def p_from_z(z, lat, geo_strf_dyn_height=0):
r"""Calculates sea pressure from height using computationally-efficient
48-term expression for density, in terms of SA, CT and p (McDougall et al.,
2011). Dynamic height anomaly, geo_strf_dyn_height, if provided, must be
computed with its pr=0 (the surface.)
Parameters
----------
z : array_like
height [m]
lat : array_like
latitude in decimal degrees north [-90..+90]
geo_strf_dyn_height : float, optional
dynamic height anomaly [ m :sup:`2` s :sup:`-2` ]
The reference pressure (p_ref) of geo_strf_dyn_height
must be zero (0) dbar.
Returns
-------
p : array_like
pressure [dbar]
See Also
--------
#FIXME: specvol_SSO_0_CT25, enthalpy_SSO_0_CT25, changed!
Examples
--------
>>> import gsw
>>> z = [-10., -50., -125., -250., -600., -1000.]
>>> lat = 4.
>>> gsw.p_from_z(z, lat)
array([ 10.05521794, 50.2711751, 125.6548857, 251.23284504,
602.44050752, 1003.07609807])
>>> z = [9.94460074, 49.71817465, 124.2728275, 248.47044828, 595.82618014,
... 992.0931748]
>>> gsw.p_from_z(z, lat)
array([ 10., 50., 125., 250., 600., 1000.])
Notes
-----
Height (z) is NEGATIVE in the ocean. Depth is -z. Depth is not used in the
gibbs library.
References
----------
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
of seawater - 2010: Calculation and use of thermodynamic properties.
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
UNESCO (English), 196 pp.
.. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
computationally efficient 48-term expression for the density of seawater
in terms of Conservative Temperature, and related properties of seawater.
.. [3] Moritz (2000) Goedetic reference system 1980. J. Geodesy, 74,
128-133.
.. [4] Saunders, P. M., 1981: Practical conversion of pressure to depth.
Journal of Physical Oceanography, 11, 573-574.
Modifications:
2010-08-26. Trevor McDougall, Claire Roberts-Thomson and Paul Barker.
2011-03-26. Trevor McDougall, Claire Roberts-Thomson and Paul Barker
"""
X = np.sin(lat * DEG2RAD)
sin2 = X ** 2
gs = 9.780327 * (1.0 + (5.2792e-3 + (2.32e-5 * sin2)) * sin2)
# get the first estimate of p from Saunders (1981)
c1 = 5.25e-3 * sin2 + 5.92e-3
p = -2 * z / ((1 - c1) + np.sqrt((1 - c1) * (1 - c1) + 8.84e-6 * z))
df_dp = db2Pascal * specvol_SSO_0_p(p) # Initial value for f derivative.
f = (enthalpy_SSO_0_p(p) + gs *
(z - 0.5 * gamma * (z ** 2)) - geo_strf_dyn_height)
p_old = p
p = p_old - f / df_dp
p_mid = 0.5 * (p + p_old)
df_dp = db2Pascal * specvol_SSO_0_p(p_mid)
p = p_old - f / df_dp
# After this one iteration through this modified Newton-Raphson iterative
# procedure, the remaining error in p is at computer machine precision,
# being no more than 1.6e-10 dbar.
return p
def p_from_z(z, lat, geo_strf_dyn_height=0):
r"""Calculates sea pressure from height using computationally-efficient
48-term expression for density, in terms of SA, CT and p (McDougall et al.,
2011). Dynamic height anomaly, geo_strf_dyn_height, if provided, must be
computed with its pr=0 (the surface.)
Parameters
----------
z : array_like
height [m]
lat : array_like
latitude in decimal degrees north [-90..+90]
geo_strf_dyn_height : float, optional
dynamic height anomaly [ m :sup:`2` s :sup:`-2` ]
The reference pressure (p_ref) of geo_strf_dyn_height
must be zero (0) dbar.
Returns
-------
p : array_like
pressure [dbar]
See Also
--------
#FIXME: specvol_SSO_0_CT25, enthalpy_SSO_0_CT25, changed!
Examples
--------
>>> import gsw
>>> z = [-10., -50., -125., -250., -600., -1000.]
>>> lat = 4.
>>> gsw.p_from_z(z, lat)
array([ 10.05521794, 50.2711751, 125.6548857, 251.23284504,
602.44050752, 1003.07609807])
>>> z = [9.94460074, 49.71817465, 124.2728275, 248.47044828, 595.82618014,
... 992.0931748]
>>> gsw.p_from_z(z, lat)
array([ 10., 50., 125., 250., 600., 1000.])
Notes
-----
Height (z) is NEGATIVE in the ocean. Depth is -z. Depth is not used in the
gibbs library.
References
----------
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
of seawater - 2010: Calculation and use of thermodynamic properties.
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
UNESCO (English), 196 pp.
.. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
computationally efficient 48-term expression for the density of seawater
in terms of Conservative Temperature, and related properties of seawater.
.. [3] Moritz (2000) Goedetic reference system 1980. J. Geodesy, 74,
128-133.
.. [4] Saunders, P. M., 1981: Practical conversion of pressure to depth.
Journal of Physical Oceanography, 11, 573-574.
Modifications:
2010-08-26. Trevor McDougall, Claire Roberts-Thomson and Paul Barker.
2011-03-26. Trevor McDougall, Claire Roberts-Thomson and Paul Barker
"""
X = np.sin(lat * rad)
sin2 = X ** 2
gs = 9.780327 * (1.0 + (5.2792e-3 + (2.32e-5 * sin2)) * sin2)
# get the first estimate of p from Saunders (1981)
c1 = 5.25e-3 * sin2 + 5.92e-3
p = -2 * z / ((1 - c1) + np.sqrt((1 - c1) * (1 - c1) + 8.84e-6 * z))
df_dp = db2Pascal * specvol_SSO_0_p(p) # Initial value for f derivative.
f = (enthalpy_SSO_0_p(p) + gs * (z - 0.5 * gamma * (z ** 2)) -
geo_strf_dyn_height)
p_old = p
p = p_old - f / df_dp
p_mid = 0.5 * (p + p_old)
df_dp = db2Pascal * specvol_SSO_0_p(p_mid)
p = p_old - f / df_dp
# After this one iteration through this modified Newton-Raphson iterative
# procedure, the remaining error in p is at computer machine precision,
# being no more than 1.6e-10 dbar.
return p
def z_from_p(p, lat, geo_strf_dyn_height=0):
r"""Calculates height from sea pressure using the computationally-efficient
48-term expression for density in terms of SA, CT and p (McDougall et
al., 2011). Dynamic height anomaly, geo_strf_dyn_height, if provided, must
be computed with its pr=0 (the surface).
Parameters
----------
p : array_like
pressure [dbar]
lat : array_like
latitude in decimal degrees north [-90..+90]
geo_strf_dyn_height : float, optional
dynamic height anomaly [ m :sup:`2` s :sup:`-2` ]
Returns
-------
z : array_like
height [m]
See Also
--------
# FIXME: enthalpy_SSO_0_CT25, changed!
Examples
--------
>>> import gsw
>>> p = [10, 50, 125, 250, 600, 1000]
>>> lat = 4
>>> gsw.z_from_p(p, lat)
array([ -9.94460074, -49.71817465, -124.2728275 , -248.47044828,
-595.82618014, -992.0931748 ])
Notes
-----
At sea level z = 0, and since z (HEIGHT) is defined to be positive upwards,
it follows that while z is positive in the atmosphere, it is NEGATIVE in
the ocean.
References
----------
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
of seawater - 2010: Calculation and use of thermodynamic properties.
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
UNESCO (English), 196 pp.
.. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
computationally efficient 48-term expression for the density of seawater
in terms of Conservative Temperature, and related properties of seawater.
.. [3] Moritz (2000) Goedetic reference system 1980. J. Geodesy, 74,
128-133.
Modifications:
2011-03-26. Trevor McDougall, Claire Roberts-Thomson and Paul Barker.
"""
X = np.sin(lat * DEG2RAD)
sin2 = X ** 2
B = 9.780327 * (1.0 + (5.2792e-3 + (2.32e-5 * sin2)) * sin2)
A = -0.5 * gamma * B
C = enthalpy_SSO_0_p(p) - geo_strf_dyn_height
return -2 * C / (B + np.sqrt(B ** 2 - 4 * A * C))
def z_from_p(p, lat, geo_strf_dyn_height=None):
r"""Calculates height from sea pressure using the computationally-efficient
48-term expression for density in terms of SA, CT and p (McDougall et
al., 2011). Dynamic height anomaly, geo_strf_dyn_height, if provided, must
be computed with its pr=0 (the surface.)
Parameters
----------
p : array_like
pressure [dbar]
lat : array_like
latitude in decimal degrees north [-90..+90]
geo_strf_dyn_height : float, optional
dynamic height anomaly [ m :sup:`2` s :sup:`-2` ]
Returns
-------
z : array_like
height [m]
See Also
--------
# FIXME: enthalpy_SSO_0_CT25, changed!
Examples
--------
>>> import gsw
>>> p = [10, 50, 125, 250, 600, 1000]
>>> lat = 4
>>> gsw.z_from_p(p, lat)
array([ -9.94460074, -49.71817465, -124.2728275 , -248.47044828,
-595.82618014, -992.0931748 ])
Notes
-----
At sea level z = 0, and since z (HEIGHT) is defined to be positive upwards,
it follows that while z is positive in the atmosphere, it is NEGATIVE in
the ocean.
References
----------
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
of seawater - 2010: Calculation and use of thermodynamic properties.
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
UNESCO (English), 196 pp.
.. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
computationally efficient 48-term expression for the density of seawater
in terms of Conservative Temperature, and related properties of seawater.
.. [3] Moritz (2000) Goedetic reference system 1980. J. Geodesy, 74,
128-133.
Modifications:
2011-03-26. Trevor McDougall, Claire Roberts-Thomson and Paul Barker.
"""
if not geo_strf_dyn_height:
geo_strf_dyn_height = np.zeros(p.shape)
X = np.sin(lat * rad)
sin2 = X ** 2
B = 9.780327 * (1.0 + (5.2792e-3 + (2.32e-5 * sin2)) * sin2)
A = -0.5 * gamma * B
C = enthalpy_SSO_0_p(p) - geo_strf_dyn_height
z = -2 * C / (B + np.sqrt(B ** 2 - 4 * A * C))
return z