4.1. PD and GW climates
In order to study the seasonal spatial variability of t2m we have applied harmonic analyses. As discussed by Aslan et al. (1997), the Fourier transformation or harmonic analysis decomposes a time-dependent periodic phenomenon into a series of sinusoidal functions, each defined by unique amplitude and phase values. The proportion of variance in the original time-series dataset accounted for by each term of the harmonic analysis can also be calculated (Jakubauskas et al. (2001)).
The first order harmonics of meteorological parameters show long-term effects, while higher order harmonics show the effects of short-term fluctuations. The phase angle can be used to determine the time when the maximum or minimum of a given harmonic occurs. The harmonic analysis is, therefore, a useful tool to characterize different climate regimes and transition regions. Moreover, the advantage of using this mathematical approach is associated with the possibility of identifying dominant climate features in the space–time domain. One may note that investigations based upon area averaged time series are embedded with small and large-scale processes dictated by distinct periodicity, this in turn may cancel out these regional climatic signals in the space–time domain. Harmonic analysis is based on the series of trigonometric functions (Wilks (1995)), as described below:
yt is the value at time t, ȳ stands for the arithmetic mean, Cj is the amplitude of harmonics, t the time, ωj is the frequency and ϕj is the phase angle, and N represents the number of observations. The amplitude is calculated from
In which Aj and Bj are given by:
The phase angle is dependent on Aj value and may be computed as follows:
Contribution by individual harmonics (j) to total variance of the timeseries is given by , where s is the timeseries variance.
The potential of the harmonic analysis approach in the classification of eco-climatic zones has been discussed by Azzali and Menenti (2001). It has also been demonstrated that fundamental characteristics related to the inter- and intra-seasonal characteristics of dynamic ecosystems, may be identified by harmonic analysis. Several studies have focussed on the semi-annual harmonic due to its climate linkage with distinct climate modes, such as the Southern Annular Mode (SAM), quasi-stationary wave-3 pattern (ZW3) and the Pacific South American pattern (PSA) (e.g. Yuan and Li (2008)). During the last four decades several studies have explored the use of harmonic analysis to characterize the SH polar climate. van Loon (1967) utilized harmonic analysis and found that the temperature contrast between middle and polar latitudes in the SH is linked to increased cyclonic activity in high latitudes over the Antarctic Ocean, where the second harmonic of the mid-tropospheric meridional temperature gradient has a magnitude exceeding that of the first harmonic. This led to the identification of the semi-annual oscillation (SAO) at middle and high southern latitudes. Meehl (1991) further investigating the SAO, argued that along with the observed upper-ocean temperature profiles, changes in the annual cycle of SST and ocean heat storage near 50°S could lead to a modulation of the observed SAO. Furthermore, it has been found that changes in Antarctic temperature may be influenced by the SAO as a result of the amplification of the wave-3 structure of the atmospheric circulation (van den Broeke (1998), Raphael and Holland (2006)).
Figure 6(a) shows the amplitude of the first harmonic of t2m based upon the ERA40 and NNR datasets. This harmonic explains at least 88% of the variance of the timeseries of t2m in the Antarctic region for both datasets. However, for the ERA40 this harmonic shows smaller variance south of 80°S. The first harmonic of t2m according to the ERA40 Reanalysis is primarily characterized by a tripolar structure over the continent around the South Pole. Over East Antarctica, the two nodes of variability are influenced by the highest parts of Antarctica.
Figure 6. Amplitude of the first harmonic of t2m for ERA40 Reanalysis. (a, b) is the amplitude of the second harmonic. (c, d) is the same but for the NNR. (e) is the orography anomalies (×102 m) between the NNR and ERA40 Reanalyses ( °C). This figure is available in colour online at wileyonlinelibrary.com/journal/joc
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A different picture is seen in the NNR data, in the sense that the largest seasonal variability is located over the Weddell and Ross seas and over the highest topographic features (Dome Fuji and Dome C). The ERA40 and NNR reanalyses also differ with regard to the amplitude values, i.e. the NNR data shows a stronger seasonal contrast (Figure 6(a) and (c)). It should be noted that differences are also identified over the coastal region over East Antarctica where the ERA40 exhibits reduced seasonal contrast. According to Monaghan and Bromwich (2008), snowfall and surface temperature variability are tightly correlated in higher elevation regions, therefore, it is possible that the seasonal changes of snowfall through changes of the radiative balance may feedback to modify the surface temperature, both upstream and downstream of the topographic features. Moreover, van den Broeke et al. (2005) argue that regions with a steep slope force seasonal katabatic winds that mix relatively warm air downward to the surface, which results in higher temperature and consequently induces a strong seasonal contrast.
Over the ACC region the amplitude of the first harmonic is less than half of the maximum over the Antarctic continent. However, the seas adjacent to West Antarctica, which include the Ross and Weddell seas, are dominated by a larger amplitude of the first harmonic (Figure 6(a) and (c)), in particular for the NNR dataset. This is probably associated with seasonal changes of sea ice which induce modifications in the radiative budget (King (1994)), and can affect the thermal advection onto the ice shelves. Additionally, the absence of katabatic winds in these areas allows for the generation of a temperature inversion in winter at the surface enhancing the seasonal contrast. By assuming that the first two harmonics explains more than 90% of the total variance of the t2m, the amplitude maxima over the Ross and Weddell seas has also been identified by van den Broeke (1998), for Halley and Belgrano stations in the area of the Weddell Sea, and for Hallett and Little America in the Ross Sea.
Figure 6(e) shows differences in the topography height between the NNR and the ERA40 reanalyses. The NNR is characterized by higher (lower) altitude in the east side (west) of the Dome Fuji than the ERA40 dataset. Moreover, differences are noted between both data in the Dome C and in the George V Land. These areas show the large disagreement between the NNR and the ERA40 in terms of their annual and semi-annual harmonics (Figure 6). It is therefore very likely that the enhanced seasonal contrast of the t2m in the NNR is due to stronger annual forcing of the katabatic winds compared to ERA40.
Turning to the second (semi-annual) harmonic, one may note that the areas with larger amplitude values are very similar to those seen in the annual harmonic. As detected for the first harmonic, higher amplitude values are found over Antarctic plateau for the NNR and over the West Antarctica ice sheet for the ERA40 dataset. By comparing our results with the semi-annual harmonic based on station data, one may note that the NNR reproduces the observed data satisfactorily, since the higher amplitude is observed in the Vostok, Dome C and Plateau station. This feature is primarily linked to the magnitude of the temperature inversion in winter associated with the loss of long wave radiation.
van den Broeke (1998) evaluating the influence of the SAO on near-surface temperatures in Antarctica, found that the variance explained by the second harmonic of the annual temperature cycle is largest on the Antarctic Plateau (11–18%), followed by the large ice shelves and coastal East Antarctica (6–12%) and stations at or close to the Peninsula (0–5%). These results match the explained variance seen in the NNR and the ERA40 over the Antarctic Plateau, but they disagree with regard to the variance over East Antarctica and Peninsula in ERA40. A comparison between the CMIP3 results and the Reanalysis data (Figure 7) clearly demonstrates that the models can satisfactorily simulate the amplitude of the first harmonic, as well as its spatial pattern as reproduced by the NNR. The CMIP3 results are primarily characterized by the topographic effects over regions such as the East Antarctica Ice Sheet (EAIS, Figures 6 and 7). The second region with higher amplitude values is located over the Ross and Weddell seas. Comparison between the CMIP3 models and the ERA40 reveals a disagreement on the areas of higher seasonal harmonic variability. This may indicate a bias in the ERA40 dataset with regard to the amplitude of the seasonal cycle. Studies of Antarctic climatology show that the largest seasonal amplitude of temperature variation is found over the high plateau, not over the relatively low-lying West Antarctica (Warren (1996), Broeke et al. (2005)).
It should be noted that despite having reasonable horizontal resolution, the CSIRO model (Table I) did not exhibit the seasonal variability as predicted to occur by the other models, as well as by the Reanalysis. One may argue that this feature could be associated with a bias in the model's representation of the wave 3 pattern (ZW3, van den Broeke (1998)). However, it has been shown by Raphael and Holland (2006) that the CSIRO model does a respectable job of simulating ZW3 spatially. This anomalous amplitude as predicted to occur by the CSIRO model is perhaps consequence of processes linked to the cloud cover, or may be associated with the treatment of the ice/snow subsurface temperature and heat flux. Phipps (2006) evaluating the CSIRO Mk3L climate system model, a simplified version of the CSIRO model evaluated here, shows that the model can be seen to have excessive cloud cover south of 60°S as compared to NCEP-DOE Reanalysis.
To further evaluate the discrepancies in simulating the seasonal changes in the CMIP3 models, we show in Figure 8 the annually zonally averaged total cloud cover (TCC) over the SH ocean and Antarctica, and the annual march of the TCC averaged between 87°S–70°S and 30°E–130°E. It may be demonstrated that the GFDL and CSIRO models show the largest values of the TCC compared to the other models (Figure (a)). This overestimation of clouds may very likely damp the annual cycle of temperature, as reproduced by the CSIRO and GFDL models. It is interesting to note, moreover, that the models differ substantially in terms of the seasonal cycle of the TCC over the Antarctic Plateau (Figure 8(b)). This may be the cause of the inter-model differences in amplitude of the t2m annual harmonic. Again, larger seasonal variability of t2m is identified for CCCma, HadCM3 and MIROC-MEDRES with values as high as 20 °C. It should be mentioned that these model results fit closely with the NNR dataset (Figures 7 and 6). The larger amplitude of the annual harmonic over seasonally ice covered regions in the CMIP3 models and the NNR, may be due to modifications in the heat flux exchange between ocean and atmosphere linked to the seasonal sea ice melting. Additionally, as proposed by Broeke et al. (2005), the amplitude of the annual cycle of t2m over coastal regions is also caused by the nonlinear response of air moisture content, clear-sky conditions and the long wave radiation balance.
Over the Antarctic continent the explanation for strong seasonality is not straightforward. Previous investigations based upon the Antarctic surface mass balance (SMB), for which precipitation (P) minus sublimation (E) is an important parameter, demonstrate that the minimum value of P-E is located over the Plateau of East Antarctica (Vaughan et al. (1999)). This analysis matches very closely to our identified area of maximum first (or annual) harmonic amplitude of t2m, as shown in Figure 7. It has been demonstrated moreover that the SMB is affected by the amount of clear-sky precipitation as proposed by Cassano et al. (2001). Based on precipitation which may be used as a proxy for the SMB (not shown), it is demonstrated that the CSIRO model does not reproduce the seasonal cycle of precipitation and also overestimates the TCC throughout the year, as previously mentioned (Figure 8(a) and (b)). On the other hand, models with higher seasonal variability of t2m are associated with small TCC amount and reasonable representation of the annual cycle of precipitation. One may argue, therefore, that the simulated amplitude of the annual cycle of t2m in the interior of Antarctic, may very likely be associated with the model treatment of the P-E rate. This involves the cloud-forced short wave and long wave radiation (up and down) balance.
Analyses of the semi-annual harmonic amplitude of t2m (Figure 9), show that the largest intra-seasonal variability is located over the EAIS with values as high as 8 °C according to the HadCM3 and MIROC-MEDRES output. Small values are simulated by CCCma and GFDL models. In addition, the second harmonic of the CMIP3 data shows a very similar spatial pattern to the NNR, except for the CSIRO model. The CMIP3 results also exhibit a higher amplitude over the Ross and Weddell seas, as found by van den Broeke (1998), which characterizes the intra-seasonal behaviour of the coupling between the sea ice and the atmospheric circulation. It should be emphasized that CCCma and CSIRO differ from the other models along the coastal region of East Antarctica. It has been demonstrated that the second harmonic of t2m is highly correlated with the second harmonic of pressure (SAO), due to the displacement of the low pressure belt during the distinct phases of the SAO (van den Broeke (1998)). Based on this, one may suggest that the linkage between the ZW3/SAO patterns with the near-surface temperature variability is inadequately simulated in CCCma and CSIRO models.
Calculations of the harmonic analysis based upon GW conditions reveal that global warming affects the annual cycle of Antarctic temperature in different ways over the ocean and the continent (Figure 10). In the interior of the Antarctic continent, there is no substantial seasonal difference between the amplitude of the first harmonic as projected by GW and PD simulations, with values between ± 1 °C. Over the ocean along the ACC the amplitude of the first harmonic is reduced in all IPCC models in the GW interval compared to the PD interval (Figure 10). The CMIP3 models show large weakening of the annual cycle over the Pacific and Atlantic sectors except for the MIROC-MEDRES. This weakening in the amplitude of the first harmonic is due to higher winter temperatures which is associated with reduced sea ice thickness and sea ice area (not shown). The CCSM model, however, shows a strengthening in the amplitude of the first harmonic in the interior of the Antarctic continent (Figure 10(b)), which is primarily a result of increased temperature during the summer season (see Figure 4). In addition, over the ACC the CCSM exhibits the largest changes in the amplitude of the seasonal cycle between the PD and GW simulations (Figure 10(b)).
An analysis of the difference in the amplitude of the first harmonic of near-surface wind (not shown), between the GW and PD intervals does not reveals a clear relationship with the temperature changes discussed here. Lefebvre et al. (2004) argued that the CCSM model overestimates the sea ice area under PD conditions in particular in the Pacific and the Indian sectors. This anomalous pattern induces very cold conditions in winter due to the isolation of the atmosphere from the underlying warm ocean. Turning to GW conditions, the opposite is verified with increased temperature as a consequence of strongly reduction in the sea ice cover, which allows a more effective heat exchange between the ocean and the atmosphere (Figure 5(b)). Concomitantly, this is associated with a reduction of the amplitude of the annual harmonic.
Since changes of the amplitude of the second harmonic as projected by the climate simulations between the two epochs are relatively small, they are not shown here. It should be noted that larger changes occur over the oceanic areas along the ACC, in particular over Weddell and Ross Seas. This highlights the importance of sea ice in driving the annual cycle of the near-surface temperature in the SH polar region. Over the continent, a strengthening of the semi-annual cycle under GW conditions is seen in the CCSM model results.