Your First Sounding Analysis¶

This tutorial walks you through a complete upper-air sounding analysis. By the end you will know how to compute every parameter a severe weather forecaster looks at and understand what the numbers mean.

No meteorology background required. Every function call is explained.

What We're Building¶

We will take a single atmospheric sounding -- pressure, temperature, dewpoint, height, wind speed, and wind direction from the surface to the tropopause -- and extract every useful parameter from it. Our sounding represents a warm, humid summer afternoon over the southern Great Plains: the kind of environment that spawns violent supercells.

The Data¶

import numpy as np
from metrust.calc import (
    potential_temperature, virtual_temperature,
    equivalent_potential_temperature,
    relative_humidity_from_dewpoint,
    mixing_ratio_from_relative_humidity, vapor_pressure,
    lcl, lfc, el, parcel_profile, cape_cin,
    wind_components, bulk_shear, storm_relative_helicity,
    significant_tornado_parameter, supercell_composite_parameter,
)
from metrust.units import units

Pressure, temperature, dewpoint¶

pressure = np.array([
    1013, 1000, 975, 950, 925, 900, 850, 800,
    750,  700,  650, 600, 550, 500, 400, 300, 250, 200,
]) * units.hPa

temperature = np.array([
    33.0, 32.0, 29.5, 27.0, 25.0, 23.0, 19.0, 14.5,
    10.0,  5.5,  1.0, -4.5, -10.0, -16.0, -30.0, -44.0, -52.0, -58.0,
]) * units.degC

dewpoint = np.array([
    23.0, 22.5, 21.0, 20.0, 18.5, 16.5, 12.0,  5.0,
     0.0, -5.0, -10.0, -17.0, -24.0, -32.0, -44.0, -55.0, -62.0, -70.0,
]) * units.degC

Pressure decreases with altitude (1013 hPa at the surface, 200 hPa near 12 km). Temperature drops at roughly 6-7 C/km. The surface dewpoint of 23 C is oppressively humid, but dewpoints drop quickly above 850 hPa -- moist boundary layer capped by dry mid-levels, the classic severe weather setup.

Height and wind¶

height = np.array([
       0,  100,  350,  600,  850, 1100, 1500, 2000,
    2550, 3100, 3700, 4350, 5050, 5800, 7500, 9500, 10700, 12100,
]) * units.m

wind_spd = np.array([
     8,  10,  12,  14,  16,  18,  22,  26,
    30,  34,  36,  37,  38,  40,  44,  50, 52, 54,
]) * units('m/s')

wind_dir = np.array([
    170, 175, 185, 195, 210, 220, 230, 240,
    245, 250, 255, 258, 260, 262, 265, 268, 270, 272,
]) * units.degree

Wind increases from 8 m/s at the surface to 54 m/s (120 mph) aloft, veering from southerly to westerly. This increasing-speed-and-veering-direction pattern is wind shear -- the key ingredient alongside instability for supercells and tornadoes.

Step 1: Basic Thermodynamics¶

Potential temperature¶

theta = potential_temperature(pressure, temperature)
print(f"Surface:  {theta[0]:.1f}")   # ~306 K
print(f"500 hPa:  {theta[13]:.1f}")  # ~310 K

Potential temperature is what air would measure if brought adiabatically to 1000 hPa. It removes the effect of pressure so you can compare air at different altitudes. Theta increasing with height means the atmosphere is stable to dry processes -- but as we will see, moisture changes everything.

Virtual temperature¶

tv = virtual_temperature(temperature, pressure, dewpoint=dewpoint)
print(f"Surface T:   {temperature[0]:.1f}")  # 33.0 degC
print(f"Surface T_v: {tv[0]:.1f}")           # ~36.1 degC

Moist air is lighter than dry air (water vapor, MW 18, replaces heavier N2 and O2). Virtual temperature adjusts for this. The ~3 C difference at the surface confirms heavy moisture loading in the boundary layer.

Equivalent potential temperature¶

theta_e = equivalent_potential_temperature(pressure, temperature, dewpoint)
print(f"Surface theta-e:  {theta_e[0]:.1f}")   # ~354 K
print(f"500 hPa theta-e:  {theta_e[13]:.1f}")  # ~315 K

Theta-e accounts for latent heat released during condensation. The steep drop from 354 K at the surface to 315 K at 500 hPa tells us the low levels are loaded with energy from both warmth and moisture, while mid-levels are relatively cold and dry. When the cap breaks, all that latent heat fuels an intense updraft.

Why theta-e matters

A large surface-to-mid-level theta-e difference is one of the clearest signals of severe weather potential. It means the atmosphere has a deep reservoir of energy waiting to be released.

Step 2: Moisture Profile¶

Relative humidity¶

rh = relative_humidity_from_dewpoint(temperature, dewpoint)
for i in [0, 6, 13]:
    print(f"{pressure[i].magnitude:.0f} hPa:  {rh[i].magnitude * 100:.1f}%")

Output

1013 hPa:  59.4%
850 hPa:   62.6%
500 hPa:   22.3%

RH is 60-67% in the boundary layer (moist but not saturated) and drops to about 22% by 500 hPa. This moist-low-dry-aloft profile is textbook severe weather.

RH can mislead

Cold air with low absolute moisture can show high RH. Use mixing ratio for a true measure of water vapor content.

Mixing ratio¶

w = mixing_ratio_from_relative_humidity(pressure, temperature, rh)
for i in [0, 6, 13]:
    print(f"{pressure[i].magnitude:.0f} hPa:  {w[i].to('g/kg').magnitude:.1f} g/kg")

Output

1013 hPa:  17.6 g/kg
850 hPa:   8.9 g/kg
500 hPa:   0.7 g/kg

The surface mixing ratio of ~18 g/kg is very high -- typical of Gulf of Mexico air masses that fuel Great Plains severe weather. By 500 hPa it has dropped to less than 1 g/kg. Almost all the moisture is concentrated in the lowest 3 km.

Vapor pressure¶

e = vapor_pressure(dewpoint)
for i in [0, 6, 13]:
    print(f"{pressure[i].magnitude:.0f} hPa:  {e[i].to('hPa').magnitude:.1f} hPa")

Output

1013 hPa:  28.1 hPa
850 hPa:   14.0 hPa
500 hPa:   0.4 hPa

Vapor pressure drops exponentially with height. The surface value of 28 hPa means nearly 3% of total atmospheric pressure is from water vapor alone.

All three are related

RH, mixing ratio, and vapor pressure are different ways to express the same thing: how much water vapor is present. Use RH for cloud formation, mixing ratio for air-mass tracking, vapor pressure for energy budgets.

Step 3: Find Key Levels¶

Three critical altitudes determine whether storms form and how strong they can become.

LCL -- Lifting Condensation Level (cloud base)¶

p_lcl, T_lcl = lcl(pressure[0], temperature[0], dewpoint[0])
print(f"LCL: {p_lcl:.0f}  ({T_lcl:.1f})")  # ~881 hPa, ~19.6 C

The LCL is where a lifted surface parcel cools to saturation and clouds form. Ours is about 881 hPa (~1100 m AGL). Low LCLs (below ~1500 m) favor tornadoes because they keep the rotating updraft close to the ground.

LFC -- Level of Free Convection (storms become self-sustaining)¶

p_lfc = lfc(pressure, temperature, dewpoint)
print(f"LFC: {p_lfc:.0f}")  # ~756 hPa

Below the LFC, a rising parcel is cooler than its surroundings and needs a push (cold front, dryline, outflow). Above the LFC, the parcel is buoyant and accelerates upward on its own. Our LFC near 756 hPa means a moderate trigger is needed.

EL -- Equilibrium Level (storm top)¶

p_el = el(pressure, temperature, dewpoint)
print(f"EL: {p_el:.0f}")  # ~195 hPa

The EL is where the parcel cools back to the environment temperature and loses buoyancy. It marks the anvil level. The LFC-to-EL gap (~756 to ~195 hPa) spans roughly 10 km of buoyant acceleration -- an enormous updraft. Storm tops would exceed 40,000 feet.

Step 4: Parcel Profile¶

prof = parcel_profile(pressure, temperature[0], dewpoint[0])
for i in [0, 6, 9, 13, 17]:
    diff = prof[i].magnitude - temperature[i].magnitude
    label = "WARMER" if diff > 0 else "cooler"
    print(f"  {pressure[i].magnitude:6.0f} hPa: env {temperature[i].magnitude:+6.1f} C  "
          f"parcel {prof[i].magnitude:+6.1f} C  ({label})")

Output

  1013 hPa: env  +33.0 C  parcel  +33.0 C  (cooler)
   850 hPa: env  +19.0 C  parcel  +17.3 C  (cooler)
   700 hPa: env   +5.5 C  parcel   +7.2 C  (WARMER)
   500 hPa: env  -16.0 C  parcel  -12.8 C  (WARMER)
   200 hPa: env  -58.0 C  parcel  -57.5 C  (WARMER)

The parcel profile traces the temperature a surface parcel would have if lifted through the sounding. Below the LCL it cools at the dry adiabatic rate (~10 C/km). Above the LCL, condensation releases latent heat and it cools more slowly (~6 C/km). The parcel is cooler than the environment in the boundary layer (CIN zone) but warmer from ~750 hPa all the way to ~195 hPa (CAPE zone).

Step 5: CAPE and CIN¶

Surface-based¶

sb_cape, sb_cin, sb_lcl_h, sb_lfc_h = cape_cin(
    pressure, temperature, dewpoint, height,
    pressure[0], temperature[0], dewpoint[0],
    parcel_type="sb",
)
print(f"SBCAPE: {sb_cape:.0f}")    # ~2687 J/kg
print(f"CIN:    {sb_cin:.0f}")     # ~-58 J/kg
print(f"LCL:    {sb_lcl_h:.0f}")   # ~1148 m AGL
print(f"LFC:    {sb_lfc_h:.0f}")   # ~2490 m AGL

CAPE (J/kg)	Instability	Typical outcome
< 300	Weak	Showers, no severe weather
300--1000	Moderate	Thunderstorms, small hail possible
1000--2500	Strong	Severe storms, large hail, damaging winds
2500+	Extreme	Violent storms, giant hail, tornadoes

CIN (J/kg)	Cap strength	Meaning
0 to -25	Weak	Storms fire with minimal trigger
-25 to -100	Moderate	Needs a front, dryline, or boundary
< -200	Very strong	Almost nothing can break through

Our CAPE of ~2700 J/kg is extreme. CIN of ~-58 J/kg is a moderate cap -- storms need a trigger, but once it breaks, the atmosphere is loaded.

Some CIN is good

A moderate cap prevents early, disorganized storms. CAPE builds through the day. When the cap finally breaks in late afternoon, the result is fewer but much more intense storms.

Mixed-layer and most-unstable¶

ml_cape, ml_cin, _, _ = cape_cin(
    pressure, temperature, dewpoint, height,
    pressure[0], temperature[0], dewpoint[0],
    parcel_type="ml",
)
mu_cape, mu_cin, _, _ = cape_cin(
    pressure, temperature, dewpoint, height,
    pressure[0], temperature[0], dewpoint[0],
    parcel_type="mu",
)
print(f"MLCAPE: {ml_cape:.0f}")  # ~2305 J/kg
print(f"MUCAPE: {mu_cape:.0f}")  # ~2780 J/kg

Three parcel types

Surface-based (SB): Uses the surface observation directly.
Mixed-layer (ML): Averages the lowest 100 hPa. More representative of what a storm actually ingests. Standard for STP.
Most-unstable (MU): Finds the single most buoyant parcel in the lowest 300 hPa. Important for elevated convection.

Step 6: Wind Analysis¶

Convert to u/v components¶

u, v = wind_components(wind_spd, wind_dir)
print(f"Surface:  u={u[0]:.1f}, v={v[0]:.1f}")
print(f"500 hPa:  u={u[13]:.1f}, v={v[13]:.1f}")

Output

Surface:  u=1.4 m/s, v=-7.9 m/s
500 hPa:  u=35.3 m/s, v=-5.6 m/s

At the surface, wind is almost entirely from the south (strong -v). Aloft, u dominates -- nearly westerly. This south-to-west veering is the classic severe weather hodograph.

0-6 km bulk shear¶

shear_u, shear_v = bulk_shear(u, v, height, bottom=0 * units.m, top=6000 * units.m)
shear_mag = np.sqrt(shear_u.magnitude**2 + shear_v.magnitude**2)
print(f"0-6 km bulk shear: {shear_mag:.1f} m/s")  # ~35 m/s

0-6 km shear (m/s)	Storm mode
< 10	Weak; short-lived pulse storms
10--20	Moderate; multicell clusters
20--30	Strong; supercells likely
30+	Extreme; long-lived violent supercells

Our ~35 m/s is extreme. Any storm that forms will almost certainly rotate.

Storm-relative helicity (SRH)¶

from metrust.calc import bunkers_storm_motion

(rm_u, rm_v), _, _ = bunkers_storm_motion(u, v, height)
rm_speed = np.sqrt(rm_u.magnitude**2 + rm_v.magnitude**2)
print(f"Bunkers right-mover: {rm_speed:.1f} m/s")

_, _, srh_01 = storm_relative_helicity(u, v, height, 1000 * units.m, rm_u, rm_v)
_, _, srh_03 = storm_relative_helicity(u, v, height, 3000 * units.m, rm_u, rm_v)
print(f"0-1 km SRH: {srh_01:.0f}")  # ~203 m^2/s^2
print(f"0-3 km SRH: {srh_03:.0f}")  # ~347 m^2/s^2

SRH measures the corkscrew rotation in the wind profile relative to the storm. Higher SRH means the updraft ingests more rotation, spinning up a mesocyclone.

0-1 km SRH (m^2/s^2)	Tornado potential
< 100	Low; tornadoes unlikely
100--200	Moderate; weak tornadoes possible
200--300	High; significant tornadoes likely
300+	Very high; violent tornadoes

Why the 0-1 km layer matters most for tornadoes

Tornadoes are a near-surface phenomenon. Strong low-level SRH means the storm can produce rotation right down to the ground. The 0-3 km SRH captures the broader mesocyclone, but it is the 0-1 km layer that discriminates tornadic from non-tornadic supercells.

Step 7: Severe Weather Composite Parameters¶

Significant Tornado Parameter (STP)¶

stp = significant_tornado_parameter(
    ml_cape,                       # mixed-layer CAPE
    sb_lcl_h,                      # LCL height AGL
    srh_01,                        # 0-1 km SRH
    shear_mag * units('m/s'),      # 0-6 km shear magnitude
)
print(f"STP: {stp:.1f}")  # ~4.6

STP combines four ingredients, each normalized by its "significant tornado" baseline:

MLCAPE / 1500 -- instability
(2000 - LCL) / 1000 -- low cloud base (0 when LCL > 2000 m)
SRH / 150 -- low-level rotation
Shear / 20 -- deep-layer organization

STP	Interpretation
< 1	Significant tornadoes unlikely
1--3	Environment supports significant tornadoes
3--6	Very favorable; multiple significant tornadoes
6+	Extremely favorable; violent (EF4+) possible

STP is not a guarantee

An STP of 4.6 means the ingredients are strongly favorable. Storms still need a trigger, and mesoscale factors determine which cells actually produce tornadoes.

Supercell Composite Parameter (SCP)¶

scp = supercell_composite_parameter(
    mu_cape,                       # most-unstable CAPE
    srh_03,                        # effective SRH
    shear_mag * units('m/s'),      # effective bulk shear
)
print(f"SCP: {scp:.1f}")  # ~17.0

SCP estimates whether storms will be supercells:

MUCAPE / 1000 -- buoyancy
SRH / 50 -- rotation supply
Shear / 20 -- organizational shear

SCP	Interpretation
< 1	Supercells unlikely
1--4	Supercells possible
4--10	Supercells very likely
10+	Discrete, intense supercells favored

Our SCP of ~17 means any storms that form will be long-lived rotating supercells.

Putting It All Together¶

print("=" * 50)
print("  SOUNDING ANALYSIS SUMMARY")
print("=" * 50)
print(f"  Surface T / Td:    {temperature[0].magnitude:.0f} C / {dewpoint[0].magnitude:.0f} C")
print(f"  LCL:  {p_lcl:.0f}  (~{sb_lcl_h:.0f} AGL)")
print(f"  LFC:  {p_lfc:.0f}    EL: {p_el:.0f}")
print(f"  SBCAPE / CIN:      {sb_cape.magnitude:.0f} / {sb_cin.magnitude:.0f} J/kg")
print(f"  MLCAPE:            {ml_cape.magnitude:.0f} J/kg")
print(f"  MUCAPE:            {mu_cape.magnitude:.0f} J/kg")
print(f"  0-6 km shear:      {shear_mag:.1f} m/s")
print(f"  0-1 km SRH:        {srh_01.magnitude:.0f} m^2/s^2")
print(f"  0-3 km SRH:        {srh_03.magnitude:.0f} m^2/s^2")
print(f"  STP: {stp.magnitude:.1f}    SCP: {scp.magnitude:.1f}")
print("=" * 50)

The forecast: This sounding shows extreme instability (CAPE ~2700 J/kg) combined with extreme deep-layer shear (35 m/s) and strong low-level rotation (0-1 km SRH ~200). A moderate cap will focus storm initiation on a mesoscale trigger. Once storms develop, discrete long-lived supercells are essentially guaranteed. The STP of 4.6 places this environment well above the significant tornado threshold -- multiple significant tornadoes are possible with any supercell that can sustain a low-level mesocyclone.

What to Try Next¶

Kill the moisture. Drop surface dewpoint from 23 C to 12 C. Watch CAPE collapse, LCL height jump, and STP fall below 1.
Remove the shear. Set wind to a constant 10 m/s from 250 degrees at all levels. CAPE stays the same, but SRH drops to zero and composites fall below 1. This is an "airmass thunderstorm" environment.
Strengthen the cap. Add 5 C to temperatures at 850 and 800 hPa. CIN becomes much more negative and storms may not fire at all.
Try all parcel types. Switch between "sb", "ml", and "mu" in cape_cin. Operational forecasters look at all three.
Use real data. Load a radiosonde from the University of Wyoming archive or a model GRIB file and run this same pipeline.