1. Introduction
Global climate models (GCMs) are the primary source of information about future climate change (IPCC 2013). Owing to the high computational demand, their spatiotemporal resolution is restricted and, hence, their output is of limited use for climate change impact research and risk assessment. To resolve this fundamental scale gap, regional climate models (RCMs) nested within GCMs are used to downscale GCM-based projections to regional scales. The higher resolution combined with more realistic parameterizations at fine scales allows RCMs to better reproduce the local mechanisms that shape regional climates (Laprise 2008; Rummukainen 2010). Both GCM and RCM fields can exhibit substantial systematic differences from gridded observational data (Christensen et al. 2008; Sillmann et al. 2013; Kotlarski et al. 2014). Such discrepancies between simulated and observed fields are commonly referred to as biases (Pan et al. 2001). Model output is recommended to be statistically processed (bias corrected) before application (Wood et al. 2004; Fowler et al. 2007; Teutschbein and Seibert 2012), although this practice is controversially discussed (Ehret et al. 2012).
A quantitative measure for climate change is the additive or multiplicative difference (ratio) between a climate statistic for a future scenario period and a historical reference period. This difference is known as the climate change signal (CCS). Generally, model biases do not cancel out in the calculation of the CCS (Buser et al. 2009; Gobiet et al. 2015), therefore the CCS is also biased. The purpose of this paper is to provide more evidence to support the hypothesis that the CCS modification due to bias correction is a desirable consequence of removing model biases. To this end, we derive and test a systematic analytical theory of the effect of bias correction on the CCS. The theory allows a quantitative analysis of the CCS modification and can serve as a tool to efficiently and effectively generate novel, improved CCS estimates. The latter will form the base for supporting climate change adaptation, mitigation, and resilience strategies for end users, stakeholders, and policy makers.
The model bias at a fixed location is determined by the climate state; hence, it is time dependent. Recent research (Christensen et al. 2008; Boberg and Christensen 2012; Gobiet et al. 2015) suggests that temperature and precipitation biases of climate models are well approximated as being dependent only on the magnitude of the simulated/observed values—a feature named intensity dependence. For example, higher precipitation amounts tend to have larger biases. Consequently, bias correction methods that apply individual corrections to different model intensities are able to successfully debias not only temperature and precipitation (Maraun et al. 2010; Piani et al. 2010; Teutschbein and Seibert 2012; Themeßl et al. 2012; Ivanov and Kotlarski 2017) but also other climate variables, including wind speed (Wilcke et al. 2013). Ivanov and Kotlarski (2017) provided new evidence that such methods also improve the joint temperature–precipitation distribution and preserve the temperature–precipitation temporal association as in the raw climate model data. Based on pseudoreality experiments, Vrac et al. (2007), Maraun (2012), Räty et al. (2014), and Ivanov and Kotlarski (2017) showed that in most regions intensity-dependent bias correction methods are relatively stable in the long term (i.e., for time scales beyond the maximum period of available observations). Assuming that the intensity-dependent model bias does not explicitly depend on time (i.e., that it is stationary), these methods use a function of intensity, called the correction function to describe the intensity-dependent corrections. Different simulated intensities correspond to different climate processes, for which climate models have different skills (e.g., Ivanov et al. 2018a,b). This provides a partial physical justification for the intensity dependence of the correction function, the derivation of which is purely statistical. The view that the stationarity assumption is not overly restrictive is supported by the successful application of such methods in various contexts. Despite that, the validity of the stationarity assumption is subject to scientific debate (e.g., Switanek et al. 2017).
The question about the effect of intensity-dependent bias correction on the CCS has been controversially discussed. In practical applications, the raw model CCS of common climate statistics is generally preserved. However, for specific geographic regions, climate models, and statistics, the alteration of the CCS is comparable to the CCS itself (Hagemann et al. 2011; Boberg and Christensen 2012; Dosio et al. 2012; Themeßl et al. 2012; Räisänen and Räty 2013; Maurer and Pierce 2014; Cannon et al. 2015; Ivanov and Kotlarski 2017). Whether or not this is a beneficial effect is debatable. For instance, the CCS modification may influence the model climate sensitivity and distort physical scaling relationships between meteorological variables such as temperature and precipitation. Hempel et al. (2013), Cannon et al. (2015), Pierce et al. (2015), and Switanek et al. (2017) developed bias correction methods that aim at preserving the raw model CCS. These methods use corrections that explicitly depend on the model scenario climatology and, hence, on time. Such bias correction methods lack physical justification for the assumed nonstationary biases. Furthermore, the validity of the raw model CCS is questioned by the fact that model biases can considerably distort the projected CCS (Buser et al. 2009; Gobiet et al. 2015). Boberg and Christensen (2012) and Gobiet et al. (2015) argue that the modification of the CCS of mean temperature by bias correction is meaningful as it alleviates the effect of intensity-dependent model biases on the CCS.
Thus, bias correction methods that keep the raw model CCS unavoidably assume artificial nonstationarities, whereas those that assume intensity dependence have some physical grounds, but modify the CCS. This controversial discussion is so far unresolved because the CCS modification by bias correction has been investigated mostly empirically. Currently, the mechanisms of that modification are analytically understood only for the distribution mean of variables that have no zero values (also known as interval variables) such as temperature (Hagemann et al. 2011; Gobiet et al. 2015). However, not only the distribution mean but also other statistics, including characteristics of extreme events, are of high relevance to applications. Current knowledge is not directly transferable to variables that have a natural zero limit (ratio variables; Finkelstein and Leaning 1984), such as (sub)daily precipitation and wind speed, which are of primary importance for assessment of the future severe flooding (Christensen and Christensen 2003) and wind energy potential (Pryor and Barthelmie 2010). This is because zeros are treated differently than positive values. Apart from recent evidence that contains qualitative speculations (Hagemann et al. 2011; Themeßl et al. 2012), the problem is yet unexplored.
This paper is structured as follows. Section 2 presents the analytical theory of intensity-dependent bias correction. In section 3, we test the theory for daily precipitation over alpine terrain. Conclusions are drawn and a short outlook given in section 4.
2. Data and method
a. Data
We use observation and model data for daily precipitation that have been studied in a recent publication by Ivanov and Kotlarski (2017). The observations for the 30-yr calibration period 1980–2009 stem from 27 stations of the Swiss National Basic Climatological Network (Swiss NBCN; Begert et al. 2007, updated). (Figure B1 and Table B1 in appendix B show a geographic map and a list of the complete station names and locations, respectively.) The model data were extracted from the database of the ENSEMBLES project (http://ensembles-eu.metoffice.com; van der Linden and Mitchell 2009) for the region of Switzerland and the 1970–2099 period. They cover a European domain at a horizontal resolution of approximately 25 km and were generated assuming the IPCC SRES A1B emission scenario (IPCC 2000). Ivanov and Kotlarski (2017) have used data from the ENSEMBLES project to enable comparison of the methodology against the Swiss Climate Change Scenarios Initiative (Appenzeller et al. 2011), which is based on the same data. The model fields were reduced to the station locations by inverse distance weighting interpolation using the four nearest grid points. (Table B2 in appendix B lists the 15 GCM–RCM model chains employed.) The RCM data were postprocessed according to the empirical quantile mapping (QM) method selected in Ivanov and Kotlarski (2017). That method uses a 91-day moving window to calibrate a nonlinear transfer function that varies with the day-of-year for percentiles of order up to 0.99. The transfer function is linearly interpolated between percentiles and constantly extrapolated for quantiles of order above 0.99.
b. Analytical theory
This section introduces the basic ideas of the theoretical considerations and provides a summary of the final results. For detailed analysis that uses the mathematical apparatus of probability calculus (Billingsley 2012), the reader is referred to section 1 of the online supplemental material.
A meteorological variable takes values from intervals of the real line 
QM defines the transfer function as the quantile–quantile (QQ) curve (Ivanov and Kotlarski 2017). To test whether linearity is plausible, we consider QQ plots of the model and observed data at the different stations. For one of these plots, shown in Fig. 1a, linearity appears to be a good approximation. The high values of the coefficient of determination shown in Fig. 1b support this conclusion for all stations.
Testing the linearity assumption. (a) QQ plot of the 99 observed vs model percentiles together with the minimum and maximum values (blue circles) for the OTL-C station-model chain combination and the 1980–2009 period in (left) winter and (right) summer. The solid dark blue and the black lines represent the linear fit and the identity line, respectively; the coefficient of determination 
Citation: Journal of Climate 31, 16; 10.1175/JCLI-D-17-0765.1
1) Interval variables
The bias-free CCS estimates obtained according to the theory in this subsection will be referred to as interval estimates.
(i) CCS of the distribution mean
(ii) CCS of the quantile of order α
2) Ratio variables
Ratio variables have a natural zero limit. Typical meteorological ratio variables are daily precipitation and wind speed. They are zero on dry/calm days and positive otherwise. Denote the positive-event probability of the random variable X by 
(i) CCS of the distribution mean
(ii) CCS of the quantile of order α
The theory developed in this section is a tool for quantitative analysis of the CCS modification due to bias correction. It allows end users to recognize model biases with high potential to distort the simulated CCS. It provides a new opportunity to efficiently estimate the bias-free CCS without performing the bias correction, provided that the bias correction assumptions hold and the model biases and raw model CCS of certain climate statistics are known. As we demonstrate in the next section, the CCS estimates are adequate despite the seemingly restrictive theoretical assumptions.
3. Results and discussion
Here, we analyze the ability of the linearized analytical theory to predict the CCS and its modification for the bias correction and downscaling example described in section 2a. The CCS is for the scenario period 2070–99 relative to the reference period 1980–2009. The analysis focuses on the multiplicative CCS as it is more commonly used for ratio variables. Section 2 in the online supplemental material includes results for the additive CCS. We only test the threshold case as 
a. Performance of the theory with respect to the CCS
The distributions of the raw, QM bias-corrected, ratio, and interval estimates of the multiplicative CCS are displayed in Figs. 2 and 3 for the distribution mean and quantile of order 0.9, respectively. The box-and-whisker plots summarize the 405 values for the 27 stations and 15 model chains. Figures S1 and S2 in the supplemental material display analogous results for the additive CCS. Compared to the distribution of the interval CCS estimates, the distribution of the ratio estimates more closely follows that of the QM bias-corrected estimates. In summer, the ratio theory tends to slightly overestimate the QM CCS, whereas the interval theory strongly underestimates the QM CCS of conditional statistics (right panels of Figs. 2, 3, S1, and S2).
Multiplicative CCS (dimensionless) between the 2070–99 and 1980–2009 climatological periods for the 27 × 15 combinations of precipitation stations and ENSEMBLES model chains in (left) winter and (right) summer. (a) CCS estimates of the unconditional mean, based on raw model output (R), quantile-mapped data 
Citation: Journal of Climate 31, 16; 10.1175/JCLI-D-17-0765.1
As in Fig. 2, but for the quantile of order α = 0.9. The scaled 
Citation: Journal of Climate 31, 16; 10.1175/JCLI-D-17-0765.1
The theoretical versus the QM bias-corrected multiplicative CCS estimates for the distribution mean and the quantile of order 0.9 are displayed in Figs. 4 and 5, respectively. Analogous results for the additive CCS are shown in Figs. S3 and S4 in the supplemental material. The ratio and interval estimates for the station–model chain combinations are displayed as red and blue circles, respectively, together with the corresponding simple linear regression fits in a darker hue. Ideally, the points should lie along the identity line. The coefficient of determination 
Test of the analytical theory for the multiplicative CCS (dimensionless) of daily precipitation between the 2070–99 and 1980–2009 climatological periods in (left) winter and (right) summer. (a) Unconditional mean: theoretical CCS estimate [Theoretical C, Eq. (13)] vs the CCS estimate from QM bias-corrected data 
Citation: Journal of Climate 31, 16; 10.1175/JCLI-D-17-0765.1
As in Fig. 4, but for the quantile of order 
Citation: Journal of Climate 31, 16; 10.1175/JCLI-D-17-0765.1
We conclude that the linearized ratio theory generally provides a good and substantially improved description of the QM bias-corrected CCS compared to the interval theory.
b. Performance of the theory with respect to the CCS modification
1) General analysis
For both the ratio and interval theories, columns 3–7 of Table 1 provide the correlations of the theoretical CCS modifications with the modification by the QM method as well as the average absolute theoretical and QM CCS modifications; absolute values prevent mutual cancellation of opposite errors. The average absolute raw model CCS shown in the last column puts the CCS modification values into context. As can be seen, the QM CCS modification is generally smaller in absolute value than the simulated CCS, so there is no certainty that the theory will be as adequate for the CCS modification as it is for the CCS. Generally, the CCS modification by the ratio theory highly correlates with the QM CCS modification (0.79–0.92); relatively low correlations are observed only for the multiplicative CCS of the unconditional mean (0.49) and unconditional quantile of order 0.9 (0.56) in summer. The interval theory estimates have substantially lower correlations (0.11–0.85) with the QM estimates; for the multiplicative CCS of the unconditional mean in summer the correlation is even negative (−0.22). The average absolute modification of the multiplicative CCS is generally small (0.07–0.1), slightly larger (0.12–0.13) for the conditional mean and the quantile of order 0.9 in summer. For the additive CCS, the modification is generally below or close to 1 mm day−1 but approaches 3 mm day−1 for the conditional quantile of order 0.9 in summer. The ratio estimates are close to the QM estimates and closer than the interval ones, except for the multiplicative CCS of the unconditional mean in summer. In the latter case, the ratio estimate (0.02) is substantially smaller than the QM estimate (0.08), whereas the interval estimate is precise. A glance at Fig. 4a reveals that the ratio theory systematically overestimates the negative CCS values, which leads to an underestimation of the absolute CCS modification. The modifications predicted by the interval theory often have a different sign from the QM modifications; this inflates the average absolute CCS modification estimated by the interval theory and artificially makes it closer to the QM estimate. In contrast to the multiplicative CCS, for the additive CCS the absolute modification has a clear seasonality, being larger in summer than in winter. This can be explained by the larger precipitation amounts in summer, which also entail larger biases.
Statistics of the CCS modification between the 2070–99 and 1980–2009 climatological periods over the sample of 27 stations of the Swiss National Basic Climatological Network (NBCN) and 15 ENSEMBLES model chains for winter (DJF) and summer (JJA). The estimates refer to the multiplicative CCS of the unconditional (UMm) and conditional (CMm) mean, the unconditional (UQm) and conditional (CQm) quantile of order 0.9, the additive CCS of the unconditional (UMa) and conditional (CMa) mean, and the unconditional (UQa) and conditional (CQa) quantile of order 0.9. The term 
To facilitate the analysis of the CCS modification based on the ratio theory, Figs. 2 and 3 as well as Figs. S1 and S2 present additional box-and-whisker plots for the CCS components. QM most substantially and systematically affects the CCS of conditional statistics in summer. The simulated CCS and hence also the scaled component are strongly negative [Eqs. (14) and (22)]. However, the increased tendency of the model to overpredict positive events (wet days) in the future, reflected by 
Thus, the linearized ratio theory well captures the average CCS modification by QM even for the statistics and seasons with the largest modifications. This indicates that the theoretical assumptions are not too restrictive. Again, the ratio theory is superior to the interval theory and performs better in winter.
2) Analysis of individual cases with large CCS modifications
As shown in Table 1, the CCS modification by QM tends to be smaller than the simulated CCS. Therefore, it is instructive to study the mechanisms by which QM modifies the CCS as it does for the few cases with large modifications. We focus on the three station–model chain combinations with the largest absolute modifications of the QM CCS. They are visualized in Figs. 2 and 3 as well as Figs. S1 and S2 with red, green, and blue circles in decreasing order. (The station abbreviations and the short references for the model chains are listed in Tables B1 and B2 in appendix B, respectively.) In the light of the ratio theory, we interpret the CCS components that are large in absolute value with respect to the rest of the sample and/or to the other CCS components; if not all of the large CCS components have the same sign, only those that have the same sign as the CCS modification are considered. To enhance the physical understanding, we further analyze each of these components in more detail.
As seen in the left panel of Fig. 2a, the three largest absolute modifications of the multiplicative CCS of the unconditional mean in winter are amplifications of the simulated positive CCS. They occur for SAM-A (0.85), SAM-O (0.79), and SIA-A (0.61) and are accurately predicted by Eq. (13). The values of the ε component [Eq. (12)] for the first two cases rank as the first and second largest and even exceed the other CCS components in absolute value. This is due to 1) the large increase of the positive-event probability in the future 
As seen in the left panel of Fig. 2b, the three largest absolute modifications of the multiplicative CCS of the conditional mean in winter are amplifications of the simulated positive CCS. They occur for SAM-A (0.43), SBE-J (0.35), and SAM-J (0.33) and are accurately predicted by Eq. (14). For SAM-A, the scaled component is large positive because the large positive-event probability bias in the scenario period 
As seen in the left panel of Fig. 3a, the three largest absolute modifications of the multiplicative CCS of the unconditional quantile of order 0.9 in winter are amplifications of the simulated positive CCS. They occur for SAM-A (0.81), SAM-O (0.74), and OTL-J (0.72) and are accurately predicted by Eq. (20). For each of them, the large positive simulated CCS 
As seen in the left panel of Fig. 3b, the three largest absolute modifications of the multiplicative CCS of the conditional quantile of order 0.9 in winter occur for OTL-K (−0.58), SAM-A (0.55), and OTL-A (−0.54) and are accurately predicted by Eq. (22). For OTL-K and OTL-A, the lower future positive-event probability bias results in the first and second largest negative 
The theory successfully predicts the largest absolute modifications of the additive CCS as well (see Figs. S1 and S2). Although the cases are different from those for the multiplicative CCS, the analysis of the CCS modification is analogous. In contrast to the multiplicative CCS (left panels of Fig. 2), the ε component has no significant role for the cases with the largest absolute modifications of the CCS of the distribution mean in winter (left panels of Fig. S1).
Although the theory generally performs well, for some cases with substantial CCS modifications it is not that successful. The majority of these cases occur in summer, which is consistent with the observation that the theory performs better in winter (Figs. 2–5; see also Figs. S1–S4). The reason is that in summer a larger proportion of precipitation stems from small-scale convective processes, the parameterization of which in RCMs is highly unlikely to result in linear biases. This is illustrated in the right column of Fig. 1a, which presents the transfer function for the OTL-C case. OTL-C systematically shows some of the highest discrepancies between the theoretical and QM CCS estimates. Crucial for the representation of the precipitation distribution are the deviations from the linear fit in the lower part of the distribution, which describes the majority of precipitation events. The linear fit leads to a substantial overestimation at this range, which results in a general overestimation of precipitation statistics. The constant extrapolation for new extremes, used in the QM method, but not accounted for by the theory, also contributes to the overestimation (right column of Fig. 1a). The transfer function of the QM method varies slowly with the day-of-year that the 91-day moving window is centered on, so the net effect on the CCS should be negligible.
In summary, we showed that the linearized ratio theory successfully predicts the QM bias-corrected CCS and the corresponding modification of the simulated CCS on average and for the individual cases with the largest absolute modifications. The analysis also demonstrated how the theory can be used to reveal and quantify the important mechanisms that modify the CCS. These mechanisms involve bias removal and are not an artifact of the bias correction method. The systematic evaluation in Ivanov and Kotlarski (2017), including pseudoreality experiments to test the stationarity assumption, indicated that the application of bias correction is scientifically appropriate. This strongly suggests that the CCS modification for this particular bias-correction example is a desirable effect.
4. Conclusions and outlook
We develop a linearized analytical description of the mechanisms by which stationary model biases affect the climate change signal (CCS). We show that the same mechanisms are responsible for the modification of the CCS by intensity-dependent bias correction methods. The issue has so far been solved for interval variables (such as temperature) and the additive CCS of the distribution mean (Hagemann et al. 2011; Gobiet et al. 2015). Our theory is applicable not only to the distribution mean of interval variables but also to ratio variables (such as daily precipitation and wind speed) and distribution quantiles. It also considers multiplicative CCS and statistics of the positive (conditional) distribution. For ratio variables, the model bias of the positive-event probability plays a crucial role as its sign defines two different treatments of the zeroes. Formally, the theory provides simple linear equations that predict the bias-free CCS based on known model biases and raw model CCS of certain climate statistics. The bias-free CCS has a scaled component that describes the removal of intensity-dependent biases and a level component that adjusts the CCS level in accordance with the future change of the positive-event probability or its bias. Adjusting the positive-event probability affects the CCS of the distribution mean and is quantified by an additional ε component. The theoretical approach can be extended in a straightforward manner for known nonstationary/nonlinear biases (e.g., linear with a break point and polynomial) and other climate statistics (variance, temporal autocorrelation coefficients, impact indices, etc.).
In an illustrative application, we test the theory for an empirical quantile mapping (QM) method. QM is employed to bias-correct and downscale 15 ENSEMBLES model chains of 25-km resolution to 27 precipitation stations in the topographically structured terrain of Switzerland. We investigate the effect of bias correction on the CCS between the 2070–99 and 1980–2009 climatological periods and its modification. Taking the values of zero into account, the linearized ratio theory generally provides a good and substantially improved description of the QM bias-corrected CCS compared to the interval theory. The ratio theory well captures the CCS modification by QM even for the station–model chain combinations with the largest modifications and quantifies the underlying mechanisms. Therefore, it can be used to analyze the results of actual bias correction in a linear approximation. In the particular application, we show that the severe amplification of the multiplicative CCS of the distribution mean for few cases in winter is due to an increase of the positive-event probability coupled with a decrease of the drizzle correction in the future. The strong dampening of the negative CCS of the conditional mean in summer is due to the correction for the increased tendency of the model to overpredict positive events (wet days) in the future. The few occurrences for which the theory performs less than optimally can be explained by the nonlinearity of the QM transfer function and the extrapolation for extremes that did not occur in the calibration period (“new” extremes). This is a challenging test because of the complex alpine topography and the presence of an additional model bias component induced by the scale difference (~25 km for the model data versus local scale for the weather stations), which is highly unlikely to be linear with intensity. Therefore, the theoretical description is expected to perform even better for other geographical regions and/or when no implicit downscaling step is involved.
Our theory and results demonstrate that intensity-dependent bias correction modifies the CCS by removing model biases rather than due to mathematical artifacts. This strongly suggests that if scientifically appropriate, this type of bias correction can be trusted not only for correcting climate statistics but also for modifying their CCS. As discussed in the introduction, there is a growing body of evidence in support of the assumptions of stationarity (Vrac et al. 2007; Maraun 2012; Räty et al. 2014; Ivanov and Kotlarski 2017) and intensity dependence (Christensen et al. 2008; Boberg and Christensen 2012; Gobiet et al. 2015) of the model bias, which must hold for bias correction to be reasonable. Further, the climate model must adequately capture changes of relevant physical/chemical/biological processes and large-scale atmospheric circulation patterns for bias correction to be legitimate (Ehret et al. 2012; Maraun et al. 2017).
For end users (impact modelers, planners, engineers, policy makers), the analytical theory is a tool 1) to detect model biases with high potential to distort the simulated CCS and 2) to analyze model output in case bias correction severely changes the raw model CCS. Moreover, this tool provides a new opportunity to efficiently and effectively debias CCS estimates: efficiently, because the estimates can be obtained without actually performing the bias correction, and effectively, because the approximation is adequate. The novel, improved CCS datasets will support adaptation, mitigation, and resilience policies for stakeholders, policy makers, and various sectors, including agriculture, water management, tourism, energy, transport, disaster risk reduction, and infrastructure.
Future work will include testing the theory for model simulations that underestimate the probability of positive events (frequency adaptation case), for variables, other than temperature and precipitation, and for other geographical regions. The theory will be extended to account for the effect of the constant extrapolation used by empirical methods, for nonlinear transfer functions (e.g., Piani et al. 2010) that allow analytical treatment, for statistics other than mean and quantiles, and for statistics of multimodel ensembles (Gobiet et al. 2015). Future research needs to focus on the development of process-based corrections (e.g., Bellprat et al. 2013; Gómez-Navarro et al. 2018) rather than preserving the raw model CCS.
Acknowledgments
The R language and environment for statistical computing (R Core Team 2016) was used to perform the quantile mapping bias correction and to create the figures. Funding was provided by the German Research Foundation Project “Ensemble projections of hydro-biogeochemical fluxes under climate change” under project number LU 1608/5-2. The bias correction was performed within the ELAPSE project (Enhancing Local and Regional Climate Change Projections for Switzerland) and was supported by the Swiss State Secretariat for Education, Research and Innovation SERI, project number C12.0089. We acknowledge the RCM data sets from the EU-FP6 project ENSEMBLES (http://ensembles-eu.metoffice.com) and the Swiss Federal Office of Meteorology and Climatology MeteoSwiss for providing observational data. We thank the reviewers for constructive criticism and many suggestions that improved the quality of the paper.
APPENDIX A
Linearized Theory for the FA Case
a. CCS of the distribution mean
b. CCS of the quantile of order α
APPENDIX B
Data Details
The 27 Swiss National Basic Climatological Network (NBCN) observation stations considered for this study are mapped in Fig. B1 and listed in Table B1. The 15 employed GCM–RCM model chains from the ENSEMBLES project are listed in Table B2.
Map of the locations of the daily precipitation observation stations (black dots) within the Swiss National Basic Climatological Network (NBCN). Red curves mark country boundaries. The elevation isolines of 500, 1500, and 3000 m above mean sea level are displayed by gray contours with growing thickness. A complete list of the station names and coordinates is given in Table B1 in appendix B.
Citation: Journal of Climate 31, 16; 10.1175/JCLI-D-17-0765.1
List of the 27 stations of Swiss National Basic Climatological Network (NBCN) considered in the present work.
List of the 15 employed GCM–RCM model chains from the ENSEMBLES project. For reasons of brevity, in this work model chains are referred to as shown in the column “Short reference.” Expansions of acronyms are available online at https://www.ametsoc.org/PubsAcronymList. C4I is the Community Climate Change Consortium for Ireland; DMI is the Danish Meteorological Institute; ICTP is the International Centre for Theoretical Physics; METO-HC is the Met Office Hadley Centre; SMHI is the Swedish Meteorological and Hydrological Institute.
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