improver.psychrometric_calculations.condensation_trails module

Module to contain Condensation trail formation calculations.

class CondensationTrailFormation(engine_contrail_factors=[3e-05, 3.4e-05, 3.9e-05])

Bases: BasePlugin

Plugin to calculate whether a condensation trail (contrail) will form based on a given set of atmospheric conditions.

The calculations require the following data:

• Temperature on pressure levels.

• Relative Humidity on pressure levels.

Alongside constants including the ratio of the molecular masses of water and air (EARTH_REPSILON), and defined values for the engine contrail factor.

The range of atmospheric conditions under which condensation trails may form are summarised by an Appleman diagram:

References

Schrader, M.L., 1997. Calculations of aircraft contrail formation critical temperatures. Journal of Applied Meteorology, 36(12), pp.1725-1729.

__init__(engine_contrail_factors=[3e-05, 3.4e-05, 3.9e-05])

Initialises the Class

Parameters:

engine_contrail_factors (list, optional) – List of engine contrail factors to use in the calculations. Defaults to [3e-5, 3.4e-5, 3.9e-5]. These values are for Non-, Low-, and High-Bypass engines from Schrader (1997). The units are kg/kg/K.

_abc_impl = <_abc._abc_data object>

_boolean_to_categorical()

Combine two boolean arrays of contrail persistency into a single categorical array of contrail formation.

Return type:

ndarray

Returns:

Array of categorical (integer) data, where 0 = no contrails, 1 = non-persistent contrails and 2 = persistent contrails.

_calculate_contrail_persistency()

Apply four conditions to determine whether non-persistent or persistent contrails will form.

Condition 1

The local vapour pressure sits above the tangent to the saturated vapour pressure curve,

\[C_1 = e_{local} - mT > I_{critical} \ \ \text{,}\]

where \(e_{local}\) is the local vapour pressure, \(m\) is the engine mixing ratio, \(T\) is the ambient air temperature, and \(I_{critical}\) is the critical intercept.

Condition 2

The air temperature is below the critical temperature,

\[C_2 = T < T_{critical} \ \ \text{.}\]

Condition 3

The local vapour pressure is higher than the atmospheric saturated vapour pressure (with respect to ice),

\[C_3 = e_{local} > e_{s,ice}(T, P) \ \ \text{.}\]

Condition 4

The air temperature is below the freezing point of water,

\[C_4 = T < 273.15 \ \text{K} \ \ \text{.}\]

Will contrails form?

\[\begin{split}\begin{aligned} \text{Any} &= C_1 \land C_2 \\ \text{Persistent} &= \text{Any} \land C_3 \land C_4 \\ \text{Non-persistent} &= \text{Any} \land \lnot \ \text{Persistent} \ \ \text{.} \end{aligned}\end{split}\]

Return type:

None

_calculate_critical_temperatures_and_intercepts()

Calculate the critical temperatures and intercepts on pressure levels for all engine contrail factors.

Return type:

None

_calculate_engine_mixing_ratios(pressure_levels)

Calculate the mixing ratio of the atmosphere and aircraft exhaust (Schrader, 1997). This calculation uses EARTH_REPSILON, which is the ratio of the molecular weights of water and air on Earth.

Returns:

The mixing ratio of the atmosphere and aircraft exhaust, provided in units: Pa/K.

Return type:

np.ndarray

_create_contrail_formation_cube(categorical_data, template_cube)

Create a contrail formation cube, populated with categorical data.

Parameters:

• categorical_data (ndarray) – Categorical (integer) data of contrail formation. Leading axes are [contrail factor, pressure level].

• template_cube (Cube) – Cube from which to derive dimensions, coordinates and mandatory attributes.

Return type:

Cube

Returns:

Categorical cube of contrail formation, where 0 = no contrails, 1 = non-persistent contrails and 2 = persistent contrails. Has the same shape as categorical_data.

_critical_temperatures_and_intercepts_for_given_contrail_factor(engine_mixing_ratio_for_contrail_factor, svp_table, svp_derivative_table)

Calculate the critical temperatures and critical intercepts on pressure levels for a single engine contrail factor.

These are calculated at each pressure level by drawing a tangent to the saturation vapour pressure curve with respect to water. The tangent gradient is equal to the engine mixing ratio.

The variation of critical temperature with relative humidity has a characteristic curve:

Parameters:

• engine_mixing_ratio_for_contrail_factor (np.ndarray) – Engine mixing ratios on pressure levels for a single contrail factor. Array axis is [pressure levels] (Pa/K).

• svp_table (iris.cube.Cube) – Lookup table of saturation vapour pressure with respect to water (Pa).

• svp_derivative_table (iris.cube.Cube) – Lookup table of the first derivative of saturation vapour pressure with respect to water (Pa/K).

Returns:

• Critical temperatures on pressure levels. Array axes are [pressure levels, latitude, longitude] (K).

• Critical intercepts on pressure levels. Array axis is [pressure levels] (Pa).

Return type:

Tuple[np.ndarray, np.ndarray]

_find_local_vapour_pressure(pressure_levels)

Calculate the local vapour pressure with respect to water at the given pressure levels using the temperature and pressure data.

Parameters:

pressure_levels (np.ndarray) – Pressure levels (Pa).

Returns:

The localised vapour pressure at the given pressure levels (Pa).

Return type:

np.ndarray

critical_intercepts = None

critical_temperatures = None

engine_mixing_ratios = None

humidity = None

nonpersistent_contrails = None

persistent_contrails = None

pressure_levels = None

process(*cubes)

Main entry point of this class for data as iris.Cubes

Parameters:

cubes (Union[Cube, CubeList]) –

air_temperature:

Cube of the temperature on pressure levels.

relative_humidity:

Cube of the relative humidity on pressure levels.

Return type:

Cube

Returns:

Categorical (integer) cube of contrail formation

• 0 = no contrails

• 1 = non-persistent contrails

• 2 = persistent contrails

Cube dimensions are [contrail factor, pressure level, latitude, longitude], where latitude and longitude are only included if present in the input cubes.

process_from_arrays(temperature, relative_humidity, pressure_levels)

Main entry point of this class for data as Numpy arrays.

Process the temperature, humidity and pressure data to calculate the contrails data.

Parameters:

• temperature (np.ndarray) – Temperature data on pressure levels where pressure is the leading axis (K).

• relative_humidity (np.ndarray) – Relative humidity data on pressure levels where pressure is the leading axis (kg/kg).

• pressure_levels (np.ndarray) – Pressure levels (Pa).

Return type:

ndarray

Returns:

Categorical (integer) array of contrail formation

• 0 = no contrails

• 1 = non-persistent contrails

• 2 = persistent contrails

Array axes are [contrail factor, pressure level, latitude, longitude], where latitude and longitude are only included if present in the temperature and relative humidity input arrays.

temperature = None

class ContrailHeightExtractor(use_max=True)

Bases: BasePlugin

Plugin to extract contrail formation heights by category. It extracts the maximum or minimum height where contrail formation is Non-persistent or Persistent.

__init__(use_max=True)

Initialize the Class

Parameters:

use_max (bool) – If True, extract maximum heights; if False, extract minimum heights.

_abc_impl = <_abc._abc_data object>

_contrail_values_from_meaning_attribute(formation_cube)

Extract the integer values corresponding to non-persistent or persistent contrails from the ‘contrail_type_meaning’ attribute of the categorical contrail formation cube.

Parameters:

formation_cube (Cube) – Categorical cube of shape (engine_contrail_factor, pressure_level, lat (optional), lon (optional))

Return type:

Tuple[int, int]

Returns:

• Integer corresponding to non-persistent contrail category

• Integer corresponding to persistent contrail category

_create_max_min_height_cubes(formation_cube, height_cube, non_persistent_result, persistent_result)

Create new cubes containing the max or min heights for persistent or non-persistent contrail formation.

Parameters:

• formation_cube (Cube) – Categorical cube of shape (contrail_factor, pressure_level, lat (optional), lon (optional))

• height_cube (Cube) – Height cube of shape (pressure_level, lat (optional), lon (optional))

• non_persistent_result (ndarray) – Extracted height data for non-persistent contrails.

• persistent_result (ndarray) – Extracted height data for persistent contrails.

Return type:

Tuple[Cube, Cube]

Returns:

• Cube of extracted heights for non-persistent contrails

• Cube of extracted heights for persistent contrails

process(formation_cube, height_cube)

Main entry point for this class to extract the maximum or minimum height where contrail formation is categorized as Non-persistent or Persistent.

Parameters:

• formation_cube (Cube) – Categorical cube of shape (engine_contrail_factor, pressure_level, lat (optional), lon (optional))

• height_cube (Cube) – Height cube of shape (pressure_level, lat (optional), lon (optional))

Return type:

Tuple[Cube, Cube]

Returns:

• Cube of extracted height values for non-persistent contrails

• Cube of extracted height values for persistent contrails

Each cube has dimensions (engine_contrail_factor, lat (optional), lon (optional)).

process_from_arrays(contrail_formation, height, non_persistent_value=1, persistent_value=2)

Main entry point of this class for data as Numpy arrays.

Extract the maximum or minimum height where contrail formation is categorized as Non-persistent or Persistent.

Parameters:

• contrail_formation (ndarray) – Integer array of contrail category with shape (engine_contrail_factor, pressure_level, lat (optional), lon (optional)).

• height (ndarray) – Float array of height above sea level with shape (pressure_level, lat (optional), lon (optional)) (m).

• non_persistent_value (int) – Integer corresponding to non-persistent contrail data.

• persistent_value (int) – Integer corresponding to the persistent contrail data.

Return type:

Tuple[ndarray, ndarray]

Returns:

• Array of extracted height values for non-persistent contrails

• Array of extracted height values for persistent contrails

Array dimensions are (engine_contrail_factor, lat (optional), lon (optional)).