Compute frost and dew point (Python function)

weather_math.py

import math


def get_frost_point_c(t_air_c, dew_point_c):
    """Compute the frost point in degrees Celsius

    :param t_air_c: current ambient temperature in degrees Celsius
    :type t_air_c: float
    :param dew_point_c: current dew point in degrees Celsius
    :type dew_point_c: float
    :return: the frost point in degrees Celsius
    :rtype: float
    """
    dew_point_k = 273.15 + dew_point_c
    t_air_k = 273.15 + t_air_c
    frost_point_k = dew_point_k - t_air_k + 2671.02 / ((2954.61 / t_air_k) + 2.193665 * math.log(t_air_k) - 13.3448)
    return frost_point_k - 273.15


def get_dew_point_c(t_air_c, rel_humidity):
    """Compute the dew point in degrees Celsius

    :param t_air_c: current ambient temperature in degrees Celsius
    :type t_air_c: float
    :param rel_humidity: relative humidity in %
    :type rel_humidity: float
    :return: the dew point in degrees Celsius
    :rtype: float
    """
    A = 17.27
    B = 237.7
    alpha = ((A * t_air_c) / (B + t_air_c)) + math.log(rel_humidity/100.0)
    return (B * alpha) / (A - alpha)

Thanks a lot for the code. Can you please tell the reference where you got the frost point formula? Would be really helpful. Thanks

https://www.omnicalculator.com/physics/dew-point has similar and refers to Alduchov and Eskridge.

This code uses the Tetens coefficients in a Magnus-type equation for T_d over a water surface. Alduchov and Eskridge recommend in their paper other coefficients, though differences are small. For upper levels, it would be more appropriate to complete this with the coefficients when over an icy surface

Nice formula. I've slightly rewritten it for my purposes and used the constants that are generally accepted as more accurate from the paper by Alduchov and Eskridge, also taking some inspiration from the wikipedia article. Cross-checked with the previously mentioned omni calculator and it seems to work well. This was the best example I found in my google searches, so thank you for the information! I was trying to convert some other formula written in C and was not getting correct results.

def calc_dewpoint(humidity, temp_c):
    a = 17.625
    b = 243.04
    alpha = math.log(humidity/100.0) + ((a * temp_c) / (b + temp_c))
    return (b * alpha) / (a - alpha)```