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"""

Rainfall Intensity

==================

This module contains functions to calculate the intensity of

a rainfall event for a given duration and return period.

This function uses the Sherman intensity-duration-frequency curve.

References

----------

- Aparicio, F. (1997): Fundamentos de Hidrología de Superficie.

Balderas, México, Limusa. 303 p.

- https://en.wikipedia.org/wiki/Intensity-duration-frequency_curve

"""

def rainfall_intensity(

coefficient_k: float,

coefficient_a: float,

coefficient_b: float,

coefficient_c: float,

return_period: float,

duration: float,

) -> float:

"""

Calculate the intensity of a rainfall event for a given duration and return period.

It's based on the Sherman intensity-duration-frequency curve:

I = k * T^a / (D + b)^c

where:

I = Intensity of the rainfall event [mm/h]

k, a, b, c = Coefficients obtained through statistical distribution adjust

T = Return period in years

D = Rainfall event duration in minutes

Parameters

----------

coefficient_k : float

Coefficient obtained through statistical distribution adjust.

coefficient_a : float

Coefficient obtained through statistical distribution adjust.

coefficient_b : float

Coefficient obtained through statistical distribution adjust.

coefficient_c : float

Coefficient obtained through statistical distribution adjust.

return_period : float

Return period in years.

duration : float

Rainfall event duration in minutes.

Returns

-------

intensity : float

Intensity of the rainfall event in mm/h.

Raises

------

ValueError

If any of the parameters are not positive.

Examples

--------

>>> rainfall_intensity(1000, 0.2, 11.6, 0.81, 10, 60)

49.83339231138578

>>> rainfall_intensity(1000, 0.2, 11.6, 0.81, 10, 30)

77.36319588106228

>>> rainfall_intensity(1000, 0.2, 11.6, 0.81, 5, 60)

43.382487747633625

>>> rainfall_intensity(0, 0.2, 11.6, 0.81, 10, 60)

Traceback (most recent call last):

...

ValueError: All parameters must be positive.

>>> rainfall_intensity(1000, -0.2, 11.6, 0.81, 10, 60)

Traceback (most recent call last):

...

ValueError: All parameters must be positive.

>>> rainfall_intensity(1000, 0.2, -11.6, 0.81, 10, 60)

Traceback (most recent call last):

...

ValueError: All parameters must be positive.

>>> rainfall_intensity(1000, 0.2, 11.6, -0.81, 10, 60)

Traceback (most recent call last):

...

ValueError: All parameters must be positive.

>>> rainfall_intensity(1000, 0, 11.6, 0.81, 10, 60)

Traceback (most recent call last):

...

ValueError: All parameters must be positive.

>>> rainfall_intensity(1000, 0.2, 0, 0.81, 10, 60)

Traceback (most recent call last):

...

ValueError: All parameters must be positive.

>>> rainfall_intensity(1000, 0.2, 11.6, 0, 10, 60)

Traceback (most recent call last):

...

ValueError: All parameters must be positive.

>>> rainfall_intensity(0, 0.2, 11.6, 0.81, 10, 60)

Traceback (most recent call last):

...

ValueError: All parameters must be positive.

>>> rainfall_intensity(1000, 0.2, 11.6, 0.81, 0, 60)

Traceback (most recent call last):

...

ValueError: All parameters must be positive.

>>> rainfall_intensity(1000, 0.2, 11.6, 0.81, 10, 0)

Traceback (most recent call last):

...

ValueError: All parameters must be positive.

"""

if (

coefficient_k <= 0

or coefficient_a <= 0

or coefficient_b <= 0

or coefficient_c <= 0

or return_period <= 0

or duration <= 0

):

raise ValueError("All parameters must be positive.")

intensity = (coefficient_k * (return_period**coefficient_a)) / (

(duration + coefficient_b) ** coefficient_c

)

return intensity

if __name__ == "__main__":

import doctest

doctest.testmod()