5.4: CAPE and CIN
- Page ID
- 46230
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The “positive area” between the parcel path and the environmental temperature profile, traced out between the LFC and the EL (where the parcel is warmer than the environment) gives a measure of the Convective Available Potential Energy, or CAPE, given in units of J·kg–1. This is an estimate of the buoyant energy of a parcel and can provide a means of estimating the strength of any convection that may occur. CAPE can also provide an estimate of the maximum updraft intensity in a thunderstorm.
\[w_{\text {max }} \sim 0.60 \cdot(2 \cdot CAPE)^{\frac{1}{2}} \nonumber \]
\(w_{\text {max }}\) is the estimated maximum vertical motion as a result of CAPE.
Convective Inhibition, or CIN is essentially negative CAPE, also in J·kg–1. It is the negative area between the parcel path and the environmental temperature curve where the parcel is cooler than the environment. The larger the value of CIN, the greater the negative buoyant energy that acts against CAPE. CIN sometimes acts as a “cap” on convection. If you have large CAPE but also large CIN, your CAPE may not be fully realized as buoyant energy and you may not have any convection. However, if your parcel is able to break through the cap, that is, if it is able to rise and become warmer than the environment, convection may be strong.
The figure below shows the locations of the LFC and EL, and shades in both positive and negative areas between the parcel path and the environmental temperature profile.
In the Lihue and Hilo soundings shown previously, values of CAPE and CIN are given in J·kg–1 in the column on the right hand side. Note that CIN is written as “CINS” and denoted as a negative value.
Locating the Tropopause
Recall that the standard temperature decreases with height within the troposphere, but becomes isothermal with height within the the tropopause, and increases with height in the stratosphere. With this knowledge, the location of the tropopause, given by its pressure level, can be determined by examining a plotted sounding. In the upper part of your sounding, look for where the temperature profile becomes isothermal (parallel to your skewed isotherms) or for an inversion (where the temperature increases with height, which will be tilted to the right more than your isotherms). The base of the isothermal layer in your sounding is the tropopause.
There are many things we can learn about the atmosphere from Skew-T Log-P diagrams. Here we’ve provided just the basics to get you started.
Chapter 5: Questions to Consider
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Query \(\PageIndex{1}\)
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Query \(\PageIndex{2}\)
- Drag and drop terms to their correct position in the atmospheric stability diagram below:
Query \(\PageIndex{3}\)
- What does the Lifting Condensation Level (LCL) represent? How can it be found on a Skew-T diagram?
- What is CAPE? How can it be found on a Skew-T diagram?
Selected Practice Question Answers:
Query \(\PageIndex{4}\)