The spread amongst ENSEMBLES regional scenarios: regional climate models, driving general circulation models and interannual variability
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Abstract
Various combinations of thirteen regional climate models (RCM) and six general circulation models (GCM) were used in FP6-ENSEMBLES. The response to the SRES-A1B greenhouse gas concentration scenario over Europe, calculated as the difference between the 2021–2050 and the 1961–1990 means can be viewed as an expected value about which various uncertainties exist. Uncertainties are measured here by variance explained for temperature and precipitation changes over eight European sub-areas. Three sources of uncertainty can be evaluated from the ENSEMBLES database. Sampling uncertainty is due to the fact that the model climate is estimated as an average over a finite number of years (30) despite a non-negligible interannual variability. Regional model uncertainty is due to the fact that the RCMs use different techniques to discretize the equations and to represent sub-grid effects. Global model uncertainty is due to the fact that the RCMs have been driven by different GCMs. Two methods are presented to fill the many empty cells of the ENSEMBLES RCM × GCM matrix. The first one is based on the same approach as in FP5-PRUDENCE. The second one uses the concept of weather regimes to attempt to separate the contribution of the GCM and the RCM. The variance of the climate response is analyzed with respect to the contribution of the GCM and the RCM. The two filling methods agree that the main contributor to the spread is the choice of the GCM, except for summer precipitation where the choice of the RCM dominates the uncertainty. Of course the implication of the GCM to the spread varies with the region, being maximum in the South-western part of Europe, whereas the continental parts are more sensitive to the choice of the RCM. The third cause of spread is systematically the interannual variability. The total uncertainty about temperature is not large enough to mask the 2021–2050 response which shows a similar pattern to the one obtained for 2071–2100 in PRUDENCE. The uncertainty about precipitation prevents any quantitative assessment on the response at grid point level for the 2021–2050 period. One can however see, as in PRUDENCE, a positive response in winter (more rain in the scenario than in the reference) in northern Europe and a negative summer response in southern Europe.
Keywords
Ensemble Europe Climate change Regional climate model Weather regime Uncertainty1 Introduction
In Europe the expected response of climate to an increase in greenhouse gas concentration during the 21st century is not just the typical 2–3°C warming (IPCC 2007). Many surface variables are likely to be affected by global warming. For instance, there is an agreement amongst models that precipitation should increase in the North and decrease in the South. However, an agreement on the sign of the response does not imply that all models converge towards the same numerical value. Many impacts on human environment or activities depend on thresholds. Two different models having the same sign in the response of temperature and precipitation, but different magnitudes of change, can lead to very different impacts. The evaluation of uncertainty is fundamental for any application. The primary source in terms of causality is the future of human emissions. This is a socio-economic question, not evaluable by the climate modeling community. The natural climate variability is a statistical question which can be approached by observed past series (Zhang et al. 2007; Brown et al. 2008), as long as the scope is limited to the interannual variability of the near future. Numerical climate models introduce two kinds of uncertainty, one coming from the large-scale GCMs, the other coming from the downscaling RCMs (e.g. Lenderink et al. 2007; Giorgi 2008). Since the FP5-PRUDENCE project (Christensen et al. 2002) a large number of 50 km or higher resolution simulations are available for Europe. The FP6-ENSEMBLES project (Hewitt and Griggs 2004; van der Linden and Mitchell 2009) has led to an update of the PRUDENCE database with two major improvements: a higher spatial resolution and a larger number of RCMs and driving GCMs.
- 1.
the sampling uncertainty, related to the fact that the model climatology is issued from a limited number of years (30); it contributes model internal variability, which includes also longer time scales (see Sect. 5)
- 2.
the model uncertainty associated with the physics and dynamics features of the different regional climate models
- 3.
the uncertainty in the lateral boundary conditions (LBC), that is the GCM used to drive the RCM
- 4.
the uncertainty associated with the scenario (A2 or B2) of emissions of greenhouse gases (GHG)
- 1.
As we concentrate on the first half of the 21st century, we neglect the uncertainty due to the greenhouse gas and aerosol concentrations.
- 2.
As the modeling effort has been put on the number of RCM × GCM pairs, each pair has been run only once; we have thus approximated the model internal variability with a simple Monte-Carlo method based on limit central theorem (Gaussian distribution).
In Sect. 2, we describe the data available. In Sect. 3 we apply the D07 matrix completion method to ENSEMBLES results and make a first assessment of the partition of variance at the European level, with comparison with D07 results. Recent works on weather regimes (e.g. Sanchez-Gomez et al. 2008) suggest another method to complete the holes in the RCM × GCM matrix. This completion and the resulting new variance partition are presented in Sect. 4, with regional description for 8 sub-areas. The interannual variability as a new source of uncertainty is introduced in Sect. 5. In Sect. 6, we use the total variance of Sect. 5 to evaluate local confidence intervals over Europe. A summary of the new features brought by the ENSEMBLES project with respect to PRUDENCE is given in the conclusive Sect. 7.
2 The ENSEMBLES-RT2B database
One of the greatest successes of the PRUDENCE project is the publicly available database with a large variety of state-of-the-art RCM experiments. In D07, 10 RCMs out of this database were used (see D07 for details about the models):
CNRM, DMI, ETHZ, GKSS, HadC, ICTP, KNMI, MPI, SMHI, UCLM
These RCMs were driven by one or more of 3 GCMs:
CNRM, HadC, MPI
All were driven by HadC, some RCMs were also driven by the other two GCMs.
C4I (Jones et al. 2004) uses a version of the RCM developed at the Swedish meteorological service (RCA)
CNRM (Radu et al. 2008) uses the RCM of French meteorological service
DMI (Christensen et al. 1996) uses the RCM of Danish Meteorological Institute
ETHZ (Böhm et al. 2006) uses the RCM of the Federal Institute of Technology in Zürich (CH)
HadC (Collins et al. 2006) uses the RCM of the UK Met Office. In fact, three versions have been used (HC-lo, HC-med and HC-hi)
ICTP (Giorgi and Mearns 1999) uses the RCM of the International Center for Theoretical Physics in Trieste (Italy)
KNMI (an Van Meijgaard et al. 2008) uses the RCM of the Dutch meteorological service
METN (Haugen and Haakensatd 2006) uses the RCM of the Norwegian meteorological service
MPI (Jacob 2001) uses the RCM of the Max Planck Institute for Meteorology in Hamburg (Germany)
SMHI (Kjellström et al. 2005) uses the RCM of the Swedish Meteorological and Hydrological Institute
UCLM (Sanchez et al. 2004) uses the RCM of the University of Toledo (Spain)
Out of the 13 models, 3 use the same modelling system: HC-lo, HC-med and HC-hi. These models share the same dynamics and a very similar description of the sub-grid processes. We have kept them as separate RCMs, however, because they have been produced by arbitrary perturbations of several sensitive but empirical model parameters, which lead to very different responses to GHG concentration in their GCM version (Murphy et al. 2007). Other models share some parenthood: SMHI and C4I are based on RCA; The dynamics of DMI, KNMI, METN, SMHI and C4I come from the HIRLAM forecast model.
BCM (Furevik et al. 2004) is the GCM of the University of Bergen (Norway), the horizontal resolution is 300 km.
CNRM (Gibelin and Déqué 2003) uses the global version of CNRM RCM with variable resolution (300 km in the Pacific to 100 km at the lateral boundaries of the RCM).
HadC (Gordon et al. 2000) uses the global version of HadC RCM; 3 driving runs are available (HC-lo, HC-med and HC-hi). The resolution is 300 km.
MPI (Roeckner et al. 2003) uses the global version of MPI RCM. The resolution is 200 km.
The RCM × GCM matrix; label X indicates that the corresponding RCM × GCM pair was available in ENSEMBLES at the time of the study
BCM | CNRM | HC-lo | HC-med | HC-hi | MPI | |
---|---|---|---|---|---|---|
C4I | X | |||||
CNRM | X | |||||
DMI | X | X | X | |||
ETHZ | X | |||||
HC-lo | X | |||||
HC-med | X | |||||
HC-hi | X | |||||
ICTP | X | |||||
KNMI | X | |||||
METN | X | X | ||||
MPI | X | |||||
SMHI | X | X | X | |||
UCLM | X |
In the following we will concentrate on winter (DJF) and summer (JJA) averages of 2 m temperature and precipitation for two periods 1961–1990 (the same reference period as in PRUDENCE) and 2021–2050. The restriction to temperature and precipitation, as well as to two seasons, has been done to maintain a reasonable size for the study, whilst focussing on the most widely documented aspects of climate change. The methodology is of course suitable for wind, soil moisture, snow and other variables. The model response we analyze is the difference between the two 30-year means. We restrict this analysis to the model land grid points which fit inside one of the 8 sub-areas (aka Rockel boxes) described in figure 4 of Christensen and Christensen (2007) and already used in D07: British Isles (BI), Iberian Peninsula (IP), France (FR), Mid-Europe (ME), Scandinavia (SC), Alps (AL), Mediterranean (MD) and East-Europe (EA).
3 Analysis of variance: first method of matrix completion
Standard deviation calculated with available RCM × GCM pairs for temperature (°C) and precipitation (mm/day) from inter-RCM, inter-GCM and all model variances
DJF | JJA | ||||||
---|---|---|---|---|---|---|---|
RCM | GCM | Total | RCM | GCM | Total | ||
Grid points | Temperature | 0.28 | 0.60 | 0.59 | 0.41 | 0.64 | 0.74 |
Precipitation | 0.18 | 0.34 | 0.27 | 0.19 | 0.22 | 0.23 | |
Sub-areas | Temperature | 0.19 | 0.47 | 0.51 | 0.32 | 0.68 | 0.69 |
Precipitation | 0.08 | 0.18 | 0.16 | 0.12 | 0.15 | 0.14 |
This basic approach does not allow to tell us how the total variance of our 18 model responses is partitioned between the inter-GCM and the inter-RCM variances, because the two contributions are not independent and calculated with different sub-samples of the ENSEMBLES database. To achieve this partition, we must use the method known as analysis of variance. In PRUDENCE, we had 10 RCMs, 3 GCMs, 2 emissions scenarios (A2 and B2) and 3 ensemble members (for the few RCMs driven by multiple GCMs members). The total variance has been decomposed as a sum of 15 positive terms representing the contribution of the 4 sources of variability (in this study variability, spread and uncertainty have the same meaning), taking into account the interactions between the 4 sources. See D07 for the full formula.
As we have at least one case for each RCM and for each GCM, X_{i·} and X_{·j} can always be estimated from Table 1. Equation 5 can be easily explained as follows: to calculate the response of RCM-A driven by GCM-B, we calculate first the mean response for all RCM × GCM. Then we add the mean anomaly of the GCM-B-driven pairs with respect to this mean. Finally we add the mean anomaly of the RCM-A-driving pairs with respect to the same mean. This is equivalent to assuming that the contribution of the GCM and of the RCM are additive.
Mean and standard deviation over Europe of the model response calculated with the original (O) and completed with PRUDENCE method (P) or weather regime method (R) RCM × GCM matrix for temperature (°C) and precipitation (mm/day) in DJF and JJA. PRUDENCE corresponds to A2 scenario and 2071–2100 time-slice
PRUDENCE | ENSEMBLES | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
Mean (O) | SD (O) | Mean (P) | SD (P) | Mean (O) | SD (O) | Mean (P) | SD (P) | Mean (R) | SD (R) | |
TDJF | 3.57 | 0.66 | 3.54 | 0.83 | 1.72 | 0.51 | 1.89 | 0.58 | 1.87 | 0.44 |
TJJA | 4.49 | 0.96 | 4.47 | 1.21 | 1.63 | 0.69 | 1.87 | 0.75 | 1.82 | 0.57 |
PDJF | 0.35 | 0.18 | 0.28 | 0.22 | 0.11 | 0.16 | 0.10 | 0.19 | 0.11 | 0.16 |
PJJA | −0.42 | 0.23 | −0.37 | 0.28 | −0.05 | 0.14 | −0.05 | 0.15 | −0.05 | 0.10 |
The comparison of the mean versus the standard deviation at European scale in Table 2 also shows that the signal to noise ratio is better (i.e., higher) in PRUDENCE than in ENSEMBLES for temperature. In the case of precipitation, there are compensations between sub-areas with an increase and sub-areas with a decrease. See Sects. 4 and 6 for geographical details of the response. The choice at the beginning of PRUDENCE to target the end of the 21st century is clearly justified here, at least for temperature, in terms of signal-to-noise ratio. In terms of adaptation to climate change, the choice of the ENSEMBLES period is, however, better for policy and decision making.
4 Weather regimes: second method of matrix completion
The D07 method for matrix completion is simple, but relies upon the argument that the GCM and the RCM contributions to the climate change response are independent. If we want to add more physics in the completion method, we can consider that the role of the GCM is to provide large-scale lateral advection of momentum, heat and moisture to the RCM. A concept which synthesizes this effect is the concept of weather regimes (Vautard 1990). Clustering the daily 500 hPa height values over the North Atlantic-Europe domain leads to large-scale patterns that can be linked to weather in Europe (Robertson and Ghil 1999; Yiou and Nogaj 2004). The most commonly studied are the positive and negative phases of the North Atlantic Oscillation (NAO; Hurrel et al. 2001). In winter, clustering in 4 regimes is a traditional approach since Michelangeli et al. (1995). We have applied the same k-means algorithm to ERA40 500 hPa daily data, filtered by the first 15 Empirical Orthogonal Functions (EOF) on the 90°W–30°E 20°N–80°N domain for the 4 seasons. For each season (we restrict discussion of results here to DJF and JJA for the sake of brevity), four centroids are produced, which are maps of 500 hPa height anomalies across the domain. For each RCM, we interpolate these centroids onto their native model grid. Each day is associated to regime N (N = 1, 2, 3 or 4) if the daily 500 hPa height anomaly with respect to the 1961–1990 RCM climatology is closer to centroid N than to any other centroids. This method is different from Sanchez-Gomez et al. (2008) who applied the k-means algorithm to ERA40 data on a domain intersecting all RCM domains, and interpolated all RCMs on this domain. With our method, the winter regimes are very close to the Michelangeli et al. (1995) centroids. They are more appropriate to represent the LBC forcing, and less appropriate to represent the large-scale dynamics of the individual RCMs, in particular those RCMs with westwards extension too far from Greenland.
Root mean square differences between an original and a reconstructed response when possible
Temperature (°C) | Precipitation (mm/day) | |
---|---|---|
E1 | 0.04 (E1r = 0.11) | 0.02 (E1r = 0.06) |
E2 | 0.82 (E2r = 0.87) | 0.20 (E2r = 0.20) |
E3 | 0.42 (E3r = 0.86) | 0.16 (E3r = 0.21) |
E4 | 0.37 (E4r = 0.86) | 0.13 (E4r = 0.21) |
Symmetrically, we have tested the second hypothesis by keeping the actual weather regime frequency and taking a weather regime composite from another pair which involves the same RCM. Here we can use only 8 pairs out of 18 because only DMI, METN and SMHI RCMs have been driven by more than one GCM. The quadratic error is E2 and its reference is E2r. E2r is calculated as E2, with the same weather regime frequencies but with a weather regime composite coming from another RCM. Table 4 shows that E2 is large and close to E2r. This indicates that the assumption that the composite does not depend on the driving GCM is wrong. This implies that the precipitation response, for example, of an RCM is determined by other constraints (such as SST, continental-scale warming and moistening) coming from the driving GCM, which are not reflected in the 4 regimes.
It is interesting at this stage to evaluate the validity of the reconstructions. A simple algorithm consists of comparing the original model response with a response reconstructed without the corresponding RCM × GCM pair. Unfortunately, the reconstruction error can only be calculated with 8 pairs (DMI, METN and SMHI RCMs). The mean square error is E3 for the PRUDENCE method (Eq. 5) and E4 for the weather regime method (Eqs. 7 + 8). As in the beginning of Sect. 4, a reference error (E3r) is obtained by comparing an actual response with the response from another RCM × GCM pair. This reference error is also valid for E4 (E4r = E3r). E3r is very close to E2r because we use the same pairs of models to compute the differences. The only difference is that in E2r we use the same weather regime frequency in the two responses to be subtracted. Table 4 shows that the second reconstruction method is somewhat better, and that both methods are more successful in reconstructing temperature than precipitation responses. However, since this verification is based on three RCMs only, we cannot draw a definite conclusion about which method actually performs better. As the weather regime method is more physically based, we use only this method in the rest of the paper.
The rightmost rectangles in Fig. 1 show the percentages of variance due to RCM and GCM in ENSEMBLES data completed with the weather regime method (ENR). One can first remark that the RG term (dark gray) is still small, which further justifies the PRUDENCE assumption to set this term to zero when completing the matrix. The second remark is that the weather regime method enhances the role of the GCM in the inter-model spread. Indeed, the GCM is involved both in the frequency of the weather regime and in the composite. This result is further confirmed because it is in agreement with the respective variances of Table 2, where no data completion is done, and the reconstruction error E4 (Table 4) is less than the error E3 with the PRUDENCE method. If we had used composites depending only on the RCMs (as in Eq. 7), the percentage due to the RCM would have been much larger. This is due to the fact that the climate change response is generally more a change in the composites than a change in the weather regime frequencies (Driouech et al. 2010). However, we know from Table 4 that this approach is not supported by the ENSEMBLES data. Note that in the case of summer precipitation, the GCM part remains less than the RCM part.
The last two columns of Table 3 give the mean and standard deviation calculated for each sub-area then averaged over Europe with the matrix completed by the weather regime method (R). The mean response is similar to the result with the PRUDENCE method (P) but the inter-model standard deviation is below the value with the existing pairs (O) (except in the case of winter precipitation, when they are identical), contrary to the PRUDENCE completion method which enhances the variability.
RCM × GCM response for JJA temperature (°C) over Europe
BCM | CNRM | HC-lo | HC-med | HC-hi | MPI | |
---|---|---|---|---|---|---|
C4I | 1.46 | 1.87 | 2.03 | 3.04 | 2.14 | 1.67 |
CNRM | 1.23 | 1.77 | 1.83 | 2.74 | 1.98 | 1.45 |
DMI | 0.63 | 1.42 | 1.43 | 2.24 | 1.60 | 0.86 |
ETHZ | 1.49 | 1.93 | 2.09 | 2.27 | 2.26 | 1.71 |
HC-lo | 1.48 | 1.92 | 2.19 | 3.10 | 2.25 | 1.68 |
HC-med | 1.77 | 2.20 | 2.35 | 2.80 | 2.53 | 1.98 |
HC-hi | 1.65 | 2.06 | 2.22 | 3.30 | 2.49 | 1.85 |
ICTP | 0.94 | 1.34 | 1.50 | 2.33 | 1.69 | 1.13 |
KNMI | 1.07 | 1.48 | 1.64 | 2.52 | 1.82 | 1.37 |
METN | 0.79 | 1.51 | 1.67 | 2.07 | 1.85 | 1.30 |
MPI | 1.04 | 1.44 | 1.60 | 2.47 | 1.78 | 1.28 |
SMHI | 0.79 | 1.40 | 1.62 | 2.41 | 1.75 | 1.25 |
UCLM | 1.62 | 2.04 | 2.18 | 2.46 | 2.36 | 1.83 |
Interannual correlation between summer temperature and precipitation over the 8 sub-areas and Europe average (EU) for the 13 RCMs
BI | IP | FR | ME | SC | AL | MD | EA | EU | |
---|---|---|---|---|---|---|---|---|---|
C4I | −0.16 | −0.16 | −0.50 | −0.33 | −0.41 | −0.53 | −0.72 | −0.48 | −0.43 |
CNRM | −0.47 | −0.70 | −0.60 | −0.79 | −0.26 | −0.61 | −0.57 | −0.45 | −0.54 |
DMI | −0.31 | −0.63 | −0.47 | −0.71 | −0.05 | −0.83 | −0.67 | −0.69 | −0.55 |
ETHZ | −0.20 | −0.76 | −0.65 | −0.58 | −0.51 | −0.68 | −0.82 | −0.82 | −0.67 |
HC-lo | −0.75 | −0.60 | −0.79 | −0.82 | −0.82 | −0.88 | −0.86 | −0.85 | −0.80 |
HC-med | −0.25 | −0.57 | −0.82 | −0.73 | 0.02 | −0.81 | −0.87 | −0.87 | −0.62 |
HC-hi | −0.46 | −0.52 | −0.86 | −0.79 | −0.39 | −0.88 | −0.80 | −0.82 | −0.69 |
ICTP | −0.51 | −0.21 | −0.41 | −0.60 | −0.22 | −0.45 | −0.76 | −0.42 | −0.45 |
KNMI | −0.59 | −0.61 | −0.52 | −0.58 | −0.18 | −0.82 | −0.88 | −0.68 | −0.61 |
METN | −0.28 | −0.50 | −0.74 | −0.57 | −0.31 | −0.78 | −0.85 | −0.73 | −0.61 |
MPI | −0.56 | −0.30 | −0.46 | −0.65 | −0.20 | −0.67 | −0.86 | −0.57 | −0.54 |
SMHI | −0.26 | −0.47 | −0.31 | −0.40 | −0.23 | −0.58 | −0.51 | −0.39 | −0.40 |
UCLM | 0.04 | −0.66 | −0.61 | −0.40 | −0.52 | −0.48 | −0.69 | −0.44 | −0.49 |
5 Interannual variability
Here we have a single member per RCM × GCM pair, but we can use the interannual variability of each single simulation as in Ferro (2004) and generate artificial ensemble members with the following simple hypothesis. The 30 year average at a single grid point, or for a sub-domain average, can be considered as the average of 30 independent variables for which the mean and variance can be easily calculated. The limit central theorem tells us that this average follows approximately a Gaussian distribution with the same mean, and a variance divided by 30. We thus generated n = 10 members by a simple Monte-Carlo procedure. If n is too small as in D07 (n = 3), the interannual variability in Eq. 9 is underestimated, because in the algebraic identity there is a division by n instead of (n − 1) which would correspond to the unbiased estimate of the variance. On the other hand, if we use unbiased estimates of the variance in Eq. 9 as we did for Table 2, the equality assumption is not satisfied. Given the number of GCMs and RCMs used here, a number n = 10 is a good compromise. Using larger values for n does not change the results dramatically.
The ENSEMBLES project offers to us a possibility to verify this Monte-Carlo method. Indeed, in the project database, we can find three simulations of the KNMI model at 50 km resolution driven by three different simulations of the MPI GCM. We have calculated the sampling variance in each sub-area by two methods: the direct one based on the 3 available ensemble members, and the indirect one using interannual variability and Monte-Carlo simulation of 10 members. For winter temperature, the average over Europe of the standard deviations is 0.46 K with the 3-member sample and 0.36 K with estimates based on the interannual variability. This indicates that our method underestimates the variability. This can be explained by the insufficient sampling of inter-decadal variability with only 30 consecutive years. However, this feature is not observed for other variables or seasons. For summer temperature, we get respectively 0.22 and 0.23 K, for winter precipitation 0.15 and 0.16 mm/day, for summer precipitation 0.11 and 0.10 mm/day. We will therefore use this method in the following to add artificial ensemble members, keeping in mind that the internal variability may be underestimated by about 30% for winter temperature. However, as we will see in the following, and in agreement with D07 results, this internal variability is one order of magnitude below the other two sources of variability, which makes our approximation acceptable.
To estimate the interannual variance, we have again the problem of missing RCM × GCM pairs. The variance is not the combination of variance per weather regime multiplied by the regime frequency as in Eq. 6. It is possible, however, to derive a formula with a sum of terms involving pairs of regimes. But the decomposition is a combination of large positive and negative terms (covariances between the regimes), and the attempts to reconstruct the variances as we did for the means led to negative variances in several cases because our samples are too short. So we used, for the interannual variances a simple interpolation as in Eq. 8.
Multi-model mean and standard deviation (°C or mm/day) over Europe, percentage of variance explained by the RCM (R), GCM (G) and interannual variability (M), including the multifactor terms RG, RM, GM and RGM; temperature and precipitation for DJF and JJA
Mean | SD | R | G | M | RG | RM | GM | RGM | |
---|---|---|---|---|---|---|---|---|---|
TDJF | 1.91 | 0.56 | 21.1 | 34.0 | 0.5 | 8.8 | 7.2 | 2.1 | 26.4 |
TJJA | 1.85 | 0.64 | 26.9 | 46.4 | 0.2 | 6.2 | 4.0 | 1.1 | 15.2 |
PDJF | 0.12 | 0.21 | 10.9 | 23.9 | 0.8 | 7.3 | 11.3 | 3.3 | 42.5 |
PJJA | −0.04 | 0.16 | 20.8 | 18.3 | 0.6 | 9.2 | 10.5 | 2.8 | 37.8 |
The uncertainty due to natural climate variability can be evaluated by V(M) = M+RM + GM + RGM which corresponds to the mean interannual spread of a given model. For DJF temperature V(M) is 36% of the total variance. In summer, it is only 21%. For DJF precipitation, the percentage is 58%, but this is to be compared with 72% for V(R) and 77% for V(G). In summer V(M) is 52% of the total precipitation variance. These percentages illustrate the well known feature that running several GCMs and RCMs produces a significantly larger spread in the response than running an ensemble of the same size with a single model (without perturbing the parameters as in HC-lo, HC-med and HC-hi), even for a moderate climate change like in the first half of the 21st century.
6 Spatial distribution
- 1.
the response to climate change is one of the 18 results of the RCM × GCM matrix
- 2.
the RCMs have a probability proportional to the weight they obtain in a series of tests based on climate simulations driven by ERA40 (Christensen et al. 2010)
- 3.
the GCMs have a probability proportional to their skill in simulating weather regime frequencies over North Atlantic-Europe
- 4.
each RCM × GCM result has a probability density function (pdf) based on the limit central theorem (Gaussian law, variance of the 30-year means divided by 30)
Hypothesis 1, which is very restrictive, can be attenuated by the use of a Gaussian kernel filter designed to make a smooth transition between the maxima of the individual model pdfs.
Here we do not consider the probability of climate response (e.g. temperature change in DJF near Paris between 1961–1990 and 2021–2050) of a model drawn at random amongst the cells of the RCM × GCM matrix as is done in Déqué and Somot (2010), but rather the probability of the average of the full matrix, as is done in D07. The mean and variance we have calculated before (e.g. Table 7) can provide a confidence interval for a new RCM × GCM drawn at random from a population with the statistical properties of the ENSEMBLES models. If we take the average of n independent models, the variance is divided by n. Here the 13 × 6 responses in the matrix are not independent, because the reconstructed terms are a combination of the actual responses and additional information (the weather regime frequencies). Taking n = 18, the number of actual runs, gives a reasonable approximation for the variance of the average. Even though the pdf of a single model is not Gaussian in particular for temperature response which is skewed (see Déqué and Somot 2010), the pdf of the average can be considered as Gaussian (limit central theorem) and a confidence interval is easy to obtain.
7 Conclusion
The most important conclusion of D07 was that for the A2 emissions scenario and 2071–2100 time slice in general the largest source of uncertainty came from the GCM. For certain sub-areas or seasons, the RCM played the major role, however. This conclusion has led to the design of the ENSEMBLES regional climate modeling study: instead of using only one GCM with all the RCMs, we have used many GCMs, distributing the RCMs amongst the driving GCMs. The result we obtain here is that for the A1B emissions scenario and 2021–2050 time slice, we confirm the larger role played by the RCMs in summer precipitation. Two different methods for filling the empty cells of the RCM × GCM matrix yield the same conclusion for this field. The first method assumes that the warming due to the GCM and RCM are additive. It produces a larger inter-model variability and shows that for the other 3 fields analysed (DJF and JJA temperature, DJF precipitation) the GCM and RCM have a similar contribution to the spread. The second method takes into account the large-scale simulation of atmospheric circulation above Europe (weather regimes) and interpolates the RCM and GCM contributions (half sum of the two). It reduces the inter-model variability and shows that, as in PRUDENCE, the GCM contributes more to the spread. When PRUDENCE and ENSEMBLES are compared with the same filling method, the contribution of the RCM is systematically enhanced. The design of a large multimodel experiment is therefore very important for analysis of the modeling uncertainties. The natural variability, which should be more important than in PRUDENCE because the signal-to-noise ratio is weaker, is still in third place.
The large spread amongst the models should not prevent us from presenting results to the impacts community as far as seasonal mean temperature is concerned. This spread provides justification for presenting them in probabilistic terms. We get spatial patterns similar to those of PRUDENCE, with an amplitude of the response coarsely divided by 2 in winter and by 3 in summer with respect to that experiment (which was for a higher emissions scenario and further into the future). In the latter season, the maximum warming is located in south-eastern Europe (compared with south-western Europe in PRUDENCE). This pattern modification between mid- and end-century in summer might be explained by the fact that the positive feedback by soil drying out with warming is not fully in place during the first half of the century. Indeed, the precipitation response is only weakly significant. Only its sign is statistically robust, with a precipitation increase in the North and a decrease in the South.
A secondary finding of this study is that two RCMs driven by the same GCM experience similar changes in weather regime frequency, as a result of global warming. However this frequency change is not sufficient to explain the temperature and precipitation changes. The changes in the conditional averages of these fields for a given weather regime depend on the RCM as well as on the driving GCM. This makes the reconstruction of the missing cells in the RCM × GCM matrix less straightforward than expected.
All the results given here depend on the ability to fill the missing values in the matrix. As we have only three RCMs driven by more than one GCM, estimating the error by removing one RCM × GCM pair and trying to reconstruct it, as was done in D07, only gives a coarse estimate of the skill. Nonetheless, such an estimation favors the second method. The results of this multi-model experiment, including the empirically reconstructed simulations, provide guidance for future model ensemble studies and the provision of better information on regional climate change responses in probabilistic terms.
Notes
Acknowledgments
This work was supported by the European Commission Programme FP6 under contract GOCE-CT-2006-037005 (ENSEMBLES). This analysis has been made possible thanks to all modeling contributors to ENSEMBLES-RT2B (and RT2A for driving GCM runs). They cannot be all co-authors, but their work is strongly acknowledged here (see http://ensemblesrt3.dmi.dk/).
Open Access
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