Daily precipitation statistics in a EURO-CORDEX RCM ensemble: added value of raw and bias-corrected high-resolution simulations

Abstract

Daily precipitation statistics as simulated by the ERA-Interim-driven EURO-CORDEX regional climate model (RCM) ensemble are evaluated over two distinct regions of the European continent, namely the European Alps and Spain. The potential added value of the high-resolution 12 km experiments with respect to their 50 km resolution counterparts is investigated. The statistics considered consist of wet-day intensity and precipitation frequency as a measure of mean precipitation, and three precipitation-derived indicators (90th percentile on wet days—90pWET, contribution of the very wet days to total precipitation—R95pTOT and number of consecutive dry days—CDD). As reference for model evaluation high resolution gridded observational data over continental Spain (Spain011/044) and the Alpine region (EURO4M-APGD) are used. The assessment and comparison of the two resolutions is accomplished not only on their original horizontal grids (approximately 12 and 50 km), but the high-resolution RCMs are additionally regridded onto the coarse 50 km grid by grid cell aggregation for the direct comparison with the low resolution simulations. The direct application of RCMs e.g. in many impact modelling studies is hampered by model biases. Therefore bias correction (BC) techniques are needed at both resolutions to ensure a better agreement between models and observations. In this work, the added value of the high resolution (before and after the bias correction) is assessed and the suitability of these BC methods is also discussed. Three basic BC methods are applied to isolate the effect of biases in mean precipitation, wet-day intensity and wet-day frequency on the derived indicators. Daily precipitation percentiles are strongly affected by biases in the wet-day intensity, whereas the dry spells are better represented when the simulated precipitation frequency is adjusted to the observed one. This confirms that there is no single optimal way to correct for RCM biases, since correcting some distributional features typically leads to an improvement of some aspects but to a deterioration of others. Regarding mean seasonal biases before the BC, we find only limited evidence for an added value of the higher resolution in the precipitation intensity and frequency or in the derived indicators. Thereby, evaluation results considerably depend on the RCM, season and indicator considered. High resolution simulations better reproduce the indicators’ spatial patterns, especially in terms of spatial correlation. However, this improvement is not statistically significant after applying specific BC methods.

Introduction

Regional climate models (RCMs) are sophisticated tools that allow representing physical processes in the atmosphere that are not yet resolved by the coarse resolution of global climate models (GCMs) (Giorgi 2006; Feser et al. 2011). During the last decade, a huge effort has been made in order to adapt and apply these models to produce regional climate change scenarios in different regions worldwide. As a result, there is nowadays a number of comprehensive datasets developed in projects such as ENSEMBLES (van der Linden and Mitchell 2009) and CORDEX (Giorgi et al. 2009), which also provide new opportunities for the intercomparison of different models, grid resolutions, boundary conditions, parameterizations (see e.g. Christensen et al. 1997; Jacob et al. 2007; Nikulin et al. 2011; García-Díez et al. 2013; Vautard et al. 2013) and model domains (Teichmann et al. 2013). For instance, the EURO-CORDEX initiative experiment design [European branch of CORDEX, http://www.euro-cordex.net/, see Jacob et al. (2014) and Kotlarski et al. (2014)] considers simulations at two horizontal resolutions, 0.44\(^{\circ }\) and 0.11\(^{\circ }\). The latter is computationally very costly and its benefits have just recently been questioned by Prein et al. (2015).

In principle, higher resolution experiments are able to capture features related to topography or land-sea mask, which are missed by coarser ones (Pryor et al. 2012; Walther et al. 2013); however, the added value of high resolution simulations is not always evident (Chan et al. 2013). Deficiencies may be caused for example by the fact that a given model is often developed and tuned in its low-resolution version (Gibelin and Déqué 2003), therefore the high resolution cannot systematically improve the model performance. Several studies point out the importance of the right combination of parameterizations and horizontal (e.g. Déqué et al. 2005; Prein et al. 2013) and vertical resolutions (Roeckner et al. 2006), highlighting for instance the role of the convection scheme (Kendon et al. 2012). Nevertheless, a single best parameterization for a specific resolution may not exist (Fernández et al. 2007; Jerez et al. 2012; García-Díez et al. 2015), and also depends on the particular application, i.e. the final use of the RCM simulation results. Thus, this situation supports the use of ensembles sampling different parameterizations and other model settings.

Model biases typically hamper the direct application of RCM output in impact studies (see e.g. Christensen et al. 2008; Kotlarski et al. 2014). Therefore, different bias correction (BC) methods were introduced in the literature (see e.g. Panofsky and Brier 1968; Durman et al. 2001) and they have recently become increasingly popular in their application. BC methods vary from very simple factor scaling (additive or multiplicative, Durman et al. 2001; Casanueva et al. 2013), to multi-variable BC techniques for particular combinations of variables (Wilcke et al. 2013; Vrac and Friederichs 2015) and methods pursuing the correction of more sophisticated bias features, such as temperature-dependent biases (Boberg and Christensen 2012; Bellprat et al. 2013). BC methods applied to precipitation have traditionally relied on the assumption that models produce more rainy days than the reference observations (drizzle effect). There are also some BC methods dealing with dry-day frequency overestimation, such as the frequency adaptation (Themeßl et al. 2012) or the Piani et al. (2010) method, modified by Argüeso et al. (2013) to be used with station data.

Against the background outlined above, the aim of this study is to, first, assess the added value of high (12 km) versus low (50 km) resolution RCM simulations regarding daily precipitation statistics. For this purpose, several precipitation derived-indicators (accounting for the mean and extreme regimes) are evaluated in a EURO-CORDEX RCM ensemble. Secondly, since RCMs are prone to systematic biases, BC methods are applied and the question whether a potential added value of the raw high-resolution experiments with respect to their low-resolution counterparts also remains after bias-correction is investigated. The considered BC methods consist of the adjustment of the first moments of the precipitation distribution (mean precipitation, wet-day intensity and wet-day frequency), which are applied separately to isolate the effect of biases in precipitation amount and occurrence on precipitation derived indicators. Note that we do not intend to provide the optimally bias-corrected data—more sophisticated BC methods correcting the whole precipitation distribution would be needed, but to attribute indicators’ biases to deficiencies in the precipitation frequency (occurrence) and the intensity (amount). By doing this, the basic precipitation features are investigated in depth to shed light on the limitations and merits of both resolutions and to inform climate scenario end users about undesired effects which may also affect more sophisticated BC methods.

Several aspects can be analysed to assess the added value of high resolution RCM simulation results. In this respect, a crucial question is the spatial scale on which the evaluation and intercomparison is carried out. An evaluation on the high resolution grid would penalize the coarse simulations because even a perfect coarse simulation would miss sub-grid-scale features (Prein et al. 2015). For this reason, all comparisons are performed on the coarse resolution (50 km), corresponding to the skillful scale of the 12 km experiments (Grasso 2000). We consider this as the ‘fairest’ approach since it compares features resolved by both resolutions. Nevertheless it is important to note that with this choice we do not consider all aspects of the added value, e.g. the more local information provided by the high resolution. See also Luca et al. (2015) for a comprehensive discussion about various definitions of added value.

A further note of caution relates to the fact that our study focuses on several extreme precipitation indicators, such as the contribution of very wet days (R95pTOT), dry spell lengths (maximum number of consecutive dry days, CDD) and percentiles (90th percentile on wet days, 90pWET). These indicators are very sensitive to the definition of a wet day, which is widely discussed throughout the paper.

We consider two target areas in Europe: Continental Spain and the European Alps, where high-resolution and high-quality gridded observational data sets are available for the evaluation and where previous versions of the same RCMs have been examined (see e.g. Frei et al. 2003; Herrera et al. 2010). These areas cover a wide range of climatic conditions, from Mediterranean to Alpine climates, and orographic complexity.

Taking into account all the above, the specific objectives of the study are to

  • examine the added value of high resolution simulations at the skillful scale (50 km) of the high resolution

  • assess the added value of the high resolution simulations before and after bias correction

  • provide some hints of possible implications of the results for more sophisticated BC methods.

This work is organized as follows. In Sect. 2 we present the data used. Section 3 introduces the methodology followed to evaluate the RCMs. The results are given in Sect. 4. Finally, the conclusion and the summary are given in Sect. 5.

Data

In the present study both high-resolution observational reference and RCM output data were used. All analyses were based on the common period 1989–2008. The study was performed on a seasonal basis, although only winter (DJF) and summer (JJA) results are shown for the sake of conciseness.

Observational data

Observations play a major role in the evaluation and bias correction procedure and, as the RCM grid cells represent areal averages, gridded observational products are usually considered for the evaluation.

Over Spain, we used the new EURO-CORDEX-compliant, gridded observational data sets (Spain011/044; Herrera et al. 2015). More than 2700 quality-controlled stations were selected to develop these gridded precipitation data sets with \(0.11^{\circ }\) and \(0.44^{\circ }\) horizontal resolution, regular in a rotated longitude–latitude system, covering the period from 1971 to 2010. They were interpolated following trivariate thin plate splines (TPS) and ordinary kriging (AA-3D method in Herrera et al. 2015). This interpolation process is equivalent to the one used to build the European-scale E-OBS data set (Hofstra et al. 2009), considering orography as covariable in the formulation of the TPS. In order to ensure the area-averaged representativeness, the interpolation method was applied at an auxiliary \(0.01^{\circ }\) horizontal resolution grid and the final grids were obtained by averaging the results into the final resolution.

For the Alps, the Alpine Precipitation Grid Dataset (APGD, Isotta et al. 2013) was used as observational reference. This data set was developed in the framework of EURO4M (European Reanalysis and Observations for Monitoring) for the period 1971–2008 and is a 5 km resolution gridded product provided by MeteoSwiss. The interpolation procedure consists of local regression (precipitation–elevation regression on independent slopes model) and angular distance weighting. In this study, the APGD was conservatively remapped onto the rotated \(0.11^{\circ }\) and \(0.44^{\circ }\) RCM grid, therefore the APGD011/044 versions exactly match the EURO-CORDEX grids (\(0.11^{\circ }\) and \(0.44^{\circ }\)). We re-gridded from the original 5 km resolution in a Lambert Azimuthal Equal Area Coordinate Reference System to 1 km grid in a rotated longitude-latitude system and afterwards we averaged the values inside every EURO-CORDEX grid-cell in order to guarantee the representation of areal averages.

Regional climate models

We evaluated daily precipitation from the EURO-CORDEX RCMs integrated at horizontal resolutions of \(0.11^{\circ }\) and \(0.44^{\circ }\) on rotated grids (Table 1). These simulations were driven by the ERA-Interim reanalysis (Dee et al. 2011) and covered the period 1989–2008. We refer the reader to Table 1 in Vautard et al. (2013) and Table 1 in Kotlarski et al. (2014) for the model details. In those tables, WRF311A and WRF311F are referred to as WRF-CRPGL and WRF-IPSL-INERIS, respectively, and these two WRF setups apply different combinations of physical parameterization schemes (details in Kotlarski et al. 2014). Most of these simulations are available via the Earth System Grid Federation (ESGF archive, http://esgf.org/) under the CORDEX initiative. Throughout this paper, the individual simulations are referred to as the name in the second column in Table 1 plus the resolution (e.g. HIRHAM011, HIRHAM044).

Table 1 EURO-CORDEX RCMs used in the present study

Methodology

Precipitation indices

Within the framework of the World Meteorological Organization, the Expert Team on Climate Change Detection and Indices (ETCCDI, http://etccdi.pacificclimate.org/) deals with the definition of climate indices in order to obtain comparable results worldwide. Based on these definitions we here used seasonal precipitation indices derived from daily precipitation amounts (Table 2).

Table 2 Precipitation and derived indices used in this study

SDII, RR and RR1 account for the mean precipitation regime, whereas 90pWET and R95pTOT are considered extreme indices in the sense that they are related to the tails of the probability distribution function, even though they are not associated to rare events. R95pTOT measures the contribution of heavy precipitation events to total precipitation. For Spain, this indicator clearly separates the different extreme regimes of the Atlantic and Mediterranean climates (see, for example, Fig. 10 in Herrera et al. 2012). CDD quantifies dry spells and is linked to precipitation occurrence. CDD and R95pTOT also present different driving mechanisms: CDD is more related to large-scale atmospheric circulation while R95pTOT has a convective origin and depends more on local processes and moisture fluxes (Casanueva et al. 2014).

As recommended by Orlowsky and Seneviratne (2012), 90pWET and R95pTOT were derived over the entire period, while CDD was calculated for each year and season before computing the median for all years.

Figure 1 shows the seasonal observed values for the indices in Table 2 for both regions as represented by APGD011 and Spain011. Note that in both regions, the spatial pattern has a paramount orographic component, especially in winter.

Fig. 1
figure1

Seasonal observed distribution of the RR, SDII, RR1, 90pWET, R95pTOT and CDD in winter (left) and summer (right), according to the APGD011/Spain011 datasets. The numbers are the spatial averages in both regions

Aggregation procedure

In order to examine the added value of high resolution simulations at their skillful scale \((0.44^{\circ }\)), a comparison between the evaluation of the coarse and high resolutions with respect to the coarse resolution observations (Spain044/APGD044) was performed. Also, the standard evaluation of the high resolution (i.e. RCMs at \(0.11^{\circ }\) with respect to Spain011/APGD011) is shown for illustrative purposes. Thus, from now on we refer to the individual resolutions as three independent datasets: \(0.44^{\circ }\) (original simulation), 0.11AGG \((0.11^{\circ }\) simulation aggregated to \(0.44^{\circ }\) resolution) and \(0.11^{\circ }\) (original simulation). By construction, the \(0.44^{\circ }\) and \(0.11^{\circ }\) EURO-CORDEX grids match each other at the grid cell boundaries, i.e. each \(0.44^{\circ }\) grid cell contains exactly 16 \(0.11^{\circ }\) grid cells. We obtained the aggregated data (0.11AGG) by spatially averaging the grid boxes from the \(0.11^{\circ }\) grid that belonged to each \(0.44^{\circ }\) grid box (i.e. 16 \(0.11^{\circ }\) grid cells were spatially averaged for each \(0.44^{\circ }\) grid box). Firstly, we obtained the 011AGG data from the original \(0.11^{\circ }\) simulations for each RCM, and secondly we calculated the derived indices from that aggregated data. By means of this procedure we address the added value of the high resolution at its skillful scale (Grasso 2000), therefore grid-point details (not only related to topography and land-sea mask, but also to better resolved local processes) from the high resolution cannot be discerned, but may be still present after smoothing them onto the coarse resolution. Note that \(0.44^{\circ }\) and 0.11AGG were defined in the same \(0.44^{\circ }\) EURO-CORDEX grid and, therefore, they can be directly compared with respect to the same observations (APGD044/Spain044).

The comparison of \(0.44^{\circ }\) and 0.11AGG on the coarse grid can be considered ‘fair’ since both resolutions are able to resolve the analysed features, however this is not a unique way to assess the added value. Comparing both resolutions on the high resolution grid would penalize the coarse resolution since, even for a perfect simulation, some sub-grid-scale features are missing. According to Prein et al. (2015) added value of high resolution is more evident in the evaluation on the high resolution grid since more fine-scale processes are captured. Note that a completely fair comparison would also imply to perform the evaluation exercise at the skillful scale of the coarse resolution experiments (for instance at \(4 \times 0.44^{\circ }=1.76^{\circ }\)), otherwise one resolution is always punished. This, however, would considerably smooth the spatial precipitation fields and also precipitation extremes. We here refrain from doing so but acknowledge that the \(0.11^{\circ }\) experiments might be slightly favored in our evaluation setup.

Assessment of simple bias correction techniques

Additionally to the evaluation of the raw RCM outputs, we assessed the results of three simple BC techniques for precipitation frequency and intensity and evaluated their effect on precipitation indices. The indicators considered in this work depend on precipitation occurrence and/or amount (see Table 2), therefore their biases can be attributed to deficiencies in the precipitation frequency and/or intensity. The three corrections considered were performed seasonally. The first one was based on mean precipitation (considering rainy and non-rainy days), while the others isolated the effect of the precipitation amount (how much) and occurrence (how often), respectively.

First, rainfall data were corrected using a multiplicative scaling factor obtained as the quotient of the observed and simulated spatially averaged precipitation over the specific region (from now on denoted as global scaling, GS):

$$\begin{aligned} RR_{GS} = RR_{RCM} {\langle \overline{RR_{OBS}}\rangle \over \langle \overline{RR_{RCM}}\rangle } \end{aligned}$$
(1)

where \(RR_{RCM}\) represents daily RCM precipitation at an individual grid point and the overline and angle brackets represent temporal and spatial averages, respectively. This scaling reduces the bulky systematic biases present in every RCM and can be considered as a minimum correction needed at both resolutions. The correction factor is the same for all grid points in a single model, resolution and season, it does not depend on the grid box but on the spatial mean precipitation for the respective analysis domain. To some extent, this bulk correction could mimic a (global) retuning of the model to better fit observations. Note that this correction would work well for overall too dry or too wet models, because it implies constant biases across grid points. As the precipitation spatial pattern presents very high variability and local features, some further corrections were needed at grid point level.

Second, a local scaling (LS) was applied at a grid point level considering the quotient of the observed and simulated wet-day precipitation:

$$\begin{aligned} RR_{LS} = RR_{RCM} {SDII_{OBS} \over SDII_{RCM}} \end{aligned}$$
(2)

Note that these two corrections, GS and LS, do not alter the values of the indicators R95pTOT and CDD.

Third, in addition to these corrections related to the precipitation amount, a correction concerning the precipitation frequency was applied. Many indicators (including those in Table 2) consider the wet day frequency (RR1) in their definitions. Thus an over/underestimation of RR1 would inevitably lead to biases in the derived indicators. A dry (wet) day is defined as a day with precipitation below (above) a given threshold. In the recent literature, the analysis of dry/wet days of observed precipitation and climate model output normally uses subjectively-selected rainfall thresholds (often 0.1 or 1 mm) to separate dry and wet days (see e.g. Lázaro et al. 2001; Herrera et al. 2010; Orlowsky and Seneviratne 2012). Some studies suggest the use of alternative wet/dry day thresholds different to the usually accepted such as 10 mm (Yoo et al. 2001), 5 and 10 mm (Fdez-Arroyabe Hernáez and Martín-Vide 2012) or the amount exceeded by 96 % of the total rainfall (Aviad et al. 2013). Bärring et al. (2006) find an optimal (according to several statistics) wet-day threshold for the whole of Europe of 0.56 and 1.20 mm (for two model versions of a specific RCM), for the reference threshold of 1 mm in point observation series. Selecting a single optimal threshold for the whole of Europe is a compromise, since this threshold depends on the location. In this study, we estimated an adjusted wet-day threshold \(P^{*}\) at grid point level by selecting the wet-day threshold value in the RCM which matches the observed wet-day frequency (RR1) computed with a 1 mm threshold:

$$\begin{aligned} P^{*} = F_{RCM}^{-1}(F_{OBS}(1\,\hbox {mm})) \end{aligned}$$
(3)

where F is the empirical cumulative distribution function (CDF), so \(F_{RCM}\) and \(F_{OBS}\) refer to the simulated and observed CDFs, respectively. This value could be different from grid cell to grid cell and was derived separately for each RCM, resolution and season. From now on we denote by \(X_{FA}\) a given indicator after the frequency adjustment (FA) is applied, i.e. \(P^{*}\) is used for the indicator calculation instead of 1 mm. Every precipitation value above this adjusted threshold was assumed to be a wet day in the RCM simulation, otherwise the day was considered dry. After this adjustment in the wet-day threshold, the observed RR1 is perfectly reproduced by the simulation and the contribution of the frequency to the biases in the derived indicators can be isolated.

Bear in mind that FA with very large (\(P^{*}\gg 1\) mm) and close to zero (\(P^{*}\ll 1\) mm) \(P^{*}\) values may lead to non reliable results, especially considering its application to impact studies. In the former case, FA and more sophisticated methods adjusting the wet-day frequency—such as quantile mapping (Panofsky and Brier 1968)—can deal with \(P^{*}\gg 1\) mm, but at the expense of mapping \(P^{*}\) values into 1 mm. For \(P^{*}<1\) mm, the FA itself is not able to provide an optimal correction since the model is drier than observations and it cannot ‘invent’ wet days (Bärring et al. 2006). For this reason, sophisticated BC methods have included additional methods such as the frequency adaptation by randomly sampling the observational distribution into the simulated first bin (Themeßl et al. 2012; Wilcke et al. 2013).

The perfect representation of the wet-day frequency does not necessarily lead to reduced biases in precipitation threshold-dependent indicators, especially in the two cases mentioned above. In the following sections we address the effect of considering \(P^{*}\) instead of 1 mm on the indicators’ biases at the different resolutions.

A fourth correction was considered combining the local scaling and the frequency adjustment. Thus, we locally scaled the daily precipitation after adjusting the wet-day threshold (i.e. \(Y_{LS}\) where \(Y=X_{FA}\), as Schmidli et al. 2006). Results were similar to the LS case, therefore, this correction is not shown in the paper.

Results

Added value in mean precipitation

Mean precipitation consists of the combination of the daily intensity and wet-day frequency. We analyse the contribution of both components separately in order to account for their effect on biases in precipitation-derived indicators (Sect. 4.2). Biases in the precipitation intensity (SDII) are shown in Figs. 2 and 3 for winter and summer, respectively, using the 1 mm threshold for the wet-day definition (same for the wet-day frequency—RR1—in the supplementary material, Figs. S1–S2). The fourth column represents the difference of the bias on the \(0.44^{\circ }\) grid minus 0.11AGG, both in absolute values. Thus, positive differences (greenish colours) show added value of the 0.11AGG and the opposite for negative differences (brownish colours). There is no overall added value of the high resolution simulations aggregated to the \(0.44^{\circ }\) grid since, depending on the model and season, biases are smaller for one resolution or the other (in agreement with Kotlarski et al. 2014). Due to the averaging procedure, in most cases, 011AGG presents smoother patterns than \(0.11^{\circ }\). In winter (Fig. 2), there is a clear orographic pattern in the bias of both regions with some improvements of the high resolution for WRF311A and WRF311F, whereas HIRHAM, RCA and REMO present the highest positive biases at both resolutions for at least one of the regions. In summer (Fig. 3), there is no common spatial bias pattern in both regions. CCLM and RCA considerably reduce biases in the high resolution (especially in the Alpine region) whereas WRF311A and WRF311F present negligible differences between both resolutions. In both seasons, opposite-sign biases at \(0.44^{\circ }\) and 0.11AGG are found in some areas, more noticeable for CCLM in winter and RCA and REMO (also HIRHAM for Spain) in summer. This means that the same parameterizations with different resolutions lead to different precipitation intensities and also different spatial patterns. REMO stands out in summer, since both regions present mainly wet biases at \(0.44^{\circ }\), but dry biases predominate at \(0.11^{\circ }\) and, therefore, at 011AGG. Apparently, some physical schemes seem more resolution dependent than others (Déqué et al. 2005). Further research about the sensitivity of seasonal biases to the different schemes (see e.g. García-Díez et al. 2013) should be performed in the specific RCMs and resolutions. Note also the patchy spatial pattern in HIRHAM011, RCA011 and REMO011 with strong, opposite biases in nearby grid boxes, i.e. there is not a gradual change across the zero bias between opposite sign biases. For HIRHAM and REMO this could be due to the use of non-smoothed orography (see the fourth column in Table 1). Previous studies have also associated biases to the excessively smoothed (Shkolnik and Efimov 2013) or non-smoothed topography (Polanski et al. 2010), being the orography another factor to take into account in RCMs evaluation.

Fig. 2
figure2

Winter SDII relative biases (%) for the RCMs (rows) at \(0.44^{\circ }\) (first column), 0.11AGG (second column) and \(0.11^{\circ }\) (third column) resolutions. Values in the upper left and lower right corner represent the relative biases of the spatially averaged SDII in both regions. The fourth column shows the difference between the first two columns in absolute values

Fig. 3
figure3

As Fig. 2, but in summer

Precipitation occurrence is characterized in terms of the wet-day frequency, which depends on the particular threshold (e.g. 1 mm) used to define a wet day. Figure 4 shows the q–q plot for three selected grid points in RCA011 for winter daily precipitation (black crosses). The vertical line corresponds to 1 mm in the observations. Therefore the intersection with the q–q plot provides the adjusted threshold equivalent to 1 mm in the observations (\(P^{*}\), see Eq. 3). On the left, the model overestimates the wet-day frequency and \(P^{*}\) is around 16 mm (intersection of black crosses with the vertical line). The center panel corresponds to a grid point where \(P^{*}\) approximates 1 mm. On the right, the model presents more dry days than observed (\(P^{*} < 1\) mm). This figure illustrates that adjusted thresholds are in some cases very far from 1 mm (left), but also close to 0 mm (right). Only the points with \(P^*\approx 1\) mm (center) would work well with the usually accepted 1 mm threshold.

When defining wet days using \(P^{*}\) instead of 1 mm, precipitation intensity (SDII) is also altered, since it is defined as the mean of the wet-day precipitation. For \(P^{*}>1\) mm, SDII would be shifted towards higher values, since low-precipitation values in the range (1 mm, \(P^{*}\)) are considered dry days. For \(P^{*}<1\) mm, dry SDII biases are expected due to the contribution of many close-to-zero precipitation values regarded as wet days.

Fig. 4
figure4

q–q Plots for 3 selected grid points from RCA011 simulations in winter (black crosses). These grid points corresponds to adjusted wet-day thresholds greatly exceeding 1 mm (left), around 1 mm (center) and under 1 mm (\(\approx 0.3\,\hbox {mm}\), right). Values are presented in squared root scale with labels in the original units. The vertical line corresponds to 1 mm in the observations; its intersection with the q–q plot provides the adjusted threshold equivalent to 1 mm in the observations \((P^{*})\). Dots show the deciles from the wet day distribution for 1 mm threshold (black), the adjusted wet day threshold (blue) and after local scaling (red). 90pWET corresponds to the last dot of each series

Figures 5 and 6 show the spatial pattern of \(P^{*}\) computed according to Eq. 3 for winter and summer, respectively. In winter, \(P^{*}\) is higher in places with complex orography (the Alps and Pyrenees) and lower in lowlands, especially for HIRHAM and RCA. In Spain, \(P^{*}\) does not reach as large values as in the Alpine region. Smaller \(P^{*}\) is also found in summer, with many zero or close to zero values (e.g. CCLM, HIRHAM, RCA especially in Spain). Notice that the definition of wet days depends on \(P^{*}\) and, therefore, the indicators (SDII, CDD, 90pWET and R95pTOT) are expected to change as the threshold \(P^{*}\) changes. Hence, the evaluation results depend on the value which is chosen as the wet-day threshold, which is usually subjectively adopted (e.g. commonly 1 or 0.1 mm) or adjusted with the observations, as done in this study.

Thus far, EURO-CORDEX RCMs present biases in SDII and RR1 at both resolutions that will propagate to the derived indices. BC methods allow to statistically correct these deviations, but the underlying physical misrepresentations will remain and may still affect higher-order moments of the corrected variables. Large \(P^{*}\) also affects sophisticated BC methods. For instance, \(P^{*}\) (Figs. 5, 6) determines the highest (or lowest) value which is mapped into 1 mm when applying a quantile mapping (Panofsky and Brier 1968) using the standard 1 mm wet-day threshold. The patchy spatial pattern shown before for SDII (Figs. 2, 3) is also found in the HIRHAM011, RCA011 and REMO011 adjusted thresholds (Figs. 5, 6). This may lead to spatial inconsistencies in sophisticated BC techniques, since two nearby grid points can have very different \(P^{*}\). These aspects constitute a theoretical discussion and need to be proven and analysed in further studies. No patchy spatial pattern is noticeable at the 011AGG scale, due to the underlying averaging procedure. Therefore, corrections in the frequency should be accomplished at the coarse scale, where no spatial inconsistencies are found and \(0.44^{\circ }\) and 011AGG present comparable results in terms of spatial coherence. Conversely, at \(0.11^\circ\) resolution, WRF and CCLM present more spatially coherent and smoothed patterns and RACMO stands out with \(P^{*}\) close to 1 mm, especially over large parts of Spain.

Fig. 5
figure5

Wet-day threshold equivalent to 1 mm in the observations for all the RCMs (rows) and resolutions (columns) in winter. For a better contrast of spatial differences, values are presented using a non-linear scale. Note that the black color represent \(P^{*}=0\)

Fig. 6
figure6

As Fig. 5, but in summer

Added value in precipitation derived indicators

We now examine the added value of the high resolution experiments for precipitation-derived indicators (low versus high resolution) and account for the effect of the biases in SDII and RR1 on derived indicators by applying BC methods at both resolutions (raw versus corrected data). All indicators considered (Table 2) depend on the wet-day threshold. Thus, they are calculated with the 1 mm and \(P^{*}\) (FA, Sect. 3.3). 90pWET is also affected by the precipitation amount, therefore GS and LS corrections are performed. Biases for 90pWET and CDD (relative) and R95pTOT (absolute) are obtained for the raw and the corrected data for 0.44\(^{\circ }\) and 011AGG.

90pWET

Results for the 90th percentile on wet days (90pWET) are summarized in Fig. 7. The ‘original’ label refers to the case when no correction is performed, i.e. without any scaling and taking 1 mm as the wet-day threshold. Global scaling does not lead to overall conclusions, it usually reduces very high biases but deteriorates smaller ones. Local scaling strongly reduces the biases, along with their spatial variability, in every RCM and resolution. This results in individual grid-point biases of similar magnitude at both resolutions (median markers close to zero, and similar-sized boxes). This means that any improvement of a resolution with respect to the other before the correction does not necessarily lead to an improvement after the local scaling since biases become comparable for both resolutions (see e.g. WRF331F in Spain). Less frequently, an improvement before the correction remains (see e.g. RCA in Spain) or turns into a deterioration (see e.g. RACMO in Spain in winter) after the LS, although these are subtle changes. The application of the frequency adjustment (using \(P^{*}\) as the wet-day threshold) leads to similar biases to those in the original case (using 1 mm wet-day threshold). Notice that especially for \(P^{*}>1\) mm, changing the threshold yields slightly different percentiles, while the scaling changes the indicator more rapidly [see dots in Fig. 4, representing the deciles from the wet day distribution for the original (black), FA (blue) and LS (red)].

Regarding the added value, neither the original nor the corrected data lead to an overall improvement of one resolution against the other since results are similar for both resolutions and the best performance is obtained for 0.44\(^{\circ }\) or 0.11AGG depending on the specific case.

Fig. 7
figure7

Boxplots summarizing the spatial distribution of 90pWET relative biases (in %) for winter (DJF) and summer (JJA) for both regions (columns). The 90th percentile is calculated with the standard 1 mm fixed threshold as reference (first row). Second to fourth rows correspond to the relative biases in 90pWET when GS, LS and FA corrections are applied, respectively. Each box corresponds to one RCM and resolution (0.44\(^{\circ }\) and 0.11AGG per RCM). The boxes show the interquartile range and the median (circle) but, for the sake of clarity, the whiskers extend only to the 5th and 95th percentiles

R95pTOT

Figure 8 summarizes the absolute biases for the contribution of very wet days (R95pTOT). In winter, negligible differences are found between resolutions in both regions and few changes are obtained after the frequency adjustment. The correction can cause a small improvement (e.g. RCA in Spain) or deterioration (e.g. CCLM in the Alpine region). Hence the R95pTOT involves more processes (related to precipitation intensity) responsible for the biases that cannot be attributed to the wet-day frequency. In summer, the \(0.44^{\circ }\) simulation in the original case in the Alpine region is slightly better or does not differ much from 0.11AGG except for CCLM. After the frequency adjustment CCLM, HIRHAM and RCA biases increase dramatically on the coarse resolution. This could be due to the very low \(P^*\) values (see Fig. 6), leading to an increase of this indicator and therefore to very large positive biases.

Fig. 8
figure8

As Fig. 7, but for the absolute biases of R95pTOT (in %). GS and LS corrections are omitted, since they do not affect this index

CDD

For the number of consecutive dry days (CDD, Fig. 9) in winter the frequency adjustment tends to reduce biases and diminish the differences between resolutions in Spain, but slightly benefits 0.11AGG in the Alpine region. Relative biases for summer CDD are very large for CCLM and HIRHAM at both resolutions—related to their large negative biases in the frequency (see Fig. S2), showing their difficulties to properly represent the lower part of the precipitation distribution and the temporal coherence. The frequency adjustment substantially reduces these biases, meaning that the spells are better captured when the wet-day frequency is adjusted to the observed one. Unlike CCLM and HIRHAM, RCA does not reduce its large bias in summer in the Alpine region after the frequency adjustment and a large negative bias remains. This is due to the zero values of the wet-day adjusted thresholds that are apparent over approximately one third of the Alpine domain (black grid boxes in Fig. 6). Since the wet-day threshold is exactly zero, there are no dry spells in these grid boxes, leading to large negative biases of CDD.

Fig. 9
figure9

Boxplots for the spatial distribution of CDD relative biases (in %) for winter (left) and summer (right). The indicator is calculated with the 1 mm fixed threshold (first row) and with the adjusted wet-day threshold (second row). See Fig. 7 for further details

Joint discussion

The above results show that 90pWET is more sensitive to the intensity whereas the CDD is affected by the wet-day threshold. Thus, they also present different sensitivities to the local scaling and frequency adjustment. On the one hand, the frequency adjustment slightly changes the 90pWET (i.e. changing the threshold yields a slightly different percentile). This means that the precipitation frequency (i.e. the lower tail of the precipitation distribution) does not have a systematic implication for the upper percentiles (i.e. upper tail based indices). In some models the correction can either make it slightly better or worse, but in very dry models the correction can even strongly deteriorate it (e.g. CCLM and RCA in summer). Precipitation intensity, however, plays a major role in 90pWET; when the precipitation distribution is scaled by SDII, the upper percentiles are scaled too (in agreement with Benestad et al. 2012). On the other hand, the frequency adjustment considerably reduces CDD biases. Once the observed and simulated wet-day frequencies are equal, the RCM better captures the dry spell durations. As mentioned before, in some cases (see e.g. RCA in summer in the Alpine region in Fig. 9) frequency adjustment does not reduce CDD biases because the time series autocorrelation and persistence (and therefore the occurrence) of specific situations are not well represented by the model and the correction is not able to resolve this. For this reason, the frequency adjustment deteriorates biases in that example for 90pWET and R95pTOT too. Unlike 90pWET and CDD, which are more sensitive to the intensity and frequency, respectively, for R95pTOT the frequency adjustment can either deteriorate or not affect the results. The definition of R95pTOT includes both the intensity and the frequency, and correcting for biases of these two aspects can have converse effects.

As shown in Figs. 78 and 9, the selected indicators are affected by very low summer \(P^{*}\). In this case, 90pWET (CDD) is lower (higher) because of too many zero-precipitation values. R95pTOT is based on a lower 95th percentile, resulting in a higher quotient of the contribution of very wet days relative to the total wet-day precipitation amount. This is a limitation in the frequency adjustment; when RCMs are too dry, an optimal threshold does not necessarily lead to an improvement because the correction cannot ‘invent’ wet days (Bärring et al. 2006). This should be carefully examined since basic bias correction techniques are not able to solve this problem and more sophisticated techniques are required to deal with this issue (Themeßl et al. 2012; Wilcke et al. 2013).

The correction methods used in this study are not able to correct all indicators at a time. The precipitation occurrence affects the indices related to spells rather than the upper-tail percentiles, which are more influenced by precipitation intensity. That result suggests that there is not a single optimal, best way of bias correcting RCMs, since methods adjusting the frequency better represent the CDD, but can deteriorate the upper tail percentiles. Further analyses should be performed to quantify this result in more sophisticated bias correction methods combining several corrections. Note that we use the same period for the calibration and validation of the BC methods, since we validate aspects that are not directly tackled by the BC procedure. Validation results might look worse if an independent validation period would be chosen.

Added value and bias correction effect on the spatial pattern

The correction methods applied in the previous section preserve the temporal structure of the data and in this section we analyse their effect on the spatial pattern. We only show results for the \(0.44^{\circ }\) and 0.11AGG data sets, since these can be directly compared against the same observations.

The ability to represent the spatial structure is summarized by means of Taylor (2001) diagrams (Fig. 10). These show several spatial scores at a time: spatial Pearson correlation coefficient (r), Centered Root Mean Squared Difference (RMSD), standard deviation (std) and biases of spatial averages (bias). Arrows join, for a given RCM, the 0.44 score (squares) with the 011AGG (circles). Therefore, arrows pointing towards the observational reference indicate that the high-resolution runs (011AGG) perform better than the coarse ones (0.44\(^{\circ }\)). To summarize the added value of 0.11AGG, the bars in the right panels show the number of RCMs (from 0 to 7) in which the 0.11AGG improves with respect to the \(0.44^{\circ }\) resolution, in terms of the four statistics shown in the Taylor diagram. In these barplots, the numbers of the right Y-axis show the statistical significance of the existence of added value, obtained by a Z-test for proportions. The results are statistically significant only when 6 or 7 RCMs (and symmetrically for 0 and 1) out of 7 improve upon the \(0.44^{\circ }\) resolution runs. For the raw RCM output (Fig. 10, first row), high-resolution RCMs generally perform better than the coarse counterparts, especially in terms of r and RMSD (bias and std are not conclusive). After the corrections (Fig. 10, second row), all the RCMs present similar validation scores for CDD and 90pWET regardless of the resolution (the squares are close to the circles). The proportion of the 0.11AGG RCMs that improves with respect to the coarse ones is not statistically significant after the corrections. R95pTOT deteriorates with the frequency adjustment except for CCLM and RACMO (labels 1 and 3, respectively) since these two RCMs present \(P^{*}\) close to 1 mm (as shown in Fig. 5). This degradation after applying the correction was also shown in the previous section, meaning that this indicator is not favoured by the frequency adjustment. The results for summer and for Spain in both seasons lead to similar conclusions and are included in the supplementary material (Figs. S3–S5).

Fig. 10
figure10

Taylor diagrams for winter 90pWET, R95pTOT and CDD in the Alpine region. The first row shows the original data using a 1 mm fixed wet-day threshold. The second row shows corrected data (LS for 90pWET and FA for R95pTOT and CDD). Squares represent \(0.44^{\circ }\) resolution and circles 0.11AGG. Their colors correspond to the biases in the spatially-averaged index. The numbers close to the square markers identify the RCMs (see codes in Table 1). The right panel shows barplots of the number of RCMs at 0.11AGG resolution that perform better than the \(0.44^{\circ }\) resolution in spatial Pearson correlation coefficient (r), centered root mean squared difference (RMSD), variability (std) and bias. The results are statistically significant only when 6 or 7 RCMs improve upon the \(0.44^{\circ }\) (see text)

Conclusions

This paper evaluates daily precipitation characteristics in the ERA-Interim-driven EURO-CORDEX RCM ensemble. Experiments at both \(0.11^{\circ }\) and \(0.44^{\circ }\) horizontal resolution are considered, and the potential added value of the \(0.11^{\circ }\) simulations is addressed. For this purpose, high-resolution RCMs are regridded onto the coarse grid by grid cell aggregation (0.11AGG). The analysis is performed in two regions of Europe where high quality gridded observational data sets are available (continental Spain and the Alpine region) considering mean precipitation and derived indicators (90th percentile on wet days—90pWET, contribution of the very wet days—R95pTOT and number of consecutive dry days—CDD).

In terms of seasonal biases we find only limited evidence for an added value of the higher resolution in the precipitation intensity, wet-day frequency and derived indicators, since results depend on the RCM, season and indicator and small differences rather randomly favour the \(0.44^{\circ }\) or the 0.11AGG resolutions. We find added value of the high resolution simulations in the spatial pattern (especially in correlation and RMSD). To adequately represent daily precipitation statistics, bias correction techniques are needed at both resolutions. Nevertheless, after applying simple bias correction techniques the proportion of the 0.11AGG RCMs that improves with respect to the coarse ones is not statistically significant and there are negligible differences between resolutions.

Note that we only partly address the potential added value, since high resolution simulations are not only used with the intention to improve the larger scale processes and features but also in order to provide better local information (i.e. the local departures of the \(0.11^{\circ }\) relative to the 0.11AGG or \(0.44^{\circ }\) simulation results should be better than a random information). Our validation on the coarse grid can be considered ‘fair’ because it compares features resolved by both resolutions, however it is not the unique way to assess the added value (Luca et al. 2015). Pursuing a fairer comparison between resolutions would also require the retuning of the high resolution simulations and the consideration of the \(0.44^{\circ }\) simulations at their skillful scale. Prein et al. (2015) claim that the added value of the high resolution is more evident when the comparison is performed on the high resolution grid but acknowledge that this procedure benefits the high resolution runs.

The present work and Prein et al. (2015) try to shed light on the added value issue by analysing different precipitation aspects taking into account precipitation-derived indices related to the intensity, frequency and extremes, and from daily to sub-daily scales. As such, both works are complementary to each other. Both show the benefits of the high resolution in spatial patterns, however we find no statistically significant results after bias correction. Prein et al. (2015) identify Spain and the Alpine area as the regions with largest net-improved-area fractions (i.e. fraction of grid boxes in which more than 75 % of the high resolution simulations improve on the coarse counterparts). However that fraction is never higher than 50 % of improvement, meaning that more than half of the grid points in each region is deteriorated or (in most of the cases) is similar in both resolutions. From our results, added value of the high resolution on seasonal mean biases depends on the indicator, RCM and season and the best performance is obtained for \(0.44^{\circ }\) or 0.11AGG depending on the specific case. Both studies are focused on different indicators for extreme precipitation, thus making it difficult to intercompare them. While Prein et al. (2015) find also added value in other aspects such as the sub-daily scale, we focus on the added value of bias corrected simulations, which could be of great interest for the impact community.

We apply three simple bias correction methods based on the correction of the first moments of the precipitation distribution. First, results show that scaling by the quotient between observed and simulated spatial mean precipitation is not enough to reduce biases in the 90pWET. Second, the local scaling with the wet-day intensity reduces the 90pWET biases dramatically (i.e. correcting the mean also corrects the percentiles) and makes both resolutions comparable after the correction. Third, the frequency adjustment improves the lower part of the probability distribution function (better representation of the CDD) but it deteriorates the upper tails (worse or negligible changes in the 90pWET and R95pTOT). Therefore, these corrections do not show an overall improvement which strongly indicates that there is no single optimal way to correct for RCM biases. Users should make a choice for one bias correction method or the other depending on the precipitation metric being assessed (e.g. local scaling is more efficient for percentiles and the frequency adjustment for dry spells), but being aware that the same method can at the same time deteriorate another feature of the distribution. This emphasizes the need to investigate more sophisticated bias correction methods that correct several aspects at a time.

Large biases remain in the derived indicators after the frequency adjustment when the adjusted threshold is zero (see e.g. CCLM in Spain and RCA in the Alpine region in summer). Bias correction has traditionally relied on the assumption that models produce more rainy days than the reference observations and these methods work well for finding optimized thresholds when the climate model overestimates the number of wet days by frequently simulating light rainfall. However, the procedure cannot improve the opposite situation because it cannot ‘invent’ wet days if the model is too dry (in agreement with Bärring et al. 2006). This problem is very noticeable in summer and further research is needed (e.g., along the lines of the frequency adaptation from Themeßl et al. 2012) since it is not possible to fully solve it with the basic bias correction techniques applied in the present work.

Sophisticated bias correction methods are well prepared to solve any problem in the precipitation Probability Density Function. In this work we identify some shortcomings (e.g. deficiencies in the representation of the wet-day frequency) in specific RCM simulations that may have implications for the suitability for such methods. For instance, some RCMs at \(0.11^{\circ }\) resolution present very high \(P^{*}\) (caused by strong biases in the precipitation frequency). Some sophisticated methods (e.g. quantile mapping) map this large \(P^{*}\) onto 1 mm and values in the range (1 mm, \(P^{*}\)) onto dry days. There are also spatial inconsistencies in some models at the high resolution which might be related to instabilities due the use of non-smoothed orographies and a spatial displacement of precipitation structures (Maraun and Widmann 2015). This could give unreliable results after applying single-site bias correction methods (i.e. point-wise methods, not considering the spatial coherence).

This study gives insight into the daily precipitation statistics in the EURO-CORDEX RCM ensemble by analysing each ensemble member individually. Better agreement with the observations is usually found when ensemble averages are validated and, moreover, this improves when only the best performing models are considered (Herrera et al. 2010). Bearing this in mind more efforts should be devoted towards the improvement of the individual models in order to avoid very strong biases. For this purpose, further research about the impact of different parameterization schemes on seasonal biases as García-Díez et al. (2013) should be performed for the specific RCMs.

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Acknowledgments

The authors are grateful to Prof. C. Schär for his helpful comments and E. van Meijgaard for making available the RACMO model data. We acknowledge the observational data providers. Calculations for WRF311F were made using the TGCC super computers under the GENCI time allocation GEN6877. The WRF331A from CRP-GL (now LIST) was funded by the Luxembourg National Research Fund (FNR) through Grant FNR C09/SR/16 (CLIMPACT). The KNMI-RACMO2 simulations were supported by the Dutch Ministry of Infrastructure and the Environment. The CCLM and REMO simulations were supported by the Federal Ministry of Education and Research (BMBF) and performed under the Konsortial share at the German Climate Computing Centre (DKRZ). The CCLM simulations were furthermore supported by the Swiss National Supercomputing Centre (CSCS) under project ID s78. Part of the SMHI contribution was carried out in the Swedish Mistra-SWECIA programme founded by Mistra (the Foundation for Strategic Environmental Research). This work is supported by CORWES (CGL2010-22158-C02) and EXTREMBLES (CGL2010-21869) projects funded by the Spanish R&D programme and the European COST ACTION VALUE (ES1102). A. C. thanks the Spanish Ministry of Economy and Competitiveness for the funding provided within the FPI programme (BES-2011-047612 and EEBB-I-13-06354). We also thank two anonymous referees for their useful comments that helped to improve the original manuscript.

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Correspondence to A. Casanueva.

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K. Goergen: (Former Département Environnement et Agro-Biotechnologies, Centre de Recherche Public Gabriel Lippmann, 41 Rue du Brill, 4422 Belvaux, Luxembourg, since January 2015 renamed to Luxembourg Science and Technology, LIST).

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Casanueva, A., Kotlarski, S., Herrera, S. et al. Daily precipitation statistics in a EURO-CORDEX RCM ensemble: added value of raw and bias-corrected high-resolution simulations. Clim Dyn 47, 719–737 (2016). https://doi.org/10.1007/s00382-015-2865-x

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Keywords

  • Regional climate models
  • EURO-CORDEX
  • Added value
  • Bias correction
  • Precipitation indices