Stability problem example sounding

Figure 7.13 shows a typical sounding. In this example the air near the surface is unsaturated since the dew point is less than the air temperature. When lifted, the air follows a dry adiabat until it reaches the LCL as depicted in the graph. Further uplifting is along a moist adiabat (indicated by the dashed line). The first intersection of this moist adiabat with the sounding curve occurs at the level of free convection (LFC on the graph). If a parcel is lifted to a height lower than the LFC, it returns toward the surface because it experiences negative buoyancy since it is

Figure 7.13 Illustration of a hypothetical sounding. Solid curves correspond to air temperature and dew point sounding, the dashed curve shows the actual path of a parcel lifting from the surface.

Figure 7.13 Illustration of a hypothetical sounding. Solid curves correspond to air temperature and dew point sounding, the dashed curve shows the actual path of a parcel lifting from the surface.

always cooler than the environment along its path. If, however, the parcel reaches the LFC, it becomes warmer than its surroundings. So, the LFC is the level where the parcel becomes positively buoyant. The positive buoyancy carries the parcel up to the level of neutral buoyancy (LNB), where the parcel's path intersects with the (measured) temperature sounding.

In Chapter 6 we discussed stability criteria for an unsaturated parcel. Let us apply these to different layers of the sounding. By layer we mean a thin slab of air along the sounding across which there is an approximately constant lapse rate. Consider the stability of layers depicted on Figure 7.13 (Figure 7.14 enlarges the part of the chart we are interested in).

Layer AB is stable since its lapse rate is less than the dry adiabatic lapse rate. Layer BC is a layer exhibiting a slight inversion. An inversion occurs in a layer when the temperature increases with height - such a layer is obviously stable. The layer CD is also stable, its lapse rate being less than the dry adiabatic lapse rate. The layer DE is neutral; it is parallel to the dry adiabat, so temperature decreases at the same rate as with a dry adiabatic process.

Now consider the case when the temperature decreases with height at a rate less than the dry adiabatic lapse rate but greater than the moist adiabatic lapse rate, rd > r > Tm (for example, layer AB). An air parcel in layer AB is negatively buoyant if lifted a short distance but could become positively buoyant if an imposed vertical motion is strong enough to bring this parcel to its level of free convection (LFC). For example, the air might be pushed up a mountainside or lifted by mechanically induced overturning (turbulence). Such a situation is called conditional instability. The layer is stable when air is unsaturated, but could become unstable with externally imposed vertical motion. We can test the layer for

Figure 7.14 The enlarged area of interest of the sounding shown in Figure 7.13.

conditional instability by calculating the vertical gradient of saturation equivalent potential temperature d0s/dz, rather than by calculating the lapse rate. In the case of conditional instability d0s/dz < 0. Indeed, one can see from the graph (Figure 7.14) that 0s(A) > 0s(B). If r = rm (A and B are on the same moist adiabat), then 0s(A) = 0s(B), and d0s/dz = 0.

To summarize, if the temperature in the particular layer decreases at a rate greater than the dry adiabatic lapse rate, this layer is unstable in any case for both saturated and unsaturated parcels. If the temperature decreases at a rate less than the moist adiabatic lapse rate, this layer is absolutely stable; the saturation equivalent potential temperature increases with height in this case. The formulas below list the stability criteria:

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