atm_funcs.cc File Reference

This file contains the code of functions releated to atmospheric physics or geometry. More...

#include <math.h>
#include <stdexcept>
#include "arts.h"
#include "matpackI.h"
#include "messages.h"
#include "math_funcs.h"
#include "make_vector.h"

Go to the source code of this file.

Functions
void	planck (MatrixView B, ConstVectorView f, ConstVectorView t)
	Calculates a blackbody radiation (the Planck function) matrix.
void	planck (VectorView B, ConstVectorView f, Numeric t)
	Calculates the Planck function for a single temperature.
void	invplanck (VectorView y, ConstVectorView f, ConstVectorView za)
	Converts a vector with radiances to Plack brightness temperatures.
void	invrayjean (VectorView y, ConstVectorView f, ConstVectorView za)
	Converts a vector with radiances to Rayleigh-Jean brightness temperatures.
Numeric	number_density (Numeric p, Numeric t)
	Calculates the number density (scalar version).
Vector	number_density (ConstVectorView p, ConstVectorView t)
	Calculates the number density (vector version).
Numeric	g_of_z (Numeric r_geoid, Numeric g0, Numeric z)
	Calculates the gravitational accelaration for a geometrical altitude.
Numeric	g_of_lat (Numeric latitude)
	Calculates the gravitational accelaration for a geocentric latitude.
void	rte_iterate (VectorView y, const Index start_index, const Index stop_index, ConstMatrixView tr, ConstMatrixView s, const Index n_f)
	Performs a single iteration for RTE calculations (one zenith angle).
void	rte (VectorView y, const Index start_index, const Index stop_index, ConstMatrixView tr, ConstMatrixView s, ConstVectorView y_space, const Index ground, ConstVectorView e_ground, ConstVectorView y_ground)
	Performs the RTE calculations for one zenith angle.
void	bl_iterate (VectorView y, const Index start_index, const Index stop_index, ConstMatrixView tr, const Index n_f)
	Performs a single iteration for BL calculations (one zenith angle).
void	bl (Vector &y, const Index start_index, const Index stop_index, ConstMatrixView tr, const Index ground, ConstVectorView e_ground)
	Performs the BL (transmission) calculations for one zenith angle.
void	z2p (VectorView p, ConstVectorView z0, ConstVectorView p0, ConstVectorView z)
	Converts an altitude vector to pressures.
void	interpp (VectorView x, ConstVectorView p0, ConstVectorView x0, ConstVectorView p)
	Interpolates a vertical profile at a new set of pressures.
void	interpp_cloud (VectorView x, ConstVectorView p0, ConstVectorView x0, ConstVectorView p)
void	interpp (MatrixView A, ConstVectorView p0, ConstMatrixView A0, ConstVectorView p)
	Interpolates a matrix, such as an absorption matrix, at a new set of pressures.
Numeric	interpp (ConstVectorView p0, ConstVectorView x0, const Numeric p)
	Interpolates a vertical profile at one pressure level.
void	interpz (VectorView x, ConstVectorView p0, ConstVectorView z0, ConstVectorView x0, ConstVectorView z)
	Interpolates a vertical profile at a new set of vertical altitudes.
Numeric	interpz (ConstVectorView p0, ConstVectorView z0, ConstVectorView x0, const Numeric z)
	Interpolates a vertical profile at a single vertical altitude.
Numeric	ztan_geom (const Numeric za, const Numeric z_plat, const Numeric r_geoid)
	Calculates the geometrical tangent altitude (no refraction).
Numeric	n_for_z (const Numeric z, ConstVectorView p_abs, ConstVectorView z_abs, ConstVectorView refr_index, const Numeric atm_limit)
	Returns the refractive index for a vertical altitude.
Numeric	refr_constant (const Numeric r_geoid, const Numeric za, const Numeric z_plat, ConstVectorView p_abs, ConstVectorView z_abs, const Numeric atm_limit, ConstVectorView refr_index)
	Determines the constant for a refractive LOS.
Numeric	ztan_refr (const Numeric c, const Numeric za, const Numeric z_plat, const Numeric z_ground, ConstVectorView p_abs, ConstVectorView z_abs, ConstVectorView refr_index, const Numeric r_geoid)
	Calculates the tangent altitude with refraction.
void	e_eq_water (VectorView e_eq, ConstVectorView t)
	Calculates the equilibrium water vapor pressure over liquid water.
void	e_eq_ice (VectorView e_eq, ConstVectorView t)
	Calculates the equilibrium water vapor pressure over ice.
Variables
const Numeric	DEG2RAD
const Numeric	RAD2DEG
const Numeric	PLANCK_CONST
const Numeric	SPEED_OF_LIGHT
const Numeric	BOLTZMAN_CONST

---

Detailed Description

This file contains the code of functions releated to atmospheric physics or geometry.

Author:

Patrick Eriksson

Date:

2000-09-18

Definition in file atm_funcs.cc.

---

Function Documentation

void bl	(	Vector &	y,
		const Index	start_index,
		const Index	stop_index,
		ConstMatrixView	tr,
		const Index	ground,
		ConstVectorView	e_ground
	)

Performs the BL (transmission) calculations for one zenith angle.

This function allows calculation of transmission spectra for single zenith angles in functions beside yBlXx.

Return values:

y

the spectrum

Parameters:

	start_index	start index for the integration
	stop_index	stop index for the integration
	Tr	transmission matrix
	ground	flag/index for ground intersection
	e_ground	ground emissivity

Author:

Patrick Eriksson

Date:

2000-04-08

Definition at line 560 of file atm_funcs.cc.

void bl_iterate	(	VectorView	y,
		const Index	start_index,
		const Index	stop_index,
		ConstMatrixView	tr,
		const Index	n_f
	)

Performs a single iteration for BL calculations (one zenith angle).

The vector Y is not initilised, Y is multiplied with the obtained values. Note that only a single iteration is performed.

This function can be used to calculate transmissions for parts of the atmosphere.

Return values:

y

the spectrum

Parameters:

	start_index	start index for the integration
	stop_index	stop index for the integration
	Tr	transmission matrix
	S	source function matrix
	n_f	number of frequencies

Author:

Patrick Eriksson

Date:

2000-04-08

Definition at line 518 of file atm_funcs.cc.

void e_eq_ice	(	VectorView	e_eq,
		ConstVectorView	t
	)

Calculates the equilibrium water vapor pressure over ice.

Calculation is done using Sontag's formula. Sonntag, D., Advancements in the field of hygrometry, Meteorologische Zeitschrift, 3, 51-66, 1994.

Sontag's formula:

e_eq = exp( a/T + b + c*T + d*T^2 + e*log(T) )

Return values:

e_eq

equilibrium water vapor pressure in [Pa]

Parameters:

t

a temperature value in [K]

Author:

Mashrab Kuvatov

Date:

2003-12-08

Definition at line 1038 of file atm_funcs.cc.

void e_eq_water	(	VectorView	e_eq,
		ConstVectorView	t
	)

Calculates the equilibrium water vapor pressure over liquid water.

Calculation is done using Sontag's formula. Sonntag, D., Advancements in the field of hygrometry, Meteorologische Zeitschrift, 3, 51-66, 1994.

Sontag's formula:

e_eq = exp( a/T + b + c*T + d*T^2 + e*log(T) )

Return values:

e_eq

equilibrium water vapor pressure in [Pa]

Parameters:

t

a temperature value in [K]

Author:

Mashrab Kuvatov

Date:

2003-12-08

Definition at line 998 of file atm_funcs.cc.

Numeric g_of_lat

(

Numeric

latitude

)

Calculates the gravitational accelaration for a geocentric latitude.

Returns:

the gravitational constant

Parameters:

lat

geocentric latitude

Author:

Axel von Engeln

Date:

2003-07-24

Definition at line 340 of file atm_funcs.cc.

Numeric g_of_z	(	Numeric	r_geoid,
		Numeric	g0,
		Numeric	z
	)

Calculates the gravitational accelaration for a geometrical altitude.

Returns:

the gravitational constant

Parameters:

	r_geoid	radius of the geoid
	g0	the gravitational constant at the geoid surface
	z	geometrical altitude

Author:

Patrick Eriksson

Date:

2000-12-04

Definition at line 322 of file atm_funcs.cc.

Numeric interpp	(	ConstVectorView	p0,
		ConstVectorView	x0,
		const Numeric	p
	)

Interpolates a vertical profile at one pressure level.

See the vector version.

Return values:

x

output: the interpolated values at p

Parameters:

	p0	original pressure grid
	x0	the profile to be interpolated
	p	a pressure level

Author:

Patrick Eriksson

Date:

2000-12-04

Definition at line 739 of file atm_funcs.cc.

void interpp	(	MatrixView	A,
		ConstVectorView	p0,
		ConstMatrixView	A0,
		ConstVectorView	p
	)

Interpolates a matrix, such as an absorption matrix, at a new set of pressures.

A linear interpolation using log. pressure is applied. In Matlab notation, the following expression is used:

A = interp1(log(p0),A0,log(p),'linear')

Return values:

A

output: the interpolated values at p

Parameters:

	p0	original pressure grid
	A0	the matrix to be interpolated
	p	new pressure grid

Author:

Patrick Eriksson

Date:

2000-04-08

Definition at line 705 of file atm_funcs.cc.

void interpp	(	VectorView	x,
		ConstVectorView	p0,
		ConstVectorView	x0,
		ConstVectorView	p
	)

Interpolates a vertical profile at a new set of pressures.

A linear interpolation using log. pressure is applied. In Matlab notation, the following expression is used:

p = interp1(log(p0),x,log(p),'linear')

Return values:

x

output: the interpolated values at p

Parameters:

	p0	original pressure grid
	x0	the profile to be interpolated
	p	new pressure grid

Author:

Patrick Eriksson

Date:

2000-04-08

Definition at line 658 of file atm_funcs.cc.

void interpp_cloud	(	VectorView	x,
		ConstVectorView	p0,
		ConstVectorView	x0,
		ConstVectorView	p
	)

Definition at line 675 of file atm_funcs.cc.

Numeric interpz	(	ConstVectorView	p0,
		ConstVectorView	z0,
		ConstVectorView	x0,
		const Numeric	z
	)

Interpolates a vertical profile at a single vertical altitude.

NOTE!! Avoid to use this function, interpolation should mainly be done in pressure, that is, use interpp when possible.

This function uses z2p and interpp to make an interpolation for a vertical altitude.

Used mainly for LOS calculations with refraction.

Return values:

x

output: the interpolated values at z

Parameters:

	p0	original pressure grid
	z0	original vertical altitude grid
	x0	the profile to be interpolated
	z	new vertical altitude grid

Author:

Patrick Eriksson

Date:

2000-10-02

Definition at line 810 of file atm_funcs.cc.

void interpz	(	VectorView	x,
		ConstVectorView	p0,
		ConstVectorView	z0,
		ConstVectorView	x0,
		ConstVectorView	z
	)

Interpolates a vertical profile at a new set of vertical altitudes.

NOTE!! Avoid to use this function, interpolation should mainly be done in pressure, that is, use interpp when possible.

This function uses z2p and interpp to make an interpolation for vertical altitudes.

Used mainly for LOS calculations with refraction.

Return values:

x

output: the interpolated values at z

Parameters:

	p0	original pressure grid
	z0	original vertical altitude grid
	x0	the profile to be interpolated
	z	new vertical altitude grid

Author:

Patrick Eriksson

Date:

2000-10-02

Definition at line 774 of file atm_funcs.cc.

void invplanck	(	VectorView	y,
		ConstVectorView	f,
		ConstVectorView	za
	)

Converts a vector with radiances to Plack brightness temperatures.

Return values:

y

spectrum vector

Parameters:

	f	frequencies
	za	zenith angles

Author:

Patrick Eriksson

Date:

2000-09-28

Definition at line 145 of file atm_funcs.cc.

void invrayjean	(	VectorView	y,
		ConstVectorView	f,
		ConstVectorView	za
	)

Converts a vector with radiances to Rayleigh-Jean brightness temperatures.

Return values:

y

spectrum vector

Parameters:

	f	frequencies
	za	zenith angles

Author:

Patrick Eriksson

Date:

2000-09-28

Definition at line 202 of file atm_funcs.cc.

Numeric n_for_z	(	const Numeric	z,
		ConstVectorView	p_abs,
		ConstVectorView	z_abs,
		ConstVectorView	refr_index,
		const Numeric	atm_limit
	)

Returns the refractive index for a vertical altitude.

The refractive index is set to 1 if the given altitude is above the atmospheric limit.

Returns:

the refrcative index

Parameters:

	z	the vertical altitude
	p_abs	absorption pressure grid
	z_abs	absorption altitude grid
	refr_index	refrective index corresponding to p_refr
	atm_limit	the upper atmospheric limit

Author:

Patrick Eriksson

Date:

2001-02-18

Definition at line 871 of file atm_funcs.cc.

Vector number_density	(	ConstVectorView	p,
		ConstVectorView	t
	)

Calculates the number density (vector version).

Returns:

number density

Parameters:

	p	pressure
	t	temperature

Author:

Patrick Eriksson

Date:

2000-04-08

Definition at line 291 of file atm_funcs.cc.

Numeric number_density	(	Numeric	p,
		Numeric	t
	)

Calculates the number density (scalar version).

Returns:

number density

Parameters:

	p	pressure
	t	temperature

Author:

Patrick Eriksson

Date:

2000-04-08

Definition at line 270 of file atm_funcs.cc.

void planck	(	VectorView	B,
		ConstVectorView	f,
		Numeric	t
	)

Calculates the Planck function for a single temperature.

Return values:

B

output: the blackbody radiation

Parameters:

	f	a frequency grid
	t	a temperature value

Author:

Patrick Eriksson

Date:

2000-04-08

Definition at line 114 of file atm_funcs.cc.

void planck	(	MatrixView	B,
		ConstVectorView	f,
		ConstVectorView	t
	)

Calculates a blackbody radiation (the Planck function) matrix.

Each row of the returned matrix corresponds to a frequency, while each column corresponds to a temperature.

Return values:

B

output: the blackbody radiation

Parameters:

	f	a frequency grid
	t	a temperature profile

Author:

Patrick Eriksson

Date:

2000-04-08

Definition at line 75 of file atm_funcs.cc.

Numeric refr_constant	(	const Numeric	r_geoid,
		const Numeric	za,
		const Numeric	z_plat,
		ConstVectorView	p_abs,
		ConstVectorView	z_abs,
		const Numeric	atm_limit,
		ConstVectorView	refr_index
	)

Determines the constant for a refractive LOS.

Calculates (Re+z)*n(z)*sin(theta) at the platform.

All observations geometries are handled. The variables za and z_plat shall be treated as the "zenith angle" and the vertical altitude of the lowest point of the LOS.

Returns:

LOS constant

Parameters:

	r_geoid	local geoid curvature
	za	zenith angle
	z_plat	platform altitude
	p_abs	absorption pressure grid
	z_abs	absorption altitude grid
	atm_limit	the upper atmospheric limit
	refr_index	refrective index corresponding to p_refr

Author:

Patrick Eriksson

Date:

2001-02-18

Definition at line 908 of file atm_funcs.cc.

void rte	(	VectorView	y,
		const Index	start_index,
		const Index	stop_index,
		ConstMatrixView	tr,
		ConstMatrixView	s,
		ConstVectorView	y_space,
		const Index	ground,
		ConstVectorView	e_ground,
		ConstVectorView	y_ground
	)

Performs the RTE calculations for one zenith angle.

This function allows calculation of emission spectra for single zenith angles in function beside yRteXx.

Return values:

y

the spectrum

Parameters:

	start_index	start index for the integration
	stop_index	stop index for the integration
	Tr	transmission matrix
	S	source function matrix
	y_space	intensity entering the atmosphre at start of LOS
	ground	flag/index for ground intersection
	e_ground	ground emissivity
	y_ground	ground blackbody radiation

Author:

Patrick Eriksson

Date:

2000-04-08

Definition at line 433 of file atm_funcs.cc.

void rte_iterate	(	VectorView	y,
		const Index	start_index,
		const Index	stop_index,
		ConstMatrixView	tr,
		ConstMatrixView	s,
		const Index	n_f
	)

Performs a single iteration for RTE calculations (one zenith angle).

The vector Y is not initilised, the obtained values are added to Y. Note that only a single iteration is performed.

This function can be used to calculate emission spectra for parts of the atmosphere.

Return values:

y

the spectrum

Parameters:

	start_index	start index for the integration
	stop_index	stop index for the integration
	Tr	transmission matrix
	S	source function matrix
	n_f	number of frequencies

Author:

Patrick Eriksson

Date:

2000-04-08

Definition at line 386 of file atm_funcs.cc.

void z2p	(	VectorView	p,
		ConstVectorView	z0,
		ConstVectorView	p0,
		ConstVectorView	z
	)

Converts an altitude vector to pressures.

The log of the pressures are interpolated linearly. In Matlab notation:

p = exp(interp1(z0,log(p0),z,'linear'))

Return values:

p

output: the pressures at z

Parameters:

	z0	original altitude grid
	p0	original pressure grid
	z	new altitude grid

Author:

Patrick Eriksson

Date:

2000-04-08

Definition at line 621 of file atm_funcs.cc.

Numeric ztan_geom	(	const Numeric	za,
		const Numeric	z_plat,
		const Numeric	r_geoid
	)

Calculates the geometrical tangent altitude (no refraction).

Returns:

the tangent altitude

Parameters:

	za	the angle between zenith and the LOS
	z_plat	the platform altitude

Author:

Patrick Eriksson

Date:

2000-04-08

Definition at line 839 of file atm_funcs.cc.

Numeric ztan_refr	(	const Numeric	c,
		const Numeric	za,
		const Numeric	z_plat,
		const Numeric	z_ground,
		ConstVectorView	p_abs,
		ConstVectorView	z_abs,
		ConstVectorView	refr_index,
		const Numeric	r_geoid
	)

Calculates the tangent altitude with refraction.

Returns:

the tangent altitude

Parameters:

	c	LOS constant
	za	the angle between zenith and the LOS
	z_plat	the platform altitude
	z_ground	the ground altitude
	p_abs	absorption pressure grid
	z_abs	absorption altitude grid
	refr_index	refrective index corresponding to p_abs

Author:

Patrick Eriksson

Date:

2000-10-02

Definition at line 940 of file atm_funcs.cc.

---

Variable Documentation

const Numeric BOLTZMAN_CONST

const Numeric DEG2RAD

const Numeric PLANCK_CONST

const Numeric RAD2DEG

const Numeric SPEED_OF_LIGHT