Image from page 785 of "Compendium of meteorology" (1951)
Title: Compendium of meteorology
Publisher: Boston : American Meteorological Society
Contributing Library: MBLWHOI Library
Digitizing Sponsor: Boston Library Consortium Member Libraries
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772 WEATHER FORECASTING maps, Petterssen has reported how the percentage fre- quency of cyclones and cyclogenesis is distributed over the whole Northern Hemisphere [62, Figs. 14-21]. He has also given the rate of alternation between cyclones and anticyclones, indicating the distribution of travel- ing disturbances [62, Figs. 22-23]. The frontogenesis builds up cyclonic shear vorticity which is transferred into vorticity of cyclonically curved flow at the apex of the frontal wave. Large initial frontal shear is therefore a sign of "stored" kinetic energy which, in being transformed to curvature vor- ticity, favors the evolution of the wave into a cyclone. The intensity of the frontal cyclogenesis may partly be conjectured by the forecaster from the observed horizontal velocity differences between the air masses. In particular, under the assumption of a normal air- mass stratification, sufficiently long waves are usually unstable provided that—according to an old rule—the wind shear along the front in knots is greater than four times the temperature discontinuity in centigrade degrees. Qualitative examples of such reasoning concerning cyclogenesis due to the individual change of vorticity of traveling particles are demonstrated in Fig. 2. The FRICTIONAL EFFECT TILT INCREASING TILT DECREASING SHARP FRONT T—r DIFFUSE FRONT I-KM ISOHYPSE OF FRONT 2-KM ISOHYPSE OF FRONT
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CYCLOGENETIC FRONT ACTIVITY ACTIVE MEDIUM PASSIVE KATAFRONT ANAFRONT Fig. 2.—Frontal activitj' and passivitj' according to Bergeron, and vorticity d-j'namics of cyclones according to Bjerknes . cold air sample a moves equatorward and partakes in the general convergence typical for the forward half of a cyclone. For both reasons cyclonic relative vorticity is acquired, which at first shows up on the surface map mainly as a horizontal cyclonic shear inside the cold air along the warm front. In passing the wave apex, this air maintains its cyclonic relative vorticity, which then is manifested as curvature vorticity. With- in the strongly cyclonically curving easterly branch b of the cold current, a low-layer frictional convergence and lifting of the polar air contributes toward in- creasing the slope of the advancing cold front surface as shown by the frontal topography in the figure. Farther behind the apex the cold air samples c and d are in a region of horizontal divergence strong enough to make their cyclonic vorticity decrease or change into anticyclonic vorticity despite the southward dis- placement. During the growth of the cyclone, more and more of the cold air is able to maintain its cyclonic vorticity after passing the wave apex, such as repre- sented by the life history a-b. Within the anticy- clonically curving westerly branch d the low-layer sub- sidence combines with the effect of ground friction to decrease the slope of the front, as shown through frontal isohypses in Fig. 2. The samples e and /, al- though moving poleward into their respective cyclones, experience sufficient horizontal convergence to acquire some cyclonic vorticity. The warm air samples g and h, passing at greater distances from their respective centers, do not have enough horizontal convergence to prevent their acquiring anticyclonic vorticity through poleward displacement. Warm air also ascends to the base of the westerly jet stream aloft and at the same time arrives at the poleward edge of the region of maximum frontal upgliding. Hence, this warm air also gains anticyclonic vorticity from the effect of the ver- tical velocity terms, which under these conditions is appreciable even in comparison with the effects of both poleward motion and divergence. Already in 1934 Scherhag  had pointed out that a cyclone with strong upper winds deepens. The stronger the upper westerlies have been built up during the frontogenetical period, the more they are apt to form unstable upper waves. A check on the possible occurrence of unstable anticyclonic curvature upwind from the cyclogenetic area will often give a clue to the deepening of the upper cold trough over the rear part of the cyclone. This shows up in the surface map as a deepening of the nonfrontal cold trough and the central part of the cyclone. (For more details, see pp. 587-597 in "Extratropical Cyclones" by J. Bjerknes in this Compendium.) The instability of the wave varies also with the difference in the static stability of the adjacent air masses. In this connection we may mention that, in general, waves on a polar front are more often unstable than those on an arctic front. Since increasing in- stability of an air mass favors cyclonic deepening, cyclones can deepen in winter by motion from land out over the sea. Moreover, where (in the analyzed upper-air maps) both the absolute isohypses^ and the total relative isohypses^ are close together and the two sets of lines intersect approximately at right angles, cyclogenesis is often occurring in the region of higher relative height^ and lower absolute height,' according to synoptic experience. In particular, if the spacing of the relative isohypses on the rear side of the low is less than that on the forward side—and this is the normal case—then, according to Pogade , the cy- clone will deepen. (In the next subsection, we mention Petterssen's rule that the cyclones also tend to mi- grate toward this anterior concentration of horizontal, 5. For definition see Table I.
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