thermo#

Sounding and Hodograph Analysis and Research Program Library (SHARPlib) :: Thermodynamic Routines

Dry Variables#

Dry thermodynamic variables.

nwsspc.sharp.calc.thermo.theta(pressure: float, temperature: float, ref_pressure: float = 100000.0) → float#

nwsspc.sharp.calc.thermo.theta(pres_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], tmpk_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], ref_pressure: float = 100000.0) → numpy.ndarray[dtype=float32, shape=(*), order='C']

Overloaded function.

theta(pressure: float, temperature: float, ref_pressure: float = 100000.0) -> float

Computes the potential temperature (K), or theta, given the air pressure (Pa), air temperature (K), and a reference pressure (default value is 100000 Pa).

Parameters:

pressure (float) – The air pressure (Pa)
temperature (float) – The air temperature (K)
ref_pressure (float, optional) – The reference pressure (default 100000.0 Pa)

Returns:

The potential temperature (K), or theta

Return type:

float

theta(pres_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], tmpk_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], ref_pressure: float = 100000.0) -> numpy.ndarray[dtype=float32, shape=(*), order='C']

Computes the potential temperature (K), or theta, given the air pressure (Pa), air temperature (K), and a reference pressure (default value is 100000 Pa).

Parameters:

pressure (numpy.ndarray[dtype=float32]) – The 1D array of air pressure (Pa)
temperature (numpy.ndarray[dtype=float32]) – The 1D array of air temperature (K)
ref_pressure (float, optional) – The reference pressure (default 100000.0 Pa)

Returns:

The 1D array of potential temperature (K), or theta

Return type:

numpy.ndarray[dtype=float32]

nwsspc.sharp.calc.thermo.theta_level(potential_temperature: float, temperature: float) → float#

nwsspc.sharp.calc.thermo.theta_level(theta_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], tmpk_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) → numpy.ndarray[dtype=float32, shape=(*), order='C']

Overloaded function.

theta_level(potential_temperature: float, temperature: float) -> float

Computes the pressure level (Pa) of a parcel given the potential temperature (K) and air temperature (K).

Parameters:

potential_temperature (float) – The potential temperature, or theta (K)
temperature (float) – The air temperature (K)

Returns:

The pressure level (Pa) corresponding to the potential temperature and air temperature.

Return type:

float

theta_level(theta_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], tmpk_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) -> numpy.ndarray[dtype=float32, shape=(*), order='C']

Computes the pressure level (Pa) of a parcel given the potential temperature (K) and air temperature (K).

Parameters:

theta_arr (numpy.ndarray[dtype=float32]) – The 1D array of potential temperature, or theta (K)
tmpk_arr (numpy.ndarray[dtype=float32]) – The 1D array of air temperature (K)

Returns:

The 1D pressure level (Pa) corresponding to the potential temperature and air temperature.

Return type:

numpy.ndarray[dtype=float32]

nwsspc.sharp.calc.thermo.lapse_rate(layer_agl: nwsspc.sharp.calc.layer.HeightLayer, height: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], temperature: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) → float#

nwsspc.sharp.calc.thermo.lapse_rate(layer: nwsspc.sharp.calc.layer.PressureLayer, pressure: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], height: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], temperature: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) → float

Overloaded function.

lapse_rate(layer_agl: nwsspc.sharp.calc.layer.HeightLayer, height: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], temperature: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) -> float

Computes the lapse rate over a given HeightLayer (meters AGL). This routine handles converting the height AGL to MSL by adding the surface height value to the HeightLayer.

Parameters:

layer_agl (nwsspc.sharp.calc.layer.HeightLayer) – a HeightLayer (meters AGL) to compute the lapse rate over
height (numpy.ndarray[dtype=float32]) – 1D NumPy array of height values (meters)
temperature (numpy.ndarray[dtype=float32]) – 1D NumPy array of temperature values (K)

Returns:

The temperature lapse rate (K)

Return type:

float

lapse_rate(layer: nwsspc.sharp.calc.layer.PressureLayer, pressure: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], height: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], temperature: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) -> float

Computes the lapse rate over a given PressureLayer (Pa).

Parameters:

layer (nwsspc.sharp.calc.layer.PressureLayer) – a PressureLayer (Pa) to compute the lapse rate over
pressure (numpy.ndarray[dtype=float32]) – 1D NumPy array of pressure values (Pa)
height (numpy.ndarray[dtype=float32]) – 1D NumPy array of height values (meters)
temperature (numpy.ndarray[dtype=float32]) – 1D NumPy array of temperature values (K)

Returns:

The temperature lapse rate (K)

Return type:

float

nwsspc.sharp.calc.thermo.lapse_rate_max(layer: nwsspc.sharp.calc.layer.HeightLayer, depth: float, height: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], temperature: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) → tuple[float, nwsspc.sharp.calc.layer.HeightLayer]#

nwsspc.sharp.calc.thermo.lapse_rate_max(layer: nwsspc.sharp.calc.layer.PressureLayer, depth: float, pressure: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], height: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], temperature: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) → tuple[float, nwsspc.sharp.calc.layer.PressureLayer]

Overloaded function.

lapse_rate_max(layer: nwsspc.sharp.calc.layer.HeightLayer, depth: float, height: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], temperature: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) -> tuple[float, nwsspc.sharp.calc.layer.HeightLayer]

Given a layer of the atmosphere (e.g. 2 - 6 km), find the maximum lapse rate over the provided depth (e.g. 2 km) within that given layer. Returns the maximum lapse rate, as well as the layer it was found in.

Parameters:

layer (nwsspc.sharp.calc.layer.HeightLayer) – a HeightLayer to search for the maximum lapse lapse_rate (meters AGL)
depth (float) – the depth used to compute a lapse rate within a layer (meters)
height (numpy.ndarray[dtype=float32]) – 1D NumPy array of height values (meters)
temperature (numpy.ndarray[dtype=float32]) – 1D NumPy array of temperature values (K)

Returns:

A tuple containing the maximum lapse rate and the layer it was found in

Return type:

tuple[float, nwsspc.sharp.calc.layer.HeightLayer]

lapse_rate_max(layer: nwsspc.sharp.calc.layer.PressureLayer, depth: float, pressure: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], height: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], temperature: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) -> tuple[float, nwsspc.sharp.calc.layer.PressureLayer]

Given a layer of the atmosphere (e.g. 800 hPa - 500 hPa), find the maximum lapse rate over the provided depth (e.g. 100 hPa) within that given layer. Returns the maximum lapse rate, as well as the layer it was found in.

Parameters:

layer (nwsspc.sharp.calc.layer.PressureLayer) – a PressureLayer to search for the maximum lapse lapse_rate (Pa)
depth (float) – the depth used to compute a lapse rate within a layer (Pa)
pressure (numpy.ndarray[dtype=float32]) – 1D NumPy array of pressure values (Pa)
height (numpy.ndarray[dtype=float32]) – 1D NumPy array of height values (meters)
temperature (numpy.ndarray[dtype=float32]) – 1D NumPy array of temperature values (K)

Returns:

A tuple containing the maximum lapse rate and the layer it was found in

Return type:

tuple[float, nwsspc.sharp.calc.layer.PressureLayer]

Dry Ascent#

Dry thermodynamic routines that are directly related to vertical ascent.

nwsspc.sharp.calc.thermo.drylift(pressure: float, temperature: float, dewpoint: float) → tuple[float, float]#

Given a parcel’s initial pressure (Pa), temperature (K), and dewpoint temperature (K), lift the parcel dry adiabaitically to its Lifted Condensation Level and return the resulting LCL pressure (Pa) and temperature (K).

The LCL temperature is computed using an approximation. See the lcl_temperature function documentation for more information.

Parameters:

pressure (float) – Parcel starting pressure (Pa)
temperature (float) – Parcel starting temperature (K)
dewpoint (float) – Parcel starting dewpoint temperature (K)

Returns:

A tuple of (lcl_pres, lcl_temperature)

Return type:

tuple[float, float]

nwsspc.sharp.calc.thermo.lcl_temperature(temperature: float, dewpoint: float) → float#

nwsspc.sharp.calc.thermo.lcl_temperature(tmpk_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], dwpk_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) → numpy.ndarray[dtype=float32, shape=(*), order='C']

Overloaded function.

lcl_temperature(temperature: float, dewpoint: float) -> float

Compute the Lifted Condensation Level (LCL) temperature (Kelvin) given an air temperature (Kelvin) and dewpoint temperature (Kelvin).

The LCL temperature is computed as in Bolton (1980) eq 15, and is considered to be within a 10th of a degree of the more exact iterative formula.

Parameters:

temperature (float) – The air temperature (Kelvin)
dewpoint (float) – The dewpoint temperature (Kelvin)

Returns:

The LCL temperature (Kelvin)

Return type:

float

lcl_temperature(tmpk_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], dwpk_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) -> numpy.ndarray[dtype=float32, shape=(*), order='C']

Compute the Lifted Condensation Level (LCL) temperature (Kelvin) given an array of air temperatures (Kelvin) and dewpoint temperatures (Kelvin).

The LCL temperatures are computed as in Bolton (1980) eq 15, and is considered to be within a 10th of a degree of the more exact iterative formula.

Parameters:

tmpk_arr (numpy.ndarray[dtype=float32]) – The 1D air temperature array (Kelvin)
dwpk_arr (numpy.ndarray[dtype=float32]) – The 1D dewpoint temperature array (Kelvin)

Returns:

The 1D array of LCL temperatures (Kelvin)

Return type:

numpy.ndarray[dtype=float32]

Moist Variables#

Moist thermodynamic variables.

nwsspc.sharp.calc.thermo.mixratio(q: float) → float#

nwsspc.sharp.calc.thermo.mixratio(pressure: float, temperature: float) → float

nwsspc.sharp.calc.thermo.mixratio(spfh_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) → numpy.ndarray[dtype=float32, shape=(*), order='C']

nwsspc.sharp.calc.thermo.mixratio(pres_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], tmpk_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) → numpy.ndarray[dtype=float32, shape=(*), order='C']

Overloaded function.

mixratio(q: float) -> float

Compute the water vapor mixing ratio (kg/kg) from specific humidity (kg/kg).

Parameters:: q (float) – The specific humidity (kg/kg)
Returns:: The water vapor mixing ratio (kg/kg)
Return type:: float

mixratio(pressure: float, temperature: float) -> float

Compute the water vapor mixing ratio (kg/kg) from the air pressure (Pa) and temperature (K). If given the air temperature, this is the saturation mixing ratio. If given the dewpoint temperature, tis is the mixing ratio.

Parameters:

pressure (float) – The air pressure (Pa)
temperature (float) – The air temperature (K)

Returns:

The water vapor mixing ratio (kg/kg)

Return type:

float

mixratio(spfh_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) -> numpy.ndarray[dtype=float32, shape=(*), order='C']

Compute the water vapor mixing ratio (kg/kg) from the specific humidity (kg/kg).

Parameters:: spfh_arr (numpy.ndarray[dtype=float32]) – The 1D array of specific humidity (kg/kg)
Returns:: The 1D array of water vapor mixing ratio (kg/kg)
Return type:: numpy.ndarray[dtype=float32]

mixratio(pres_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], tmpk_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) -> numpy.ndarray[dtype=float32, shape=(*), order='C']

Parameters:

pres_arr (numpy.ndarray[dtype=float32]) – The 1D array of air pressure (Pa)
tmpk_arr (numpy.ndarray[dtype=float32]) – The 1D array of air temperature (K)

Returns:

The 1D array of water vapor mixing ratio (kg/kg)

Return type:

numpy.ndarray[dtype=float32]

nwsspc.sharp.calc.thermo.mixratio_ice(pressure: float, temperature: float) → float#

nwsspc.sharp.calc.thermo.mixratio_ice(pres_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], tmpk_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) → numpy.ndarray[dtype=float32, shape=(*), order='C']

Overloaded function.

mixratio_ice(pressure: float, temperature: float) -> float

Compute the ice water mixing ratio (kg/kg) from the air pressure (Pa) and temperature (K). If given the air temperatuer, this is the saturation mixing ratio. If given the dewpoint temperature, this is the mixing ratio.

Parameters:

pressure (float) – The air pressure (Pa)
temperature (float) – The air temperature (K)

Returns:

The ice water mixing ratio (kg/kg)

Return type:

float

mixratio_ice(pres_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], tmpk_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) -> numpy.ndarray[dtype=float32, shape=(*), order='C']

Parameters:

pres_arr (numpy.ndarray[dtype=float32]) – The 1D array of air pressure (Pa)
tmpl_arr (numpy.ndarray[dtype=float32]) – The 1D array of air temperature (K)

Returns:

The ice water mixing ratio (kg/kg)

Return type:

numpy.ndarray[dtype=float32]

nwsspc.sharp.calc.thermo.vapor_pressure(pressure: float, temperature: float) → float#

nwsspc.sharp.calc.thermo.vapor_pressure(pres_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], tmpk_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) → numpy.ndarray[dtype=float32, shape=(*), order='C']

Overloaded function.

vapor_pressure(pressure: float, temperature: float) -> float

Compute the vapor pressure with respect to liquid water.

The vapor pressure (or saturation vapor pressure) is computed with respect to liquid water when the dewpoint temperature (or air temperature) is passed (in Kelvin), along with the air pressure (Pa). The air pressure is used as a minimum floor value for extremely cold temperatures at low pressures, and is consistent with how vapor pressure is treated in CM1.

This function uses the formulation by Bolton (1980), and is accurate to within 0.3% for the temperature range of -35C <= T <= 35C.

Parameters:

pressure (float) – The air pressure (Pa)
temperature (float) – The air temperature (K) or dewpoint temperature (K)

Returns:

The vapor pressure (Pa) given dewpoint temperature, or the saturation vapor pressure given the air temperature.

Return type:

float

vapor_pressure(pres_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], tmpk_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) -> numpy.ndarray[dtype=float32, shape=(*), order='C']

Compute the vapor pressure with respect to liquid water.

This function uses the formulation by Bolton (1980), and is accurate to within 0.3% for the temperature range of -35C <= T <= 35C.

Parameters:

pres_arr (numpy.ndarray[dtype=float32]) – The 1D array of air pressure (Pa)
tmpk_arr (numpy.ndarray[dtype=float32]) – The 1D array of air temperature (K) or dewpoint temperature (K)

Returns:

The 1D array of vapor pressure (Pa) given dewpoint temperature, or the saturation vapor pressure given the air temperature.

Return type:

numpy.ndarray[dtype=float32]

nwsspc.sharp.calc.thermo.vapor_pressure_ice(pressure: float, temperature: float) → float#

nwsspc.sharp.calc.thermo.vapor_pressure_ice(pres_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], tmpk_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) → numpy.ndarray[dtype=float32, shape=(*), order='C']

Overloaded function.

vapor_pressure_ice(pressure: float, temperature: float) -> float

Compute the vapor pressure with respect to ice.

The vapor pressure (or saturation vapor pressure) is computed with respect to ice when the dewpoint temperature (or air temperature) is passed (in Kelvin), along with the air pressure (Pa). The air pressure is used as a minimum floor value for extremely cold temperatures at low pressures, and is consistent with how vapor pressure is treated in CM1.

This function uses the formulation by Bolton (1980), and is accurate to within 0.3% for the temperature range of -35C <= T <= 35C.

Parameters:

pressure (float) – The air pressure (Pa)
temperature (float) – The air temperature (K) or dewpoint temperature (K)

Returns:

The vapor pressure (Pa) given dewpoint temperature, or the saturation vapor pressure given the air temperature.

Return type:

float

vapor_pressure_ice(pres_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], tmpk_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) -> numpy.ndarray[dtype=float32, shape=(*), order='C']

Compute the vapor pressure with respect to ice.

This function uses the formulation by Bolton (1980), and is accurate to within 0.3% for the temperature range of -35C <= T <= 35C.

Parameters:

pres_arr (numpy.ndarray[dtype=float32]) – The 1D array of air pressure (Pa)
tmpk_arr (numpy.ndarray[dtype=float32]) – The 1D array of air temperature (K) or dewpoint temperature (K)

Returns:

The 1D array of vapor pressure (Pa) given dewpoint temperature, or the saturation vapor pressure given the air temperature.

Return type:

numpy.ndarray[dtype=float32]

nwsspc.sharp.calc.thermo.specific_humidity(rv: float) → float#

nwsspc.sharp.calc.thermo.specific_humidity(mixr_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) → numpy.ndarray[dtype=float32, shape=(*), order='C']

Overloaded function.

specific_humidity(rv: float) -> float

Compute the specific humidity (kg/kg) from a mixing ratio (kg/kg).

Parameters:: rv (float) – The water vapor mixing ratio (kg/kg)
Returns:: The specific humidity (kg/kg)
Return type:: float

specific_humidity(mixr_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) -> numpy.ndarray[dtype=float32, shape=(*), order='C']

Compute the specific humidity (kg/kg) from a mixing ratio (kg/kg).

Parameters:: mixr_arr (numpy.ndarray[dtype=float32]) – The 1D array of water vapor mixing ratios (kg/kg)
Returns:: 1D NumPy array of specific humidity (unitless)
Return type:: numpy.ndarray[dtype=float32]

nwsspc.sharp.calc.thermo.relative_humidity(pressure: float, temperature: float, dewpoint: float) → float#

nwsspc.sharp.calc.thermo.relative_humidity(pressure: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], temperature: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], dewpoint: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) → numpy.ndarray[dtype=float32, shape=(*), order='C']

Overloaded function.

relative_humidity(pressure: float, temperature: float, dewpoint: float) -> float

Compute the relative humidity of water vapor with respect to liquid water. NOTE: The pressure variable is only used as a sanity check when computing vapor pressure at extremely low pressures and temperatures. If you do not want or need this behavior, you can pass the THETA_REF_PRESSURE constant in place of an air pressure.

Parameters:

pressure (float) – the ambient air pressure (Pa)
temperature (float) – the ambient air temperature (K)
dewpoint (float) – the ambient dewpoint temperature (K)

Returns:

Relative Humidity (fraction, unitless)

Return type:

float

relative_humidity(pressure: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], temperature: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], dewpoint: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) -> numpy.ndarray[dtype=float32, shape=(*), order='C']

Compute the relative humidity of water vapor with respect to liquid water. NOTE: The pressure variable is only used as a sanity check when computing vapor pressure at extremely low pressures and temperatures. If you do not want or need this behavior, you canpass in an array of THETA_REF_PRESSURE in place of air pressure.

Parameters:

pressure (numpy.ndarray[dtype=float32]) – 1D NumPy array of ambient air pressure Pa)
temperature (numpy.ndarray[dtype=float32]) – 1D NumPy array of ambient air temperature (K)
dewpoint (numpy.ndarray[dtype=float32]) – 1D NumPy array of ambient dewpoint temperature (K)

Returns:

1D NumPy array of relative humidity values (fraction, unitless)

Return type:

numpy.ndarray[dtype=float32]

nwsspc.sharp.calc.thermo.temperature_at_mixratio(wv_mixratio: float, pressure: float) → float#

nwsspc.sharp.calc.thermo.temperature_at_mixratio(mixr_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], pres_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) → numpy.ndarray[dtype=float32, shape=(*), order='C']

Overloaded function.

temperature_at_mixratio(wv_mixratio: float, pressure: float) -> float

Computes the temperature (K) of air at the given water vapor mixing ratio (kg/kg) and air pressure (Pa). Can be used to compute the dewpoint temperature from mixing ratio.

The routine is implemented as in Bolton (1980) eq 11, and is considered to be accurate to 0.03 K for -35C <= T <= 35C.

Parameters:

wv_mixratio (float) – The water vapor mixing ratio (kg/kg)
pressure (float) – The air pressure (Pa)

Returns:

The temperature (K) of an air parcel at a given mixing ratio and pressure.

Return type:

float

temperature_at_mixratio(mixr_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], pres_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) -> numpy.ndarray[dtype=float32, shape=(*), order='C']

Computes the temperature (K) of air at the given water vapor mixing ratio (kg/kg) and air pressure (Pa). Can be used to compute the dewpoint temperature from mixing ratio.

The routine is implemented as in Bolton (1980) eq 11, and is considered to be accurate to 0.03 K for -35C <= T <= 35C.

Parameters:

mixr_arr (numpy.ndarray[dtype=float32]) – The 1D array of water vapor mixing ratio (kg/kg)
pres_arr (numpy.ndarray[dtype=float32]) – The 1D array of air pressure (Pa)

Returns:

The 1D array of temperature (K) of an air parcel at a given mixing ratio and pressure.

Return type:

numpy.ndarray[dtype=float32]

nwsspc.sharp.calc.thermo.virtual_temperature(temperature: float, rv: float, rl: float = 0.0, ri: float = 0.0) → float#

nwsspc.sharp.calc.thermo.virtual_temperature(tmpk_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], rv_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], rl_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False] | None = None, ri_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False] | None = None) → numpy.ndarray[dtype=float32, shape=(*), order='C']

Overloaded function.

virtual_temperature(temperature: float, rv: float, rl: float = 0.0, ri: float = 0.0) -> float

Returns the virtual temperature in Kelvin given the dry-bulb temperature (Kelvin), the water vapor mixing ratio (kg/kg), the liquid water mixing ratio (kg/kg), and the ice water mixing ratios (kg/kg). The liquid and ice water mixing ratios have default values of zero, if unspecified.

Parameters:

temperature (float) – The dry-bulb temperature (K)
rv (float) – The water vapor mixing ratio (kg/kg)
rl (float) – The liquid water mixing ratio (kg/kg)
ri (float) – The ice water mixing ratio (kg/kg)

Returns:

The virtual temperature (K)

Return type:

float

virtual_temperature(tmpk_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], rv_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], rl_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False] | None = None, ri_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False] | None = None) -> numpy.ndarray[dtype=float32, shape=(*), order='C']

Parameters:

tmpk_arr (numpy.ndarray[dtype=float32]) – The 1D array of dry-bulb temperature (K)
rv_arr (numpy.ndarray[dtype=float32]) – The 1D array of water vapor mixing ratio (kg/kg)
rl_arr (numpy.ndarray[dtype=float32], optional) – The 1D array of liquid water mixing ratio (kg/kg)
ri_arr (numpy.ndarray[dtype=float32], optional) – The 1D array of ice water mixing ratio (kg/kg)

Returns:

The 1D array of virtual temperature (K)

Return type:

numpy.ndarray[dtype=float32]

nwsspc.sharp.calc.thermo.buoyancy(parcel_temperature: float, environment_temperature: float) → float#

nwsspc.sharp.calc.thermo.buoyancy(parcel_temperature: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], environment_temperature: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) → numpy.ndarray[dtype=float32, shape=(*), order='C']

Overloaded function.

buoyancy(parcel_temperature: float, environment_temperature: float) -> float

Compute buoyancy given parcel & environment temperatures.

Parameters:

parcel_temperature (float) – parcel temperature (K)
environment_temperature (float) – environment temperature (K)

Returns:

Buoyancy (m/s^2)

Return type:

float

buoyancy(parcel_temperature: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], environment_temperature: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) -> numpy.ndarray[dtype=float32, shape=(*), order='C']

Compute buoyancy given arrays of parcel & environment temperatures.

Parameters:

parcel_temperature (numpy.ndarray[dtype=float32]) – 1D NumPy array of parcel temperatures (K)
environment_temperature (numpy.ndarray[dtype=float32]) – 1D NumPy array of environment temperatures (K)

Returns:

1D NumPy array of buoyancy values (m/s^2)

Return type:

numpy.ndarray[dtype=float32]

nwsspc.sharp.calc.thermo.thetae(pressure: float, temperature: float, dewpoint: float) → float#

nwsspc.sharp.calc.thermo.thetae(pressure: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], temperature: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], dewpoint: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) → numpy.ndarray[dtype=float32, shape=(*), order='C']

Overloaded function.

thetae(pressure: float, temperature: float, dewpoint: float) -> float

Compute the equivalent potential temperature (K) given the air pressure (Pa), air temperature (K), and dewpoint temperature (K). The equivalent potential temperature is computed as in Bolton 1980. It was found in Davies-Jones 2009 to be the most accurate non-iterative formulation of theta-e.

References

Bolton 1980: https://doi.org/10.1175/1520-0493(1980)108%3C1046:TCOEPT%3E2.0.CO;2

Davies-Jones 2009: https://doi.org/10.1175/2009MWR2774.1

Parameters:

pressure (float) – the ambient air pressure (Pa)
temperature (float) – the ambient air temperature (K)
dewpoint (float) – the dewpoint temperature (K)

Returns:

The equivalent potential temperature (K)

Return type:

float

thetae(pressure: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], temperature: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], dewpoint: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) -> numpy.ndarray[dtype=float32, shape=(*), order='C']

References

Bolton 1980: https://doi.org/10.1175/1520-0493(1980)108%3C1046:TCOEPT%3E2.0.CO;2

Davies-Jones 2009: https://doi.org/10.1175/2009MWR2774.1

Parameters:

pressure (numpy.ndarray[dtype=float32]) – 1D NumPy array of ambient air pressure (Pa)
temperature (numpy.ndarray[dtype=float32]) – 1D NumPy array of ambient air temperature (K)
dewpoint (numpy.ndarray[dtype=float32]) – 1D NumPy array of dewpoint temperature (K)

Returns:

1D NumPy array of equivalent potential temperature (K)

Return type:

numpy.ndarray[dtype=float32]

nwsspc.sharp.calc.thermo.wetbulb(lifter: nwsspc.sharp.calc.parcel.lifter_wobus, pressure: float, temperature: float, dewpoint: float) → float#

nwsspc.sharp.calc.thermo.wetbulb(lifter: nwsspc.sharp.calc.parcel.lifter_cm1, pressure: float, temperature: float, dewpoint: float) → float

nwsspc.sharp.calc.thermo.wetbulb(lifter: nwsspc.sharp.calc.parcel.lifter_wobus, pressure: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], temperature: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], dewpoint: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) → numpy.ndarray[dtype=float32, shape=(*), order='C']

nwsspc.sharp.calc.thermo.wetbulb(lifter: nwsspc.sharp.calc.parcel.lifter_cm1, pressure: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], temperature: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], dewpoint: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) → numpy.ndarray[dtype=float32, shape=(*), order='C']

Overloaded function.

wetbulb(lifter: nwsspc.sharp.calc.parcel.lifter_wobus, pressure: float, temperature: float, dewpoint: float) -> float

Compute the wet bulb temperature (K) given the ambient pressure (Pa), temperature (K), and dewpoint temperature (K).

First, it lifts a parcel with the given pressure, temperature, and dewpoint temperature to its Lifted Condensation Level (LCL). To compute the temperature and pressure of the LCL, an approximation is used. See the lcl_temperature function for further detail.

After the parcel has reached the LCL, the lifter passed to the function lowers the parcel to its initial pressure level along a moist adiabat or pseudoadiabat.

Parameters:

lifter (nwsspc.sharp.calc.parcel.lifter_wobus) – a parcel lifter (e.g. lifter_cm1 or lifter_wobus)
pressure (float) – The ambient pressure (Pa)
temperature (float) – The ambient temperature (K)
dewpoint (float) – The ambient dewpoint temperature (K)

Returns:

The wetbulb temperature (K)

Return type:

float

wetbulb(lifter: nwsspc.sharp.calc.parcel.lifter_cm1, pressure: float, temperature: float, dewpoint: float) -> float

Compute the wet bulb temperature (K) given the ambient pressure (Pa), temperature (K), and dewpoint temperature (K).

After the parcel has reached the LCL, the lifter passed to the function lowers the parcel to its initial pressure level along a moist adiabat or pseudoadiabat.

Parameters:

lifter (nwsspc.sharp.calc.parcel.lifter_cm1) – a parcel lifter (e.g. lifter_cm1 or lifter_wobus)
pressure (float) – The ambient pressure (Pa)
temperature (float) – The ambient temperature (K)
dewpoint (float) – The ambient dewpoint temperature (K)

Returns:

The wetbulb temperature (K)

Return type:

float

wetbulb(lifter: nwsspc.sharp.calc.parcel.lifter_wobus, pressure: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], temperature: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], dewpoint: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) -> numpy.ndarray[dtype=float32, shape=(*), order='C']

Compute the wet bulb temperature (K) given the ambient pressure (Pa), temperature (K), and dewpoint temperature (K).

After the parcel has reached the LCL, the lifter passed to the function lowers the parcel to its initial pressure level along a moist adiabat or pseudoadiabat.

Parameters:

lifter (nwsspc.sharp.calc.parcel.lifter_wobus) – a parcel lifter (e.g. lifter_cm1 or lifter_wobus)
pressure (numpy.ndarray[dtype=float32]) – 1D NumPy array of ambient pressures (Pa)
temperature (numpy.ndarray[dtype=float32]) – 1D NumPy array of ambient temperatureds (K)
dewpoint (numpy.ndarray[dtype=float32]) – 1D NumPy array of ambient dewpoint temperatures (K)

Returns:

1D NumPy array of wetbulb temperatures (K)

Return type:

numpy.ndarray[dtype=float32]

wetbulb(lifter: nwsspc.sharp.calc.parcel.lifter_cm1, pressure: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], temperature: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], dewpoint: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) -> numpy.ndarray[dtype=float32, shape=(*), order='C']

Compute the wet bulb temperature (K) given the ambient pressure (Pa), temperature (K), and dewpoint temperature (K).

After the parcel has reached the LCL, the lifter passed to the function lowers the parcel to its initial pressure level along a moist adiabat or pseudoadiabat.

Parameters:

lifter (nwsspc.sharp.calc.parcel.lifter_cm1) – a parcel lifter (e.g. lifter_cm1 or lifter_wobus)
pressure (numpy.ndarray[dtype=float32]) – 1D NumPy array of ambient pressures (Pa)
temperature (numpy.ndarray[dtype=float32]) – 1D NumPy array of ambient temperatureds (K)
dewpoint (numpy.ndarray[dtype=float32]) – 1D NumPy array of ambient dewpoint temperatures (K)

Returns:

1D NumPy array of wetbulb temperatures (K)

Return type:

numpy.ndarray[dtype=float32]

nwsspc.sharp.calc.thermo.theta_wetbulb(lifter: nwsspc.sharp.calc.parcel.lifter_wobus, pressure: float, temperature: float, dewpoint: float) → float#

nwsspc.sharp.calc.thermo.theta_wetbulb(lifter: nwsspc.sharp.calc.parcel.lifter_cm1, pressure: float, temperature: float, dewpoint: float) → float

nwsspc.sharp.calc.thermo.theta_wetbulb(lifter: nwsspc.sharp.calc.parcel.lifter_wobus, pressure: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], temperature: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], dewpoint: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) → numpy.ndarray[dtype=float32, shape=(*), order='C']

nwsspc.sharp.calc.thermo.theta_wetbulb(lifter: nwsspc.sharp.calc.parcel.lifter_cm1, pressure: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], temperature: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], dewpoint: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) → numpy.ndarray[dtype=float32, shape=(*), order='C']

Overloaded function.

theta_wetbulb(lifter: nwsspc.sharp.calc.parcel.lifter_wobus, pressure: float, temperature: float, dewpoint: float) -> float

Compute the wet-bulb potential temperature (K) given the pressure (Pa), temperature (K), and dewpoint temperature (K).

After the parcel has reached the LCL, the lifted passed to the function lowers the parcel to the standard parcel reference pressure level (1000 hPa) along a moist adiabat.

Parameters:

lifter (nwsspc.sharp.calc.parcel.lifter_wobus) – a parcel lifter (e.g. lifter_cm1 or lifter_wobus)
pressure (float) – the ambient air pressure (Pa)
temperature (float) – the ambient air temperature (K)
dewpoint (float) – the ambient dewpoint temperature

Returns:

The wet-bulb potential temperature (K)

Return type:

float

theta_wetbulb(lifter: nwsspc.sharp.calc.parcel.lifter_cm1, pressure: float, temperature: float, dewpoint: float) -> float

Compute the wet-bulb potential temperature (K) given the pressure (Pa), temperature (K), and dewpoint temperature (K).

After the parcel has reached the LCL, the lifted passed to the function lowers the parcel to the standard parcel reference pressure level (1000 hPa) along a moist adiabat.

Parameters:

lifter (nwsspc.sharp.calc.parcel.lifter_cm1) – a parcel lifter (e.g. lifter_cm1 or lifter_wobus)
pressure (float) – the ambient air pressure (Pa)
temperature (float) – the ambient air temperature (K)
dewpoint (float) – the ambient dewpoint temperature

Returns:

The wet-bulb potential temperature (K)

Return type:

float

theta_wetbulb(lifter: nwsspc.sharp.calc.parcel.lifter_wobus, pressure: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], temperature: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], dewpoint: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) -> numpy.ndarray[dtype=float32, shape=(*), order='C']

Compute the wet-bulb potential temperature (K) given the pressure (Pa), temperature (K), and dewpoint temperature (K).

After the parcel has reached the LCL, the lifted passed to the function lowers the parcel to the standard parcel reference pressure level (1000 hPa) along a moist adiabat.

Parameters:

lifter (nwsspc.sharp.calc.parcel.lifter_wobus) – a parcel lifter (e.g. lifter_cm1 or lifter_wobus)
pressure (numpy.ndarray[dtype=float32]) – 1D NumPy array of ambient air pressure (Pa)
temperature (numpy.ndarray[dtype=float32]) – 1D NumPy array of ambient air temperature (K)
dewpoint (numpy.ndarray[dtype=float32]) – 1D NumPy array of ambient dewpoint temperature

Returns:

1D NumPy array of wet-bulb potential temperatures (K)

Return type:

numpy.ndarray[dtype=float32]

theta_wetbulb(lifter: nwsspc.sharp.calc.parcel.lifter_cm1, pressure: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], temperature: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], dewpoint: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) -> numpy.ndarray[dtype=float32, shape=(*), order='C']

Compute the wet-bulb potential temperature (K) given the pressure (Pa), temperature (K), and dewpoint temperature (K).

After the parcel has reached the LCL, the lifted passed to the function lowers the parcel to the standard parcel reference pressure level (1000 hPa) along a moist adiabat.

Parameters:

lifter (nwsspc.sharp.calc.parcel.lifter_cm1) – a parcel lifter (e.g. lifter_cm1 or lifter_wobus)
pressure (numpy.ndarray[dtype=float32]) – 1D NumPy array of ambient air pressure (Pa)
temperature (numpy.ndarray[dtype=float32]) – 1D NumPy array of ambient air temperature (K)
dewpoint (numpy.ndarray[dtype=float32]) – 1D NumPy array of ambient dewpoint temperature

Returns:

1D NumPy array of wet-bulb potential temperatures (K)

Return type:

numpy.ndarray[dtype=float32]

Moist Ascent#

Moist thermodunamic routines directly related to vertical ascent.

class nwsspc.sharp.calc.thermo.adiabat(*values)#

An enum class used to flag which type of parcel ascent is desired for nwsspc.sharp.calc.parcel.lifter_cm1

pseudo_liq = 1#: Pseudoadiabatic liquid-only parcel ascent.

pseudo_ice = 3#: Pseudoadiabatic liquid and ice based parcel ascent.

adiab_liq = 2#: Adiabatic liquid-only parcel ascent.

adiab_ice = 4#: Adiabatic liquid and ice based parcel ascent.

nwsspc.sharp.calc.thermo.wobf(temperature: float) → float#

nwsspc.sharp.calc.thermo.wobf(tmpk_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) → numpy.ndarray[dtype=float32, shape=(*), order='C']

Overloaded function.

wobf(temperature: float) -> float

Computes the difference between the wet-bulb potential temperatures (Kelvin) for saturated and dry air, given the temperature (Kelvin).

The Wobus Function (wobf) is defined as the difference between the wet-bulb potential temperature for saturated air (WBPTS) and the wet-bulb potential temperature for dry air (WBPTD) given an iput air temperature. This function is used in the computation of moist adiabatic ascent as part of the Wobus parcel lifter (lifter_wobus).

WOBF(T) := WBPTS - WBPTD

Although WBPTS and WBPTD are functions of both pressure and temperature, it is assumed their difference is a function of temperature only. The difference is also proportional to the heat imparted to a parcel of air.

This function uses a polynomial approximation to the wobus function, fitted to value in Table 78 of PP.319-322 of the Smithsonian Meteorological Table by Rolan List (6th Revised Edition). Herman Wobus, a mathematician for the Navy Weather Research Facility in Norfolk, VA computed these coefficients a very long time ago, as he was retired as of the time of the documentation found on this routine written in 1981.

It was shown by Robert Davies-Jones (2007) that the Wobus function has a slight dependence on pressure, which results in errors of up to 1.2 Kelvin in the temperature of a lifted parcel.

Parameters:: temperature (float) – The air temperature (Kelvin)
Returns:: The Wobus function temperature (Kelvin)
Return type:: float

wobf(tmpk_arr: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False]) -> numpy.ndarray[dtype=float32, shape=(*), order='C']

Computes the difference between the wet-bulb potential temperatures (Kelvin) for saturated and dry air, given the temperature (Kelvin).

WOBF(T) := WBPTS - WBPTD

It was shown by Robert Davies-Jones (2007) that the Wobus function has a slight dependence on pressure, which results in errors of up to 1.2 Kelvin in the temperature of a lifted parcel.

Parameters:: tmpk_arr (numpy.ndarray[dtype=float32]) – The 1D array of air temperatures (Kelvin)
Returns:: The 1D array of Wobus function temperatures (Kelvin)
Return type:: numpy.ndarray[dtype=float32]

nwsspc.sharp.calc.thermo.wetlift(pressure: float, temperature: float, lifted_pressure: float, converge: float = 0.0010000000474974513) → float#

nwsspc.sharp.calc.thermo.wetlift(arg0: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], arg1: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], arg2: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], /) → numpy.ndarray[dtype=float32, shape=(*), order='C']

Overloaded function.

wetlift(pressure: float, temperature: float, lifted_pressure: float, converge: float = 0.0010000000474974513) -> float

Compute the temperature of a parcel lifted moist adiabatically to a new level.

With a given parcel defined by a pressure (Pa) and temperature (K), lift it moist adiabatically to a new pressure level (Pa) and return the temperature of the parcel at that level.

This function relies on the Wobus Function (thermo.wobf), and it was shown by Robert Davies-Jones (2007) that the WObus function has a slight dependence on pressure, which results in errors of up to 1.2 K in the temperature of a lifted parcel.

Parameters:

pressure (float) – The air pressure (Pa)
temperature (float) – The saturated air temperature (K)
lifted_pressure (float) – The new pressure level to lift to (Pa)
converge (float) – The iterative convergence criteria (K; default = 0.001)

Returns:

The new temperature (K) when lifted moist adiabatically to the new pressure level

Return type:

float

wetlift(arg0: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], arg1: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], arg2: ndarray[dtype=float32, shape=(*), order='C', device='cpu', writable=False], /) -> numpy.ndarray[dtype=float32, shape=(*), order='C']

Compute the temperature of a parcel lifted moist adiabatically to a new level.

With a given parcel defined by a pressure (Pa) and temperature (K), lift it moist adiabatically to a new pressure level (Pa) and return the temperature of the parcel at that level.

Parameters:

pressure (numpy.ndarray[dtype=float32]) – The 1D array of air pressures (Pa)
temperature (numpy.ndarray[dtype=float32]) – The 1D array of saturated air temperatures (K)
lifted_pressure (numpy.ndarray[dtype=float32]) – The 1D array of new pressure levels to lift to (Pa)

Returns:

The 1D array of new temperatures (K) when lifted moist adiabatically to the new pressure levels

Return type:

numpy.ndarray[dtype=float32]