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Page Title: Critical eccentricity
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CRITICAL ECCENTRICITY. When a migratory system is unusually intense, the system may extend vertically beyond the 300-hPa level. Advection considerations, contour-isotherm relationships, convergence and divergence considerations, and the location of the jet max will yield the movement vector. These principles are applied in the same manner as when the movement of long waves are determined. The eccentricity formula may be applied to derive a movement vector, but only when a nearly straight eastward or westward movement is apparent.

Migratory lows also follow the steering principle and the mean climatological tracks. The climatological tracks must be used cautiously for the obvious reasons. The rise and fall centers of the time differential charts are of great aid in determining an extrapolated movement vector, and extrapolation is the primary method by which the movement of a closed low is determined.

Certain cutoff lows and migratory dynamic cold lows lend themselves to movement calculation by the eccentricity formula. The conditions under which this formula may be applied are:

. The low must have one or more closed contours (nearly circular in shape).

. The strongest winds must be directly north or south of the center. The location of the max winds determines the direction of movement. When the strongest winds are the easterlies north of the low, the low moves westward; when the strongest winds are the westerlies south of the low, the low will move eastward.

The low will also move toward the weakest diverging cyclonic gradient and parallel to the strongest current. Systems moving eastward must have a greater speed in order to overcome convergence upstream-there is normally convergence east of a low system.

The eccentricity formula is written:

E c =V -V -2C

or

2 C =V -V -EC

where

Ec is the critical eccentricity y value.

V is the wind speed south of the closed low.

V is the wind speed north of the closed low.

C is the speed of the closed low (in knots).

To obtain the value of C, it is necessary to determine the latitude of the center of the low and the spread (in degrees latitude) between the strongest winds in the low and the center of the low. Apply these values to table 2-1 to determine the tabular value. Apply the tabular value to the critical eccentricity formula to obtain 2C, thus C. In determining the critical eccentricity of a system, it is necessary to interpolate both for latitude and the spread. A negative value for C indicates westward movement; a positive value indicates eastward movement.

LOCATION OF THE JET STREAM. As long as a jet maximum is situated, or moves to the western side of a low, this low will not move. When the jet center has rounded the southern periphery of the low, and is not followed by another center upstream, the low will move rapidly and fill.

Table 2-1.-Critical Eccentricity Value

ISOTHERM-CONTOUR RELATIONSHIP. Little movement will occur if the isotherms and contours are symmetrical (no advection). Lows will intensify and retrogress if cold air advection occurs to the west and fill and progress eastward if warm air advection occurs to the west.

FORECASTING THE INTENSITY OF UPPER LEVEL AND ASSOCIATED SURFACE FEATURES

Many of the same considerations used in the movement of closed centers aloft may also apply to forecasting their intensity. Extrapolation and the use of time differentials aid in forecasting the change and magnitude of increases and decreases. Again, rise and fall indications must be used in conjunction with advection considerations, divergence indications, and other previously discussed factors.

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