Experiments with time-invariant basic states

The case studies discussed above show that, during periods of transition to blocking, finite-time unstable barotropic perturbations tend to develop dipole structures which (with the appropriate sign) can resemble the tendency patterns associated with blocking onset. However, one must remember that part of the observed tendency (namely, its projection onto spherical harmonics with total wavenumber < 10) is already included in the time-evolving basic state. One may ask whether finite-time barotropic instability would generate such dipole structures even in the presence of a stationary basic state.

To verify this, we have constructed two composite basic states representative of flows preceding the onset of Pacific and Euro-Atlantic blocks, and we have computed barotropic singular vectors keeping these basic states constant during the optimization period. More precisely, using the planetary wave profile from the Hovmoller diagram in Fig. 4.1 we have selected the 18 days (out o f 90) with the largest positive wave amplitude in the sectors 180° to 140°W (for Pacific blocking) and 5°W to 35°E (for Euro-Atlantic blocking). The basic states for the computation of /z-day singular vectors have been defined as the averages of the 30 kPa vorticity fields occurring n days before

the 18 selected dates. The computation has been performed for optimization times o f 4 and 6 days; results are qualitatively similar, and those for the

shorter time {n -4 ) will be discussed here.

For both the Pacific and the Euro-Atlantic sector, Fig. 4.12 shows the 30 kPa stream function o f the basic state defined above, together with the composite stream function 4 days later (when the maxima in wave amplitude are observed). In the Pacific basic state (Fig. 4.12a), a large-scale ridge is located on the north-eastern side of the ocean. Four days later (Fig. 4.12b), this feature evolves into a well-defined blocking pattern; around 170°W, the stream function gradient between 60° and 40°N is reversed, satisfying the

Lejenas and Okland (1983) blocking criterion. In the Euro-Atlantic sector, the four-day development is even more pronounced: a strongly diffluent flow in the basic state (Fig. 4.12c) evolves into a blocking pattern four days later (Fig. 4.12d), with reversed zonal flow around 20°E.

Figure 4.13 shows the structure of the first three singular vectors of the Pacific basic state at the initial and final time (note that the area shown in Fig. 4.13 comprises the tropics to show the initial location of the singular vectors). All o f them are confined to the Pacific-north American region; their amplification factors are 4.5, 3.7 and 3.6 respectively (compared with the values in Fig. 4.3b). As already noted by Molteni and Palmer (1993), using a composite, time-invariant basic state instead of actual, time evolving fields considerably reduces the growth rate of both barotropic and baroclinie singular vectors.

At final time, the first singular vector has indeed a dipole structure over the central Pacific, with zonally elongated features; however, because of its large meridional scale it resembles more Wallace and GutzlePs (1981) Pacific- north American teleconnection pattern than a typical blocking anomaly. In the second singular vector, the features over the north-east Pacific are again zonally elongated, with a more northerly position than in the first singular vector. The third singular vector also has a dipole structure between 60° and 40°N, although its northern component is relatively weak.

At the initial time, all these singular vectors have a large component in the tropical regions around Indonesia and the Philippines, and in the first two singular vectors there is also considerable amplitude in the north-west Pacific

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Figure 4.12. C om posite basic states, a): Pacific com posite com puted averaging the 30 kPa stream function fields occurring 4 days before the selected dates (see text), b): P acific com posite 4 days later, c): as a) but for the Atlantic com posite, d): Atlantic com posite 4 days later. Contour internal 15 10^ nds'^. (From Buizza and M olteni, 1996.)

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Figure 4.13. First 3 singular vectors (stream function) o f the Pacific com posite at initial (left panels) and final (right panels) time (note that the area shown in the figure has been extended to include the tropics), a-b): -singular vector 1. c-d): singular vector 2. e-f): singular vector 3. Contour interval JO^ m~s'^ at initial time and 5 10^ m's ‘ at final tim e. (From Buizza and Molteni, 1996.)

and eastern Siberia.

When the Atlantic basic state (Fig. 4.12c) is used, one finds that again the first three singular vectors are located in the Pacific region. It seems that the vorticity gradients in the Atlantic diffluent flow are not able to 'overcome' the strong meridional gradient in the region of the Pacific jet as a source of barotropic instability. However, as shown in Fig. 4.14a (note that the area shown in Fig. 4.14 comprises the tropics to show the initial location of the singular vectors), in the absence of strong difluence downstream, the structure of the first singular vector at final time is very different from the first singular vector obtained in the previous case: it consists of a meridionally elongated wave train propagating along 30°N, with no sign of a north-south dipole. Its amplification factor is also reduced to 3.7. The structure at initial time shows that this perturbation has primarily a tropical origin.

In order to find perturbations localized in the Euro-Atlantic sector, one has to consider the fourth and sixth singular vectors, which may be considered a rather disappointing result since the amplification factor reduces to 2.9 and 2.8 respectively. On the other hand, at final time these two singular vectors (Figs. 4.14d-f) have a very well defined dipole structure with zonally elongated features, and their spatial scale is in good agreement with typical blocking anomalies.

At initial time, these singular vectors have most o f their amplitude in the western Atlantic, although their pattern extends to the eastern part of the ocean in the tropics.