasets of
meteorological variables.
The resulting Z500 anomaly clusters and any outliers are considered as
“reference” extremal circulation patterns against which candidate days from a
given dataset can be classified as PEDs, based on their similarity to these
references. To this end, the area-weighted Pearson pattern correlation ρi,j
(uncentred) between the Z500 anomaly fields of the candidate
day i and the cluster centroid j is used; for our clustering
domain (Figs. 3 and 4) this encompasses 1935 data points (i.e. grid cells). A
perfect ρi,j would have a value of 1. With the guiding aim of
correctly classifying as many extreme days (i.e. P≥P99D) and rejecting as many non-extreme days as possible, a
ρ threshold (ρjt) is chosen for each cluster centroid j
and days with a ρi,j below this threshold are rejected.
ρjt for each cluster is simply the minimum intra-cluster pattern
correlation, reduced by 10 % so that days with a ρ comparable to the
lowest intra-cluster ρ are not rejected. To account for clusters with a
particularly high ρjt due to few members, ρjt is capped
at two-thirds.
As in Fig. 3, except for summer.
Assessment of local-scale meteorological predictors
All remaining days not rejected based on their ρi,j are next
assessed in terms of relevant meteorological predictors at the local-scale,
i.e. in the vicinity of the catchment. The choice of meteorological predictor
and the area around the catchment in which it is assessed are flexible. In
general, they may depend on the catchment, season and variables available
from the coarser parent model. advise choosing
predictors that are easy to diagnose from coarse-resolution models and
consistent with meteorological knowledge of precipitation extremes,
e.g. circulation and stability metrics. Guidance may also be sought from
statistical downscaling techniques that have been successfully applied in
the region.
Predictor variables, thresholds and region. Note that these thresholds
are relative to the model's and reanalysis' own climatology, so that the absolute
values of the anomalies and percentiles will vary depending on the model and reanalysis
on which the classification algorithm is being applied. On the Gaussian N128
grid, one cell has a width of roughly 75 km. These predictors and thresholds could
be used as a starting point if applying the method to other catchments, though
they should not be directly transferred without first considering meteorological
characteristics specific to heavy rainfall events in the new catchment.
For the Wupper catchment in summer (JJA) and winter (DJF) we
select daily maxima (06:00–05:59 UTC) of relative humidity (700 hPa JJA,
300 hPa DJF) as an indicator of (near-)saturated air masses in the
troposphere, 500 hPa horizontal divergence (JJA, DJF) as an indicator of
tropospheric vertical ascent (of a frontal or convective nature), convective
available potential energy (CAPE; JJA) as an indicator of atmospheric
instability, and daily accumulated coarse-model precipitation (JJA, DJF). As
with the Z500 data, variables are extracted from ERA-Interim on a Gaussian
N128 grid (∼0.7∘). To account for the transient nature of many
extreme weather systems and the often low temporal resolution of
reanalysis or model data (e.g. 6-hourly in the case of ERA-Interim), it is not
only the nearest ERA-Interim grid cell to the catchment centre that is
considered, but an entire area of 7×7 grid cells around it (3×3 in the case of
coarse-model precipitation). With the guiding aim of “catching” the highest
number of observed precipitation extremes (i.e. P≥P99D)
while excluding as many other days as possible,
exceedance thresholds for each variable are empirically chosen, either
as exceedances of a given percentile (divergence, CAPE, coarse-model
precipitation) or as absolute values (relative humidity). The thresholds used
for the Wupper catchment are summarized in Table 1. To account for different
model climatologies and thus facilitate transferability to other models, the
(absolute) relative humidity threshold (RHthresh) determined from the
training data can be redefined as a function of the model's climatological
mean (RH‾), i.e. RHthresh=A⋅RH‾, with
A a constant; this function can be applied to another model's RH‾
to get RHthresh for that model.
In order to be classified as a PED, each threshold must be exceeded at any
one of the grid cells (not necessarily the same cell) around the catchment. A
schematic summarizes the full two-step selection algorithm (Algorithm 1).
Extremal patterns identified for the Wupper catchment are presented in Sect. 3.1.
Validation and simulation
The combination of variables, thresholds and clusters for detecting observed
precipitation extremes and excluding non-extreme days is, as discussed above,
empirically determined on the basis of the ERA-Interim and REGNIE datasets.
Once this has been achieved, the method is applied identically to
0.11∘ (∼12.2 km) evaluation simulations over the pan-European
EURO-CORDEX domain , roughly
25–72∘ N, 20∘ W–50∘ E, covering the period 1979–2015.
Simulations were performed with the regional climate model COSMO-CLM
CCLM; version 4.8, with ERA-Interim reanalysis
as lateral boundary forcing. CCLM is the community model of the
German regional climate research community jointly further developed by the
CLM-Community. The years 1989–2008 were simulated by the CLM-Community as
part of the EURO-CORDEX experiment .
The years 1979–1988 and 2009–2015 (up to 31 July 2015) were simulated by the present
authors using identical model version and settings.
Z500 CCLM data are interpolated to the clustering domain and the selected
meteorological variables are conservatively regridded to a grid of similar
spatial resolution to that used in the training stage, i.e. 0.7∘, and
centred on the Wupper catchment. All winter and summer days are then either
classified as PEDs for further dynamical downscaling with CCLM to a
convection-permitting resolution of 0.02∘ (∼2.2 km) or
rejected; the nesting ratio of 5.5:1 is in line with that recommended in the
literature . The enhanced performance of CCLM at
convection-permitting resolution (relative to coarser resolutions) in
reproducing precipitation statistics, particularly extreme statistics, over
central Europe has been extensively documented .
The additional downscaling step is performed using the same version of CCLM
with a 221×221 grid cell domain centred on the Wupper catchment (Figs. 3 and 4),
giving sufficient spatial spin-up upstream.
A total of 161 of the CCLM grid cells fit inside the catchment. The simulations are carried
out in “weather forecast mode”, i.e. initialized with interpolated values
from the parent model. The multi-year simulations of the parent model ensure
that soil moisture and temperature are spun-up at the 12 km scale, though not
necessarily at the scale of the CPM. The soil moisture climatology tends to
be drier in CPMs due to the sparser nature of their precipitation events
. While studies suggest that the transient
boundary conditions are of first-order importance for the occurrence of
precipitation e.g., precipitation extremes highly
sensitive to localized soil-moisture anomalies may be inadequately
represented under such a procedure.
Lateral boundary conditions are updated every 3 h and 50 unevenly spaced
terrain-following vertical levels are used. For each identified PED, the
0.02∘ simulation is initialized at 12:00 UTC the preceding day to
allow abundant precipitation spin-up time; as little as 3–6 h are
typically sufficient in CPMs though
. PEDs on consecutive days are downscaled
continuously to save resources. For validation, the precipitation statistics
of the dynamically downscaled PEDs from the CCLM evaluation runs are compared
with those of the observed PEDs identified from ERA-Interim. Area averages of
daily precipitation over the Wupper catchment are considered, using REGNIE
and 0.02∘ model output. The REGNIE and CCLM grids are of similar
spatial resolution (1 and 2.2 km, respectively). Users should nonetheless
be cognizant that datasets of different resolution may exhibit differing
statistical characteristics simply because of their different resolutions,
e.g. for the area mean. The evaluation and validation of the identified PEDs
is presented in Sect. 3.2.
Verification via seasonal time-slice simulations
To provide a sterner test of the method, we additionally perform two sets of
30-season convection-permitting time-slice simulations over the Wupper
catchment so that the method can also be assessed in reverse – of the
actually simulated 0.02∘ extreme days (P≥P99D),
how many would have been identified as PEDs from the 0.11∘ coarse model?
A different GCM – the Max Planck Institute's Earth System Model (MPI-ESM-LR) – at
the start of the modelling chain provides a new challenge for the
method from the previous ERA-Interim-driven simulations. The MPI-ESM-LR runs
are continuous transient simulations performed as part of the CMIP5 project
, using observed greenhouse gas concentrations from 1949–2005
(historical) and Representative Concentration Pathway 8.5
RCP8.5; from 2006 to 2100. One MPI-ESM-LR
member (1949–2100) has been continuously downscaled with CCLM over the
EURO-CORDEX domain to 0.11∘ resolution by the CLM-Community
; model settings are as in the previously discussed
ERA-Interim-driven evaluation runs, greenhouse gas concentrations excepted.
For the present study, we have dynamically downscaled the aforementioned
0.11∘ CCLM transient simulations to 0.02∘ over 30 summers
from the historical and RCP8.5 periods, 1970–1999 and 2070–2099 respectively.
The 0.02∘ model domain and set-up are the same as in Sect. 2.3
(greenhouse gas concentrations aside); simulations are initialized in April
and run continuously until the end of August each year, with analysis
restricted to JJA. Summertime extreme precipitation in the Wupper basin tends
to be of a convective and more catchment-scale nature than its wintertime
counterpart, with small-scale variability and chaotic processes playing an
enhanced role in event intensity. In addition to this, potential differences
in large-scale circulation found in a future climate pose an additional
challenge for the classification algorithm. The choice of 30 summers,
historical and future, is thus intended to ensure a robust testing of our
method. The performance testing via seasonal time-slice simulations is
presented in Sect. 3.3.
Results and discussionExtremal circulation patterns for the Wupper catchment
The greater diversity of synoptic patterns that can lead to extreme
precipitation in the Wupper catchment in summer, compared to winter, can be
seen in the number of clusters K necessary before our stability
criterion (see Sect. 2.1) is reached (Figs. 3 and 4). The higher K also
hints at the generally more challenging nature of forecasting summertime
intense precipitation, when synoptic forcing tends to be weaker and
small-scale chaotic processes play an increased role. In winter (Fig. 3),
precipitation extremes in the Wupper catchment are most often associated with
a dipole-like structure characteristic of a strong positive phase of the
North Atlantic Oscillation , with various shifts of
the dipole centres (clusters 1–3). Such a synoptic pattern gives a strong
zonal forcing, sweeping deep low-pressure systems and associated frontal
precipitation across the catchment; similar clusters have previously been
identified for north-eastern Switzerland . For
the remaining cluster (cluster 4) and the outlier, shallower depressions
become embedded in a relatively weak zonal flow, depositing their albeit less
intense precipitation over a more prolonged period; these patterns account
for less than one-sixth of all extreme days (P≥P99D)
though. In summer, a dipole-like pattern can also be seen on some extreme
days (cluster 1), though accounting for just over one-seventh of all
extremes; such events in summer can also be expected to include enhanced
frontal convection. The remainder of the summertime extremes are associated
with a weaker zonal forcing. High pressure over eastern Europe often advects
warm, moist air from the Mediterranean into central Europe (clusters 2 and 4),
enhancing instability and increasing the chance of deep convection;
also identified such a pattern as bringing
intense precipitation to south-west Germany during summer. Another common
pattern is that of a front, often with a small embedded low, extending across
the catchment (clusters 3 and 8) in the wake of an eastward moving ridge and
triggering frontal lifting as it passes. Quasi-stationary mid-tropospheric
cut-off lows (clusters 5–7) are the most common cause of summertime extremes
in our catchment, allowing slow-moving surface lows to advect a persistent
moisture stream, within which intense convective cells can develop, across
the catchment. A not dissimilar pattern was also identified by
in their study of extreme precipitation in Austria.
Evaluation and validation of identified PEDs
While still capturing more or less all observed extreme days, the constraints
derived from ERA-Interim variables enable the classification algorithm to
reduce the number of PEDs to well below 10 % of all days (Table 2). In the
process, the number of “redundant days” (i.e. P<P90D)
falls from about 3000 to 48 in winter and 126 in summer. The “redundant
days” thus occupy a much smaller fraction in the PEDs than in the set of all
days. Such a good performance in the training dataset is, however, no surprise.
Applying the same methodology to the 0.11∘ CCLM evaluation runs
(ERA-Interim driven) over the same period, a similar number of PEDs are
identified for dynamical downscaling to 0.02∘ (Table 2). The PEDs
again represent well below 10 % of all days, slashing the computational
expense against a continuous simulation of the whole period by an order of
magnitude. Of note is that although the 0.11∘ CCLM simulations are
forced at the lateral boundaries by ERA-Interim, only 123 of the 320 dates
identified as PEDs in CCLM in summer are also found amongst the ERA-Interim
PEDs. This is attributable to the fact that RCMs without interior constraints
(i.e. some form of internal nudging) cannot synchronously reproduce the
local-scale day-to-day variability of their parent model
. RCMs of sufficiently large domain size
thus often generate large internal variability
e.g., often comparable to that found in
GCMs , which can cause the local RCM solution
to significantly deviate from that of its parent model. In the presence of a
strong zonal throughflow, e.g. in winter, the growth of differing internal
solutions is limited due to small-scale perturbations being more rapidly
swept out of the domain . This explains the higher
fraction of common days that we find in winter (150 / 220).
Summary table of the performance of the classification algorithm for training
period (ERA-Interim) and CCLM evaluation runs. “Redundant days” are defined
as days with precipitation below the 90th percentile (all days). The third column
shows the percentage of total days identified as PEDs, with the fourth column
showing the percentage of actual extreme days contained within these PEDs. The
rightmost column compares the fraction of redundant days (P<P90D)
contained in the PEDs and amongst the set containing all days (“All days”).
Empirical cumulative distribution functions of daily precipitation
for all days (red, observed), PEDs (blue, observed), and CCLM PEDs (green,
downscaled to 0.02∘) in (a) winter 1980–2015 and
(b) summer 1979–2015 (up to 31 July 2015). Differences between the
blue and red curves (REGNIE) highlight the increased likelihood of heavy
rainfall events amongst the PEDs. All values are area averages over the
Wupper catchment. Vertical red lines mark important percentiles of the
all-day distribution. The area of the Wupper catchment encompasses 753 and
161 grid cells of REGNIE and CCLM data, respectively. Stations in and around
the Wupper catchment are marked in Fig. 2. The similarity of the
blue (REGNIE) and green (CCLM) PED curves shows that, with skilful
identification of PEDs, convection-permitting downscaling can reproduce
the observed PED statistics well.
Comparing the empirical cumulative distribution functions (ECDFs) for
catchment-averaged precipitation (observed) of all days and PEDs from the
training dataset (ERA-Interim), the greatly increased probability of heavy
precipitation on a randomly selected PED becomes apparent (Fig. 5, blue
curve): in the set of PEDs, the probability of exceeding the climatological
winter (a) 99th (90th) percentile is about 20 % (80 %), whereas in the set
of all days it is only 1 % (10 %). For summer (b), the situation is less
pronounced but the climatological (JJA) 99th (90th) percentile is exceeded on
about 15 % (60 %) of the days in the PED set.
Taking all days, the ECDF can be well described by a typical gamma distribution; the gamma
distribution is known to represent the bulk of the daily precipitation
distribution well, though it performs less well for the tails .
The form of the ECDF of the observed PEDs (blue curve), however, is far
removed from that of the set of all days (red curve), as the probability is
shifted towards more intense precipitation. The change in form of the ECDF – from
one dominated by dry to light-rain days, to one dominated by heavy- to
extreme-rain days – results from the classification algorithm's removal of
days with a low potential for intense precipitation.
Illustrative modelled PEDs. (a) Example summer PED
downscaled to 0.02∘ and (b) the same day in the
0.11∘ parent model. In this example, the strongest precipitation
directly strikes the catchment in the 0.02∘ CCLM despite missing the
catchment in the parent 0.11∘ CCLM. (c) Example summer PED
with highly localized intense precipitation that falls outside the catchment
in the 0.02∘ CCLM. (d) The corresponding day in the
0.11∘ CCLM.
Dynamically downscaling all CCLM 0.11∘ PEDs to 0.02∘
produces ECDFs of daily precipitation that closely resemble those of the
observed PEDs, for both seasons (Fig. 5, green curve); both ECDFs are again
dominated by heavy to extreme precipitation events, with dry days
(PD<0.1 mm) almost completely eliminated. Indeed, many of
the seemingly dry to light-rain days counted over the Wupper catchment in the
convection-permitting simulations do still feature heavy precipitation,
though displaced to neighbouring regions of the 0.02∘ simulation
domain (Fig. 6); this occurs most often in summer, owing to the more
small-scale and chaotic nature of convective precipitation. The good match
between the ECDFs of observed and downscaled PEDs shows that, with skilful
classification of the PEDs, selective downscaling can be relied on to
realistically reproduce the same range of precipitation events over the
catchment as expected from the training dataset and observations, allowing of
course for known model biases e.g.. In the
process, computational expense is reduced by over 90 % (Table 2) compared
to the computational efforts that would be required for a continuous
simulation over the same period at such high spatial resolution. While the
spatial resolutions of REGNIE and CCLM are similar (1 and 2.2 km,
respectively), users should beware that area means in datasets with
considerably different grid resolutions may differ simply because of the
different sample sizes, i.e. the number of grid cells contained within the
averaging area, in particular for small catchments and large differences in
the grid-box area.
Performance testing on seasonal time-slice simulations
The dynamical-downscaling of two sets of 30-summer time slices – historical (1970–1999)
and RCP8.5 (2070–2099) – from 0.11 to 0.02∘
provides an additional set of tests for the classification algorithm, namely:
what fraction of the actually simulated extreme days in the 0.02∘
model would the method have identified as PEDs from the 0.11∘ model?
In addition, is classification performance degraded in a future climate? The
summer season is chosen to ask these questions due to the greater challenges
in predicting summertime intense precipitation (see Sects. 2.4 and 3.1).
Summary table of performance of classification algorithm for 0.11∘
CCLM historical and RCP8.5 simulations, continuously downscaled to 0.02∘
over 30 summers. “Redundant days” are defined as days with precipitation below
the 90th percentile (all days). The third column shows the percentage of total
days identified as PEDs, with the fourth column showing the percentage of actual
extreme days contained within these PEDs. The rightmost column compares the
fraction of redundant days (P<P90D) contained in the PEDs and amongst
the set containing all days (“All days”).
Data/experimentTime periodPEDsP99D capturedRedundant days (No. of days)(No. of days)(days / total days)(days / total days) PEDsAll daysMPI-ESM-LR/CCLM-0.11∘JJA 1970–19999.8 %75 %49.8 %90.0 %CORDEX-EU/Historical(2760)(271)(21 / 28)(135 / 271)(2484 / 2760)MPI-ESM-LR/CCLM-0.11∘JJA 2070–20999.5 %82 %42.9 %90.0 %CORDEX-EU/RCP8.5(2760)(261)(23 / 28)(112 / 261)(2484 / 2760)
Applying the classification algorithm, identically to in Sect. 3.2, to the
0.11∘ historical and RCP8.5 simulations again yields selections of
PEDs representing less than 10 % of the total days (Table 3). Amongst these
PEDs, at least 75 % of 0.02∘-simulation extreme days are captured
in both time slices. In the case of the historical simulations, the fraction
of redundant days (i.e. P<P90D) climbs by almost six
percentage points relative to the training dataset; for the RCP8.5
simulations, the fraction falls marginally. The former increase may simply be
an artefact of the fewer summers (30 vs. 37) present in this testing dataset. The similarity of performance between the historical and future
simulations is noteworthy, particularly in light of RCP8.5
2070–2099 representing the end of the most extreme RCP scenario. Projected changes in
large-scale extratropical circulation can be considerable
e.g. and are known to
exert strong control on regional precipitation climatologies
. In the case of the MPI-ESM-LR model used in
this study, for example, a northward shift of the annual-mean jet in the
Atlantic sector and reduction in the frequency of
both North Atlantic and Eurasian summertime anticyclonic blocking
are projected under the RCP8.5 scenario. Despite
this, the classification algorithm performs more or less the same in
historical and future climates. While the classification algorithm
unsurprisingly fails to capture all extreme days in either the historical or
RCP8.5 simulations, the fact that the performance is the same across both
climates indicates the added value of employing our downscaling methodology,
allowing more robust conclusions to be drawn from the output. Of the extreme
days that are not captured, 6 out of 7 (historical) and 4 out of 5 (RCP8.5)
are lost due to their circulation patterns not matching any of the
pre-defined extremal clusters well. This could indicate that the training period
for identifying the extremal patterns is too short to encompass sufficient
diversity or, more likely, that the GCM in question (MPI-ESM-LR) does not
adequately represent the frequency and/or persistence of the large-scale
circulation patterns that lead to observed extremes in our catchment. For
example, CMIP5 GCMs are known to underestimate the frequency of Eurasian
blocking and GCMs in general often underestimate the
persistence of blocking systems e.g.;
the poleward flank of such blocking anticyclones often transports warm moist
air into central Europe, enabling intense convective precipitation (see Sect. 3.1).
In the case of MPI-ESM-LR during summer, a southward bias in the
storm-track axis and over-active North Atlantic blocking are also evident in
the CMIP5 historical simulations .
The similar performance of the classification algorithm across climates, as
well as the evaluation period, is confirmed by looking at the historical and
RCP8.5 ECDFs (Fig. 7). As in the training dataset, the ECDFs of the PEDs are
shifted towards more intense precipitation compared to the ECDFs for the sets
of all days. For the PEDs, the probability of exceeding the respective
climatological (JJA) 99th (90th) percentile in the historical and RCP8.5
simulations is similar to that found in the training dataset and the dynamically
downscaled PEDs of the evaluation period, roughly 10 % (55 %) (compared to
1 % (10 %) for all days), and the
ECDFs are dominated by heavy to extreme events with dry days almost absent.
To quantify differences in the distributions of precipitation events amongst
all days and the PEDs for discrete intensity ranges, we compute the relative
likelihoods (R) of finding a precipitation event within a given
intensity range for the historical and RCP8.5 simulations (Fig. 8); this is
simply the ratio of the respective probabilities, e.g. P(E|PED):P(E),
with the smaller of the two probabilities used as the denominator for
plotting purposes.
Empirical cumulative distribution functions of daily precipitation
for all days (red) and PEDs (blue) downscaled to 0.02∘.
(a) Historical (JJA, 1970–1999), (b) RCP8.5 (JJA,
2070–2099). All values are area averages over the Wupper catchment. Vertical
red lines mark important percentiles of the all-day distribution.
Relative likelihoods of precipitation on a randomly sampled day from
the set of all days and the PEDs being within a given intensity range for the
(a) historical and (b) RCP8.5 0.02∘ simulations.
Note that precipitation intensities are based on the percentiles of wet days
(PD≥0.1 mm).
The greatest difference between all days and the PEDs is found in the
relative likelihoods of a randomly sampled day being dry, which is an
order of magnitude lower in the PEDs. Indeed, considering the set of
non-PEDs, the probability density function exhibits an even higher density of
dry days than that found for all days (not shown). Focusing on just wet-day
percentiles, a regime shift from a higher R for all days to a higher R
for PEDs occurs above the median wet-day event. The higher R
for the PEDs grows further as event intensity nears the most extreme
precipitation events, consistent across historical and RCP8.5 experiments and
approaching a factor of 10 in places (Fig. 8). For the most extreme events
(PD≥PW99.9), more variability between
historical and RCP8.5 R values emerges as the number of days involved
limits towards zero. Future changes in the fraction of wet days, and the
sensitivity of wet-day percentiles to such changes
, likely contribute to some of the small
differences in relative likelihood between the historical and RCP8.5 experiments.
Percentage change in daily precipitation intensity between the
historical and RCP8.5 periods (JJA), conditional on extremal circulation
pattern, from the 0.02∘ simulations. The numbers indicate the total
number of PEDs for each pattern (i.e. cluster) in the historical (left) and
RCP8.5 (right) periods, while vertical bars represent 90 % confidence
intervals. Clusters with less than 10 days in either period are excluded from
the calculations. On the right hand side, the corresponding climate change
signal for the 95th and 99th percentile of all days is provided for reference.
Applications and outlook
The preconditioning of PEDs on known extremal circulation patterns does not
just reduce the total number of days to dynamically downscale. Importantly,
it also allows conclusions to be drawn about changes in catchment-relevant
precipitation between two periods, e.g. present and future climates, for
these circulation patterns. A classification method that does not
guarantee the capture of all extreme days clearly cannot be used to
draw overall conclusions about precipitation changes in a given catchment.
Preconditioning on circulation types does, however, allow conclusions to be
drawn about changes in specific classes of precipitation extreme (Fig. 9),
e.g. as identified via the clustering methodology outlined in Sect. 2.1. For
example, for a known extremal circulation pattern, will the likelihood that
the accompanying precipitation exceeds some catchment-relevant threshold be
higher or lower in the future? This approach is in a way analogous to the
framework used in conditional event attribution
e.g., where the
question is posed: for some observed circulation pattern, how is the event's
intensity affected by known thermodynamic changes in the Earth's climate
system? A major advantage of such an approach is the relative robustness of
projected thermodynamic changes in the climate system compared to projected
dynamical changes . From a catchment-hydrology
perspective, one could imagine this being particularly useful for catchments
vulnerable to specific compound extremes, for example intense precipitation
in an estuarine catchment compounded by a shoreward moving low-pressure
system with strong onshore winds e.g..
Beyond the extremal patterns identified from the training period, however,
there remains the possibility that a future climate may also contain new
extremal circulation patterns that were previously either not associated
with extreme precipitation or simply not present at all. Such systematic
effects could only be explored with continuous dynamical downscaling of the
different climates.
Further discussion
The consistent performance of the classification scheme across historical and
future climates further demonstrates its utility for studying changes in
defined classes of precipitation extreme, for example those preconditioned on
an identified extremal synoptic pattern that is known to severely affect a
given catchment. In this regard, our method is complementary to current
trends in how the projected impacts of climate change are communicated and
adapted to end-user needs. Recent literature advocates the use of
high-resolution weather models to create bespoke storylines of high-impact
weather events for a given catchment in a future climate
. In the so-called “Tales” approach of
, the broad statistical terms in which climate
change projections are typically communicated are replaced by high-resolution
simulations of carefully selected past and future weather events over a given
catchment in order to study the catchment-specific impacts of individual
hydrometeorological events from past and future climates. This approach is
designed to form part of a collaborative process in which end users play a
key role in selecting the type of events to be studied, providing vivid
case-studies on which adaptation strategies can be decided
. Our methodology could be integrated seamlessly
into this workflow. An additional advantage of this type of modelling
framework is that anthropogenic factors extraneous to global climate change
can easily be implemented into the modelling chain
, for example adding potential changes in land-use
to a high-resolution hydrological model, or changes in hydraulic
infrastructure to a hydraulic model for assessing impacts on reservoirs,
water-treatment plants, drainage systems, etc.
An important element in the transferability of the method to other catchments
is its inherent flexibility, allowing in particular for the active involvement
of end users. End users can contribute and integrate their empirical
knowledge towards the identification of the local-scale meteorological
predictors most suitable for their own catchment, perhaps taking the ones we
use or those suggested in as a starting point. Data
availability in the models to be downscaled may, however, require choosing
parameters that are only approximate indicators of the most suitable ones.
For the Wupper catchment studied here, for example, we found daily maximum
700 hPa vertical velocity to perform better than daily maximum 500 hPa
horizontal divergence as an indicator of extreme precipitation in the
training dataset. The regional model that we wished to downscale, however,
had saved vertical velocity at too low a temporal resolution to meaningfully
calculate daily maxima. The adoption of horizontal divergence was thus
necessitated, allowing the PEDs to still be appropriately classified while
avoiding an unacceptable increase in computational expense. The method is
additionally adaptable to the computing capacity of the user. With the caveat
that excessively high thresholds will result in more undesirably rejected
days, thresholds for the identification of PEDs can be either raised or
lowered based on available computational resources.
Data produced via a method like ours are indeed useful for many applications,
though not universally so, and do also come with their own limitations. Care
must therefore be taken when applying such data and interpreting subsequent
results. The issue of stationarity should be acknowledged: one can never be
certain that a future climate will not include heavy precipitation events
caused by previously unimportant circulation patterns. Non-stationarity may
also, positively or negatively, impact the effectiveness of local-scale
predictors. Non-stationarity is indeed a common issue also affecting model
parametrization schemes and statistical downscaling – a motivating factor
for anchoring our method with a convection-permitting model. Additionally,
the catalogue of downscaled PEDs is no random sample of high-resolution
climate data and thus cannot be treated as traditional projections.
Traditional projections can only be made with continuous, multi-decadal
downscaling, and not with the discontinuous time series that we produce.
Our method is instead ideal for applications requiring high-resolution data
suitable as input for modelling the catchment-scale impacts of extremes. Such
applications include (i) design situations and stress testing for hydraulic
infrastructure, e.g. dams, canal networks, urban sewerage systems, and
(ii) process-oriented case studies of the catchment's response to extremes,
e.g. runoff formation processes leading to flooding. In such applications, the
emphasis is on combining realistic initial conditions with
physically plausible and realistic extremes, as input for the hydrological
models. Typical problems with using observational data for such studies are
that the spatial and/or temporal coverage of the observational network was
insufficient to capture suitably extreme historical events to use in, e.g.
design situations. Coarser model data present problems too, in that they also
tend not to realistically capture the peak intensities and spatial
variability of such intense events (see Sect. 1). For such studies,
hydrological models would need to be calibrated with either observations or
lower-resolution RCM data. Realistic initial conditions, e.g. for design
situations, can also be obtained from such sources or, as is often the case,
prescribed and varied in order to test the sensitivity to initial conditions
of the catchment's response to a given extreme. For example, the reservoir
level prior to a rain-on-snow event – such events can quickly mobilize large
volumes of water into runoff, potentially overwhelming hydraulic infrastructure.
A further means through which our methodology can be used to limit
computational expense is in the selection of individual models from
multi-model ensembles (e.g. CMIP) to downscale over a given region, avoiding
the computational expense of dynamically downscaling an entire multi-model
ensemble. GCMs whose historical runs fail to satisfactorily reproduce the
observed PED climatology, i.e. the seasonal frequency of PEDs, could be
considered to poorly represent the regional extremal circulation patterns and
thus be rejected in favour of the top N best-performing models, with
N a function of both available computing resources and the reduction
in intra-ensemble spread that can be tolerated. Such a region-targeted
selection of GCMs could even be combined with the
aforementioned “Tales” approach, making a potent tool.
Conclusions
Hydrological modellers, amongst others, benefit greatly from high-resolution
climate data at the catchment scale – particularly for studying the impacts
of extreme precipitation. In achieving these high resolutions O(1 km)
while maintaining data quality, dynamical downscaling to
convection-permitting resolution presents numerous advantages, though it comes
at an often prohibitive computational expense. To reduce the overall
computational burden and instead dynamically downscale only those days for
which there is an elevated likelihood of extreme precipitation in a
catchment, we have developed a flexible and transferable classification
algorithm for identifying potential extreme days (PEDs) and rejecting days
unlikely to produce intense precipitation. While reducing computational
expense by over 90 %, the precipitation distribution of the training
dataset's PEDs – in which more or less all extreme days were captured – was
well reproduced via convection-permitting dynamical downscaling, showing an
ECDF dominated by heavy precipitation events. Testing the classification
algorithm on continuous datasets driven by a different global model, at least
three-quarters of the convection-permitting model's summertime extremes – which
are intrinsically more challenging to identify than their wintertime
counterparts – were caught and computational expenses were again slashed by
over 90 %.
Our method represents a computationally inexpensive procedure to produce
high-resolution climate data, focused on extreme rainfall events, for
hydrological modellers and decision-makers, while retaining the advantages of
the convection-permitting modelling framework (see Sect. 1). The
explicit simulation of fine-scale processes along the modelling chain gives
additional confidence in the end product, as fine-scale processes can
substantially modulate the regional climate change signal
. Irrespective of increases in processor power,
regional models will always be able to be run at higher spatial resolutions
than their global counterparts. Should global models some day run at
convection-permitting resolution as standard, classification algorithms can
still be utilized for downscaling to ever-higher resolutions at which even
more processes can be explicitly simulated, e.g. turbulence. Classification
algorithms, such as the one presented here, for selective dynamical
downscaling preconditioned on known extremal circulation patterns can thus
play an important and enduring role in climate modelling.
ERA-Interim reanalyses (Dee et al., 2011) are available
from the ECMWF (ECMWF: http://apps.ecmwf.int/datasets/data/interim-full-daily/,
last access: 25 July 2018). REGNIE precipitation data (Rauthe et al., 2013) are
available from the German weather service (DWD: https://www.dwd.de/DE/leistungen/regnie/regnie.html,
last access: 25 July 2018). The 0.11∘ CORDEX data used within this study
are distributed within the CORDEX framework by the Earth System Grid Federation
(ESGF: e.g. https://esgfdata.dkrz.de/projects/esgf-dkrz/, last access:
25 July 2018). All remaining simulation data and scripts are available from
the corresponding author on request.
EM developed the method, performed the analysis and wrote
the paper. HR and UU contributed ideas and comments on the method, analysis
and paper.
The authors declare that they have no conflict of interest.
Acknowledgements
We thank Rasmus Benestad and Patrick Laux for their helpful reviews.
This study was funded by the European Commission through the H2020 project
BINGO (http://www.projectbingo.eu/, last access: 25 July 2018), grant agreement 641739.
Edmund Meredith additionally received part funding from the EUREX project of the
Helmholtz Association (HRJRG-308).
Simulations were carried out at the North-German Supercomputing Alliance (HLRN)
and the German Climate Computing Centre (DKRZ). We thank the German
weather service (DWD) for producing and making available the REGNIE
precipitation dataset. We thank the EU COST Action 733 for producing and
making available the clustering software
(http://cost733.geo.uni-augsburg.de, last access: 25 July 2018). Analyses and plotting were
performed with NCL (Version 6.4.0, 10.5065/D6WD3XH5) and R. We thank
Tim aus der Beek, Martin Göber, Komlan A. Kpogo-Nuwoklo, Tobias Pardowitz,
Marc Scheibel, Christos Vagenas and Claudia Volosciuk for helpful discussions.
Edited by: Andràs Bàrdossy
Reviewed by: Patrick Laux and Rasmus Benestad
References
Ban, N., Schmidli, J., and Schär, C.: Evaluation of the convection-resolving
regional climate modeling approach in decade-long simulations, J. Geophys.
Res.-Atmos., 119, 7889–7907, 2014.
Bárdossy, A.: Atmospheric circulation pattern classification for South-West
Germany using hydrological variables, Phys. Chem. Earth A/B/C, 35, 498–506, 2010.
Barnes, E. A. and Polvani, L.: Response of the midlatitude jets, and of their
variability, to increased greenhouse gases in the CMIP5 models, J. Climate,
26, 7117–7135, 2013.Benestad, R. E., Hanssen-Bauer, I., and Chen, D.: Empirical-statistical
downscaling, World Scientific Publishing Company, Singapore, 10.1142/6908, 2008.Bevacqua, E., Maraun, D., Hobæk Haff, I., Widmann, M., and Vrac, M.:
Multivariate statistical modelling of compound events via pair-copula
constructions: analysis of floods in Ravenna (Italy), Hydrol. Earth Syst. Sci.,
21, 2701–2723, 10.5194/hess-21-2701-2017, 2017.
Boberg, F., Berg, P., Thejll, P., Gutowski, W. J., and Christensen, J. H.:
Improved confidence in climate change projections of precipitation evaluated
using daily statistics from the PRUDENCE ensemble, Clim. Dynam., 32, 1097–1106, 2009.
Brigode, P., Bernardara, P., Gailhard, J., Garavaglia, F., Ribstein, P., and
Merz, R.: Optimization of the geopotential heights information used in a
rainfall-based weather patterns classification over Austria, Int. J. Climatol.,
33, 1563–1573, 2013.
Brisson, E., Demuzere, M., and van Lipzig, N. P.: Modelling strategies for
performing convection-permitting climate simulations, Meteorol. Z., 25, 149–163, 2016a.
Brisson, E., Van Weverberg, K., Demuzere, M., Devis, A., Saeed, S., Stengel, M.,
and van Lipzig, N. P.: How well can a convection-permitting climate model
reproduce decadal statistics of precipitation, temperature and cloud characteristics?,
Clim. Dynam., 47, 3043–3061, 2016b.Chan, S. C., Kendon, E. J., Roberts, N., Blenkinsop, S., and Fowler, H. J.:
Large-Scale Predictors for Extreme Hourly Precipitation Events in
Convection-Permitting Climate Simulations, J. Climate, 31, 2115–2131,
10.1175/JCLI-D-17-0404.1, 2018.
Christensen, O., Gaertner, M., Prego, J., and Polcher, J.: Internal variability
of regional climate models, Clim. Dynam., 17, 875–887, 2001.Dee, D. P., Uppala, S. M., Simmons, A. J., Berrisford, P., Poli, P., Kobayashi,
S., Andrae, U., Balmaseda, M. A., Balsamo, G., Bauer, P., Bechtold, P., Beljaars,
A. C. M., van de Berg, L., Bidlot, J., Bormann, N., Delsol, C., Dragani, R.,
Fuentes, M., Geer, A. J., Haimberger, L., Healy, S. B., Hersbach, H., Hólm,
E. V., Isaksen, L., Kållberg, P., Köhler, M., Matricardi, M., McNally,
A. P., Monge-Sanz, B. M., Morcrette, J.-J., Park, B.-K., Peubey, C., de Rosnay,
P., Tavolato, C., Thépaut, J.-N., and Vitart, F.: The ERA-Interim reanalysis:
configuration and performance of the data assimilation system, Q. J. Roy. Meteorol.
Soc., 137, 553–597, 10.1002/qj.828, 2011.
Denis, B., Laprise, R., and Caya, D.: Sensitivity of a regional climate model
to the resolution of the lateral boundary conditions, Clim. Dynam., 20, 107–126, 2003.
Diffenbaugh, N. S., Pal, J. S., Trapp, R. J., and Giorgi, F.: Fine-scale
processes regulate the response of extreme events to global climate change, P.
Natl. Acad. Sci. USA, 102, 15774–15778, 2005.
Di Luca, A., de Elía, R., and Laprise, R.: Potential for added value in
precipitation simulated by high-resolution nested regional climate models and
observations, Clim. Dynam., 38, 1229–1247, 2012.
Feser, F., Rockel, B., von Storch, H., Winterfeldt, J., and Zahn, M.: Regional
climate models add value to global model data: a review and selected examples,
B. Am. Meteorol. Soc., 92, 1181–1192, 2011.
Fosser, G., Khodayar, S., and Berg, P.: Benefit of convection permitting
climate model simulations in the representation of convective precipitation,
Clim. Dynam., 44, 45–60, 2015.
Giannakaki, P. and Martius, O.: Synoptic-scale flow structures associated with
extreme precipitation events in northern Switzerland, Int. J. Climatol., 36, 2497–2515, 2016.
Giorgi, F. and Bi, X.: A study of internal variability of a regional climate
model, J. Geophys. Res.-Atmos., 105, 29503–29521, 2000.
Hazeleger, W., Van den Hurk, B., Min, E., Van Oldenborgh, G., Petersen, A.,
Stainforth, D., Vasileiadou, E., and Smith, L.: Tales of future weather, Nat.
Clim. Change, 5, 107–113, 2015.
Heikkilä, U., Sandvik, A., and Sorteberg, A.: Dynamical downscaling of ERA-40
in complex terrain using the WRF regional climate model, Clim. Dynam., 37, 1551–1564, 2011.
Hidalgo-Muñoz, J., Argüeso, D., Gámiz-Fortis, S., Esteban-Parra,
M., and Castro-Díez, Y.: Trends of extreme precipitation and associated
synoptic patterns over the southern Iberian Peninsula, J. Hydrol., 409, 497–511, 2011.
Hofstra, N., New, M., and McSweeney, C.: The influence of interpolation and
station network density on the distributions and trends of climate variables
in gridded daily data, Clim. Dynam., 35, 841–858, 2010.
Hohenegger, C., Brockhaus, P., and Schaer, C.: Towards climate simulations at
cloud-resolving scales, Meteorol. Z., 17, 383–394, 2008.
Hurrell, J. W.: Decadal trends in the North Atlantic Oscillation: regional
temperatures and precipitation, Science, 269, 676–678, 1995.Jacob, D., Petersen, J., Eggert, B., Alias, A., Christensen, O. B., Bouwer, L.
M., Braun, A., Colette, A., Déqué, M., Georgievski, G., Georgopoulou,
E., Gobiet, A., Menut, L., Nikulin, G., Haensler, A., Hempelmann, N., Jones, C.,
Keuler, K., Kovats, S., Kröner, N., Kotlarski, S., Kriegsmann, A., Martin,
E., van Meijgaard, E., Moseley, C., Pfeifer, S., Preuschmann, S., Radermacher,
C., Radtke, K., Rechid, D., Rounsevell, M., Samuelsson, P., Somot, S., Soussana,
J.-F., Teichmann, C., Valentini, R., Vautard, R., Weber, B., and Yiou, P.:
EURO-CORDEX: new high-resolution climate change projections for European impact
research, Reg. Environ. Change, 14, 563–578, 10.1007/s10113-013-0499-2, 2014.
Kendon, E. J., Roberts, N. M., Senior, C. A., and Roberts, M. J.: Realism of
rainfall in a very high-resolution regional climate model, J. Climate, 25, 5791–5806, 2012.
Kendon, E. J., Roberts, N. M., Fowler, H. J., Roberts, M. J., Chan, S. C., and
Senior, C. A.: Heavier summer downpours with climate change revealed by weather
forecast resolution model, Nat. Clim. Change, 4, 570–576, 2014.
Kendon, E. J., Ban, N., Roberts, N. M., Fowler, H. J., Roberts, M. J., Chan, S.
C., Evans, J. P., Fosser, G., and Wilkinson, J. M.: Do convection-permitting
regional climate models improve projections of future precipitation change?,
B. Am. Meteorol. Soc., 98, 79–93, 2017.
Keuler, K., Radtke, K., Kotlarski, S., and Lüthi, D.: Regional climate
change over Europe in COSMO-CLM: Influence of emission scenario and driving
global model, Meteorol. Z., 25, 121–136, 2016.Kotlarski, S., Keuler, K., Christensen, O. B., Colette, A., Déqué, M.,
Gobiet, A., Goergen, K., Jacob, D., Lüthi, D., van Meijgaard, E., Nikulin,
G., Schär, C., Teichmann, C., Vautard, R., Warrach-Sagi, K., and Wulfmeyer,
V.: Regional climate modeling on European scales: a joint standard evaluation
of the EURO-CORDEX RCM ensemble, Geosci. Model Dev., 7, 1297–1333, 10.5194/gmd-7-1297-2014, 2014.
Lean, H. W., Clark, P. A., Dixon, M., Roberts, N. M., Fitch, A., Forbes, R.,
and Halliwell, C.: Characteristics of high-resolution versions of the Met
Office Unified Model for forecasting convection over the United Kingdom, Mon.
Weather Rev., 136, 3408–3424, 2008.
Lucas-Picher, P., Caya, D., de Elía, R., and Laprise, R.: Investigation of
regional climate models' internal variability with a ten-member ensemble of
10-year simulations over a large domain, Clim. Dynam., 31, 927–940, 2008.Ly, S., Charles, C., and Degré, A.: Geostatistical interpolation of daily
rainfall at catchment scale: the use of several variogram models in the Ourthe
and Ambleve catchments, Belgium, Hydrol. Earth Syst. Sci., 15, 2259–2274,
10.5194/hess-15-2259-2011, 2011.Maraun, D. and Widmann, M.: The representation of location by a regional climate
model in complex terrain, Hydrol. Earth Syst. Sci., 19, 3449–3456, 10.5194/hess-19-3449-2015, 2015.Maraun, D., Wetterhall, F., Ireson, A. M., Chandler, R. E., Kendon, E. J.,
Widmann, M., Brienen, S., Rust, H. W., Sauter, T., Themeßl, M., Venema, V.
K. C., Chun, K. P., Goodess, C. M., Jones, R. G., Onof, C., Vrac, M., and
Thiele-Eich, I.: Precipitation downscaling under climate change: Recent
developments to bridge the gap between dynamical models and the end user, Rev.
Geophys., 48, RG3003, 10.1029/2009RG000314, 2010.Maraun, D., Shepherd, T. G., Widmann, M., Zappa, G., Walton, D., Gutierrez, J.
M., Hagemann, S., Richter, I., Soares, P. M. M., Hall, A., and Mearns, L. O.:
Towards process-informed bias correction of climate change simulations, Nat.
Clim. Change, 7, 764–773, 10.1038/nclimate3418, 2017.
Masato, G., Hoskins, B. J., and Woollings, T.: Winter and summer Northern
Hemisphere blocking in CMIP5 models, J. Climate, 26, 7044–7059, 2013.Matsueda, M.: Predictability of Euro-Russian blocking in summer of 2010, Geophys.
Res. Lett., 38, L06801, 10.1029/2010GL046557, 2011.
Meredith, E. P., Maraun, D., Semenov, V. A., and Park, W.: Evidence for added
value of convection-permitting models for studying changes in extreme precipitation,
J. Geophys. Res.-Atmos., 120, 12500–12513, 2015.
Merino, A., Fernández-Vaquero, M., López, L., Fernández-González,
S., Hermida, L., Sánchez, J. L., García-Ortega, E., and Gascón, E.:
Large-scale patterns of daily precipitation extremes on the Iberian Peninsula,
Int. J. Climatol., 36, 3873–3891, 2016.
Pall, P., Patricola, C. M., Wehner, M. F., Stone, D. A., Paciorek, C. J., and
Collins, W. D.: Diagnosing conditional anthropogenic contributions to heavy
Colorado rainfall in September 2013, Weather Clim. Extrem., 17, 1–6, 2017.Pan, Z., Takle, E., Gutowski, W., and Turner, R.: Long Simulation of Regional
Climate as a Sequence of Short Segments, Mon. Weather Rev., 127, 308–321,
10.1175/1520-0493(1999)127<0308:LSORCA>2.0.CO;2, 1999.
Philipp, A., Della-Marta, P.-M., Jacobeit, J., Fereday, D. R., Jones, P. D.,
Moberg, A., and Wanner, H.: Long-term variability of daily North Atlantic–European
pressure patterns since 1850 classified by simulated annealing clustering, J.
Climate, 20, 4065–4095, 2007.
Philipp, A., Beck, C., Huth, R., and Jacobeit, J.: Development and comparison
of circulation type classifications using the COST 733 dataset and software,
Int. J. Climatol., 36, 2673–2691, 2016.
Prein, A. F., Gobiet, A., Suklitsch, M., Truhetz, H., Awan, N., Keuler, K., and
Georgievski, G.: Added value of convection permitting seasonal simulations,
Clim. Dynam., 41, 2655–2677, 2013.
Prein, A. F., Langhans, W., Fosser, G., Ferrone, A., Ban, N., Goergen, K.,
Keller, M., Tölle, M., Gutjahr, O., Feser, F., Brisson, E., Kollet, S.,
Schmidli, J., van Lipzig, N. P., and Leung, R.: A review on regional
convection-permitting climate modeling: Demonstrations, prospects, and
challenges, Rev. Geophys., 53, 323–361, 2015.Rauthe, M., Steiner, H., Riediger, U., Mazurkiewicz, A., and Gratzki, A.: A
Central European precipitation climatology – Part I: Generation and validation
of a high-resolution gridded daily data set (HYRAS), Meteorol. Z., 22, 235–256,
10.1127/0941-2948/2013/0436, 2013.
Roberts, N.: Assessing the spatial and temporal variation in the skill of
precipitation forecasts from an NWP model, Meteorol. Appl., 15, 163–169, 2008.
Rockel, B., Will, A., and Hense, A.: The regional climate model COSMO-CLM (CCLM),
Meteorol. Z., 17, 347–348, 2008.
Romero, R., Sumner, G., Ramis, C., and Genovés, A.: A classification of the
atmospheric circulation patterns producing significant daily rainfall in the
Spanish Mediterranean area, Int. J. Climatol., 19, 765–785, 1999.
Rummukainen, M.: State-of-the-art with Regional Climate Models, Wiley
Interdisciplin. Rev.: Clim. Change, 1, 82–96, 2010.
Rust, H. W., Vrac, M., Lengaigne, M., and Sultan, B.: Quantifying differences
in circulation patterns based on probabilistic models: IPCC AR4 multimodel
comparison for the North Atlantic, J. Climate, 23, 6573–6589, 2010.
Rust, H. W., Vrac, M., Sultan, B., and Lengaigne, M.: Mapping weather-type
influence on senegal precipitation based on a spatial-temporal statistical
model, J. Climate, 26, 8189–8209, 2013.
Schär, C., Ban, N., Fischer, E. M., Rajczak, J., Schmidli, J., Frei, C.,
Giorgi, F., Karl, T. R., Kendon, E. J., Tank, A. M. K., O'Gorman, P. A.,
Sillmann, J., Zhang, X., and Zwiers, F. W.: Percentile indices for assessing
changes in heavy precipitation events, Climatic Change, 137, 201–216, 2016.
Shepherd, T. G.: Atmospheric circulation as a source of uncertainty in climate
change projections, Nat. Geosci., 7, 703–708, 2014.
Shepherd, T. G.: A common framework for approaches to extreme event attribution,
Curr. Clim. Change Rep., 2, 28–38, 2016.
Sun, J., Trier, S. B., Xiao, Q., Weisman, M. L., Wang, H., Ying, Z., Xu, M.,
and Zhang, Y.: Sensitivity of 0–12-h warm-season precipitation forecasts over
the central United States to model initialization, Weather Forecast., 27, 832–855, 2012.
Takayabu, I., Kanamaru, H., Dairaku, K., Benestad, R., von Storch, H., and
Christensen, J. H.: Reconsidering the quality and utility of downscaling, J.
Meteorol. Soc. Jpn. Ser. II, 94, 31–45, 2016.
Taylor, K. E., Stouffer, R. J., and Meehl, G. A.: An overview of CMIP5 and the
experiment design, B. Am. Meteorol. Soc., 93, 485, 2012.Torma, C., Giorgi, F., and Coppola, E.: Added value of regional climate modeling
over areas characterized by complex terrain – Precipitation over the Alps, J.
Geophys. Res.-Atmos., 120, 3957–3972, 2015.
Trenberth, K. E., Fasullo, J. T., and Shepherd, T. G.: Attribution of climate
extreme events, Nat. Clim. Change, 5, 725–730, 2015.
Van Vuuren, D. P., Edmonds, J., Kainuma, M., Riahi, K., Thomson, A., Hibbard,
K., Hurtt, G. C., Kram, T., Krey, V., Lamarque, J.-F., Masui, T., Meinshausen,
M., Nakicenovic, N., Smith, S. J., and Rose, S. K.: The representative
concentration pathways: an overview, Climatic Change, 109, 5–31, 2011.Veljovic, K., Rajkovic, B., Fennessy, M. J., Altshuler, E. L., and Mesinger, F.:
Regional climate modeling: Should one attempt improving on the large scales?
Lateral boundary condition scheme: Any impact?, Meteorol. Z., 19, 237–246,
10.1127/0941-2948/2010/0460, 2010.
Volosciuk, C., Maraun, D., Semenov, V. A., and Park, W.: Extreme precipitation
in an atmosphere general circulation model: impact of horizontal and vertical
model resolutions, J. Climate, 28, 1184–1205, 2015.
Weisman, M. L., Davis, C., Wang, W., Manning, K. W., and Klemp, J. B.:
Experiences with 0–36-h explicit convective forecasts with the WRF-ARW model,
Weather Forecast., 23, 407–437, 2008.
Wilby, R. L. and Wigley, T.: Downscaling general circulation model output: a
review of methods and limitations, Prog. Phys. Geogr., 21, 530–548, 1997.
Zappa, G., Shaffrey, L. C., Hodges, K. I., Sansom, P. G., and Stephenson, D. B.:
A multimodel assessment of future projections of North Atlantic and European
extratropical cyclones in the CMIP5 climate models, J. Climate, 26, 5846–5862, 2013.