Annual and semiannual cycles of midlatitude surface temperature and baroclinicity : reanalysis data and AOGCMs simulations

Reviewer #1 The authors investigate the annual and semiannual cycles of atmospheric near surface temperature and baroclinicity (maximum Eady growth rate) in midlatitudes. They analyze the statistical relationship between the two quantities, and assess the ability of CMIP3 and CEMIP5 models to reproduce properties derived from ERA Interim reanalysis. The results show high coherence between the two variables for both the annual and the semiannual cycle, but with different relative phases. The CMIP models show good agreement with reanalysis for coherence at annual and semiannual frequency. For relative phase at semiannual frequency larger differences between models and reanalysis and among the models are observed. Improvements for CMIP5 models compared to CMIP3 are found.


Introduction
The seasonal cycle of the heating of the atmosphere to which contributes mostly the upward energy fluxes from the surface (i.e., longwave, latent and sensible heat fluxes) and to a lesser extent the direct shortwave absorption, is one of the most prominent features of the Earth's climate (e.g., Kiehl and Trenberth, 1997;Trenberth and Stepaniak, 2004).A recent study by Donohoe and Battisti (2013) suggested that while the annual average heating is dominated by upward energy fluxes from 5 the surface, most of the seasonal heating is due to the shortwave absorption within the atmosphere that is quite constant throughout the troposphere.This would be explained by the fact that in the annual cycle the insolation transmitted to the surface goes primarily into storage (especially over the ocean) and the atmosphere is heated from below.It is estimated that the variation of solar insolation, due to the orbital movement of the Earth around the Sun, accounts for about 90 % of the total variance of surface temperature (Trenberth, 1983).10 Observations show that at midlatitudes the annual harmonic is by far the largest component of the seasonal cycle, while other sub-harmonics capture only the finer structure of the cyclic variation.Approaching the equatorial regions, the seasonal cycle has a more complicated behavior and the annual and semiannual harmonics are both large components.The semiannual signal characterizes also high-latitude regions.Furthermore, there are observed differences in the seasonality of atmospheric temperature and eddy activity between the Northern and Southern Hemispheres (hereafter NH and SH), with the NH 15 exhibiting stronger seasonal variation due to the larger portion of land surface (Peixoto and Oort, 1992).
Since the first efforts on the climate impact of increasing atmospheric carbon dioxide (Hansen et al., 1981), surface temperature is taken as a proxy in climate change studies.Moreover, due to its decorrelation length (about 1200 km; Hansen and Lebedeff, 1987) and the key role in radiative transfer, it is considered a useful variable for studying large-scale processes and climate sensitivity.Large-scale seasonal variability of surface temperature has been successfully simulated in earlier 20 energy balance models (EBMs), with "passive" ocean and atmospheric heat transports parameterized as a diffusive process (e.g., North et al., 1983;Kim and North, 1992).The simulation of the seasonal cycle of near-surface air temperature has long been considered a test of performance of climate models (Covey et al., 2000).The ability of coupled General Circulation Models (GCMs) to simulate a reasonable seasonal cycle is, in fact, a necessary condition for confidence in their prediction of long-term climatic behavior, including global changes (e.g., Bye et al., 2013).Furthermore, the amplitude of the seasonal 25 cycle in surface temperature has been used to verify the climate sensitivity of models (Lindzen et al., 1995;Knutti et al., 2006), and the magnitude of the seasonal cycle has been found to be a good predictor of the magnitude of decadal variability in regional surface temperatures (Huybers and Curry, 2006).
The seasonal cycle is also the main modulator of weather variability at midlatitudes.It is well known that transient eddies, which transport heat and momentum in the extratropics, are generated by the horizontal temperature gradient in the mean 30 flow through a process of energy conversion from available potential to kinetic.Such a temperature gradient (often referred to as baroclinicity) is the basis for eddies' development in linear instability theories, nonlinear models of geostrophic turbulence, and observations (e.g., Lindzen and Farrell, 1980;Held and Larichev, 1996;Hoskins and Valdes, 1990).Several Earth Syst.Dynam. Discuss., doi:10.5194/esd-2016-28, 2016 Manuscript under review for journal Earth Syst.Dynam.Published: 14 July 2016 c Author(s) 2016.CC-BY 3.0 License.
analyses have pointed out that there are regions of enhanced eddy activity, where weather systems preferentially grow through baroclinic instability and subsequently decay, which are referred to as storm tracks.In NH, such regions lie downstream, and slightly poleward, of the cores of the jet stream over the North Atlantic and Pacific Oceans (e.g., Blackmon et al., 1977).It has also been shown that, like most of atmospheric processes, baroclinic activity is characterized by a seasonal cycle.Previous studies, in fact, provided evidences for some kind of midwinter suppression of baroclinic wave 5 activity in the NH Pacific, with large variances during spring and autumn (see Nakamura 1992 and references therein).This finding was supported by the harmonic analysis of air temperature and sea level pressure fields carried out by Yashyayaev and Zveryaev (2001), by observations as illustrated by Chang (2003), or the recent study by Chen et al. (2012).
In SH midlatitudes, an important signature of the seasonal cycle is the Southern Hemisphere Semiannual Oscillation (SAO), a coupled ocean-atmosphere phenomenon that involves the different annual cycles of temperature between the Antartic polar 10 continent and the surroundings midlatitude oceans (van Loon, 1967;Meehl, 1991).The twice-yearly intensification of temperature gradient between midlatitudes (ocean dominated) and polar latitudes (continental) is associated with a fluctuation in the storm activity.
The persistent character of these regional features in both hemispheres suggests that some processes are acting on the system to self-sustain the storm tracks, i.e. external forcing and/or feedback mechanisms.Thus, investigating the possible 15 relationship between baroclinicity and surface temperature seasonal cycles may help to better understand the role played by the latter (which is directly related to solar forcing and heat fluxes) in modulating the atmospheric processes at midlatitudes.Following Lorenz (1979), variations of weather and climate are forced or free according to whether they result from changes in the external conditions or not.Such a characterization is usually analyzed by examining the correlation between two variables of interest, for example the eddy heat fluxes and baroclinicity (e.g., Stone et al., 1982).20 In the present paper, the annual and semiannual harmonics of midlatitude surface temperature and baroclinicity in both hemispheres are studied by applying spectral analysis to ERA-Interim reanalysis and Coupled Model Intercomparison Project (CMIP) data.Furthermore, the relationship (coherency and relative phase) between surface temperature and baroclinicity, which is here estimated using the maximum Eady growth rate, is investigated.The aim is to assess the ability of coupled atmosphere-ocean general circulation models (AOGCMs) to properly reproduce the amplitude and phase of the 25 observed annual and semiannual periodicities that are of interest for seasonal forecasts.
The structure of the paper is as follows.Section 2 describes data and methods, while Section 3 provides a description of the main results obtained from spectral analysis.A summary and conclusions are given in the final section.

Data 30
Data used for the study are derived from (i) the ERA-Interim archive and (ii) the Coupled Model Intercomparison Project phase 3 (CMIP3) multi-model dataset, including the most recent phase 5 of the project (CMIP5) for comparison.
ERA-Interim (hereafter ERAI) is the latest global atmospheric reanalysis product delivered by the European Centre for Medium Range Weather Forecasts (ECMWF; Berrisford et al., 2011).The data assimilation system used to produce ERAI is based on the 2006 release of the Integrated Forecasting System (IFS) that includes a 4-dimensional variational analysis (4D-Var) with a 12-hour analysis cycle.In each cycle, all available observations (in situ measurements, radiosondes, satellites, etc.) are combined with prior information from the forecast model to estimate the evolving state of the atmosphere (Dee et 5 al., 2011).The model has T255 horizontal spectral resolution (~ 80 km) with 60 vertical levels from the surface up to 0.1 hPa.ERAI improved on several deficiencies reported in the previous reanalysis ERA-40, in particular the water cycle that was too wet in the tropics and breaks in the time series of some products that are likely related to the introduction of satellites into the assimilation scheme (Poli et al., 2010).
In the present study, monthly means of daily means of 2-meter temperature (T2m) and tropospheric temperature (T) covering 10 the period January 1979-September 2015, at 1-degree horizontal resolution and 8 vertical levels in the troposphere (from 1000 hPa to 300 hPa), are considered and analyzed.
Under the World Climate Research Programme (WCRP), the Working Group on Coupled Modelling (WGCM) established the CMIP as a standard experimental protocol for studying the outputs of coupled AOGCMs.The phase 3 multi-model dataset is here used: it accounts for historical climate reconstruction performed by models, from the pre-industrial era to the 15 beginning of the 21 st century (Meehl et al., 2007).The integration period, the radiative forcing parameterization and the horizontal resolution vary from model to model.Whatever is the model vertical resolution, a minimum number of pressure levels for vertical discretization of 3D atmospheric outputs is required to be 17 specified levels from 1000 to 10 hPa.For the present analysis 8 pressure levels from 1000 to 300 hPa are considered (see for details http://wwwpcmdi.llnl.gov/ipcc/model_documentation/ipcc_model_documentation.php).20 Based on the intraseasonal and interannual variability analysis at milatitudes carried out by Lucarini et al. (2007), for the purpose of the present study, a subset of 6 models over 27 were chosen (see Table 1).The selection has been made taking into account models' performance, when compared with reanalyses, and the horizontal resolution.For CMIP3, the subset comprises one high-resolution model (MIROC3.2),four medium-resolution models (CGCM3.1,ECHAM5/MPI-OM, FGOALS-g1.0,GFDL-CM2.1)and one coarse resolution model (INM-CM3.0).According to Lucarini et al. (2007), while 25 CGCM3.1,GFDL-CM2.1 and MIROC3.2high-resolution compare well with the reanalysis, ECHAM5/MPI-OM and FGOALS-g1.0have been found to overestimate both intraseasonal and interannual variability.INM-CM3.0 is here considered as an example of a coarse-resolution model.
Aiming to verify any improvement in the model representation of the features of interest, the most recent multi-model dataset CMIP5 has been also considered (Taylor et al., 2012; http://cmip-pcmdi.llnl.gov/cmip5/guide_to_cmip5.html).30 CMIP5 differs from earlier phases in the wider variety of scientific issues to be addressed, the larger number of models participating into the project, the generally higher spatial model resolution, a richer set of output fields archived, and the two time scales of the experiments (i.e., long-term and near-term decadal prediction runs).For the present analysis, 6 CMIP5 models, which represent the updated versions of the ones described above, have been selected (see Table 1).It is worth Earth Syst.Dynam. Discuss., doi:10.5194/esd-2016-28, 2016 Manuscript under review for journal Earth Syst.Dynam.Published: 14 July 2016 c Author(s) 2016.CC-BY 3.0 License.noticing that, in the new ensemble dataset (CMIP5), the model ECHAM5/MPI-OM (CMIP3) has been replaced by MPI-ESM-MR, which is the ECHAM6 model coupled with the same ocean model MPIOM used in phase 3. Furthermore, INM-CM4 and MIROC5 horizontal resolutions are close to those of the medium-resolution CMIP3 models.As for CMIP3, the same 17 vertical pressure levels are required for the atmospheric outputs and 8 levels (up to 300 hPa) have been considered for the representation of the tropospheric mean conditions.5

Baroclinicity
Synoptic eddy activity in midlatitudes has long been related to the baroclinic instability that converts available potential energy of the time mean flow to eddy kinetic energy (e.g., Charney, 1947;Eady, 1949;Lorenz, 1955).One of the measures of atmospheric baroclinicity is the maximum growth rate of the linear Eady model, which has been shown to be a useful 10 estimate of the growth rate of the most rapidly growing instability in a wide range of baroclinic instability problems (Lindzen and Farrell, 1980).The maximum Eady growth rate has been found to be a suitable parameter to quantify the geographical location and intensity of the storm tracks (i.e., Hoskins and Valdes, 1990;Wu et al., 2011), to evaluate the impact of increasing greenhouse gases and sulphate aerosols on extratropical cyclone activity (Carnell and Senior, 1998;Geng and Sugi, 2003), and to measure the baroclinicity of the mean state of the atmosphere (e.g., Heo et al., 2012).In the 15 present paper, it is applied to the reanalysis and model data.Making use of the thermal wind equation, an accurate estimate of the dimensional growth rate (hereafter referred to as baroclinicity index) is given by (Lindzen and Farrell, 1980):

∂T ∂φ
(1) 20 with f the Coriolis parameter, U the horizontal wind vector, a the Earth's radius, φ the latitude, g the gravity acceleration ,  the mean temperature in the troposphere and N the Brunt-Väisälä frequency, a measure of the static stability.As can be noted, the dry Eady growth rate (moist processes generally lead to an increase of the rate; see Emanuel et al., 1987) is affected by changes of both meridional temperature gradient (or vertical wind shear) and static stability.However, in the present study, N is taken to be constant and equal to the mean tropospheric value of 1.2•10 -2 s -1 (Holton, 2004).The average 25 over both hemispheres here considered, in fact, cuts off most of the variability of the Brunt-Väisälä frequency that occurs mainly near the surface and at high latitudes (Simmons and Hoskins, 1980).
As introduced in the previous section, surface temperature is taken as the air temperature at 2 meters height, while tropospheric temperature takes into account the 8 pressure levels between 1000 and 300 hPa for both ERAI and AOGCMs.al., 2007a); in SH, the latitude band 30 o -70 o S is considered where the bulk of baroclinic and low-frequency planetary waves activity is observed (Dell'Aquila et al., 2007b).The meridional temperature gradient in ( 1) is computed as the difference between the two boundaries of the considered midlatitude belt, while vertical average of tropospheric temperature is obtained without weighting for the air mass.

Spectral analysis
The spectral components of surface air temperature and baroclinicity have been estimated and tested for statistical significance by using the Multi Taper Method (MTM), which is a nonparametric technique widely applied to problems in the analysis of geophysical signals (Thomson, 1982;Percival and Walden, 1993).MTM attempts to reduce the variance of spectral estimates by using a small set of tapers (or spectral windows) rather than single data taper used by other methods 10 like Blackman-Tukey.Data are pre-multiplied by orthogonal tapers (or eigentapers), which are constructed to minimize the spectral leakage due to the finite length of the data series, and, by performing a Fourier Transform, a set of independent power spectral density (PSD) estimates is computed.The optimal tapers belong to a family of functions known as Discrete Prolate Spheroidal Sequences (DPSS) or Slepian sequences, which solve the variational problem of minimizing leakage outside of a frequency band of half bandwidth pf n , where f n = 1/(N Δt) is the Rayleigh frequency (i.e., the minimum 15 frequency that can be resolved by a finite duration time window), Δt the sampling time, and p an integer.Typically, the number of tapers used K should be less than (2p -1), i.e. the minimum number of tapers that provide small spectral leakage (Ghil et al., 2002).Thus, the bandwidth 2pf n and the number of tapers K represent the key parameters for the stability of the power spectral estimate, which become: where x(t) denotes the signal, DPSS t,k is the k th taper function at time point t.
The confidence intervals in the PSD estimates are computed using the chi-squared approach at the 97.5 % confidence level.
To investigate the relation between the two fields of interest (surface temperature and baroclinicity) in the frequency domain, 25 the bivariate spectral analysis is performed.The relationship between two time series in the Fourier domain can be expressed in terms of the cross-spectrum, the phase difference, and the cross-coherence, which is defined as follows.
Being P A (f) and P B (f) be the complex Fourier spectra of two time series, the cross-spectrum is defined as: with the convention that a value between 0 o and 180 o means that A leads B (in our case T2m leads σ BI ) and vice versa for a value between 180 o and 360 o .5 The coherence spectrum is a measure of the correlation of the two spectra as a function of frequency and can be written as: The angle brackets denote the expectation value and can be approximated by a mean over many short spectra (Von Storch 10 and Zwiers, 1999).

Results
To provide a frame of reference for the subsequent analysis, we first present the time series of midlatitude surface temperature and baroclinicity in both hemispheres as derived by ERAI reanalysis.The seasonal behavior of some averaged fields (i.e., TOA solar radiation, mean sea level pressure, and meridional gradient of geopotential height field at 300 hPa and 15 500 hPa) introduce and complement this preliminary analysis.
For illustrative purposes, the spectral analysis for selected CMIP3 coupled models follows; results for both hemispheres are illustrated and compared with those from the most recent CMIP5 models.

Time series analysis
In Figure 1 the observed seasonal variability in both hemispheres of ERAI surface temperature and baroclinicity are 20 displayed with that of solar radiation at TOA, the meridional gradient (defined as the difference between 30 o and 70 o ) of the geopotential height (GPT) field at 300 hPa and 500 hPa, and the mean sea level pressure (MSLP) variance in the midlatitude belt.The annual mean cycles have been computed by averaging daily values over the entire time record of the reanalysis data and applying 15-day moving average to filter out the high-frequency variability; then, they have been standardized for comparison.For illustrative purposes, the baroclinicity, GPT, and MSLP variance cycles have been reversed so that their 25 maxima occur in summer as for the other fields.
From Figure 1a (NH) it can be noted that, moving from January to December, the incoming solar radiation precedes the land and ocean.As known, in both hemispheres surface temperature follows solar heating and is dominated by the annual cycle, with a weak semiannual component (Peixoto and Oort, 1992).Moreover, the amplitude of the NH surface temperature annual cycle is roughly twice as strong as the SH and they are in phase opposition so that, on the global scale, the mean surface temperature has a weaker residual seasonal cycle (Covey et al., 2000).Also, to be noted is the phase opposition between surface temperature and baroclinicity index, with the latter showing a semiannual modulation of the annual cycle 15 (Figure 3 when compared with Figure 2).Such a modulation, which in SH is a signature of SAO phenomenon (van Loon, 1967;Meehl, 1991), is found also in NH.
As an example, the time series of surface temperature and baroclinicity from the 6 selected CMIP3 models are shown in Figure 4 for the common time section 1979-1999.For the sake of clarity, the time series of T2m and σ BI are standardized and plotted into the same graphs.As expected, there is an opposite phase relationship between baroclinicity and surface 20 temperature; furthermore, as shown by the reanalysis data, there is evidence in model data of the semiannual oscillation in both hemispheres, suggesting the robustness of such a feature in the time series.A few outliers are found in baroclinicity records, likely related to anomalous values in air temperature data.

Spectral estimates
The power spectral density (PSD) estimates of ERAI mean baroclinicity and surface temperature, for the NH and SH 25 midlatitudes, computed using the MTM method are shown in Figure 5 (p = 3, K = 5).Peaks are tested for significance at 95 % level relative to the null hypothesis of a red noise background estimated from the data.
As already suggested by Figure 2 and 3, in both surface temperature and baroclinicity spectra most power is at the annual frequency, leading to a peak that is statistically significant.A secondary harmonic lies at the semiannual frequency, which, for the baroclinicity index, is statistically significant or marginally significant in both hemispheres (i.e., the red noise 30 spectrum lies within the confidence interval of PSD estimate), while for surface temperature it is not in NH and marginally statistically significant in SH.This means that in NH midlatitudes surface temperature is dominated by the annual cycle modulated by a weaker semiannual periodicity embedded into the red noise background, suggesting a more regional nature Earth Syst.Dynam.Discuss., doi:10.5194/esd-2016-28,2016 Manuscript under review for journal Earth Syst.Dynam.Published: 14 July 2016 c Author(s) 2016.CC-BY 3.0 License.
of the semiannual component.Since we are interested to investigate the relationship between surface temperature and baroclinicity annual/semiannual cycles, we selected ocean regions in NH midlatitudes where baroclinic eddies are known to be particularly active and requiring that also the semiannual component in T2m is present (statistically significant).
Candidate regions of interest are: NH oceans, Pacific Ocean, and Atlantic Ocean, all in the latitude band 30-60 o N.For these regions, power spectra of baroclinicity index (not shown) are characterized by statistically significant annual and semiannual 5 cycles, with the exception of the Atlantic Ocean where no semiannual harmonic is found.The power spectra estimates of surface temperature are shown in Figure 6: as can be noted, for the Pacific Ocean the red noise spectrum falls within the confidence interval of the PSD estimate.Hence, for NH, we decided to focus the subsequent analysis on this region.
Results of bivariate spectral analysis (coherency and phase spectra) are shown in Figure 7 for the reanalysis ERAI and in Figures 8-9 for model outputs, respectively.According to the adopted convention, in case of a phase value between 0 o and 10 180 o surface temperature is leading with respect to baroclinicity, and vice versa in case of a phase value between 180 o and 360 o .
Consistently with Figure 5 and 6, the coherency spectra between observed surface temperature and baroclinicity in NH and SH (Figures 7a and 7c) show peaks at the annual frequency very close to the level of 1 (total coherency), implying strong correlation between the two time series.Similarly, at the semiannual frequency high coherency is found in both hemispheres.15 This finding provides evidence for the already mentioned SAO and, more importantly, confirms the relationship between the two variables at the semiannual periodicity also in NH Pacific Ocean.
For most frequencies, phase spectra (Figures 7b and 7d) depart from the condition of null phase.In particular, in the NH Pacific Ocean at the annual frequency, a phase shift of about 213 o is found (i.e., about 30 o with respect to the opposition of phase), and about 258 o at the semiannual one.In the SH, at the annual frequency a phase shift of about 214 o is observed and 20 at the semiannual frequency about 235 o , showing, in both cases, a delay of the mean surface temperature with respect to the baroclinicity index.
Results obtained for the annual frequency in NH Pacific Ocean and SH are consistent with the baroclinic activity at midlatitudes that is particularly intense during winter when the meridional temperature gradients are stronger than during summer.The lag with respect to the perfect opposition of phase, observed in both NH and SH, which is of about 1 month in 25 terms of time (Grinsted et al., 2004), is likely associated to the larger thermal inertia of the oceans when compared with land surfaces as it is for the NH Pacific Ocean and SH midlatitudes.This is supported by a comparative analysis of the annual component of the time series that shows for the NH midlatitudes (dominated by land continents) an almost full opposition of phase between surface temperature and baroclinicity, and for the ocean regions a shift of about 1 month with respect to the phase opposition.30 At the semiannual frequency, a phase shift of about 50 o is observed in SH and about 80 o in NH Pacific, with surface temperature delaying by about 1 month or more compared to the opposition of phase: results seem in agreement with the SAO phenomenon and may be indicative of the role of the semiannual variability in shaping eddy activity (an example is the midwinter suppression characterizing the North Pacific storm tracks).Also, the high values of coherency found at the Earth Syst.Dynam. Discuss., doi:10.5194/esd-2016-28, 2016 Manuscript under review for journal Earth Syst.Dynam.Published: 14 July 2016 c Author(s) 2016.CC-BY 3.0 License.
semiannual frequency suggest that, as it is in the SH, the contribution of such harmonic to the NH ocean variability is not negligible.
Bivariate spectral analysis is applied to CMIP3 model outputs by considering the common time section 1900-1999 and the same number of tapers as for the reanalysis (K = 5).The latter choice implied the same degrees of freedom and, hence, the same confidence level estimate.Results are shown in Figures 8-9. 5 With regard to the coherence spectra (Figures 8a, 9a), at the annual and semiannual frequencies, all CMIP3 models show high values well above the confidence level threshold both in NH Pacific and SH, in agreement with ERAI.Phase spectra (Figures 8b, 9b), instead, show some discrepancies with the reanalysis and among models (Table 2).Generally, in both hemispheres, there is more uncertainty in the reproduction of the phase of the semiannual cycle than of the annual one.In particular, while at the annual frequency almost all CMIP3 models reproduce quite well the opposition of phase with 1-10 month delay of surface temperature (exceptions are CGCM3.1 and ECHAM5/MPI-OM for NH Pacific and GFDL-CM2.1 for SH), at the semiannual frequency three (NH Pacific) and two (SH) out of six models display phase values within the reanalysis error intervals (see Table 2).However, it is worth noticing that no CMIP3 model reproduces the reanalysis values at both the annual and semiannual frequencies in the two hemispheres.Moreover, it emerges that larger errors characterize phase estimates at the semiannual frequency when compared to those obtained for the annual one, likely due to the less 15 power of the six-month peak as resulted from the power spectra (Figure 5, 6).
To better illustrate the discrepancy among models, the scatter plots of the relative phase between surface temperature and baroclinicity at the annual and semiannual frequency, for both NH and SH, are shown in Figure 10a, b, respectively, for ERAI (green) and CMIP3 (blue).On the same plots results obtained from CMIP5 are also displayed (red) for comparisons, see also Table 2 for phase values.In performing the bivariate spectral analysis for CMIP5, the same time period used for 20 CMIP3 has been considered (i.e., 1900for 20 CMIP3 has been considered (i.e., -1999)), with the exception of CanCM4 model that has a different time section .It clearly emerges that for CMIP3 while the uncertainty in the phase at the annual frequency is bounded between about ±15 o around an average value of about 220 o , phase estimates at the semiannual frequency span a wider range of values (from 240 o to 360 o in NH Pacific, from 120 o to 300 o in SH).Findings seem to suggest that there is no evidence of the relationship between models' horizontal resolution and their performance.Furthermore, it is worth noting that for the 25 semiannual frequency model errors are larger when compared with those obtained for the annual one (twice or more).
Results obtained for the most recent multi-model dataset CMIP5 show several improvements compared with CMIP3, especially for the semiannual frequency in NH: phase values span between about 220 o and 300 o (i.e., about 1 month phase shift) for NH Pacific, and between about 180 o and 280 o (i.e., about 2 months) for SH.Larger errors of model estimates allow their overlap with the reanalysis error bars; the non-overlapping among some models errors also occurs, denoting a degree of 30 uncertainty in model data also in CMIP5.
Although MIROC5 show improved results, at the stage of the present analysis, overall, it is not possible to determine whether model changes, involving for example the horizontal resolution, have a significant impact on the representation of the semiannual period variability.

Summary and conclusions
The annual and seasonal cycles in the time series of surface air temperature and baroclinicity are analyzed in both hemispheres using ERAI reanalysis data covering the period 1979-2015 and AOGCM outputs from CMIP3 and CMIP5 experiments of different record lengths.
The baroclinicity index time series is estimated through the tropospheric meridional temperature gradient (Eady maximum 5 growth rate), which is computed as the difference between the poleward and equatorward edges midlatitude band (30 o -60 o   for the NH and 30 o -70 o for the SH, respectively), and zonally and vertically averaged in each hemisphere, while surface temperature time series is obtained by zonally and meridionally averaging over the same latitude band.
The spectral analysis carried out applying the MTM method shows that annual and semiannual periodic components are the dominating features in the reanalysis time series and model outputs.In particular, results show the occurrence of the 10 semiannual oscillation in the zonally averaged baroclinic activity in both hemispheres.The presence of the semiannual peak in the NH baroclinicity may be considered a signature of the midwinter Pacific suppression as suggested by Nakamura et al. (1992), but further investigations are necessary.
The bivariate analysis of coherency and phase spectra between baroclinicity and surface temperature show discrepancies between ERAI and model data, as well as among models, especially for the semiannual frequency.In particular, for ERAI it 15 is found that: At the annual and semiannual frequencies, a very high coherency between the two selected variables is observed; (ii) At the annual frequency, in both hemispheres baroclinicity leads surface temperature of about 30 o with respect to the phase opposition; 20

(iii)
At the semiannual frequency, the relative phase is shifted by about 70 o with respect to the opposite phase condition in NH Pacific and by about 55 o in SH (i.e., about 1 month delay of surface temperature with respect baroclinicity).
For models outputs: For what concerns the coherency spectra, at the annual and semiannual frequency, coherency is well 25 represented by all models in both hemispheres and well exceeds the confidence level.Results for CMIP5 models are in agreement with those presented for CMIP3; (v) At the annual frequency, phase estimates in both hemispheres are bounded between about ±15 o around an average value of 220 o (i.e., about 1 month phase shift).At the semiannual frequency, model relative phases between surface temperature and baroclinicity show wider dispersion in both hemispheres, denoting 30 discrepancies among models and wider uncertainty in the estimates.Results for CMIP5 display improvements when compared with CMIP3 with a reduction of the discrepancy among models, especially in NH Pacific.
Larger errors found at the semiannual frequency make phase estimates of most models consistent with the reanalysis (i.e., they fall within the ERAI confidence interval) but discrepancies still occur especially in SH.
In performing the present analysis two assumptions have been made that might be considered restrictive with possible impacts on the obtained results.They are the vertical averaging, which has not been weighted for the mass of the atmosphere, and the choice of the monthly mean of daily means data.About the former, it has been observed that the 5 discretization of the vertical pressure levels already accounts for that, while the impact of the latter choice has been verified against the results obtained using daily means with not statistically significant differences.
Furthermore, the choice of the maximum Eady growth rate as an index of baroclinicity has been considered suitable for the purpose of the present paper because it has been widely used in the international literature and, in the framework of zonally averaged atmosphere, the variability of the tropospheric static stability (unlike the static stability ratio between troposphere 10 and stratosphere) has been found to have a secondary effect on baroclinic activity (Bordi et al., 2002;Fantini, 2004).It is worth noticing that the presence of a statistically significant semiannual peak in surface temperature spectral estimates, may suggest that the internal forcing exerted by baroclinic eddies play a role in modulating the annual cycle.
The six-month modulation of the baroclinicity index is somewhat not surprising, since the relationship between baroclinic activity and SAO has been widely investigated (e.g., Walland and Simmonds, 1999).It has been found that the SAO 15 phenomenon is related to the half-yearly wave in the meridional temperature gradient at high southern latitudes that implies seasonal fluctuations of baroclinicity and surface pressure; moreover, the variation of the static stability during the year seems to modulate the efficiency of baroclinic conversion.Some evidences of a semiannual modulation have been found also in NH at regional scale (e.g., Wikle and Chen, 1996), suggesting a mechanism for the SAO in NH based on the eastwest land-sea contrast, similarly to the north-south differential heating in SH proposed by van Loon (1967).However, to the 20 best of our knowledge, it is the first time this oscillation has been found in the zonally averaged NH midlatitudes.It is left to a future study whether it is just the projection on the zonal average of regional scale processes or it is the signature of a global scale phenomenon.
Present findings contribute to better characterize the cyclic response of current global atmosphere-ocean models to the external solar forcing that is of particular interest for seasonal forecasts.The discrepancies emerged with reanalysis and 25 among models, at least for the AOGCMs here considered, in properly reproducing the seasonal cycle of surface temperature and baroclinicity require further investigations.A larger set of models should be considered and the performance of a model ensemble against reanalysis should be assessed rather than that of a single model.In doing this, a simple metric for the seasonal cycle should be developed and tested (see for example Gleckler et al., 2008).
Both fields, surface temperature and tropospheric temperature, are separately considered for the NH and SH.In NH, 30 baroclinicity index is computed over the latitude band 30 o -60 o N, the area of most intense baroclinic activity (Dell'Aquila et Earth Syst.Dynam.Discuss., doi:10.5194/esd-2016-28,2016   Manuscript under review for journal Earth Syst.Dynam.Published: 14 July 2016 c Author(s) 2016.CC-BY 3.0 License.
other signals: in particular, it is followed by surface temperature and baroclinicity index.The meridional geopotential Earth Syst.Dynam.Discuss., doi:10.5194/esd-2016-28,2016   Manuscript under review for journal Earth Syst.Dynam.Published: 14 July 2016 c Author(s) 2016.CC-BY 3.0 License.gradient at 300 hPa and 500 hPa appears in phase with the baroclinicity index, while surface temperature shows a delay of 30-45 days with respect to the incoming solar radiation, and of about 20 days with respect to baroclinicity and geopotential gradients.The annual cycles for the SH (Figure1b) show similar features with a more pronounced semiannual oscillation in the geopotential gradient and baroclinicity index.A hint of SAO is also observed in MSLP variance cycle.Furthermore, the standardization allows estimating the relative amplitude of the annual cycles that can be grouped as: on one hand, surface 5 temperature and MSLP variance, and on the other hand, meridional geopotential gradients and baroclinicity index.Monthly mean time series (1979-2015) of both ERAI surface temperature and baroclinicity averaged over the NH and SH midlatitude belts are shown in Figure 2 and 3, respectively.Figures clearly show that the periodic components account for most of the variability of the time series: the annual cycle characterizes the time series with larger amplitude in NH than in SH, likely explained by the different land distribution in the two hemispheres and by the difference in the heat capacity of 10

Table 1 :Figure 1 : 5
Figure 1: Mean annual cycles of midlatitude ERAI fields for the Northern (a) and Southern Hemispheres (b): surface temperature (T2m, green), baroclinicity index (σ BI , purple), solar radiation at the top of the atmosphere (TOA, blue), mean sea level pressure variance (MSLP, red), meridional gradient of the geopotential field at 300 hPa and 500 hPa (yellow and khaki, respectively).5

Figure 4 :
Figure 4: CMIP3: Time series of surface temperature (T2m, blue) and baroclinicity (σ BI , black) for the 6 selected AOGCMs for the common time period 1979-1999.Time series are standardized.

Figure 5 :
Figure 5: Power spectral density (PSD) estimates of ERAI mean surface temperature (T2m) and baroclinicity (σ BI ), for the Northern (a, c) and Southern Hemispheres (b, d) midlatitudes, computed using the MTM method (parameters p = 3, K = 5).The 0.99 confidence intervals (dashed lines) are obtained by the Chi-squared distribution with 7 degrees of freedom; the red noise 5

Figure 7 :
Figure 7: Bivariate spectral analysis (coherency and phase spectra) of ERAI surface temperature and baroclinicity for the period January 1979-September 2015: a)-b) NH midlatitude band 30 o -60 o N over the Pacific Ocean; c)-d) SH midlatitude band 30 o -70 o S. Dashed horizontal line in the coherency plot represents the 97.5% significance level; shaded areas in the phase plots represent the 95% level of significance obtained by means of 2 13 Montecarlo simulations.Frequency on the x-axis is in yr -1 .5

Figure 8 :
Figure 8: Bivariate spectral analysis (coherence and phase spectra) of surface temperature and baroclinicity for the 6 selected CMIP3 models computed over the time period 1900-1999.Plots refer to the NH midlatitude band 30 o -60 o N over the Pacific Ocean.Dashed horizontal line represents the 97.5% significance level; shaded areas represent the 95% level of significance obtained by means of 2 13 Montecarlo simulations.5

Figure 9 :
Figure 9: As in Figure 8 but for the SH midlatitude band 30 o -70 o S.