Convective processes driving lightning, hail, and tornadoes
2026-02-27
At 5:00 pm on 3 June 2020, a Storm Prediction Center mesoscale discussion noted enhanced shear values across central Kansas and Nebraska, surface dewpoints near 20°C, and CAPE values exceeding 4,000 J/kg. By 6:30 pm, a supercell thunderstorm had developed near Ellinwood, Kansas. By 8:00 pm it had produced a wedge tornado more than 1.5 km wide. Forecasters had seen the ingredients in the morning’s soundings and model output — the extraordinary instability, the deep-layer wind shear that would organise convection into a rotating supercell — and the Storm Prediction Center had issued a high-risk outlook before noon. The physics that transforms an unstable air mass and vertical wind shear into a thunderstorm complex capable of producing violent tornadoes is the same physics that makes severe weather forecasting both possible and imperfect.
A thunderstorm is a heat engine powered by the latent heat released when water vapour condenses. The key metric — Convective Available Potential Energy, or CAPE — measures how much energy is available to an air parcel as it rises from the surface, measured by integrating the buoyancy force (the temperature excess of the parcel over its environment) over the depth of the atmosphere. High CAPE produces strong updrafts; strong updrafts produce large hail; organised updraft rotation, driven by wind shear, produces supercells; supercells produce the most extreme severe weather. The path from a thermodynamic sounding to a severe weather forecast involves calculating CAPE and its complement CIN (Convective Inhibition), assessing the wind shear profile, and identifying the trigger that will release the instability. This model derives those calculations from thermodynamic principles and shows how they combine to characterise storm potential.
Will today’s atmospheric conditions produce tornadoes?
Thunderstorm requirements:
Storm types:
Single-cell: Short-lived (30-60 min), pulse storms
Multicell: Cluster, longer-lived (2-4 hours)
Supercell: Rotating updraft, most severe (hours)
Severe criteria (USA): - Hail ≥1 inch (2.5 cm) - Wind ≥58 mph (93 km/h, 50 kt) - Tornado (any intensity)
Applications: - Severe weather forecasting - Warning lead time - Aviation safety - Agriculture (hail damage) - Insurance risk assessment
Energy available for updrafts:
CAPE = g \int_{LFC}^{EL} \frac{T_v' - T_{v,env}}{T_{v,env}} dz
Where: - g = 9.81 m/s² - LFC = level of free convection (m) - EL = equilibrium level (m) - T_v' = virtual temperature of parcel (K) - T_{v,env} = environmental virtual temperature (K)
Virtual temperature:
T_v = T (1 + 0.61 q)
Where q = mixing ratio (kg/kg)
Units: J/kg (energy per unit mass)
Typical values: - CAPE < 1000: Weak instability - CAPE = 1000-2500: Moderate - CAPE = 2500-4000: Strong - CAPE > 4000: Extreme (supercell environment)
Maximum updraft velocity:
w_{max} = \sqrt{2 \times CAPE}
Example: CAPE = 3000 J/kg
w_{max} = \sqrt{6000} = 77 \text{ m/s}
Extreme updraft!
Change in wind with height:
Bulk shear (0-6 km):
S = \sqrt{(u_6 - u_0)^2 + (v_6 - v_0)^2}
Where u, v = wind components at surface (0) and 6 km.
Critical thresholds: - S < 10 m/s: Disorganized storms - S = 10-20 m/s: Organized multicells - S > 20 m/s: Supercells likely
Storm-relative helicity (SRH):
Measures streamwise vorticity:
SRH = \int_0^{z} (V - C) \cdot \frac{\partial V}{\partial z} dz
Where: - V = environmental wind vector - C = storm motion vector
SRH > 150 m²/s²: Tornadic supercells favored
Rotating updraft:
Mesocyclone (2-10 km diameter, rotation).
Key features:
Updraft: 20-50 m/s, tilted (shear)
Downdraft: Rear-flank, forward-flank
Hook echo: Radar signature (tornado possible)
Overshooting top: Penetrates tropopause
Vorticity sources:
Environmental shear → horizontal vorticity
Updraft tilts → vertical vorticity (rotation)
Lifted parcel:
Starts at surface with temperature T_0, pressure p_0.
Dry adiabatic ascent:
T = T_0 \left(\frac{p}{p_0}\right)^{R/c_p}
Where: - R/c_p = 0.286 (dry air)
Condensation occurs at LCL (lifting condensation level):
LCL \approx 125 (T_0 - T_d)
Where T_d = dew point temperature (°C).
Above LCL:
Moist adiabatic (slower cooling, ~6°C/km vs 10°C/km dry).
Buoyancy:
B = g \frac{T_v' - T_{v,env}}{T_{v,env}}
Positive B → acceleration upward.
Vertical momentum:
\frac{dw}{dt} = B - \frac{1}{\rho} \frac{dp}{dz} - \varepsilon w
Where: - w = vertical velocity - B = buoyancy - \varepsilon = entrainment/drag coefficient
Simplified (neglecting pressure gradient, drag):
w^2 = 2 \times CAPE
More realistic (with entrainment):
w^2 = 2 \times CAPE \times (1 - \varepsilon)
Typical \varepsilon = 0.3-0.5
Actual updrafts: 50-70% of theoretical maximum.
Embryo ascent in updraft:
Hailstone grows by accretion (collecting supercooled droplets).
Terminal velocity balance:
w = V_t
Where V_t = hailstone fall speed.
For spherical hailstone:
V_t = \sqrt{\frac{8 r g \rho_h}{3 C_d \rho_a}}
Where: - r = radius (m) - \rho_h = 900 kg/m³ (ice density) - C_d = 0.6 (drag coefficient) - \rho_a = air density
Updraft required for large hail:
1 inch (2.5 cm): w \approx 25 m/s
2 inch (5 cm): w \approx 35 m/s
4 inch (10 cm): w \approx 50 m/s
Extreme CAPE enables giant hail.
Problem: Calculate CAPE and predict severe weather potential.
Sounding data (simplified):
Surface (1000 mb): - Temperature: 30°C - Dew point: 24°C
500 mb (5.5 km): - Temperature: -10°C
Environmental lapse rate: 7°C/km (average)
Wind profile: - Surface: 180°/10 kt - 6 km: 240°/40 kt
Calculate LCL, CAPE, bulk shear, severe potential.
Step 1: LCL
LCL = 125 \times (30 - 24) = 125 \times 6 = 750 \text{ m}
Step 2: Parcel path
Assume moist adiabatic above LCL: ~6°C/km
At 5.5 km:
From surface (30°C): - Dry ascent to 0.75 km: T = 30 - 10(0.75) = 22.5°C - Moist ascent 4.75 km: T = 22.5 - 6(4.75) = -6.0°C
Parcel temperature at 5.5 km: -6°C
Environment: -10°C
Buoyancy: Parcel warmer by 4°C!
Step 3: CAPE (simplified)
Assume average buoyancy from LFC (1 km) to EL (12 km):
Average \Delta T = 3°C, depth = 11 km
CAPE = 9.81 \times \frac{3}{273} \times 11000 = 9.81 \times 0.011 \times 11000 = 1187 \text{ J/kg}
Moderate CAPE
Step 4: Maximum updraft
w_{max} = \sqrt{2 \times 1187} = \sqrt{2374} = 48.7 \text{ m/s}
Strong updrafts possible
Step 5: Bulk shear
Wind at surface: u_0 = 10 \sin(180°) = 0, v_0 = 10 \cos(180°) = -10 kt
Wind at 6 km: u_6 = 40 \sin(240°) = -34.6 kt, v_6 = 40 \cos(240°) = -20 kt
S = \sqrt{(-34.6 - 0)^2 + (-20 - (-10))^2} = \sqrt{1197 + 100} = \sqrt{1297} = 36 \text{ kt} = 18.5 \text{ m/s}
Moderate-strong shear
Step 6: Severe weather potential
Severe thunderstorm watch warranted.
Below is an interactive severe weather parameter simulator.
<label>
Surface temperature (°C):
<input type="range" id="surface-temp" min="20" max="38" step="1" value="30">
<span id="temp-val">30</span>
</label>
<label>
Surface dew point (°C):
<input type="range" id="dew-point" min="10" max="28" step="1" value="22">
<span id="dewpt-val">22</span>
</label>
<label>
Mid-level temperature (°C):
<input type="range" id="mid-temp" min="-15" max="-5" step="1" value="-10">
<span id="midtemp-val">-10</span>
</label>
<label>
Bulk shear 0-6km (m/s):
<input type="range" id="shear" min="5" max="35" step="2.5" value="15">
<span id="shear-val">15</span>
</label>
<div class="severe-info">
<p><strong>CAPE:</strong> <span id="cape">--</span> J/kg</p>
<p><strong>Max updraft:</strong> <span id="updraft">--</span> m/s</p>
<p><strong>Severe potential:</strong> <span id="potential">--</span></p>
<p><strong>Storm type:</strong> <span id="storm-type">--</span></p>
</div><canvas id="severe-canvas" width="700" height="400" style="border: 1px solid #ddd;"></canvas>Observations: - CAPE increases with surface warmth and mid-level cooling - High moisture (small T-Td spread) increases CAPE - Shear determines storm organization and severity - Combination of high CAPE and strong shear = supercells - Hodograph shows wind turning with height (directional shear) - Straight hodograph = less favorable for rotation
Key insights: - Both instability (CAPE) and shear required for severe weather - Supercells need 2500+ J/kg CAPE and 20+ m/s shear - Maximum updraft velocity scales with square root of CAPE - Storm type predictable from environmental parameters
Ingredients:
Significant Tornado Parameter (STP):
STP = \frac{CAPE}{1500} \times \frac{SRH}{150} \times \frac{2000 - LCL}{1000} \times \frac{S}{20}
STP > 1: Significant tornado (EF2+) environment
STP > 3: Violent tornado possible
May 20, 2013 Moore, OK: - CAPE: 3500 J/kg - SRH: 400 m²/s² - Shear: 25 m/s - STP: ~6 - Result: EF5 tornado
MESH (Maximum Expected Size of Hail):
Based on radar-derived maximum reflectivity and height.
Environmental indicators: - CAPE > 2000 J/kg - Strong mid-level winds (advect hail) - Wet-bulb zero height ~2.5-3.5 km (growth zone)
Record hail: 8 inch diameter (20 cm), South Dakota 2010.
Required updrafts ~60+ m/s (CAPE >5000 J/kg).
Thunderstorms dangerous for aircraft:
Turbulence: Updrafts/downdrafts exceed aircraft capability
Icing: Supercooled droplets
Lightning: Electronics damage, structural
Hail: Airframe damage, windscreen cracks
Avoidance: 20+ nautical miles from severe storms
Microbursts:
Localized downdraft (< 4 km diameter).
Surface wind divergence: 100+ kt possible.
Windshear: Fatal on takeoff/landing.
Warm layer aloft prevents lifting to LFC.
CAPE exists but storms never initiate.
Forecaster dilemma:
Severe environment, but no storms (false alarm).
Solution: Monitor for triggers (fronts, outflow boundaries).
Organized complex of storms.
Different dynamics than isolated supercells.
MCS: Squall line, bow echo, derecho
Challenges: - Evolving structure - Complex outflow interactions - Rapid changes
Derechos: Widespread wind damage (>100 mph possible).
Multiple storms interact.
Can intensify or weaken depending on configuration.
Example - Fujiwara effect:
Storms orbit each other, merge.
Unpredictable evolution.
Radar detects lofted debris, not tornado itself.
TDS = tornado confirmed
But: Tornado may dissipate before reaching target.
Warning verification challenge.
Polarimetric variables:
ZDR (differential reflectivity): - Shape information - Large hail (ZDR < 0 dB, tumbling)
KDP (specific differential phase): - Rain rate, hail discrimination
ρHV (correlation coefficient): - Mixed hydrometeors - Debris (ρHV < 0.90)
Improved: - Hail detection - Heavy rain estimation - Tornado warning (TDS)
Vertical pressure gradient:
\frac{dp}{dz} = -\rho g
Hydrostatic equation
Buoyancy:
Deviation from hydrostatic produces vertical acceleration.
\frac{dw}{dt} = -\frac{1}{\rho} \frac{dp}{dz} - g = B
Where B = buoyancy force.