GeographicLib::GravityModel Class Reference

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

#include <GravityModel.hpp>

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 NormalGravity &	ReferenceEllipsoid () 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	DefaultGravityName ()
static std::string	DefaultGravityPath ()

Private Types
enum	captype {   CAP_NONE = 0U, CAP_G = 1U<<0, CAP_T = 1U<<1, CAP_DELTA = 1U<<2 | CAP_T,   CAP_C = 1U<<3, CAP_GAMMA0 = 1U<<4, CAP_GAMMA = 1U<<5, CAP_ALL = 0x3FU }
typedef Math::real	real

Private Member Functions
	GravityModel (const GravityModel &)
Math::real	InternalT (real X, real Y, real Z, real &deltaX, real &deltaY, real &deltaZ, bool gradp, bool correct) const
GravityModel &	operator= (const GravityModel &)
void	ReadMetadata (const std::string &name)

Private Attributes
real	_amodel
std::vector< real >	_CC
SphericalHarmonic	_correction
real	_corrmult
std::vector< real >	_CS
std::vector< real >	_Cx
std::string	_date
std::string	_description
std::string	_dir
SphericalHarmonic1	_disturbing
real	_dzonal0
NormalGravity	_earth
std::string	_filename
real	_GMmodel
SphericalHarmonic	_gravitational
std::string	_id
std::string	_name
SphericalHarmonic::normalization	_norm
std::vector< real >	_Sx
real	_zeta0
std::vector< real >	_zonal

Static Private Attributes
static const int	idlength_ = 8

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 atmosphere above the point in question; see gravityatmos. Determining the height of the geoid above the ellipsoid 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):

• V = gravitational potential;
• Φ = rotational potential;
• W = V + Φ = T + U = total potential;
• V₀ = normal gravitation potential;
• U = V₀ + Φ = total normal potential;
• T = W − U = V − V₀ = anomalous or disturbing potential;
• g = ∇W = γ + δ;
• f = ∇Φ;
• Γ = ∇V₀;
• γ = ∇U;
• δ = ∇T = gravity disturbance vector = g_P − γ_P;
• δg = gravity disturbance = g_P − γ_P;
• Δg = gravity anomaly vector = g_P − γ_Q; here the line PQ is perpendicular to ellipsoid and the potential at P equals the normal potential at Q;
• Δg = gravity anomaly = g_P − γ_Q;
• (ξ, η) deflection of the vertical, the difference in directions of g_P and γ_Q, ξ = NS, η = EW.
• X, Y, Z, geocentric coordinates;
• x, y, z, local cartesian coordinates used to denote the east, north and up directions.

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

References:

• W. A. Heiskanen and H. Moritz, Physical Geodesy (Freeman, San Francisco, 1967).

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;
  }
}

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

Definition at line 83 of file GravityModel.hpp.

Member Typedef Documentation

typedef Math::real GeographicLib::GravityModel::real

private

Definition at line 85 of file GravityModel.hpp.

Member Enumeration Documentation

enum GeographicLib::GravityModel::captype

private

Enumerator
CAP_NONE
CAP_G
CAP_T
CAP_DELTA
CAP_C
CAP_GAMMA0
CAP_GAMMA
CAP_ALL

Definition at line 104 of file GravityModel.hpp.

enum GeographicLib::GravityModel::mask

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 GravityModel &  )

private

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 src/GravityModel.cpp.

Member Function Documentation

Math::real GeographicLib::GravityModel::AngularVelocity ( ) const

inline

Returns

ω the angular velocity of the model and the ReferenceEllipsoid() (rad s⁻¹).

Definition at line 483 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

• caps |= GravityModel::GRAVITY
• caps |= GravityModel::DISTURBANCE
• caps |= GravityModel::DISTURBING_POTENTIAL
• caps |= GravityModel::SPHERICAL_ANOMALY
• caps |= GravityModel::GEOID_HEIGHT

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 gravityparallel for an example of using GravityCircle (together with OpenMP) to speed up the computation of geoid heights.

Definition at line 307 of file src/GravityModel.cpp.

const std::string& GeographicLib::GravityModel::DateTime ( ) const

inline

Returns

date of the model; if absent, return "UNKNOWN".

Definition at line 441 of file GravityModel.hpp.

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 354 of file src/GravityModel.cpp.

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 341 of file src/GravityModel.cpp.

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 436 of file GravityModel.hpp.

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 s−2).
[out]	deltay	the northerly component of the disturbance vector (m s−2).
[out]	deltaz	the upward component of the disturbance vector (m s−2).

Returns

T the corresponding disturbing potential (m² s⁻²).

Definition at line 297 of file src/GravityModel.cpp.

Math::real GeographicLib::GravityModel::Flattening ( ) const

inline

Returns

f the flattening of the ellipsoid.

Definition at line 489 of file GravityModel.hpp.

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 gravitygeoid.

Definition at line 275 of file src/GravityModel.cpp.

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 s−2).
[out]	gy	the northerly component of the acceleration (m s−2).
[out]	gz	the upward component of the acceleration (m s−2); this is usually negative.

Returns

W the sum of the gravitational and centrifugal potentials (m² s⁻²).

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

Definition at line 289 of file src/GravityModel.cpp.

const std::string& GeographicLib::GravityModel::GravityFile ( ) const

inline

Returns

full file name used to load the gravity model.

Definition at line 446 of file GravityModel.hpp.

const std::string& GeographicLib::GravityModel::GravityModelDirectory ( ) const

inline

Returns

directory used to load the gravity model.

Definition at line 457 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 452 of file GravityModel.hpp.

Math::real GeographicLib::GravityModel::InternalT ( real  X, real  Y, real  Z, real &  deltaX, real &  deltaY, real &  deltaZ, bool  gradp, bool  correct  ) const

private

Definition at line 198 of file src/GravityModel.cpp.

Math::real GeographicLib::GravityModel::MajorRadius ( ) const

inline

Returns

a the equatorial radius of the ellipsoid (meters).

Definition at line 462 of file GravityModel.hpp.

Math::real GeographicLib::GravityModel::MassConstant ( ) const

inline

Returns

GM the mass constant of the model (m³ s⁻²); 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 470 of file GravityModel.hpp.

GravityModel& GeographicLib::GravityModel::operator= ( const GravityModel &  )

private

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 s−2).
[out]	fY	the Y component of the centrifugal acceleration (m s−2).

Returns

Φ the centrifugal potential (m² s⁻²).

This calls NormalGravity::Phi for ReferenceEllipsoid().

Definition at line 381 of file GravityModel.hpp.

void GeographicLib::GravityModel::ReadMetadata ( const std::string &  name )

private

Definition at line 119 of file src/GravityModel.cpp.

const NormalGravity& GeographicLib::GravityModel::ReferenceEllipsoid ( ) const

inline

Returns

the NormalGravity object for the reference ellipsoid.

Definition at line 430 of file GravityModel.hpp.

Math::real GeographicLib::GravityModel::ReferenceMassConstant ( ) const

inline

Returns

GM the mass constant of the ReferenceEllipsoid() (m³ s⁻²).

Definition at line 476 of file GravityModel.hpp.

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 s−2).
[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 gravitygeoid.

Definition at line 249 of file src/GravityModel.cpp.

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 s−2).
[out]	deltaY	the Y component of the gravity disturbance (m s−2).
[out]	deltaZ	the Z component of the gravity disturbance (m s−2).

Returns

T = W - U the disturbing potential (also called the anomalous potential) (m² s⁻²).

Definition at line 326 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 s⁻²).

Definition at line 339 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 s−2).
[out]	gammaY	the Y component of the normal acceleration (m s−2).
[out]	gammaZ	the Z component of the normal acceleration (m s−2).

Returns

U = V₀ + Φ the sum of the normal gravitational and centrifugal potentials (m² s⁻²).

This calls NormalGravity::U for ReferenceEllipsoid().

Definition at line 363 of file GravityModel.hpp.

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 s−2).
[out]	GY	the Y component of the acceleration (m s−2).
[out]	GZ	the Z component of the acceleration (m s−2).

Returns

V = W - Φ the gravitational potential (m² s⁻²).

Definition at line 228 of file src/GravityModel.cpp.

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 s−2).
[out]	gY	the Y component of the acceleration (m s−2).
[out]	gZ	the Z component of the acceleration (m s−2).

Returns

W = V + Φ the sum of the gravitational and centrifugal potentials (m² s⁻²).

This calls NormalGravity::U for ReferenceEllipsoid().

Definition at line 240 of file src/GravityModel.cpp.

Friends And Related Function Documentation

friend class GravityCircle

friend

Definition at line 86 of file GravityModel.hpp.

Member Data Documentation

real GeographicLib::GravityModel::_amodel

private

Definition at line 89 of file GravityModel.hpp.

std::vector<real> GeographicLib::GravityModel::_CC

private

Definition at line 92 of file GravityModel.hpp.

SphericalHarmonic GeographicLib::GravityModel::_correction

private

Definition at line 96 of file GravityModel.hpp.

real GeographicLib::GravityModel::_corrmult

private

Definition at line 89 of file GravityModel.hpp.

std::vector<real> GeographicLib::GravityModel::_CS

private

Definition at line 92 of file GravityModel.hpp.

std::vector<real> GeographicLib::GravityModel::_Cx

private

Definition at line 92 of file GravityModel.hpp.

std::string GeographicLib::GravityModel::_date

private

Definition at line 88 of file GravityModel.hpp.

std::string GeographicLib::GravityModel::_description

private

Definition at line 88 of file GravityModel.hpp.

std::string GeographicLib::GravityModel::_dir

private

Definition at line 88 of file GravityModel.hpp.

SphericalHarmonic1 GeographicLib::GravityModel::_disturbing

private

Definition at line 95 of file GravityModel.hpp.

real GeographicLib::GravityModel::_dzonal0

private

Definition at line 93 of file GravityModel.hpp.

NormalGravity GeographicLib::GravityModel::_earth

private

Definition at line 91 of file GravityModel.hpp.

std::string GeographicLib::GravityModel::_filename

private

Definition at line 88 of file GravityModel.hpp.

real GeographicLib::GravityModel::_GMmodel

private

Definition at line 89 of file GravityModel.hpp.

SphericalHarmonic GeographicLib::GravityModel::_gravitational

private

Definition at line 94 of file GravityModel.hpp.

std::string GeographicLib::GravityModel::_id

private

Definition at line 88 of file GravityModel.hpp.

std::string GeographicLib::GravityModel::_name

private

Definition at line 88 of file GravityModel.hpp.

SphericalHarmonic::normalization GeographicLib::GravityModel::_norm

private

Definition at line 90 of file GravityModel.hpp.

std::vector<real> GeographicLib::GravityModel::_Sx

private

Definition at line 92 of file GravityModel.hpp.

real GeographicLib::GravityModel::_zeta0

private

Definition at line 89 of file GravityModel.hpp.

std::vector<real> GeographicLib::GravityModel::_zonal

private

Definition at line 92 of file GravityModel.hpp.

const int GeographicLib::GravityModel::idlength_ = 8

staticprivate

Definition at line 87 of file GravityModel.hpp.

---

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

• GravityModel.hpp
• src/GravityModel.cpp