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# -*- coding: utf-8 -*-
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from __future__ import division
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from constants import gamma, earth_radius, OMEGA
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from gsw.utilities import match_args_return
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from conversions import z_from_p
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r"""Calculates the Coriolis parameter (f) defined by:
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omega = 7.292115e-5 (Groten, 2004) [radians s :sup:`-1`]
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latitude [degrees north]
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Coriolis paramter [s :sup:`-1`]
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.. [1] Groten, E., 2004: Fundamental Parameters and Current (2004) Best
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Estimates of the Parameters of Common Relevance to Astronomy, Geodesy, and
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Geodynamics. Journal of Geodesy, 77, pp. 724-797.
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.. [2] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
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of seawater - 2010: Calculation and use of thermodynamic properties.
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Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
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UNESCO (English), 196 pp.
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1993-04-20. Phil Morgan
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2010-07-28. Paul Barker
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lat = np.asanyarray(lat)
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return 2 * OMEGA * np.sin(lat * RAD)
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r"""Calculates acceleration due to gravity as a function of latitude and as
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a function of pressure in the ocean.
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latitude in decimal degrees north [-90...+90]
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p : number or array_like. Default p = 0
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gravity [m s :sup:`2`]
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In the ocean z is negative.
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>>> lat = [-90, -60, -30, 0]
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array([ 9.83218621, 9.81917886, 9.79324926, 9.780327 ])
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.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
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of seawater - 2010: Calculation and use of thermodynamic properties.
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Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
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UNESCO (English), 196 pp.
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.. [2] Moritz (2000) Goedetic reference system 1980. J. Geodesy, 74,
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.. [3] Saunders, P.M., and N.P. Fofonoff (1976) Conversion of pressure to
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depth in the ocean. Deep-Sea Res.,pp. 109 - 111.
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2011-03-29. Trevor McDougall & Paul Barker
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X = np.sin(lat * RAD)
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gs = 9.780327 * (1.0 + (5.2792e-3 + (2.32e-5 * sin2)) * sin2)
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# z is the height corresponding to p.
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grav = gs * (1 - gamma * z)
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def distance(lon, lat, p=0):
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r"""Calculates the distance in met res between successive points in the
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vectors lon and lat, computed using the Haversine formula on a spherical
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earth of radius 6,371 km, being the radius of a sphere having the same
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volume as Earth. For a spherical Earth of radius 6,371,000 m, one nautical
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mile is 1,853.2488 m, thus one degree of latitude is 111,194.93 m.
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R = earth's radius (mean radius = 6,371 km)
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a = \sin^2(\delta \text{lat}/2) +
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\cos(\text{lat}_1) \cos(\text{lat}_2) \sin^2(\delta \text{lon}/2)
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c = 2 \times \text{atan2}(\sqrt{a}, \sqrt{(1-a)})
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decimal degrees east [0..+360] or [-180 ... +180]
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latitude in decimal degrees north [-90..+90]
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p : number or array_like. Default p = 0
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distance between points on a spherical Earth at pressure (p) [m]
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z is height and is negative in the oceanographic.
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Distances are probably good to better than 1\% of the "true" distance on
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the ellipsoidal earth.
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>>> gsw.distance(lon, lat)
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array([[ 10030974.652916]])
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>>> gsw.distance(lon, lat, p)
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array([[ 10030661.63878009]])
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>>> p = [[200], [1000]]
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>>> gsw.distance(lon, lat, p)
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array([[ 10030661.63878009],
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[ 10029412.58776001]])
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.. [1] http://www.eos.ubc.ca/~rich/map.html
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2000-11-06. Rich Pawlowicz
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2011-04-04. Paul Barker and Trevor McDougall
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#FIXME? The argument handling seems much too complicated.
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# Maybe we can come up with some simple specifications of
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# what argument combinations are permitted, and handle everything
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# with broadcasting. - EF
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#FIXME: Eric what do you think? This assume p(stations, depth)
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lon, lat, = np.atleast_2d(lon), np.atleast_2d(lat)
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if (lon.size == 1) & (lat.size == 1):
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raise ValueError('more than one point is needed to compute distance')
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elif lon.ndim != lat.ndim:
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raise ValueError('lon, lat must have the same dimension')
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lon, lat, p = np.broadcast_arrays(lon, lat, p)
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dlon = np.diff(lon * RAD)
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dlat = np.diff(lat * RAD)
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a = ((np.sin(dlat / 2.)) ** 2 + np.cos(lat[:, :-1] * RAD) *
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np.cos(lat[:, 1:] * RAD) * (np.sin(dlon / 2.)) ** 2)
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# FIXME: Do we need np.ma here?
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angles = 2. * np.arctan2(np.ma.sqrt(a), np.ma.sqrt(1 - a))
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p_mid = 0.5 * (p[:, 0:-1] + p[:, 0:-1])
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lat_mid = 0.5 * (lat[:, :-1] + lat[:, 1:])
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z = z_from_p(p_mid, lat_mid)
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distance = (earth_radius + z) * angles
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if __name__ == '__main__':
added
removed
gsw/gibbs/earth.py
