Potential Temperature Poisson

Compute pressure-normalized dry potential-temperature sounding under caller R/cp/reference pressure; no moisture normalization or actual measured parcel temperature at reference pressure.

Description

Potential temperature is the temperature a dry air parcel would reach if moved adiabatically to a reference pressure.

Potential temperature is the temperature a dry air parcel would reach if moved adiabatically to a reference pressure. This removes the temperature change attributable to dry compression or expansion and helps compare observations at different pressures.^[1]

Compute pressure-normalized dry potential-temperature sounding under caller R/cp/reference pressure; no moisture normalization or actual measured parcel temperature at reference pressure.

When to use Potential Temperature Poisson

Use this tool to compute pressure-normalized dry potential-temperature sounding under caller R/cp/reference pressure; no moisture normalization or actual measured parcel temperature at reference pressure.

Prepare the climate observations and any independently chosen thresholds or model parameters. Confirm units, daily coverage, time order and the intended seasonal window.

How to use Potential Temperature Poisson and understand its results

Prepare the climate observations and any independently chosen thresholds or model parameters. Confirm units, daily coverage, time order and the intended seasonal window.
Enter temperaturesK, pressuresHpa, referencePressureHpa, dryGasHeatCapacityRatio using the field table and calculation rules, then run the tool.
Read potentialTemperaturesK. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
temperaturesK	Temperatures k	list of number	Required
pressuresHpa	Pressures hPa	list of number	Required
referencePressureHpa	Reference pressure hPa	number	Required
dryGasHeatCapacityRatio	Dry gas heat capacity ratio	number	Required

Enter aligned positive temperatures in kelvin and pressures in hPa, a positive reference pressure in hPa and a positive ratio Rd/cp. The tool applies the Poisson relation separately to every observation and returns potential temperatures in kelvin. Observations at the reference pressure retain their supplied temperature.

Paired lists must be nonempty and have equal lengths.

θ = T(P_reference/P)^(Rd/cp)

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
potentialTemperaturesK	Potential temperatures k	list of number

json

{
  "input": {
    "temperaturesK": [
      300,
      280
    ],
    "pressuresHpa": [
      1000,
      500
    ],
    "referencePressureHpa": 1000,
    "dryGasHeatCapacityRatio": 1
  },
  "output": {
    "potentialTemperaturesK": [
      300,
      560
    ]
  }
}

Limitations and assumptions

The calculation assumes dry adiabatic behavior and a constant supplied heat-capacity ratio. It does not include latent heating, moisture loading or a moist-adiabatic parcel trajectory. Reference and observation pressures must use the same unit.

Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Virtual Temperature Correction: Compute exact ideal moist-air virtual temperature with vapor and suspended-liquid specific mass fractions relative to total mixture; differs from vapor mixing-ratio approximations and excludes ice unless caller independently models it. For a complementary task, use Lifting Condensation Level Height: Compute named Bolton LCL temperature then caller dry-adiabatic pressure/height for a surface parcel; not existing dewpoint-spread fog proxy, inferred environmental cloud base or moist-convective ascent.

References

Potential Temperature Poisson — tool.io

Similar or alternative tools

Virtual Temperature Correction
Compute exact ideal moist-air virtual temperature with vapor and suspended-liquid specific mass fractions relative to total mixture; differs from vapor mixing-ratio approximations and excludes ice unless caller independently models it.
Lifting Condensation Level Height
Compute named Bolton LCL temperature then caller dry-adiabatic pressure/height for a surface parcel; not existing dewpoint-spread fog proxy, inferred environmental cloud base or moist-convective ascent.