The climatological storm-track activity simulated by 17 Intergovernmental Panel on Climate Change Fourth Assessment Report (IPCC AR4)/phase 3 of the Coupled Model Intercomparison Project (CMIP3) models is compared to that in the interim ECMWF Re-Analysis (ERA-Interim). Nearly half of the models show significant biases in storm-track amplitude: four models simulate storm tracks that are either significantly (>20%) too strong or too weak in both hemispheres, while four other models have interhemispheric storm-track ratios that are biased by over 10%. Consistent with previous studies, storm-track amplitude is found to be negatively correlated with grid spacing. The interhemispheric ratio of storm-track activity is highly correlated with the interhemispheric ratio of mean available potential energy, and this ratio is biased in some model simulations due to biases in the midlatitude temperature gradients. In terms of geographical pattern, the storm tracks in most CMIP3 models exhibit an equatorward bias in both hemispheres. For the seasonal cycle, most models can capture the equatorward migration and strengthening of the storm tracks during the cool season, but some models exhibit biases in the amplitude of the seasonal cycle.
Possible implications of model biases in storm-track climatology have been investigated. For both hemispheres, models with weak storm tracks tend to have larger percentage changes in storm-track amplitudes over the seasonal cycle. Under global warming, for the NH, models with weak storm tracks tend to project larger percentage changes in storm-track amplitude whereas, for the SH, models with large equatorward biases in storm-track latitude tend to project larger poleward shifts. Preliminary results suggest that CMIP5 model projections also share these behaviors.
The midlatitude storm tracks are marked by regions frequented by baroclinic waves and their associated surface cyclones (Chang et al. 2002). These storms bring with them strong winds and heavy precipitation, seriously affecting regional weather and climate. In addition, the storm tracks also transport large amounts of heat, momentum, and moisture poleward, and make up an important part of the global circulation. How the storm tracks may change under the warming climate is thus of huge societal interests. Current projections of how storm tracks may change are mainly based on predications made by climate models (e.g., Yin 2005; Ulbrich et al. 2008). Thus it is important to assess how well these models do in simulating the storm tracks under current climate conditions.
One fundamental property of the storm tracks is their climatological amplitude or activity. Heat and momentum transports by the storm tracks act as forcing on the large-scale circulation and participate in wave–mean flow interactions (e.g., Branstator 1992). Thus, biases in storm-track amplitudes in climate model simulations could impact model simulation of eddy forcing of, and feedback to, mean flow changes, and affect the time scale of model-simulated low-frequency variability (Lorenz and Hartmann 2001; Yang and Chang 2007). Such biases could in turn affect the sensitivity of the model’s response to external forcing (Gerber et al. 2008). While model deficiencies in current climate simulations need not necessarily give rise to similar deficiencies in simulations of future climate change (Ulbrich et al. 2008), it is still difficult to justify why one should expect that models that simulate significantly biased dynamics under current climate conditions will accurately project dynamical changes under global warming.
Our best knowledge of storm-track climatology and variability is based on the various atmospheric reanalysis datasets. With large numbers of in situ observations over the Northern Hemisphere (NH), NH storm-track amplitude agrees closely among the different reanalyses. However, Southern Hemisphere (SH) storm-track activity as computed based on two of the most popular datasets, the National Centers for Environmental Prediction (NCEP)–National Center for Atmospheric Research (NCAR; Kistler et al. 2001) and 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40; Uppala et al. 2005) reanalyses, differs by more than 20% (Guo and Chang 2008). Guo et al. (2009) made the first quantitative estimate of global storm-track activity based on observations alone using Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) radio occultation data (Anthes et al. 2008), and found that SH storm-track activity in NCEP–NCAR reanalysis is biased low by over 25% because of its assimilation of satellite-retrieved temperature data (Guo and Chang 2008), while that in ERA-40 is also biased low by 5%–10%. Their results suggested that storm-track activity derived from the more recent interim ECMWF Re-Analysis (ERA-Interim) data (Simmons et al. 2007) agrees closely with that derived based on COSMIC observations.
In this study, we will use storm-track activity derived from ERA-Interim data as the current best estimate to assess how well models that participated in phase 3 of the Coupled Model Intercomparison Project (CMIP3; Meehl et al. 2007) that were considered in the Intergovernmental Panel on Climate Change Fourth Assessment Report (IPCC AR4; Solomon et al. 2007) do in simulating storm-track activity. The data and methodology will be presented in section 2, and the results will be shown in section 3. As discussed below, we find some biases in model simulations, and in section 4 we will discuss several reasons that may have given rise to these model biases, as well as possible impacts of such biases. The conclusions will be presented in section 5.
2. Data and methodology
Many different quantities have been used to indicate storm-track activity (Chang et al. 2002). Guo et al. (2009) compared the variance of daily mean 300-hPa geopotential height (Z) derived from COSMIC radio occultation observations to the same quantity derived based on reanalysis data to assess whether there are biases in the reanalysis data. However, most CMIP3 models do not have daily Z in the archives. In this study, we will use variance computed based on daily 300-hPa meridional velocity (υ) as an indicator of storm-track activity (Chang and Fu 2002). The daily υ data is first filtered using a 24-h difference filter (Wallace et al. 1988):
This filter has peak response at a period of 2 days, and half-power points at 1.2 and 6 days, thus highlighting the synoptic time scale. Monthly mean variance of this quantity is then used to indicate the storm-track activity for each month:
The overbar in (2) represents time mean, usually over a month. These variances are first computed at each grid point, and hemispheric mean of the variance is then computed by averaging over all grid points between 20° and 70° latitude, weighted by the cosine of the latitude.
Six-hourly ERA-Interim data on a 1.5° × 1.5° lat–lon grid from 1980 to 1999 are used in this study. To facilitate comparisons with the CMIP3 models for which only daily values are available, daily averages are computed based on the 6-hourly data. Similar data taken from the National Aeronautics and Space Administration (NASA) Modern-Era Retrospective Analysis for Research and Applications (MERRA) reanalysis (Rienecker et al. 2011), ERA-40, and NCEP–NCAR reanalysis have also been analyzed for comparison. Daily mean 300-hPa υ data from 17 CMIP3 models1 (Table 1) from the last 20 years of the twentieth-century runs are examined. (Model details can be obtained from the Program for Climate Model Diagnosis and Intercomparison (PCMDI) CMIP3 climate model documentation web page: http://www-pcmdi.llnl.gov/ipcc/model_documentation/ipcc_model_documentation.php.) We have also examined future projections from 11 models (italicized in Table 1) based on the A2 (business as usual) scenario (Solomon et al. 2007). For models with several ensemble members, only one member has been examined. All model and reanalysis data are interpolated to the same T42 horizontal grid [~(2.8° × 2.8°)].
a. Storm-track amplitude
The geographical distribution of the climatological storm tracks, as indicated by the 20-yr average of υυ300 computed based on ERA-Interim data, is shown in Fig. 1a. In the NH, the Pacific and Atlantic storm tracks are clearly visible. The SH storm track forms a more or less continuous band across the hemisphere, with a peak over the Indian Ocean. Similar plots based on five CMIP3 models are also shown in Fig. 1 and they will be discussed later.
The zonal mean climatological storm-track distribution as a function of latitude is shown in Fig. 2. In the annual mean, the storm track in both hemispheres peaks around 50° latitude, and the SH storm track is stronger than the NH storm track in ERA-Interim data (black solid line) as well as in all CMIP3 models (gray dashed lines; see also Fig. 3c). Figure 2 shows that the storm-track amplitude (or strength) in CMIP3 models varies by nearly a factor of 2. In section 4a we will discuss factors that may contribute to such amplitude differences among the models.
The average NH storm-track amplitude, as indicated by the average of 20-yr mean υυ300 over 20°–70°N, is shown in Fig. 3a. In each panel of Fig. 3, the solid horizontal line represents the value computed from ERA-Interim data, while the dashed lines represent increments every 10% above or below this value. Models 1–17 correspond to the CMIP3 models listed in Table 1, while 18 corresponds to MERRA data, 19 for ERA-40, and 20 for NCEP–NCAR reanalysis.
From Fig. 3a, it is clear that the NH storm-track amplitude derived from the various reanalysis datasets are in close agreement with each other. Storm-track amplitudes found in MERRA and ERA-40 data are about 2% less than that based on ERA-Interim data, while those in NCEP–NCAR reanalysis data is about 5% weaker. These results suggest that NH storm-track activity during 1980–99 is likely to be within 5% of the value derived from ERA-Interim data.2
How about the storm tracks in the CMIP3 models? From Fig. 3a, we find that only three models have NH storm-track amplitude within 10% of that based on ERA-Interim data. Eleven models have the storm-track activity too weak, while three models have it too strong. These results are summarized in the fourth column of Table 1. In Table 1, a blank grid means that model results are within 10% of ERA-Interim. A plus sign (+) means model results are between 10% and 20% too strong, two plus signs (++) means 20%–30% too strong, a minus sign (−) means 10%–20% too weak, and so on.
Similar results for the SH storm track are shown in Fig. 3b. For the SH, the differences between the various reanalysis datasets are significantly larger. Storm-track activity in MERRA data is about 5% weaker than that in ERA-Interim, while that in ERA-40 is about 8% weaker, and that in NCEP–NCAR reanalysis data over 30% too weak. In addition, Guo et al. (2009) showed that the SH storm track in the older 15-yr ECMWF Re-Analysis (ERA-15) data is stronger than that found in ERA-40. Thus from ERA-15 to ERA-40 to ERA-Interim, the SH storm-track activity decreases and then increases, and the process does not seem to be converging. These results suggest that SH storm-track activity during 1980–99 may still be uncertain by 5%–10% or more, even though we regard that based on ERA-Interim as the current best estimate.
For the CMIP3 models, five models have their SH storm-track activity within 10% of that derived from ERA-Interim. Eight models have it too weak and four models have it too strong.
From Figs. 3a and 3b, it is apparent that not all models display the same bias in the two hemispheres, thus it is of interest to also examine the ratio of SH to NH storm-track activity. This ratio is shown in Fig. 3c. ERA-Interim gives a ratio of just over 1.4, while MERRA and ERA-40 give slightly smaller ratios. The ratio in NCEP–NCAR reanalysis data is more than 20% smaller because the SH storm track is biased weak.
For this quantity, results from most CMIP3 models fall within 10% of the value derived from ERA-Interim data. Only one model simulates a smaller ratio, and three models have the SH storm track being too active as compared to that in the NH.
These results are summarized in Table 1. Only two models [Commonwealth Scientific and Industrial Research Organisation Mark version 3.5 (CSIRO-Mk3.5) and ECHAM and the global Hamburg Ocean Primitive Equation (ECHO-G)] have all three quantities (the NH and SH storm-track amplitudes, as well as the SH to NH ratio) within 10% of the values derived from ERA-Interim data. The climatological storm-track distribution for ECHO-G is shown in Fig. 1b. For seven models, one or both storm tracks are either slightly (10%–20%) too weak [CSIRO Mark version 3.0 (CSIRO-Mk3.0), Geophysical Fluid Dynamics Laboratory Climate Model versions 2.0 and 2.1 (GFDL-CM2.0 and -CM2.1; see Fig. 1c), L’Institut Pierre-Simon Laplace Coupled Model, version 4 (IPSL CM4), and Meteorological Research Institute Coupled General Circulation Model, version 2.3.2 (MRI CGCM2.3.2)] or too strong [Canadian Centre for Climate Modelling and Analysis (CCCma) Coupled General Circulation Model, version 3.1 (CGCM3.1), both T47 and T63 versions], but the ratio between the two storm tracks still lie within 10% of that derived from ERA-Interim data. We can consider that these nine models provide somewhat adequate simulations of climatological storm-track activity.
The remaining eight models show significant biases in simulating storm-track activity. ECHAM5/Max Planck Institute Ocean Model (MPI-OM) (Fig. 1d) has both storm tracks 20%–30% stronger than those found in ERA-Interim data. The Goddard Institute for Space Studies Model E-H (GISS-EH), Centre National de Recherches Météorologiques Coupled Global Climate Model, version 3 (CNRM-CM3; Fig. 1e), and Institute of Numerical Mathematics Coupled Model, version 3.0 (INM-CM3.0) have both storm tracks over 20% weaker than those found in ERA-Interim. Nevertheless, for these four models, the ratios between the two storm tracks are still reasonable. The remaining four models have relative (SH–NH) storm-track activity that is biased by >10% as compared to ERA-Interim data. The Flexible Global Ocean–Atmosphere–Land System Model gridpoint version 1.0 (FGOALS-g1.0) has both storm tracks being significantly too weak, with the bias larger in the SH leading to a ratio that is biased low. GISS Model E-R (GISS-ER) again has both biased low, but the bias is larger in the NH, giving rise to a ratio that is biased high. The Model for Interdisciplinary Research on Climate 3.2, high-resolution version [MIROC3.2(hires)] simulates NH storm-track activity similar to that found in ERA-Interim, but SH activity is biased high, giving a ratio that is biased high. The GISS Atmosphere–Ocean Model (GISS-AOM; Fig. 1f) simulates SH activity similar to that found in ERA-Interim, but NH activity is significantly biased low, leading to a ratio that is biased high by over 20%.
b. Geographical distribution
Figures 1c–f show that while the storm tracks simulated by some CMIP3 models exhibit significant biases in their amplitudes, their spatial patterns are still quite reasonable. The pattern correlations of hemispheric (20°–70° latitude) storm tracks between individual models and the ERA-Interim are generally above 0.9 (14 out of 17 models for both hemispheres). The correlations between the multimodel ensemble mean and ERA-Interim are as high as 0.97 for both hemispheres.
Nevertheless, several models have pattern correlations that are 0.8 or below. For the SH, the pattern correlation between the storm track simulated by IPSL CM4 and that derived from ERA-Interim data is only 0.68, and is 0.74 for GISS-AOM. Difference maps between υυ300 derived from both models and that based on ERA-Interim show a prominent dipole in the SH (not shown), suggesting a significant equatorward bias in these models’ SH storm track. Inspection of Fig. 2 suggests that many of the CMIP3 models simulate SH storm tracks that show some equatorward biases.
Comparing the zonal mean storm-track profiles simulated by individual models to that derived from ERA-Interim, it is found that the profile differences are dominated by biases in the amplitude, latitude, and width of the simulated profiles. These can be expressed as follows:
In (3), φ is the latitude, ranging from 20° to 70° latitude; f(φ) is the latitudinal distribution of zonal mean υυ300 (weighted by cosφ to account for the variation in length of the latitude circles), with the subscript M denoting a value derived from a model, while the subscript EC denotes a value based on ERA-Interim data. The first term on the RHS corresponds to a relative amplitude bias (δA is equal to the fractional difference between the model’s storm-track amplitude and that in ERA-Interim), the second corresponds to a latitudinal shift,3 and the third term corresponds to change of shape (broadening/narrowing if the structure of f resembles those shown in Fig. 2) of the storm track. Given fEC(φ), the derivatives required for (3) can be computed based on centered differencing. Using multiple linear regression, the parameters δA, δφ, and B can be derived for each model for the NH and SH storm tracks separately.
The values of δA derived based on this technique are nearly identical to those computed based on the ratios between the hemispheric mean υυ300 (Figs. 3a,b; correlations between these values and δA across the models are over 0.99). Hence here we will focus on δφ. These are shown in Figs. 4a and 4b for the NH and SH, respectively. For the SH (Fig. 4b), more than half of the models (9 out of 17) show an equatorward (positive) bias of more than 1° latitude, with the largest biases of over 5° given by the IPSL CM4 and GISS-AOM models. Only two models (the two CSIRO models) show a poleward (negative) shift of more than 1°.
For the NH (Fig. 4a), 13 of the 17 models show an equatorward (negative) bias of more than 1°, and none of the models show a poleward bias of more than 1°. The model with the lowest pattern correlation with ERA-Interim (INM-CM3.0; pattern correlation equals 0.80) also has the largest equatorward bias (−5°).
What leads to the different latitudinal biases in the model storm tracks is still an open question (Kidston and Gerber 2010) and needs further studies. Across the CMIP3 ensemble, the correlation between NH and SH δφ is −0.46 (significant at 90%), suggesting that there is a weak tendency for models to have both storm tracks biased in the same direction (poleward or equatorward at the same time). A similar but stronger tendency has also been found in our preliminary analyses of storm-track data derived from 16 CMIP5 models (correlation between NH and SH δφ equals −0.72).
Note that for (3), the third term involving B is generally not important in the regression (i.e., inclusion of this term does not change the regressed values of δA and δφ significantly). It is included here for the purpose of completeness since it turns out that in fitting storm-track variations over the seasonal cycle [see Eq. (4) in next subsection], inclusion of this term greatly improves the quality of the regression, especially for the SH storm track, since the SH storm track is significantly narrower during SH summer [December–February (DJF)].
In the NH Atlantic, the storm track has a distinct southwest–northeast tilt (Fig. 1a). The model storm tracks are generally too zonally oriented in most CMIP3 model simulations (see Fig. 1; see also Ulbrich et al. 2008). This tendency shows up in the model ensemble mean, and is most prominent for INM-CM3.0, which is another reason contributing to its low pattern correlation with ERA-Interim in the NH. Among all the models, this model has the lowest pattern correlation (0.76) with ERA-Interim over North Atlantic and Europe (20°–70°N, 90°W–30°E).
c. Seasonal cycle
Over the seasonal cycle, the storm track migrates equatorward and is broader during the cool season, and shifts poleward and becomes narrower during the summer (see, e.g., Trenberth 1991). The storm track is generally stronger during winter than summer due to enhanced baroclinicity in winter. Equation (3) can be modified to estimate the latitudinal shift and amplitude change over the seasonal cycle, as follows:
In (4), fAnn corresponds to the annual mean zonal mean storm-track distribution for ERA-Interim (or any CMIP3 model), while fSeason corresponds to the same distribution for an individual season. As mentioned above, including the third term on the RHS of (4) to represent variations in storm-track shape significantly improves the quality of the fit because of change in storm-track width between winter and summer. However, note that direct comparison of the fitted values of B between different models is not very meaningful, since the fitted value of B is quite sensitive to the shape of the annual mean profile and the storm tracks simulated by different models have slightly different shapes. Here we will focus on latitudinal shift and change in normalized amplitude (normalized by the annual mean amplitude for each model) across the seasons.
The fits for δφ are shown in Figs. 5a and 5c, while those for seasonal change in normalized amplitude are shown in Figs. 5b and 5d. It is clear that the NH storm track undergoes a seasonal cycle that is larger than its SH counterpart. The models generally do a relatively decent job in capturing this seasonal cycle, with the multimodel ensemble mean (gray dashed curve) closely following the seasonal cycle exhibited by ERA-Interim (black solid line). Individual models do show some biases. For example, the NH storm track in FGOALS-g1.0 shows very little latitudinal migration over the year (Fig. 5a, small asterisks), as well as an exaggerated winter to summer contrast in normalized amplitude (Fig. 5b). Both storm tracks simulated by CNRM-CM3 (small filled circle) display an exaggerated winter to summer contrast in amplitude (Figs. 5b,d), while GISS-EH (small filled triangles) and GFDL-CM2.1 (small “x”) display exaggerated seasonal cycles in NH storm-track amplitudes and latitudinal migrations (Figs. 5a,b).
The models also do a decent job in capturing the midwinter suppression of NH Pacific storm-track activity (Nakamura 1992), with 15 of the 17 models showing a clear relative minimum either in January or February (not shown) and the remaining two models showing nearly constant NH Pacific storm-track activity over the entire cool season.
In section 3a, we found that 8 out of the 17 CMIP3 models that we examined simulate storm-track amplitudes that are significantly biased compared to ERA-Interim data. In this section we will explore some factors that may have given rise to such biases, as well as possible implications of such biases.
a. Storm-track amplitude
As discussed above, four CMIP3 models have large biases in storm-track amplitudes, with three models simulating storm tracks that are significantly too weak in both the NH and SH, and one model having them both too strong. Previous studies (e.g., Kageyama et al. 1999; Boville 1991; Senior 1995) have suggested that biases in storm-track amplitudes in GCM simulations may be mainly due to horizontal resolution, with low-resolution models simulating storm-track amplitudes that are systematically too low. From Table 1, we see that lower-resolution models do frequently have weak storm tracks (e.g., GISS-EH, GISS-ER, and INM-CM3.0). In Fig. 6, the hemispheric averaged υυ300 for CMIP3 models is plotted as a function of model horizontal grid spacing (using an average of the longitude and latitude grid size). The correlation between model grid spacing and NH υυ300 is −0.51 (with an R2 value of 26%), while the correlation between grid spacing and SH υυ300 is −0.44 (R2 equals 19%), with the former significant at the 95% level and the latter at the 90% level based on a Student’s t test. From Fig. 6, we can see that lower-resolution models do not always have weaker storm tracks, as ECHO-G (Fig. 1b) is a lower-resolution model that has reasonable storm-track amplitude. Meanwhile, higher-resolution models do not necessarily have stronger storm tracks. For example, CNRM-CM3 is a higher-resolution model that simulates very weak storm tracks. Models with the same horizontal resolution (e.g., T63) can have storm tracks that are either significantly too strong (ECHAM5/MPI-OM; see Fig. 1d) or too weak (CNRM-CM3; see Fig. 1e). Since horizontal resolution can only explain less than 30% of the variance in υυ300, it does not seem to be the only (or perhaps even primary) controlling factor of model simulated storm-track amplitude.
Since storm tracks are made up of baroclinic waves, one would expect storm-track activity to depend on the midlatitude baroclinicity. O’Gorman and Schneider (2008) performed a series of idealized model experiments and found that over a wide range of climates with varying equator-to-pole temperature differences, the average eddy kinetic energy in each model simulation is nearly linearly proportional to the dry mean available potential energy (dry MAPE). O’Gorman (2010) also showed that the dry MAPE works about as well as the MAPE that includes the effects of moisture in scaling with eddy kinetic energy (EKE) over the seasonal cycle. Hence in Figs. 7a and 7b we have plotted υυ300 against dry MAPE for each hemisphere, computed based on the climatological zonal mean temperature profile between 925 and 250 hPa from 30° to 60° latitude. We have also tried computing MAPE centered at the latitude of maximum poleward heat flux at 700 hPa but the results do not improve the correlation.
From Figs. 7a and 7b, we can see that model-based MAPE shows a large spread, with many models showing significantly larger MAPE compared to that derived based on ERA-Interim. However, υυ300 in neither hemisphere shows any significant correlation with MAPE. Recall that O’Gorman (2010) showed that projected change in MAPE under global warming scales well with projected change in EKE across 11 CMIP3 models. We believe that our results are not inconsistent with his, since O’Gorman compared projected percentage (or relative) change in MAPE versus EKE instead of the absolute magnitude of such quantities across models as we attempt to do in Figs. 7a and 7b. See Fig. 7c and discussions in the next subsection.
Currently it is not clear what else, apart from horizontal resolution, gives rise to the biases in the storm-track strength, but model formulation (Greeves et al. 2007) and model physical parameterizations are other possible contributing factors. For the models that simulate both storm tracks that are significantly too weak or too strong, we have also examined the unfiltered variance of 300-hPa υ and found similar biases. Thus in these models, the bias in eddy activity is not only limited to synoptic-scale eddies but is also found for all transient eddies. Hence we hypothesize that these models are either too dissipative or not sufficiently dissipative, with the differences in dissipation among the models obscuring the impact of the variations in MAPE among the models, such that the linear relationship between the absolute magnitude of storm track and MAPE is not found.
b. Interhemispheric storm-track ratio
Four models have SH to NH storm-track ratios that are biased by more than 10% (Fig. 3c). Here we will explore what controls the interhemispheric ratio of storm-track activity and thus what may have given rise to these model biases.
As discussed above, we have found that υυ300 and MAPE do not significantly correlate with each other across CMIP3 models and we hypothesize that this is due to differences in dissipation among the models obscuring the impact of variations of MAPE. To eliminate (or reduce) the impact of the model differences in dissipation, we correlate the SH to NH ratio of MAPE with the SH to NH ratio of storm-track activity (quantity shown in Fig. 3c), and their relationship is shown in Fig. 7c. The correlation between these two quantities is 0.79 (R2 equals 63%), significant at the 99.9% level. These results are consistent with those of O’Gorman (2010) that relative change in EKE is well correlated with relative change in MAPE.
Examining Fig. 7c in more detail, we can see that the model with the largest ratio in SH to NH MAPE (GISS-AOM) also gives the largest ratio in SH to NH storm-track activity, while the model with the smallest ratio in MAPE (FGOALS-g1.0) also has the smallest ratio in SH to NH storm-track activity. To see why there are such biases in the MAPE, we further examine the temperature gradient at 700 hPa, which correlates significantly with MAPE (r of 0.8 or above). For GISS-AOM, the temperature gradient in the SH is the largest among the 17 models and is about 9% higher than that found in ERA-Interim, while the NH temperature gradient is slightly (~5%) larger than that in ERA-Interim, giving rise to a SH to NH temperature gradient ratio of 1.14, the largest among all CMIP3 models and larger than that found in ERA-Interim. For FGOALS-g1.0, the SH temperature gradient is about 15% smaller than that found in ERA-Interim, while the NH temperature gradient is about 6% higher than ERA-Interim, giving rise to a SH to NH temperature gradient ratio that is about 20% smaller than the ratio found in ERA-Interim. Thus it appears that biases in model simulated lower tropospheric temperature gradients go a long way in explaining model biases in MAPE. What gives rise to such biases is of interest, and it would be useful to examine Atmospheric Model Intercomparison Project (AMIP)-type experiments made with prescribed sea surface temperature based on the same group of models to see whether these biases arise due to model errors in atmosphere–ocean coupling.
c. Biases in eddy momentum and heat fluxes
Up to now, we have focused on assessing model simulation of υυ300, which is part of the eddy kinetic energy. Interactions between baroclinic waves and the large-scale, low-frequency circulation are more closely related to eddy momentum flux than to eddy kinetic energy (e.g., Chang 1996; Lorenz and Hartmann 2001). Since eddy kinetic energy and eddy momentum flux are associated with the same baroclinic waves, eddy momentum flux is expected to have similar biases as those displayed by the eddy kinetic energy. Hence we have also compared eddy momentum flux simulated by CMIP3 models with that derived from ERA-Interim data.
To highlight momentum transport by eddies of synoptic time scale, the 24-h difference filter is again employed. The eddy momentum flux is defined as
In (5), an overbar again denotes time mean, and φ is the latitude.
The climatological (1980–99) 300-hPa zonal mean eddy momentum flux based on ERA-Interim data is shown as the black solid line in Fig. 8. It can be seen that poleward eddy momentum fluxes dominate in both hemispheres, peaking at around 40° latitude. The same fluxes computed from the 17 CMIP3 models are shown as gray dashed lines. Similar to υυ300 (Fig. 2), eddy momentum flux also displays a large spread among the models. As expected, there is significant correlation between the amplitude of υυ300 and uυ300 simulated by each model. In Fig. 8, we also show the average of uυ300 from the three models with the strongest global mean υυ300 [ECHAM5/MPI-OM, CGCM3.1(T47), and CGCM3.1(T63); black dashed line], as well as the average from the three models with the weakest υυ300 (CNRM-CM3, INM-CM3.0, and FGOALS-g1.0; black dotted line). It is clear that the models with stronger υυ300 also have significantly stronger poleward eddy momentum fluxes. In fact, the correlation between hemispheric mean υυ300 and the maximum value of zonal mean poleward eddy momentum flux near 40° latitude for the 17 CMIP3 models is 0.73 for the SH and 0.69 for the NH.
We have also examined model simulations of the 700-hPa poleward eddy heat flux. The amplitude of maximum zonal mean eddy heat flux in CMIP3 model simulations correlates significantly with that of υυ300 (0.57 and 0.68 for NH and SH, respectively) and uυ300 (0.75 and 0.73), suggesting that the biases in all eddy quantities are closely related. Poleward heat flux and MAPE only correlate weakly (0.47 in the NH and 0.04 in the SH, both not significant at the 95% level), while the correlation between the ratios of SH to NH poleward heat flux and SH to NH MAPE is much higher (0.77), again suggesting that the effect of differences in model dissipation plays a significant role in determining the absolute magnitude of eddy fluxes for individual models.
Similar to υυ300, the amplitude of uυ300 is also significantly correlated with mean grid spacing. The correlation between the maximum value of poleward eddy momentum flux and grid spacing is −0.58 for the SH and −0.73 for the NH. Thus, higher-resolution models (smaller grid spacing) generally have stronger poleward eddy momentum flux. Held and Phillipps (1993) suggested that eddy momentum fluxes are more sensitive to meridional resolution. We correlated the magnitude of eddy momentum fluxes with meridional grid spacing and found slightly lower values than those based on the mean grid spacing. Note that 10 of the 17 models use spectral triangular truncation that is isotropic in latitude and longitude (Table 1). Similar correlations are also found between poleward heat flux and grid spacing but are weak (−0.35 and −0.27 for the SH and NH, respectively, both not significant at the 95% level).
d. Possible impacts of model biases
So far we have presented results that suggest that many CMIP3 models show biases in simulating the amplitude of storm-track activity, including eddy energy and eddy fluxes. Since eddy fluxes are essential in eddy interactions with the large-scale flow (e.g., Lorenz and Hartmann 2001; Branstator 1992), one may argue that if a model does not simulate eddy fluxes correctly, one should not expect it to be able to accurately simulate wave–mean flow interactions and thus may also have biases in its simulation of the large-scale climate. Alternatively, one could also argue that biases in model simulations of eddy fluxes reflect model deficiencies in their simulations of the mean climate. However, with all the complexities and nonlinearity involved in climate simulations, it is generally hard to pinpoint how a model’s biases in eddy energy and fluxes in particular, and biases in its climatology in general, may impact its climate response. Nevertheless, several studies (e.g., Kidston and Gerber 2010; Barnes and Hartmann 2010) have suggested that biases in a model’s climatological latitude of the midlatitude jet could have significant impacts on the model jet’s response to global warming as well as its variability. In our preliminary analyses, we have also come across several interesting correlations that may indicate the impact of a model’s biases in storm-track simulations on its response to external forcing.
The first is a negative correlation between the model’s climatological storm-track amplitude and its magnitude of seasonal cycle of normalized storm-track amplitude. The seasonal cycle of normalized storm-track amplitude has been shown in Figs. 5b and 5d. While the multimodel mean (gray dashed line) displays a seasonal cycle that closely follows that given by ERA-Interim data (black solid line), we have noted that some individual models show biases in the magnitude of the seasonal cycle. The magnitude of the seasonal cycle (or the magnitude of winter to summer contrast) of normalized storm-track amplitude is defined by subtracting the normalized amplitude in summer [see Figs. 5b,d: June–August (JJA) for the NH, DJF for the SH] from its value in winter (DJF for the NH, JJA for the SH). This value is plotted against the model’s climatological annual mean storm-track amplitude (quantities shown in Figs. 3a,b) in Figs. 9a and 9b for the NH and the SH, respectively.
Figures 9a and 9b show that CMIP3 models having climatological storm-track amplitudes that are biased weak tend to have large amplitudes in its seasonal cycle of normalized storm-track amplitude. The correlation between these two quantities is −0.81 for the NH and −0.64 for the SH, both significant at the 99% level.
Furthermore, a weak but significant negative correlation is found between a model’s climatological storm-track amplitude in the NH and its response to global warming forcing in terms of projected percentage change in the NH storm-track amplitude. We have examined CMIP3 model response to increasing greenhouse gas forcing based on the A2 scenario. Eleven of the 17 models (indicated by italicized model names in Table 1) provide daily data for 2081–2100. The percentage change in storm-track amplitude between 1981–2000 and 2081–2100, in terms of hemispheric mean υυ300, is plotted against the climatological storm-track amplitude (1981–2000) for each model in Figs. 9c and 9d for the NH and SH, respectively. Models having weak storm tracks tend to project larger percentage change in storm-track amplitude. For the NH, the correlation between climatological storm-track amplitude and projected percentage change is −0.53, significant at the 90% level, while the correlation for the SH is −0.35 and is not statistically significant. Similar correlations have also been found in our preliminary analyses of projected storm-track changes based on 16 CMIP5 models under the Representative Concentration Pathway (RCP)-8.5 scenario, with a correlation between climatological storm-track amplitude and projected percentage change in storm-track amplitude4 being −0.54 for the NH (significant at the 95% level) and −0.23 for the SH (not significant) respectively.
It is currently not clear what the physical link is between a model’s climatological storm-track amplitude and its seasonal cycle and projected change in storm-track amplitude. These correlations may not necessarily indicate causality, but may be indicative of some model physics or dynamics that simultaneously affect these quantities.
Kidston and Gerber (2010) found that for 11 CMIP3 models, a model’s bias in its climatological latitude of the SH jet (as defined by the maximum in surface wind) is significantly negatively correlated with its projected SH jet shift under global warming, such that models displaying large equatorward biases in the climatological jet latitude tend to project larger poleward shifts under global warming. Given that surface winds can only be maintained against friction by eddy momentum fluxes, we expect that the jet latitude is strongly tied to the latitude of the storm track, and indeed the correlation between SH storm-track and jet latitudes across the CMIP3 multimodel ensemble is 0.92. We have examined whether a similar relationship to that found by Kidston and Gerber (2010) also holds between a model’s climatological storm-track latitude and its projected storm-track shift under global warming. The correlation is −0.60 (significant at the 95% level; see Fig. 10) in the SH, consistent with the results of Kidston and Gerber (2010). For the NH, the correlation is only −0.15. Again, similar results are found in our preliminary analyses of 16 CMIP5 models (r = −0.53 and −0.14 for the SH and the NH, respectively).
The amplitude of storm-track activity is a fundamental quantity in the global circulation. A recent study (Guo et al. 2009) has shown that among the various reanalysis datasets, storm-track activity computed from ERA-Interim data is most consistent with that derived from observations. In this study, we compare the climatological storm-track activity (measured by 24-h difference filtered meridional velocity variance at 300 hPa) as simulated by 17 IPCC AR4/CMIP3 models to that based on ERA-Interim data to assess how well these models do.
In terms of storm-track amplitudes, our results show that only 2 of the 17 models have both the NH and SH storm-track activity within 10% of that based on ERA-Interim. Seven models simulate one or both storm tracks that are either slightly (10%–20%) stronger or slightly weaker than those in ERA-Interim, but the interhemispheric storm-track ratio is unbiased. Four models simulate storm tracks that are either both significantly (>20%) too strong or too weak. Previous studies have suggested that GCM simulated storm-track amplitude depends strongly on horizontal resolution. Our results show that while model storm-track amplitude is negatively correlated with model grid spacing, lower-resolution models do not necessarily have weaker storm tracks, while higher-resolution models can also have storm tracks that are very weak, suggesting that horizontal resolution may not be the only (or perhaps even primary) factor controlling the amplitude of model simulated storm tracks. The remaining four models have storm-track activity ratios that are biased by more than 10%. We find that the SH to NH ratio of storm-track activity is highly and positively correlated with the SH to NH ratio of mean available potential energy (MAPE), and that this ratio is biased in some model simulations due to biases in midtropospheric temperature gradients.
The geographical pattern and seasonal cycle of model-simulated storm tracks have also been investigated. Our results show that the storm tracks in most CMIP3 models exhibit an equatorward bias in both hemispheres. For the seasonal cycle, most models can capture the equatorward migration and strengthening of the storm tracks during the winter season. Nevertheless, some models exhibit biases in the amplitude of the seasonal cycle.
We have also examined model simulated eddy momentum and heat fluxes, and our results show that models having a strong (weak) bias in storm-track activity also have a strong (weak) bias in poleward eddy momentum and heat fluxes, suggesting that wave–mean flow interactions may not be accurately simulated by these models.
Preliminary investigations have been conducted on the possible implications of model biases in storm-track climatology. We find that there is significant negative correlations between model climatological storm-track amplitude and the magnitude of the seasonal cycle in normalized storm-track amplitude for both hemispheres, such that models with weak storm tracks exhibit a larger percentage change in storm-track amplitude over the seasonal cycle. In addition, for the NH, we find a negative correlation between a model’s climatological storm-track amplitude and its projected percentage change in storm-track amplitude, such that models with weak NH storm tracks tend to project a larger percentage increase in NH storm tracks between 1981–2000 and 2081–2100 under the A2 scenario. In the SH, there is a significant negative correlation between a model’s bias in storm-track latitude and its projected shift in storm-track latitude under global warming, such that models with large equatorward (positive) biases tend to project larger poleward (negative) shifts under global warming, consistent with the results of Kidston and Gerber (2010). Our preliminary analyses of Fifth Assessment Report (AR5)/CMIP5 model data suggest that CMIP5 model simulations also exhibit somewhat similar behaviors between biases in a model’s storm-track climatology and its projected change under global warming. Currently, it is not known what physical mechanisms may have given rise to such correlations. With a lot more data and many more experiments available under CMIP5, detailed diagnoses will be conducted to further examine these phenomena.
In this study, we have compared climatological storm-track activity simulated by CMIP3 models with that derived from reanalysis data. Wave–mean flow interactions depend not only on the climatological amplitude of eddy variance and covariance statistics, but also on how these statistics change in conjunction with changes in the low-frequency flow. In a separate study we will examine whether the relationship between storm track and mean flow variations in climate model simulations is consistent with that derived from reanalysis data.
The authors thank the comments made by three anonymous reviewers. The authors would also like to thank ECMWF, NASA, and NOAA for making their reanalysis data available. The CMIP3 and CMIP5 model data were obtained from the PCMDI data archives. This work is partially supported by NOAA Grants NA06OAR4310084 and NA11OAR4310081, and NSF Grant ATM0757250.
Based on the standard deviation (std) of the year-to-year variability of storm-track amplitude computed from 32 years of ERA-Interim data, the uncertainty of the 20-yr mean amplitude (95% confidence level equals 2.1 times the std divided by ; note that year-to-year lagged correlation is not significant and each year is assumed to be independent) is less than 2%. This is consistent with the variations of storm-track amplitude among five runs made using the GFDL-CM2.1 model.
If the model storm track has the same shape as that derived from ERA-Interim data except that its amplitude is increased by δA and its latitude is shifted northward by δφ, then fM(φ) = (1+δA)fEC(φ − δφ), and the first two terms of the Taylor’s expansion give the first two terms on the RHS of (3). See also the appendix in Lu et al. (2010). We have also estimated latitude bias by fitting f(φ) using a cubic polynomial near its peak. The values obtained are consistent with those estimated using Eq. (3) (correlation over 0.95).
For CMIP5 models, storm-track amplitude is defined by variance of 24-h difference filtered meridional velocity at 250 hPa, since 300-hPa level data are not available.