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Climate Dynamics

, Volume 52, Issue 3–4, pp 1343–1357 | Cite as

An effective drift correction for dynamical downscaling of decadal global climate predictions

  • Heiko PaethEmail author
  • Jingmin Li
  • Felix Pollinger
  • Wolfgang A. Müller
  • Holger Pohlmann
  • Hendrik Feldmann
  • Hans-Jürgen Panitz
Article

Abstract

Initialized decadal climate predictions with coupled climate models are often marked by substantial climate drifts that emanate from a mismatch between the climatology of the coupled model system and the data set used for initialization. While such drifts may be easily removed from the prediction system when analyzing individual variables, a major problem prevails for multivariate issues and, especially, when the output of the global prediction system shall be used for dynamical downscaling. In this study, we present a statistical approach to remove climate drifts in a multivariate context and demonstrate the effect of this drift correction on regional climate model simulations over the Euro-Atlantic sector. The statistical approach is based on an empirical orthogonal function (EOF) analysis adapted to a very large data matrix. The climate drift emerges as a dramatic cooling trend in North Atlantic sea surface temperatures (SSTs) and is captured by the leading EOF of the multivariate output from the global prediction system, accounting for 7.7% of total variability. The SST cooling pattern also imposes drifts in various atmospheric variables and levels. The removal of the first EOF effectuates the drift correction while retaining other components of intra-annual, inter-annual and decadal variability. In the regional climate model, the multivariate drift correction of the input data removes the cooling trends in most western European land regions and systematically reduces the discrepancy between the output of the regional climate model and observational data. In contrast, removing the drift only in the SST field from the global model has hardly any positive effect on the regional climate model.

Keywords

Drift correction Decadal prediction Dynamical downscaling 

1 Introduction

In recent years, increasing effort has been undertaken to close the gap between seasonal climate predictions and long-term climate change projections. Multi-year and decadal climate predictions are of tremendous importance for manifold economic and agricultural activities and planning (Meehl et al. 2009; Murphy et al. 2010). Decadal climate predictions are by now at the threshold of becoming operational and first real-time decadal forecasts are already available (Smith et al. 2013a; Meehl and Teng 2014). Decadal climate prediction systems require a combination of adequate initial and boundary conditions as forcing data and imply a specific experimental design with oceanic and atmospheric observations being assimilated in coupled climate models (Boer 2011; IPCC 2013). Taking initial states from such assimilation runs for freely evolving coupled model simulations make decadal climate predictions particularly prone to drift phenomena. i.e. extensive artificial trends in various model variables and regions, because after the initial “shock” the coupled model tends towards its own climatology (Goddard et al. 2013; Magnusson et al. 2013; Kröger et al. 2017). This is particularly relevant when the decadal climate predictions are initialized by full fields instead of anomalies from the assimilation run (Smith et al. 2013b). Therefore, various authors have pointed to the necessity of bias and drift correction in decadal climate prediction (ICPO 2011; Kharin et al. 2012; Goddard et al. 2013; Fuċkar et al. 2014; Hawkins et al. 2014; Kruschke et al. 2015; Sansom et al. 2016). Some authors even argue that a drift correction should always be carried out for initialized climate predictions, whatever initialization method is used (cf. Kim et al. 2012; Hazeleger et al. 2013; Smith et al. 2013b).

Drift correction methods are mostly based on simple statistical approaches, e.g. by removing the mean drift over several ensemble members (ICPO 2011; Choudhury et al. 2016), accounting for trends (Kharin et al. 2012), start dates (Fuċkar et al. 2014; Kruschke et al. 2015) and refer to individual variables such as the SST field (Narapusetty et al. 2014). Longer-term, i.e. multi-year to multi-decadal, drifts typically occur in the ocean component of coupled climate models and can be found to a minor extent even in uninitialized climate change projections (Sen Gupta et al. 2013). Therefore, the SST field represents the main interface by which drifts in the ocean penetrate into the atmosphere (Kim et al. 2012). Indeed, Pattantyús-Ábrahám et al. (2016) have demonstrated that climate drifts emanating from the central North Atlantic can be detected in various atmospheric variables up to the higher troposphere. Kruschke et al. (2015) established a drift correction for extra-tropical storm tracks. For many issues, it is sufficient to apply drift correction methods to individual output variables of the decadal climate prediction system. Yet, for specific issues such as dynamical downscaling, a multivariate drift correction approach is required for the input data of the regional climate model that filters the drift out of all relevant oceanic and atmospheric variables and, additionally, retains the co-variability between the variables. This is more useful and computationally less expensive than an a-posteriori drift correction of every output variable from the regional climate model because of nonlinear error growth in the transmission from global to regional climate model and within the regional climate model’s computing process itself (e.g. Diaconescu et al. 2007; Danforth and Kalnay 2008). In the present study, we present such a multivariate approach of drift correction dedicated to the dynamical downscaling of global decadal climate predictions in the European–Atlantic sector.

This sector has been chosen because recent studies have revealed a comparatively high multi-year to decadal predictability in the North Atlantic (Keenlyside et al. 2008; Branstator and Teng 2012; Garcia-Serrano et al. 2015). In addition, substantial drifts prevail in the deep ocean and in the SST field in most decadal climate prediction systems subsumed under the Coupled Model Intercomparison Project version 5 (CMIP5) initiative (Kim et al. 2012; IPCC 2013). According to our current understanding, decadal predictability in the North Atlantic is linked to the meridional overturning circulation (Matei et al. 2012b; Müller et al. 2016), the Atlantic multi-decadal oscillation (Knight et al. 2006) and the SST field (Smith et al. 2007). Therefore, adequate ocean initialization is a main challenge for accurate decadal climate predictions (Hawkins et al. 2016). In addition, greenhouse gas and aerosol concentrations play an important role as boundary conditions prescribed over the simulation period (van Oldenborgh et al. 2012; Mehta et al. 2013; Hawkins et al. 2016). In the light of these sources of decadal climate predictability, it is not surprising that the predictive skill in most climate variables increases with averaging time because the external forcing stands out against internal variability (Garcia-Serrano and Doblas Reyes 2012). Emanating from the North Atlantic, there is also significant decadal climate predictability over Europe (Corti et al. 2012; Müller et al. 2014) and in the tropical Atlantic region (Dunstone et al. 2011). Note that another source region of multi-year to decadal predictability is located in the tropical Pacific in the form of the Pacific Decadal Oscillation (Jia and DelSole 2012; Knight et al. 2014), whereas the North Pacific suffers from ocean mixing processes that are insufficiently represented in many coupled climate models (Guemas et al. 2012).

The dynamical downscaling of global decadal climate predictions pursued in the present study is motivated by the added value achieved by regional climate models (RCMs) in former works. Mieruch et al. (2014) have shown that dynamical downscaling with the RCM COSMO-CLM enhances the predictive skill of summer and winter precipitation in most parts of Europe. The same was reported for the multi-year predictability of the West African monsoon where most RCMs exhibit a clear added value with respect to summer monsoon precipitation along the Guinean Coast and Sahel regions (Paeth et al. 2017). Downscaling with the same RCMs also leads to a substantial reduction of the precipitation bias in these sub-Saharan regions (Paxian et al. 2016). Here, we use a high-resolution RCM nested into a global decadal climate prediction system that is based on full-field forcing and, hence, subject to a remarkable drift in the central North Atlantic (Smith et al. 2013b; Kröger et al. 2017). The objective is to perform a multivariate drift correction comprising all variables from the global model that are used as input for the RCM, and to retain a physically consistent drift-corrected input data set that accounts for the co-variability among all input variables. Our approach emanates from three hypotheses: (1) the drift can be filtered out by means of an EOF analysis based on a very large data matrix, (2) the drift-corrected input data set is physically consistent and still accounts for realistic low-frequency components of climate variability, and (3) the drift correction of the input data leads to an improved representation of European climate as simulated by the RCM.

The next section is dedicated to the considered model data and observations and describes the drift correction approach. Results are presented in Sect. 3. In Sect. 4, our results are discussed in the light of previous studies and major conclusions are drawn.

2 Data and methods

We apply the drift correction to output data from the German decadal climate prediction system which is based on the coupled Earth system model MPI-ESM (Müller et al. 2012; Pohlmann et al. 2013; Marotzke et al. 2016; Kröger et al. 2017). It is composed of the atmospheric component ECHAM6 (Stevens et al. 2013) and the ocean model MPI-OM (Jungclaus et al. 2015). The experimental design and initialization technique of the decadal predictions are described in detail by Müller et al. (2012) and Pohlmann et al. (2013). The individual hindcast experiment considered here uses ocean temperature and salinity data from the ORAS4 ocean reanalysis (Balmaseda et al. 2013) and covers the time period 2001–2010. It is part of a sequence of several generations of the decadal prediction system developed in the framework of the German MiKlip project (Marotzke et al. 2016) and the only version (named Prototype version) with full-field forcing, i.e. the 10-year hindcasts are initialized by absolute values in the ocean instead of anomalies from the long-term assimilation run (Kröger et al. 2017). The Prototype system provides decadal hindcasts (and forecasts) with start years varying from 1960 to 2013 and 15 ensemble members each with initial conditions varying at the daily scale before January 1st of each start year (Kröger et al. 2017). Smith et al. (2013b) have pointed to the prevalent problem of substantial drifts in oceanic regions in decadal predictions based on full-field forcing. Indeed, the Prototype version of the MiKlip decadal climate prediction system has been shown to exhibit a striking cooling tendency In the central North Atlantic that mainly affects the Atlantic meridional overturning circulation and respective heat transports and the SST field (Marotzke et al. 2016; Kröger et al. 2017), but is also detectable in various tropospheric variables (Pattantyús-Ábrahám et al. 2016). A very similar signature of oceanic cooling has been reported by Hazeleger et al. (2013) in their decadal prediction system based on the EC-Earth V2.3 Earth system model (ESM) when applying full-field forcing. The Prototype system has been considered here because it is marked by a remarkable artificial drift that, according to our underlying hypotheses mentioned above, may be clearly distinguished from other components of low-frequency climate variability during the simulation period.

The dynamical downscaling is carried out with the non-hydrostatic RCM COSMO-CLM (CCLM) (Rockel et al. 2008). It is applied over the European-Atlantic sector, and run in a horizontal resolution of 0.22° (~ 25 km). The model domain, which corresponds to the EURO-CORDEX region (http://www.cordex.org/community/domain-euro-cordex.html), is indicated in Fig. 6. CCLM has been successfully nested in previous versions of the MiKlip decadal climate prediction system and revealed a statistically significant added value compared with the driving global model in various climate phenomena and variables in Europe, especially in components of the atmospheric water cycle and precipitation extremes (Panitz et al. 2014; Mieruch et al. 2014), and in terms of the West African summer monsoon rainfall (Paxian et al. 2016; Paeth et al. 2017). In the present study, it is nested for the first time in the Prototype version of the MiKlip decadal climate prediction system. We perform three types of experiments with CCLM: (1) using the input data without drift correction, (2) using the drift correction applied to all input variables and levels, and (3) applying the drift correction only to the surface temperature field as suggested for instance by Narapusetty et al. (2014).

To expose the spurious character of the climate drift at the interface between ocean and atmosphere in the North Atlantic we compare SST trends from the Prototype version with observed trends from the gridded SST data set HadISST (Rayner et al. 2003) and the 20th-century reanalysis NOAA-20CR (Compo et al. 2011; in the following the acronym NOAA is used). Both data sets use virtually the same underlying in-situ measurements of SST, but emanate once from a statistical and once from a process-based physical interpolation. The effect of drift correction on the performance of the RCM output will be assessed in comparison with the version 14.0 of E-OBS gridded observations at 0.25° horizontal resolution (Haylock et al. 2008).

For the purpose of dynamical downscaling, a drift correction approach is required that complies with three constraints: (1) it must account for the drift in all input variables of the global climate within the RCM domain, (2) the remaining input data set must be physically consistent, retaining the co-variability between the input variables, and (3) it must distinguish between the artificial signature of the climate drift and realistic components of low-frequency variability in the decadal climate predictions. Our drift correction approach is based on an EOF analysis based on a three-dimensional set of input variables from the Prototype global prediction system. Ideally, the drift is captured by one single EOF that accounts for a preferably small portion of total variability.

The input data needed for the RCM CCLM comprises six three-dimensional atmospheric variables that stretch across 47 vertical levels [air temperature (T), zonal (U) and meridional (V) wind components, specific humidity (Q), cloud liquid water content (LWC), cloud ice content] and three two-dimensional variables at the surface (surface pressure, surface temperature, snow amount). For the chosen model domain of CCLM, the input data covers the domain 58.1°W–80.6°E and 12.1°N–81.1°N in a horizontal resolution of about 1.85° (see Fig. 2). We apply the drift correction to the input data in the entire model domain and not just at the lateral and lower boundary conditions in order to achieve a consistent data set also at the upper boundary. This is important for realistic atmospheric wave breaking and reflection in the upper stratosphere. Over all variables, levels and horizontal grid boxes (75 in west–east and 38 in north–south direction) this implies a total of (6 × 47 + 3) × 75 × 38 = 812,250 spatial degrees of freedom in the input data set. For the third type of experiment, the EOF analysis is confined to the surface temperature field, reducing the spatial degrees of freedom to 75 × 38 = 2,850. The time step of the input data is 6-h, i.e. 14,608 time steps over the 2001–2010 period. Yet, the drift correction refers to monthly means because the drift clearly emerges at this time scale. This reduces the temporal degrees of freedom to 120. Thus, anomalies of the 6-h input data from the respective uncorrected monthly means are retained and, after the drift correction has been carried out, the corrected monthly means are superimposed by these original short-term anomalies. Note that the corrected monthly means are slightly shifted such that the first monthly mean (here January 2001) remains unchanged in order to avoid an offset between the initial state from the assimilation run and the corrected input data. The mean seasonal cycle is removed and the monthly time series scaled by their standard deviation prior to applying the EOF analysis and finally added to the corrected monthly means.

For the purpose of drift correction, we search for eigenvectors that represent spatial patterns, and principal components (PCs) that represent time series, at least one of them capturing the climate drift. Applying the EOF analysis in the classical form to a data matrix X with m spatial elements arranged in columns and n temporal elements arranged in rows, implies that a covariance matrix:
$$C=\frac{1}{n}{X^T}X,$$
(1)
of dimension m × m must be diagonalized (von Storch and Zwiers 1999). In the present case, m equals 812,250 which is by far too large for commonly available computing resources—alone the main memory for the covariance matrix consumes more than 2.6 Terabyte. Therefore, we utilize a theorem of matrix algebra saying that given an n × m dimensional matrix X the eigenvalues of the temporal covariance matrix XTX are identical with the eigenvalues of the spatial covariance matrix XXT and their eigenvectors have the following simple linear relationship
$$\vec {e}=\frac{{X\vec {g}}}{{\left| {X\vec {g}} \right|}},$$
(2)
with \(\overrightarrow{g}\) representing the eigenvector from XXT and \(\overrightarrow{e}\) being the eigenvector from XTX (von Storch and Zwiers 1999). Thus, our proceeding is as follows: the covariance matrix is computed by:
$$C=\frac{1}{n}X{X^T},$$
(3)
the resulting n × n (= 120 × 120) dimensional covariance matrix is diagonalized, leading to n eigenvectors \(\overrightarrow{g}\), and the target eigenvectors are derived by Eq. (2). The original data matrix is projected onto the eigenvectors \(\overrightarrow{e}\) which results in n = 120 PC time series that partly carry the drift signal. The drift-corrected input data set is finally composed by a linear combination of all EOFs, leaving out the one(s) with the drift signal. This generally represents an appropriate treatment of data matrices with the sample size being smaller than the dimension of data vector \(\overrightarrow{x}\)—a typical situation with climatological data sets where the number of grid boxes often outmatches the number of available time steps.

3 Results

3.1 Visualizing the drift in the input data

In Fig. 1, the appearance of the drift problem is illustrated on the basis of North Atlantic SSTs from the global MPI-ESM decadal prediction system, averaged over the domain 0°–60°W and 40°–60°N. Kröger et al. (2017) have shown that SSTs are particularly prone to the drift issue. SSTs also represent the lower oceanic boundary condition for the RCM and are supposed to contribute substantially to long-term climate predictability. For start years between 1960 and 2013, the time series denote annual means averaged over 15 ensemble members and, hence, refer to the entire data set provided by the Prototype decadal prediction system. For all start years, the drift emerges as a rather uniform and steady cooling tendency of about 2 °C over almost the entire hindcast period. It is evident that the drift is more than a short-term initial shock during the first years after initialization. Yet, the system tends towards an equilibrium state in the last year of each hindcast decade. Furthermore, the drift is largely independent of the initial state. There is a certain offset during the 1990s related to a shift towards warmer SSTs initialized in the North Atlantic, but the cooling amplitude is only slightly reduced. Given the homogeneity of the drift over various start years and initial conditions, the subsequent drift correction approach and dynamical downscaling is exemplified using one ensemble member of the hindcast period 2001–2010. This period is chosen because it is quite recent and covered by the various observational data considered in this study.

Fig. 1

Regional-mean time series of annual-mean SST in the North Atlantic (0°–60°W, 40°–60°N) simulated by the MPI-ESM decadal prediction system with annually varying start years from 1960 until 2013, each averaged over 15 ensemble members

In Fig. 2 (top), the climate drift in the central North Atlantic is visualized by the linear trend pattern of sea and land surface temperature over the European–Atlantic sector as simulated by the individual MPI-ESM hindcast during the 2001–2010 period. Except for some parts of the Arctic Ocean, this domain is characterized by substantial negative trends ranging between − 0.5 and − 2 °C per decade. The most striking feature, however, is an area in the western transition zone between the subpolar and subtropical gyres around 45°N where temperatures decrease by up to 5 °C over 10 years. This remarkable drift also prevails in the regional-mean time series, albeit with some superposed inter-annual variability. The cooling signal appears to propagate along the Canary current into the eastern subtropical North Atlantic and also affects surface air temperature (SAT) over the landmasses east of the mid-latitude and subtropical Atlantic. In contrast to the decadal hindcast simulated by the Prototype system, no such cooling tendency occurs in the HadISST gridded SST observations (Fig. 2, bottom panel) nor in the NOAA reanalysis (Fig. 2, second panel from bottom). In detail, both observational data sets exhibit some noticeable differences, but nowhere SST trends exceed 0.5 °C per decade and the respective time series do not show a linear trend at all. Thus, the artificial nature of the climate drift in the North Atlantic can be clearly delineated, although a part of the differences between simulated and observed SST changes during the 2001–2010 period may arise from the limited decadal predictability of North Atlantic SSTs (cf. Müller et al. 2012; Pohlmann et al. 2013).

Fig. 2

Linear trend patterns of surface air temperature (SAT) in °C per decade and de-seasonalized time series of monthly-mean sea surface temperature (SST) averaged over the region marked by the green box, before and after drift correction in MPI-ESM and as derived from reanalysis and observational data sets

3.2 Drift correction of input data

The multivariate EOF analysis that is used for drift correction is first applied to all input variables and levels, delivering 120 eigenvectors (see Sect. 2). The part of each eigenvector that represents the SST field is spatially correlated with the simulated SST trend pattern displayed in Fig. 2 (top left). In fact, the leading EOF correlates quite closely with the drift pattern, reaching a correlation coefficient of almost 0.8 (Fig. 3, top). The corresponding eigenvector is highly congruent with the drift pattern (Fig. 3, bottom left) and the PC time series exhibits hardly any inter-annual variations but a prominent cooling tendency (Fig. 3, bottom right). The shape of the PC time series is very close to the drift time series of the whole Prototype data set displayed in Fig. 1, reaching also some equilibrium state during the last year of the decade. Thus, it can be concluded that the drift in the Prototype decadal prediction system is captured by one single EOF that accounts for 7.7% of total variability of the multivariate input data set used for dynamical downscaling. This implies that when this EOF is removed the retained input data set still accounts for a major part of the original information of the model data, presumably even the multi-year to decadal changes (see below).

Fig. 3

Identification of the EOFs derived from all variables and levels that project best on the original SAT trend pattern from MPI-ESM (top), and eigenvector and annual-mean principal component of this EOF pattern (EOF1) for SAT (bottom). Note that the y-axis in the bottom right panel is inverted

Figure 4 demonstrates that the drift in the decadal hindcast leaves a mark in various atmospheric variables and levels as well. The six three-dimensional atmospheric variables are presented for a lower (925 hPa), middle (500 hPa) and upper (200 hPa) tropospheric level, while the top panels refer to the two-dimensional surface fields. The temporal evolution of these patterns is indicated by the PC time series in Fig. 3 (bottom right), describing a steady transition from negative to positive anomalies. The surface pressure field associated with the climate drift is reminiscent of the pattern of the North Atlantic Oscillation (NAO). During the 10-year simulation period a strengthening of the NAO occurs which is related to a warming tendency in the eastern branch of the subpolar gyre, advecting warm water into the region of extratropical cyclogenesis around Iceland (cf. Paeth et al. 2003). The bipolar pattern of snow amount shows rather weak magnitudes and is related to the surface pressure response, inducing less snow fall in areas with increasing pressure. The substantial cooling in the lower troposphere is contrasted by a slight warming in the higher troposphere. The horizontal wind components indicate a strengthening of the cyclonic (anticyclonic) circulation in the northern (subtropical) Atlantic, being consistent with the positive trend of the NAO. At higher levels, the zonal wind exhibits a stronger horizontal shear with increasing westerlies (easterlies) over central (northern) Europe. Specific humidity is characterized by a distinct reduction in most levels and regions, arising from weaker latent heat fluxes over cold sea and land surfaces. Liquid water content and cloud ice content are barely affected by the drift as it is represented in the leading EOF. Yet, there is a striking opposite anomaly of cloud liquid water content in the lower troposphere directly over the peak region of SST cooling in the central North Atlantic which can be explained by a decrease of the condensation level in this area. In summary, the patterns in Fig. 4 point to a wide spectrum of atmospheric responses to the climate drift in the Prototype decadal prediction system that need to be accounted for.

Fig. 4

Patterns of the leading EOF from Fig. 3 for a selection of atmospheric variables in different vertical levels, indicating how other processes in the atmosphere co-vary with the drift in the SAT field. SST/SAT, sea level pressure and snow amount as two-dimensional variables are shown in the first row, and underneath from top to bottom the three-dimensional variables atmospheric temperature, zonal wind, meridional wind, specific humidity, liquid water content, and cloud ice content in a lower, middle and upper tropospheric level (from left to right)

Figure 5 demonstrates how the elimination of the drift-related leading EOF affects the temporal evolution of SST in the peak region of cooling in the central North Atlantic. The monthly-mean time series give insight into the seasonal, inter-annual and decadal variations. The original time series without drift correction is marked by a clear tendency towards colder SST. It is exactly reproduced by a linear combination of all 120 EOFs, proving that the EOF decomposition basically retains the entire information of the high-dimensional input data set. When the leading EOF is removed and the linear combination is based on the remaining 119 EOFs, the drift disappears but other components of low-frequency SST variability are maintained, e.g. the year-to-year changes of the SST amplitude during the seasonal cycle.

Fig. 5

Time series of monthly-mean North Atlantic SSTs in Kelvin averaged over the major drift region (green box in Fig. 2) before and after drift correction and respective time series emanating from a linear combination of all EOFs over all variables and levels from MPI-ESM

In addition, Fig. 6 shows that the drift-corrected input data set still includes the major modes of slowly varying SST/SAT changes over the 2001–2010 period. Here, the EOF analysis is based only on surface temperature and not on all input variables, implying that the leading EOFs do not necessary represent the drift when the latter is not the main driver of SST/SAT variability in the model domain. In fact, the leading three EOFs exhibit multi-year fluctuations and a slight linear trend. They are identical with the leading three EOFs of SST/SAT in the uncorrected input data set (not shown). The drift pattern displayed in Fig. 2 is captured by the seventh EOF in the SST/SAT field before drift correction and does not show up after the drift correction approach has been applied. This implies that our approach is quite successful by identifying and removing the drift by means of one single EOF and by producing a data set that still accounts for the major components of low-frequency variability within a decade. This is crucial in order to retain the dominant time scales of multi-year to decadal climate predictability (cf. Garcia-Serrano and Doblas Reyes 2012).

Fig. 6

EOFs 1–3 after drift correction derived from the SAT/SST field in MPI-ESM, including eigenvectors (left) and principal component time series in °C (right)

Finally, the linear trend pattern of SST/SAT after drift correction is displayed in Fig. 2 (left panel in second row from top). It is obvious that most of the striking cooling tendency in the North Atlantic has been suppressed, although the peak area in the central North Atlantic can still be recognized by a slightly negative SST trend of almost 1 °C per decade. However, the corresponding regional mean time series reveals that this cooling mainly arises from a drop of temperature during the first four months after initialization—probably a peculiarity of this particular year. Note that the inter-annual variability of the SST time series is barely affected by the drift correction when comparing the time series in the first and second row from top of Fig. 2.

3.3 Effects on trend and performance of the RCM

The following results are derived from the RCM experiments. There are three simulations with different levels of drift correcting the input from MPI-ESM: without any correction, with full multivariate correction, and with correcting only the SST/SAT field (see Sect. 2). We refer only to atmospheric variables over the land masses that are most relevant to regional climate prediction, i.e. near-surface temperature at 2 m height, precipitation and sea level pressure (for weather-type statistics, storminess etc.). Figure 7 illustrates how the uncorrected drift in the central North Atlantic as produced by the Prototype global prediction system is transferred to linear 2 m temperature trends over Europe simulated by CCLM. Especially in western and central Europe, a statistically significant cooling by 1–2 °C over 10 years can be noticed. This pattern is not identical but very similar to the drift pattern shown in Fig. 2 (top left). Thus, the drift is more or less entirely passed from the global model to the RCM.

Fig. 7

Linear trend pattern of annual-mean near-surface temperature in K per decade over the period 2001–2010 as simulated by the RCM CCLM without drift-correcting the input data from MPI-ESM, white dots indicate trends significant at the 5% level. The red rectangles frame the regions used for averaging in the subsequent analyses

For the subsequent analysis, we define four western and central European regions that exhibit a significant cooling tendency, i.e. the Iberian Peninsula (IP), the British Isles (BI), France (FR), and Middle Europe (ME). They are chosen in accordance with the western European standard regions defined in the framework of the Coordinated Regional Climate Downscaling Experiment (http://www.euro-cordex.net). The effect of drift correction is assessed separately for each regional mean time series and different seasons (DJF = December–February etc.), including annual means (ANN). The top panel of Fig. 8 demonstrates that in the uncorrected CCLM experiment decreasing near-surface temperature prevails in all regions and seasons, particularly in the cold seasons and in the annual mean. The multivariate drift correction systematically reduces the negative trends, except for France in winter (Fig. 8, middle). The resulting linear temperature trend is near zero and in agreement with the observed trends from the NOAA reanalysis (see Fig. 2, second trend pattern from bottom). Applying the drift correction only to the surface temperature field from MPI-ESM barely has any implication for the resulting temperature trends simulated by the RCM (Fig. 8, bottom). This univariate drift correction tends to mitigate the cooling but the effect is minor.

Fig. 8

Linear trends of regional-mean time series of near-surface temperature in K per decade for the four European regions with significant cooling according to Fig. 7 and for annual and seasonal means. The top panel denotes total trends in the original CCLM experiment without drift correction, both bottom panels show changes in trends due to two methods of drift correction. Trends statistically significant at the 5% level are marked by black dots

So far, we could show that the multivariate drift correction is effective in reducing the presumably unrealistic cooling tendency over maritime European land masses in the RCM. However, this does not necessarily imply that the hindcast simulations are closer to observational data during the 2001–2010 period. Figure 9 (top) displays the temperature departures of the uncorrected CCLM experiment from the E-OBS data set, measured by the root mean-square error (RMSE, cf. Doblas-Reyes et al. 2013) based on annual- and seasonal-mean time series, respectively. When the input from the Prototype system is not drift corrected, CCLM systematically underestimates the observed temperatures, resulting in an RMSE of 1–3 °C, especially in summer and autumn. The multivariate drift correction tends to diminish this discrepancy by 25–50% (Fig. 9, middle), but still a noticeable cold bias remains that may represent the intrinsic bias of CCLM, independent of any drift problem. Hardly any effect exists when the drift correction is confined to the SST/SAT field (Fig. 9, bottom).

Fig. 9

Same as Fig. 8 but for the discrepancy between CCLM and E-OBS data, expressed as RMSE

The CCLM run that is based on uncorrected input data is also characterized by large differences between simulated and observed precipitation and sea level pressure (Fig. 10, top panels). The RMSE of precipitation peaks in winter over the Iberian Peninsula where it ranges in the order of 25% of the long-term climatology. In contrast, the annual mean RMSE of precipitation over Middle Europe and the British Isles is below 2%. The misrepresentation of mean sea level is in the order of 2–12 hPa with a maximum in winter over the British Isles. The drift correction effectuates a less coherent impact on the regional and seasonal RMSE in terms of precipitation and sea level pressure: a reduction clearly prevails, but the effect is minor compared with the original RMSE and in some seasons and regions the situation even deteriorates (Fig. 10, bottom panels). Thus, removing the drift in the North Atlantic in the input data set implies a more consistent and distinct improvement of near-surface temperature than of precipitation and sea level pressure in the RCM.

Fig. 10

Discrepancy between CCLM and E-OBS data, expressed as RMSE, for precipitation (left panels) and mean sea level pressure (right panels). The top panels denote the total RMSE of the original CCLM experiment without drift correction, the bottom panels show changes in RMSE due to drift correction of all input variables

4 Discussion and conclusions

In this paper, we tackle a new challenge of drift correction in decadal climate prediction, i.e. a multivariate approach that retains the co-variability between various atmospheric variables and levels and that still accounts for presumably realistic components of low-frequency climate variability within a decade. The approach is developed on the basis of the MiKlip global climate prediction system with full-field initialisation and its effect is assessed by means of dynamical downscaling of the global climate predictions over the European–Atlantic sector. It is explored to what extent the climate drift can be removed and how this affects the quality of regional climate decadal predictions. This goes beyond the scope of previous studies on drift correction of global climate models that are mainly based on individual output variables and simple methods of model output statistics and removal of ensemble mean drifts (e.g. ICPO 2011; Goddard et al. 2013; Magnusson et al. 2013; Choudhury et al. 2016).

The full-field initialization in the Prototype system induces a striking cooling pattern in the surface temperature field that is largely independent of the initial state and peaks over the central North Atlantic with up to 5 °C over 10 years. It arises from a mismatch between observed ocean flow, temperature and salinity prescribed in the initial state and the coupled model’s own climatology (Kröger et al. 2017). The drift is a typical problem of initialized global coupled models with full-field forcing as reported by several authors (e.g. Hazeleger et al. 2013; Smith et al. 2013b; Pattantyús-Ábrahám et al. 2016; Samson et al. 2016). It does not occur in equal measure in the other versions of the Miklip decadal climate prediction system that use anomaly initialization (Müller et al. 2012; Pohlmann et al. 2013; Marotzke et al. 2016).

The drift is indeed captured by one single EOF derived from all variables and atmospheric levels contained in the input data set for dynamical downscaling with the RCM CCLM. This is favored by the fact that the drift pattern has a rather artificial appearance that clearly differs from natural modes of low-frequency variability in the North Atlantic ocean, such as the meridional overturning circulation, the Atlantic multi-decadal oscillation and the subtropical and subpolar gyres (cf. Paeth et al. 2003; Knight et al. 2006; Kim et al. 2012; Matei et al. 2012b). In addition, the drift exhibits a signature in various tropospheric variables that can be physically explained in relation to anomalies in North Atlantic SSTs (see Paeth et al. 2003; Gastineau et al. 2013). This was also reported by Pattantyús-Ábrahám et al. (2016), comparing the output of the Prototype prediction system with radiosonde observations. Another encouraging result is that the drift-induced EOF accounts for less than 8% of total variance and that the remaining information in the input data set still comprises multi-year changes and noticeable decadal trends. These low-frequency components of climate variability constitute the basis of medium-range climate predictability and must not be eliminated by drift correction (Garcia-Serrano and Doblas Reyes 2012; van Oldenborgh et al. 2012).

The cooling of near-surface temperature in the uncorrected global climate prediction system is more or less entirely adopted by the considered RCM. A substantial and statistically significant temperature decrease of partly more than 2 °C per decade still prevails over western and central European land masses, to a larger extent in autumn and winter than during spring and summer. The comprehensive and physically consistent drift correction of all input variables for dynamical downscaling leads to an almost complete removal of the exorbitant cooling tendency in the regional climate predictions with CCLM and brings the model output closer to the observed trend. This holds for most regions and seasons, except for Northern Hemisphere winter. In contrast, the drift correction of the surface temperature field alone, as suggested by Narapusetty et al. (2014), has barely any impact on the 2 m temperature simulated by the RCM.

The RMSE between CCLM and E-OBS data in terms of near-surface temperature, precipitation and sea level pressure are mostly reduced by the drift correction, but not removed. Obviously, the drift is responsible only for a part of the total RMSE of the RCM. It is conceivable that the RMSE can be further reduced by a statistical bias reduction tailored to individual output variables from the RCM, as suggested by several other authors (e.g. Paeth 2011; Kharin et al. 2012; Goddard et al. 2013; Sansom et al. 2016).

We have also examined the phase relationship between the CCLM and E-OBS time series of near-surface temperature, precipitation and sea level pressure (not shown), although the individual hindcast experiment considered here does not allow for a proper assessment of predictability. In fact, correlation coefficients between simulated and observed regional-mean time series tend to increase in many regions and seasons due to drift removal, but there is still no statistically significant predictability given. The drift correction cannot produce predictability in the RCM where there is no predictability inherent in the global climate prediction system. Marotzke et al. (2016) have pointed to the specific problems of the Prototype system considered here in comparison to other versions (see also Matei et al. 2012a; Müller et al. 2012, 2016; Pohlmann et al. 2013; Kröger et al. 2017). Nonetheless, we have used the Prototype system with full-field forcing because it represents a paradigm for the drift correction issue.

There are three main conclusions to be drawn from this study: (1) EOF analysis applied to a large multivariate model data set represents an appropriate method to identify and remove drifts in decadal climate predictions, retaining the multi-collinearity between the climate variables. If the drift signature is striking and clearly different from realistic modes of climate variability, the remaining model data set still accounts for low-frequency variations that are potentially predictable over several years up to one decade ahead. (2) Dynamical downscaling alone does not improve the drift problem. (3) Yet, the drift correction of the input data set largely removes spurious trends in the RCM output and mostly brings it closer to observational data. This is only true when the drift correction pertains to all input variables and levels, and not just to the surface temperature field.

Note that our drift correction approach does not require observational data over the hindcast period and, hence, can also be transferred to forecasts for which no observational data is yet available. When the output of the global decadal prediction system is used for dynamical downscaling, it is mandatory to apply the EOF analysis to every single period and ensemble member, at the expense of additional computing time. This is the only option to retain a physically consistent multi-variate data set after drift correction.

Finally, the question arises whether a drift correction should generally be applied to all decadal climate predictions, whatever initialization is used (cf. Kim et al. 2012; Goddard et al. 2013; Hazeleger et al. 2013; Smith et al. 2013b; Hawkins et al. 2014). This, however, bears the risk of eliminating a part of the predictable climate signal, if the drift does not distinctly stand out from realistic processes of climate variability. To tackle this important issue, the next step will be to apply the drift correction approach also to the newest version of the MiKlip decadal climate prediction system with anomaly initialization.

Notes

Acknowledgements

We thank the Max-Planck Institute for Meteorology for providing the MPI-ESM decadal predictions and the EU-FP6 project ENSEMBLES and the ECA&D project for making the E-OBS 14.0 data set available. The NOAA-20C reanalysis was kindly provided by the National Oceanic and Atmospheric Administration (NOAA) and the Cooperative Institute for Research in Environmental Sciences (CIRES). The HadISST data set has been made available by the Met Office Hadley Centre. This work was carried out in the framework of the German MiKlip project and supported by the German Minister of Education and Research (BMBF) under Grants no. 01LP1129A-F and 01LP1519A.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Geography and GeologyUniversity of WürzburgWürzburgGermany
  2. 2.Deutscher Wetterdienst, Seewetteramt HamburgHamburgGermany
  3. 3.Max Planck Institute for MeteorologyHamburgGermany
  4. 4.Institute of Meteorology and Climate ResearchKarlsruhe Institute of TechnologyKarlsruheGermany

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