Alpine catchments show a high sensitivity to climate
variation as they include the elevation range of the snow line. Therefore,
the correct representation of climate variables and their interdependence is
crucial when describing or predicting hydrological processes. When using
climate model simulations in hydrological impact studies, forcing
meteorological data are usually downscaled and bias corrected, most often by
univariate approaches such as quantile mapping of individual variables,
neglecting the relationships that exist between climate variables. In this
study we test the hypothesis that the explicit consideration of the relation
between air temperature and precipitation will affect hydrological impact
modelling in a snow-dominated mountain environment. Glacio-hydrological
simulations were performed for two partly glacierized alpine catchments
using a recently developed multivariate bias correction method to
post-process EURO-CORDEX regional climate model outputs between 1976 and
2099. These simulations were compared to those obtained by using the common
univariate quantile mapping for bias correction. As both methods correct
each climate variable's distribution in the same way, the marginal
distributions of the individual variables show no differences. Yet,
regarding the interdependence of precipitation and air temperature, clear
differences are notable in the studied catchments. Simultaneous correction
based on the multivariate approach led to more precipitation below air
temperatures of 0
With global change, hydrological processes in high elevation regions have been significantly impacted (Messerli et al., 2004). In the European Alps, the observed increase in air temperature is a trend that is expected to continue in the future. Future precipitation changes are less clear, with an expected slight increase in winter precipitation (Gobiet et al., 2014; Kotlarski et al., 2016). The hydrology of alpine catchments is especially sensitive to these changing climate variables (Köplin et al., 2010). High elevations in the Alps are still characterized by snow cover and the existence of glaciers. However, rising air temperatures and a consequent upward shift of the zero-degree isotherm has led to a decrease in snow accumulation and an increase in glacier melt (Pellicciotti et al., 2010). Due to shrinking glacier areas, the glacial influence in these streamflow regimes has decreased. This is especially notable during late summer when water from ice melt can constitute a notable percentage of total streamflow. With progressive glacier retreat, the ice melt contribution to streamflow is expected to decrease (Jansson et al., 2003; Hock, 2005; Moore et al., 2009; Huss and Hock, 2018). The interdependence of air temperature and precipitation is particularly important for hydrological systems as it determines the physical state of precipitation. Bosshard et al. (2014) showed that an air-temperature-dependent shift from snowfall to rain has notable effects on catchment water storage and seasonal water availability in such an environment. A correct representation of climate variables and their interdependence is therefore essential in hydrological simulations of glacierized catchments.
In hydrological climate change impact studies, post-processing of climate model data has become a standard procedure. Despite continuous progress, raw outputs from regional climate models differ largely from observational reference data due to both spatial mismatches and systematic biases. Therefore, climate model outputs are downscaled and biases are adjusted statistically before being used in hydrological simulations (Ehret et al., 2012; Maraun, 2016; Teutschbein and Seibert, 2012). Many empirical statistical techniques have been developed to post-process climate model outputs for these purposes. For hydrological impact studies quantile mapping approaches, which correct for biases in the data's entire distribution, have often been recommended (Teutschbein and Seibert, 2012; Gudmundsson et al., 2012; Chen et al., 2013). However, these approaches correct the climate variables independently from one another. The interdependence of key climate variables, such as air temperature and precipitation, can be especially important when modelling snow-dominated catchments due to the aforementioned threshold effects of the transition of rain to snowfall or the conditions required for snowmelt and ice melt.
Studies that analysed inter-variable aspects of bias correction showed that univariate quantile mapping retains the inter-variable dependencies as represented by the raw climate model output data (Wilcke et al., 2013; Ivanov and Kotlarski, 2017). But these may not correspond to the local interdependencies in observations. To account for interdependencies, multivariate bias correction approaches have been developed that allow for the preservation of the interdependence of climate variables as represented by the target observation data throughout the bias correction process (Li et al., 2014; Cannon, 2016, 2018a; Mehrotra and Sharma, 2015, 2016). A correction procedure that preserves the climate variables' interdependence may be considered more appropriate for subsequent impact analyses, such as the application of a calibrated hydrological model using multiple variables, than univariate techniques that ignore biases in inter-variable relationships (Cannon, 2018a).
While many studies have evaluated bias correction methods in terms of their effects on the actual variables of precipitation and air temperature themselves, studies that use impact models to investigate the consequence of bias correction in the modelled impacts are still rare. So far, there have been only a few studies (Räty et al., 2018; Chen et al., 2018) that investigated the effect of using a multivariate bias correction technique on hydrological projections. Chen et al. (2018) found that jointly corrected precipitation and air temperature data better modelled eleven out of twelve catchments in the calibration period than the meteorological data that was corrected with a univariate method. An advantage of using a bivariate bias correction approach was not evident for the coldest snow-dominated catchment of the sample though. Hydrological simulations by Räty et al. (2018) generally did not substantially benefit from bivariate bias correction approaches, but when looking more specifically, simulations of high flows and snow water equivalents in snow-influenced catchments improved slightly.
In this study we investigate the hypothesis that the explicit consideration of the relation between air temperature and precipitation in bias correction will affect hydrological impact modelling in environments dominated by snowmelt and glacier melt. Here, dependencies are known to matter most as they have cumulative effects over a season through snow storage and at multi-year timescales through the glacier mass balance. The approach of this study was therefore to conduct climate impact modelling experiments that allow comparison of the effects of univariate and multivariate bias correction of precipitation and air temperature input on the hydrological change in alpine catchments. The model experiments were conducted for two meso-scale partly glacierized catchments in the Swiss Alps, for which snow accumulation, glacier mass balance, and streamflow were simulated from 1976 to 2099.
Catchment characteristics including glacier cover information.
Map of the two study catchments and their location in Switzerland:
Hinterrhein
Two partly glacierized meso-scale catchments in the Swiss Alps, in the headwater of the Rhine River, were examined in this study: the Hinterrhein catchment and the larger Schwarze Lütschine catchment (Fig. 1, Table 1). Based on the dataset by Freudiger et al. (2018), used in this study, around the year 1900 glacier coverage was approximately 32 % of the Hinterrhein catchment area and around 25 % of the Schwarze Lütschine catchment area. Glaciers in both catchments retreated considerably during the 20th century. The Hinterrhein catchment is characterized by small, scattered glaciers, which by 1973 lost around half their area, leading to a glacier coverage of only 7 % in 2010 (Table 1). In the Schwarze Lütschine catchment losses in relative glacier area have been smaller. This difference in glacier coverage is related to elevation with considerably higher maximum elevations in the Schwarze Lütschine catchment compared to the Hinterrhein catchment (Table 1).
The application of bias correction algorithms to climate model outputs is
generally based on three datasets: historical observations as reference
(also called “target”) data, historical climate model simulations, and the
corresponding climate model projections. In the present study the historical
reference data for the study catchments were derived from an observation-based interpolation product, i.e., the 1 km
GCM–RCM combinations from the EURO-CORDEX initiative used in this study.
GCM institutions:
The climate model datasets were obtained from the Coordinated Regional
Climate Downscaling Experiment (CORDEX,
Precipitation (
The application of the hydrological model requires catchment mean time
series of
Daily streamflow data for model calibration were provided by the Swiss Federal Office for the Environment (FOEN) and the “Amt für Wasser und Abfall des Kantons Bern”. The available streamflow record for the station Gündlischwand (operated by the Cantone of Berne) at the outlet of the Schwarze Lütschine study catchment covered only the period 1992–1999. By using the record of a downstream station of the Lütschine River (station Gsteig) and subtracting the streamflow of its other major headwater tributary (record from the station Zweilütschinen of the Weisse Lütschine) the streamflow for the Schwarze Lütschine study catchment could be reconstructed for the entire simulation period. This reconstructed streamflow time series was validated with the available streamflow data from the station Gündlischwand for the sub-period 1992–1999 and then used for model calibration. Snow water equivalent (SWE) and snow cover data were derived from a snow map (interpolated grid) product by the OSHD-SLF (2013). The glacier area was assessed based on glacier inventory data by Müller et al. (1976) and Maisch et al. (2000) for the state in the year 1973, by Paul et al. (2011) for the state in 2003, and by Fischer et al. (2014) for the year 2010 (see Table 1). Estimates of glacier volume were derived based on gridded ice thickness data available for the years 1973 and 2010, which were computed using the approach by Huss and Farinotti (2012) and provided by Matthias Huss. Glacier volume for the year 2003 was estimated based on the glacier cover according to Paul et al. (2011) and glacier volume–area scaling. The glacier volume estimate for 1973 was used for model initialization. The estimate for 2003 was incorporated in the model calibration for the period 1976–2006. The estimate for 2010 was not directly used in the calibration but served the validation of model simulations beyond the year 2006.
Depending on the GCM–RCM combination, raw climate variables (noBC) of the
control period (1976–2006) differ from the reference data (HOCD). To
correct these biases, two different bias correction methods were applied to
each climate model's
The MBCn algorithm by Cannon (2018a) is based
on the
Climate model data is often simultaneously bias corrected and downscaled as
the reference data stems from stations or higher-resolution observations in
comparison to the coarse grid resolution of RCMs. Undesirable effects in
downscaling to finer scales have been one of the major limitations of
current bias correction methods (Maraun, 2013; Ehret et al., 2012; Maraun
et al., 2017). Such artefacts can occur in complex terrain in particular and if
the scale gap between climate model outputs and impact model data is
considerable. In general, bias correction based on spatial resolutions that
differ substantially should be avoided or handled with great care. In this
study the discrepancy in resolution is assumed to be acceptable as the bias
correction was based on spatially aggregated mean climate variables for the
meso-scale catchments (54 and 180 km
Model performance criteria for the calibration (1 October 1976–30 September 2003) and validation (1 October 2003–31 December 2006) of the hydrological model formulated (see footers) that the ideal value for a perfect fit is 1.0.
Formulation of model performance criteria:
The HBV model (Bergström, 1976; Lindström et al., 1997) is a
semi-distributed bucket-type runoff model. Here the software implementation
HBV-light (Seibert and Vis, 2012) was used, which recently has been
extended to represent coupled glacio-hydrological processes of partly
glacierized catchments (Seibert et al., 2018). This version of the HBV
model also allows tracking of the different components of streamflow resulting
from rainfall (
The model was calibrated for the period from 1976–2003, preceded by a
3-year warm-up period, by optimizing a weighted objective function, giving
special attention to streamflow dynamics (50 %), snow simulation (25 %),
and glacier volume change (25 %). The Lindström measure
(Lindström, 1997) was used for the streamflow's general dynamic and
volume errors, while the Nash–Sutcliffe efficiency (Nash and Sutcliffe,
1970) was computed based on logarithmically transformed streamflow.
Additionally the Nash–Sutcliffe efficiency was computed for the streamflow
only during the summer months, from June to September. To calibrate the snow
simulations the snow-covered area fraction of the catchment and the
mean SWE of the elevation range
Annual precipitation sums for days with air temperatures above or
below 0
Effects of the bias correction approaches on the hydrological simulation
were based on comparisons of the simulation results for the historical
reference period 1976–2006 using
The two applied bias correction methods led to differences concerning the
interdependence of
Application of the climate scenarios clearly revealed a decreasing role of snow for both study catchments. Figure 3 illustrates a distinctly smaller snow accumulation in the course of a year simulated for the period 2070–2099 (compared to the historical reference period 1977–2006) and a more complete melt during the summer. This extended the snow-free period during the summer in the Hinterrhein catchment. The spread between the simulations diverged for the simulations of future conditions. In the Schwarze Lütschine catchment with its higher maximum elevations all effects were comparable, yet a permanent snow cover remained still present based on most scenarios. As expected, simulations based on the RCP4.5 scenario (not shown) led to a clear but less severe decrease in mean SWE than for the RCP8.5 scenario.
Mean annual SWE regime, calculated using the 11-day moving average
of daily simulated SWE (catchment mean) during the
historical reference period
The differences in the interdependence of precipitation and air temperature
resulting from the application of QDM versus MBCn to the GCM–RCM data can
be seen in the simulated SWE (Fig. 3). The state of precipitation defined by
the calibrated threshold air temperature parameter TT (Schwarze
Lütschine TT
Simulated glacier ice volume from 1977 to 2099 using the RCP8.5
scenario forcing in the two catchments
For the period 1976 to 2099 the glacier volume was simulated to decrease in
both catchments. In the Hinterrhein catchment, glaciers diminished
continuously from the beginning of the simulation period and were simulated
to have disappeared between 2028 and 2055 under the RCP 8.5 scenario
depending on the GCM–RCMs and the applied bias correction method (Fig. 4).
In the Schwarze Lütschine catchment, data from a few GCM–RCMs resulted
in an increase in simulated glacier volume in the 1970s and 1980s, which is
in line with the historical reference simulation (Sim
Observed total streamflow and simulated streamflow components for the
historical reference period and for the different simulations under the RCP8.5
scenario. Stacked bar plots show mean values over the historical reference
period
Focusing on systematic differences between simulations using data corrected
based on QDM and MBCn, the simulations of glacier volume showed similar
tendencies to those found for SWE. For both catchments, but again more
clearly for the Hinterrhein catchment, MBCn-corrected GCM–RCM data resulted
in a slower decline in glacier volume in comparison to simulations based on
QDM-corrected data. All projections led to complete glacier disappearance in
the Hinterrhein catchment by about the year 2050, with a clear tendency
towards earlier dates for QDM-based simulations (2028–2041, mean: 2036)
compared to MBCn-based simulations (2040–2055, mean: 2047). For the
Schwarze Lütschine catchment the range of QDM- and MBCn-based glacier
volume simulations overlapped largely as simulations in general diverged
considerably. However, for each individual GCM–RCM dataset, glacier melt
was simulated to be faster using the QDM-corrected data compared to the
MBCn-corrected data. The less intense decline in glacier volumes resulting
from MBCn-corrected forcing data appeared to correspond better with the
reference simulation (Sim
Time changes of annual variables and mean monthly hydrological regimes were
assessed for streamflow
Streamflow regimes based on 11-day moving averages of daily streamflow
during 30-year periods in the historical reference period and as projected for
the period 2070–2099 under the RCP8.5 scenario for the two catchments.
Simulation results for each ensemble member are shown as semi-transparent
polygons. For the historical reference period the results of the simulations
based on the historical reference
The streamflow simulations reflected the changes from the different bias
correction methods found for the cryosphere. Simulations based on
QDM-corrected data led to slightly different total streamflow than
MBCn-corrected data (Fig. 5a, d and e). These differences were much more
pronounced regarding the individual streamflow components. Modelling based
on QDM-corrected climate data led to an approximately 10 % higher rain
component of streamflow
Simulated streamflow and its components,
Both bias correction methods employed in this study, univariate QDM (Cannon
et al., 2015) and multivariate MBCn (Cannon, 2018a), are based on the same
quantile mapping approach and by definition the marginal distributions of
the corrected
As air temperature determines the distinction between liquid precipitation
and snow, differences in the climate variables' interdependence can lead to
differences in simulated snowfall (Fig. 2), and consequently in snow
accumulation and the catchments' seasonal water storage (Figs. 3–6). For the
MBCn-corrected data in this study there was clearly more precipitation at
air temperatures below 0
It bears noting that results from QDM and MBCn in the historical reference period are, as for example also in Zscheischler et al. (2019), evaluated without cross-validation. However, because the univariate and multivariate bias correction algorithms are applied in an asynchronous fashion to freely running climate simulations – adjusting the marginal and joint distributions – it is, by construction, almost guaranteed that they will perform well in terms of cross-validated measures of distributional fit (Maraun and Widmann, 2018). Cross-validation does make sense when performance – especially for aspects not explicitly adjusted – is measured in a setting where climate model simulations are synchronized with the real-world climate state, for example in climate prediction or perfect boundary condition (e.g., reanalysis-driven) setups. We note that such reanalysis-driven cross-validation experiments have been performed in Cannon (2018a) for the two algorithms used in this study. This was done over a large continental domain for a complicated multivariate fire weather index that combines, in a nonlinear fashion, the current and lagged effects of air temperature, precipitation, wind, and humidity. Hence, it is expected that results reported here are robust and would be similar in an out-of-sample evaluation.
There have long been concerns over climate change impacts on mountain water
towers. Many climate impact studies for snow-dominated catchments agree that
due to continued warming, a decrease in snow cover characteristics and
time-shifted snowmelt contributions to streamflow are to be expected under
climate change scenarios (e.g., Barnett et al., 2005; Farinotti et al.,
2012; Köplin et al., 2014; Addor et al., 2014; Milano et al., 2015;
Coppola et al., 2018; Jenicek et al., 2018; Hanzer et al., 2018). In fact,
the shift and decrease in the snowmelt peak are one of the most robust
results of such studies. In this study we showed that the snow component
strongly depends not only on the GCM–RCM outputs but also on whether the
bias correction method applied incorporates inter-variable dependence of
These results also require the discussion of implications on common conceptual
hydrological modelling concepts that are needed to simplify meteorological
and hydrological complexity. The use of a threshold air temperature for the
distinction of precipitation in snow and rainfall is a key concept of the
HBV model and many other hydrological models. Hence, it may be expected that
the simulations of the snow-dominated catchments respond particularly
sensitively to changes and biases in
This study demonstrates the importance of considering the representation of the interdependence of precipitation and air temperature in the specific case of hydrological impact modelling of snow- and glacier-dominated catchments. As shown, in the representation of the climate variables' interdependence, the multivariate bias correction approach leads to results closer to the climatological historical reference data as well as partly to hydrological simulations closer to the historical reference simulations, such as for instance for the simulated glacier volumes. Cannon (2016, 2018a) also demonstrated better results for multivariate-corrected data in other examples, including fire weather indices and atmospheric river detection. In practice, some kind of bias correction is needed for many impact studies, although it is known that recent literature is rich in controversial debate of its use and major limitations of the application of empirical–statistical bias correction methods (e.g., Ehret et al., 2012; Addor and Seibert, 2014; Maraun, 2013, 2016; Clark et al., 2016; Maraun et al., 2017; Casanueva et al., 2018; Zscheischler et al., 2019). Some of the fundamental issues, the details of which are beyond the scope of this study, are shared with univariate bias correction, for example, the question of stationarity (regarding biases in marginal distributions). In addition, joint correction is often based on the assumption that the structure of the bias in variables' interdependence is stationary, i.e., the same for control as for projections. This is not strictly true for MBCn, which allows the multivariate distribution to evolve in the projection period. However, the extent to which model-projected changes in dependence structure are preserved by MBCn has yet to be evaluated closely. More generally, whether the preservation of inter-variable dependence structures is a robust assumption or dependence structures should evolve from the reference to the future period are still open questions for the development of multivariate bias correction methods (Vrac, 2018). Furthermore, the correction of the multivariate dependence structure will necessarily affect the time sequencing of the climate model variables (Cannon, 2016), which can lead to modification of temporal autocorrelation. Maraun (2016) cautions that modifications of spatial, temporal, or multi-variable interdependence may break the consistency with the driving climate model and many others have argued for the least possible transformation of GCM–RCM outputs for this reason. This study does not address these fundamental questions and critiques nor does it generally recommend or not recommend the use of multivariate bias correction methods. The objective of the study was to compare the differences resulting from univariate vs. multivariate methods. We demonstrated a case in which biases in inter-variable dependencies can affect hydrological simulations considerably. This is important, particularly as it is common practice to use hydrological models calibrated to climatic conditions represented by historical climate variable series. In the same way that the use of several climate and hydrological models is recommended, the incorporation of uncorrected and univariate- and multivariate-corrected scenario data in the ensemble may be considered as one part of a transparent and honest communication of the full range of uncertainties.
This study systematically tested the effects of multivariate bias correction of projected air temperature and precipitation versus a traditional univariate bias correction on hydrological impact modelling in alpine environments. Jointly corrected air temperature and precipitation series simulated more snowfall and consequently up to 50 % more snow accumulation than univariate-corrected GCM–RCM data. Subsequently, glacier volume was simulated to decrease by up to a decade slower under multivariate-corrected scenarios. These differences also impact the simulations of streamflow and its components with higher snowmelt components and accordingly smaller rainfall components under multivariate-corrected scenarios compared to univariate-corrected scenarios. These are relevant systematic differences despite variations in the GCM–RCM ensemble. The choice between a univariate and a multivariate bias correction approach may therefore have implications for future water resources planning, as the snow component presents an important seasonal storage, and for the protection against hydrological hazards such as a higher vulnerability to drought.
Beyond this specific case this study suggests that the effect of bias correction methods may be generalized for catchments that include the elevation range of the snow line. Mountain hydrology modelling relies on the correct representation of the interdependence of air temperature and precipitation due to a crucial role of threshold air temperature concepts for the distinction of liquid and solid precipitation. This study makes an argument for the explicit consideration of interdependencies of climate variables by using multivariate bias correction methods in hydrological climate change impact studies in snow-dominated catchments. But many other threshold effects also drive relevant climate impacts and are parameterized in many models or indices. The study provides a strong incentive to test similar effects in hydrological systems and their model representations that may be dominated by other climate variable interdependencies.
An R package (R Core Team, 2018) including the MBCn and the
QDM algorithm is available for download from
EURO-CORDEX data can be accessed via different European
data nodes, available at
The supplement related to this article is available online at:
JM, IK, KS, and JS designed the study. JM carried out bias correction, modelling, and all analyses and wrote the first draft. IK calibrated the hydrological model and prepared snow, glacier, and hydrological data. KH prepared the EURO-CORDEX data for the catchments. AC provided and helped with his bias correction scripts. All co-authors contributed to and edited the paper.
The authors declare that they have no conflict of interest.
Work for this study was based on data acquired and methods developed within the project “The snow and glacier melt components of the streamflow of the River Rhine and its tributaries considering the influence of climate change” (ASG-Rhein, see Stahl et al., 2017) funded by the International Commission for the Hydrology of the Rhine basin (CHR). We thank Urs Beyerle for his assistance with the retrieval of EURO-CORDEX data and further thank all data providers (see Data availability). The article processing charge was funded by the German Research Foundation (DFG) and the University of Freiburg in the funding programme Open Access Publishing. Valuable comments by the editor and the reviewers helped to improve the paper. Edited by: Luis Samaniego Reviewed by: Ole Rössler and Sven Kotlarski