Severe Weather

Functions for computing convective indices, composite parameters, and fire weather diagnostics. All functions accept Pint Quantities and return Pint Quantities (or plain values where noted).

---

Composite Parameters

significant_tornado_parameter

Significant Tornado Parameter (STP). The primary composite used by the Storm Prediction Center to discriminate between significant tornadic supercells (EF2+) and non-tornadic supercells. STP combines mixed-layer CAPE, LCL height, 0--1 km storm-relative helicity, and 0--6 km bulk wind shear into a single dimensionless number. Values above 1 indicate environments increasingly favorable for significant tornadoes; most significant tornadoes occur with STP in the 1--8 range. An STP of 0 means one or more ingredients are absent or below threshold.

significant_tornado_parameter(mlcape, lcl_height, srh_0_1km, bulk_shear_0_6km)

Parameters

Name	Type	Description
mlcape	Quantity (J/kg)	Mixed-layer CAPE (typically 100 hPa mixed-layer parcel).
lcl_height	Quantity (m)	Lifting condensation level height above ground.
srh_0_1km	Quantity (m^2/s^2)	0--1 km storm-relative helicity.
bulk_shear_0_6km	Quantity (m/s)	0--6 km bulk wind shear magnitude.

Returns

Quantity (dimensionless) -- the STP value.

Example

from metrust.calc import significant_tornado_parameter
from metrust.units import units

stp = significant_tornado_parameter(
    2500 * units("J/kg"),
    800 * units.m,
    250 * units("m**2/s**2"),
    25 * units("m/s"),
)
print(stp)  # > 1 indicates significant tornado environment

---

supercell_composite_parameter

Supercell Composite Parameter (SCP). Discriminates supercell environments from ordinary thunderstorms. SCP multiplies most-unstable CAPE, effective-layer storm-relative helicity, and effective bulk shear, each normalized by climatological thresholds. Values above 1 favor supercell development; values above 4--5 are associated with long-lived, strongly rotating supercells. SPC mesoanalysts use SCP alongside STP to gauge the supercell and tornado threat.

supercell_composite_parameter(mucape, srh_eff, bulk_shear_eff)

Parameters

Name	Type	Description
mucape	Quantity (J/kg)	Most-unstable CAPE.
srh_eff	Quantity (m^2/s^2)	Effective-layer storm-relative helicity.
bulk_shear_eff	Quantity (m/s)	Effective bulk wind shear magnitude.

Returns

Quantity (dimensionless) -- the SCP value.

Example

from metrust.calc import supercell_composite_parameter
from metrust.units import units

scp = supercell_composite_parameter(
    3000 * units("J/kg"),
    300 * units("m**2/s**2"),
    20 * units("m/s"),
)

---

critical_angle

Critical angle between the storm-relative inflow vector and the 0--500 m shear vector. Research by Esterheld and Giuliano (2008) found that a critical angle near 90 degrees is strongly associated with tornadic supercells. Angles well below 90 degrees suggest the low-level shear and inflow are poorly aligned for mesocyclone intensification.

critical_angle(storm_u, storm_v, u_sfc, v_sfc, u_500m, v_500m)

Parameters

Name	Type	Description
storm_u	Quantity (m/s)	Storm motion u-component.
storm_v	Quantity (m/s)	Storm motion v-component.
u_sfc	Quantity (m/s)	Surface u-wind component.
v_sfc	Quantity (m/s)	Surface v-wind component.
u_500m	Quantity (m/s)	500 m AGL u-wind component.
v_500m	Quantity (m/s)	500 m AGL v-wind component.

Returns

Quantity (degree) -- the critical angle in degrees.

Example

from metrust.calc import critical_angle
from metrust.units import units

ca = critical_angle(
    10 * units("m/s"), 5 * units("m/s"),   # storm motion
    2 * units("m/s"), 8 * units("m/s"),    # surface wind
    12 * units("m/s"), 15 * units("m/s"),  # 500 m wind
)
# Values near 90 degrees favor tornadic supercells

---

bulk_richardson_number

Bulk Richardson Number (BRN). The ratio of CAPE to the kinetic energy of the 0--6 km bulk wind shear. BRN helps distinguish between supercellular and multicellular convective modes. Values of 10--45 favor supercells; values below 10 suggest the shear may be too strong relative to buoyancy (splitting or shear-dominated failure), and values above 45 favor multicell storms.

bulk_richardson_number(cape, shear_0_6km)

Parameters

Name	Type	Description
cape	Quantity (J/kg)	Convective available potential energy.
shear_0_6km	Quantity (m/s)	0--6 km bulk wind shear magnitude.

Returns

Quantity (dimensionless) -- the BRN value.

Example

from metrust.calc import bulk_richardson_number
from metrust.units import units

brn = bulk_richardson_number(2000 * units("J/kg"), 20 * units("m/s"))
# BRN 10-45: supercell likely; > 45: multicell; < 10: too much shear

---

Stability Indices

showalter_index

Showalter Index (SI). A parcel-based stability index that lifts air from 850 hPa to 500 hPa and compares the parcel temperature to the environment. Negative values indicate instability; values below -3 suggest moderate-to-strong instability. The Showalter Index is less sensitive to boundary-layer moisture than the Lifted Index, making it useful when an elevated mixed layer or cap is present.

showalter_index(pressure, temperature, dewpoint)

Parameters

Name	Type	Description
pressure	array Quantity (pressure)	Pressure profile (hPa).
temperature	array Quantity (temperature)	Temperature profile.
dewpoint	array Quantity (temperature)	Dewpoint profile.

Returns

Quantity (delta_degC) -- the Showalter Index value.

Example

from metrust.calc import showalter_index
from metrust.units import units

p  = [1000, 925, 850, 700, 500] * units.hPa
T  = [25, 20, 15, 5, -15] * units.degC
Td = [20, 15, 10, -5, -25] * units.degC

si = showalter_index(p, T, Td)
# Negative values = unstable; < -3 = significant instability

---

lifted_index

Lifted Index (LI). Computes the difference between the 500 hPa environmental temperature and the temperature of a surface-based parcel lifted to 500 hPa. Negative values mean the parcel is warmer than the environment (unstable). Operational thresholds: 0 to -2 is marginally unstable, -2 to -6 is moderately unstable, and below -6 is extremely unstable with the potential for intense convection.

lifted_index(pressure, temperature, dewpoint)

Parameters

Name	Type	Description
pressure	array Quantity (pressure)	Pressure profile (hPa).
temperature	array Quantity (temperature)	Temperature profile.
dewpoint	array Quantity (temperature)	Dewpoint profile.

Returns

Quantity (delta_degK) -- the Lifted Index value.

Example

from metrust.calc import lifted_index
from metrust.units import units

p  = [1000, 925, 850, 700, 500] * units.hPa
T  = [30, 24, 18, 4, -18] * units.degC
Td = [22, 18, 14, -4, -28] * units.degC

li = lifted_index(p, T, Td)
# LI < 0: unstable; LI < -6: extreme instability

---

k_index

K-Index (KI). A multi-level stability index that combines low-level moisture depth and mid-level lapse rate into a single number. Higher values indicate greater potential for air-mass thunderstorms. Thresholds: below 20 means thunderstorms unlikely; 20--25 means isolated storms possible; 26--30 means widely scattered storms; 31--35 means scattered storms likely; above 35 means numerous storms. The K-Index does not account for wind shear and is best suited for air-mass (non-severe) convection forecasting.

k_index(t850, td850, t700, td700, t500)

Parameters

Name	Type	Description
t850	Quantity (temperature)	850 hPa temperature (degC).
td850	Quantity (temperature)	850 hPa dewpoint (degC).
t700	Quantity (temperature)	700 hPa temperature (degC).
td700	Quantity (temperature)	700 hPa dewpoint (degC).
t500	Quantity (temperature)	500 hPa temperature (degC).

Returns

Quantity (delta_degC) -- the K-Index value.

Example

from metrust.calc import k_index
from metrust.units import units

ki = k_index(
    20 * units.degC,   # T 850
    16 * units.degC,   # Td 850
    8 * units.degC,    # T 700
    4 * units.degC,    # Td 700
    -12 * units.degC,  # T 500
)
# KI > 30: scattered thunderstorms likely

---

total_totals

Total Totals Index (TT). The sum of the Vertical Totals (T850 - T500) and Cross Totals (Td850 - T500). Values above 44 indicate a possibility of thunderstorms; above 50--55 suggests a risk of severe thunderstorms with large hail. TT is widely used in operational forecasting because it requires only standard-level data and is straightforward to compute.

total_totals(t850, td850, t500)

Parameters

Name	Type	Description
t850	Quantity (temperature)	850 hPa temperature (degC).
td850	Quantity (temperature)	850 hPa dewpoint (degC).
t500	Quantity (temperature)	500 hPa temperature (degC).

Returns

Quantity (delta_degC) -- the Total Totals index value.

Example

from metrust.calc import total_totals
from metrust.units import units

tt = total_totals(20 * units.degC, 16 * units.degC, -12 * units.degC)
# TT > 44: thunderstorms possible; > 55: severe storms possible

---

cross_totals

Cross Totals (CT). Defined as Td850 - T500. The Cross Totals component captures the combined effect of low-level moisture and mid-level cold air. Values above 18 indicate moderate instability; above 22 suggests strong instability favorable for convection.

cross_totals(td850, t500)

Parameters

Name	Type	Description
td850	Quantity (temperature)	850 hPa dewpoint (degC).
t500	Quantity (temperature)	500 hPa temperature (degC).

Returns

Quantity (delta_degC) -- the Cross Totals value.

Example

from metrust.calc import cross_totals
from metrust.units import units

ct = cross_totals(16 * units.degC, -12 * units.degC)

---

vertical_totals

Vertical Totals (VT). Defined as T850 - T500. Measures the temperature lapse rate between 850 hPa and 500 hPa. Values above 26 indicate steep lapse rates favorable for deep convection, though Vertical Totals alone do not account for moisture.

vertical_totals(t850, t500)

Parameters

Name	Type	Description
t850	Quantity (temperature)	850 hPa temperature (degC).
t500	Quantity (temperature)	500 hPa temperature (degC).

Returns

Quantity (delta_degC) -- the Vertical Totals value.

Example

from metrust.calc import vertical_totals
from metrust.units import units

vt = vertical_totals(20 * units.degC, -12 * units.degC)

---

sweat_index

Severe Weather Threat Index (SWEAT). An older composite that blends low-level moisture, instability (via the Total Totals), wind speeds at 850 and 500 hPa, and directional wind shear (veering) between those two levels. Values above 300 indicate a significant severe weather threat; above 400 suggests tornado potential. Because SWEAT relies on fixed-level wind data and lacks direct shear-profile information, it has been largely superseded by STP and SCP in U.S. operations but remains in use internationally.

sweat_index(t850, td850, t500, dd850, dd500, ff850, ff500)

Parameters

Name	Type	Description
t850	Quantity (temperature)	850 hPa temperature (degC).
td850	Quantity (temperature)	850 hPa dewpoint (degC).
t500	Quantity (temperature)	500 hPa temperature (degC).
dd850	Quantity (degrees)	850 hPa wind direction.
dd500	Quantity (degrees)	500 hPa wind direction.
ff850	Quantity (speed)	850 hPa wind speed (knots).
ff500	Quantity (speed)	500 hPa wind speed (knots).

Returns

Quantity (dimensionless) -- the SWEAT index value.

Example

from metrust.calc import sweat_index
from metrust.units import units

sweat = sweat_index(
    20 * units.degC,      # T 850
    16 * units.degC,      # Td 850
    -12 * units.degC,     # T 500
    210 * units.degree,   # wind dir 850
    250 * units.degree,   # wind dir 500
    30 * units.knot,      # wind speed 850
    50 * units.knot,      # wind speed 500
)
# SWEAT > 300: severe threat; > 400: tornado potential

---

boyden_index

Boyden Index. A European stability index originally developed for thunderstorm forecasting in the UK. It combines the 1000--700 hPa thickness with the 700 hPa temperature. Values above 94--95 have been associated with thunderstorm development in mid-latitude maritime environments.

boyden_index(z1000, z700, t700)

Parameters

Name	Type	Description
z1000	Quantity (m)	1000 hPa geopotential height.
z700	Quantity (m)	700 hPa geopotential height.
t700	Quantity (temperature)	700 hPa temperature.

Returns

Quantity (dimensionless) -- the Boyden Index value.

Example

from metrust.calc import boyden_index
from metrust.units import units

bi = boyden_index(120 * units.m, 3100 * units.m, 4 * units.degC)
# Values > 94 suggest thunderstorm potential (European climates)

---

CAPE and CIN Variants

downdraft_cape

Downdraft CAPE (DCAPE). Estimates the maximum kinetic energy available to a descending parcel driven by evaporative cooling. Larger DCAPE values correlate with stronger thunderstorm outflow and damaging surface winds. Values above 1000 J/kg indicate potential for significant wind damage; above 1500 J/kg suggests extreme outflow potential.

downdraft_cape(pressure, temperature, dewpoint)

Parameters

Name	Type	Description
pressure	array Quantity (pressure)	Pressure profile (hPa).
temperature	array Quantity (temperature)	Temperature profile.
dewpoint	array Quantity (temperature)	Dewpoint profile.

Returns

Quantity (J/kg) -- the DCAPE value.

Example

from metrust.calc import downdraft_cape
from metrust.units import units

p  = [1000, 925, 850, 700, 500, 300] * units.hPa
T  = [28, 22, 16, 4, -14, -38] * units.degC
Td = [22, 16, 10, -8, -30, -50] * units.degC

dcape = downdraft_cape(p, T, Td)
# DCAPE > 1000 J/kg: strong outflow potential

---

convective_inhibition_depth

Convective inhibition depth. Computes the pressure depth (in hPa) of the layer through which convective inhibition acts on a lifted parcel. This supplements the CIN magnitude by indicating how deep the capping inversion extends. A shallow but strong cap may break more easily than a deep cap with the same total CIN.

convective_inhibition_depth(pressure, temperature, dewpoint)

Parameters

Name	Type	Description
pressure	array Quantity (pressure)	Pressure profile (hPa).
temperature	array Quantity (temperature)	Temperature profile.
dewpoint	array Quantity (temperature)	Dewpoint profile.

Returns

Quantity (hPa) -- the pressure depth of the CIN layer.

Example

from metrust.calc import convective_inhibition_depth
from metrust.units import units

p  = [1000, 950, 925, 900, 850, 700, 500] * units.hPa
T  = [30, 26, 24, 22, 18, 4, -14] * units.degC
Td = [22, 20, 18, 14, 10, -6, -28] * units.degC

cin_depth = convective_inhibition_depth(p, T, Td)

---

Sounding Diagnostics

dendritic_growth_zone

Dendritic growth zone bounds. Identifies the pressure layer where temperatures fall between -12 degC and -18 degC, the range in which dendritic ice crystals grow most efficiently. This zone is operationally significant for snowfall forecasting: a deep dendritic growth zone with adequate moisture supports higher snow-to-liquid ratios and greater snowfall accumulation.

dendritic_growth_zone(temperature, pressure)

Parameters

Name	Type	Description
temperature	array Quantity (temperature)	Temperature profile.
pressure	array Quantity (pressure)	Pressure profile (hPa).

Returns

tuple of (Quantity (hPa), Quantity (hPa)) -- bottom and top pressure of the dendritic growth zone.

Example

from metrust.calc import dendritic_growth_zone
from metrust.units import units

T = [-5, -8, -12, -15, -18, -22] * units.degC
p = [850, 800, 750, 700, 650, 600] * units.hPa

bot, top = dendritic_growth_zone(T, p)
# A deeper zone (larger pressure difference) favors heavier snow

---

warm_nose_check

Check for a warm nose -- a layer above the surface where the temperature exceeds 0 degC in an otherwise sub-freezing profile. Warm noses are critical for winter precipitation type forecasting: their presence and depth govern whether falling snow melts completely (producing rain or freezing rain) or only partially (producing sleet/ice pellets).

warm_nose_check(temperature, pressure)

Parameters

Name	Type	Description
temperature	array Quantity (temperature)	Temperature profile.
pressure	array Quantity (pressure)	Pressure profile (hPa).

Returns

bool -- True if a warm nose is detected in the profile.

Example

from metrust.calc import warm_nose_check
from metrust.units import units

T = [-2, 1, 3, 1, -4, -12] * units.degC
p = [1000, 950, 900, 850, 700, 500] * units.hPa

has_warm_nose = warm_nose_check(T, p)
# True indicates a melting layer aloft -- freezing rain or sleet risk

---

freezing_rain_composite

Freezing rain composite index. A multi-factor diagnostic that combines thermal profile information and precipitation type into a single index for assessing the likelihood of freezing rain. Higher values indicate environments more conducive to freezing rain accumulation.

freezing_rain_composite(temperature, pressure, precip_type)

Parameters

Name	Type	Description
temperature	array Quantity (temperature)	Temperature profile.
pressure	array Quantity (pressure)	Pressure profile (hPa).
precip_type	int	Precipitation type flag.

Returns

Quantity (dimensionless) -- the freezing rain composite index value.

Example

from metrust.calc import freezing_rain_composite
from metrust.units import units

T = [-2, 1, 3, 1, -5, -15] * units.degC
p = [1000, 950, 900, 850, 700, 500] * units.hPa

fzra = freezing_rain_composite(T, p, precip_type=1)

---

galvez_davison_index

Galvez-Davison Index (GDI). A stability index developed specifically for tropical environments where traditional mid-latitude indices (LI, CAPE) often perform poorly. The GDI uses temperatures and dewpoints at 950, 850, 700, and 500 hPa along with sea surface temperature to assess the potential for tropical thunderstorm development. Positive values indicate instability; values above 25--30 suggest conditions favorable for deep tropical convection. Widely used by NWS offices in Puerto Rico and the tropical Pacific.

galvez_davison_index(t950, t850, t700, t500, td950, td850, td700, sst)

Parameters

Name	Type	Description
t950	Quantity (temperature)	950 hPa temperature.
t850	Quantity (temperature)	850 hPa temperature.
t700	Quantity (temperature)	700 hPa temperature.
t500	Quantity (temperature)	500 hPa temperature.
td950	Quantity (temperature)	950 hPa dewpoint.
td850	Quantity (temperature)	850 hPa dewpoint.
td700	Quantity (temperature)	700 hPa dewpoint.
sst	Quantity (temperature)	Sea surface temperature.

Returns

Quantity (dimensionless) -- the GDI value.

Example

from metrust.calc import galvez_davison_index
from metrust.units import units

gdi = galvez_davison_index(
    24 * units.degC,   # T 950
    20 * units.degC,   # T 850
    10 * units.degC,   # T 700
    -8 * units.degC,   # T 500
    22 * units.degC,   # Td 950
    18 * units.degC,   # Td 850
    4 * units.degC,    # Td 700
    28 * units.degC,   # SST
)
# GDI > 25-30: favorable for tropical deep convection

---

Fire Weather

fosberg_fire_weather_index

Fosberg Fire Weather Index (FFWI). Combines temperature, relative humidity, and wind speed into a single index that measures the potential for wildfire spread. Values are scaled 0--100; higher values indicate greater fire danger. The FFWI is standard in U.S. fire weather forecasting and is included in NWS fire weather spot forecasts. Values above 50 are considered high; above 75 is extreme.

fosberg_fire_weather_index(temperature, relative_humidity, wind_speed)

Parameters

Name	Type	Description
temperature	Quantity (temperature)	Temperature in Fahrenheit.
relative_humidity	Quantity (percent) or float	Relative humidity (0--100 scale).
wind_speed	Quantity (speed)	Wind speed in mph.

Returns

Quantity (dimensionless) -- the FFWI value.

Example

from metrust.calc import fosberg_fire_weather_index
from metrust.units import units

ffwi = fosberg_fire_weather_index(
    95 * units.degF,
    15 * units.percent,
    25 * units.mph,
)
# FFWI > 50: high fire danger; > 75: extreme

---

haines_index

Haines Index (Lower Atmosphere Severity Index). A fire weather index that combines the stability and moisture content of the lower atmosphere to assess the potential for large, erratic fire behavior. Uses 950 and 850 hPa temperatures along with the 850 hPa dewpoint depression. The index ranges from 2 to 6: values of 2--3 are low potential, 4 is moderate, 5 is high, and 6 is very high potential for large fire growth.

haines_index(t_950, t_850, td_850)

Parameters

Name	Type	Description
t_950	Quantity (temperature)	950 hPa temperature.
t_850	Quantity (temperature)	850 hPa temperature.
td_850	Quantity (temperature)	850 hPa dewpoint.

Returns

int -- the Haines Index value (2--6).

Example

from metrust.calc import haines_index
from metrust.units import units

hi = haines_index(
    22 * units.degC,  # T 950
    18 * units.degC,  # T 850
    6 * units.degC,   # Td 850
)
# 5-6: high potential for large, erratic fire behavior

---

hot_dry_windy

Hot-Dry-Windy Index (HDW). A composite fire weather diagnostic that captures the combined effect of temperature, moisture deficit, and wind on fire behavior. Unlike the Fosberg index, HDW explicitly includes vapor pressure deficit (VPD), which better represents the drying power of the atmosphere. When vpd is set to 0, it is computed internally from the temperature and humidity inputs. Higher values indicate more dangerous fire weather conditions.

hot_dry_windy(temperature, relative_humidity, wind_speed, vpd=0.0)

Parameters

Name	Type	Description
temperature	Quantity (temperature)	Temperature.
relative_humidity	float or Quantity (percent)	Relative humidity.
wind_speed	Quantity (m/s)	Wind speed.
vpd	float	Vapor pressure deficit in hPa. If 0, computed internally from temperature and humidity.

Returns

Quantity (dimensionless) -- the HDW index value.

Example

from metrust.calc import hot_dry_windy
from metrust.units import units

hdw = hot_dry_windy(
    35 * units.degC,
    12 * units.percent,
    15 * units("m/s"),
)

---

See Also

• Thermodynamics -- CAPE/CIN, parcel profiles, LCL/LFC/EL, and moisture calculations.
• Wind -- Bulk shear, storm-relative helicity, Bunkers storm motion, and Corfidi vectors.
• Kinematics -- Divergence, vorticity, advection, and frontogenesis.