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Examining Flow Variability in a Simple Model: Friction in Jet Stream Behavior

Zhang, Y., Yang, X.Q., Nie, Y. and Chen, G. 2012. Annular Mode-Like Variation in a Multilayer Quasigeostrophic Model. Journal of the Atmospheric Sciences 69: 2940-2958, DOI: 10.1175/JAS-D-11-0214.1.
Typically an examination of dynamic models and their problems involves looking at the representation or inclusion of physics such as clouds or ground-atmosphere heat exchange and/or the numerical schemes used. However, the atmosphere is a fluid, and like all fluids, there are inherent internal complexities that can make predictability of their future states difficult. In the Earth's atmosphere, dynamic predictability beyond 10-14 days is impossible. Beyond that, only statistics can be gathered from model runs in order to make projections or scenarios.

Internal dynamic motions in the atmosphere are the result of pressure and temperature differences, the mixture of gasses present, and the rotation rate of the Earth. These produce waves in the fluid, which in the atmosphere are manifest as troughs and ridges in the jet stream. These waves vary in amplitude and size roughly every 10-14 days, which is the same limit as predictability, and results in latitudinal variations in the zonal jet location. This observed behavior in the jet stream is called the annular mode (a.k.a. Artic Oscillation in the Northern Hemisphere), and explains weekly, monthly, seasonal, and yearly variability in the jet stream. Thus, it can influence regional climates.

Zhang et al. (2012) examine the behavior of jet stream in a channel model that was of similar length to Earth's diameter and about 10,000 km in the "north-south" (meridional) direction, with 17 vertical levels centered on a jet maximum. The simplified model uses equations representing the basic conservation laws (mass, momemtum, and energy), and allowed the "rotation speed" to vary linearly (in reality, it gets stronger from equator to pole). This model also allowed the variation of atmospheric stability in the meridional direction, as well as a meridional temperature difference of 43 degrees Celsius. This is comparable to terrestrial equator-to-pole temperature differences. The model even contains surface friction, and this parameter was varied in order to examine the behavior of the jet.

It was no surprise that when the surface friction was increased, there were discernible differences in the zonally and time averaged wind (Fig. 1) and temperature gradient (Fig. 2) profiles. The differences were more discernible in the temperature fields, and as the friction was increased, the prominent wave number in the model increased from four to six. Values smaller (greater) than wave numbers four (six) are associated with the larger (smaller) scale which is considered the planetary (synoptic) scale. Annular mode behavior could only be found in the larger-scale 'climate' for the model at weak frictional values.

Figure 1. Adapted from Fig. 3 in Zhang et al. (2012), the latitudinal distribution of the zonal and time-averaged zonal winds at (a) 437.5 and (b) 875 hPa for a range of surface friction values. The latitude distance on the abscissa is in kilometers (0 km the channel center) positive (negative) values are the distance poleward (equatorward).

Figure 2. As in Fig. 1 here except for temperature gradients, and adapted from Fig. 4 in Zhang et al. (2012).

The main result of this study was to demonstrate a) the importance of larger waves in maintaining large-scale jet stream baroclinicity (density differences), and b) a baroclinic mechanism for the cooperation between synoptic and large-scale eddies in maintaining the persistence of annular mode behavior. Nonetheless, as the authors even note; "As an internal mode of variability, understanding the mechanism that sustains the zonal wind anomalies is useful not only to predict the intraseasonal variability in the extratropics but also for climate change projections."

These internal variations in the jet stream can represent the maintenance of atmospheric blocking, and both are important to account for in useful seasonal range forecasting. Also, as the climate changes there may be a change in jet stream behavior, but the internal variations will remain. Conversely, if more complicated models cannot replicate annular mode behavior noted in the observations and the simpler model here in future climate change scenarios, the model projections would be worthless.

Archived 30 October 2012