## Convective available potential energy CAPE

In previous sections we analyzed the stability of the displacement of a small parcel in terms of temperature lapse rate. In this section we will continue to analyze stability, but in terms of energy. We have already shown that when there is a positive area in the closed loop between environmental and adiabatic curves on a T-ln p diagram or, in other words, if a parcel (after a nudge) is positively buoyant, the parcel's kinetic energy increases. Consider a parcel being initially unsaturated in a conditionally unstable atmosphere. We denote the parcel's initial location by A in the example of a temperature sounding shown in Figure 7.13. When lifted, the parcel first follows a dry adiabat until it reaches the LCL. With further lifting, it follows a moist adiabat. If the upward motion is strong enough to bring the parcel to its LFC, the parcel becomes positively buoyant. Figure 7.16 shows the same sounding as Figure 7.13. The positive area (shaded dark on Figure 7.16) between the parcel's path and the sounding bounded by the LFC and the LNB is called the convective available potential energy (CAPE). CAPE represents the maximum kinetic energy that a positively buoyant parcel can acquire by ascending without exchanging momentum (eddy friction), heat and moisture with its environment. -20 -10 0 10 20 30 40 0.6 1.0 2.0 3.0 5.0 10.0 20.0 40.0

g/kg

Figure 7.16 The same sounding as in Figure 7.13. Dark and light gray areas represent convective available potential energy (CAPE) and convective inhibition energy (CIN) correspondingly.

600 700 800 900 1000

-20 -10 0 10 20 30 40 0.6 1.0 2.0 3.0 5.0 10.0 20.0 40.0

g/kg

Figure 7.16 The same sounding as in Figure 7.13. Dark and light gray areas represent convective available potential energy (CAPE) and convective inhibition energy (CIN) correspondingly.

We can calculate the ideal change of kinetic energy per unit mass due to positive buoyancy by integrating (7.5) from LFC to LNB. The amount of kinetic energy released in this situation is f ZLNB Ta - Te CAPE = AK = g—-- dz.

CAPE is a useful measure of thunderstorm severity, since it allows us to estimate the value of maximum possible vertical velocity. Indeed, if a parcel has zero vertical velocity at the LFC, then from (7.17)

wmax

In this consideration we have neglected the effect of water condensation, which reduces buoyancy slightly. Values of CAPE greater than 1000 J kg-1 imply the possibility of strong convection. Even if the final vertical velocity is less than the maximum value, the energy is still dissipated in turbulence within the cloud.

Let us return now to Figure 7.13. Before the parcel starting at point A reaches its LFC, it has to overcome a potential energy barrier between the LCL and the LFC, where a parcel is cooler than its environment and negative buoyancy tends to return the parcel toward the surface. This negative area between the parcel's path and environment bounded by the LCL and the LFC is called the convective inhibition energy (CIN). It is shown as the light gray area in Figure 7.16. CIN controls whether convection actually occurs. It is a measure of how much energy is required to overcome the negative buoyancy and allow convection. To find CIN we have to integrate (7.5) from the LCL to the LFC, namely rZLFc Ta - Te CIN = / g dz.

If the CIN is greater than 100 J kg 1, a significant source of lifting is needed to bring the parcel to its LFC in order to create favorable conditions for deep convection. Figure 7.17 The same sounding as in Figure 7.13. For a parcel originating at point B, CAPE is zero.

600 700 800 900 1000

Figure 7.17 The same sounding as in Figure 7.13. For a parcel originating at point B, CAPE is zero. 0.1 0.2 0.6 1.0 2.0 3.0 5.0 10.0 20.0 40.0 g/kg Figure 7.18 Illustration of a hypothetical sounding.

0.1 0.2 0.6 1.0 2.0 3.0 5.0 10.0 20.0 40.0 g/kg Figure 7.18 Illustration of a hypothetical sounding.

If we, for example, are interested in the CAPE of an air parcel starting at point B rather than at point A on the same sounding diagram (Figure 7.17), then the CAPE is zero. The path of the parcel starting at point B is shown by a dashed line on Figure 7.17. This parcel is always cooler than its local environment. It is important to note that the value of CAPE depends on the initial parcel location.

Consider the sounding shown in Figure 7.18. A parcel starting from the surface will experience negative buoyancy. The area corresponding to the CIN is shown in light gray in Figure 7.19, which simply enlarges the part of Figure 7.18 we are interested in. The area shaded in darker gray corresponds to the CAPE. To become positively buoyant, a parcel started from the surface (point A on the graph) has to overcome this "light gray" area. Imagine now that we expect the surface to be warmed in the next couple of hours. Then, instead of point A, the parcel starts from point A1 (Figure 7.20). It does not experience negative buoyancy any longer; its LFC coincides with its LCL, and these are excellent conditions for severe thunderstorm activity. If, on the contrary, we expect the surface to be cooled (Figure 7.21, point Figure 7.19 The same sounding as in Figure 7.18. CAPE and CIN for the parcel started from the surface (point A) are shown in dark and light gray correspondingly. Figure 7.20 The same sounding as in Figure 7.18. Illustration of a hypothetical surface warming. For the parcel originating at point Ai, there is no CIN.

A2), then the situation is reversed. CIN becomes larger, and CAPE is smaller than the previous situation. This means that the conditions for a thunderstorm are no longer favorable.

Fortunately for the forecaster, the values of many of the parameters discussed above (CAPE, CIN, etc.) are printed right on the skew T charts that are published at many sites on the internet. Hence, no tedious computations of areas are necessary by the user. Figure 7.21 The same sounding as in Figure 7.18. Illustration of a hypothetical surface cooling. For the parcel originated from point A2, CAPE decreases, but CIN increases in comparison with the parcel started from A.