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  • Wilks, D. S., 1995: Statistical Methods in the Atmospheric Sciences: An Introduction. Academic Press, 467 pp.

  • View in gallery

    Map showing multimodel ESD results for 1119 locations across the world, for which the ESD analysis has been applied to more than 45 different SRES A1B GCM runs from CMIP3 (for most cases, the ESD was applied to 50 runs). The color code is used to grade the quality of the ESD results based on the R2 statistics from the stepwise multiple regression, and one estimate was derived for each month, GCM, and century, resulting in typically ∼1200 values for each site. Maps like these can also be used to provide a diagnostics of stations with suspect data quality.

  • View in gallery

    The most essential features of the multimodel ESD results can be captured by the 5th-order polynomials that provide approximations of the ensemble mean, q05 and q95. These are shown here for Oslo, Norway, as the shaded region and thick central curve. The multimodel ensemble included 47 ensemble members, excluding 1e GCM [Bjerknes Centre for Climate Research (BCCR)]. The observations are shown as black symbols for comparison.

  • View in gallery

    Multimodel ESD results for Oslo projected for year 2040–60 presented as seasonal Gaussian distributions. The mean and standard deviations were estimated from the regression coefficients ci describing the 5th-order polynomials for the ensemble mean and q95.

  • View in gallery

    A worst-case example for which the observations are highly suspect. The ESD results shown are for Mongu, Zambia (WMO station code 67633), presented as a shaded region and thick central curve. The observations are shown as black symbols for comparison. The ESD is not strongly affected by the strong negative trend in the observations because it uses detrended data for calibration.

  • View in gallery

    Details showing how the R2 scores for Mongu, Zambia (red color code in Fig. 1), vary with calendar month. The R2 scores are plotted for both centuries and all GCMs, but the values are not very sensitive to the choice of GCM.

  • View in gallery

    The ESD diagnostics for Mongu, Zambia, and the HadGEM1 GCM: (a) projected 2000–2100 linear trend (yellow) and R2 (blue) as a function of season; (b) detrended observations and T(2m) projection for a HadGEM1 SRES A1B run; (c) As in (a), but with the year is repeated twice. The regression residuals for the calibration period where different lines represent different calendar months; (d) The large-scale February T(2m) pattern in ERA-40 associated with variations in the adjusted GHCN data from Mongu, Zambia. The location of Mongu is marked with a point symbol in (d).

  • View in gallery

    A comparison between local T(2m) series for Mongu, Zambia, and compared with interpolated values from ERA-40 and NCEP reanalyses.

  • View in gallery

    A comparison between c1 (linear term in the polynomial trend fit) estimated through the geographical regression model. The values have been arbitrarily scaled to fit the plot, as the different geographical parameters have different units. The vertical lines mark the error bars (one standard error).

  • View in gallery

    Maps showing (a) the gridded 95th percentile for the downscaled JJA mean T(2m) in Europe for year 2100 and (b) changes in the 95th percentile for the downscaled JJA mean T(2m) in Europe over 2000–2100.

  • View in gallery

    Maps showing (a) gridded probability estimated for below-freezing downscaled DJF mean T(2m) for same year and (b) changes in the probability estimated for below-freezing downscaled DJF mean T(2m) over 2000–2100.

  • View in gallery

    Maps presenting (a) the gridded 95th percentile for the downscaled JJA mean T(2m) in Africa for year 2100 and (b) the probability that the downscaled JJA mean T(2m) in Africa exceeds 35°C by 2100.

  • View in gallery

    Maps showing (a) 2000–2100 changes in the gridded ensemble mean for the DJF mean T(2m) in northwestern Russia for year and (0.1°C) and (b) the gridded probability estimated for downscaled DJF mean T(2m) < −10°C by 2100.

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A New Global Set of Downscaled Temperature Scenarios

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  • 1 Climate Department, Norwegian Meteorological Institute, Oslo, Norway
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Abstract

A new set of empirical–statistical downscaled seasonal mean temperature scenarios is presented for locations spread across all continents. These results are based on the Coupled Model Intercomparison Project phase 3 (CMIP3) simulations, the Special Report on Emissions Scenarios (SRES) A1B story line, and arguably represent the largest downscaled multimodel ensemble to date in terms of worldwide distribution, length of time interval, and the number of global climate model simulations. The ensemble size of ∼50 members enables a crude uncertainty analysis for simulated future local temperature, and maps have been constructed for Europe, Africa, and the northwestern part of Russia and Scandinavia of the ensemble mean and 95th percentile for seasonal mean temperatures projected for 2100, as well as simulated probabilities for low or high temperatures. The results are stored as matrices of coefficients describing best-fit fifth-order polynomials, used to approximate the long-term trends in the temperature. These results suggest that the 95th percentile of the summer temperature is expected to increase 3°–5°C by 2100 over most of Europe, and that there will be reduced probabilities of winter temperature lower than 0°C for all European locations, with the greatest reduction of ∼60% in areas where the winter temperature presently is around freezing point. A similar analysis for Africa suggests that the June–August mean temperatures may exceed 35°C in isolated regions by 2100. For the northwestern part of Russia and Scandinavia, the analysis yields a 4.5°–7.5°C increase for the ensemble mean December–February temperature, with the most pronounced warming in the northeast, north, and over Finnmark County in Norway.

Corresponding author address: R. E. Benestad, Climate Department, Norwegian Meteorological Institute, P.O. Box 43 Blindern, 0313 Oslo, Norway. E-mail: rasmus.benestad@met.no

Abstract

A new set of empirical–statistical downscaled seasonal mean temperature scenarios is presented for locations spread across all continents. These results are based on the Coupled Model Intercomparison Project phase 3 (CMIP3) simulations, the Special Report on Emissions Scenarios (SRES) A1B story line, and arguably represent the largest downscaled multimodel ensemble to date in terms of worldwide distribution, length of time interval, and the number of global climate model simulations. The ensemble size of ∼50 members enables a crude uncertainty analysis for simulated future local temperature, and maps have been constructed for Europe, Africa, and the northwestern part of Russia and Scandinavia of the ensemble mean and 95th percentile for seasonal mean temperatures projected for 2100, as well as simulated probabilities for low or high temperatures. The results are stored as matrices of coefficients describing best-fit fifth-order polynomials, used to approximate the long-term trends in the temperature. These results suggest that the 95th percentile of the summer temperature is expected to increase 3°–5°C by 2100 over most of Europe, and that there will be reduced probabilities of winter temperature lower than 0°C for all European locations, with the greatest reduction of ∼60% in areas where the winter temperature presently is around freezing point. A similar analysis for Africa suggests that the June–August mean temperatures may exceed 35°C in isolated regions by 2100. For the northwestern part of Russia and Scandinavia, the analysis yields a 4.5°–7.5°C increase for the ensemble mean December–February temperature, with the most pronounced warming in the northeast, north, and over Finnmark County in Norway.

Corresponding author address: R. E. Benestad, Climate Department, Norwegian Meteorological Institute, P.O. Box 43 Blindern, 0313 Oslo, Norway. E-mail: rasmus.benestad@met.no

1. Introduction

In a high-level declaration from the World Climate Conference-3 (WCC-3; 2009), the heads of state and government, ministers and heads of delegation decided to establish a Global Framework for Climate Services to strengthen production, availability, delivery, and application of science-based climate prediction and services.

A great deal of climate information can already be found in the Fourth Assessment Report (AR4) of the Intergovernmental Panel on Climate Change (IPCC), which provides an overview of the status of the climate research of 2006 and an assessment of the most advanced general circulation model (GCM) simulations for the future (Christensen et al. 2007). The IPCC AR4 also provides projected climate statistics for different parts of the world, based on a multimodel ensemble commonly referred to as the Coupled Model Intercomparison Project phase 3 (CMIP3) (Meehl et al. 2007) with 23 different GCMs. These projections are given with estimated uncertainties associated with the differences between the GCM results, but they do no account for model biases nor reflect the local scales necessary for studies on real impacts and adaptation.

Useful and reliable climate services must also account for the degree of uncertainty involved in making local scenarios for the future (Goddard et al. 2009). A large source of uncertainty regarding climate information stems from the GCMs used to simulate the global climate, as these tend to have systematic errors and only provide a crude description of processes and phenomena with large spatial scales. GCMs have nevertheless demonstrated skill in reproducing key elements of the global circulation and climate at the large scale, but their coarse resolution restricts the degrees of realism with which they can represent local or regional detail. Different GCMs may have different biases and systematic errors, and as long as these errors are independent and of similar magnitude, they are assumed to give a sample of the data space that spans the true value when climate information is derived from statistics based on many different GCMs. It is therefore important to include as many independent models as possible that are equally realistic. Furthermore, the use of arbitrary initial conditions in the GCM simulations may have an effect on the description of local internal variations on interannual to multidecadal time scales (Hawkins and Sutton 2009). It is also acknowledged that GCMs are unable to provide accurate and detailed description of the local climate (Easterling 1999; Wilby et al. 1999), and it is therefore common to downscale the information on the large spatial scales to local scales. Hence, the WCC-3 declaration implies a downscaling of climate information and an assessment of prediction skill and uncertainties.

Downscaling is often carried out through the means of a nested regional climate model (RCM), describing the atmospheric and surface state in a limited region with a higher spatial resolution than the GCM, or through statistical analysis [empirical–statistical downscaling (ESD)] (Wilby and Wigley 1997; Wilby et al. 1999; Fowler et al. 2007; Schmidli et al. 2007; Timbal et al. 2008; Benestad et al. 2008). The basic assumption for ESD is that the relationship established between the large and local scales is strong and holds for the future, that the large-scale predictor carries the relevant climate change signal, and that the GCMs are able to skillfully reproduce the large-scale pattern used as predictor. ESD can involve a wide range of various methods, but good understanding of statistics and local knowledge is needed for successful implementation. Furthermore, the interpretation of the results requires that the statistical models reflect real physical processes.

ESD results can often represent the end product of an advanced analysis that incorporates a quality assessment of global climate models, both with regard to their skill in reproducing observed spatial modes and as the temperature evolves over the twentieth century.

Running RCMs is often computationally demanding, and such efforts tend to be limited to a small number of GCMs, regions, and time slices—for example, in research projects such as the Prediction of Regional Scenarios and Uncertainties for Defining European Climate Change Risks and Effects (PRUDENCE), Climate Change and its impacts (ENSEMBLES), North American Regional Climate Change Assessment Program (NARCCAP), and Coordinated Regional Climate Downscaling Experiment (CORDEX) (Déqué et al. 2007; Mearns et al. 2009; van der Linden and Mitchell 2009). Various RCMs tend to produce different results when driven with the same GCM (Giorgi et al. 2008), but it is also true that there is a multitude of statistical models used in ESD that also gives different results. In fact, it is relatively easy to construct a poor statistical model for downscaling, and hence ESD has to be based on careful considerations about the downscaling problem. Thus, the downscaling demonstrates an additional level of uncertainty associated with regionalization, not readily seen directly in the GCM results.

In contrast to RCMs, ESD is relatively computationally cheap, and the low computational costs allow ESD to be carried out for long time series as well as many GCM simulations. The results presented here illustrate the value of ESD in such situations. Despite a number of studies with several different RCMs, there have been few genuinely large independent multimodel scenarios for the local scale based on many different GCMs.

A set of ESD results is presented for a large number of locations across different continents (Fig. 1). In this case, the local 2-m temperature [T(2m)] scenarios were derived from a large multimodel ensemble representing 45–50 GCM simulations, representing the twentieth century (20C3M) as well as the Special Report Emissions Scenarios (SRES) A1B emission scenario for the twenty-first century, thus spanning the time interval 1900–2100 (∼50 simulations with 23 different GCMs for both centuries, thus ∼50 20C3M runs and ∼50 A1B runs). Since future scenarios usually are used to infer changes, it is important to evaluate the models’ ability to reproduce the trends and variance during the past 100 years.

Fig. 1.
Fig. 1.

Map showing multimodel ESD results for 1119 locations across the world, for which the ESD analysis has been applied to more than 45 different SRES A1B GCM runs from CMIP3 (for most cases, the ESD was applied to 50 runs). The color code is used to grade the quality of the ESD results based on the R2 statistics from the stepwise multiple regression, and one estimate was derived for each month, GCM, and century, resulting in typically ∼1200 values for each site. Maps like these can also be used to provide a diagnostics of stations with suspect data quality.

Citation: Journal of Climate 24, 8; 10.1175/2010JCLI3687.1

2. Data

Large-scale T(2m) from the 40-yr European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-40) (Simmons and Gibson 2000) was used for calibration against local T(2m) series and is referred to as “predictor,” whereas the local variable is the “predictand.” Corresponding large-scale predictors taken from a set of GCMs were then used as input in the regression models to derive local scenarios for both the past (20C3M) and the future (SRES A1B). The GCM data were retrieved from the multimodel data portal of the Program for Climate Model Diagnosis and Intercomparison (PCMDI) at the Lawrence Livermore National Laboratory (available at http://www-pcmdi.llnl.gov/).

The local T(2m) series are listed in Table 1 and were taken from several different sources according to their regional coverage. The temperature series outside Europe were obtained from the Global Historical Climate Network (GHCN) (Peterson and Vose 1997) through the Climate Explorer (available online at http://climexp.knmi.nl) (here only “adjusted” values were used). In addition, the National Centers for Environmental Prediction (NCEP) and National Center for Atmospheric Research (NCAR) reanalysis (Kalnay et al. 1996) was used in a comparison with station data and ERA-40 for data assessment.

Table 1.

List of data sources for the predictand.

Table 1.

3. Methods

The ESD analysis was implemented using the tool clim.pact (Benestad 2004a); more details concerning the quality control and postprocessing the results are provided in Benestad (2009). It incorporated a form of quality control through the requirement of realistic regional “fingerprints” in the GCM results, which involved common empirical orthogonal functions (EOFs) (Sengupta and Boyle 1993) for ensuring that the large-scale spatial temperature structures being used to derive the scenarios (GCMs) are the same as those identified with the past observed local variations (ERA-40) (Benestad 2001). Common EOFs are the same as traditional EOFs but with a data matrix that consists of anomalies from a combination of two or more sources. Typically, the GCM data are regridded onto the same grid as the reanalysis and then concatenated before a singular value decomposition (SVD) (Press et al. 1989).

The ESD involved a stepwise regression of local monthly-mean T(2m) series against a set of principal components describing the eight leading regional large-scale spatial T(2m) temperature anomaly patterns, and the multiple regression analysis was only carried out if more than 30 years of data were available. It is also possible to use other types of predictors, such as geopotential heights, but changes in the atmospheric composition (humidity) may affect the lapse rate and hence make fields from the free troposphere more susceptible to nonstationarity issues (Chase et al. 2004).

For most locations, the number of predictors was low compared to the number of data points, reducing the risk of overfit (Wilks 1995). The statistical model was based on the well-known physics-based relation between large- and small-scale temperature structures; this also boosts the expected confidence in these results. For a small arbitrary selection of locations, the spatial structure of the regression weights was also inspected, confirming the expected geographical dependency between the local site and the surrounding T(2m) (not shown).

Both predictand and predictor series were detrended before the calibration procedure to avoid the interference of arbitrary trends, and the mean value was subtracted from both to emphasis the changes associated with the anomalies. Some systematic biases associated with imperfect GCMs were bypassed through this procedure. The downscaling was also carried out for the twentieth and twenty-first centuries separately and then combined (Benestad 2009), as the simulations for these were archived in different files in the PCMDI CMIP3 archive.

The regression was done on each of the 12 calendar months separately, and the final results were then obtained by combining the results for the different months. The subsampling of the monthly data reduced the risk of dependency between the data points. For a small set of stations, the results for the different calendar months were compared, and the similarity between the adjacent months suggested robustness in the analysis (e.g., all January months versus all February months). The final results were obtained by adding the observed climatology to the downscaled anomalies and by combining the series for the twentieth and twenty-first centuries, respectively (Benestad 2009).

4. Results

a. Downscaling to single locations

The multiple regression analysis provided an indication of the quality of the results in terms of an analysis of variance (ANOVA) (Wilks 1995), and a comparison of the R2—the coefficient of determination—statistics from nearby stations can provide a basis for judging the data quality. Different color coding in Fig. 1 indicates the quality of the multimodel ESD for 1119 different sites around the world, with the densest representation from Europe. A large number (∼1200) of regression analyses were carried out for each site, returning a set of R2 statistics for each GCM across all calendar months over both centuries. Many of the African sites shown in this map are shown with orange and red symbols, signifying low R2 values and hence a weak relationship between the local T(2m) series (the predictand) and the large-scale predictor [ERA-40 T(2m)].

A comparison between the variance observed and captured by the ESD analysis of a single GCM simulation provides the same information as the R2 statistics—that is, the proportion of the variance that can be represented by the ESD models. Furthermore, an ensemble of ESD results from different GCMs contains information about model differences as well as the interannual fluctuations and hence provides a picture of uncertainties associated with both the models as well as natural variability. Here, the envelope between the 5th percentile (q05) and 95th percentile (q95) is used to describe the uncertainty associated with these two aspects, representing the multimodel ensemble 90% confidence interval, calculated separately for each respective year.

The long-term evolution of the time series was approximated by best-fit fifth-order polynomials [y(t) = c0 + c1t2 + … + c5t5]—here used to provide a crude and approximate description of q05 and q95 over 1900–2100 as well as the ensemble mean. These curves were fitted using an ordinary multiple regression, and the regression coefficients (c0c5 will be referred to as “ci,” with i ∈ [0, 5]) describing the polynomials were saved to reconstruct and map the trends. In this analysis, the trend fit was done on seasonal mean values rather than monthly results. For an ensemble of 50 runs for both twentieth and twenty-first centuries (200 years in total), the information about the main features of the multimodel ESD results could then be reduced in terms of data volume to (4 × 3 × 6)/(12 × 50 × 200) = 0.6% of the original data size through the representation of these three statistics as fifth-order polynomials of seasonal mean T(2m) trends. Figure 2 illustrates how this information can be used to describe the multimodel ESD results for the seasonal mean T(2m) in Oslo, Norway.

Fig. 2.
Fig. 2.

The most essential features of the multimodel ESD results can be captured by the 5th-order polynomials that provide approximations of the ensemble mean, q05 and q95. These are shown here for Oslo, Norway, as the shaded region and thick central curve. The multimodel ensemble included 47 ensemble members, excluding 1e GCM [Bjerknes Centre for Climate Research (BCCR)]. The observations are shown as black symbols for comparison.

Citation: Journal of Climate 24, 8; 10.1175/2010JCLI3687.1

The statistics describing the envelope of the model results in terms of percentiles can easily be used to construct a probability distribution of the multimodel ensemble, assuming that the ensemble members are normally distributed and using a well-defined relationship between the q95 and the standard deviation (one standard deviation was taken to be (q95x)/1.64, where x is the mean; Fig. 3). It is then possible to use these distributions to estimate probabilities based on the associated cumulative distribution functions. However, it is important to keep in mind that these distributions do not represent a true probabilistic forecast but merely provide some indication about the uncertainties associated with internal variability and model differences, given an SRES A1B emission scenario. Thus, the estimated probability distribution represents conditional distributions in a similar sense as discussed in Benestad (2004b) with the caveat that all models may exhibit a common bias or potentially neglect an essential aspect of the system.

Fig. 3.
Fig. 3.

Multimodel ESD results for Oslo projected for year 2040–60 presented as seasonal Gaussian distributions. The mean and standard deviations were estimated from the regression coefficients ci describing the 5th-order polynomials for the ensemble mean and q95.

Citation: Journal of Climate 24, 8; 10.1175/2010JCLI3687.1

The quality of the downscaled scenarios can also be assessed through comparing the evolution over the past century with downscaled climate model results, and the observed T(2m) variations were mainly within the q05q95 envelope of the downscaled series. However, there were some exceptions—for example, in eastern Africa (Fig. 4), where the R2 scores were low (Fig. 1). Mongu [Zambia; World Meteorological Organization (WMO) station code 67633] is deliberately presented here as a worst case, with both low R2 scores and local observations that suggests a pronounced—but suspect—cooling trend. The ESD results, however, are not affected by the trend itself, as detrended data were used for the calibration. Differences in the interannual variations between the predictand and the predictor, on the other hand, will result in low R2 and an underestimation of any future change.

Fig. 4.
Fig. 4.

A worst-case example for which the observations are highly suspect. The ESD results shown are for Mongu, Zambia (WMO station code 67633), presented as a shaded region and thick central curve. The observations are shown as black symbols for comparison. The ESD is not strongly affected by the strong negative trend in the observations because it uses detrended data for calibration.

Citation: Journal of Climate 24, 8; 10.1175/2010JCLI3687.1

In some cases, the ESD analysis may yield low R2 for a few months only, and Fig. 5 shows how R2 for Mongu varies with the calendar months. The lowest R2 score of ∼30% was seen in February and a maximum of ∼75% in January. Figure 6 shows further diagnostics from the ESD analysis for Mongu and one GCM [Hadley Centre Global Environmental Model version 1 (HadGEM1); Martin et al. 2006; Meehl et al. 2007], with the projected linear trend as a function of season (Fig. 6a), a single-GCM projection Fig. 6b), a time series of the regression residual (Fig. 6c), and the predictor pattern for the month of February (Fig. 6d). The low R2 score in February (Fig. 6a) is associated with a substantially lower trend estimate than for the other months, probably due to the underestimation of the variance for that month. These diagnostics also show that the detrending of the observations removed the worst trend, and the example shown for one GCM demonstrates that the trends derived through the ESD analysis are independent of the trend seen in the observations (Fig. 6b).

Fig. 5.
Fig. 5.

Details showing how the R2 scores for Mongu, Zambia (red color code in Fig. 1), vary with calendar month. The R2 scores are plotted for both centuries and all GCMs, but the values are not very sensitive to the choice of GCM.

Citation: Journal of Climate 24, 8; 10.1175/2010JCLI3687.1

Fig. 6.
Fig. 6.

The ESD diagnostics for Mongu, Zambia, and the HadGEM1 GCM: (a) projected 2000–2100 linear trend (yellow) and R2 (blue) as a function of season; (b) detrended observations and T(2m) projection for a HadGEM1 SRES A1B run; (c) As in (a), but with the year is repeated twice. The regression residuals for the calibration period where different lines represent different calendar months; (d) The large-scale February T(2m) pattern in ERA-40 associated with variations in the adjusted GHCN data from Mongu, Zambia. The location of Mongu is marked with a point symbol in (d).

Citation: Journal of Climate 24, 8; 10.1175/2010JCLI3687.1

It is important to examine the regression residuals, that is, the difference between predictions over the calibration interval, based on the regression model, and the observations [, where T is the T(2m), t is the time, and is the predicted value]. Single large errors can flag suspect data, such as seen in May and December 1983 for Mongu (Fig. 6c). Large single errors explain low R2 scores.

An additional diagnostic for data consistency is the predictor pattern, derived through ESD. These are a weighted combination of the spatial (common) EOF patterns, where the weights are given by the multiple regression used in the ESD analysis. The large-scale spatial T(2m) pattern associated with the interannual T(2m) variations for February exhibited features with a maximum near the location of the station but with weak amplitudes (Fig. 6d). Hence, the link between the large-scale and the local T(2m) can be regarded as weak in February for Mongu, because of observational errors or shortcomings in the ERA-40 model.

Another interesting aspect is the long-term trend in the T(2m) recorded at Mongu. Figure 7 shows a comparison between the annual mean T(2m) anomaly at Mongu, taken from the Climate Explorer database (adjusted GHCN values), and interpolated from the ERA-40 (thin solid) and NCEP reanalysis (dashed). The local T(2m) and interpolated values, derived from the reanalyses, differed in terms of interannual variations and trend. Other places in Africa had local T(2m) data that were in better agreement with the reanalyses (not shown). However, the two reanalyses also differed for many African sites, probably because of the sparse data coverage in this region. The mean T(2m) levels (not shown) were also different in the three datasets, part of which may be due to the different representation of the surface (altitude) in the atmospheric models used to derive the reanalyses. However, the ESD analysis is not strongly affected by such biases, as it is carried out on the T(2m) anomalies rather than the total T(2m).

Fig. 7.
Fig. 7.

A comparison between local T(2m) series for Mongu, Zambia, and compared with interpolated values from ERA-40 and NCEP reanalyses.

Citation: Journal of Climate 24, 8; 10.1175/2010JCLI3687.1

b. Gridding the data to produce maps

The ESD results for the European sites were gridded through mapping the regression coefficients ci, enabling a quick reconstruction of the multimodel envelope and trend for any of the grid points. The multiple regression used for gridding was different from the multiple regression carried out in the ESD in terms of both variables as well as dimension. Whereas ESD was based on temporal variability, the geographical regression analyzed the spatial dimension. An identical approach was used for Africa, northwest Russia, and Scandinavia, and the detailed statistics associated with the gridding is given in Table 2.

Table 2.

Adjusted R2 scores (%) for the regression coefficients ci against geographical parameters for Europe, Africa, and northwestern Russia. The columns represent ci, and the rows indicate the type of statistic and season [DJF, March–May (MAM), JJA, and September–November (SON) represents winter–autumn]. Here, N represents the number of data points in the multiple regression that was carried out on 7 independent variables representing the following geographical aspects: Z, d, y, x, ln(d), , and .

Table 2.

The gridding of ci involved both a multiple regression against geographical parameters and kriging-based interpolation of the regression residuals. The geographical regression over Europe used ci from 495 locations within the region 35°–75°N, 30°W–60°E (Africa: 173 sites in the region 40°S–40°N, 25°–60°E; northwestern Russia and Scandinavia: 148 sites in the region 60°–80°N, 5°E–180°) and used altitude (Z), distance (d) from the coast, eastings (X), northings (Y), , ln(d), and as predictors. Because of the transfer between the different types of coordinates (°E and °N used in the gridded maps km east–west and km north–south used in eastings and northings) and the requirement of a rectangular grid, the final domain of the gridded results would vary slightly from the initial specifications. The altitude Z was taken from station meta data, but a gridded 5-min gridded elevation data (available online at http://www.ngdc.noaa.gov/mgg/global/etopo5.HTML) product was used to predict values for empty boxes, implying a spatial resolution of ∼10 km over Europe.

The residuals represent the part of the polynomial coefficient that could not be associated with geographical parameters of the regression analysis, and this part was then added to the regression-based predictions through kriging. The gridding procedure is similar to that in Benestad (2005), except for the handling of the residuals (different kriging routine) and that it used a slightly modified regression model for relating the coefficients to geographical conditions by including , ln(d), and .

An indication of the quality of the regression results could be gleaned from a regression between ci and geographical conditions from the gridding analysis (Table 2). The value of c0 was given by the observed mean values from the station data (Benestad 2009), and hence it does not constitute a good test of the ESD model skill. The constant term c0 was associated with the highest values of R2, because of a clear systematic association between the mean T(2m) and the geographical situation. The higher-order terms (c1, …, c5) reflect the variance at these sites—the proportion of the variability captured by the ESD model (R2 from the ESD analysis shown in Fig. 1).

In Europe, the higher-order coefficients had relatively low R2 scores for the q05 in winter, suggesting either weaker geographical dependency or lower quality of these results. The corresponding results for the summer season in Europe [June–August (JJA)] gave R2 scores in the range 23%–57%. Hence, the gridded results were more strongly influenced by the geography-based regression in the summer, while residual kriging became more important for the winter results. It is also possible that other geographical factors, unaccounted for in the present analysis, are important.

For Africa, the values of R2 associated with gridding the ESD results were in general lower than for Europe despite fewer data points used in the regression. Low scores may reflect weak results (red color code in Fig. 1), errors in the data (Fig. 7), or a weak relationship between the downscaled trends and the geographical situation.

The adjusted R2 statistics associated with the gridding in northwestern Russia and Scandinavia were high for c0 but lower than for Europe for the higher-order polynomial trend coefficients. It is also useful to examine how the values of ci relate to the geographic parameters in the regression geographical model (RGM). Figure 8 illustrates how the value of c1 varies with Z, d, X, Y, , ln(d), and , suggesting that the linear term in the polynomial fit is lower at higher altitudes when the Z dominates over , but increases away from the coast. Furthermore, the higher terms c2c5 also influence the trends. There is a stronger c1 interior-coast contrast in northwestern Russia than in Europe and Africa for the December–February (DJF) season (blue symbols). Inversion situations may play a role in both the effect from altitude as well as distance from the coast for cold places such as northwestern Russia and Scandinavia. For all the regions, the linear component of the trend diminished northward and westward (X > 0). The estimates for the regression coefficients for , ln(d), and were most uncertain with substantial error bars.

Fig. 8.
Fig. 8.

A comparison between c1 (linear term in the polynomial trend fit) estimated through the geographical regression model. The values have been arbitrarily scaled to fit the plot, as the different geographical parameters have different units. The vertical lines mark the error bars (one standard error).

Citation: Journal of Climate 24, 8; 10.1175/2010JCLI3687.1

Figure 9 shows maps of q95 of the projected 2100 June–August mean T(2m) over Europe, derived from gridded multimodel ESD results. The projections suggests an increase in q95 everywhere compared to year 2000, ranging from ∼3°C in the north to ∼5°C in the south (Fig. 10b). Pronounced changes are also projected over the high-altitude regions in southern Europe. The estimated change is insensitive to c0 but depends on c1c5.

Fig. 9.
Fig. 9.

Maps showing (a) the gridded 95th percentile for the downscaled JJA mean T(2m) in Europe for year 2100 and (b) changes in the 95th percentile for the downscaled JJA mean T(2m) in Europe over 2000–2100.

Citation: Journal of Climate 24, 8; 10.1175/2010JCLI3687.1

Fig. 10.
Fig. 10.

Maps showing (a) gridded probability estimated for below-freezing downscaled DJF mean T(2m) for same year and (b) changes in the probability estimated for below-freezing downscaled DJF mean T(2m) over 2000–2100.

Citation: Journal of Climate 24, 8; 10.1175/2010JCLI3687.1

Figure 10 shows the calculated probability of the 2100 DJF mean temperatures being lower than 0°C, indicating the reduced likelihood of below-freezing mean winter T(2m) for all locations. The analysis also suggests that the high mountain regions still will have below-freezing temperatures in 2100, under the SRES A1B scenario. The greatest change in the simulated probability were ∼60% lower than for 2000 in areas where the winter T(2m) presently is around freezing (southern Sweden and parts of eastern Europe).

The map of q95 for JJA mean T(2m) in Africa is shown in Fig. 11a, and the probability of the JJA T(2m) exceeding 35°C is shown in Fig. 11b. The threshold value of 35°C can be regarded as a limit above which severe human heat stress may occur (Sherwood and Huber 2010), and the ESD results suggest that this limit may be superseded in small parts of central northern Africa in 2100, albeit with all the caveats associated with these projections. The observations and the ESD results (Fig. 6) may exhibit different spread, and it is difficult to judge the veracity of the ESD results when the quality of observations is highly suspect.

Fig. 11.
Fig. 11.

Maps presenting (a) the gridded 95th percentile for the downscaled JJA mean T(2m) in Africa for year 2100 and (b) the probability that the downscaled JJA mean T(2m) in Africa exceeds 35°C by 2100.

Citation: Journal of Climate 24, 8; 10.1175/2010JCLI3687.1

Northwestern Russia and Scandinavia may be faced with different challenges associated with a future climate change. Figure 12 presents maps showing the ensemble mean DJF mean T(2m) and conditional probabilities for simulated DJF T(2m) being lower than −10°C. The projected winter warming is most pronounced (∼7.5°C over the period 2000–2100) in the northern and northwestern parts of the sector, but there is also a second maxima (∼6°C) over Finnmark County in Norway. The T(2m) change over the Ural mountain range is estimated to be lower (∼4.5°C). The probability of mean DJF T(2m) below −10°C in 2100 is projected to be highest in the southeastern part of the region despite higher trends.

Fig. 12.
Fig. 12.

Maps showing (a) 2000–2100 changes in the gridded ensemble mean for the DJF mean T(2m) in northwestern Russia for year and (0.1°C) and (b) the gridded probability estimated for downscaled DJF mean T(2m) < −10°C by 2100.

Citation: Journal of Climate 24, 8; 10.1175/2010JCLI3687.1

These results are accessible to other scientists, and the polynomials describing the q05, q95, and ensemble means can be reconstructed through the R-package “esd4all,” (available online at http://noserc.met.no/grtools/esd4all.html) from which the essential data on the percentiles, gridded maps, and scripts for making plots are available. The R-packages “clim.pact” (available online at http://cran.r-project.org) and “met.no.REB” (available online at http://noserc.met.no/grtools/reb.html) were used to carry out the ESD. All these R-packages are freely available, open source, and contain documentation in form of R-package help pages. The ESD results have also been incorporated into Google Earth (available at http://eklima.met.no/metno/esd/esd.google.earthTemp.kmz).

5. Discussion

The use of ESD has also long been limited to just getting a scenario (van der Linden and Mitchell 2009), rather than seeing it as a means for advanced analysis and the provision of diagnostics that can flag the quality of the observations, shed light on the GCM performance, and improve our understanding about real physical mechanisms in the climate system. Since the ESD is cheap in terms of computer resources, the neglect of this method is unfortunate for the climate research community and constitutes a missed opportunity.

ESD assumes that the local climates are influenced by the surrounding large-scale climatic situation and the local geography; hence, it is, in principle, well-suited for gridding based on a regression against geographical parameters. Furthermore, fitting polynomials to the time series gives a set of parameters ci that can be used to examine spatial relationships (Fig. 8) that can be used for gridding (Figs. 912). ESD assumes that the statistical relationship between the local and large scales holds for the future, a strong and systematic link between the predictor and predictand, that the predictor carries the signal, and that the predictor is skillfully simulated by the GCM (Benestad et al. 2008). RCMs, on the other hand, embody a set of well-established physical equations in combination with a more uncertain statistical description of subgrid processes in the form of parameterization schemes.

Large ensembles also facilitate crude conditional probability-based analyses (Collins 2007), such as making scenarios for percentiles. But it is important to reiterate that an ensemble of GCM results, as presented here, does not constitute a true description of probabilities (Allen 2003; Murphy et al. 2007; Frame et al. 2007). For one, all the models may be wrong and have similar biases, and the models all share similarities that may invalidate the principle of independence. The principle of independence is only relevant for model errors and not the signal itself, as it is expected that these all describe the same essential feature if they are to be regarded as useful.

For proper probabilistic treatment, it is necessary to derive the probability distribution function (PDFs) describing the future climate (Pryor et al. 2005; Benestad 2007) or use Bayesian statistics (Wilks 1995). Nevertheless, the statistical distribution for the ESD results can still provide percentiles in terms of simulated T(2m). Furthermore, time series of modeled range and percentiles can be compared with observed values for the past to assess whether the models provide a realistic description of how the statistics may shift in time.

This study underscores the importance of good quality observations from a dense network. ESD can only give information about local climate variables for which there is a long record of high-quality observations, and it is further restricted to those observations that exhibit a close association with the large-scale predictors, such as the T(2m). But RCMs too need such observations for evaluation.

The ability of ESD to detect cases of inconsistencies between predictand and predictor and to provide additional diagnostics of the situation is valuable for getting further insight. The diagnostics from the ESD provide some information about the quality of the local measurements or the regional representation in ERA-40, both of which may have errors.

The quality for African sites can be questioned on the background of the R2 statistics from the ESD analysis (Fig. 1), the inconsistency between the different reanalyses and local measurements (Fig. 7), and the R2 statistics from the geographical analysis used in the gridding (Table 2).

A lack of homogeneity (Wijngaard et al. 2003; Hanssen-Bauer and Førland 1994; Nordli et al. 1996) may be an issue for the local T(2m) series, especially in Africa with a high proportion of sites with poor R2 scores. The T(2m) series may be inhomogeneous because of uncorrected changes in the local environment (e.g., deforestation, irrigation, urbanization) or instrumentation. Nevertheless, the calibration of the ESD model was based on linearly detrended series; hence, it is not as strongly affected by differences in trends as the interannual differences (Benestad et al. 2008, section 8.2).

The comparison between local T(2m) measurements and interpolated values from the reanalyses, however, is also limited by the fact that circulation models and station measurements represent different scales, and that general circulation models, such as those used to produce reanalyses, have a minimum skillful scale (Benestad et al. 2008). Single grid cells may be affected by “numerical noise” associated with the algorithms used to solve equations with discrete numbers (Press et al. 1989) or subgrid parameterization schemes. Furthermore, the topography is often smoothed to ensure stable solutions.

Low R2 leads to conservative estimates of change, for example, for Africa, as the ESD analysis captured less of the variance. It is therefore important to compare such results with similar projections derived from RCMs or to aggregate the data and compare with GCM results. According to the IPCC AR4, the JJA maximum T(2m) change between the periods of 1980–99 and 2080–99, given an SRES A1B emission scenario, range between 4.7 and 5.8 (Christensen et al. 2007, Table 11.1), whereas the gridded ESD analysis suggested a minimum of 1.4°C over the eastern and central parts of Democratic Republic of the Congo to a maximum of 5°C over the mountain ranges in Ethiopia (not shown). The ENSEMBLES project, however, suggests an increase over western parts of Africa ranging from 2° to 5°C for the mean JJA T(2m) (van der Linden and Mitchell 2009, Fig. 5.9).

These ESD results also serve as a useful means for comparing with other ESD results, in addition to providing valuable inputs to various impact studies. They furthermore provide a basis for a consistent RCM assessment for the different regions to which RCMs have been applied, as the ESD results have been derived using one common strategy for all continents and over the entire span of 1900–2100.

A reliance upon a set of RCM or ESD results driven with a single or a small selection of GCM simulations can result in “overselling” these simulations. At the very least, ESD should provide benchmarks for the T(2m) simulated by RCMs, although it comes with its own set of shortcomings and uncertainties. The two different main approaches are independent in terms of methodology, systematic errors, and assumptions and therefore have different strengths and weaknesses.

ESD also has the benefit of simplicity, transparency, and reproducibility, and it avoids problems in bias in terms of mean levels and annual cycle (Bergant et al. 2007). Yet, there have been some misunderstandings regarding downscaling, which give the wrong impression that RCMs are superior to ESD because they are seen to be “internally consistent,” sometimes confused as “physically consistent.”1 However, RCMs often involve different parameterization schemes to the GCMs or reanalyses used to prescribe the lateral boundary conditions. Furthermore, different combinations of different parameterization schemes—for example, for clouds and the boundary layer—can produce solutions that are mutually inconsistent.

There are further issues concerning the lateral boundaries, as most RCMs do not involve air–sea or land–air coupling, and different domain choices can affect the results. One problem is that a large domain can result in a different description of the large-scale flow within the RCM, and a technique called “spectral nudging” has sometimes been used to ensure a consistency between the large-scale features in the RCM and GCM (von Storch et al. 2000). The choice of domain can also affect the ESD analysis. Whereas it can affect the influx of moisture and momentum through the lateral boundaries in RCMs, large domains can also result in spurious trends from anticorrelated features in ESD (Benestad 2002). RCMs may also produce more precipitation than the driving GCMs because of better resolved topography and hence describe different moisture transports (L. Smith 2010, personal communication). Some types of ESD, on the other hand, have a tendency to underestimate the precipitation amount (Benestad et al. 2007). Synoptic-scale phenomena resolved by RCMs but not GCMs, such as storms, may also have an impact on the large-scale environment (“upscaling”) and hence they should alter the boundary conditions. Nevertheless, RCMs have often been applied to different parts of the world, where they provide a realistic representation of many of the real climatological phenomena seen in the atmosphere, and they provide a coherent picture of all variables and their spatial distribution.

Hence, despite these caveats, both ESD and RCMs have demonstrated that they provide a realistic description of many local climatic features. ESD nevertheless seems to have been undervalued in the past2 despite the two methods being equally skillful (Hanssen-Bauer et al. 2005). Complimenting RCM studies with ESD will strengthen our confidence in the results; however, it is important to remember that all models are just tools, and they should not be confused with reality.

Future work will involve comparison between RCMs and ESD results [e.g., U.K. Climate Projections 2009 (UKCP09)], but it is also important to carry out similar exercise for monthly precipitation. Benestad et al. (2007) found that the ESD could account for a smaller proportion of the precipitation variance than T(2m), and an improvement of these analyses could involve a stochastic modeling of the residuals. Further work is also envisaged for other regions of the world and for other statistics. Future studies should also include diagnostics of more locations—including predictor patterns, details about the R2 statistics, common EOF products, a test of stationarity (Benestad et al. 2007)—and a comparison between the local series and interpolated values. Here the different GCMs have been treated as equal, and it is also possible to weight the different model results in a Bayesian fashion (Wilks 1995; Knutti 2010; Santer et al. 2009). These exercises will also be repeated when new GCM scenarios (CMIP5) become available. Remote sensing images from satellites can furthermore be used in a more sophisticated gridding procedure, using vegetation indices as proxies for precipitation or T(2m). More high-quality observations are also needed, and further progress also hinges on improving both GCMs and RCMs.

6. Conclusions

Empirical statistical downscaling has been carried out on a large set of seasonal mean T(2m) measurements for ∼1000 locations scattered across the globe, based on the CMIP3 database of ∼50 GCM simulations following the SRES A1B emission scenario, resulting in O(106) ESD exercises. The results from this exercise are condensed into an R-package and gridded for three different regions with a 5-min spatial resolution, taking different geographic parameters into account.

The downscaled results project an increase in the 95th percentile of the JJA mean temperatures over Europe in the range of 3°–5°C by 2100. This upper limit of the simulations reflects both interannual variability as well as the different response among the GCMs. In regions with DJF mean temperatures around zero, the ESD analysis suggests a reduction in the probability of below-freezing conditions by ∼60% in 2100.

The empirical statistical downscaling for Africa revealed low scores, because of inconsistencies between local measurements and reanalyses. Hence, more high-quality observations are needed to obtain more reliable results. Nevertheless, a tentative and conservative analysis for Africa suggest that the high-end JJA mean temperatures in 2100 may exceed 35°C in some limited regions in the vicinity of the Sahara Desert.

For the northwestern part of Russia and Scandinavia, the downscaling analysis projected a winter warming between 4.5° and 7.5°C, with the greatest response in the north and the northeast regions and weakest warming in the mountain regions.

This study demonstrates how empirical statistical downscaling can provide far more insight than in more conventional work, and that it is a valuable supplement to regional climate models. Both approaches have different strengths and shortcomings, but they are independent means of deriving local climate information, so that consistency between the two can give increased confidence in the projections. ESD can be robust with respect to both spurious trends as well as biases in annual cycle and mean, in addition to being transparent.

Acknowledgments

I wish to thank Øyvind Nordli and Eirik Førland for having read through the manuscript. Also, I am grateful for the valuable comments from two anonymous reviewers. The work was done under the projects Norclim, EALAT, CAVIAR, CELECT, and NorAdapt—all funded by the Norwegian Research Council. I acknowledge the international modeling groups for providing their data for analysis, the Program for Climate Model Diagnosis and Intercomparison (PCMDI) for collecting and archiving the model data, the JSC/CLIVAR Working Group on Coupled Modelling (WGCM) and their Coupled Model Intercomparison Project (CMIP) and Climate Simulation Panel for organizing the model data analysis activity, and the IPCC WG1 TSU for its technical support. The IPCC Data Archive at Lawrence Livermore National Laboratory is supported by the Office of Science, U.S. Department of Energy. Ferret from NOAA/PMEL (available online at ferret.pmel.noaa.gov) was used to generate some of the plots.

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1

“Although RCMs are preferable due to physical consistency” (Landman et al. 2009).

2

In the IPCC Fourth Assessment Report and the EU project ENSEMBLE, ESD is more or less delegated to the appendices, and it appears to be completely neglected in the U.S. NARCCAP project, even though comparisons have demonstrated equal skill for the two approaches.

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