ASRAdvances in Science and ResearchASRAdv. Sci. Res.1992-0636Copernicus PublicationsGöttingen, Germany10.5194/asr-15-107-2018Bias adjustment for threshold-based climate indicatorsBias adjustment for threshold-based climate indicatorsHoffmannPeterpeterh@pik-potsdam.deMenzChristophhttps://orcid.org/0000-0001-5127-1554SpekatArnePotsdam Institute for Climate Impact Research (PIK), Member of the
Leibniz Association, P.O. Box 60 12 03, 14412 Potsdam,
GermanyPeter Hoffmann (peterh@pik-potsdam.de)8June20181510711615February201811April201818April2018This 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://asr.copernicus.org/articles/15/107/2018/asr-15-107-2018.htmlThe full text article is available as a PDF file from https://asr.copernicus.org/articles/15/107/2018/asr-15-107-2018.pdf
A method is presented which applies bias adjustments to climate indicators
that are based on fixed thresholds, e.g., the number of hot days with the
maximum temperature exceeding 30∘C or the number of days with
heavy precipitation in exceedance of 20 mm rainfall. The bias adjustment
first identifies the percentile of the required threshold value in reference
climate data. Then it computes the value of this percentile for the
individual historical climate model simulations – here an ensembles of
EURO-CORDEX model runs, including dynamical and statistical models. Finally,
the climate indicator is re-calculated for each model. The method is applied
to climate projections as well, giving further insight into the projected
development of the ensemble for extreme conditions. It is assessed that
communication to the public and decision makers is improved by expressing
these changes in extremes based on absolute values.
IntroductionContext
The majority of climate models – global climate models as well as regional
climate models – exhibit systematic differences between the observed current
climate (e.g. in the reference period 1971–2000) and the simulated
climate. The technical term for this deviation is bias. Statistical
regional climate models, also called Empirical Statistical Downscaling Models
(ESDs) typically have a smaller bias than dynamical models, also called
Regional Climate Models (RCMs), since they are based on observation data.
Climate and climate impact research relies on simulations with no
considerable bias in order to be applicable for future time frames
. Thus, it is self-evident to reduce it by a bias
adjustment, as stated in .
Most bias adjustment approaches are based on the stationarity assumption of
the bias , i.e., they assume that the model bias is
not changing in time. This underlying assumption needs to be taken into
account when analysing bias adjusted model results or using them in impact
assessments, since it can distort the time series or add an artificial
component to the modeled climate change .
The standard procedure of bias adjustment is to apply it to individual
parameters of a climate simulation, e.g., precipitation or near-surface
temperature. However, interrelations between different modelled variables
(e.g., between temperature and humidity or between precipitation, soil water
contents and air temperature) are not taken into account. This assumption
ignores the reality of a fully coupled climate system and can potential
result in spurious model fields, rendered by the bias adjustment
. It could be shown, that this deficiency
have a significant impact on the adjusted fields and impair the usage of the
adjusted fields introducing
artificial errors. However recently more and more bias adjustment approaches
emerge, taking care of the multivariate structure of the system under
adjustment . Advantages and
limitations of bias adjustment methods are summarized in .
Pooled EURO-CORDEX simulations (green) and added simulations by
ReKliEs-De (orange).
The stationarity assumption and univariability of most bias adjustment
approaches used to-date can yield to artificial errors in model fields that,
in turn, could influence decisions by end users. It is therefore important to
communicate the side effects of applying a bias adjustment. The Project
ReKliEs-De (Regionale Klimaprojektionen Ensemble für Deutschland; Ensemble
of regional climate projection for Germany) not only had a focus on
contributing to EURO-CORDEX by producing runs of dynamical and statistical
climate models see; it also had a
focus on addressing end user needs
see. ReKliEs-De produced geographical
distributions of 24 climate indicators, mostly temperature- and
precipitation-based
For nomenclature and definitions of climate
indicators, see http://etccdi.pacificclimate.org/list_27_indices.shtml,
last access: 4 June 2018.
This posed a new challenge since so far bias
adjustments were devised to be applied to climate parameters but not to
indicators.
Within ReKliEs-De we use three different approaches to deal with model
inherent biases. We tried to use bias-independent indicators as much as
possible to circumvent potential deficiencies introduced by the model bias.
In all other cases we applied two different types of bias adjustment.
Indicators based on fixed thresholds were adjusted using the method described
in this article. All other indicators were adjusted using a classical bias
adjustment approach. Both bias adjustment approaches used in ReKliEs-De were
applied to single variables (ignoring covariables) and assume bias
stationarity.
Bias-independent indicators
Whenever the indicators are based on a relative measure, such as a
quantile, they are bias-free by definition. Examples for this type of
indicators are tx90p (number of days above the 90th
percentile of daily maximum temperature), tx10p (number of days below the
10th percentile of daily maximum temperature), wsdi (warm spell
duration index) csdi (cold spell duration index), r95ptot (precipitation
amount above the 95th percentile) and r99ptot (precipitation
amount above the 99th percentile). The threshold itself is
subject to the individual model's bias.
Indicators based on fixed thresholds
Numerous climate indicators are computed using prescribed thresholds. The
indicator su30, for example, counts the days on which the maximum
temperature exceeds a threshold of 30∘C. However, this
threshold is influenced by the model bias. The bias adjustment is then
performed by determining the percentile belonging to this threshold from
climate reference data and subsequently modifying the threshold itself
according to that percentile. Then the procedure of determining the day count
is repeated using the modified threshold which
will lead to similar values as the reference. The bulk of this paper will
deal with this threshold-modifying approach.
Classical bias adjustment approaches
A bias adjustment of this type directly changes simulated variables using a
set of prescribed rules to adapt the simulations to fit the reference data.
Those rules are devised in view of the target variable, e.g., the monthly
mean precipitation or the distribution of daily precipitation intensities.
Moreover, there is a dependency upon the reference dataset used. A rather
simple bias adjustment would consist of a linear shift of the data (adding to
or subtracting from the values). More sophisticated bias adjustment methods
result in complex effects on climate change signals. Two methods are
frequently applied: (i) Local Intensity Scaling (LOCI) described, e.g., in
and (ii) Analytical Quantile Mapping (AQM), described,
e.g., in or . An overview of these and
further bias adjustment methods can be found in .
Structure of the paper
The paper continues with a summary description of the ReKliEs-De simulation
matrix (GCM-RCM combination) as the basis for the climate extreme assessment
by calculating threshold-based climate indicators (Sect. 2). In order to
minimize the existing bias of the raw data against observations we introduce
a new approach which defines a model-specific adjusted threshold without
touching or manipulating the raw data (Sect. 3). For the climate indicators
su30 and r20mm all patterns in historical simulations with and without
adjusted threshold are compared and discussed (Sect. 4). Comparisons to
other approaches are summarized in the end (Sect. 5).
Dataset
The ensemble contains regional climate model simulations of the ReKliEs-De
and EURO-CORDEX projects (Table ). Besides
state-of-the-art dynamical regional downscaling models (RCMs) also
empirical-statistical downscaling models (ESDs) were used. The total ensemble
consists of 6 different RCMs (WRF, CCLM, HIRHAM5, RACMO22E, REMO and
RCA4) and 2 ESDs (WETTREG2013 and STARS3) driven by 7 different
Global Climate Models (EC-EARTH, CNRM-CM5, CanESM2, HadGEM2-ES,
MPI-ESM-LR, IPSL-CM5A-MR, MIROC5). Table
displays all combinations of RCMs and GCMs that were analyzed and allocates
them to their respective project. Within ReKliEs-De, GCMs were selected with
the aim to cover the spread of anticipated near-to-midterm (until 2100)
temperature and precipitation changes in the area Germany drawn from all
available CMIP5 models.
Following the CORDEX-EUR11 protocol all RCM simulations cover the European
continent on a 0.11∘ (approx. 12 km) grid. The ESD simulations use
the same grid, but covering just the Central European part of the domain, due
to their inherent methodological restrictions. Our analysis encompasses the
historical and RCP8.5 model runs for a total period of
1971–2100.
EURO-CORDEX grid cells used for the analyses – the ReKliEs-De area.
It includes Germany and several catchments of rivers discharging into
Germany.
In some cases, specific GCM and RCM versions are used for different
combinations. See for a detailed model
matrix, which specifies the model names and versions.
We focus our analysis on a Central European domain according to the
ReKliEs-De project definitions. This domain is defined by all grid boxes over
land areas that belong to river catchments discharging into German territory.
The eight main river catchments are Danube, Elbe, Ems, Main, Mosel, Neckar,
Rhine and Weser. The resulting mask covers mainly Germany and parts of the
Czech Republic as well as parts of the alpine region. Figure shows a map of all grid boxes considered in our
analysis.
Within the ReKliEs-De project 24 standard climate indicators were
calculated, including those which are used in this study:
tasmax [∘C]: daily maximum near surface (2m) air temperature;
pr [mm]: daily sum of precipitation;
su30 [days]: number of hot days (tasmax >30∘C);
r20mm [days]: number of days with very heavy precipitation (pr >20 mm).
The quality of the bias adjustment depends on the quality of the reference
data set. The reference dataset used in this study is based on a combination
of two data sources interpolated onto the same grid as the model data (the
CORDEX-EUR11 grid): (1) the climate station network provided by the
German Weather Service (DWD) and (2) the European gridded dataset
EOBS-0.22deg-rot-v15.0. The interpolation is based on
which utilizes a distance and directional weight. Hence
two stations lying in the same direction of the grid point (e.g. both north
of the grid point) will have a lower weight than two stations lying in
opposite directions (e.g. north and south of the grid point). As for the
reference orography, we selected an orography based on SRTMv3 which was
bilinearly interpolated onto the 0.11∘ CORDEX-EUR11 grid. For the
interpolation of the temperature fields a constant lapse rate of
0.65K/100m was applied. We used no height adjustment
for the precipitation fields.
Work flow of the threshold adjustment approach, indicated
by (a)–(d). First row: tasmax (OBS) → su30
(OBS). Second row: → tasmax (RCM) → su30 (RCM).
Larger graph (e): Resulting map for su26.6 (RCM). The box in the
upper left corner of each subfigure indicates the areal average
(∅) for the ReKliEs-De domain. The box in the center of each
subfigure shows the temperature threshold [∘C] used to determine the
number of hot days. The percentile of the temperature threshold is given in
the right-hand side of the bar over the figure. This bar also shows on its
left-hand side which period is used and the text in its center denotes if
observations (OBS) or a GCM-RCM combination (in this example: MPI-CLM) is
used.
Comparison of su30 (hot days with a maximum above
30∘C) regionalizations using 20C/historical runs data from the
period 1971–2000. The forcing GCMs are arranged in columns and the RCMs
in rows. Each row contains three pairs of maps for the three GCMs used,
showing su30 without (left) and with (right) bias adjustment.
As in Fig. but for r20mm (number of
days with heavy precipitation of 20 mm or more).
Simulations of two threshold-based climate indicators (top: su30;
bottom: r20mm) within the ReKliEs-De region and the period 1971–2000.
Columns of every table – forcing global models. Lines of every table – RCMs
or ESDs. Pairs of tables are displayed, left – simulated values, right –
adjusted thresholds for the indicator. Light grey boxes – value is below the
climatological average. Light yellow boxes – value is above the
climatological average. Green boxes – average is met within a margin of
0.5 units (top left and bottom left: days, top right: ∘C; bottom
right: mm). Numbers above each table denote the threshold value
(sw), the frequency of occurrence in days (n) and the
percentile of the threshold (perc) computed from climate
averages.
Method description
The method was designed to adjust the bias for climate extremes, e.g. the number
of hot days (su30) and the number of very wet days (r20mm) in regional climate model
simulations. It is important to note that it had been a priority not to alter the
simulation data, themselves. A basic assumption is that climate indicators using
fixed thresholds must be applicable for the entire area of interest, encompassing
mountainous as well as lowland regions. The underlying idea is to identify thresholds
in the simulations of the reference period (1971–2000) which are specific to the
individual GCM-RCM combinations and compare them to the defined fixed
thresholds in the observed climate for the same period.
An overview of the work flow for the temperature indicator su30 is given in
Fig. . The algorithm is as follows: We start by calculating
the percentile values Psu30 and Pr20mm in the
gridded daily observation data (1971–2000). Subsequently, the
historical simulations for the period 1971–2000 by the GCM-RCM
combinations are used to determine the values related to the percentiles
calculated in the observation data. This is performed for every GCM-RCM
combination. In most cases the resulting thresholds are exhibiting a bias,
i.e., the thresholds are not matching those from the observation data, with
model-specific deviations towards higher or lower thresholds. Therefore the
thresholds need to be adjusted. The indicators for the period 1971–2000
are calculated a second time, using the bias-adjusted thresholds instead of
the fixed thresholds (30∘C for su30 or 20 mm for r20mm,
respectively). Their values are then very close to the observations, meeting
the aim of the bias adjustment. For intercomparison purposes, threshold
matrices are given in Table for the model ensemble
with su30 in the upper and r20mm in the lower row.
Scatterplot of the projected number of hot days (su30) and very
wet days (r20mm) using threshold adjusted RCM (red) and ESD (magenta)
simulations until 2041–2070 (RCP8.5). The simulations are numbered for
reference in the right-hand tabulation. The window in the top left corner
enlarges the a segment of the graph near the label for model chain 31
(MPI-CLM) where several labels are overlapping. Thick blue lines mark the
baseline period (1971–2000) conditions for su30 and r20mm.
To further illustrate the steps of the method, details from an analysis
using a simulation of the global model MPI-ESM r1i1p1 (MP1) forcing
the regional model CCLM (CLM) are presented here for su30. Within the
reference period (1971–2000) and for the ReKliEs-De domain, the
simulated long-term annual mean of tasmax is 1.8K lower
than the observed annual mean of the maximum temperature, cf. the boxes in the
upper left part of Fig. c and a. As a
consequence of the simulated lower mean of the maximum temperature, the number of
hot days (su30), averaged over the whole domain is much lower in the climate simulation by
MP1–CLM (0.7 days, Fig. d) than in the observed climate
(4.5 days, Fig. b). According to our method, we adjust
the threshold of 30∘C, so that the count of hot days approaches
the observed 4.5 days. This is achieved by using all grid points of the
ReKliEs-De domain from the years 1971–2000 of the gridded observation
data to calculate the percentile which belongs to the fixed threshold of
30∘C. For this paricular threshold, a percentile of 98.80 is
determined. In the next step the tasmax value belonging to the percentile of
98.80 is identified in the MP1–CLM simulation for the period
1971–2000 and all grid points of the ReKliEs-De domain. It is found to
be 26.6∘C. This constitutes the new bias adjusted threshold for
the recalculation of su30 for MP1–CLM which turns from a su30 to a
su26.6. As Fig. e shows, the resulting area average for
the indicator su30 simulated by the bias-adjusted MP1–CLM (4.4 days)
is very close to that from observed data in Fig. b.
Moreover, the spatial patterns of modelled and observed data have a close
resemblance, too (cf. Fig. b and e).
In the frame of the ReKliEs-De project, further climate indicators based on
fixed thresholds (e.g., id, su, r10mm, gsl) are subjected to the same bias
adjustment process. With the bias adjustment for those indicators
established, the model specific-thresholds are used to determine the
indicators in model projections for the entire 21st century.
Results and discussion
The method, described in Sect. has been applied to the entire
ReKliEs-De ensemble in order to assess climate extremes and their climate
sensitivity. In the following paragraphs we discuss the individual patterns
(maps) for su30 and r20mm with and without threshold adjustment. We also
discuss the underlying threshold matrix and present the results of future
projections.
The left-hand tables in Table show the
simulated su30 and r20mm values averaged over the RekliEs-De domain for
the historical period (1971–2000) without threshold adjustment. The
colors indicate the direction of the model bias, negative (light grey) and
positive (light yellow) compared to the climate indicators derived from
observations. Similar values are colored in light green. Since most of the
RCMs have a cold bias , the su30 numbers
are frequently underestimated, e.g., for EC-EARTH forcing REMO (ECE–REM),
1.4 occurrences of su30 are computed for the ReKliEs-De area in the
simulation of the period 1971–2000, whereas the measurements yield a
count of 4.5 days. There is a reversed situation for r20mm. Here, the
RCMs frequently overestimate the mean precipitation patterns for the
ReKliEs-De domain and also the r20mm indicator.
The right-hand tables of Table depict the adjusted
thresholds for su30 and r20mm, respectively. They range from
25.6∘C (ECE–HIR) to 31.4∘C (CA2–W13 and
MP1–W13) for su30 and from 25.1 mm (ECE–HIR) to 17.9 mm
(ECE–W13 and MI5–W13) for r20mm. Applying these threshold
adjustments, the values of su30 and r20mm amount to nearly 4.5 and
5.1 days, respectively, for all ensemble members.
The resulting patterns for the 1971–2000 period with
and without adjusted thresholds are shown in Fig.
(su30) and Fig. (r20mm) for three GCMs
(MP1, ECE and HG2). After adjustment, all patterns show similar regional
characteristics with just minor differences. Without threshold adjustments
most of the model members underestimate the averaged number of su30 by
almost 4 days (e.g. MPI-CLM, MPI-RCA, ECE-CLM, ECE-RCA). Simulations with
HG2-REM and HG2-WRF, on the other hand, exhibit a rather close match to
the climate conditions. The comparison of the r20mm patterns with and
without threshold adjustments reveals positive bias up to about 3 days
(e.g. MPI–CLM and MPI–WRF).
In order to assess the future development of su30 and r20mm for the
ReKliEs-De domain the climate indicators were calculated for every model
member in an RCP8.5 simulation by using the adjusted threshold,
respectively. Figure depicts the changes for each model
combination. It shows the climate signals between the periods 2041–2070
and 1971–2000. The RCMs are represented in Fig. by
red lines and the ESDs by magenta lines. The observed state for the baseline
period is indicated by thick blue lines. The conditions of the period
1971–2000 for all ensemble members after bias adjustment are gathered at
the 4.5;5.1 days point, i.e., they closely approximate the observations.
Since the signals are determined from projections using an RCP8.5 scenario
it can be inferred that without climate protection the number of hot days
(su30) will change until 2041–2070 between 8.8 and 21.5 days –
the range is determined using the 10th and the 90th percentile of the
ensemble. This behaviour is corroborated by all models. For r20mm two
modelling families can be distinguished: RCMs and ESDs. They exhibit
different trend directions with a decrease in r20mm for the ESDs and a
clear increase for the RCMs. Model combinations which simulate a strong
increase of su30 show a smaller increase of r20mm, and vice versa. All
RCMs in the ReKliEs-De ensemble simulate an increase in the number of extreme
weather days (su30 and r20mm).
Summary and outlook
Simulations of regional climate models suffer from model bias and users
should be aware of this fact. The simulated climate average for the
historical period may be 1–2K below the observed average
whereas, e.g., the number of hot days (su30) is clearly lower. This also
strongly varies depending on the reference dataset used.
By the approach described in this paper we adjusted the point of view for each climate indicator in order to arrive at a similar mean level.
This enhances the comparability of regional features and climate sensitivity
considerations.
This approach does not aim at replacing established bias adjustments as an
important intermediate stage for regional impact assessments. Yet, it
improves the qualitative evaluation of features in regional climate ensembles
without injecting too much complexity.
Such an application has its spatial
limitations. The ReKliEs-De area is rather large and stretches the concept of
obtaining feasible area statistics for climate indicators. However, the
method could also be applied to single grid boxes or sub-domains. In that
case the area must be of sufficient size and appropriate location, so that
there are enough events defined by the threshold in the model simulations and
the observations. In addition, border effects might occur, once the area in
which the amount of threshold correction is determined differs from
that in which the threshold correction is applied. It should be
added that the quality of the results highly depends on the quality of the
observation data. A final remark: An investigation to what extent the derived
adjusted threshold matrix can be transferred to other variables would have
been beyond the scope of this study.
Data of regionalizations was provided by ReKliEs-De model
runs, augmented by other EURO-CORDEX runs, available from the World Data
Center for Climate, Hamburg, Germany, through their website at
http://cera-www.dkrz.de (WDC Climate, 2018). Access to the ReKliEs-De
data is provided through http://reklies.hlnug.de/startseite/ (HLNUG,
2018). Please select the last entry on that web page and subsequently scroll
to the table at the end of this web document.
PH has developed the methodology. PH and CM devised the computational
algorithms and performed the computations. PH and AS produced graphic and
tabular material. AS and PH compiled the paper, all authors discussed and
corrected the paper. All authors read and approved the final manuscript.
The authors declare that they have no conflict of
interest.
This article is part of the special issue “17th EMS Annual
Meeting: European Conference for Applied Meteorology and Climatology 2017”.
It is a result of the EMS Annual Meeting: European Conference for Applied
Meteorology and Climatology 2017, Dublin, Ireland, 4–8 September 2017.
Acknowledgements
The project ReKliEs-De was carried out under grant 01LK1401 of the German
Ministry of Education and Research (BMBF). The
article processing charges for this open-access publication
were covered by the Potsdam Institute for Climate Impact
Research (PIK). Edited by: Fulvio Stel
Reviewed by: Teodoro Georgiadis, Massimo Enrico Ferrario,
and one anonymous referee
ReferencesCannon, A.: Multivariate Bias Correction of Climate Model Output: Matching
Marginal Distributions and Intervariable Dependence Structure, J. Climate, 29, 7045–7064, 10.1175/JCLI-D-15-0679.1, 2016.Chen, J., Brissette, F., and Lucas-Picher, P.: Assessing the limits of
bias-correcting climate model outputs for climate change impact studies, J.
Geophys. Res.-Atmos., 120, 1123–136, 10.1002/2014JD022635,
2015.Christensen, J., Boberg, F., Christensen, O., and Lucas-Picher, P.: On the need
for bias correction of regional climate change projections of temperature and
precipitation, Geophys. Res. Lett., 35, L20709, 10.1029/2008GL035694, 2008.Chun, K., Wheater, H., and Barr, A.: A multivariate comparison of the BERMS
flux-tower climate observations and Canadian Coupled Global Climate Model
(CGCM3) outputs, J. Hydrol., 519, 1537–1550, 10.1016/j.jhydrol.2014.08.059, 2014.Ehret, U., Zehe, E., Wulfmeyer, V., Warrach-Sagi, K., and Liebert, J.: HESS
Opinions “Should we apply bias correction to global and regional climate
model data?”, Hydrol. Earth Syst. Sci., 16, 3391–3404,
10.5194/hess-16-3391-2012, 2012.Fang, G. H., Yang, J., Chen, Y. N., and Zammit, C.: Comparing bias correction
methods in downscaling meteorological variables for a hydrologic impact study
in an arid area in China, Hydrol. Earth Syst. Sci., 19, 2547–2559,
10.5194/hess-19-2547-2015, 2015.Gobiet, A., Suklitsch, M., and Heinrich, G.: The effect of
empirical-statistical correction of intensity-dependent model errors on the
temperature climate change signal, Hydrol. Earth Syst. Sci., 19, 4055–4066,
10.5194/hess-19-4055-2015, 2015.Grillakis, M. G., Koutroulis, A. G., Daliakopoulos, I. N., and Tsanis, I. K.:
Addressing the assumption of stationarityin statistical bias correction of
temperature, Earth Syst. Dynam. Discuss.,
10.5194/esd-2016-52, 2016.Haylock, M. R., Hofstra, N., Klein Tank, A. M. G., Klok, E. J., Jones, P. D.,
and New, M.: A European daily high-resolution gridded data set of surface
temperature and precipitation for 1950–2006, J. Geophys. Res., 113, D20119,
10.1029/2008JD010201, 2008.HLNUG (Hessisches Landesamt für Naturschutz, Umwelt und Geologie):
Regionale Klimaprojektionen Ensemble für Deutschland (ReKliEs-De),
available at: http://reklies.hlnug.de/startseite/, last access: 6 June
2018.
Hoffmann, P., Menz, C., and Spekat, A.: Threshold Correction of Regional
Climate Model Ensembles for Climate – Extreme Assessments on the Country
Level, in: 17th Annual Meeting of the European Meteorological Sociey, Dublin,
4–8 September 2017, Session UP1.3, Presentation P93, 2017.
Hübener, H., Bülow, K., Fooken, C., Früh, B., Hoffmann, P., Höpp, S.,
Keuler, K., Menz, C., Mohr, V., K.Radtke, Ramthun, H., Spekat, A., Steger,
C., Toussaint, F., Warrach-Sagi, K., and Woldt, M.: ReKliEs-De
Ergebnisbericht, Tech. rep., Hessian Agency for Nature,
Environment and Geology (HLNUG), 2017a (in German).
Hübener, H., Spekat, A., Bülow, K., Früh, B., Keuler, K., Menz, C.,
K.Radtke, Ramthun, H., Rathmann, T., Steger, C., Toussaint, F., and
Warrach-Sagi, K.: ReKliEs-De Nutzerhandbuch, Tech. rep., Hessian
Agency for Nature, Environment and Geology (HLNUG), 2017b (in German).Jacob, D., Petersen, J., Eggert, B., Alias, A., Bøssing Christensen, O.,
Bouwer, L., 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. Env. Change,
14, 563–578, 10.1007/s10113-013-0499-2, 2013.
Maraun, D.: Nonstationarities of regional climate model biases in European
seasonal mean temperature and precipitation sums, Geophys. Res. Lett., 39,
L06706,
10.1029/2012GL051210, 2012.Maraun, D.: Bias Correcting Climate Change Simulations – a Critical Review,
Curr. Clim. Change Rep., 2, 211–220, 10.1007/s40641-016-0050-x, 2016.Muerth, M. J., Gauvin St-Denis, B., Ricard, S., Velázquez, J. A., Schmid,
J., Minville, M., Caya, D., Chaumont, D., Ludwig, R., and Turcotte, R.: On
the need for bias correction in regional climate scenarios to assess climate
change impacts on river runoff, Hydrol. Earth Syst. Sci., 17, 1189–1204,
10.5194/hess-17-1189-2013, 2013.Piani, C. and Haerter, J. O.: Two dimensional bias correction of temperature
and precipitation copulas in climate models, Geophys. Res. Lett., 39, L20401, 10.1029/2012GL053839, 2012.Rocheta, E., Evans, J., and Sharma, A.: Assessing atmospheric bias correction
for dynamical consistency using potential vorticity, Env. Res. Lett., 9,
124010, 10.1088/1748-9326/9/12/124010, 2014.Rudolf, B., Hauschild, M., Reiss, M., and Schneider, U.: Die Berechnung der
Gebietsniederschläge im 2.5∘-Raster durch ein objektives
Analyseverfahren, Meteorol. Z., 1, 32–50, 1992.Schmidli, J., Frei, C., and Vidale, P.: Downscaling from GC precipitation: A
benchmark for dynamical and statistical downscaling methods, Int. J.
Climatol., 26, 679–689, 10.1002/joc.1287, 2006.Sun, F., Roderick, M., Lim, W., and Farquhar, G.: Hydroclimatic projections
for the Murray-Darling Basin based on an ensemble derived from
Intergovernmental Panel on Climate Change AR4 climate models, Water Res.
Res., 47, W00G02, 10.1029/2010wr009829, 2011.
Themeßl, M., Gobiet, A., and Heinrich, G.: Empirical-statistical
downscaling and error correction of regional climate models and its impact on
the climate change signal, Clim. Change, 112, 449–468, 2012.Vrac, M. and Friederichs, P.: Multivariate-Intervariable, Spatial, and
Temporal-Bias Correction, J. Climate, 28, 218–237, 10.1175/JCLI-D-14-00059.1, 2015.WDC Climate (World Data Center for Climate): DKRZ long term archive,
available at: https://cera-www.dkrz.de, last access: 6 June 2018.White, R. H. and Toumi, R.: The limitations of bias correcting regional climate
model inputs, Geophys. Res. Lett., 40, 2907–2912, 10.1002/grl.50612, 2013.