Intercomparison of temperature trends in IPCC CMIP5 simulations with observations, reanalyses and CMIP3 models

On the basis of the fifth Coupled Model Intercomparison Project (CMIP5) and the climate model simulations covering 1979 through 2005, the temperature trends and their uncertainties have been examined to note the similarities or differences compared to the radiosonde observations, reanalyses and the third Coupled Model Intercomparison Project (CMIP3) simulations. The results show noticeable discrepancies for the estimated temperature trends in the four data groups (radiosonde, reanalysis, CMIP3 and CMIP5), although similarities can be observed. Compared to the CMIP3 model simulations, the simulations in some of the CMIP5 models were improved. The CMIP5 models displayed a negative temperature trend in the stratosphere closer to the strong negative trend seen in the observations. However, the positive tropospheric trend in the tropics is overestimated by the CMIP5 models relative to CMIP3 models. While some of the models produce temperature trend patterns more highly correlated with the observed patterns in CMIP5, the other models (such as CCSM4 and IPSL_CM5A-LR) exhibit the reverse tendency. The CMIP5 temperature trend uncertainty was significantly reduced in most areas, especially in the Arctic and Antarctic stratosphere, compared to the CMIP3 simulations. Similar to the CMIP3, the CMIP5 simulations overestimated the tropospheric warming in the tropics and Southern Hemisphere and underestimated the stratospheric cooling. The crossover point where tropospheric warming changes into stratospheric cooling occurred near 100 hPa in the tropics, which is higher than in the radiosonde and reanalysis data. The result is likely related to the overestimation of convective activity over the tropical areas in both the CMIP3 and CMIP5 models. Generally, for the temperature trend estimates associated with the numerical models including the reanalyses and global climate models, the uncertainty in the stratosphere is much larger than that in the troposphere, and the uncertainty in the Antarctic is the largest. In addition, note that the reanalyses show the largest uncertainty in the lower tropical stratosphere, and the CMIP3 simulations show the largest uncertainty in both the south and north polar regions.


Introduction
The fifth phase of the Coupled Model Intercomparison Project (CMIP5) provides quantitative data sets for estimating climate change based on a suite of climate models (Taylor et al., 2012).Compared to the third phase of the Coupled Model Intercomparison Project (CMIP3), conventional atmosphere-ocean global climate models (AOGCMs) and Earth System Models of Intermediate Complexity (EMICs) are for the first time being joined by more recently developed Earth System Models (ESMs).The reliability of the new climate model products is an important question for the climate change detection.Evaluating climate model results using observational data sets is necessary to understand the capabilities and limitations of climate change simulations.
As the models get more complicated, they must handle a greater number of complex processes that often interact.Subtle changes can lead to unintended results.Also, it is difficult to rigorously test each process, each pathway in the software, and understand the way it is represented in the model and how it interacts with the other modeled processes.
Temperature trend is an important component for measuring global climate change.It provides evidence of both natural impacts and those from anthropogenic forcing.However, a lot of evidence is found in the literature (Santer et al., 1999;Seidel et al., 2004;Christy and Norris, 2006;Sakamoto and Christy, 2009;Xu and Powell, 2010) that the temperature trend estimation is sensitive to the data source (radiosondes, satellite observations, and reanalysis products).Radiosonde coverage extends back to the late 1950s.However, radiosondes only reach altitude levels below 20 hPa and do not provide data over the ocean, Arctic and Antarctic zones.Also, due to discontinuous observations caused by instrumentation changes, the raw radiosonde record includes remarkable inhomogeneities (Lanzante et al., 2003;Seidel et al., 2004).
The first generation of reanalysis products created by National Centers for Environmental Prediction (NCEP), National Aeronautics and Space Administration (NASA) and European Centre for Medium-Range Weather Forecasts (ECMWF) was successfully used in the study of global atmospheric and oceanic processes and their dynamics, especially over the data-sparse poles, Southern Hemisphere, and ocean regions.The updated or second-generation reanalyses have been implemented by several weather and climate prediction centers.However, the reanalysis products showed a number of uncertainties and deficiencies (Kanamitsu et al., 2002;Trenberth, 2001).
Because of these and other difficulties involved with complex data implementation, observation systems, and processing algorithms, objectively identifying one or more reliable data sets is a difficult task.This paper compares three types of data sets with the CMIP5 simulations on the basis of the same fundamental analyses.The goal is to (1) compare the temperature trends in the CMIP5 simulations with radiosonde observations and reanalyses and (2) evaluate whether there has been an improvement from CMIP3 to CMIP5.
For the two purposes, an ensemble analysis for the temperature trends and spread will be implemented.The data sets used here are described in Sect. 2. The analysis includes intercomparisons between the stratosphere and troposphere (Sect.3), and intercomparisons between the tropics, Arctic and Antarctic (Sect.4).Section 5 provides a final summary.

Data and calculations
Three groups of data sets, including radiosonde observations, reanalysis products and the CMIP3 model simulations, are used to be compared to the CMIP5 climate model simulations.All data sets span the period from 1979 through 2005 and the levels between 850 and 30 hPa.

Reanalysis and radiosonde data sets
The eight reanalysis products used in this study include NCEP-R1, NCEP-R2, NCEP-CFSR, ERA40, ERA-Interim, JRA25, MERRA and 20CR.Detailed information about these reanalyses can be found in our previous publication (Xu and Powell, 2012).The five radiosonde data sets used in this study include HadAT2, RATPAC, IUK, RAOBCORE and RICH.More information about these radiosonde products can also be found in our previous publication (Xu and Powell, 2010).

The CMIP3 simulations
The CMIP3 model simulations were introduced in the study by Meehl et al. (2007).To get a comparable number of climate and reanalysis products, eight climate models (Table 1) were selected from the larger group and were matched with eight reanalyses using temperature fields from the Climate of the 20th Century experiments (20C3M) (selected from 1979 through 1999) and the committed climate change experiment (COMMIT) (selected from 2000 through 2005).

The CMIP5 simulations
Similar to the CMIP3 experiments, the CMIP5 simulations provide a framework for coordinated climate change experiments aimed at evaluating climate simulations of the recent past, providing projections of climate change, and quantifying climate feedbacks (Taylor et al., 2012).Compared to CMIP3, the climate models used in CMIP5 generally are more comprehensive in the processes they include and are of higher spatial resolution.Corresponding to the selected CMIP3 models, eight models from the same group (Table 1) in the "historical" run of CMIP5 are used in this study.The "historical" run (1860The "historical" run ( -2005) ) is forced by observed atmospheric composition changes (reflecting both anthropogenic and natural sources) including time-evolving land cover.Each of the CMIP3 and CMIP5 models has been run with different ensemble members, but only one of the ensemble members (r1i1p1) from each model is used here.

Trend calculation
The annually averaged data are first calculated based on the monthly data sets listed above.In order to be consistent with the radiosonde data set locations, zonal means are calculated from the annual data by selecting areas over land only.The zonal means are calculated with a resolution of 10 • latitude and the global mean is then calculated using latitudinal weighting.The trend is computed with the methodology of linear least squares fitting.The t test analysis was employed to calculate the statistical significance of the temperature trends.3 Intercomparison of temperature trends between the stratosphere and troposphere

Vertical structure
In terms of the linear least squares fitting of the temperature time series in the period from 1979 through 2005 for the four data groups, Fig. 1 displays the vertical and latitudinal distribution of the temperature trend for the levels between 850 hPa and 30 hPa.First, the vertical and latitudinal distribution of temperature trends in all five radiosonde data sets (left panel in Fig. 1) match quite well.Strong maximum cooling is clearly observed in the tropical and subtropical stratosphere, while strong warming appeared in the lower troposphere in the northern middle and high latitudes and the tropical upper troposphere.The temperature trend switched from positive to negative at approximately 150 hPa.The strongest warming in RAOBCORE was on the order of 0.5 • C decade −1 , which occurred in the lower northern high latitudes and was higher than that in the other four radiosonde data sets.The largest cooling trend in the stratosphere reached −1.2 • C decade −1 in the southern tropical stratosphere in IUK.The results confirmed the high consistency among the five radiosonde data sets revealed in our previous study (Xu and Powell, 2012), although there are some differences in these five data sets.Unfortunately, based on current understanding, we cannot identify which one is closest to the true observational temperature.
Second, within the group of reanalysis (left middle panel in Fig. 1), 20CR and JRA25 reanalyses do not display the feature of tropospheric warming and stratospheric cooling that is consistently seen in the other six reanalyses.The maximum cooling on the order of −1.6 • C decade −1 in the tropical tropopause layer is observed in the NCEP-R1 and NCEP-R2, which is a much stronger cooling than in the other six reanalyses and all the radiosonde observations.Relatively strong warming appeared in the upper tropical troposphere in the ERA40 and NCEP-CFSR, while the warming at the lower tropospheric northern high latitudes is comparable to the magnitude in the radiosondes.Note that the cooling in the northern stratosphere in 20CR shows abnormal values compared to the other seven reanalyses.It is worth noting that significant discrepancies can be found between the different reanalyses, and it is hard to say which one best reproduces the true atmospheric trends even with the new data sets and algorithms used in new data assimilation systems.For example, the NCEP-CFSR is a new generation data assimilation system from NCEP developed from NCEP-R1 and NCEP-R2.However, according to the radiosonde observation measurements, the NCEP-CFSR reanalysis overestimated the tropospheric warming compared to the previous system in NCEP-R1 or NCEP-R2.
Third, the CMIP3 simulations (right middle panel in Fig. 1) show a similar transition from tropospheric warming to stratospheric cooling in all eight models except for the tropical zone in the CNRM_CM3 and the high latitudes in IPSL_CM4 and MRI_CGCM2.However, four of the eight models (CCSM3, CNRM_CM3, CSIRO_MK3.5 and UKMO_HADCM3.1)indicated relatively strong stratospheric cooling outside the tropical and subtropical areas, in contrast to the radiosonde observations.
Compared to the CMIP3 simulations, the CMIP5 simulations (right panel in Fig. 1) display a better vertical and latitudinal structure, and all eight models show a relatively strong cooling in the tropical and subtropical stratosphere, which matches the distribution in the radiosonde observations.Similar to the reanalysis and CMIP3 simulations, the CMIP5 simulations portrayed stronger warming in the upper tropical troposphere than in the radiosonde data sets.
The statistical significance at the 99 % level, according to a t test (the line with the value of ± 2.5 in Fig. 1), shows that the trends are believable in most of the troposphere and stratosphere.However, the significance cannot be found in the tropopause layer.
The vertical and latitudinal structure indicates four significant characteristics.(1) The temperature trends show noticeable discrepancies in the four data groups, although commonalities can be observed.(2) Most of the data sets exhibit a sharp cooling in the tropical and subtropical stratosphere and a strong warming in the lower troposphere in the northern middle and high latitudes and the tropical upper troposphere.

Similarities and differences
To quantify similarities and differences between these data sets, the global mean temperature trend and spatial correlations between model simulations and observations were calculated.The mean of all five radiosonde data sets is used to represent the observations.In the troposphere (500 hPa), the radiosonde global mean temperature trends range from 0.11 • C decade −1 to 0.13 • C decade −1 (Table 2), which reflects consistency among the radiosonde data sets.The trends in the reanalysis group show a significant divergence, with the largest warming reaching 0.24 • C decade −1 in the NCEP-CFSR while the trend value goes down to 0.04 • C decade −1 in the ERA40.However, compared to the radiosondes, the values in all eight CMIP3 simulations are increased, with values from 0.15 • C decade −1 in HADCM3 to 0.29 • C decade −1 in CCSM3.The magnitude of the warming in the CMIP5 simulations is higher than the CMIP3 simulations, except for the MRI model, and the temperature trend ranges from 0.17 The mean trend and standard error show (Fig. 2a) that the tropospheric mean trend in the CMIP5 (0.293 • C decade −1 ) is much larger than in the radiosonde observations (0.12 • C decade −1 ) and the CMIP3 simulations (0.215 • C decade −1 ), while the divergence in the eight CMIP5 models is also larger than the other three data groups.In other words, the CMIP5 simulations show not only the greatest tropospheric warming, but also the largest uncertainty in the temperature trend estimation.
In contrast, in the stratosphere (50 hPa), the cooling trends in all the radiosonde data sets are larger than −0.70 • C decade −1 (Table 2), which shows a strong similarity among the five radiosonde data sets.Most of the reanalyses have a cooling trend larger than −0.60 • C decade −1 , except for the estimations from the 20CR and JRA25.However, the cooling trends in the CMIP3 simulations are significantly reduced, except for the HADCM3 model, and five of the eight CMIP5 models show that their cooling trend exceeds −0.50 • C decade −1 , which is closer to the radiosonde observations than the cooling trends of the CMIP3 simulations.It is worth noting that the uncertainty in the stratospheric cooling trend estimates in the CMIP5 models is significantly decreased (Fig. 2b).
Similar to the CMIP3, the CMIP5 simulations overestimate the tropospheric warming and underestimate the stratospheric cooling, although the stratospheric estimates are improved in comparison with the radiosonde observations (Fig. 2a and b).In addition, the large uncertainty in the stratospheric cooling trend estimates in the reanalysis group is mainly due to the 20CR and JRA25.
Furthermore, the spatial correlations between the model simulations and the radiosonde observations indicate (Fig. 3) that the temperature trend in most of the reanalyses is in very good agreement with the radiosonde observations in both the stratosphere (100-30 hPa) and troposphere (850-300 hPa), but the stratospheric trends in the 20CR, ERA40 and JRA25 significantly differ from the observations (Fig. 3a).The CMIP3 simulations (Fig. 3b) have a worse structure than the analyses, especially in the stratosphere; four of the eight models show negative correlations with the radiosonde observations.The correlations of the CMIP5 simulations with the radiosonde observations (Fig. 3c) in the stratosphere are higher than those in the previous version regarding the CMIP3 simulations, except for CCSM4 and IPSL_CM5A-LR (Fig. 3b).However, three of the eight CMIP5 models in the troposphere have negative correlations with the radiosonde observations.
To summarize, 20CR and JRA25 reanalyses show a large discrepancy in the stratosphere compared to the other six reanalyses, which is probably related to the surface data assimilated only in the 20CR reanalysis system and the wrong stratospheric ozone assimilated in the JRA25 reanalysis system (Xu and Powell, 2012).Similar to the CMIP3 models, the CMIP5 simulations overestimate the tropospheric warming and underestimate the stratospheric cooling.also the largest uncertainty in the temperature trend estimates.The large uncertainty is mainly from CNRM_CM5 and IPSL_CM5A-LR.Based on the spatial correlation analysis, most of the CMIP5 simulations have higher correlations in the stratosphere but lower ones in the troposphere compared to the CMIP3 simulations.

Intercomparison between tropics, Arctic and Antarctic
Figure 4 shows the vertical profiles of the temperature trend that represents the three latitudinal bands, including the Arctic (60-90 • N), tropics (15 • S-15 • N) and Antarctic (60-90 • S), in the four data groups.The distribution is zonally averaged, and the period of 1979-2005 is used with altitudes ranging from 850 to 30 hPa.The five radiosonde data sets agree reasonably well with each other in the Arctic and tropics (Fig. 4a and e) in both the troposphere and stratosphere.However, a large discrepancy can be found in the Antarctic (Fig. 4i), where the Hadat2 shows a noticeable difference to the other two available data sets in the stratosphere.
For the reanalyses, the trends in the tropics and Antarctic (Fig. 4f and j) display a large divergence, and the discrepancy among the eight reanalyses is much larger than shown in the radiosondes.In the tropical tropopause layer (∼ 100 hPa), the trend ranges from ∼ 0.3 • C decade −1 in the ERA40 to ∼ −1.4 • C decade −1 in the NCEP-R1 and NCEP-R2 (Fig. 4f).In the tropics, the JRA25 shows a significant warming in the stratosphere, while the 20CR exhibits a warming in the study domain from the troposphere to stratosphere.In the Antarctic (Fig. 4j), most of the reanalyses show cooling in the troposphere, except for the ERA40, and the warming trend is observed again in the stratosphere in JRA25.However, the trends are highly consistent in the Arctic except for the 20CR reanalysis (Fig. 4b).
For the CMIP3 simulations, the trends are in very good agreement in the tropics (Fig. 4g) but don't show similar agreement in the stratosphere in both polar areas (Fig. 4c  and k).For example, in the Arctic, the CNRM_CM3 and MRI_CGCM2 simulations display a warming in the stratosphere compared to a cooling in the other six models (Fig. 4c), with the UKMO_HadCM3 simulation having the most extreme stratospheric cooling of −1.4 • C decade −1 in the Antarctic (Fig. 4k).Compared to the CMIP3 simulations, the CMIP5 simulations have very good agreement in the three selected regions (Fig. 4d, h and l), except for a strong cooling (−1.4 • C decade −1 ) in the Antarctic lower stratosphere in the GISS_E2-R simulation (Fig. 4l) and a strong warming (0.7 • C decade −1 ) in the tropical upper troposphere in the IPSL_CM5A-LR (Fig. 4h).The trend range in the stratospheric Arctic and Antarctic zone among the CMIP5 models is significantly reduced; these results imply that the uncertainty in the CMIP5 models has improved, especially in the stratosphere.
Furthermore, the vertical profile of the ensemble mean and spread shows (Fig. 5) that there is a clear difference among the three regions in the vertical trend structure (Fig. 5a-d) and the ensemble spreads (Fig. 5e-h).First, in the radiosondes, the strongest positive trends appear in the lower tropospheric Arctic zone and the negative trends occur in the tropical middle stratosphere (Fig. 5a).In contrast, in the reanalyses, the whole atmospheric layer in the Antarctic shows a cooling, with the coldest trend occurring in the lower stratosphere (Fig. 5b).The tropospheric vertical trend profile in the Antarctic looks reasonable in the CMIP3 simulations (Fig. 5c) but the stratospheric cooling is much higher than in the radiosonde and reanalysis data sets.In the CMIP5 simulations, the vertical trend structure in the Antarctic is slightly improved, but the upper tropospheric warming exceeds the other three data groups (Fig. 5d).Second, the crossover point that expresses the transition from tropospheric warming to stratospheric cooling is largely different in the tropics.The crossover point in the CMIP3 and CMIP5 simulations occurs near 100 hPa, which is higher than in the radiosondes and reanalyses.The high crossover point is likely related to an overestimation of convective activity over the tropical areas in both the CMIP3 and CMIP5 models.
Finally, the ensemble spread among the radiosondes (Fig. 5e) remains nearly constant near ∼ 0.1 • C decade −1 from the troposphere to the stratosphere, except for the lower stratosphere in the Antarctic.However, in the reanalyses, the ensemble spread (Fig. 5f) increases substantially with height, reaching a maximum value of 0.6 • C decade −1 in the tropical lower stratosphere.The large ensemble spread mainly is due to overestimation of the cooling in both the NCEP-R1 and NCEP-R2 around 100 hPa and the warming in the 20CR, ERA40, and JRA25.Note that the uncertainty of the trend in the Antarctic is much larger than the Arctic in the stratosphere.In the CMIP3 simulations, the trends (Fig. 5g) show a substantial spread with 0.8 • C decade −1 in the Antarctic stratosphere.The spread at both poles is significantly reduced in the CMIP5 simulations (Fig. 5h).It is worth noting that the spread in the tropics retains similar values in the CMIP3 and CMIP5 simulations.This result implies that the uncertainty in the CMIP5 simulations over the Arctic and Antarctic has significantly improved compared to the CMIP3 simulations.In summary, the CMIP5 model trend uncertainty in the Arctic and Antarctic zones in the stratosphere is improved compared to the CMIP3 models.The crossover point in the CMIP3 and CMIP5 simulations occurs near 100 hPa, which is higher than in the radiosonde and reanalysis data sets.The result is likely related to overestimated convective activity over the tropical areas in both the CMIP3 and CMIP5 models.

Summary
Temperature trends were analyzed for four data groups (radiosonde, reanalysis, CMIP3 and CMIP5) over the period 1979 through 2005 and at levels between 850 and 30 hPa, and the results are summarized as follows: 1.The temperature trends show a noticeable discrepancy in the four data groups, although similarities can be observed.Most of the data sets exhibit a sharp cooling (∼ −1.0 • C decade −1 ) in the tropical and subtropical stratosphere and a strong warming (∼ 0.6 • C decade −1 ) in the lower troposphere in the northern middle and high latitudes and the tropical upper troposphere.The CMIP5 simulations display a relatively strong cooling in the tropical and subtropical stratosphere, which matches the distribution in the radiosonde observations.
2. Similar to the CMIP3, CMIP5 models overestimate the tropospheric warming and underestimate the stratospheric cooling.The eight CMIP5 simulations show not only the largest tropospheric warming, but also the largest uncertainty in the estimated temperature trend.The uncertainty in the CMIP5 simulations has improved in the stratosphere but is worse in the troposphere compared to the CMIP3 simulations.
3. The tropospheric warming is overestimated in the tropics in the Southern Hemisphere by the CMIP3 and CMIP5 simulations compared to the radiosonde observations.The reanalyses show a large uncertainty in the estimated trends in the lower tropical stratosphere, and the CMIP3 simulations show a large uncertainty in the Arctic and Antarctic stratosphere.
4. The trend uncertainty in the stratospheric Arctic and Antarctic zones among CMIP5 models has improved compared to the CMIP3 models.The crossover point in the CMIP3 and CMIP5 simulations occurs near 100 hPa in the tropics, which is higher than in the radiosonde and reanalysis data sets.The result is likely related to overestimation of the convective activity over the tropical areas in both CMIP3 and CMIP5 models.

Discussion
The results of this study appear to have achieved the two goals presented in Sect. 1, including (1) evaluation of the temperature trends in the CMIP5 simulations in comparison with radiosonde observations and reanalyses and (2) evaluation of the improvement of CMIP5 simulations compared to CMIP3.
1. Compared to the radiosondes, CMIP5 overestimates tropospheric warming, and the tropospheric warming shows significant differences in the different regions; for example, the CMIP5 simulation shows an extreme warming in the tropical upper troposphere in the IPSL_CM5A-LR compared to the other models.Meanwhile, it is worth noting that the trend range in the stratospheric Arctic and Antarctic zone among the CMIP5 models is significantly reduced.When the CMIP5 simulations are compared to reanalysis, we should note that although reanalysis is recognized as one of the best data sets for understanding atmospheric dynamic processes by previous studies, uncertainties exist in the reanalysis data sets, for example, the large discrepancy of the stratospheric cooling trend estimates in the 20CR and JRA25 reanalyses.In addition, the CMIP5 models have their own tropospheric variability that is not expected to exactly match past reanalysis in any detail.Some internal climate variabilities in the reanalysis data sets, such as El Niño/Southern Oscillation (ENSO) and Madden-Julian Oscillation (MJO), are not completely represented in the CMIP5 simulations, which might obscure the intercomparison.So we should consider how we can best use reanalysis products to help us to enable better evaluation of climate model simulations.
2. Compared to CMIP3, CMIP5 models are more comprehensive and are of higher spatial resolution compared to CMIP3.Five of the eight CMIP5 models show that their cooling trends exceed −0.50 • C decade −1 in the stratosphere, which is closer to the radiosonde observations than the cooling trends of the CMIP3 simulations.However, the CMIP5 simulations overestimate the tropospheric warming and underestimate the stratospheric cooling, although the stratospheric estimates have improved in comparison with the radiosonde observations.Note that all the selected CMIP5 models are coupled with land and ocean models including many kinds of physical processes focusing on the lower atmosphere, which is theoretically beneficial for describing the tropospheric atmosphere.Unfortunately, the above comparison shows that these CMIP5 model simulations provide a worse result in the troposphere for the global mean temperature trend.The results warn us to develop more comprehensive processes to reduce the uncertainty in model simulation in the troposphere.Meanwhile, it is necessary to improve representation of the stratosphere with higher vertical resolution and higher model tops, and/or with improved stratospheric chemical processes for improvement of simulation of stratospheric temperature trends.Given the differences noted, it remains an open question what the key factor(s) are that affect the performance of a climate model.

Fig. 1 .
Fig. 1.Vertical-latitudinal distribution of zonal mean temperature trends ( • C decade −1 ) from 1979 to 2005.Radiosondes: left panel; reanalyses: left middle panel; CMIP3 models: right middle panel; CMIP5 models: right panel.The dashed line with the value of ± 2.5 indicates the statistical significance t test at 99 % level.

( 3 )
Compared to the CMIP3 simulations, the CMIP5 simulations display a relatively strong cooling in the tropical and subtropical stratosphere, which matches the distribution in the radiosonde observations.(4) The height of the crossover point where tropospheric warming changes into stratospheric cooling depends on the individual data set, ranging from ∼ 100 hPa in the tropics to ∼ 200 hPa in the extratropics.

Table 1 .
Lists of the CMIP3 and CMIP5 model simulations.

Table 2 .
Global mean temperature trends in the stratosphere (50 hPa) and the troposphere (500 hPa) in the four data set groups.