Minutes of the Radiative Transfer Workshop
Bremen, April 26-29, 1999
*** List of Participants: (name, affiliation, email, initials) ****
(in alphabetical order)
Stefan Buehler IFE firstname.lastname@example.org SB
Patrick Eriksson IFE email@example.com PE
Johannes Kaiser IFE firstname.lastname@example.org JK
Yasuko Kasai CRL email@example.com YK
Miriam von Koenig IFE firstname.lastname@example.org MK
Klaus Kuenzi IFE email@example.com KK
Thomas Kuhn-Sander IFE firstname.lastname@example.org TK
Nicolas Lautie OBX email@example.com NL
Frank Merino MISU firstname.lastname@example.org FM
Jungang Miao IFE email@example.com JM
Satoshi Ochiai CRL firstname.lastname@example.org SO
Joachim Urban OBX email@example.com JU
Carmen Verdes IFE firstname.lastname@example.org CV
*** Addresses: ******************************************
Communications Research Laboratory
Global Environment Division
Institute of Remote Sensing
University of Bremen
28353 Bremen, Germany
Observatoire de Bordeaux
33270 Floirac, France
===== April 26, Afternoon ======
1. Welcome by Prof. KK.
2. Introduction by SB
o Goals of the workshop:
- Need of a new forward model in Bremen
- No discussions about the implementation, we want to
- focus on physics and algorithms. Gather alternatives.
- Contributions of the participants will be collected after the
workshop and published as a report or something similar.
o Finished model
- Will be public available, similarly to GNU programs
- Strong emphasis on modularity
o The agenda
3. Presentation of existing models
o measures scattered sunlight
o absorption is included, but no thermal emission
o pseudo-spherical geometry
o full spherical geometry
- data bases
- includes thermal emission
o everything else similar to GOMETRAN
o there already was a single scattering prototype
Q: KK: Mie Scattering
PE: Quasi analytical weighting functions, what means
answer: exactly what you mean by "analytical w.f."
JU: Is spherical standard?
o Nov 96 Workshop in Gothenburg, organised by PE
o two parallel codes, skuld and moliere
- user friendly
- accurate and fast (weighting functions!)
o controlled by control file
o user manual available (plus report)
o geometries: limb/ground
- line by line
- Liebe 93 for O2, H2O, N2
- Verdandi catalogue
- line shape specified by the user
- optional refraction (Snell's law)
- tangent altitudes specified as viewing angles
- integration along the line of sight with arbitrary step length
- sum up homogenous layers
o instrumental effects
- antenna pattern
+ Odin simulated
+ static or moving beam
- side bands
+ primary plus image band
+ frequency dependent sideband ratio stored in file
+ shape of each channel described by response curve
- Doppler shift
- data binning
- thermal noise
- weighting functions
Skuld part 2 (PE)
o data binning
- different binning pattern for each viewing angle
(but same number!)
- spectra can be removed (e.g., if opacity is too high)
- binning data stored in file
o species weighting functions
- treated as part of the forward model
- incl. sensor characteristics
- normalised to a priori, VMR, number density
- arbitrary grid, but same for all species
- retrieval grid consists of layers
o other weighting functions
- spectro parameters
- pointing offset
- interfering species
- frequency shift (not useful, too non-linear)
- 3 geometries
- no hard coded frequency limit
- sensor model by matrix approach
- weighting functions:
+ for as many variables as possible
+ analytical for T, no hydrostatic eq.
+ both offset and polynomial representation for pointing and
Q: JU: Scattering in IR? --- No
MOLIERE (JU and NL)
o Philippe Baron's
o different models
o combined forward/inversion model
o abs line by line using Verdandi
- Liebe 93
Q: KK: Cross check with Skuld? --- Yes (difference only due to
different Voigt algorithm)
MAES at CRL (SO, YK)
o catalogue JPL or HITRAN
o LS: Lorenz or Voigt, dep. on pressure
o limb or ground-based
- total abs coef. for each layer
- calculate tau
- integrate by trapezoidal method
o antenna pattern included
o C/UNIX program
o config file, ASCI
- pressure broadening parameter database
- p-shift, Doppler shift missing
- far wing line shape (is this really a problem?)
- speed, necessary:
+ line selection
+ different frequency grid between emission and tau calculation
(for weighting functions)
- how to quickly calculate the average emission in the passband
of a filter
Q: KK: Who includes p-shift? --- just IFE
IFE - forward model (SB)
o Long history, presently model started early 90īs
o Implementation well validated by several intercomparison
o Mix of Pascal, Fortran and C
o Standard structure
o Absorption coefficients:
- JPL and MYTRAN
- All species of JPL/HITRAN
- Pressure shift
- Special treatment of 60 GHz oxygen cluster
- Several continuum models (Liebe, CKD and Rosenkranz)
- Twin-Voigt lineshape based on Drayson Voigt-algorithm
- P-shift included where data available
- Geometries: zenith, limb and nadir
- Tangent altitudes are used (not viewing angles)
- Adaptive layer breakup, depending on opacity
- Linear or exponential interpolation of abs. coefficients
- Ground: two emissivities (horizontal and vertical polarisation)
- Refraction (needs very fine layering to be accurate)
o Instrumental parameters
- Antenna, sideband and spectrometer
o Meta features
- Line selection (only for JPL)
- Frequency grid selection (only JPL and narrow bands)
o Missing features
- Analytical limb WF
- Automatic selection of angular and frequency grids
- General, validated and accurate
- Chaotic code
- Not portable, runs only on IBM RS 6000
- No documentation
- No dynamical memory handling
o Scattering so far has been handled by separate code
4. Discussion of desired features for the new model. Results:
o 1 = essential, 2 = ----, 3 = optional, 4 = not at all
o Refraction, 1
o Zeeman, 3 (but leave this possibility, not to be discussed here)
o Scattering, 2
o 2-D, 3
o Pressure shift: 1
o Geometries: up, down and limb
o Only emission measurements
o Continuum: 1
o The range around 60 GHz, 2
o Only LTE
o Weighting functions: 1
o Data binning: 1
o Sensor: 1
- Antenna: 1
- Sideband: 1
- Spectrometer: 1
- Baseline ripple: ? -- 4
- Doppler: 4
5. Discussion of line catalogue contents and format:
o Line format, changes to the MYTRAN/Verdandi format
- Add reference temperature for pressure broadening (already in MYTRAN)
- Add reference temperature for intensity
- Add overlap parameters
- Add Zeeman splitting constant(s)
- Not include degree of freedom for the molecule
- The source of the spectral data should be included
o Labelling of lines
- Two schemes exist, JPL and HITRAN
- Symbolic representation, e.g. H2O-18
- Difficult to find a symbolic name scheme. Is it possible?
- AI: IFE looks into this problem and sends out a specific
suggestion after the workshop
o Partition functions
- The total partition function shall be given
- Different interpolation schemes can give differences of some percent
- Give the the partition function as polynomial coefficient
- Interesting temperature range 150 - 300 K
- Frequency range as HITRAN
===== April 27, Morning ======
1. Introduction of PE: Again about the purpose of the workshop:
o Participants should state what he/she wants to have integrated in
2. Topic of discussion: Radiative transfer equation (RTE)
o theoretical introduction of this problem by PE (geometrical
considerations sensor <-> path of view and refraction).
o short presentations of the different ways to tackle the problem
for the different existing FMs:
* Equally spaced horizontal grid points (129 points
between tangent altitude point and end of 120 km thick
radial atmospheric layer).
* Logarithmic interpolation between horizontally successive
points of calculated absorption coefficients to calculate the
* Calculating absorption coefficients at each tangent altitude.
* Linear interpolation in the vertical direction.
* Calculating the tangent altitude first. Then divide the
horizontal line of view into equidistant parts. These
grid points are different from the points where the absorption
coefficients are calculated. To get the information of the
abs. coeff. at the horizontal grid points of interest, a linear
interpolation is used.
=> SB: Far from line center an exponential interpolation is
But the accuracy is also strongly dependent on
the grid spacing.
* The absorption coeff. is assumed to be constant in each
horizontal grid interval respectively.
* The atmosphere along the line of view is assumed
symmetric to the tangent point (space <-> tangent point
and tangent point <-> sensor).
* The effect of refraction bends the "line of view" to the
earth due to Snellīs law for spherical layers (see
PEīs thesis p. 246).
* code is very similar to that of Skuld. The way how the
refraction is implemented is different to the Swedish one.
The expression for the refraction is linearized in a
Taylor series around the known (but false) geometrical tangent height.
But a problem can be, that the true tangent height can
differ considerably from the geometrical tangent
height and this can lead to not reliable results of the
=> SB: how can the refraction be treated in an
experiment with limb sounding from a balloon or aircraft.
=> PE: occultation sounding is even more difficult to
implement into a FM.
=> PE: refraction index for dry air and water vapor
depends differently on frequency. Dry air is more
or less constant below 1 THz, where the refraction index
for water vapor shows some resonance structures at strong
water vapor lines (picture from his thesis).
* Calculating the contribution to the intensity from each vertical
* A normal sum over all vertical intervals is not very
accurate near the tangent point. If the opacity is too
high (above a threshold value), then the interval will
be split in further smaller intervals. But this is
a danger of the FM, because it is not really transparent
what actually is done by the FM (-> frequency dependence?).
=> JUR: this threshold vale is not optimized for speed.
Therefore this way of doing is in fact not so
obscure. But anyway it should be removed.
o Question of interpolation: Temperature is constant
throughout an interval and the abs. coeff. is
supposed to be linear increasing in the BREMEN-FM.
PE ran into the error function when he assumed
both Temperature and abs. coeff. as linear increasing.
-> what should be assumed inside a layer for temp. and
abs. coeff. constant or linear?
o Integration in equal opacity levels? --> Theoretically better,
but not very efficient (opacity has to be calculated on fine grid
o ->Problems: how to interpolate VMR and number density (pressure).
VMR is assumed linear, and number density (or pressure) exponential.
This point is connected with the question which coordinate system,
pressure or tangent altitude, is used. Temperature is also assumed linear.
The absorption coefficient is proportional to pressure in the far
wing of the line but not near the line center. Therefore one should
implement linear as well as exponential interpolation. The
selection of an interpolation method for the abs. coeff. in a layer
depends strongly on the width of this layer.
o approaches for interpolations?
Skuld interpolates linearly between vertical VMR profile points.
=> SB: what is meant with effective abs. coeff. and effective
temp. in an vertical layer?
PE: if the temp. is constant then eff. abs. coeff. is the
Conclusion: implementation of both strategies: linear and
constant for the abs. coeff and constant for temperature for
vertical layers. But there is no general rule because it also
depends strongly on the vertical layers you implement in the FM.
===== April 27, Afternoon ======
o Definition of observation geometries?
=> PE: viewing angle is the natural coordinate for limb sounding.
o RTE in pressure steps?
Pressure, temperature and altitude are the three quantities of
concern. but with hydrostatic equilibrium assumption and ideal gas law
these three are correlated.
Spherical geometry has to be considered for this question
(air mass function).
Conclusions: do not assume hydrostatic equilibrium in advance. One
has to consider all three variables as input into
the FM. Hydrostatic balance can be enforced before,
o Because of the future need, the new FM should be usable for limb
sounding from the aircraft and the balloon.
o 2 D
- Horizontal structure.
- Particularly useful if observation in the orbit plane.
- Approach: ray tracing (needs alpha and T on 2 D grid).
- One looses the symmetry around the tangent point.
- No principal problems, just higher computation time.
- Usual approach to antenna convolution not possible (because
sensor movement). Needs explicit set of pencil beam
calculations for each tangent altitude.
- There are smart ways to avoid calculating so many absorption
coefficients (e.g., pre-calculate for mean and some other
states and interpolate).
- Just practical (computation time), no principal difficulties.
o Single scattering (Intro by JK)
- need to do pencil beam computation in all directions for
radiation scattered into the beam.
- SB: Most dramatic difference comes from the change in
EXTINCTION. (For limb geometry, according to MASTER study,
conducted at IFE)
- different sources:
+ thermal emission in place
+ direct solar light
+ thermal emission around (from all directions)
- MK: What about polarization.
- JM: Calculation of phase function is the real problem.
- For inclusion in extinction only you don't need phase function,
just scattering coefficient.
- JM: How to calculate weighting functions?
- JM: Quantitative results only with polarization
- The hierarchy of increasing effort:
1. Extinction only
o need scattering coefficients (spherical particles)
o absorption == extinction no longe holds, but this is just a
small change in the RTE
2. Also include radiation scattered into LOS from other
o Different possible sources (sun, thermal)
o RTE integration in all directions (no azimuthal dependency,
for this `correction' maybe assume flat earth.)
3. Same thing polarized (has been done for nadir, by Evans)
4. Above thing with multiple scattering, but not polarized
(This has already been done, e.g., SHDOM)
5. Both multiple-scattering and polarized.
(This has never been done so far.)
3. Calculation of absorption coefficient revisited
o Spectral line catalogue --> yesterday
o Format/units --> skipped
o Merging/conversion tools
- AI Bordeaux to look for Philippes program which appears to be
- Reliable parameters: Quantum numbers
- YK: JPL quantum number system is better
- AI YK: Write document how to convert JPL QN to HITRAN QN
o Line shape function
- Use single Voigt function for all altitudes for all species
except H2O and O2
- (nu/nu_0)^2 term? --> yes
- Problem: oxygen, h2o
o What is the best Voigt implementation?
o Speed issues:
- maybe tabulated line shape functions
- JU: neglecting something only way to really improve speed
o Should refractive index be calculated for all gases, or just for
oxygen and water vapor (continua)?
--> PEs data indicates that effect of lines is small
--> Simple, so include it.
o Overlap correction:
+ O2, HNO3?, HCl?
- Additional parameter delta (needs three additional line
- PE: Define outside the model (don't hardcode)
+ Rosenkranz or NEW CKD (look at new CKD).
TASK LIST for Proceedings (starting yesterday)
o Summary of existing models
o Absorption (Line catalogue)
- YK: JPL and HITRAN quantum numbers
- NL to look for Philippes program which appears to be lost
- Verdandi description (PE)
- Draft a format (IFE)
o Absorption (general)
- Absorption intro (SB)
- Continuum Models (TK)
- Planned lab measurements (YK)
- How to calculate p-shift (SB)
- Simple parameterizations for refraction (NL)
( - ask Agnes Perrin where p-shift and line mixing effects have to be
expected (SB) )
- Sources for extinction coefficients (Spherical cloud particles) (JM)
- Detailed descriptions for Skuld (as intro) (PE)
- 2 D (IFE)
- Need of altitude profiles (think over, possibly write something,
or discuss later during the workshop) (all)
- Scattering (JK)
===== April 28, Morning ======
o Weighting Functions: which variables should be included ?
Species, Temperature, Absorption offsets etc.
- SB gave an introduction about weighting functions.
- PE shows the analytical derivation of WFs inside Skuld.
In this program the FM is split up into two sub-models: one
for the atmospheric physics (FMP) and one for the sensor (FMS),
FM = FMP & FMS. FMP is an input of FMS.
Another question is the units one uses inside the FM, e.g. for the
concentrations of the species.
=> MK: If the weighting functions are calculated at slightly
different points from the retrieved VMR, then an
interpolation has to be done. She interpolate linearly,
where PE uses a step function for Skuld. The grid for the
weighting functions should be finer than that for the
The retrieval grid is not as fine as the calculation grid for the weighting
function (normally). Therefore the question is how the weighting
function value for the coarser retrieval grid can be calculated
from the weighting functions for the finer grid. (Two issues:
1. Conversion from grid equally spaced along line of sight to grid
equally spaced in the vertical; 2. How to assign weights, so that
the weighting functions on the vertical grid are consistent with
the idea that the profile is represented by point values with
linear interpolation between points.)
=> JK: The weighting functions already have a
internal weight proportional to the layer thickness
they cover. Therefore a weighted sum of the weighting
functions is not necessary, instead an ordinary sum
=> JM: Explained the meaning of total and differential weighting functions.
The differential weighting functions have already
the information about their covered layer thickness.
- SO showed how MAES tackles the problem of weighting function
calculations. He said that MAES is not in a final state and has to be
refined, checked and verified in future. This FM uses a completely
different concept/approach for weighting functions as, e.g., Skuld
- NL: if the weighting function is divided by the vertical
layer thickness then this new term is free of thickness weighting
and one can use this expression ("normalized weighting function")
for the contribution along the line of sight in limb sounding.
- SB: for which quantities should the weighting functions be
- Trace gas species (analytically)
+ without hydrostatic ( (semi)-analytically )
+ with hydrostatic (by perturbation)
- Absorption offsets (analytically)
o Work for the proceedings:
description (e.g. which quantities ?) of the concept/approach of the
weighting function algorithms will be written by the following
PE / FM (Skuld)
JU / NL (Moliere)
SO / YK (MAES)
MK should think and write (for the proceedings!) about the topic of
a proper normalizing of the weighting functions.
o Weighting Functions: how to calculate - numerically or analytically?
- SB: for the species it should be possible to calculate the
weighting functions analytically.
For the temperature, it should be analytically in the case of
non hydrostatic equilibrium and numerically (perturbed) in the
case of hydrostatic equilibrium.
- Analytical calculation is much faster than numerical in the
case of weighting functions.
- PE: one can analytically express the derivative of the
abs. coeff. to temperature if one makes some approximations.
- SB: description of the absorption offset used in the MASTER
study. Which assumption about the abs. offset is taken depends on
the width of the frequency band considered. For wide bands, a
quadratic offset gives good results, but for narrow bands, a
linear offset is more appropriate, because one can badly determine
the quadratic shape in this case.
In the FM, weighting functions for a quadratic/linear abs. offset
should be implemented.
- SB: The pointing can be described by a polynomial.
- Perturbation calculations for other parameters:
Should these really be implemented in the FM or should they be
done by the retrieval model in the sense, that in the retrieval
model one can call the FM with slightly different parameters.
====== April 28, Afternoon ======
- Weighting functions by perturbation (continued)
List (not necessary complete) of parameters which could be considered:
# spectroscopic parameters
# instrumental parameters
antenna far wing, sideband, spectrometer
o Modeling of instrumental parameters is the new topic.
- Inventory of instrument characteristics
# sideband integration
# filterbank integration
# antenna integration
# Doppler shift (?)
- Does it have an impact in which order the steps are taken?
SB: Gives the formulas for sideband and antenna integration,
how the IFE-FM is doing this.
FM: it makes a difference in which order the antenna and
sideband integration is done, because the antenna pattern is
The correct order of the instrumental effects is:
1. antenna pattern
2. sideband convolution
3. filterbank (it has then to be mirrored).
SB: is it allowed from the physical point of view to
interchange point 2. and 3. ?
--> Probably yes. Anyway, keeping the right order is no problem.
- The question was after discussed, in which way one should
implement these three points. Each effect can be expressed as a
matrix vector multiplication. Instead of doing repeated matrix vector
multiplications, one can multiply the matrices associated with the
different effects directly.
- SB: Shows the formulas for the calculation of the
side band ratio. There are two different formulations in the
literature (see SBs thesis).
PE: Writes down his formula, which is again different from those that
SB showed. But one can easily transform each formula into one of
- How should two continuous functions be integrated when only
discrete values at different grid spacings are given. This leads to
the question how the interpolation is treated. It is stated, that
standard methods are given in textbooks.
- Data binning is the next point. This means reduction of data in
the sense to group data in appropriate sets (e.g. reduction of
PE: data binning is included in Skuld. There are binning
patterns defined. These patterns should depend on the altitude
because in the spectrum at low altitude the lines are very wide
(more flat and only few data points are needed) and at
higher altitudes the line width is small and a lot of data points
around the peak are needed, therefore a pattern which is
valid for all altitudes is not very helpful.
The main question is how to group the data in a good way. SB
suggests a relation with the weighting functions. PE think
orthogonal functions should also be appropriate and standard
methods should be available form other fields (e.g. image processing).
The further question is how the grouped data points should be
treated, just the mean of them?
JK: he says that he has a paper about it from peoples from
Oxford. He will distribute this paper to the participants.
SB: question if a reduction is also practicable for the internal
frequency grid. A rough method is already used in the
o The question of modules and their interfaces depends strongly on the
implementation. The figure of the
schematic description of the FM of PE (see thesis) was used
to discuss this topic.
===== April 28, after Dinner ======
Working out detailed descriptions of the three modules `absorption',
`RTE', and `weighting functions' in two parallel groups.
===== April 29, Morning ======
o Results of the group work last evening:
The Absorption group and the RTE/Weighting function group presented
their results. (See transparencies)
o Presentation of JM: Atmospheric Parameters in Polar
Regions. (From SSM/I and SSM/T2 data)
- Water vapor
- Clouds? (LWP from SSM/I with improved algorithm)
o Discussion of meta features / higher level features
- Spectral line selection
MAES: take all lines
Skuld: full calculation for each line (pencil beam)
- calc. abs (f=f0, or closest end of band)
- RTE for ztan = max(abs)
- check if Tb > Tb_lim
- if Tb > Tb_lim/factor: check a few lower
ztan Do some combination.
- Viewing angle grid:
+ Antenna pattern can depend on viewing angle (if you model
continuous scan by boxcar convolution of antenna).
+ Angular grid should be specified explicitly (analogously to frequency
and altitude) (potential for optimization)
- Integration grid along LOS:
+ This can be equidistant
SO: Exchange Antenna convolution and RTE?
PE+SB: It seems that this only works if you assume the optically
AI SO: Write about his approach to weighting functions / antenna.
+ Splining in frequency should work well for uplooking, but
probably not for limb sounding.
--> We don't do this.
o User interface
- Interactive use: PE wants it
+ JU also
+ SB: Must be handled in a simple and generic way.
- Controlfile structure:
+ Parameters specified on the command line can override parameters
(So you can use the controlfile as a template)
o General program structure
- Strongly modular
--> Much smaller and simpler blocks than in current programs
JK: Modules `knowing' what they need. (Recursive approach)
So the `user' just calls the `last' module (the one that
generates the measurement vector). This then call the module
that generates its input.
o Input for proceedings:
- Send LaTeX
- Figures in Postscript
- Deadline June 5.
- Ask ESTEC if they want to print it.
o Raw notes will be sent by Email
o Goal: First Beta version by autumn.
o Thanks to all participants and goodbye by SB.
List of action items for the proceedings
Deadline: June 5, 1999
o Short description of Moliere.
o Weighting function calculation in Moliere.
o Frequency optimization.
o Look for Philippes Baron's Catalogue merging program, which appears
to be lost.
o Write about the simple parameterization for the refractive index.
o Short description of MAES.
o Weighting function calculation in MAES, in particular concerning the
o Write documentation how to convert JPL QN to HITRAN QN and vice
o Write about planed laboratory measurements
o Suggestion for line catalogue format (send out draft to the
others to comment on).
o A scheme for tag groups / species naming, that allows arbitrary
grouping of lines
o A few words about 2D
o Write about continuum models
o Weighting function calculation for uplooking
o How to properly normalize the weighting functions
- What is the best definition of a normalized weighting function
(independent of layer thickness)?
- How to compute it practically?
o Short description of the old IFE/forward program.
o Description of MYTRAN
o Absorption intro
o Describe explicitly how to calculate p-shift
o Short description of Skuld
o Description of Verdandi
o RTE intro
o Line selection
o Describe weighting function calculation in Skuld
o Short description of GOMETRAN/SCIATRAN
o Write something about scattering (just very basic intro)
o Weighting function calculation in GOMETRAN.
o Distribute the Oxford paper on data binning
o Write about sources for extinction coefficients (for spherical cloud