GeographicLib::GravityModel Class Reference

Model of the earth's gravity field. More...

#include <GeographicLib/GravityModel.hpp>

List of all members.

Public Types

enum  mask {
  NONE, GRAVITY, DISTURBANCE, DISTURBING_POTENTIAL,
  SPHERICAL_ANOMALY, GEOID_HEIGHT, ALL
}

Public Member Functions

Setting up the gravity model



 GravityModel (const std::string &name, const std::string &path="")
Compute gravity in geodetic coordinates



Math::real Gravity (real lat, real lon, real h, real &gx, real &gy, real &gz) const
Math::real Disturbance (real lat, real lon, real h, real &deltax, real &deltay, real &deltaz) const
Math::real GeoidHeight (real lat, real lon) const
void SphericalAnomaly (real lat, real lon, real h, real &Dg01, real &xi, real &eta) const
Compute gravity in geocentric coordinates



Math::real W (real X, real Y, real Z, real &gX, real &gY, real &gZ) const
Math::real V (real X, real Y, real Z, real &GX, real &GY, real &GZ) const
Math::real T (real X, real Y, real Z, real &deltaX, real &deltaY, real &deltaZ) const
Math::real T (real X, real Y, real Z) const
Math::real U (real X, real Y, real Z, real &gammaX, real &gammaY, real &gammaZ) const
Math::real Phi (real X, real Y, real &fX, real &fY) const
Compute gravity on a circle of constant latitude



GravityCircle Circle (real lat, real h, unsigned caps=ALL) const
Inspector functions



const NormalGravityReferenceEllipsoid () const
const std::string & Description () const
const std::string & DateTime () const
const std::string & GravityFile () const
const std::string & GravityModelName () const
const std::string & GravityModelDirectory () const
Math::real MajorRadius () const
Math::real MassConstant () const
Math::real ReferenceMassConstant () const
Math::real AngularVelocity () const
Math::real Flattening () const

Static Public Member Functions

static std::string DefaultGravityPath ()
static std::string DefaultGravityName ()

Friends

class GravityCircle

Detailed Description

Model of the earth's gravity field.

Evaluate the earth's gravity field according to a model. The supported models treat only the gravitational field exterior to the mass of the earth. When computing the field at points near (but above) the surface of the earth a small correction can be applied to account for the mass of the atomsphere above the point in question; see The effect of the mass of the atmosphere. Determining the geoid height entails correcting for the mass of the earth above the geoid. The egm96 and egm2008 include separate correction terms to account for this mass.

Definitions and terminology (from Heiskanen and Moritz, Sec 2-13):

See Gravity models for details of how to install the gravity model and the data format.

References:

Example of use:

// Example of using the GeographicLib::GravityModel class

#include <iostream>
#include <exception>
#include <GeographicLib/GravityModel.hpp>

using namespace std;
using namespace GeographicLib;

int main() {
  try {
    GravityModel grav("egm96");
    double lat = 27.99, lon = 86.93, h = 8820; // Mt Everest
    double gx, gy, gz;
    grav.Gravity(lat,lon, h, gx, gy, gz);
    cout << gx << " " << gy << " " << gz << "\n";
  }
  catch (const exception& e) {
    cerr << "Caught exception: " << e.what() << "\n";
    return 1;
  }
  return 0;
}

Gravity is a command-line utility providing access to the functionality of GravityModel and GravityCircle.

Definition at line 83 of file GravityModel.hpp.


Member Enumeration Documentation

Bit masks for the capabilities to be given to the GravityCircle object produced by Circle.

Enumerator:
NONE 

No capabilities.

GRAVITY 

Allow calls to GravityCircle::Gravity, GravityCircle::W, and GravityCircle::V.

DISTURBANCE 

Allow calls to GravityCircle::Disturbance and GravityCircle::T.

DISTURBING_POTENTIAL 

Allow calls to GravityCircle::T(real lon) (i.e., computing the disturbing potential and not the gravity disturbance vector).

SPHERICAL_ANOMALY 

Allow calls to GravityCircle::SphericalAnomaly.

GEOID_HEIGHT 

Allow calls to GravityCircle::GeoidHeight.

ALL 

All capabilities.

Definition at line 121 of file GravityModel.hpp.


Constructor & Destructor Documentation

GeographicLib::GravityModel::GravityModel ( const std::string &  name,
const std::string &  path = "" 
) [explicit]

Construct a gravity model.

Parameters:
[in] name the name of the model.
[in] path (optional) directory for data file.
Exceptions:
GeographicErr if the data file cannot be found, is unreadable, or is corrupt.
std::bad_alloc if the memory necessary for storing the model can't be allocated.

A filename is formed by appending ".egm" (World Gravity Model) to the name. If path is specified (and is non-empty), then the file is loaded from directory, path. Otherwise the path is given by DefaultGravityPath().

This file contains the metadata which specifies the properties of the model. The coefficients for the spherical harmonic sums are obtained from a file obtained by appending ".cof" to metadata file (so the filename ends in ".egm.cof").

Definition at line 37 of file GravityModel.cpp.

References GeographicLib::SphericalHarmonic::Coefficients(), DefaultGravityPath(), GeographicLib::NormalGravity::MassConstant(), GeographicLib::SphericalEngine::coeff::mmx(), GeographicLib::SphericalEngine::coeff::N(), GeographicLib::SphericalEngine::coeff::nmx(), GeographicLib::SphericalEngine::coeff::readcoeffs(), and GeographicLib::Math::sq().


Member Function Documentation

Math::real GeographicLib::GravityModel::Gravity ( real  lat,
real  lon,
real  h,
real &  gx,
real &  gy,
real &  gz 
) const

Evaluate the gravity at an arbitrary point above (or below) the ellipsoid.

Parameters:
[in] lat the geographic latitude (degrees).
[in] lon the geographic longitude (degrees).
[in] h the height above the ellipsoid (meters).
[out] gx the easterly component of the acceleration (m s2).
[out] gy the northerly component of the acceleration (m s2).
[out] gz the upward component of the acceleration (m s2); this is usually negative.
Returns:
W the sum of the gravitational and centrifugal potentials.

The function includes the effects of the earth's rotation.

Definition at line 285 of file GravityModel.cpp.

References GeographicLib::NormalGravity::Earth(), and W().

Math::real GeographicLib::GravityModel::Disturbance ( real  lat,
real  lon,
real  h,
real &  deltax,
real &  deltay,
real &  deltaz 
) const

Evaluate the gravity disturbance vector at an arbitrary point above (or below) the ellipsoid.

Parameters:
[in] lat the geographic latitude (degrees).
[in] lon the geographic longitude (degrees).
[in] h the height above the ellipsoid (meters).
[out] deltax the easterly component of the disturbance vector (m s2).
[out] deltay the northerly component of the disturbance vector (m s2).
[out] deltaz the upward component of the disturbance vector (m s2).
Returns:
T the corresponding disturbing potential.

Definition at line 293 of file GravityModel.cpp.

References GeographicLib::NormalGravity::Earth().

Math::real GeographicLib::GravityModel::GeoidHeight ( real  lat,
real  lon 
) const

Evaluate the geoid height.

Parameters:
[in] lat the geographic latitude (degrees).
[in] lon the geographic longitude (degrees).
Returns:
N the height of the geoid above the ReferenceEllipsoid() (meters).

This calls NormalGravity::U for ReferenceEllipsoid(). Some approximations are made in computing the geoid height so that the results of the NGA codes are reproduced accurately. Details are given in Details of the geoid height and anomaly calculations.

Definition at line 271 of file GravityModel.cpp.

References GeographicLib::NormalGravity::Earth(), GeographicLib::Math::hypot(), and GeographicLib::NormalGravity::SurfaceGravity().

void GeographicLib::GravityModel::SphericalAnomaly ( real  lat,
real  lon,
real  h,
real &  Dg01,
real &  xi,
real &  eta 
) const

Evaluate the components of the gravity anomaly vector using the spherical approximation.

Parameters:
[in] lat the geographic latitude (degrees).
[in] lon the geographic longitude (degrees).
[in] h the height above the ellipsoid (meters).
[out] Dg01 the gravity anomaly (m s2).
[out] xi the northerly component of the deflection of the vertical (degrees).
[out] eta the easterly component of the deflection of the vertical (degrees).

The spherical approximation (see Heiskanen and Moritz, Sec 2-14) is used so that the results of the NGA codes are reproduced accurately. approximations used here. Details are given in Details of the geoid height and anomaly calculations.

Definition at line 244 of file GravityModel.cpp.

References GeographicLib::Math::degree(), GeographicLib::NormalGravity::Earth(), GeographicLib::Math::hypot(), and GeographicLib::NormalGravity::U().

Math::real GeographicLib::GravityModel::W ( real  X,
real  Y,
real  Z,
real &  gX,
real &  gY,
real &  gZ 
) const

Evaluate the components of the acceleration due to gravity and the centrifugal acceleration in geocentric coordinates.

Parameters:
[in] X geocentric coordinate of point (meters).
[in] Y geocentric coordinate of point (meters).
[in] Z geocentric coordinate of point (meters).
[out] gX the X component of the acceleration (m s2).
[out] gY the Y component of the acceleration (m s2).
[out] gZ the Z component of the acceleration (m s2).
Returns:
W = V + the sum of the gravitational and centrifugal potentials (m2 s2).

This calls NormalGravity::U for ReferenceEllipsoid().

Definition at line 235 of file GravityModel.cpp.

References GeographicLib::NormalGravity::Phi(), and V().

Referenced by Gravity().

Math::real GeographicLib::GravityModel::V ( real  X,
real  Y,
real  Z,
real &  GX,
real &  GY,
real &  GZ 
) const

Evaluate the components of the acceleration due to gravity in geocentric coordinates.

Parameters:
[in] X geocentric coordinate of point (meters).
[in] Y geocentric coordinate of point (meters).
[in] Z geocentric coordinate of point (meters).
[out] GX the X component of the acceleration (m s2).
[out] GY the Y component of the acceleration (m s2).
[out] GZ the Z component of the acceleration (m s2).
Returns:
V = W - the gravitational potential (m2 s2).

Definition at line 223 of file GravityModel.cpp.

Referenced by W().

Math::real GeographicLib::GravityModel::T ( real  X,
real  Y,
real  Z,
real &  deltaX,
real &  deltaY,
real &  deltaZ 
) const [inline]

Evaluate the components of the gravity disturbance in geocentric coordinates.

Parameters:
[in] X geocentric coordinate of point (meters).
[in] Y geocentric coordinate of point (meters).
[in] Z geocentric coordinate of point (meters).
[out] deltaX the X component of the gravity disturbance (m s2).
[out] deltaY the Y component of the gravity disturbance (m s2).
[out] deltaZ the Z component of the gravity disturbance (m s2).
Returns:
T = W - U the disturbing potential (also called the anomalous potential) (m2 s2).

Definition at line 324 of file GravityModel.hpp.

Math::real GeographicLib::GravityModel::T ( real  X,
real  Y,
real  Z 
) const [inline]

Evaluate disturbing potential in geocentric coordinates.

Parameters:
[in] X geocentric coordinate of point (meters).
[in] Y geocentric coordinate of point (meters).
[in] Z geocentric coordinate of point (meters).
Returns:
T = W - U the disturbing potential (also called the anomalous potential) (m2 s2).

Definition at line 337 of file GravityModel.hpp.

Math::real GeographicLib::GravityModel::U ( real  X,
real  Y,
real  Z,
real &  gammaX,
real &  gammaY,
real &  gammaZ 
) const [inline]

Evaluate the components of the acceleration due to normal gravity and the centrifugal acceleration in geocentric coordinates.

Parameters:
[in] X geocentric coordinate of point (meters).
[in] Y geocentric coordinate of point (meters).
[in] Z geocentric coordinate of point (meters).
[out] gammaX the X component of the normal acceleration (m s2).
[out] gammaY the Y component of the normal acceleration (m s2).
[out] gammaZ the Z component of the normal acceleration (m s2).
Returns:
U = V0 + the sum of the normal gravitational and centrifugal potentials (m2 s2).

This calls NormalGravity::U for ReferenceEllipsoid().

Definition at line 361 of file GravityModel.hpp.

Math::real GeographicLib::GravityModel::Phi ( real  X,
real  Y,
real &  fX,
real &  fY 
) const [inline]

Evaluate the centrifugal acceleration in geocentric coordinates.

Parameters:
[in] X geocentric coordinate of point (meters).
[in] Y geocentric coordinate of point (meters).
[out] fX the X component of the centrifugal acceleration (m s2).
[out] fY the Y component of the centrifugal acceleration (m s2).
Returns:
the centrifugal potential (m2 s2).

This calls NormalGravity::Phi for ReferenceEllipsoid().

Definition at line 379 of file GravityModel.hpp.

GravityCircle GeographicLib::GravityModel::Circle ( real  lat,
real  h,
unsigned  caps = ALL 
) const

Create a GravityCircle object to allow the gravity field at many points with constant lat and h and varying lon to be computed efficiently.

Parameters:
[in] lat latitude of the point (degrees).
[in] h the height of the point above the ellipsoid (meters).
[in] caps bitor'ed combination of GravityModel::mask values specifying the capabilities of the resulting GravityCircle object.
Exceptions:
std::bad_alloc if the memory necessary for creating a GravityCircle can't be allocated.
Returns:
a GravityCircle object whose member functions computes the gravitational field at a particular values of lon.

The GravityModel::mask values are

The default value of caps is GravityModel::ALL which turns on all the capabilities. If an unsupported function is invoked, it will return NaNs. Note that GravityModel::GEOID_HEIGHT will only be honored if h = 0.

If the field at several points on a circle of latitude need to be calculated then creating a GravityCircle object and using its member functions will be substantially faster, especially for high-degree models. See Geoid heights on a multi-processor system for an example of using GravityCircle (together with OpenMP) to speed up the computation of geoid heights.

Definition at line 303 of file GravityModel.cpp.

References GeographicLib::SphericalHarmonic1::Circle(), GeographicLib::SphericalHarmonic::Circle(), GeographicLib::NormalGravity::Earth(), GravityCircle, GeographicLib::Math::hypot(), GeographicLib::Math::NaN(), GeographicLib::NormalGravity::Phi(), GeographicLib::NormalGravity::SurfaceGravity(), and GeographicLib::NormalGravity::U().

const NormalGravity& GeographicLib::GravityModel::ReferenceEllipsoid (  )  const [inline]
Returns:
the NormalGravity object for the reference ellipsoid.

Definition at line 428 of file GravityModel.hpp.

const std::string& GeographicLib::GravityModel::Description (  )  const [inline]
Returns:
the description of the gravity model, if available, in the data file; if absent, return "NONE".

Definition at line 434 of file GravityModel.hpp.

const std::string& GeographicLib::GravityModel::DateTime (  )  const [inline]
Returns:
date of the model; if absent, return "UNKNOWN".

Definition at line 439 of file GravityModel.hpp.

const std::string& GeographicLib::GravityModel::GravityFile (  )  const [inline]
Returns:
full file name used to load the gravity model.

Definition at line 444 of file GravityModel.hpp.

const std::string& GeographicLib::GravityModel::GravityModelName (  )  const [inline]
Returns:
"name" used to load the gravity model (from the first argument of the constructor, but this may be overridden by the model file).

Definition at line 450 of file GravityModel.hpp.

const std::string& GeographicLib::GravityModel::GravityModelDirectory (  )  const [inline]
Returns:
directory used to load the gravity model.

Definition at line 455 of file GravityModel.hpp.

Math::real GeographicLib::GravityModel::MajorRadius (  )  const [inline]
Returns:
a the equatorial radius of the ellipsoid (meters).

Definition at line 460 of file GravityModel.hpp.

Math::real GeographicLib::GravityModel::MassConstant (  )  const [inline]
Returns:
GM the mass constant of the model (m3 s2); this is the product of G the gravitational constant and M the mass of the earth (usually including the mass of the earth's atmosphere).

Definition at line 468 of file GravityModel.hpp.

Math::real GeographicLib::GravityModel::ReferenceMassConstant (  )  const [inline]
Returns:
GM the mass constant of the ReferenceEllipsoid() (m3 s2).

Definition at line 474 of file GravityModel.hpp.

Math::real GeographicLib::GravityModel::AngularVelocity (  )  const [inline]
Returns:
the angular velocity of the model and the ReferenceEllipsoid() (rad s1).

Definition at line 481 of file GravityModel.hpp.

Math::real GeographicLib::GravityModel::Flattening (  )  const [inline]
Returns:
f the flattening of the ellipsoid.

Definition at line 487 of file GravityModel.hpp.

std::string GeographicLib::GravityModel::DefaultGravityPath (  )  [static]
Returns:
the default path for gravity model data files.

This is the value of the environment variable GEOGRAPHICLIB_GRAVITY_PATH, if set; otherwise, it is $GEOGRAPHICLIB_DATA/gravity if the environment variable GEOGRAPHICLIB_DATA is set; otherwise, it is a compile-time default (/usr/local/share/GeographicLib/gravity on non-Windows systems and C:/ProgramData/GeographicLib/gravity on Windows systems).

Definition at line 337 of file GravityModel.cpp.

References GEOGRAPHICLIB_DATA.

Referenced by GravityModel().

std::string GeographicLib::GravityModel::DefaultGravityName (  )  [static]
Returns:
the default name for the gravity model.

This is the value of the environment variable GEOGRAPHICLIB_GRAVITY_NAME, if set; otherwise, it is "egm96". The GravityModel class does not use this function; it is just provided as a convenience for a calling program when constructing a GravityModel object.

Definition at line 350 of file GravityModel.cpp.

References GEOGRAPHICLIB_GRAVITY_DEFAULT_NAME.


Friends And Related Function Documentation

friend class GravityCircle [friend]

Definition at line 86 of file GravityModel.hpp.

Referenced by Circle().


The documentation for this class was generated from the following files:
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