Convective Available Potential Energy (CAPE) & Lifted Index: Calculating Updraft Speeds and Thunderstorm Severity

1. Outdoor Observer Field Notes: The Calm, the Swelter, and the Towering Sky

On a suffocating midsummer afternoon across the continental mid-latitudes, the atmosphere often assumes an ominous, breathless stillness. The air feels palpable—thick, humid, and heavy with moisture. Dew points climb past $20^\circ\text{C}$ ($68^\circ\text{F}$), coating the skin in persistent perspiration that refuses to evaporate. In the grass and tree canopies, the breeze dies to an absolute lull. The barometric altimeter on a hiker’s wrist watch or an outdoor barometer begins a slow, perceptible descent, dropping millibar by millibar as solar insolation pumps gigawatts of thermal energy into the planetary boundary layer.

To the untrained eye, the sky appears deceptively tranquil, save for small, flat-bottomed cumulus clouds drifting across the blue. Yet to an atmospheric physicist or experienced outdoor observer, these innocent flecks of white are the visible exhaust tips of rising thermal plumes.

                          THE LIFE CYCLE OF A SEVERE UPDRAFT

       Equilibrium Level (EL) ~ 12 km ----------------------- +------------------ (Overshooting Top)
                                                             /  Anvil (Incus)     \
                                                            /                      \
                                                           |   Hail Growth Zone    |
                                                           |   (-10°C to -30°C)    |
                                                           |                       |
                                                           |    Violent Updraft    |
                                                           |   w_max = sqrt(2*CAPE)|
                                                           |       [ > 40 m/s ]    |
                                                           |                       |
       Level of Free Convection (LFC) ~ 2 km --------------\                       /
                                                            |  Capped Layer (CIN)  |
       Lifting Condensation Level (LCL) ~ 1 km -------------+----------------------+ (Cloud Base)
                                                                 ^    ^    ^
       Surface Boundary Layer -----------------------------------|----|----|------- (Solar Heating / Inflow)

Within an hour, the morphology of the sky undergoes a violent transformation. The puffy cumulus humilis aggregate and swell into cumulus congestus—cauliflower-like towers that billow upward with ferocious speed. If the mid-troposphere is suitably unstable, these towers pierce the capping inversion in minutes. Crisp, hard-edged plumes surge into the upper troposphere at speeds exceeding 30 to 50 metres per second, flattening against the stable stratosphere into a sprawling, fibrous anvil: cumulonimbus incus.

A sudden, sharp drop in ambient temperature heralds the arrival of the gust front. The sweet, metallic fragrance of ozone and petrichor fills the nostrils as rain-cooled downdrafts slam into the ground and radiate outward. Overhead, the storm’s underbelly turns a bruised slate-green—a spectral signature caused by the scattering of sunlight through billions of suspended ice hydrometeors and giant hailstones. The stage is set: the atmosphere is violently balancing a thermodynamic disequilibrium, converting invisible potential energy into the raw kinetic fury of a convective storm.

2. Physical Principles & Intuitive Science: The Atmosphere as a Giant Heat Engine

To understand how a placid summer day metastasizes into an explosive storm, one must treat the troposphere as a massive thermodynamic heat engine governed by Archimedes' principle and the ideal gas law. Convection is fundamentally the vertical transport of heat and moisture driven by density differences between an air parcel and its surrounding environment.

       ENVIRONMENTAL PROFILE                           RISING AIR PARCEL

       Cold Upper Troposphere (T_env)                  Warm, Condensing Parcel (T_parcel)
       Dense, High Density (rho_env)                   Low Density, Highly Buoyant (rho_parcel)
             |                                               |
             |                                               |
             +------------------- BUOYANCY FORCE ------------+
                                  B = g * (rho_env - rho_parcel) / rho_parcel
                                    = g * (T_parcel - T_env) / T_env

Parcel Theory and Hydrostatic Balance

Meteorologists employ an idealized conceptual framework known as parcel theory. Imagine a discrete, flexible, thermally insulated bubble of air—a "parcel"—moving vertically through the ambient atmosphere. The ambient air is governed by the hydrostatic equation, which describes the balance between the downward pull of gravity and the upward pressure gradient force:

$$\frac{dP}{dz} = -\rho_{\text{env}} g$$

Where $P$ is pressure, $z$ is geopotential height, $\rho_{\text{env}}$ is the environmental air density, and $g \approx 9.81\text{ m/s}^2$ is gravitational acceleration.

When a parcel of air is forced upward (by solar surface heating, topography, or a frontal boundary), it enters regions of progressively lower atmospheric pressure. To maintain mechanical equilibrium with its surroundings, the parcel expands. Expansion requires thermodynamic work, and because air is a poor conductor of heat, this process is approximately adiabatic: the parcel expends its own internal thermal energy, causing its temperature to drop.

The Duel of Lapse Rates

The rate at which a rising parcel cools depends strictly on its moisture content:

1. Dry Adiabatic Lapse Rate ($\Gamma_d$): An unsaturated parcel cools at a constant rate of approximately $9.8^\circ\text{C}$ per kilometre ($9.8\text{ K/km}$).
2. Saturated (Moist) Adiabatic Lapse Rate ($\Gamma_m$): Once the rising parcel cools to its dew point, moisture condenses into liquid cloud droplets at the Lifting Condensation Level (LCL). Condensation releases vast reservoirs of latent heat of vaporization ($L_v \approx 2.5 \times 10^6\text{ J/kg}$). This latent heat partially offsets adiabatic cooling, reducing the lapse rate to between $4^\circ\text{C/km}$ (in warm, tropical lower tropospheres) and $7^\circ\text{C/km}$ (in colder mid-tropospheric air).

  Height (km)
      ^
   12 |                      \  Environmental Sounding (T_env)
   10 |                       \       /  Moist Adiabat (T_parcel)
    8 |                        \     / 
    6 |                         \   /   <--- POSITIVE AREA (CAPE)
    4 |                          \ /         (Parcel is warmer than environment)
    2 |  --- LFC -----------------X
      |  --- LCL ---------       / \    <--- NEGATIVE AREA (CIN)
    0 +------------------+------+---+-----------------------------> Temperature (°C)
                       -40    -20   0   +20

Atmospheric instability emerges when the environmental lapse rate ($\Gamma_e = -dT_{\text{env}}/dz$)—the actual temperature profile measured by weather balloons launched by agencies like the National Oceanic and Atmospheric Administration (NOAA) or the Met Office—is steeper than the moist adiabatic lapse rate ($\Gamma_e > \Gamma_m$). Under these conditionally unstable conditions, once a saturated parcel is pushed above its Level of Free Convection (LFC), it becomes inherently warmer and less dense than the ambient air at every subsequent altitude, accelerating skyward like a submerged cork released under water until it strikes the Equilibrium Level (EL) near the tropopause.

3. Accessible Mathematical Foundations: Buoyancy, CAPE, and Updraft Kinetics

To quantify the explosive potential of this buoyant engine, atmospheric physicists integrate the net buoyant force across the vertical depth of the troposphere. Let us trace this derivation from basic Newtonian mechanics to the operational metrics displayed on weather forecast soundings.

Derivation of Parcel Buoyancy

Consider a parcel of volume $V$, density $\rho_p$, and mass $m = \rho_p V$, immersed in environmental air of density $\rho_e$. The net vertical force $F_{\text{net}}$ acting on the parcel is the vector sum of the upward Archimedean buoyant force ($F_B = \rho_e V g$) and the downward gravitational weight ($F_g = -\rho_p V g$):

$$F_{\text{net}} = F_B - F_g = (\rho_e - \rho_p) V g$$

Dividing by the parcel's mass $m = \rho_p V$ yields the vertical acceleration, defined as the buoyancy parameter $B$ (with units of $\text{m/s}^2$):

$$B = \frac{F_{\text{net}}}{m} = g \left( \frac{\rho_e - \rho_p}{\rho_p} \right)$$

Invoking the ideal gas law for dry air ($P = \rho R_d T$, where $R_d = 287.058\text{ J/(kg}\cdot\text{K)}$ is the specific gas constant for dry air), and assuming isobaric equilibrium between the parcel and its immediate environment ($P_p = P_e = P$), we substitute density with temperature:

$$\rho_e = \frac{P}{R_d T_e}, \quad \rho_p = \frac{P}{R_d T_p}$$

Substituting these relationships into our buoyancy equation yields:

$$B = g \left( \frac{\frac{P}{R_d T_e} - \frac{P}{R_d T_p}}{\frac{P}{R_d T_p}} \right) = g \left( \frac{\frac{1}{T_e} - \frac{1}{T_p}}{\frac{1}{T_p}} \right) = g \left( \frac{T_p - T_e}{T_e} \right)$$

To account for the molecular weight of water vapour (which is lighter than diatomic nitrogen and oxygen, making moist air intrinsically more buoyant than dry air at identical temperatures), meteorologists replace thermodynamic temperature $T$ with virtual temperature $T_v \approx T(1 + 0.61q)$, where $q$ is the specific humidity. Thus, the rigorous buoyancy equation becomes:

$$B(z) = g \left( \frac{T_{v,p}(z) - T_{v,e}(z)}{T_{v,e}(z)} \right)$$

Convective Available Potential Energy (CAPE)

Convective Available Potential Energy (CAPE) represents the total positive work done by the buoyant force per unit mass as an air parcel ascends from the Level of Free Convection ($z_{\text{LFC}}$) to the Equilibrium Level ($z_{\text{EL}}$). Mathematically, it is the line integral of buoyancy over vertical distance:

$$\text{CAPE} = \int_{z_{\text{LFC}}}^{z_{\text{EL}}} B(z) \, dz = \int_{z_{\text{LFC}}}^{z_{\text{EL}}} g \left( \frac{T_{v,p}(z) - T_{v,e}(z)}{T_{v,e}(z)} \right) dz$$

In operational meteorology, thermodynamic profiles are plotted on thermodynamic diagrams such as the Skew-T ln-P diagram standardized by the World Meteorological Organization (WMO). Using the hydrostatic relation $dz = -(R_d T_{v,e} / g) \, d\ln P$, we transform the integral into pressure coordinates:

$$\text{CAPE} = R_d \int_{P_{\text{EL}}}^{P_{\text{LFC}}} \left( T_{v,p} - T_{v,e} \right) d\ln P$$

On a Skew-T diagram, CAPE corresponds directly to the bounded two-dimensional area where the parcel trajectory temperature curve lies to the right of the environmental temperature profile.

+-----------------------------------------------------------------------------+
|                           THE CAPE INTEGRAL                                 |
|                                                                             |
|       CAPE = \int_{z_LFC}^{z_EL} g * [ (T_v,p - T_v,e) / T_v,e ] dz         |
|                                                                             |
|       Units:  [ (m / s^2) * (K / K) * m ] = m^2 / s^2                       |
|       Recall: 1 Joule = 1 kg * m^2 / s^2  ==>  1 J / kg = 1 m^2 / s^2       |
+-----------------------------------------------------------------------------+

Deriving the Theoretical Maximum Updraft Velocity ($w_{\max}$)

How does this integrated potential energy translate into vertical velocity inside a thunderstorm? We apply the Work-Energy Theorem from classical mechanics.

Neglecting friction, the work done on a parcel by buoyant forces equals the change in its vertical kinetic energy per unit mass:

$$dW = B(z) \, dz = d\left(\frac{1}{2} w^2\right) = w \, dw$$

Integrating from the base of the buoyant layer ($z_{\text{LFC}}$, where initial vertical velocity $w(z_{\text{LFC}}) \approx 0$) to the peak updraft height ($z_{\text{EL}}$):

$$\int_{z_{\text{LFC}}}^{z_{\text{EL}}} B(z) \, dz = \int_{0}^{w_{\max}} w \, dw$$

The left-hand side is, by definition, CAPE. Evaluating the right-hand side integral:

$$\text{CAPE} = \left[ \frac{1}{2} w^2 \right]0^{w{\max}} = \frac{1}{2} w_{\max}^2$$

Solving directly for $w_{\max}$:

$$w_{\max} = \sqrt{2 \cdot \text{CAPE}}$$

Dimensional Analysis Verification

Let us verify the dimensional consistency: - The units of CAPE are Joules per kilogram ($\text{J/kg}$). - Since $1\text{ Joule} = 1\text{ N}\cdot\text{m} = 1\text{ kg}\cdot\text{m/s}^2\cdot\text{m} = 1\text{ kg}\cdot\text{m}^2/\text{s}^2$: $$\text{Units of CAPE} = \frac{\text{kg}\cdot\text{m}^2/\text{s}^2}{\text{kg}} = \frac{\text{m}^2}{\text{s}^2}$$ - Taking the square root: $$\sqrt{\frac{\text{m}^2}{\text{s}^2}} = \text{m/s}$$

The units resolve cleanly to velocity ($\text{m/s}$).

===============================================================================
               THEORETICAL MAXIMUM UPDRAFT VELOCITY TABLE
===============================================================================
 CAPE (J/kg)    Instability Regime     w_max (m/s)    w_max (km/h)    w_max (mph)
-------------------------------------------------------------------------------
   300          Marginal / Weak           24.5            88.2           54.8
  1,250         Moderate                  50.0           180.0          111.8
  2,500         Strong                    70.7           254.6          158.2
  4,000         Extreme                   89.4           322.0          200.1
  5,000         Violent (High-End)       100.0           360.0          223.7
===============================================================================

Physical Caveat for Observers: The formula $w_{\max} = \sqrt{2 \cdot \text{CAPE}}$ represents an idealized upper limit. In reality, actual peak updrafts reach roughly $0.5 \times w_{\max}$ to $0.6 \times w_{\max}$. Three primary damping mechanisms sap updraft momentum: 1. Water Loading: The weight of billions of condensed cloud droplets, raindrops, and hailstones exerts a downward gravitational drag on the rising parcel. 2. Turbulent Entrainment: Dry, cool environmental air is drawn into the storm flanks, evaporating cloud droplets and diluting parcel buoyancy. 3. Non-hydrostatic Perturbation Pressures: Dynamic pressure perturbations within rotating storms create localized vertical resisting forces.

Even after accounting for these damping factors, a storm in a $3,500\text{ J/kg}$ CAPE environment regularly sustains updrafts of $40\text{ to }45\text{ m/s}$ ($144\text{ to }162\text{ km/h}$)—more than sufficient to suspend grapefruit-sized hail in the mid-levels of a supercell.

Convective Inhibition (CIN): The Pressure Cooker Lid

Just as CAPE measures the positive buoyant energy available for storm growth, Convective Inhibition (CIN) measures the negative buoyant energy that an air parcel must overcome to reach its Level of Free Convection:

$$\text{CIN} = \int_{z_{\text{surface}}}^{z_{\text{LFC}}} \min\left(0, B(z)\right) dz = R_d \int_{P_{\text{LFC}}}^{P_{\text{surface}}} \min\left(0, T_{v,p} - T_{v,e}\right) d\ln P$$

CIN typically arises from a capping inversion—a warm, dry layer of air in the low-to-mid troposphere (frequently an Elevated Mixed Layer advected from arid plateaus).

                               THE CAPPING MECHANISM

   [ Without CIN Cap ]                            [ With Strong CIN Cap ]
   Weak, disorganized thermals bubble             Heat and moisture pool in boundary layer;
   early, producing widespread, mild              pressure builds until a violent, explosive
   showers that consume instability.              supercell breaches the inversion.

       ^   ^   ^   ^   ^                                 ================================= (Cap)
       |   |   |   |   |                                 WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW
     ~~~~~~~~~~~~~~~~~~~~~ (Surface)                     Heat & Moisture Accumulate Below

CIN acts as a thermodynamic safety valve. Without a cap, weak morning thermals break early, producing widespread, pulse-type showers that gently bleed off potential instability. A moderate cap ($-25\text{ to }-75\text{ J/kg}$), however, suppresses premature convection, allowing solar radiation to heat the ground and pump moisture into the boundary layer all afternoon. When a localized trigger (a cold front, dryline, or mountain ridge) finally forces a parcel past the LFC, the stored energy erupts catastrophically.

The Lifted Index (LI): A Single-Level Operational Diagnostic

While CAPE integrates buoyancy across the entire vertical depth of the atmosphere, early severe storm forecasters needed a quick, single-number index. In 1956, meteorologist Joseph G. Galway introduced the Lifted Index (LI), defined as the temperature difference between the ambient environment at the $500\text{ hPa}$ constant pressure surface (roughly $5.5\text{ km}$ above sea level) and an air parcel lifted adiabatically from the boundary layer:

$$\text{LI} = T_{\text{env}}(500\text{ hPa}) - T_{\text{parcel}}(500\text{ hPa})$$

Note the sign convention: If the parcel is warmer than the environment at $500\text{ hPa}$, $T_{\text{parcel}} > T_{\text{env}}$, producing a negative Lifted Index. More negative values indicate greater instability.

+-----------------------------------------------------------------------------+
|                     LIFTED INDEX (LI) CLASSIFICATION                        |
+-------------------+---------------------------------------------------------+
| LI Value (°C)     | Atmospheric Stability Interpretation                    |
+-------------------+---------------------------------------------------------+
| > 0               | Stable: Convection unlikely; stratiform clouds if any.  |
| 0 to -2           | Marginally Unstable: Isolated weak thunderstorms.       |
| -3 to -5          | Moderately Unstable: Thunderstorms probable.            |
| -6 to -9          | Very Unstable: Severe thunderstorms likely.             |
| < -9              | Extremely Unstable: Violent severe weather & tornadoes. |
+-------------------+---------------------------------------------------------+

While simple, the Lifted Index has limitations: it evaluates only a single atmospheric level ($500\text{ hPa}$). If a thick layer of instability resides between $850\text{ hPa}$ and $600\text{ hPa}$ but stabilizes rapidly above $550\text{ hPa}$, the Lifted Index may read near zero while the total integrated CAPE remains high. Hence, modern forecasters at the Storm Prediction Center (SPC) treat LI as a rapid screening tool, relying on integrated CAPE and sounding morphology for detailed threat assessments.

4. Sounding Analysis: Decoding Atmospheric Profiles

Meteorologists visualize thermodynamic soundings through radiosonde balloon data plotted on Skew-T ln-P diagrams. Analyzing the distribution of buoyancy—not merely its gross magnitude—reveals the specific storm mode likely to emerge.

       "SKINNY" CAPE PROFILE                         "FAT" CAPE PROFILE
       (Tropical / High Precipitation)               (Severe Supercell / Large Hail)

   p (hPa)                                       p (hPa)
   150 |           |                             150 |           |
       |          /                                  |          /
   300 |         /|                              300 |        /  |
       |        / |   Skinny, tall positive          |       /   |   Broad, wide positive
   500 |       /  |   area: slow acceleration,   500 |      /    |   area in -10°C to -30°C
       |      /   |   warm-rain efficiency.          |     (     |   zone: explosive upward
   700 |     /    |                              700 |      \    |   acceleration, giant hail.
       |    /     |                                  |       \   |
   900 |   /      |                              900 |        \  |
       +-----------------------> T                   +-----------------------> T

1. Moderate Thunderstorm Sounding ("Skinny CAPE")

• Total CAPE: $800 - 1,500\text{ J/kg}$
• CIN: Negligible ($-5\text{ to }-20\text{ J/kg}$)
• Morphology: The parcel path stays only $1^\circ\text{C to }3^\circ\text{C}$ warmer than the ambient environment, but does so over a deep vertical layer extending from $1.5\text{ km}$ to $13\text{ km}$.
• Convective Consequence: Updrafts accelerate gradually, rarely exceeding $15\text{ to }20\text{ m/s}$. These storms produce torrential localized rain, frequent lightning, and modest wind gusts, but lack the kinetic punch required to suspend severe hail.

2. High-CAPE Supercell Sounding ("Fat CAPE")

• Total CAPE: $3,000 - 5,000+\text{ J/kg}$
• CIN: Moderate ($-50\text{ to }-100\text{ J/kg}$)
• Lifted Index: $-8^\circ\text{C to }-12^\circ\text{C}$
• Morphology: The parcel profile bulges dramatically to the right of the environmental curve in the mid-troposphere ($700\text{ to }400\text{ hPa}$). In the critical Hail Growth Zone (temperatures between $-10^\circ\text{C}$ and $-30^\circ\text{C}$), the parcel temperature exceeds the ambient air by $8^\circ\text{C to }12^\circ\text{C}$.
• Convective Consequence: Extreme vertical acceleration. Parcels rocket through the mid-levels at speeds exceeding $45\text{ m/s}$, pushing cloud tops past the tropopause in an overshooting top. When paired with deep-layer vertical wind shear (e.g., speed shear exceeding $20\text{ m/s}$ over the lowest $6\text{ km}$), these updrafts tilt, rotate, and develop into long-lived supercells capable of dropping giant hail and generating destructive tornadoes.

5. Outdoor Guidance: The Observer's Toolkit for Horizon Assessment

For mountaineers, aviators, sailors, and severe weather spotters, translating thermodynamic numbers into real-world, situational decisions on the ground is a life-saving skill. Use the following structured checklist when assessing convective potential.

+-----------------------------------------------------------------------------+
|                  OUTDOOR OBSERVER'S CONVECTIVE CHECKLIST                    |
+-----------------------------------------------------------------------------+
| [ ] 1. Morning Sounding Review:                                             |
|     - Check regional 12:00 UTC sounding (CAPE > 1,500 J/kg? LI < -4?).      |
|     - Note CIN magnitude: Is there a cap holding storms back until 15:00?   |
|                                                                             |
| [ ] 2. Visual Horizon Scanning:                                             |
|     - Watch cumulus development: Flat tops (stable) vs. towers (congestus). |
|     - Look for pileus caps: Smooth, silken hoods over rising towers indicate|
|       updrafts pushing violently against moist mid-level stable layers.     |
|     - Check cloud edges: Crisp, hard edges = violent, rapid ascent;         |
|       fuzzy, glaciated edges = cloud top freezing and converting to ice.    |
|                                                                             |
| [ ] 3. Tactile & Instrument Checks:                                         |
|     - Sudden wind shift / temperature drop: Gust front arrival (runout      |
|       distance can precede heavy rain by 15-30 minutes).                    |
|     - Barometer trend: Rapid needle drop (> 1 hPa/hr) indicates intense     |
|       mesolow / approaching convective core.                                |
|     - Static interference on AM radio: Distant crackles reveal lightning    |
|       discharges beyond visual horizon.                                     |
+-----------------------------------------------------------------------------+

Interpreting Cloud Morphology

• The "Cauliflower" Stage: If cumulus towers grow wider than they are tall, convection is struggling against entrainment of dry air. If they shoot vertically with razor-sharp margins, the updraft is dense, buoyant, and accelerating.
• Pileus Hoods: When a rising thermal punches through a humid, stable layer, it forces that layer upward to saturation, forming a smooth, cap-like cloud (pileus) draped over the convective dome. A pileus is a signature of explosive vertical acceleration ($w > 20\text{ m/s}$).
• Mammatus Pouches: Bulbous, downward-hanging cloud pouches under the anvil indicate negative buoyancy driven by the evaporative cooling of descending ice hydrometeors—a clear marker of a mature, severe storm system.

6. Authoritative Meteorological Resources

To deepen your understanding of upper-air sounding analysis and numerical weather prediction, consult these primary meteorological authorities:

1. National Oceanic and Atmospheric Administration (NOAA) - Sounding Analysis Portal
2. Met Office UK - Convective Forecast Principles
3. World Meteorological Organization (WMO) - Guide to Meteorological Instruments and Methods of Observation
4. American Meteorological Society (AMS) - Glossary of Meteorology: CAPE Definition
5. NOAA Storm Prediction Center (SPC) - Sounding and Mesoscale Analysis Archive
6. European Centre for Medium-Range Weather Forecasts (ECMWF) - Convective Parameterization
7. Wikipedia - Detailed Overview of Convective Available Potential Energy

7. Takeaway Box: Today's Meteorological Rule of Thumb

+=============================================================================+
|             METEOROLOGICAL RULE OF THUMB: THE UPDRAFT FORMULA               |
+=============================================================================+
|                                                                             |
|   1. THE INSTABILITY THUMB-RULE:                                            |
|      - CAPE < 1,000 J/kg  ==>  Tame / Pulse Summer Showers                  |
|      - CAPE 1,000 - 2,500 ==>  Scattered Strong Thunderstorms               |
|      - CAPE > 2,500 J/kg  ==>  Severe Supercell & Large Hail Potential      |
|                                                                             |
|   2. THE SPEED HEURISTIC:                                                   |
|      To mentally estimate maximum updraft velocity in m/s:                  |
|                                                                             |
|                 w_max ≈ sqrt( 2 * CAPE )                                    |
|                                                                             |
|      For quick field estimation, double the CAPE value and take the         |
|      square root. Then divide by 2 for the realistic real-world updraft     |
|      sustained speed (accounting for water loading and entrainment).        |
|                                                                             |
|      Example: CAPE = 2,000 J/kg                                             |
|        w_max,theory = sqrt(4,000) ≈ 63 m/s (227 km/h)                       |
|        w_actual     ≈ 0.5 * 63    ≈ 31.5 m/s (113 km/h)                     |
|                                                                             |
|   3. THE LIFTED INDEX QUICK-CHECK:                                          |
|      If LI is more negative than -4°C and CAPE exceeds 1,500 J/kg, the      |
|      atmosphere has loaded its chamber. Any cloud tower breaching the       |
|      capping inversion will turn severe within 20 to 30 minutes.            |
|                                                                             |
+=============================================================================+