There are a number of possible causes of the errors in the model representation of the CGT. There may be errors in the way that it is forced, or errors relating to wave propagation within the model. The propagation of Rossby waves is an important part of the CGT mechanism, thus differences in the Rossby wave propagation characteristics between model and observations, possibly related to errors in the Rossby wave source or jet biases, have the potential to cause large errors in the CGT. We now examine several of these possible causes and determine the role that each has in causing errors in the teleconnection.
Errors in the D&W region
We first look at the variance of the D&W Index in the model compared to observations, noting that if the model variability in that region is small, the variance associated with that in other centres of action may be reduced. If the variance is weak, it is an indication that the region is not being forced as it should be. If the variance is strong, this suggests that it is the model teleconnection mechanism that is wrong.
Figure 6 shows the distribution of the variance of the D&W Index in the model and observations. The variance of the D&W Index is greatest in June, and the model reflects this, with the observations lying well within the interquartile range of the model distribution. However, in July and August the model underestimates the variance in this region, most notably in July when the observed variance falls well outside of the model distribution. In August the observed variance does lie within the model distribution but falls in the 92nd percentile. The underestimation of the variance in this region by the model suggests that even if the teleconnection pathway is correctly represented in the model, it will still underestimate the strength of the teleconnection.
To identify a possible cause of the low variance in the model D&W Index in July and August we examine the relationship between geopotential height in this region and precipitation in the North Indian Summer Monsoon region (NISM), a region first defined in Ding and Wang (2007). We know from observations that there is a significant correlation between precipitation in this region and the D&W Index (correlations of 0.51, 0.61, 0.56 for June, July and August respectively) as a result of a Gill-type response to the off-equatorial diabatic heating associated with the ISM (Gill 1980; Ding and Wang 2005). Therefore if the model does not represent the relationship between these regions well, this will affect its ability to correctly simulate the CGT.
Figure 7a shows the observed and model correlations between the D&W Index and NISM precipitation. During July and August, when the variance in the D&W Index is reduced, the model underestimates the correlation between NISM precipitation and the D&W Index (Fig. 7a) and also underestimates the variance in NISM precipitation during these months (Fig. 7b). This suggests that the poor variance of the D&W Index in July and August may be linked to poor representation of NISM precipitation in the model.
It was shown in Ding et al. (2011) that the CGT pattern is favoured in summers preceding the peak phases of ENSO. Correlating the difference in the Nino3.4 Index in the preceding winter (DJF) and the subsequent winter against individual centres of action results in negative but not significant correlations. The equivalent model correlations are also not significant but are generally less negative than the observations (not shown). Therefore while the CGT itself may be correlated with ENSO, there is no obvious link between ENSO and the individual centres of action. This may be because there are a number of other drivers for each of the centres of action individually which may mask the influence of ENSO.
Rossby wave source
The CGT mechanism relies on the generation and propagation of Rossby waves. The Rossby wave source (RWS) describes the forcing of Rossby waves by the divergent flow, and can be written as:
$$\begin{aligned} RWS = -\zeta D - \mathbf {v}_{\chi }\cdot \nabla \zeta \end{aligned}$$
(1)
where \(\zeta\) is the absolute vorticity, D is the horizontal divergence and \(\mathbf {v}_{\chi }\) is the divergent part of the wind field. This is derived from the vorticity equation for a single level in the atmosphere (e.g. James 1995), and the RWS is calculated using the u and v components of the wind at 200 hPa. Given the likely interaction between Rossby waves generated by the ISM and the CGT, we compare the RWS in the model to ERA-Interim to help understand the role of any errors in RWS in the representation of the CGT in the model. We first focus on the D&W region, given its key role as a centre of action of the CGT, and the fact that there is a significant correlation between the D&W Index and RWS located near the D&W region in July and August (\(-\,0.50\) and \(-\,0.42\) respectively).
Figure 8a shows the RWS averaged over the D&W region in the model and observations. It is clear that the model RWS in this region is too low in all months, with the observations lying well outside the model distribution. The variance of the RWS in this region is also too low (Fig. 8b) in the model in both July and August, and to a slightly lesser extent in June. If the strength and variance of the forcing in this region are not accurately represented then Rossby waves that are excited may be weaker than observed and this will affect their propagation characteristics and as such will result in errors in the modelled CGT.
To gain an understanding of the reasons for the differences seen in Fig. 8 we examine the mean RWS across a wider region. All of the panels in Fig. 9 are for August only, as this month has the strongest CGT wavetrain and the patterns are representative of those seen in June and July (not shown). Figure 9a, b show the mean August RWS term, calculated using Eq. (1), in ERA-Interim and the model ensemble mean respectively in the coloured contours, and the 200 hPa zonal wind in the black contours. The first thing we note is that the centre of positive RWS located at approximately \(40{^{\circ }} \hbox {N}\), \(60{^{\circ }} \hbox {E}\), which, along with the source over the Mediterranean, is a major wave source (Enomoto et al. 2003), is broader and is located further to the north in the model than in ERA-Interim. This appears to be associated with a northward displacement of the model jet stream by several degrees when compared to ERA-Interim, and also explains the lower than observed RWS in the D&W region in the model shown in Fig. 8a. This displacement in both RWS and jet location is also present in both June and July (not shown).
Figure 8b shows that the variance of the RWS in the D&W region is lower in the model than in observations, however we see from Fig. 9c, d that this is generally not the case over a wider region. Indeed, in most parts of the region of interest the variance of the RWS in ERA-Interim (Fig. 9c) is lower than in the model (Fig. 9d). This is because the amplitude of the RWS in the model is generally larger, therefore horizontal gradients in the RWS are larger. This means that horizontal displacements in the centres of maxima and minima from year-to-year give greater variance. The northward position of the jet stream in the model may also account for the generally larger variance in RWS between \(50{^{\circ }} \hbox {N}\) and \(60{^{\circ }} \hbox {N}\), due to the increased vorticity gradient here.
The mean divergence field (D in Eq. 1) is shown in Figs. 9e (ERA-Interim) and 9f (model). The centre of negative divergence (convergence) located at approximately \(40{^{\circ }} \hbox {N}\), \(60{^{\circ }} \hbox {E}\) (in the same location as the centre of large RWS in Fig. 9a) is both larger in magnitude and located further to the north in the model than in ERA-Interim. This centre of convergence was shown to be localised in this region by the presence of the Zagros mountain chain (Rodwell and Hoskins 1996). Where the jet is located may determine where the divergence and convergence is, but we know, by comparing to the RWS computed from the rotational flow of ERA-Interim with the model divergent flow, that errors in the RWS primarily come from errors in the divergent flow (not shown). The errors in divergence are largest over both the Arabian Sea and the Bay of Bengal. Here, the divergence is much greater in the model than in ERA-Interim, associated with too much precipitation in the model in these regions (Figs. 9g, h). If the greater precipitation in the model is also associated with larger monsoon variability, this may affect the forcing of the CGT in the model. The RWS term is also dominated by the divergence component, and therefore the convergence in the model (which is both too strong and located in the wrong place) is likely to be an important factor in the errors in RWS in the model. These errors in the RWS may impact on European summer forecast skill through errors in the CGT, so more accurate representation of the link between monsoon heating and the extratropical circulation is likely to be important for improving European summer forecasts.
We also note that the jet biases over the Mediterranean are much smaller than over west-central Asia, and the location of the centre of convergence in the model in this region closer resembles ERA-Interim. Where there are larger wind biases over west-central Asia there is a greater displacement of the centre of convergence, and this strengthens the argument that the jet location is an important factor in these errors.
The propagation of Rossby waves generated in this region relies on the jet stream, which acts as a waveguide. As seen in Figs. 9a, b, the model jet stream is located too far to the north over Asia. It can be seen from Fig. 10 that there is a clear northward bias in the position of the jet over much of the northern hemisphere, particularly in June, July and August. This is shown by the positive biases to the north and negative biases to the south of the observed jet stream. The wind biases are smallest early on in the simulation, when the maximum biases are around 4 \(\hbox {ms}^{-1}\). However, these biases quickly become larger, reaching a maximum of around 8 \(\hbox {ms}^{-1}\) in June. The magnitude of the maximum biases then remains approximately constant for the remainder of the hindcast period. The largest wind biases are seen in the RWS region over Asia which means that Rossby waves forced in this region will have different wave propagation characteristics to reality—they may propagate at the incorrect speed, in the wrong direction or may not propagate at all. The combination of the errors in RWS along with the model jet biases are likely to be crucial in the poor representation of the CGT in the model.