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Reading the Numbers -- A Meteorological Cheat Sheet

So you ran cape_cin() and got back 3500 J/kg. Is that a lot?

This page is your field reference. Every parameter that metrust can compute is listed here with its units, operational thresholds, and plain-English meaning. Bookmark it, print it, tape it to your monitor.

Instability

CAPE -- Convective Available Potential Energy

Units: J/kg

CAPE is the total energy available to a thunderstorm's updraft. On a thermodynamic diagram, it is the area between the lifted parcel curve and the environmental temperature where the parcel is warmer. Bigger CAPE means a more violent updraft, stronger hail, and heavier rain.

CAPE (J/kg) Category What to expect
0--500 Marginal instability Weak showers, maybe isolated thunder.
500--1000 Weak instability Thunderstorms likely if triggered.
1000--2500 Moderate instability Strong thunderstorms, large hail possible.
2500--4000 Strong instability Severe thunderstorms, very large hail.
4000+ Extreme instability Violent storms if anything triggers them.

CAPE alone does not equal severe weather

A sounding can have 5000 J/kg of CAPE and produce nothing. Without a trigger mechanism (front, dryline, outflow boundary) and sufficient wind shear, all that energy just sits there. Conversely, strong tornadoes have occurred with CAPE as low as 500 J/kg when shear and low-level moisture were favorable. Always evaluate CAPE alongside shear and CIN.

Variants you will encounter:

  • SBCAPE -- Surface-based. Uses the observed surface parcel.
  • MLCAPE -- Mixed-layer. Averages the lowest ~100 hPa. This is the standard for SPC operations and the input to STP.
  • MUCAPE -- Most-unstable. Uses the parcel with the highest theta-e in the lowest 300 hPa. Best for elevated convection.
from metrust.calc import cape_cin

# Surface-based CAPE
cape, cin, h_lcl, h_lfc = cape_cin(
    p, t, td, hgt, psfc, t2m, td2m, parcel_type="sb"
)

# Mixed-layer CAPE
cape, cin, h_lcl, h_lfc = cape_cin(
    p, t, td, hgt, psfc, t2m, td2m, parcel_type="ml"
)

# Most-unstable CAPE
cape, cin, h_lcl, h_lfc = cape_cin(
    p, t, td, hgt, psfc, t2m, td2m, parcel_type="mu"
)

CIN -- Convective Inhibition

Units: J/kg (negative values)

CIN is the energy barrier a parcel must overcome before it can rise freely -- the "cap." It is the area on a sounding where the lifted parcel is cooler than the environment, below the LFC. CIN is why not every hot, humid day produces storms.

CIN (J/kg) Category What to expect
0 to -25 Weak cap Storms initiate easily; widespread convection likely.
-25 to -50 Moderate cap Need a trigger (front, dryline, terrain).
-50 to -100 Strong cap Hard to break. If broken: explosive development.
< -100 Very strong cap Unlikely to break without extreme forcing.

The cap is not always your enemy

A moderate cap (-25 to -75 J/kg) can actually help severe weather forecasts. It prevents storms from firing early and scattering the instability across many weak cells. Instead, the boundary layer continues to heat and moisten throughout the day, building even more CAPE. When the cap finally breaks -- often along a front or dryline in late afternoon -- the result is fewer but much more intense storms. Forecasters call this "uncapping."

metrust: Returned as the second value from cape_cin(). See CAPE section above.

Lapse Rates

Units: deg C/km

The rate at which temperature decreases with height. The 700--500 hPa lapse rate is the standard mid-level measure. Steeper lapse rates mean a parcel that starts rising stays warmer than its surroundings longer, producing stronger buoyancy.

Lapse Rate (deg C/km) Category What to expect
< 6 Stable Weak convection, limited hail growth.
6--7 Conditionally unstable Moderate storms with adequate moisture.
7--8 Steep Strong updrafts, favorable for large hail.
> 8 Very steep Extreme instability. Approaching dry adiabatic (~9.8).

Mid-level lapse rates and hail

The 700--500 hPa lapse rate is one of the best discriminators for significant hail. Steep mid-level lapse rates (> 7 deg C/km) keep hailstones suspended in the updraft longer, allowing them to grow larger before falling out. When you see steep lapse rates combined with high CAPE, think "big hail day."

metrust: Compute from temperature profiles at 700 and 500 hPa, or derive from dry_lapse() / moist_lapse().

Sounding Levels

LCL -- Lifting Condensation Level

Units: hPa (pressure) or m AGL (height)

The height where clouds form when surface air is lifted. Air cools dry-adiabatically until it saturates -- that point is the LCL. The LCL marks the base of cumulus clouds and is one of the critical factors for tornado potential.

LCL Height (m AGL) What it means
< 1000 Very low cloud bases. Favorable for tornadoes.
1000--1500 Moderate. Tornadoes possible.
> 1500 High cloud bases. Tornadoes less likely.

Low LCL = tornado risk factor

A low LCL means less distance between the cloud base and the ground. When a mesocyclone's rotation stretches downward from cloud base, a shorter distance means it is more likely to reach the surface as a tornado. Most significant tornadoes occur with LCL heights below 1500 m AGL. The STP formula explicitly penalizes LCL heights above 2000 m.

from metrust.calc import lcl
from metrust.units import units

p_lcl, t_lcl = lcl(1000 * units.hPa, 30 * units.degC, 20 * units.degC)

LCL height AGL is also returned as the third value from cape_cin().

LFC -- Level of Free Convection

Units: hPa

The height where a lifted parcel becomes warmer than its surroundings and starts rising on its own. Below the LFC, external forcing (a front, outflow boundary, terrain) must push the parcel upward. Above the LFC, buoyancy takes over and the parcel accelerates freely.

A lower LFC (higher pressure) means less forcing is needed to initiate convection. The gap between the LCL and LFC corresponds roughly to CIN -- a large gap means a strong cap.

from metrust.calc import lfc

p_lfc = lfc(p, t, td)

LFC height AGL is also returned as the fourth value from cape_cin().

EL -- Equilibrium Level

Units: hPa

The height where the rising parcel stops being warmer than the environment. This is approximately the storm cloud top. A higher EL (lower pressure) means taller storms with more total energy. The CAPE integral runs from the LFC to the EL, so a high EL directly implies large CAPE.

Storm tops near or above the tropopause (roughly 100--200 hPa, depending on season and latitude) indicate deep, powerful updrafts. Overshooting tops -- where the updraft punches above the EL -- are a radar signature of the most intense storms.

from metrust.calc import el

p_el = el(p, t, td)

Wind Shear and Rotation

Bulk Wind Shear (0--6 km)

Units: m/s or knots

The vector difference in wind between two heights. The 0--6 km layer is the standard measure for deep-layer shear, which controls storm mode: whether a thunderstorm is a brief pulse, a multicell cluster, or a long-lived supercell.

0--6 km Shear Category Storm mode
< 10 m/s (< 20 kt) Weak Single-cell storms, brief and disorganized.
10--18 m/s (20--35 kt) Moderate Multicell storms, some organization.
18--25 m/s (35--50 kt) Strong Supercells likely.
> 25 m/s (> 50 kt) Extreme Long-lived, potentially violent supercells.

Low-level shear matters too

The 0--1 km shear is a better discriminator for tornadoes than the 0--6 km shear. Strong low-level shear (> 10 m/s in the lowest kilometer) increases the likelihood that a supercell will produce a tornado, even when deep-layer shear is only moderate.

from metrust.calc import bulk_shear
from metrust.units import units

su, sv = bulk_shear(u, v, height, bottom=0 * units.m, top=6000 * units.m)

SRH -- Storm-Relative Helicity

Units: m^2/s^2

SRH measures the potential for rotating updrafts (mesocyclones). It answers: "How much does the wind vector curl with height, relative to the storm motion?" The 0--1 km layer targets low-level rotation (tornado potential); the 0--3 km layer targets overall supercell and mesocyclone potential.

0--1 km SRH (tornado potential):

SRH (m^2/s^2) Category What to expect
< 50 Weak Minimal low-level rotation.
50--150 Moderate Weak tornadoes possible.
150--300 Strong Significant tornadoes possible.
300+ Extreme Violent tornadoes possible.

0--3 km SRH (supercell/mesocyclone potential):

SRH (m^2/s^2) Category What to expect
< 100 Weak Minimal mesocyclone potential.
100--250 Moderate Mesocyclones likely with storms.
250--450 Strong Long-lived supercells.
450+ Extreme Violent long-track supercells. 
from metrust.calc import storm_relative_helicity, bunkers_storm_motion
from metrust.units import units

# Get storm motion first
(rm_u, rm_v), _, _ = bunkers_storm_motion(u, v, height)

# 0-1 km SRH
pos, neg, total_1km = storm_relative_helicity(
    u, v, height, 1000 * units.m, rm_u, rm_v
)

# 0-3 km SRH
pos, neg, total_3km = storm_relative_helicity(
    u, v, height, 3000 * units.m, rm_u, rm_v
)

Composite Parameters

These indices combine multiple ingredients into a single number. They are the workhorses of operational severe weather forecasting.

STP -- Significant Tornado Parameter

Units: dimensionless

The primary composite used by the Storm Prediction Center to assess tornado threat. STP combines four ingredients, each normalized so that a value of 1 represents a climatologically favorable threshold:

STP = (MLCAPE / 1500) * ((2000 - LCL) / 1000) * (SRH_1km / 150) * (shear_6km / 20)
STP Category What to expect
< 0.5 Low Significant tornadoes unlikely.
0.5--1 Conditional Need a strong trigger. Watch for mesocyclones.
1--3 Moderate Significant tornadoes possible.
3--6 High Multiple significant tornadoes likely.
> 6 Extreme Violent tornado outbreak. Particularly dangerous situation.

What the components tell you

When STP is high, look at which terms are contributing. An STP of 4 driven primarily by extreme CAPE (4000+ J/kg) with modest SRH is a different threat than an STP of 4 driven by extreme SRH (400+ m^2/s^2) with moderate CAPE. The latter pattern -- high SRH, moderate CAPE -- is often associated with strong, long-track tornadoes in the Southeast US, sometimes embedded in squall lines where they are hard to see on radar.

from metrust.calc import significant_tornado_parameter

stp = significant_tornado_parameter(
    mlcape,           # J/kg
    lcl_height,       # m AGL
    srh_0_1km,        # m^2/s^2
    bulk_shear_0_6km, # m/s
)

SCP -- Supercell Composite Parameter

Units: dimensionless

Discriminates supercell environments from ordinary thunderstorm environments. SCP combines most-unstable CAPE, effective-layer storm-relative helicity, and effective bulk shear.

SCP Category What to expect
< 1 Low Supercells unlikely.
1--4 Moderate Supercells possible if storms initiate.
4--10 High Supercells likely with any convective trigger.
> 10 Extreme Long-lived violent supercells favored.

SCP does not predict tornadoes

SCP tells you whether supercells will form, not whether those supercells will produce tornadoes. A high SCP with low 0--1 km SRH and high LCL heights favors supercells that produce large hail and damaging winds but not tornadoes. Use STP for tornado discrimination.

from metrust.calc import supercell_composite_parameter

scp = supercell_composite_parameter(
    mucape,          # J/kg
    srh_eff,         # m^2/s^2
    bulk_shear_eff,  # m/s
)

SHIP -- Significant Hail Parameter

Units: dimensionless

SHIP estimates the likelihood of significant hail (diameter >= 2 inches / 5 cm). It combines MUCAPE, mixing ratio, 700--500 hPa lapse rate, 500 hPa temperature, and 0--6 km bulk shear. The freezing level and mid-level lapse rates are the key discriminators: steep lapse rates aloft keep hailstones in the growth zone longer.

SHIP Category What to expect
< 0.5 Low Significant hail unlikely.
0.5--1 Moderate Large hail possible with strong updrafts.
1--2 High Significant hail likely.
> 2 Very high Very large hail (> 2 in) strongly favored.

SHIP and the freezing level

SHIP works best in environments where the freezing level is between about 3000 and 4500 m AGL. If the freezing level is very low (< 2500 m), hailstones melt before reaching the surface. If it is very high (> 5000 m), the warm layer below is deep enough to melt even large stones. The sweet spot for giant hail is a high freezing level combined with steep mid-level lapse rates and extreme CAPE.

metrust: Compute SHIP from its component parts:

import numpy as np
from metrust.calc import cape_cin, bulk_shear, mixing_ratio
from metrust.units import units

# Gather components, then:
# SHIP = (MUCAPE * W * LR * (-T500) * SHEAR) / 44000000
# where W = mixing ratio (g/kg), LR = 700-500 hPa lapse rate,
# T500 = 500 hPa temperature (degC, negative), SHEAR = 0-6 km (m/s)

Moisture

Precipitable Water (PWAT)

Units: mm (or inches)

Total water vapor in the atmospheric column if all of it condensed out. PWAT does not tell you how much rain will fall, but it sets an upper bound and indicates how much moisture is available for storms to tap.

Thresholds are regional and seasonal

A PWAT of 40 mm in July over Oklahoma is unremarkable. The same value in January over Montana is extraordinary. Always compare PWAT to local climatological normals, not to a fixed table. The SPC sounding climatology and the NWS precipitable water climatology pages provide percentile ranks by station and month.

The table below gives rough warm-season mid-latitude guidelines:

PWAT (mm) PWAT (in) Category What to expect
< 25 < 1.0 Dry Limited moisture for storms.
25--40 1.0--1.6 Moderate Adequate moisture for convection.
40--60 1.6--2.4 Moist Heavy rain potential with any lift.
60--75 2.4--3.0 Very moist Flash flood risk. Near-tropical moisture.
> 75 > 3.0 Extreme Tropical air mass. Extreme flood risk. 
from metrust.calc import precipitable_water

pw = precipitable_water(p, td)  # result in mm

Kinematics

Divergence and Vorticity

Units: 1/s (per second)

Divergence measures whether air is spreading apart (positive) or converging (negative) at a given level. Vorticity measures the spin of the air -- positive values indicate cyclonic (counterclockwise in the Northern Hemisphere) rotation.

The classic pattern that supports deep convection:

  • Upper-level divergence (air spreading out aloft) removes mass from the column, lowering surface pressure.
  • Low-level convergence (air piling in near the surface) forces upward motion to replace the evacuated air.
  • Positive vorticity advection (PVA) at 500 hPa enhances upward motion downstream of a trough axis.
Feature Typical magnitude Interpretation
Upper-level divergence 1e-5 to 5e-5 1/s Supports ascent; stronger = more lift.
Low-level convergence -1e-5 to -5e-5 1/s Forces upward motion into convection.
Positive vorticity (500 hPa) 1e-5 to 1e-4 1/s Cyclonic spin; PVA = storm support.

Divergence-vorticity coupling

In an idealized setting, upper-level divergence exceeding low-level convergence produces net mass evacuation from the column -- surface pressure falls and lift intensifies. When you see a diffluent jet-stream pattern over a surface low with converging winds, you have the textbook setup for explosive cyclogenesis or a severe weather outbreak.

from metrust.calc import divergence, vorticity
from metrust.units import units

div  = divergence(u_grid, v_grid, dx, dy)   # 1/s, 2-D field
vort = vorticity(u_grid, v_grid, dx, dy)    # 1/s, 2-D field

Precipitation Type

Wet-Bulb Temperature

Units: deg C

The wet-bulb temperature is the lowest temperature air can reach through evaporative cooling alone. It sits between the dewpoint and the air temperature, and it is the single best predictor of surface precipitation type.

As precipitation falls through a layer, it cools the air toward the wet-bulb temperature via evaporation and melting. If the wet-bulb temperature is below freezing through the entire column, snow reaches the surface. If it is above freezing, rain reaches the surface.

Wet-Bulb Temp (deg C) Precipitation type
< 0 Snow likely (all ice to the surface).
0--1.3 Transition zone: snow, sleet, or freezing rain.
> 1.3 Rain (enough warmth to fully melt frozen precip).

The 1 deg C rule of thumb

Many forecasters use a surface wet-bulb of 1 deg C as the rain/snow line, but this is only a starting point. Precipitation intensity matters: heavy precipitation cools the column toward the wet-bulb faster than light precipitation. A surface wet-bulb of 2 deg C can still produce accumulating snow at the onset of heavy precipitation before the column has fully cooled. The full wet-bulb profile through the column matters more than the surface value alone.

from metrust.calc import wet_bulb_temperature
from metrust.units import units

tw = wet_bulb_temperature(
    1000 * units.hPa, 2 * units.degC, -1 * units.degC
)

Stability Indices

Quick-look numbers computed from fixed pressure levels. Less sophisticated than CAPE/shear composites, but fast and widely used.

Index Thunderstorm Threshold Severe Threshold Direction
K-Index > 30 > 40 Higher = worse
Total Totals > 44 > 50--55 Higher = worse
Showalter Index < 0 < -3 More negative = worse
Lifted Index < 0 < -3 (very), < -6 (extreme) More negative = worse
SWEAT > 300 (severe) > 400 (tornadoes) Higher = worse 
from metrust.calc import (
    k_index, total_totals, showalter_index, lifted_index, sweat_index,
)
from metrust.units import units

ki = k_index(t850, td850, t700, td700, t500)
tt = total_totals(t850, td850, t500)
si = showalter_index(p, t, td)
li = lifted_index(p, t, td)
sw = sweat_index(t850, td850, t500, dd850, dd500, ff850, ff500)

Other Composites

EHI -- Energy-Helicity Index

Units: dimensionless

A simple composite that multiplies buoyancy and rotation potential:

EHI = (CAPE * SRH) / 160000
EHI What to expect
< 1 Minimal tornado potential.
1--2 Significant tornado potential.
> 2 Strong tornado potential. 
ehi = (cape.magnitude * srh.magnitude) / 160000.0

BRN -- Bulk Richardson Number

Units: dimensionless

The ratio of CAPE to the kinetic energy of the 0--6 km bulk wind shear. Distinguishes supercellular from multicellular storm modes.

BRN Storm mode
< 10 Shear-dominated. Storms may split or fail to sustain.
10--45 Supercells favored.
> 45 Buoyancy-dominated. Multicell storms. 
from metrust.calc import bulk_richardson_number
from metrust.units import units

brn = bulk_richardson_number(2000 * units("J/kg"), 20 * units("m/s"))

Comfort and Safety

Heat Index

Units: deg C or deg F

Apparent temperature accounting for humidity.

Heat Index Category Risk
27--32 deg C (80--90 deg F) Caution Fatigue possible with prolonged exposure.
32--41 deg C (90--105 deg F) Extreme caution Heat cramps and exhaustion possible.
41--54 deg C (105--130 deg F) Danger Heat cramps/exhaustion likely. Heatstroke possible.
> 54 deg C (> 130 deg F) Extreme danger Heatstroke highly likely. 
from metrust.calc import heat_index

hi = heat_index(35 * units.degC, 80)  # 80% RH

Wind Chill

Units: deg C or deg F

Apparent temperature accounting for wind.

Wind Chill Risk
-18 to -28 deg C (0 to -18 deg F) Frostbite possible in 30 minutes.
-28 to -40 deg C (-18 to -40 deg F) Frostbite possible in 10--15 minutes.
-40 to -48 deg C (-40 to -55 deg F) Frostbite possible in 5--10 minutes.
< -48 deg C (< -55 deg F) Frostbite possible in under 5 minutes. 
from metrust.calc import windchill

wc = windchill(-10 * units.degC, 8 * units("m/s"))

Quick Reference Card

One table to rule them all. Clip this for the field.

Parameter Units "Watch out" threshold "This is serious" threshold
CAPE J/kg > 1000 > 2500
CIN J/kg -50 (strong cap) < -100 (very strong cap)
700--500 hPa LR deg C/km > 7 (steep) > 8 (very steep)
LCL height m AGL < 1500 (tornado risk) < 1000 (high tornado risk)
LFC hPa Low LFC = easy initiation Very low LFC + low CIN = explosive
EL hPa < 250 hPa (tall storms) < 200 hPa (extreme depth)
0--6 km shear m/s > 18 (supercells possible) > 25 (violent supercells)
0--1 km SRH m^2/s^2 > 150 (sig tornadoes possible) > 300 (violent tornadoes)
0--3 km SRH m^2/s^2 > 250 (long-lived supercells) > 450 (extreme rotation)
STP dimensionless > 1 (sig tornado environment) > 4 (PDS-level tornado environment)
SCP dimensionless > 1 (supercells possible) > 4 (supercells very likely)
SHIP dimensionless > 1 (sig hail possible) > 2 (very large hail favored)
PWAT mm > 40 (heavy rain potential) > 60 (flash flood risk)
Wet-bulb temp deg C 0--1.3 (wintry mix zone) < 0 (snow likely)
K-Index dimensionless > 30 (thunderstorms) > 40 (numerous storms)
Total Totals dimensionless > 44 (storms possible) > 55 (severe storms)
Lifted Index deg C < -3 (very unstable) < -6 (extreme instability)
Divergence (upper) 1/s > 1e-5 (ascent support) > 3e-5 (strong forcing)
Vorticity (500 hPa) 1/s > 1e-5 (PVA likely) > 5e-5 (strong PVA)
Heat Index deg C > 32 (extreme caution) > 41 (danger)
Wind Chill deg C < -18 (frostbite in 30 min) < -40 (frostbite in 5 min)
EHI dimensionless > 1 (sig tornado potential) > 2 (strong tornado potential)
BRN dimensionless 10--45 (supercell sweet spot) < 10 or > 45 (less favorable)

How to use this table

Do not treat these thresholds as on/off switches. Weather is a continuous spectrum, and these numbers represent climatological tendencies, not physical laws. A parameter at 90% of its "watch out" threshold in combination with three other parameters all near their thresholds can be more dangerous than one parameter that is off the charts while everything else is zero. Always evaluate the full parameter space, not a single number.

See Also