Statistical bias correction (BC) is a widely used tool to
post-process climate model biases in heat-stress impact studies, which are
often based on the indices calculated from multiple dependent variables.
This study compares four BC methods (three univariate and one multivariate)
with two correction strategies (direct and indirect) for adjusting two
heat-stress indices with different dependencies on temperature and relative
humidity using multiple regional climate model simulations over South
Korea. It would be helpful for reducing the ambiguity involved in the
practical application of BC for climate modeling and end-user communities.
Our results demonstrate that the multivariate approach can improve the
corrected inter-variable dependence, which benefits the indirect correction
of heat-stress indices depending on the adjustment of individual components,
especially those indices relying equally on multiple drivers. On the other
hand, the direct correction of multivariate indices using the quantile delta
mapping univariate approach can also produce a comparable performance in the
corrected heat-stress indices. However, our results also indicate that
attention should be paid to the non-stationarity of bias brought by climate
sensitivity in the modeled data, which may affect the bias-corrected results
unsystematically. Careful interpretation of the correction process is
required for an accurate heat-stress impact assessment.
Korea Meteorological AdministrationKMI2021-00912Introduction
Climate models unavoidably produce biased representations of the simulated
variables, and it is more problematic not to know how these biases translate
into the modeled response to external forcings such as the CO2
concentration, which is known to be responsible for global warming.
Therefore, statistical bias correction (BC) of climate model outputs has
been progressively adopted as a standard procedure to improve their
performance, in particular when feeding them into various climate change
impact assessments (e.g., G. Kim et al., 2020; Kim et al., 2022;
Masaki et al., 2015; Qiu et al., 2022; Schwingshackl et al., 2021). Indeed,
the visible benefits archived by adjusting simple statistics (e.g., mean,
variance) have led to the wide application of BC. A significant body of
research demonstrated that the systematic biases observed in the long-term
pattern of the current climate can be well eliminated even when using a very
simple technique (e.g., linear scaling). However, the effectiveness of BC
methods and their improper assumptions (e.g., statistical stationarity)
remain a topic for debate (Maraun et al., 2017). For example, the
non-stationary model bias and the large monthly/seasonal correction factor
can potentially degrade the BC's performance, particularly with respect to
misleading interpretations of extremes (Chen et al., 2021; Lee et al.,
2019). Meanwhile, the choice of BC approaches in different contexts
(e.g., heat-stress impact study, hydrological impact study, adjustment of
boundary conditions in downscaling) needs careful assessment on a case-by-case basis (Ehret et al., 2012; Rocheta et al., 2017; Kim et al., 2022; Zscheischler et
al., 2019).
A variety of BC methods with different levels of complexity and performance
have been developed and implemented for both global and regional climate
simulations (François et al., 2020; Teutschbein and Seibert, 2012; Kim
et al., 2021). Generally, their aim is to correct certain features in the
target's distribution, such as the simple statistics of the mean (linear
scaling, LS; Teutschbein and Seibert, 2012) and variance (variance scaling,
VA; Chen and Dudhia, 2001) or the more advanced quantiles (quantile
mapping, QM) for adjusting the entire distribution by parametric (PQM) or
empirical (EQM) transformation (Switanek et al., 2017; Gudmundsson et al.,
2012). Continuous efforts have also been made to eliminate the drawbacks of
existing BC approaches. Quantile delta mapping (QDM; Cannon et al., 2015),
for example, is designed to explicitly preserve the long-term trend that may
be artificially distorted in QM. Nonetheless, all the approaches described
above correct bias in a univariate context. They cannot adjust the
inter-variable dependencies, which are important for representing physical
processes and estimating compound hazards. It was not until quite recently
that the multivariate BC technique was considered and proposed (e.g.,
Bárdossy and Pegram, 2012; Cannon, 2018; Mehrotra and Sharma, 2015,
2016; Robin et al., 2019; Vrac, 2018), and they have been applied to various
climate change impact studies (Zscheischler et al., 2019; Qiu et al., 2022;
Meyer et al., 2019; Dieng et al., 2022). Although it is intuitively
recognized that multivariate BC could be more suitable for dealing with
climate variables characterized by a strong physical linkage in nature, an
unambiguous assessment of univariate and multivariate BC methods is
essential to understand the potential limitations of individual methods and
to avoid misleading application.
Despite the BC method used, when correcting the multivariate indices
representing compound hazards, the index can also be either directly
adjusted using BC techniques, as in the majority of studies (Schwingshackl
et al., 2021; Kang et al., 2019; Coffel et al., 2017), or indirectly
corrected so that its components are individually corrected prior to the index
calculation (Casanueva et al., 2019; Zscheischler et al., 2019). In this
regard, there have been few systematic comparisons of how the direct and
indirect use of univariate and multivariate BC methods, respectively, affect
the multivariate indices' adjustment. Only Casanueva et al. (2018) tested the
direct and indirect use of EQM in correcting the multivariate fire danger
index, while several studies compared the indirect use of univariate and
multivariate BC methods in impact assessments (e.g., Cannon, 2018;
François et al., 2020; Zscheischler et al., 2019). Although Casanueva et
al. (2018) pointed out that the direct application of EQM outperforms the
indirect one, how it compares with the multivariate BC method remains
unknown. Therefore, there is room for a more comprehensive assessment of the
effects of univariate and multivariate BC under direct and indirect application
strategies, which may vary along with the dependence structure of the
multivariate indices and may affect correction efficiency since the
multivariate approach has a higher computation cost.
In this study, we investigate the effects of different BC methods
(univariate vs. multivariate) applied with different strategies (direct vs.
indirect) on the statistical adjustment of heat-stress indices that
represent the combined effect of human exposure to temperature (T) and
relative humidity (RH), using regionally tailored, fine-scale climate
information in Korea from multiple regional climate models (RCMs). The
extreme heat is one of the most critical impacts of climate change, and we
adopt two heat-stress indices with different sensitivities to humidity
(Sherwood, 2018), namely wet-bulb globe temperature (WBGT) and apparent
temperature (AT). A comparative assessment of the two indices derived from
different BC methods and different strategies will provide valuable insights
into understanding how the relationship between heat-stress index and its
drivers (e.g., T and RH) affects the performance of univariate and
multivariate BC for modeled heat stress. This study will be helpful for
reducing the ambiguity involved in the practical application of BC for
climate modeling as well as end-user communities.
Data and methodsData
The 3-hourly data used for BC are the near-surface T and RH during the
historical period (1979–2014) generated by five RCMs (Table S1 in the Supplement) over the
CORDEX-East Asia domain (Lee et al., 2020). It is the dynamical downscaling
product of the UK Earth System Model (UKESM) in Coupled Model
Intercomparison Project Phase 6 (CMIP6). The same variables from ERA5
reanalysis (Hersbach et al., 2023) during the same period are adopted as the
observation for BC and validation procedures. For consistency, the variables
from all RCMs are first interpolated spatially onto the 0.25∘× 0.25∘ regular latitude–longitude grid of ERA5 and
temporally interpolated onto a standard Gregorian calendar. The analysis
focuses only on the land area in South Korea.
Heat-stress indices
Two popular heat-stress indices are evaluated in this study: WBGT (ACSM,
1984) and AT (Steadman, 1984). There are several different formulations for
both indices, and we employ the versions using only T and RH as input
variables (i.e., the simplified WBGT and the AT without the wind effect; Eqs. 1–3). Although both indices are calculated as a function of T and RH, their
T/RH dependences are different (Fig. 1). WBGT is more evenly dependent on T
and RH, whereas AT relies mostly on T. Also, each index has strengths and
limits in evaluating heat-stress impacts (Sherwood, 2018; Schwingshackl et
al., 2021); thus, they are selected for a more comprehensive evaluation of
BC techniques' applicability.
1WBGT=0.567T+0.393e+3.942AT=0.92T+0.22e-1.3T is the near-surface temperature in degrees Celsius, and RH is the
near-surface relative humidity in percent; e is the vapor pressure (hPa) that
can be calculated by
e=RH100×6.105exp17.27T237.7+T.
Contours lines of equal-level heat-stress indicators: WBGT (red)
and AT (blue).
All 3-hourly data are used for the BC procedure, but the daily maximum of
WBGT/AT during summer (June–July–August, JJA), together with the T and RH at
the corresponding time, are selected for analysis in order to facilitate the
use of heat-stress impact studies.
Bias correction
The principle of BC is to use observations to calibrate the simulated output
(e.g., climate model output). In this study, four BC methods are applied,
including LS, VA, QDM, and a multivariate BC algorithm with an N-dimensional
probability density function (MBCn). Information on each BC approach is
provided in the Supplement. The four transformation algorithms cover a
varying range of complexity, with MBCn being selected as an example of
multivariate correction methods and the trend-preserving QDM being a more
“advanced” member of the QM family. Several different
multivariate BC methods have been developed recently based on different statistical
techniques and/or assumptions (e.g., rank resampling for distributions and
dependences (R2D2; Vrac, 2018), matrix recorrelation (MRec; Bárdossy and Pegram, 2012)). Different multivariate methods have their
pros and cons, depending on the varying perspectives considered
(François et al., 2020). The MBCn adopted here is based on an image
processing algorithm that repeatedly rotates the multivariate matrices and
applies QDM correction on individual variables until the multivariate
distribution is matched to observation. It is selected in this study not
only due to its wide application in various kinds of climate studies; more
importantly, it facilitates the comparison with the univariate QDM as it is
built on the latter.
During the BC process, univariate BC methods are applied to T, RH, and
WBGT/AT, respectively, after WBGT/AT has been calculated from the original
RCM output (ORI). For MBCn, the multivariate approach is applied
simultaneously to T, RH, and WBGT (or T, RH, and AT). As the 3-hourly data
are adopted, BCs are applied separately to each 3 h interval in each
calendar month (e.g., June, 00:00 UTC). The direct correction of heat-stress
levels is defined as WBGT/AT directly adjusted by BC, while the levels
calculated from the bias-corrected T and RH are treated as an indirect
correction of the heat-stress indices (marked as WBGT′/TW′). ENS is the
unweighted ensemble mean of the five RCM models.
As an illustrative example, Fig. 2 provides the quantile–quantile plots of
the WBGT corrected using various approaches for one grid point from one RCM
during 1979–1996. ORI shows a cold bias inherited from the driving global climate model (GCM; M.-K. Kim
et al., 2020), leading to a notable underestimation over the entire
distribution compared to ERA5. For the direct correction of WBGT, LS reduces
the cold bias, but with a non-negligible overestimation, especially in the
range of 30–32.5 ∘C. This is due to the asymmetric distribution of
T being corrected with a single correction coefficient taken only from the
monthly mean. VA, on the other hand, provides a significant improvement by
additionally taking the variance into account. QDM, equivalent to EQM for
the calibration period, manages to show a perfect match with ERA5 across all
the quantiles since the empirical distribution is designed to fit the
observation. However, moving to the WBGT′ obtained from the corrected T and
RH, all univariate BC approaches show a degraded performance, while only MBCn
retains a qualified correction output. The MBCn's algorithm ensures that the
observed multivariate relations (e.g., the T–RH–WBGT pairwise dependency)
are reflected in the corrected distribution, resulting in a better indirect
correction outcome.
For cross-validation of the BC methods, we use a historical period of
1979–2014 and adopt the “jack-knifing” split-sample test that first
splits the historical period into two halves and uses one part for
calibration and the other for validation, and then we reverse the two parts
systematically (Refsgaard et al., 2014). Specifically, the 18-year period of
1979–1996 is first set as the calibration part with the period of 1997–2014
as the validation part; then, the periods are swapped using 1997–2014 for
calibration and 1979–1996 for validation. For each test, the ERA5 data in
the corresponding calibration period are used to obtain the correcting
algorithms that are then applied to the validation period. To distinguish
the two tests, the one using 1997–2014 for calibration is marked with a
letter “r”, standing for “reverse”, and the default is the one using
1979–1996 for calibration. The statistical metrics used for evaluation are
noted in the Supplement.
The quantile–quantile plots of ORI (blue) and data after BC (red)
adjusted by (a, e) LS, (b, f) VA, (c, g) QDM, and (d, h) MBCn. The x axis is
for quantiles from ERA5, and the y axis is for quantiles from model simulations;
the unit is ∘C. Panels (a)–(d) are WBGT from direct correction, and (e)–(h)
are WBGT′ from indirect correction (calculated from directed T and RH). The
data are from one point in the GRIMs model (one of the five RCMs) over South Korea land during the calibration
period.
Results
Figure 3 presents the performance of WBGT and AT in ORI simulations.
Substantial bias can be seen across the entire distribution of the
heat-stress indices. For 1979–1996, both WBGT and AT generally exhibit a
cold bias covering the whole domain. There is more bias in the bottom and
top 15 % of the distribution, but the bias of WBGT is more skewed to the
left tail, whereas that of AT is more skewed to the right. Taking the
90th percentile (90p) as an indicator representing heat events, Fig. 3b
and c show a greater cold bias in the low-elevation regions (e.g., basins
in southeastern Korea), where an RCM with a spatial resolution of
around 20 km is highly unlikely to capture the local high temperatures owing
to an inadequate representation of topography (Qiu et al., 2020). For
1997–2014, however, i.e., the next 18 years within the historical period,
the cold bias is systematically reduced, with a certain area even displaying a
slight warm bias. This can be explained by the high climate sensitivity in
the driving GCM (i.e., UKESM; Zelinka et al., 2020), leading to a different
level of warming between the simulations and ERA5 during this historical
period. According to Fig. 3d and e, the model shows around 0.5 ∘C
more warming than ERA5 between the two periods, which could in turn
“compensate” for the models' cold bias and result in a reduced bias in
1997–2014. However, while the biased presentation of the heat-stress indices
emphasizes the necessity of BC application, the difference in bias between
the two historical periods underscores the need for caution when using and
interpreting BC output in climate models since BC is built on the
fundamental assumption of stationary bias (Teutschbein and Seibert, 2012).
In particular, the combined bias from climate representation and the
long-term trend may amplify the non-stationarity of model biases, thereby
causing potential problems in the BC output.
(a) Root mean square error (RMSE; Eq. S1 in the Supplement) over the land area of
South Korea in percentiles 1–99 during 1979–1996 (blue) and 1997–2014 (red).
The lines and shading indicate the median and the range, respectively, of
the five RCMs. (b, c) Spatial map of the bias in the 90p from ENS during the
calibration (C; 1979–1996) and validation (V; 1997–2014) period,
respectively. (d, e) The difference between the validation and the
calibration period in 90p from ENS and ERA5, respectively. The upper row is
for WBGT, and the lower row is for AT.
Figure 4 shows the median absolute error (MAE; Eq. S2 in the Supplement) over South Korea
(land only) in all RCMs after BC using different methods. Two
indicators – the 90p and the mean of monthly maximum (MMX) – are selected to
represent extreme heat events. The diamonds standing for ENS are marked for
ease of comparison. During the calibration period, LS, as the simplest BC
approach used in this study, shows the largest bias among the four methods.
For direct correction of WBGT, the other four methods have a reasonable MAE
of less than 0.25 ∘C in the 90p and less than 0.5 ∘C in
the MMX for ENS, with QDM slightly outperforming the VA and MBCn approaches.
For the indirect correction, however, there is more variability among the
methods and a larger bias than the direct correction. In this case, while LS
still shows the worst performance, QDM presents a degraded performance, with
the MAE for WBGT′ reaching 0.6 and 1.2 ∘C in the 90p
and MMX, respectively. Surprisingly, VA outperforms the more advanced QM
methods (i.e., QDM) in ENS, indicating the complexity of using univariate approaches to
apply an indirect correction for multivariate hazards. In this case, the
multivariate approach, i.e., MBCn, clearly demonstrates its strengths in
such indirect correction, regardless of the indicators or periods
considered. MBCn performs comparably to the direct correction of QDM during
the calibration period; however, for the validation period, MBCn surpasses
direct correction with an MAE of roughly 0.5 ∘C for both the 90p
and MMX. In addition, MBCn shows less variability among the RCMs in WBGT′.
For example, the range of MAE for WBGT′ during the calibration period as
corrected by QDM is 0.38–1.23 ∘C, while that corrected by MBCn is
0.12–0.14 ∘C.
The MAE over South Korea (land only) for the calibration period
(1979–1996, x axis) and validation period (1997–2014, y axis) in terms of
the (a, b, e, f) 90p and (c, d, g, h) MMX from (a, c) WBGT, (c, d) WBGT′,
(e, f) TW, and (g, h) TW′. The different colors stand for different BC
methods, and the different markers stand for different RCMs.
Similar results are found in AT and AT′ according to Fig. 4e–h. However,
for the indirect correction of AT′, the weakness of QDM is less significant, and the advantage of MBCn is also weakened compared to WBGT′. The ability to
additionally correct the multivariate dependency despite their individual
distributions leads to a better result in the indirect correction of the
heat-stress indices, which are functions of T and RH. In this case, since AT
is more reliant than WBGT on T, the effect of correcting T–RH
interdependence is less critical to its correction outcome. On the other
hand, because T and RH both play important roles in WBGT, multivariate BC is
more likely to demonstrate its importance in this case. Not surprisingly,
the performances of different BC methods are retained in the reverse test,
although with different magnitudes of MAE (Fig. S1 in the Supplement). MBCn shows an even
better performance in this case, outperforming all other methods despite the
heat indices and matrices considered.
To assess the quantitative differences in the marginal distributions
corrected by different BC methods, Fig. 5a, b, e, and f present the maximum
differences calculated from the Kolmogorov–Smirnov (K–S) test (Eq. S3)
between the observed (i.e., ERA5) and bias-corrected empirical cumulative
distribution functions (CDFs). A smaller value stands for a better
correction output. For the direct correction, QDM and MBCn show better
performances than LS and VA across all the indices and matrices considered.
However, for indirect correction, MBCn shows its unique advantage in the
multivariate index, depending unequally on the components (i.e., WBGT′ in
this study), in that it can provide a similarly good result in either the
direct or indirect correction. In this aspect, QDM shows the largest
difference between the direct and indirect applications. Figure 5c, d, g, and f show the D value calculated between outputs from direct and indirect
applications of the same BC method, and a smaller value stands for more
similar outputs. This clearly indicates a higher similarity seen in the
multivariate method than the univariate methods in WBGT, as MBCn
successfully retains the inter-variable dependence during the correction
procedure.
K–S test D value between bias-corrected output and observation for
(a, e) 90p and (b, f) MMX and between direct and indirect corrected output
for (c, g) 90p and (d, h) MMX. The D value is the ensemble mean of five RCMs averaged
over South Korea (land only). The different colors stand for different BC
methods. Panels (a)–(d) are for the calibration period (C), and (e)–(h) are
for the validation period (V). In (a), (b), (e), and (f), the solid and patterned fill
is for the direct and indirect BC, respectively.
Figure 6 investigates the spatial distribution of bias in the QDM and MBCn
corrections, using the 90p as an example for WBGT and AT. A similar pattern
can also be seen in the case of MMX (Fig. S3). For the calibration period,
the biases are well reduced to less than 0.5 ∘C, with only
indirect correction by QDM showing a warm bias in the southeastern part.
Specifically, the resultant bias magnitude from indirect QDM correction is
even larger than in ORI (Fig. 3b) over southeastern Korea. The spatial
pattern of the warm bias persists in the validation period, although with
greater magnitude, which can be explained by the different bias magnitudes
for the two periods in ORI simulations. This behavior is seen in both WBGT
and AT, but more strongly in WBGT, which is more affected by the T–RH
dependency. The overall cold bias in the model simulations during the
calibration period must result in a positive correction coefficient (i.e.,
towards a warmer condition). However, as discussed above, a reduced cold
bias in the RCMs is seen in the validation period because of overestimated
warming in the models. Such a “trimmed” bias in the validation period may
be over-corrected by the correction coefficient derived from the calibration
period, even causing a larger bias than in ORI over the eastern part of the
country, with a warm bias in the validation period. The results from the reverse
test (Figs. 7 and S4) can further prove the impact of non-stationary
bias on the result. In this case, the validation period of 1979–1996 retains
a cold bias after BC for the reason that the correction coefficient derived
in 1997–2014 is not large enough to compensate for its negative bias. Again,
this highlights the importance of the careful interpretation of bias-corrected climate data,
especially in the context of future warming projections.
Spatial maps of the bias in the 90p during the calibration period
(C) and validation (V) period corrected by QDM and MBCn in ENS. The first
and third rows are the directly corrected WBGT and AT. The second and
fourth rows are the WBGT′ and AT′ calculated by the corrected T and RH.
Same as Fig. 6 but for the reverse test.
Spatial patterns of T vs. RH Spearman's rank correlation
(α=001) computed in each grid cell during the calibration
(rows 1 and 3) and validation (rows 2 and 4) period. Column (a) shows the
results from ORI simulations. Columns (b) and (d) are the heat-stress
indices directly corrected by QDM and MBCn. Columns (c) and (e) are the
heat-stress indices indirectly corrected by QDM and MBCn. Column (f) is from
ERA5.
On the other hand, the spatial maps of bias also clearly demonstrate the
superiority of MBCn for the indirect correction of the heat-stress indices
over the entire domain in both the calibration and validation periods. Since
the heat-stress indices are functions of T and RH, we investigate the T vs.
RH Spearman's rank correlation at a confidence interval of 99 % using
daily T and RH at the time when the heat-stress indices reach their daily
maxima (Fig. 8). ERA5 shows a negative correlation ranging from -0.4 to
-0.6 that gradually increases from northeast to southwest. Comparatively,
ORI has a significantly weaker negative correlation and does not adequately
reflect the spatial gradient. The correction with QDM, even with the good
outcome in the direct correction of the heat-stress indices, cannot properly
present the T–RH relation. In fact, it even further weakens their
correlation during the calibration period. In contrast, MBCn calibrates
the multivariate dependency according to the observed correlation pattern,
which explains why it significantly improves the correction of WBGT′ and
AT′. The correlation derived from the calibration period is also passed to
the validation period by MBCn, which in this case shows no significant
change between the two historical periods according to ERA5.
Discussion and conclusion
Previous studies have challenged the applicability of univariate BC for
adjusting individual components of multivariate hazard indicators and proved
the benefit of multivariate BC in compound event evaluations (François
et al., 2020; Zscheischler et al., 2019). Our study also demonstrates MBCn's
advantage in correcting the interdependence of the relevant variables, which
results in a substantial improvement in the indirect BC of heat-stress
indices. Such an advantage is more prominent for the index relying more
equally on the composing variables (e.g., WBGT), which was also pointed out
by Zscheischler et al. (2019). However, to the best of our knowledge, no
study has been conducted to compare the multivariate BC methods with the
direct application of univariate BC on multivariate indices. Our results
show that QDM applied directly to the multivariate indices can provide a
similar result to MBCn in heat-stress assessments, while MBCn additionally
provides a more reasonable underlying inter-variable dependence. In this
regard, if only considering heat-stress indices, the more
computationally efficient direct QDM correction may be sufficient for the
impact assessment. However, if the relationship between T/RH and the
heat-related impacts is of interest, the multivariate BC is suggested for
maintaining the physical linkage of the variables.
On the other hand, regarding the study of heat stress under future warming
that is not evaluated in this study, more aspects should be considered. This
study uses historical climate simulations comprising non-stationarity
combined with two “jack-knifing” split-sample tests. It is found that the
non-stationarity of bias in the modeled heat-stress indices, as combined
effects of internal climate variability and climate model sensitivity, can
significantly affect the BC output. Teutschbein and Seibert (2012) once
suggested that the more advanced correction methods (e.g., QM) are more
robust to a non-stationary bias compared to the simpler ones (e.g., LS), but
our result shows no significant difference. In fact, lying under the
fundamental assumption of stationary bias, current BC approaches may not be
able to provide a suitable solution to this issue. Therefore, a case-by-case
evaluation of BC approaches for a certain climate model and study area, as
well as a clear understanding of the relevant processes including the
uncertainties underlying original model data, is required for reliable data
post-processing using BC methods. Meanwhile, for the continuous development
in future projections of multivariate heat-stress indices, there are also
potential problems worth investigating. For example, we may need to consider
whether there is any substantial change in the modeled multivariate dependence
structure, which is also highly likely under global warming (Singh et al.,
2021; Hao et al., 2019). Although both QDM and MBCn are supposed to preserve
the simulated trend in the corrected variables, MBCn, as well as other
multivariate BC methods, does not consider the change in the multivariate
relationships. In this regard, the direct correction of QDM may outperform
MBCn. However, as direct correction of QDM may discard the physical
consistency in the input variables, in terms of both the variable
representation and the projected change, it can hide the compensating bias
(Schwingshackl et al., 2021) and thus introduce additional uncertainty in
climate change signal (Casanueva et al., 2018) in the multivariate
heat-stress indices. To solve these problems, a deeper understanding and
continuous enhancement in climate models, particularly for the uncertainty
and credibility of projections, may be prerequisites for better evaluation
and application of the statistical procedures (i.e., BC approaches).
Code and data availability
Near-surface temperature and relative humidity data from the CORDEX-East
domain downscaling product used in this study are archived in the
institutional repository at 10.14711/dataset/GTXJVQ (Qiu et al., 2023). ERA5 hourly data on single levels
are downloaded from the Climate Data Store via 10.24381/cds.adbb2d47 (Hersbach et al., 2023; ERA5 hourly data on single levels
from 1979 to present). The R package “qmap”
(https://CRAN.R-project.org/package=qmap; Gudmundsson, 2016) is used for
applying EQM and QDM, and the R package “MBC”
(https://CRAN.R-project.org/package=MBC; Cannon, 2020) is used for
applying MBCn. The Climate Data Operators (CDO) open-source package is used for
(1) computations in LS and VA, (2) temporal and spatial correlation, and (3) statistical analysis.
The supplement related to this article is available online at: https://doi.org/10.5194/esd-14-507-2023-supplement.
Author contributions
ESI and SKM conceptualized the study. LQ
was responsible for investigation, formal analysis, methodology, software,
and visualization. ESI supervised all LQ's work and provided
investigations. LQ and ESI wrote the original draft, and ESI and
SKM reviewed and edited it. LQ, SKM, YHK, DHC, SWS, JBA,
ECC, and YHB created the data used in the study.
Competing interests
The contact author has declared that none of the authors has any competing interests.
Disclaimer
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
We thank the reviewers, who have provided valuable comments for the study.
Financial support
This study was supported by the Korea Meteorological Administration Research and Development Program under grant no. KMI2021-00912.
Review statement
This paper was edited by Sagnik Dey and reviewed by Nicholas Osborne and one anonymous referee.
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