Closely related to the previously mentioned situation are cases of sharply curved ridges where the gradient in the sharply curved portion (usually the northern portions of a north-south ridge) has momentarily built up to a strength that is incompatible with the anticyclonic curvature. Such ridges often collapse with great rapidity prior to the development of such excessive gradients, causing rapid filling of the adjacent downstream trough, and large upper contour falls. The gradient wind relation implies that subsequent trajectories of the high-speed parcels generated in the strong ridge line gradient must be less anticyclonically curved than the contours in the ridge.

It can also be shown from the gradient wind equation that the anticyclonic curvature increases as the difference between the actual wind and the geostrophic wind increases, until the actual wind is twice the geostrophic wind, when the trajectory curvature is at a maximum. This fact can be used in determining the trajectory of high-speed parcels approaching sharply curved stationary ridges or sharply curved stationary ridges with strong gradients. By measuring the geostrophic wind in the ridge, the maximum trajectory curvature can be obtained from the gradient wind scale.

This trajectory curve is the one that an air parcel at the origin point of the scale will follow until it intersects the correction curve from the geostrophic speed to the displacement curve of twice the geostrophic speed.

If actual wind speed observations are available for parcels approaching the ridge, comparison can be made with the geostrophic winds (pressure gradient) in the ridge. If the actual speeds are more than twice the measured geostrophic wind in the ridge, the anticyclonic curvature of these high-speed parcels will be less than the maximum trajectory curvature obtained from the gradient wind scale, and even greater overshooting of these high-speed parcels will occur across lower contours. Convergence in the west side of the downstream trough results in lifting of the tropopause with dynamic cooling and upper-level contour rises.

Low-speed winds approaching an area of stronger gradient become subject to an unbalanced gradient force toward the left due to the weaker Coriolis force. These subgradient winds are deflected toward lower pressure, crossing contours and producing contour rises in the area of cross-contour flow. This cross-contour flow accelerates the air until it is moving fast enough to be balanced by the stronger pressure gradient. Due to the acceleration of the slower oncoming parcels of air, the contour rises propagate much faster than might be expected on the basis of the slow speed of the air as it initially enters the stronger pressure gradient.

The following two rules summarize the discussion of subgradient winds:

. High-speed winds approaching low-speed winds with weak cyclonically curved contour gradients are indicative of divergence and upper-height falls downstream to the left of the current.

. Low-speed winds approaching strong, cyclonically curved contour gradients or high-speed winds approaching low-speed winds with weak anticyclonically curved contour gradients are indicative of convergence and upper height rises downstream and to the left and right of the current, respectively.

IMPORTANCE OF CONVERGENCE AND DIVERGENCE

Convergence and divergence have a pronounced effect upon the weather occurring in the atmosphere. Vertical motion, either upward or downward, is recognized as an important parameter in the atmosphere. For instance, extensive regions of precipitation associated with extratropical cyclones are regions of large-scale upward motion. Similarly, the nearly cloud-free regions in large anticyclones are regions in which air is subsiding. Vertical motions also affect temperature, humidity, and other meteorological elements.

When convergence or divergence occurs, whether on a large or small scale, it may have a very pronounced effect on the stability of the air. For example, when convection is induced by convergence, air is forced to rise without the addition of heat. If this air is unsaturated, it cools first at the dry adiabatic rate; or if saturated at the moist rate. The end result is that the air is cooled, which will increase the instability y of that air column due to a net release of heat. Clouds and weather often result from this process.

Conversely, if air subsides, and this process is produced by convergence or divergence, the sinking air will heat at the dry adiabatic lapse rate due to compression. The warming at the top of an air column will increase the stability of that air column by reducing the lapse rate. Such warming often dissipates existing clouds or prevents the formation of new clouds. If sufficient warming due to the downward motion takes place, a subsidence inversion is produced.

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