def test_under_1000m():
"""Tests for altitude values under 1000.0 m
"""
z = np.array([50.0, 550.0, 850.0])
h = util.geometric_to_geopotential(z)
expected_h = np.array([50.0, 550.0, 850.0])
expected_T = np.array([287.825, 284.575, 282.626])
expected_p = np.array([100720.0, 94890.0, 91523.0])
expected_rho = np.array([1.2191, 1.1616, 1.1281])
h, T, p, rho = coesa.table(h)
assert_array_almost_equal(h, expected_h, decimal=0)
assert_array_almost_equal(T, expected_T, decimal=3)
assert_array_almost_equal(p, expected_p, decimal=-1)
assert_array_almost_equal(rho, expected_rho, decimal=4)
def test_under_86km():
"""Tests for altitude values between 35 and 86 km
"""
z = np.array([50000.0, 70000.0, 86000.0])
h = util.geometric_to_geopotential(z)
expected_h = np.array([49610.0, 69238., 84852.0])
expected_T = np.array([270.65, 219.585, 186.87])
expected_p = np.array([79.779, 5.2209, 0.37338])
expected_rho = np.array([0.0010269, 0.000082829, 0.000006958])
h, T, p, rho = coesa.table(h)
assert_array_almost_equal(h, expected_h, decimal=0)
assert_array_almost_equal(T, expected_T, decimal=2)
assert_array_almost_equal(p, expected_p, decimal=3)
assert_array_almost_equal(rho, expected_rho, decimal=7)
def test_under_11km():
"""Tests for altitude values between 1 and 11 km
"""
z = np.array([500.0, 2500.0, 6500.0, 9000.0, 11000.0])
h = util.geometric_to_geopotential(z)
expected_h = np.array([500.0, 2499.0, 6493.0, 8987.0, 10981.0])
expected_T = np.array([284.900, 271.906, 245.943, 229.733, 216.774])
expected_p = np.array([95461.0, 74691.0, 44075.0, 30800.0, 22699.0])
expected_rho = np.array([1.1673, 0.95695, 0.62431, 0.46706, 0.36480])
h, T, p, rho = coesa.table(h)
assert_array_almost_equal(h, expected_h, decimal=0)
assert_array_almost_equal(T, expected_T, decimal=3)
assert_array_almost_equal(p, expected_p, decimal=0)
assert_array_almost_equal(rho, expected_rho, decimal=4)
def test_under_35km():
"""Tests for altitude values between 11 and 35 km
"""
z = np.array([15000.0, 25000.0, 35000.0])
h = util.geometric_to_geopotential(z)
expected_h = np.array([14965.0, 24902., 34808.0])
expected_T = np.array([216.65, 221.552, 236.513])
expected_p = np.array([12111.0, 2549.2, 574.59])
expected_rho = np.array([0.19476, 0.040084, 0.0084634])
h, T, p, rho = coesa.table(h)
assert_array_almost_equal(h, expected_h, decimal=0)
assert_array_almost_equal(T, expected_T, decimal=3)
assert_array_almost_equal(p, expected_p, decimal=0)
assert_array_almost_equal(rho, expected_rho, decimal=5)
def test_under_1000m():
"""Tests for altitude values under 1000.0 m
"""
z = np.array([50.0, 550.0, 850.0])
h = util.geometric_to_geopotential(z)
expected_h = np.array([50.0, 550.0, 850.0])
expected_T = np.array([287.825, 284.575, 282.626])
expected_p = np.array([100720.0, 94890.0, 91523.0])
expected_rho = np.array([1.2191, 1.1616, 1.1281])
h, T, p, rho = coesa.table(h)
assert_array_almost_equal(h, expected_h, decimal=0)
assert_array_almost_equal(T, expected_T, decimal=3)
assert_array_almost_equal(p, expected_p, decimal=-1)
assert_array_almost_equal(rho, expected_rho, decimal=4)
def test_under_86km():
"""Tests for altitude values between 35 and 86 km
"""
z = np.array([50000.0, 70000.0, 86000.0])
h = util.geometric_to_geopotential(z)
expected_h = np.array([49610.0, 69238., 84852.0])
expected_T = np.array([270.65, 219.585, 186.87])
expected_p = np.array([79.779, 5.2209, 0.37338])
expected_rho = np.array([0.0010269, 0.000082829, 0.000006958])
h, T, p, rho = coesa.table(h)
assert_array_almost_equal(h, expected_h, decimal=0)
assert_array_almost_equal(T, expected_T, decimal=2)
assert_array_almost_equal(p, expected_p, decimal=3)
assert_array_almost_equal(rho, expected_rho, decimal=7)
def test_under_35km():
"""Tests for altitude values between 11 and 35 km
"""
z = np.array([15000.0, 25000.0, 35000.0])
h = util.geometric_to_geopotential(z)
expected_h = np.array([14965.0, 24902., 34808.0])
expected_T = np.array([216.65, 221.552, 236.513])
expected_p = np.array([12111.0, 2549.2, 574.59])
expected_rho = np.array([0.19476, 0.040084, 0.0084634])
h, T, p, rho = coesa.table(h)
assert_array_almost_equal(h, expected_h, decimal=0)
assert_array_almost_equal(T, expected_T, decimal=3)
assert_array_almost_equal(p, expected_p, decimal=0)
assert_array_almost_equal(rho, expected_rho, decimal=5)
def test_under_11km():
"""Tests for altitude values between 1 and 11 km
"""
z = np.array([500.0, 2500.0, 6500.0, 9000.0, 11000.0])
h = util.geometric_to_geopotential(z)
expected_h = np.array([500.0, 2499.0, 6493.0, 8987.0, 10981.0])
expected_T = np.array([284.900, 271.906, 245.943, 229.733, 216.774])
expected_p = np.array([95461.0, 74691.0, 44075.0, 30800.0, 22699.0])
expected_rho = np.array([1.1673, 0.95695, 0.62431, 0.46706, 0.36480])
h, T, p, rho = coesa.table(h)
assert_array_almost_equal(h, expected_h, decimal=0)
assert_array_almost_equal(T, expected_T, decimal=3)
assert_array_almost_equal(p, expected_p, decimal=0)
assert_array_almost_equal(rho, expected_rho, decimal=4)
def test_geometric_to_geopotential():
z = np.array([50.0, 5550.0, 10450.0])
h = util.geometric_to_geopotential(z)
expected_h = np.array([50.0, 5545.0, 10433.0])
assert_array_almost_equal(h, expected_h, decimal=0)
def table(x, kind="geopotential"):
"""Computes table of COESA atmosphere properties.
Returns temperature, pressure and density COESA values at the given
altitude.
Parameters
----------
x : array_like
Geopotential or geometric altitude (depending on kind) given in meters.
kind : str
Specifies the kind of interpolation as altitude x ('geopotential' or 'geometric'). Default is 'geopotential'
Returns
-------
h : array_like
Given geopotential altitude in meters.
T : array_like
Temperature in Kelvin.
p : array_like
Pressure in Pascal.
rho : array_like
Density in kilograms per cubic meter.
Note
----
Based on the U.S. 1976 Standard Atmosphere.
"""
# check the kind of altitude and raise an exception if necessary
if kind == "geopotential":
alt = x
elif kind == "geometric":
alt = util.geometric_to_geopotential(x)
else:
raise ValueError(
"%s is unsupported: Use either geopotential or " "geometric." % kind
)
h = np.asarray(alt)
# check if altitude is out of bound and raise an exception if necessary
if (h < H[0]).any() or (h > H[-1]).any():
raise ValueError(
"the given altitude x is out of bound, this module is "
"currently only valid for a geometric altitude between 0. and 86000. m"
)
# K, molecule-scale temperature from eq. [23] of Notes reference
tm = f_TM(h) + f_LM(h) * (h - f_H(h))
# K, absolute temperature from eq. [22] of Notes reference
T = tm * f_M_o_M0(h)
if h.shape: # if h is not a 0-d array (like a scalar)
# Pa, intialization of the pressure vector
p = np.zeros(len(h))
# points of h for which the molecular-scale temperature gradient is
# zero
zero_gradient = f_LM(h) == 0.0
# points of h for which the molecular-scale temperature gradient is not
# zero
not_zero_gradient = f_LM(h) != 0.0
# Pa, pressure from eq. [33b] of Notes reference
p[zero_gradient] = f_P(h[zero_gradient]) * np.exp(
-constants.g
* M_0
* (h[zero_gradient] - f_H(h[zero_gradient]))
/ (Rs * f_TM(h[zero_gradient]))
)
# Pa, pressure from eq. [33a] of Notes reference
p[not_zero_gradient] = f_P(h[not_zero_gradient]) * (
f_TM(h[not_zero_gradient])
/ (
f_TM(h[not_zero_gradient])
+ f_LM(h[not_zero_gradient])
* (h[not_zero_gradient] - f_H(h[not_zero_gradient]))
)
) ** (constants.g * M_0 / (Rs * f_LM(h[not_zero_gradient])))
else:
if f_LM(h) == 0:
# Pa, pressure from eq. [33b] of Notes reference
p = f_P(h) * np.exp(-constants.g * M_0 * (h - f_H(h)) / (Rs * f_TM(h)))
else:
# Pa, pressure from eq. [33a] of Notes reference
p = f_P(h) * (f_TM(h) / (f_TM(h) + f_LM(h) * (h - f_H(h)))) ** (
constants.g * M_0 / (Rs * f_LM(h))
)
rho = p * M_0 / (Rs * tm) # kg / m^3, mass density
return alt, T, p, rho
def test_geometric_to_geopotential():
z = np.array([50.0, 5550.0, 10450.0])
h = util.geometric_to_geopotential(z)
expected_h = np.array([50.0, 5545.0, 10433.0])
assert_array_almost_equal(h, expected_h, decimal=0)
def table(x, kind='geopotential'):
"""Computes table of COESA atmosphere properties.
Returns temperature, pressure and density COESA values at the given
altitude.
Parameters
----------
x : array_like
Geopotential or geometric altitude (depending on kind) given in meters.
kind : str
Specifies the kind of interpolation as altitude x ('geopotential' or
'geometric'). Default is 'geopotential'
Returns
-------
h : array_like
Given geopotential altitude in meters.
T : array_like
Temperature in Kelvin.
p : array_like
Pressure in Pascal.
rho : array_like
Density in kilograms per cubic meter.
Notes
-----
Based on the U.S. 1976 Standard Atmosphere.
.. _`U.S. 1976 Standard Atmosphere`: http://ntrs.nasa.gov/search.jsp?R=19770009539
"""
# check the kind of altitude and raise an exception if necessary
if kind == 'geopotential':
alt = x
elif kind == 'geometric':
alt = util.geometric_to_geopotential(x)
else:
raise ValueError("%s is unsupported: Use either geopotential or "
"geometric." % kind)
h = np.asarray(alt)
# check if altitude is out of bound and raise an exception if necessary
if (h < H[0]).any() or (h > H[-1]).any():
raise ValueError(
"the given altitude x is out of bound, this module is "
"currently only valid for a geometric altitude between 0. and 86000. m"
)
# K, molecule-scale temperature from eq. [23] of Notes reference
tm = f_TM(h) + f_LM(h) * (h - f_H(h))
# K, absolute temperature from eq. [22] of Notes reference
T = tm * f_M_o_M0(h)
if h.shape: # if h is not a 0-d array (like a scalar)
# Pa, intialization of the pressure vector
p = np.zeros(len(h))
# points of h for which the molecular-scale temperature gradient is zero
zero_gradient = (f_LM(h) == 0.)
# points of h for which the molecular-scale temperature gradient is not
# zero
not_zero_gradient = (f_LM(h) != 0.)
# Pa, pressure from eq. [33b] of Notes reference
p[zero_gradient] = f_P(h[zero_gradient]) * np.exp(
-constants.g * M_0 * (h[zero_gradient] - f_H(h[zero_gradient])) /
(Rs * f_TM(h[zero_gradient])))
# Pa, pressure from eq. [33a] of Notes reference
p[not_zero_gradient] = f_P(h[not_zero_gradient]) * (
f_TM(h[not_zero_gradient]) /
(f_TM(h[not_zero_gradient]) + f_LM(h[not_zero_gradient]) *
(h[not_zero_gradient] - f_H(h[not_zero_gradient]))))**(
constants.g * M_0 / (Rs * f_LM(h[not_zero_gradient])))
else:
if f_LM(h) == 0:
# Pa, pressure from eq. [33b] of Notes reference
p = f_P(h) * np.exp(-constants.g * M_0 * (h - f_H(h)) /
(Rs * f_TM(h)))
else:
# Pa, pressure from eq. [33a] of Notes reference
p = f_P(h) * (f_TM(h) / (f_TM(h) + f_LM(h) *
(h - f_H(h))))**(constants.g * M_0 /
(Rs * f_LM(h)))
rho = p * M_0 / (Rs * tm) # kg / m^3, mass density
return alt, T, p, rho
