The definition of viewing geometry depends on which of three
possible representations of the atmosphere are used.
In order of increasing complexity these are:
- Plane-parallel (1D)
- Circular (2D)
The homogeneous case, suitable for representing lab measurements or
horizontal paths in the free atmosphere, is trivial and, apart from
temperature, pressure and composition, the only additional parameter required
to define the 'view' is the path length. For such cases, usually the only
calculation required is of path transmittance.
The plane-parallel representation treats the atmosphere as a set of
horizontal layers. The viewing direction
is specified by secθ (equivalent to an 'air mass factor'),
is the angle with respect to the vertical.
Provided that θ represents the viewing
angle at the surface rather than the satellite,
this generally provides an acceptable simulation for nadir-viewing
instruments, at least for secθ≲2 (or θ≲60°)
The circular atmosphere is the most general case, allowing for the
curvature of the earth, refraction and field-of-view convolution.
The curvature is assumed
fixed over the path length, i.e., profile levels forming concentric circles
in the viewing plane. Viewing directions can be
specified either as tangent heights (for limb-viewing) or elevation
angles α relative to the observer horizontal
(suitable for geometries which intersect the surface or upward views
from within the atmosphere),
in which case the observation altitude is also required.
In principle, nadir-views for the circular
(α=-90°) and plane-parallel (θ=0°) atmospheres are
identical, refraction and curvature having no effect;
however small differences arise from the different path
When running the RFM, the basic viewing geometry is specified in the
driver table by the appropriate flag
in the *FLG section and further
details in the sixth primary section
(labelled *TAN, *GEO, *ELE, *SEC or *LEN).
RFM Homogeneous Path Configuration
For homogeneous path calculations
it is necessary to specify the following in the driver
| The user specifies
volume mixing ratios xi
of absorbing molecules and
a path length S, from which
representing transmittance, absorption or optical depth is calculated.
A radiance R can also be calculated (left of plot)
which will be the sum of the
cell emission Rc and the attenuated
emission Rs of a background surface
of temperature Tsfc.
For surface emissivity
εsfc < 1, Rs
will also include a reflected
component of Rc.
The 'atmosphere' (i.e., temperature, pressure and composition)
for a homogeneous path is specified in the
*ATM section of the driver table, either
using a single profile level
.atm file, and/or directly within the
*ATM section itself using a series
of PARAMETER=VALUE pairs, e.g. TEM=296, CO2=400
- *FLG section
- Add HOM flag, which tells the RFM
that there is a single path segment to be modelled.
- *TAN (or *LEN) section
- Length of path, in km. In fact multiple path lengths can be calculated
at the same time, although I doubt you'll need this feature. The path
length is specified in km for consistency with the units used in the tangent
height definition for limb-viewing, but for
RFM v5.10 onwards you can also specify
alternative units, eg UNITS=CM.
It is assumed that most homogeneous path calculations will be for transmittance
but radiance can also be calculated. Then it is necessary to consider the
boundary condition at the remote end of the path. By default, the RFM assumes
a space view, but by using the SFC flag
and *SFC section, any boundary
temperature and emissivity can be specified.
RFM Plane Parallel Configuration
The plane parallel assumption treats the atmosphere as a series of
horizontally-uniform layers, and the viewing geometry is simply defined by
the (constant) angle of the ray-path with respect to the vertical
The user selects either a Zenith or a Nadir view
and specifies an air-mass factor secθ, where θ is the
angle of the path to the vertical (secθ=1 for a vertical path).
The user specifies atmospheric profiles of
temperature Tj and
volume mixing ratios xi,j
of absorbing molecules at N pressure levels pj.
From this the RFM defines N-1 layers,
each characterised by
parameters TCG, pCG and
partial columns ui.
The upward-looking radiance (at the surface)
Rzen is initialised with the
space background radiance Tspa (usually negligible except
for microwave region).
The downward-looking radiance (from space)
Rnad, for a non-reflective surface
is initialised with the surface emission. Both calculations
then proceed though the atmosphere treating each layer as a homogeneous path.
(For a reflective surface there is first a downward radiance calculation, of
which a reflected component is added to the surface emission.)
Atmospheric transmittance, absorption or optical depth,
represented by τ, is the same for both nadir and zenith directions.
An advantage of this assumption is that Curtis-Godson equivalent paths can
be calculated analytically from the atmospheric profile values, and are the
same for all paths through a layer (for a given absorber) at any angle.
In principle effects such as refraction and field-of-view convolution
could be applied to such an atmosphere, but the RFM only applies these for
the circular geometry.
For basic ray calculations through a plane-parallel atmosphere
it is necessary to specify the
following in the driver table
If nadir-viewing (NAD flag), then the
surface flag (SFC) is also required.
The RFM assumes, by default, that the surface has an emissivity of 1
(i.e., blackbody) and a temperature equal to the temperature at the base of
the atmosphere. These values may be altered using the
*SFC section of the driver table.
ZEN (upward viewing) or
NAD (downward viewing) flags.
*TAN (or *SEC section)
- secθ value of path(s), where θ is the angle to the vertical.
Thus only values secθ ≥ 1 are allowed and secθ=1
specifies a vertical path.
If an observer altitude is specified within the atmosphere
(OBS flag) then the viewing geometry
may alternatively be specified by an elevation angle α, in degrees,
relative to the horizontal. This is done by replacing the
section label *TAN (or *SEC) with *ELE. The RFM
accepts values of 0.1 ≤ |α| ≤ 90.0, where
α=90 corresponds to viewing vertically upward.
Flux calculations (FLX Flag), which
involve integration over solid angle, also use the plane-parallel assumption.
RFM Limb-Viewing Configuration
The default option (ie in the absence of
FLX flags) is for viewing a
circular atmosphere. This includes refraction and allows for
field-of-view convolution. It is necessary to include an altitude
profile in the *ATM section of
driver file since this is required to establish
the local curvature of the atmosphere for ray-tracing.
The ray-path, shown in red can be specified in three ways:
Altitudes are defined (z=0) relative to the radius of curvature
re which also sets the curvature.
- By the refracted tangent height
- By the geometric (or projected) tangent height
- By elevation angle
α, which also requires the observation
The atmosphere is defined in the same way as the plane parallel atmosphere,
although in this case the Curtis-Godson equivalent parameters are
derived for each path separately.
The ray path is specified
how the *TAN section of the
driver file is labelled.
The radius of curvature
for the atmosphere is defined for the altitude 0 km.
By default this is set to a typical earth value (6367.421 km, in
phyadj_dat.f90), but can be altered using the
RADCRV parameter in the
*PHY section of the
- *TAN (usual case)
- Path specified by refracted, or actual, tangent height [km]
- Path specified by geometric, or projected tangent height [km].
That is: the tangent height that would be expected in the absence of any
- Path specified by elevation angle [deg] above horizontal from the
observer. Viewing from above the atmosphere (ie satellites)
this would be a negative number. This also requires the observer
altitude to be set (OBS flag and
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