tephpy.transforms#

Coordinate transforms for the tephigram projection.

Pure numpy functions between the three coordinate frames of the tephigram (spec §3.1): pressure/temperature (p, T), temperature/potential-temperature (T, theta), and the rotated tephigram (x, y) plane, where

x = MA * ln(theta_K) + T y = MA * ln(theta_K) - T

with MA = 300 and theta_K the potential temperature in Kelvin. The construction is derived from Met Office Factsheet 13 and Stull, Practical Meteorology ch. 5, and cross-validated against tephi as an oracle (tests/test_oracle.py) — not ported from it.

This module is the documented exemption to the pint units policy (spec §5): bare float64 arrays in diagram-native units — pressure in hPa, temperatures in degrees Celsius, x/y dimensionless. Out-of-domain input (non-positive pressure, potential temperatures theta at or below absolute zero) propagates NaN; exception-carrying validation lives at the quantified boundaries above this module (spec §6).

Functions#

`theta_from_pressure_temperature`(...)	Convert pressure and temperature to potential temperature.
`pressure_from_temperature_theta`(...)	Convert temperature and potential temperature to pressure.
`xy_from_temperature_theta`(...)	Convert temperature and potential temperature to tephigram (x, y).
`temperature_theta_from_xy`(...)	Convert tephigram (x, y) coordinates back to temperature and theta.

Module Contents#

tephpy.transforms.theta_from_pressure_temperature(pressure: numpy.typing.ArrayLike, temperature: numpy.typing.ArrayLike) → numpy.typing.NDArray[numpy.float64][source]#

Convert pressure and temperature to potential temperature.

Poisson’s equation: theta_K = T_K * (P_REF / p) ** kappa.

Parameters:

pressureArrayLike: Pressure in hPa. Non-positive values yield NaN.
temperatureArrayLike: Temperature in degrees Celsius.

Returns:

numpy.ndarray: Potential temperature in degrees Celsius, float64, broadcast over the inputs.

tephpy.transforms.pressure_from_temperature_theta(temperature: numpy.typing.ArrayLike, theta: numpy.typing.ArrayLike) → numpy.typing.NDArray[numpy.float64][source]#

Convert temperature and potential temperature to pressure.

Inverse of theta_from_pressure_temperature(): p = P_REF * (T_K / theta_K) ** (1 / kappa).

Parameters:

temperatureArrayLike: Temperature in degrees Celsius.
thetaArrayLike: Potential temperature in degrees Celsius. Values at or below absolute zero yield NaN.

Returns:

numpy.ndarray: Pressure in hPa, float64, broadcast over the inputs.

tephpy.transforms.xy_from_temperature_theta(temperature: numpy.typing.ArrayLike, theta: numpy.typing.ArrayLike) → tuple[numpy.typing.NDArray[numpy.float64], numpy.typing.NDArray[numpy.float64]][source]#

Convert temperature and potential temperature to tephigram (x, y).

The rotated tephigram mapping: x = MA * ln(theta_K) + T and y = MA * ln(theta_K) - T, which renders isotherms and dry adiabats as exactly perpendicular straight lines.

Parameters:

temperatureArrayLike: Temperature in degrees Celsius.
thetaArrayLike: Potential temperature in degrees Celsius. Values at or below absolute zero yield NaN.

Returns:

tuple of numpy.ndarray: The tephigram (x, y) coordinates (the axes’ data space), float64, broadcast over the inputs.

tephpy.transforms.temperature_theta_from_xy(x: numpy.typing.ArrayLike, y: numpy.typing.ArrayLike) → tuple[numpy.typing.NDArray[numpy.float64], numpy.typing.NDArray[numpy.float64]][source]#

Convert tephigram (x, y) coordinates back to temperature and theta.

Inverse of xy_from_temperature_theta(): T = (x - y) / 2 and theta_K = exp((x + y) / (2 * MA)).

Parameters:

xArrayLike: Tephigram x coordinate (dimensionless, the axes’ data space).
yArrayLike: Tephigram y coordinate (dimensionless, the axes’ data space).

Returns:

tuple of numpy.ndarray: (temperature, theta) in degrees Celsius, float64, broadcast over the inputs.