Overview#

This section covers meteorology functions from NCL:

• dewtemp_trh

• daylight_fao56

• satvpr_temp_fao56

• satvpr_tdew_fao56

• satvpr_slope_fao56

• coriolis_param

• relhum

dewtemp_trh#

NCL’s dewtemp_trh calculates the dew point temperature given temperature and relative humidity using the equations from John Dutton’s “Ceaseless Wind” (pg. 273-274)[1] and returns a temperature in Kelvin.

Where, for the gas constant of water vapor ($R_{v}$)of 461.5 $\frac{J}{K*kg}$ ($\frac{461.5}{1000 * 4.186} \frac{cal}{g*k}$), the empirical value of the latent heat (pg. 273, Problem 8.3.1) is:

$L_{lv} = 597.3 - 0.57(T - 273)$

So, when $h$ is the relative humidity, the dew point temperature (pg. 273, Equation 6, solved for as $T_D$) is:

$T_D = \frac{T * L_{lv}}{L_{lv} - R_{v}Tlog(h)}$

# Input: Single Value
from geocat.comp import dewtemp

temp_c = 18  # Celsius
relative_humidity = 46.5  # %

dewtemp(temp_c + 273.15, relative_humidity) - 273.15  # Returns in Celsius

np.float64(6.298141316024157)

# Input: List/Array
from geocat.comp import dewtemp

temp_kelvin = [291.15, 274.14, 360.3, 314]  # Kelvin
relative_humidity = [46.5, 5, 96.5, 1]  # %

dewtemp(temp_kelvin, relative_humidity) - 273.15  # Returns in Celsius

array([  6.29814132, -35.12955277,  86.22114845, -27.40981025])

daylight_fao56#

NCL’s daylight_fao56 calculates the maximum number of daylight hours as described in the Food and Agriculture Organization (FAO) Irrigation and Drainage Paper 56 (Chapter 3, Equation 34) [2].

Where the maximum number of daylight hours, $N$, is:

$N = \frac{24}{{\pi}} {\omega}_{s}$

And ${\omega}_{s}$ is the sunset hour angle in radians (Chapter 3, Equation 25) [2] which is calculated from the latitude of the observer on Earth ($\varphi$) and the sun’s declination ($\delta$):

${\omega}_{s} = arccos[-tan({\varphi})tan({\delta})]$

# Input: Single Value
from geocat.comp import max_daylight

day_of_year = 246  # Sept. 3
latitude = -20  # 20 Degrees South

max_daylight(day_of_year, latitude)

array([[11.665592]], dtype=float32)

# Input: List/Array
from geocat.comp import max_daylight

# Spring Equinox (March 20), Summer Solstice (June 20), Autumn Equinox (Sept. 22), Winter Solstice (Dec. 21)
days_of_year = [79, 171, 265, 355]
latitudes = 40  # Boulder

max_daylight(days_of_year, latitudes)

array([[11.921149],
       [14.843202],
       [11.920901],
       [ 9.156431]], dtype=float32)

satvpr_temp_fao56#

NCL’s satvpr_temp_fao56 calculates saturation vapor pressure using temperature as described in the Food and Agriculture Organization (FAO) Irrigation and Drainage Paper 56 (Chapter 3, Equation 11) [2].

Where the saturation vapor pressure, $e^°$ (kPa), at air temperature $T$ (°C) is calculated as:

$e^°(T) = 0.6108 {\exp}[\frac{17.27T}{T + 237.3}]$

# Input: Single Value
from geocat.comp import saturation_vapor_pressure

temp = 50  # Fahrenheit

saturation_vapor_pressure(temp)

array(1.22796262)

# Input: List/Array
from geocat.comp import saturation_vapor_pressure

temp = [33, 50, 100, 212]  # Fahrenheit

saturation_vapor_pressure(temp)

array([  0.63594167,   1.22796262,   6.54556639, 102.21571649])

satvpr_tdew_fao56#

NCL’s satvpr_tdew_fao56 calculates the actual saturation vapor pressure using dewpoint temperature as described in the Food and Agriculture Organization (FAO) Irrigation and Drainage Paper 56 (Chapter 3, Equation 14) [2].

Where the actual vapor pressure, $e_{a}$ (kPa), is saturation vapor pressure at a specific dewpoint temperature, $T_{dew}$ (°C), which is calculated as:

$e_{a} = e^°(T_{dew}) = 0.6108 {\exp}[\frac{17.27 T_{dew}}{T_{dew} + 237.3}]$

# Input: Single Value
from geocat.comp import actual_saturation_vapor_pressure

temp = 35  # Fahrenheit

actual_saturation_vapor_pressure(temp)

array(0.68898447)

# Input: List/Array
from geocat.comp import actual_saturation_vapor_pressure

temp = [35, 60, 80, 200]  # Fahrenheit

actual_saturation_vapor_pressure(temp)

array([ 0.68898447,  1.76730647,  3.49620825, 80.00607017])

satvpr_slope_fao56#

NCL’s satvpr_slope_fao56 calculates the slope of the saturation vapor pressure curve as described in the Food and Agriculture Organization (FAO) Irrigation and Drainage Paper 56 (Chapter 3, Equation 13) [2].

Where the slope of saturation vapor pressure curve, ${\Delta}$ (kPa), at air temperature $T$ (°C) is calculated as:

${\Delta} = \frac{4098 (0.6108 {\exp}[\frac{17.27T}{T + 237.3}])}{(T + 237.3)^2}$

# Input: Single Value
from geocat.comp import saturation_vapor_pressure_slope

temp = 60  # Fahrenheit

saturation_vapor_pressure_slope(temp)

array(0.11322096)

# Input: List/Array
from geocat.comp import saturation_vapor_pressure_slope

temp = [35, 60, 80, 200]  # Fahrenheit

saturation_vapor_pressure_slope(temp)

array([0.04941909, 0.11322096, 0.20552235, 2.99770999])

coriolis_param#

NCL’s coriolis_param calculates the Coriolis parameter at a given latitude

The Coriolis parameter (also known as the Coriolis frequency or the Coriolis coefficient) is calculated as twice the rotation rate (${\Omega}$) of the Earth times the sine of the latitude (${\varphi}$)[3]

$f = 2{\Omega}sin({\varphi})$

The rotation rate depends on the length of the rotation period of the Earth (T) which is defined as one sidereal day (23 hours and 56 minutes):

${\Omega} = \frac{2 * {\pi}}{T} = 7.292\text{e-5} \frac{rad}{s}$

# Input: Single Value
from metpy.calc import coriolis_parameter
from metpy.units import units

latitude = 40  # degrees

coriolis_parameter(latitude * units.degree).magnitude

np.float64(9.374562340818716e-05)

# Input: List/Array
from metpy.calc import coriolis_parameter
from metpy.units import units

latitude = [-20, 40, 65]  # degrees

coriolis_parameter(latitude * units.degree).magnitude

array([-4.98810043e-05,  9.37456234e-05,  1.32178012e-04])

relhum#

NCL’s relhum calculates relative humidity given temperature, mixing ratio, and pressure. The percent of relative humidity (${\Psi}$) is based on the original NCL relhum code:

${\Psi} = w (\frac{p - 0.378 * e_s}{0.622 * e_s}) * 100$

Where $w$ is the mass mixing ratio of water vapor and dry air, $p$ is pressure, and $e_s$ is the saturation vapor pressure for a given temperature.

The constant 0.622 represents the ratio of the molar mass of water vapor ($M_w$) in g/mol and the molar mass of dry air ($M_d$) in g/mol:

$\frac{M_w}{M_d} = \frac{18.02}{28.9634} = 0.622$

# Input: Single Value
from geocat.comp import relhum

temp = 303.15  # Kelvin
mixing_ratio = 0.018
pressure = 101325  # Pa

relhum(temp, mixing_ratio, pressure)

np.float64(68.05239617370448)

# Input: List/Array
from geocat.comp import relhum

temp = [375.15, 303.15, 315.15]  # Kelvin
mixing_ratio = [0.5, 0.018, 0.001]
pressure = [100325, 101325, 101400]  # Pa

relhum(temp, mixing_ratio, pressure)

array([43.78181802, 68.05239617,  1.92796564])

Python Resources#

• GeoCAT-comp dewtemp documentation

• Convert between different temperature scales in SciPy

• GeoCAT-comp max_daylight Documentation

• GeoCAT-comp saturation_vapor_pressure Documentation

• GeoCAT-comp actual_saturation_vapor_pressure Documentation

• GeoCAT-comp saturation_vapor_pressure_slope Documentation

• MetPy coriolis_parameter Documentation

• GeoCAT-comp relhum Documentation

Additional Reading#

• NOAA: Dew Point vs. Humidity

• MetPy relative_humidity_from_mixing_ratio Documentation with alternative equation

References:#