Using Satellite Imagery to Visualize Patterns due to Horizontal Divergence in the Atmosphere and the Ocean

Three dimensional velocity divergence is an important kinematic variable in both dynamic/synoptic meteorology and physical oceanography. Since the atmosphere is compressible, but the ocean is basically incompressible, the manner in which divergence "appears" in the atmosphere differs a bit from the manner it appears in the ocean. Scaling mass continuity for incompressibility is called the "Boussinesq Approximation."

However, it is interesting to point out that at the synoptic scale, the atmosphere CAN be treated as an incompressible fluid. That's the way we get to an important conceptual principle in meteorology called Dine's Compensation, which is, basically, the principle of Conservation of Mass applied to the atmosphere. It also applies to the oceans.

Meteorological and Oceanographic Applications

Dines Compensation, physically interpreted, says that if lateral spreading occurs at the top of a layer, then upward motion occurs through the bottom of the layer, and vice versa.

Upper tropospheric (ocean surface) divergence tends to be associated with rising motion in the mid-troposphere (upwelling in the layer beneath the ocean surface) and lower tropospheric (bottom layer) convergence.

Divergence at the top of the troposphere (ocean) surmounts upward motions.  Convergence at the top of the troposphere (ocean) surmounts subsidence.

The inset just below gives a quick derivation of the pertinent equation in meteorology and oceanography, with an overview of how to calculate it. This should be a review for the students who had Metr 201/430 and Ocn 420.

divergence equations(1a, b, c)

finite difference

The core of the concept of Dine’s Compensation is embedded in Equation (1b, c).

Divergence/Convergence in the Atmosphere and Ocean

You will learn that divergence/convergence can occur in the atmosphere and the ocean in association with certain geometries or patterns evident in the streamline patterns of flow. With respect to the major jet streams and currents in the ocean, the following generally can be observed (and will be discussed at length in future Metr 430/520/530 or Ocn 420).

A good deal of the divergence and convergence in the atmosphere's troposphere is associated with the changes in the heights of air columns (changing densities) and disruption of geostrophy that occurs with differential heating and cooling (Link to Metr 201 Discussion). This is a minor effect in the oceans, because of the ocean's near incompressibility. However, divergence and convergence patterns occur in association with disturbances in the jet stream and ocean currents that are in near-geostrophic equilibrium.

It turns out that a good deal of the MOTION of the disturbances (meanders) found in the jet or in currents can be explained by divergence and convergence patterns....generally, the troughs (areas of low heights or low altimetry in meanders) progress in the direction of the current, while large closed eddies retrogress (move towards the west):

Atmosphere

1. Meanders in the Jet in Upper Troposphere

Divergence found on eastern side of troughs and western side of ridges (from trough axis to ridge axis). Convergence on eastern side of ridges and western side of troughs (from ridge axis to trough axis). (Subsidiary result, troughs and ridges move eastward, in the direction of the flow).

2. Large Cut-off Lows and Highs (Eddies) (Perfectly Symmetric)

Very weak divergence found on the western side of cut-off lows and eastern side of cut-off highs. Very weak convergence found on eastern side of cut-off lows and western side of cut-off highs. (Subsidiary result is that eddies tend to move westward against the direction of the flow).

Oceans

1. Meanders at the Surface of the Ocean in the Major Currents

Divergence found on eastern side of areas of low altimetry (troughs) and western side of areas of high altimetry. Convergence on eastern side of high altimetry and western side of low altimetry. (Subsidiary result, meanders move eastward, in the direction of the flow). (Compare schematic chart for ocean currents, with schematic chart for upper troposphere. Do you see cloud or temperature patterns that appear to have the same sort of geometry?)

2. Large Enclosed Eddies (Cold and Warm Rings)

Divergence found on the western side of cold rings and eastern side of warm rings. Convergence found on eastern side of cold rings and western side of warm rings. (Subsidiary result is that eddies tend to move westward against the direction of the flow). Closed Eddies (Cold and Warm Rings)