1. APPLICABLE AND REFERENCE DOCUMENTS

2. TERMINOLOGY

2.1 ACRONYMS
2.2 A FEW KEY WORDS

3.1 NOAA SATELLITES
3.2 INSTRUMENTS INVOLVED IN THE INVERSION PROCESS
3.2.1 IR and m-wave sounders:
3.2.2 AVHRR imagers

4.1 AIMS
4.2 GENERAL DESCRIPTION
4.3 ICI PROCESSING SYSTEM MODULES

5.1 A FEW PHYSICAL SOUNDING PRINCIPLES

Diagram 1:Description of the ICI inversion processing system
Diagram 2 : Satellite - ground total transmission for IR frequencies.
Diagram 3 : the weight functions of the NOAA15 HIRS channels
Diagram 5: weight functions of the MSU (left), AMSU-A (middle) and AMSU-B (right) channels.
Diagram 6 : statistics on the computed - observed brightness temperature errors for Noaa15
Diagram 7 : Noaa14: Quality of the retrieved profiles as compared to the observed profiles
Diagram 8:  Noaa15: Quality of the retrieved profiles as compared to the observed profiles

Table 1: the instruments involved in the inversion process
Table 2: Centre frequencies of the IR HIRS channels for Noaa15 in cm-1.
Table 3: Centre frequencies of micro-wave channels in GHz.
Table 4 : emissivity values used on land depending on the nature of the ground
 
 

[1]: 'NOAA KLM user's guide'.
[2]: 'AAPP Module Design'- 'AAPP Data Set Definition'.
[3]: General specifications for the AAPP pre-processing operations related to the NOAA meteorological orbiting satellites. V1 : scientific description. V2 : software architecture.
[4]: Description document for the ICI sounding software related to the meteorological NOAA orbiting satellites. Software architecture.
[5] : Menzel P., ?Notes on Satellite Meteorology?. Internal circular. 1995
[6]: Eyre J.R., "A fast radiative transfer model for satellite sounding systems", ECMWF technical Memorandum no 176. 1991.
[7]: Clough S.A., F. Kneizys, G.P. Anderson, E. Shettle, J.H. Chetwynd, L.W. Abreu, "FASCOD3 Spectral simulation", IRS'88. 1988.
[8]: Rothman L.S. and al, "HITRAN Molecular Database: Edition 92", J.Q.S.R.T. Special Edition1992.
[9]: English S.J, T.J. Hewinson, ?A fast generic millimetre-wave emissivity model?, Microwave Remote Sensing of the Atmosphere and Environment. SPIE, Vol 3503. 1998
[10] : Masuda K, T. Takashima, Y. Takayama, Emissivity of pure and sea water for the model sea surface in the infrared window regions. Remote Sensing of Environment, 1988
[11]: Report to the sounding product oversight panel : Specifications for the processing of data from the Noaa-k sounder. Internal report. 1996.
[12]: Prigent C, E. Mathews, R. Rossow, Microwave land surface emissivities estimated from SSM/I observations. J. Geophys. Res. 102, 21867-21890. 1997.
[13]: Chedin A.,N. Scott, C. Wahiche, P. Moulinier : The Improved Initialization Inversion Method : a high resolution physical method for temperature retrievals from satellites of the TIROS-N series, J. Clim. And Appl. Met.,24,1985.
[14]: Lavanant L..,P. Brunel, G. Rochard, "TOVS sounding products at the CMS. The ICI model", IRS'96.1996
[15]: Brunel P.,L. Lavanant, G. Rochard, "Infrared transmittance data base for radiative transfer model", ITSC no 8. 1995
[16]: Chabrillat S., ``Optimization and use of Hedin's atmospheric empirical model MSIS'', Aeronomica acta B-N 55 - 1995.
[17]: Saunders R., M. Matricardi, P. Brunel, An improved fast radiative transfer model for assimilation of satellite radiance observations, 1998
[18]: Eyre J.R, Inversion of cloudy satellite sounding radiance by non-linear optimal estimation : theory and simulation for TOVS, 1989. J.Q.R Meteor. Soc, 115.
[19]: Karcher F. ?Détermination des profils atmosphériques de référence pour la mesure de constituants par spectroscopie de l?absorption? (Determining reference atmospheric profiles for measuring components by absorption spectroscopy. In-house report for Météo-France . January 1990
[20]: Manuel des codes internationaux Vol 3. Organistion Météorologique Mondiale. No 305. 1995.

1. Acronyms

AAPP: ATOVS and AVHRR Processing Package.
AMSU: Advanced Microwave Sounding Unit.
ATOVS: Advanced TIROS Vertical Sounder.
AVHRR: Advanced Very High Resolution Radiometer.
CMS: Centre de Météorologie Spatiale (Spatial Meteorology Center).
FOV: Field Of View
HIRS: High Resolution Infra Red Sounder.
HRPT: High Resolution Picture Transmission.
ICI : Imagery Coupled Inversion
IR: InfraRed.
MSIS : Mass Spectrometer and Incoherent Scatter data, atmosphere model
MSU: Microwave Sounding Unit.
m-waves: micro waves.
NOAA: National Oceanic and Atmospheric Administration.
NESDIS: National Environmental Satellite Data Information Service.
NESDISPR : Set of NOAA/NESDIS profiles.
RTTOV : fast Radiative Transfer model for ATOVS
SSU: Stratospheric Sounding Unit.
TOVS: TIROS Operational Vertical Sounder.
TIGR : LMD's set of profiles
 

2. A FEW KEY WORDS

Ta                          atmospheric profile vector: inverted profile ('p40' format)
Tag                         Initial atmospheric profile or ``guess profile''.
Tao                         observed profile (by analysis, radio sounding)
G                              Error covariance matrix of the initial profile.
O                              Error covariance matrix of satellite Observations.
F                               Error covariance matrix of the direct model.
delta                         direct model bias computed by statistics over computed Tb - measured Tb
S_tb                                          Standard deviation of computed Tbs for profiles from the initial library.
S_fw                            Standard error deviation: statistics over computed Tb - measured Tb.
DTag                      guess profile bias, guess profile statistics - observed profile.
CovTb                     Tb covariance matrix computed for profiles from the initial library
Fw                            Forward model = RTTOV
Tb_mes                       Observed brightness temperatures vector
Tbcal                       Brightness temperatures computed with the Fw forward model
Tbcl                         cleared brightness temperatures
K(Ta) Fw (Ta)      partial derivative according to the Ta elements. It uses the RTTOV assistant.
t_s                            total transmittance for a channel between the satellite and the ground
e_s                             surface emissivity.
E_up , E_do                 up and down radiance
Ts                            skin surface temperature

 
 
3. DESCRIPTION OF NOAA SATELLITES AND ON-BOARD INSTRUMENTS
4. NOAA SATELLITES

American meteorological polar orbit satellites are monitored by NOAA. This series of satellites was first used when the TIROS N satellite was launched in 1978 and has been followed since 1979 by the NOAAxx series (NOAA6 to NOAA14) and more recently by NOAA15 (NOAA-K before launch). Each one has a life cycle of about 4 years. Two satellites have to be simultaneously operational. The current system, comprising NOAA15 (which replaces NOAA12) and NOAA14 collects multispectral images (several wave-length channels) of the earth?s surface on the one hand and on the other hand permits the elaboration of the atmosphere temperature and moisture profiles.

Such satellites were designed to move around a polar helio synchronous orbit, at an altitude of about 835 km. They work in pairs: NOAA14 for the middle of the day and the middle of the night, NOAA15 for mornings and evenings. Since the Earth rotates, the satellites track moves westwards at each passing. Their nodal time is close to 102 minutes, that is to say 14.2 orbits per day. Since the number of orbits is not an integer, satellite orbit parameters slowly change position from day to day, thus generating different observation conditions and a change in their time of passing. A similar orbit configuration appears every nine days.. This is taken into account for reconstituting the data.
 

5. INSTRUMENTS INVOLVED IN THE INVERSION PROCESS

Narrow-band passive radiometers (adjusted on certain wave lengths) take spectral radiance measurements.

If the wave-length energy is quite not absorbed by the atmosphere but stopped by thick clouds, the instruments are called imagers (e.g. AVHRR). They are supposed to provide continental and oceanic surface data (in the form of reflectance or temperature) or cloud top data.

If a large part of the wave-length energy is absorbed by the atmosphere, the instruments are then called sounders (e.g. TOVS/ATOVS assembly with IR soundings (HIRS) and micro-waves (MSU/AMSU)) They are supposed to measure radiations from specific altitudes so as to restitute the vertical structure of the atmosphere after inversion.

 

NOAA (6-14)		NOAA15 (L,M,N)
TOVS	HIRS/2  MSU		ATOVS	HIRS/3  AMSU-A  AMSU-B
AVHRR/2		AVHRR/3

 
Table 1: the instruments involved in the inversion process
Table 1 shows the instruments taken on-board the NOAA satellites mentioned in this document.

New sounder and imager versions are and will be installed the NOAA15 series (L,M,N) from 1998. Here is a brief description of the sensors used:
 

1. IR and m-wave sounders:

With passive observation in several wave-lengths (from 23 channels for TOVS to 39 for ATOVS) it is possible to reconstitute the vertical structure of atmospheric temperature and moisture fields with a space resolution of a few dozen kilometers. As an IR sounder cannot "see" through the clouds (because of absorption), microwave soundings are required; their wave-length ranges are indeed less absorbed by the atmosphere.

TOVS (NOAA6-14) is a set of sounders which provide the data required for computing the temperature and atmospheric vapor profiles. This system is made up of three instruments:

1. The HIRS: a sounder using 19 IR channels (4 to 15 m m) to measure the radiance values corresponding to the vibration/rotation bands of carbon dioxide CO2 (4.3 m m and 15 m m), water H20 (6.3 m m) and ozone O3 (9.6 m m). This sounder also uses a VIS channel to measure reflectance (albedo %). By means of a rotating mirror (± 49.5°) the instrument scans a wide observation area (± 1120 km) all around the satellite?s ground track. Each scanning line comprises 56 FOVs and lasts for 6.4 seconds. The Instantaneous angle Field of View (IFOV) is close to 1.25°, with a 17.4-km resolution (size of the pixel or point of impact on the ground) at the nadir and 58.5 km on the edge of the orbit (maximum mirror diversion).
2. The MSU: a sounder using 4 micro-wave channels of nearly 50 GHz, corresponding to the rotation bands of oxygen O2 (5 mm). By means of a rotating mirror (± 47°) the instrument scans an observation area of ± 1173 km all around the satellite?s ground track. Each scanning line comprises 11 FOVs. The resolution is 109 km at the nadir and 323 km at the edge of the orbit (maximum mirror diversion). Before any processing, the MSU channels are subjected to a linear interpolation in the HIRS ellipsis.
3. The SSU: a spectrometer using 3 channels in the far IR (around 15 m m) for stratospheric measurements. This radiometer is not used in the ICI software.
ATOVS (NOAA series-K,L,M,N) is an upgraded release of the TOVS:
1. HIRS/3: it has the same spectral features as the former release. The radiance measuring method for thermal channel calibration is simplified.
2. AMSU-A and AMSU-B: replace MSU and SSU so as to improve the elaboration of temperature and water vapor profiles. AMSU-A is a sounder which uses 15 m -wave channels around 23, 30, 50 and 90 GHz, corresponding to the oxygen absorption bands. The resolution is 50 km at the nadir, and 52 km at the end of the scanning line which comprises 30 FOVs (mirror rotating by (± 48°). AMSU-B is a sounder which uses 5 m -wave channels around 90,150 and 190 GHz, with a 17-km resolution at the nadir. A scanning line is made up of 90 FOVs in the water vapor absorption bands.

1. AVHRR imagers

Imagers are processed in the AAPP pre-processing software in order to supply two pieces of information to the HIRS sounder?s FOVs: the cloud cover and the skin surface temperature if the surface is visible. Such information, when available in the FOV of the HIRS, improves the sounder?s inversion process.

AVHRR/2 is a high resolution IR imager which uses 5 channels (0.63 to 12 m m). The first channel is used for measuring the radiance in the VIS band. The second channel is centered on the close-by IR (0.86 m m). The next three channels (3.74, 10.80, 12.00 m m) are all located in the IR band. Thanks to a rotating mirror (± 55°) the instrument scans an observation area of ± 1450 km around the satellite?s ground track, with a space resolution of 1km at nadir. The cloud cover can be estimated using all channels together. The IR channels are used for defining the skin surface temperature.

AVHRR/3 avails of a sixth channel (channel 3a: 1.61 m m, the 3.74-m m channel becomes channel 3b) in the close-by IR in order to obtain a better discrimination between snow and clouds as well as a finer detection of aerosols. Scanning and ground resolution characteristics remain unchanged for AVHRR/2.

The characteristics of these instruments are detailed in sections [1] and [2].

1. GENERAL DESCRIPTION OF THE ICI INVERSION SYSTEM

The purpose of the ICI inversion system is to reconstitute the vertical structure of the atmosphere in terms of temperature and moisture by inverting the radiative transfer equation. This is done using observations from the sounders, each measured radiative energies originating from a different atmospheric region for each channel.
 

2. AIMS

The aim of the ICI inversion package is to process the observations collected by an HRPT local station for the NOAA orbiting satellites. It is therefore located downstream in relation to the HRPT data pre-processing software and is interfaced with the output files of the AAPP package.

The ICI package system is meant to be operational in spite of the constraints involved: software environment control, durable product quality, quick response to a change of satellite...

The first aim of the ICI line of products was to supply inverted products to Météo-France for nowcasters help and for the monitoring of Météo-France numerical weather prediction model "Arpège". This line of products has been operational at the CMS since march 1996 (release 1) for Noaa12 and Noaa14 [14], and since september 98 for Noaa15 (release 2). The retrieved profiles are broadcast in real time in the SATEM international format.

The advantage of an inversion line of products for HRPT local observations is that the temperature field can be obtained in real time a few minutes after acquisition, at the HIRS sensor?s resolution (30 km on average) and that mapping of the imager inside the sounder?s field can be used to improve the quality of the product. This is particularly interesting for mobile stations or stations that are isolated from an overall numerical forecasting context.

An effort was then made to allow the software to be exported to other HRPT acquisition stations by using computer standards (UNIX, Fortran77) and by developing automatic environment updating procedures.

This software has been named ICI, for 'Imager Coupled Inversion'.
 

3. GENERAL DESCRIPTION

Diagram 1 shows the main modules of the ICI inversion system.

The ICI system reads level1d TOVS/ATOVS input data that are navigated, temperature calibrated, mapped on the HIRS grid and documented after AAPP pre-processing. The maps currently being designed are the MSU on the HIRS grid for TOVS as well as the AMSU-A and AMSU-B on the HIRS grid for ATOVS. The main information associated with each HIRS fov is the type of surface (land/sea/mixed) and the altitude extracted from topographic files, the cloud cover and the skin surface temperature results of in the AVHRR cloud mask and, specifically for ATOVS, the rainfall and surface type flags following the preprocessing of the AMSU in the ATOVPP module of AAPP.

Pre-processing scientific processes are described in [3] Vol.1. The AAPP level1d file format is described in detail in document [2] Vol.2.



Diagram 1:Description of the ICI inversion processing system

Files from the ICI inversion software are sequential access binary files with one record per situation, containing the level1 input data, environment data, surface meteorological forecasts, the atmospheric profile used for initializing the inversion as well as the retrieved profile. See detailed description of format in the ICI software description [4].
 

4. ICI PROCESSING SYSTEM MODULES

The inversion system is made up of several modules corresponding to some main programs and unrelated scripts. These modules are run at different times of the day. The main modules are the following:

ICI: it is the heart of the software. Activated in real time after acquisition and just after pre-processing a new orbit, it reads the observation file in the level1d format, output of the AAPP preprocesses. It also reads the surface parameters forecasted by a numerical weather model, computes cleared radiance if necessary, initializes the inversion with a probable atmospheric profile, carries out the inversion and writes the inverted profile into the output file.

Four coding routines can be activated automatically according to the user?s requirements: ASCII files likely to be used by an occasional user, the AAPP level2 standard files, SATEM format files (to be assimilated in the monitoring of the numerical forecasting model) or files in the GRIB meteorological standard, a format used in particular for their display on the Météo-France Synergie graphic display units. ASCII files are described in [4] and the AAPP level2 files are described in [2] Vol.2. At the CMS, the ASCII, SATEM and GRIB files are presently being compiled.

BASE_METEO: this module creates a meteorological library containing radio soundings, analyses as well as forecasts on temperature and moisture in altitude and on the surface. Supplied by BDM and BDAP data, the library is meant to provide the meteorological data required for the ICI inversion (forecast), the BASE_INITIALE (analyses) and the MONITORING (radio soundings and analyses). This module is activated four times a day at the CMS by ?crontab? independently from real time processing of acquisitions.

BASE_PROFIL: this module creates a library containing temperature and moisture atmospheric profiles used for initializing the inversion with a vertical profile (guess) close to the retrieved one. The profiles of the library should be representative of the meteorological situation encountered. If it is not possible to construct such a data set, it is then necessary to consult a climatology library. Each profile is associated with up and down synthetic radiance as well as with the total satellite-surface transmittance. The module is run once a day at the CMS by crontab.

MONITORING : this module has a double purpose: first, to reset the inversion model in order to ensure a stable and durable quality for the retrieved profiles by readjusting the statistic coefficients of the software on a regular basis (tuning), and secondly to provide a regular quality follow-up (validation). For both actions co-located data files (co-location) are used. They contain satellite data, the retrieved profile, the radio-sounding and/or the closest analysis in time and space. The module is activated four times a day at the CMS, after acquiring meteorological observed data.

A more comprehensive scientific description of each module is given in section 6, and other details can be found in the software architecture, document [4].

Release 1 of ICI, operational since march 1996, used to process Noaa12 and Noaa14. It was replaced in September 1998 by a second release which processes TOVS and ATOVS (Noaa14 and Noaa15) simultaneously.

Research and development is still in progress so that the characteristics of the new AMSU sounder are considered and that the accuracy of inversions is improved. That is why the developments planned for release 3 are mentioned in the description. This release should come out in the middle of 1999.
 

 

5. SCIENTIFIC DESCRIPTION OF INVERSION ALGORITHMS

 
6. A FEW PHYSICAL SOUNDING PRINCIPLES

 
1. Spectral absorption by the atmosphere

Due to the concentration and distribution of the atmospheric components, the atmosphere acts as a filter over radiation; some wave-lengths are largely reduced while others are freely go through the atmosphere. As a matter of fact, each component absorbs and transmits electromagnetic radiations at very precise frequencies and can be specified by a spectral signature indicating the wave-lengths absorbed by this component. The most important absorbing agents in the atmosphere are CO2, H2O, O2 and N2O, the main ones, for our observations, being CO2 for temperature profile retrieval and the H2O for moisture profile retrieval. Such emissions are due to 3 factors:
 
• transition of an atom electron from one energy level to another:

Diagram 2 : Satellite - ground total transmission for IR frequencies.

Table 2 gives the central frequencies, expressed in cm-1, of the 19 IR channels of HIRS for Noaa15.

Diagram 3 represents the contribution of each layer (therefore the "sounded" atmospheric area) for each channel of the HIRS radiometer in the case of NOAA15 (very similar in the case of NOAA14) by means of a weight function. The vertical axis of the diagram corresponds to atmospheric pressures (in hPa). Sounding a specific wave-length provides information on the layer in which the weight function is highest. In each wave-length the maximum is different and the information obtained concerns a different atmospheric layer.
 

The following observations have been made:

• HIRS1-8 and 10: these channels are located in the CO2 absorption band which is temperature sensitive (15-mm area; 600-800cm-1). They scan all the atmospheric layers from the stratosphere (HIRS 1) to the surface (HIRS 8 and 10).
• HIRS9: this is the only absorbing channel in the ozone band (9.6mm ;1000cm-1) .
• HIRS11 and 12: both channels are located in the water vapor band (6.3mm;1200-2000cm-1) and sound the atmospheric layers around 600hpa and 400hpa. On NOAA 6-14, they are the only water vapor sensitive channels.
• HIRS13-16:nitrogen oxide and carbon dioxide absorb energy in the 4.3-mm band (2200-2350cm-1). Their lines become more intense as the temperature rises.
• HIRS 17-19 : they are located in the 3.7-mm band, which is the close-by infrared (with a visible contribution). These surface channels are not used much in the inversion process.

Table 3 gives the centre frequencies of MSU for Noaa14 and AMSU A/B for Noaa15. Expressed in GHz. The numbers of AMSU-B channels 1 to 5 corresponds to AMSU 16 to 20.

Diagram 5 shows the weight functions of the microwave channels for MSU (NOAA14) and AMSU-A/B (NOAA15).

The MSU and AMSU-A channels absorb energy within the oxygen frequency bands and are temperature sensitive. The AMSU-A channels sound all the atmosphere layers continuously, several channels in particular (AMSU 12, 13, 14) looking at the stratosphere and one channel sounding the tropopause (AMSU 9). The AMSU-B channels absorb energy within the water vapor frequency bands, with 2 surface channels and 3 altitude channels (around 800, 600 and 500hpa), which should help describing the vertical moisture profile in the lower atmosphere when added to HIRS channels 11 and 12. The AMSU-A15 and AMSU-B1 channels have the same frequency (89Ghz) so that both radiometers can be adjusted.

1. A few observations

For a given channel, the energy measured by the TOVS/ATOVS comes from a region of the atmosphere rather than from a specific level, for 2 reasons: first because atmospheric gases emit at a given frequency for several pressure levels in the atmosphere, then because the radiometer channels are not monochromatic but correspond to a spectral region.

Consequently, the channels weight functions are very broad and overlapping, which means that the measurements provided by the sounders are correlated. Analyses of the main components have revealed only 6 or 7 degrees of freedom (or independent information) in the TVOS channels in clear conditions. In other words, in an inverted profile, only 6 or 7 information items really originate from the TOVS. For ATOVS, the degrees of freedom are not much better.
 
 

1. DIRECT RADIATIVE transfer model

"Physical" inversion software programs (such as ICI) are always coupled with a forward radiative transfer software which simulates the E radiance values measured by the sounder for a vertical atmospheric profile by using the radiative transfer equation  :

E= es.ts B(Ts ) + ò _{ps ->0} [B(Tp) (dt(p)/d(lnp)) d(lnp) ] (6.2.1)

es surface emissivity

ts surface/satellite transmittance

B(Ts ), B(Tp) planck function of the surface temperature and of the pressure layer p temperature

The layer transmittance derivatives: dt(p)/d(lnp) are called weight functions.

Synthetic brightness temperature Tbcal is obtained by inverting the Planck function: Tbcal = B-1(E).

The radiative transfer software works at different levels in the ICI processing system in the real-time ICI inversion module, when the cost function is computed for each situation (see chapter 6.4.11), but also off-line in the BASE_PROFIL module when creating the initial library, as well as in the MONITORING module.

This software must be very precise because its aptitude to reproduce the observations as accurately as possible will determine the accuracy of the retrieved vertical profile. That is why the computed brightness temperatures are systematically compared with the observations by using a close-by observed profile (radio sounding, analysis), in the MONITORING module (see chapter 6.8). This way, the model will be adjusted statistically to the observation by means of time-related coefficients according to the viewing angle and the type of atmosphere encountered; moreover, it will be possible to follow up the quality of each channel of the sounder.

Within an operational framework, the selected software must be fast because it is run in real time at each inversion. Monochromatic (line by line) models are very precise for physical descriptions but far too slow for operational applications. It is thus necessary to use a faster model, generally adapted to the sounder channel filters by means of a statistic method using the computations previously performed with a line-by-line model for a number of vertical profiles selected for their atmosphere representativity.

The selected software is RTTOV [6]. It was developed for the European Center and it is used in the French numerical forecasting model Arpège. This software is very fast and is associated with an adjoint model, a mathematical and computing technique used for quickly calculating the partial derivatives of the direct model in relation to the profile (weight functions) which are necessary for calculating the cost function of the real-time ICI module. Computed brightness temperatures are as precise as that of the reference line-by-line model.

There is no detailed description of RTTOV in this document (see [6]), although it is required for performing the ICI inversion and the European Center has allowed it to be part of the package.

The CMS has compiled a monochromatic transmittance file [15] using the line-by-line model FASCOD [7] [8], for a set of 32 vertical profiles representing all possible atmospheric conditions. Computations were performed for various scanning angles and surface pressures and for 3 groups of atmospheric components (CO2, H2O, mixed gases). This file is used for computing the internal RTTOV coefficients for each channel off-line and outside the ICI processing system. By computing coefficients for a new set of channels (new satellite), which requires about 2 hours on a work station, it is possible to perform inversions with ICI as soon as a new satellite is received.

The RTTOV3 release currently installed in ICI reads the atmospheric profile in terms of temperature, moisture and ozone over 40 fixed pressure levels ranging from 1000hpa to 0.1hpa: this requires an interpolation and extrapolation interface for the observed profiles (radio sounding, analysis) on such levels. Interpolation doesn?t present any particular problem. However, radio soundings generally stop between 50 and 20hpa and Arpège analyses at 10hpa at present. The profile is extrapolated in the stratosphere by means of statistic or climatological software programs. We have tested several programs (ITPP, 3I, MSIS). None is satisfactory and the currently used climatological model is MSIS [16]. Extrapolation is affected by a variable seasonal bias also found in the synthetic radiance of stratospheric channels (HIRS 1,2). This can be detected by error statistics, between computed and measured brightness temperatures that are downgraded in bias and standard deviation for these channels. This difficult problem has not been solved yet.

A climatological ozone profile related to the season and latitude is added on to the ?observed? atmospheric profiles (radio soundings, analyses), as they have none. In reality, this profile is so far unique (US standard atmosphere no76).

 

2. CHANNEL SELECTION CONSTRAINTS

The number of IR and m-wave channels for the TOVS/ATOVS sounders is 23 and 39 respectively. However, for various reasons, the channels are not all used for inversion. The following sections explain how the channels were selected in the ICI software.

1. Sounding in clear conditions

This section deals with clear conditions in the HIRS field of view in terms of IR, that is to say without cloud detected by the AVHRR in the AAPP preprocessing.

In theory, all the channels of the sounder can be used. However, we have decided to ignore a number of channels because of statistics concerning errors detected between computed and observed temperatures within the monitoring framework. Indeed, if they were used, they would downgrade the retrieved profile.

Note that in these statistics, it is not possible to differentiate the errors originating from different sources: satellite measurement, radio sounding, co-location, direct radiative transfer model used. All errors are mixed together. But if the total number of errors for a channel is high (significant standard deviation), using this channel would downgrade the retrieval since the observation cannot be properly reproduced during the inversion process.

Diagram 6 gives an example of statistics obtained for the NOAA15 channels on sea, the standard deviation appearing at the top and the bias at the bottom of the diagram. For an easier reading of the graph, the values have been artificially saturated at 5K in standard deviation and at -3K and +5K in bias. The channels tinted in gray are not used in the inversion process. Channels 21 to 35 are the AMSU-A channels 1 to 15 and channels 36 to 40 are the AMSU-B channels 1 to 5.

As a general rule, the following channels are not used in the inversion  process:

• Stratosphere-directed channels  (HIRS1 channel for Noaa14 and Noaa15 ; AMSU 13, 14). Indeed, statistics are not satisfactory for these channels, partly due to the profile extrapolation problem.
• The ozone channel (HIRS 9). Since no ozone profile has been observed in a systematic way, it would not be realistic to monitor this channel.
• Water vapour band channels (HIRS 11 and 12) are not used at present. Their error statistics are rather poor, probably due to of several reasons (the direct model is not perfect, water vapour measured by means of radio soundings is of poor accuracy ...). Some tests performed with Noaa14, to try and use these channels together with other channels have revealed that they downgrade the quality of the temperature vertical profile. In the current release of the ICI inversion system, we have chosen to give priority to the quality of the temperature profile rather than the retrieved moisture profile. At present, the moisture profile is no better than a climatology. The next software release should solve this problem.
• Surface channels in the close-by infra-Red (HIRS 17-19) are not used because their visible contribution cannot be monitored.
• m-wave surface channels (MSU1, AMSU-A 1,2,3,4,15) are not used in the current ICI release because surface emissivity is very difficult to handle. A study is under way to try and solve the problem for the next release.
• The present release does not take account of the AMSU-B channels either since their measurements are so far polluted by interference at satellite level. A correction of interferences has just been published. This should soon be implemented and we foreseen to use these channels together with HIRS11 and 12 to provide a more realistic moisture profile in the next release.
The next software release is due to come out in 1999.

In short, when the HIRS field of view is declared as clear (from AVHRR cloud mask), the sounder's channels used in this software release are the following:

• TOVS : HIRS 2,3,4,5,6,7,8,10,13,14,15 MSU 2,3,4
• ATOVS : HIRS 2,3,4,5,6,7,8,10,13,14,15,16 AMSU 5,6,7,8,9,10,11,12
Note that: channel HIRS16 of the TOVS is not considered, due to a scintillation problem during measurements.
 
• Sounding in cloudy conditions

The IR radiations at the HIRS radiometer frequencies are canceled or attenuated by the clouds whereas the MSU/AMSU micro-wave channels go through the clouds when the latter are not too diffusing (e.g.: rainfall, ice crystals in the cloud). IR observations polluted by clouds cannot be used as such since an extra unknown factor is added to the inversion problem: the cloud?s characteristics. They must therefore either be suppressed from the ICI processing or decontaminated before inversion.

1. TOVS

The only cloud-related information in the AAPP pre-processing comes from the AVHRR cloud mask formed in the field of view of the HIRS. For further details on the cloud mask, refer to [3]. The information obtained is the cloud cover expressed in %. Any field of view containing more than 70% clouds is declared as cloudy and is considered as partly cloudy for a cover between 10% and 70%.

In cloudy conditions, it is considered that no information below the cloud can contribute to the HIRS measurement. The only useful channels for inversion are therefore the IR stratospheric HIRS channels 2,3 located above the cloud and the MSU micro-wave channels 2,3,4 (supposedly non absorbed) for the part located below the cloud.

If the field of view is partly cloudy, part of the tropospheric HIRS channel information comes from the atmosphere below the cloud. Some more or less performing techniques exist for clearing the channels aiming at the middle part of the atmosphere (estimating the brightness temperature that would have been measured in a cloudless sky). These methods are method N* of the NOAA [11] and PSI of the LMD [10] in particular. In ICI, the PSI method is currently used. Cleared channels are then used in the inversion process, in addition to the channels retained in cloudy conditions. The channels used are the following :

HIRS 2,3,4,5,15 MSU 2,3,4

2. ATOVS

Some tests are carried out on the AMSU-A channels in AAPP preprocessing (ATOVPP module) in order to estimate, in terms of micro-waves, whether the situation is clear (clouds do not absorb the micro-wave radiance emitted in the lower layers), cloudy (absorption of lower atmosphere channels) or diffusing (rainfalls, hydrometeors, ice in the clouds). Three cases may then arise:

cloudy (IR) and clear (m-waves) : HIRS 2,3 AMSU 5,6,7,8,9,10,11,12

cloudy (IR + m-waves) : HIRS 2,3 AMSU 9,10,11,12

diffusing (m-waves) : this situation is not processed.

The numbers corresponding to the channels selected in the inversion according to the cloud cover are indicated in a chart in the "include" file described in [4].
 

1. THE ICI MODULE

The ICI software is simultaneously operational for TOVS and ATOVS ; a routine is called at the start of the process to initialize all the charts required in the course of the software in relation to the satellite (e.g.: channels involved in the process) and routings to processes that are specific to each satellite are planned (e.g.: surface emissivity, channel clearing).

This chapter provides a scientific description of real-time processes applied to each observation.

The main steps of the software are the following :

It reads the input data (satellite observations, forecast data...) and extracts the situations which will be processed..

For each processed situation, it :

defines the environment data, in particular the cloud class, the surface parameters, the IR m-wave surface emissivities and the air-mass type

applies some corrections on the observations before the inversion process (ex : forward model bias, cloud clearing)

selects a guess profile to be used during inversion in the cost function

makes the inversion

writes the results in a binary file.

1. Input data

This is what the ICI module reads :
1. level1d file, AAPP pre-processing output containing:

Calibrated, navigated and mapped observations made by the sounder. For TOVS, MSU data are mapped on the HIRS grid. For ATOVS, the AMSU-B is first mapped in the AMSU-A, both instruments are then mapped on the HIRS grid.

The average HIRS fov altitude and a land/sea/coast flag.

Three pieces of information resulting from the AVHR cloud mask of AAPP are available: cloud cover, skin surface temperature (AVHRR split-window) when part of the AVHRR pixels mapped in the ellipsis are clear, the forecast air surface temperature (on land) or a climatology of the skin surface temperature (on sea).

Two information items extracted from the AMSU pre-processes: a type of surface in terms of m-waves and a clear/cloudy/precipitating flag.

The level1d file format is specified in [2].

2. A 12-hour forecast file (or 36-hour if there is no 12-hour file) on the ATOUR10 grid containing the sea pressure, the air temperature at 1000hpa and the wind on sea at 10m of altitude module.
3. The initial library, which contains 4 files, one with atmospheric profiles in the RTTOV input format as well as two others with first the associated total transmittance and second the up and down synthetic radiance. A fourth file contains the airmas covariance matrix. With the parameterization chosen for the CMS system, the profile number is in the order of 1600 to 1800. For further details, refer to chapter 6.7.
4. Two distinct files, which contain the values of the statistic adjustment coefficients useful for inversion (see chapter 6.8).
5. Two files containing the internal coefficients of the RTTOV forward model and the values used in the computation of the m-wave emissivities.

1. Selection of the processed situation

The software works at the HIRS fov resolution. However, it is possible to sample the inversions by the parametrization in input. At CMS, the ICI system runs with a sample of 1 pixel/2, 1 line/2. The software then selects the clearest spot into the 4 situations of the 2*2 box.

2. Cloud class

The cloud cover, expressed in %, is the output product of the AVHRR cloud detection. It is used to allocate a cloud class to the considered situation. This class determines the channels used for the guess selection and the inversion process, as explained in chapter 6.3, and also the activation of some processes (ex : cloud clearing).

For TOVS, a situation is ?clear? if the cloud cover is less than 10%, ?partly-cloudy? for a cover between 10 and 70% and otherwise ?cloudy?.

For ATOVS, the cloud class depends on the AVHRR cloud mask but also on the AMSU preprocessing. A situation is ?clear? if the IR cover is less than 10%, ?partly-cloudy? if it is greater than 10% with a ?clear? AMSU flag, ?cloudy? when the AMSU flag is ?cloudy?. The situation is not processed if the AMSU radiation is diffused by hydrometeors.

3. Surface parameters

The sea pressure and the wind module forecasted at the grid point closest to the position of the HIRS fov are taken into account for measurement.

The software computes the surface pressure using the forecast on sea pressure and HIRS fov altitude, according to the following formula:

Ps= Psea * exp(-alt / hscale) ps : surface pressure;  alt= altitude ; hscale=8150

It initializes the surface temperature as follows: if the fov is clear, the skin surface temperature, originating from the split-window AVHRR, is used. Otherwise, the surface temperature used will be the climatological surface temperature on sea or the forecast air temperature on the land surface.

The surface temperature, estimated independently from the inversion software, is important to compute the synthetic brightness temperatures of the initial library in order to focus on the part purely related to the atmosphere, without any mistake from the surface energy when selecting the initial profile. Moreover, if the conditions are cloudy or partly cloudy, the surface temperature is useful for extrapolating the atmospheric profile under the cloud.

4. Infra-red surface emissivity

On the sea, the IR emissivity depends on the frequency, the scanning angle, the wind speed, the salinity and the sea temperature. In the ICI software, emissivity is classified in charts for the different sounder channels, according to the scanning secant, for an average wind speed and surface temperature, using the values given in document [10].

On land, emissivity is considered as a constant and set to 1.

5. m-wave surface emissivity

This part mainly deals with the AMSU sounder. It is important to carefully take note of the surface emissivity in the direct model if you wish to use channels that can see the surface (about 10 channels for AMSU). Indeed, an error of 0.1 leads to an error of the synthetic brightness temperature of about 20K.

1. on sea

The sea surface emissivity is of around 0.6. This is used as default value (e.g. for MSU) when no other data is available.

However, emissivity is greatly affected by the wind speed (because of the formation of small waves on the sea surface), the skin surface temperature, the foam, the scanning angle and the channel polarization. Values ranging from 0.4 to 0.7 can be observed.

The model of emissivity e [9] used is noted as follows:

e(U,T_s)= (1- R_s(T_s)*B(U)) + De(U))(1-F(U)) + F(U)

with: U : wind speed, T_s  : surface temperature

R_s(T_s) Fresnel?s specular reflection computed at the surface temperature T_s , as a function of the sea refraction index and of the scanning angle.

B(U) : correction of the specular reflection to take account of capillary waves which wave-lengths could be compared with that of the channel.

De(U) : correction to take account of the large scale sea roughness (in relation to the channel?s wave length) causing a slope in the specular reflection. It is a polynomial function which depends on polarization, frequency, wind speed and scanning angle.

F(U) : foam cover. As a matter of fact, foam is a blackbody at all frequencies and varies with the wind speed.

The model?s accuracy ranges from 0.005 to 24Ghz and from 0.01 to 157Ghz.

The FASTEM routine, developed at the UK Met Office by S. English [9], estimates the micro-wave emissivity of the sea surface in the ICI system on the basis of the input surface temperature (chapter 6.4.4) and wind module forecast.

The FASTEM routine is currently used without the direct radiative transfer software. However it is included in release 5 of the RTTOV radiative transfer model which will soon replace release 3 in ICI [17].

2. on land

For MSU, two constant values, 0.85 and 0.95 (for altitudes over 1000m) are allocated in ICI.

For AMSU, the AAPP pre-processing software documents the observations in terms of surface type. This information is used to allocate an average value to emissivity according to the nature of the ground. The values used are extracted from the NOAA [11] and are indicated in table 4.

 

	1	2	3	4	5	6	7	8	9
	Young ice	Dry land	dry snow	multi-year ice	sea	wet forest	wet land	Wet snow	desert
Amsu-a	.95	.95	.68	.71	.6	.79	.79	.85	.93
Amsu-b	.95	.97	.64	.65	.6	.85	.85	.83	.93

Table 4 : emissivity values used on land depending on the nature of the ground
 
But these values, even though useful and important for using the channels that can see the surface in certain conditions (e.g.: high altitudes), are not precise for a routinely use of the surface viewing channels. In particular, emissivities largely depend on the scanning angle. That is why a development is under way for defining a rolling emissivity climatology by means of the C. Prigent method [12]. This technique will be integrated in the new ICI release.
6. Air mass

In the list of specifications in the TIGR profile library, five types of air mass are defined in [13]: Northern Hemisphere polar, Southern Hemisphere polar, tropical, Northern Hemisphere mid-latitude, Southern Hemisphere mid-latitude. An air mass type has been allocated to the observations at the start of the ICI process. It is obtained by reducing the distances between brightness temperatures to a minimum (channels HIRS2,3,4 , MSU2,3,4 for Noaa14 and HIRS2,3,4 , AMSU6,7,8,9 for Noaa15 ) between observations and an average profile representative of the 5 types.

The method used for computing the average profile and its associated covariance matrix is explained in chapter 6.7.

7. Direct model bias

Before any processing, the observations supplied by the Tbmes sounders are corrected by applying the direct model biases. Synthetic like brightness temperatures are thus obtained and it is then possible to compare the two magnitudes all along the process. The correction is defined as follows:

Tbmes(i) = Tbmes (i) + delta(i) i: channel; delta: direct model bias

Biases are a polynomial function of the observations and of the scanning angle Q (for the 2 satellites).

delta(i) = a₀(i) + S_{k=1,N [ak(i) * Tbmes(k)] Noaa14 : k= HIRS 1,2,3 - MSU 2,3,4 ,} Q

Noaa15 : k= HIRS 1,2,3 - AMSU 6,7,8,9, Q

Regression coefficients are computed in the MONITORING module (chapter 6.7).

Adapting biases dynamically to observations, it is also a way to take account of the air mass type encountered for each situation.

8. Channel clearing

This stage only applies to the TOVS for partly cloudy situations. It takes place just before the search for the guess.

In ICI, HIRS channels are cleared according to the PSI of 3I method [13]. This method is based on a preliminary search for a realistic profile T0 in the guess library by using HIRS channels 2, 3 + MSU 2, 3, 4 (see chapter 6.4.8). Tb_mes observations are cleared for HIRS tropospheric channels 4, 5, 15 as follows:

Tbcl(i) = Tb_mes(i) + (Tb_mes(msu2) - Tbcal(msu2)0 ) i= channel

In the original version of 3I, additional regressions are applied in order to clear other channels. They haven?t been implemented in ICI because they are adapted to a specific satellite and have to be computed again.

Cleared brightness temperatures are then considered as if they were the sounder?s observations in the whole software.

From a practical viewpoint, the quality of inversions for the partly cloudy type is not much better than for the cloudy type. The method will then have to be reviewed. That is why the clearing process has not been repeated for Noaa15 in release 2 : cloudy and partly cloudy situations (in terms of IR) are treated in the same way.

9. Search for the initial profile

In section 6.1.3, we saw that the weight functions of the instruments are overlapping and that only 6 to 8 independent pieces of information are available to estimate the profile. This, more than the fact that there is some noise in the observation and that the radiative transfer model is not perfect, does not make it possible to directly rebuild a realistic and precise atmospheric profile from the satellite observation. It is therefore necessary to acquire a realistic atmospheric profile, initial profile or "guess", close to the one required, before inverting the sounder?s observations. The initial profile provides an external piece of information which forces the solution (by giving it the form of an atmospheric profile). Its accuracy determines the accuracy of the retrieved profile. The inversion process by itself will then consist of correcting the initial profile in terms of temperature and moisture to reduce the difference between the brightness temperatures as measured by the sounder and the temperatures as simulated from the profile to a minimum.

The first purpose of this stage is to avail of a number of channels (within the space of the brightness temperatures) corresponding to the profiles of the guess library (representing the meteorological situation searched for). The initial profile is then selected by comparing the measurements ( after applying forward model biases and if necessary cloud clearing) taken by the sounder with the computed brightness temperatures.

1. Adapting the guess library to the observation

Before selecting a guess profile, the guess library informations are adapted to the observation environment (Ps, Ts, es, q). Brightness temperatures are computed for each profile as well as a corresponding Tb covariance matrix.

The ICI module reads the file containing the representative profiles of the initial library, as well as the total transmittance (satellite - ground) t_s, the up Eup and down Edo radiance of each profile for the scanning angle of the actual situation considered. Transmittances and radiances are interpolated at the surface pressure (refer to chapter 6.7 for creating the library).

The temperature and surface emissivity contribution to the synthetic brightness temperature is significant for the channels that can see the surface. It is necessary to adjust them well to the proper surface conditions so that the selection of an atmospheric profile is not polluted by an erroneous surface contribution. Moreover, since atmospheric layers are considered as a whole, a brightness temperature error on the surface induces errors at the upper layers level.

For this reason, synthetic brightness temperatures are no longer computed upon creating the library as in release 1 of ICI, but in real time for each situation, with surface temperature and emissivity values adapted to the actual situation.

For each profile and the N channels used for the inversion (depending on the cloud class, see chapter 6.3), the software program computes the brightness temperatures for the surface temperature and the IR and surface m-wave emissivity values in the given situation, according to the following formula:

E(p,i)= e_s t_{s E(Ts) + Eup + Edo*(1-} e_{s )} t_s²                                 p= profile ; i= 1,N

                                              t_{s, Eup, Edo} read for q and interpolated at Ps

The synthetic brightness temperature Tbcal is given by the inverse value of the planck function:

Tbcal (p,i) = B-1(E).

An additional "channel" is added to the synthetic brightness temperatures space: the air temperature at 1000hpa extracted from the profile itself. The aim is to ?force? the profile selected at this level because since weight functions are very broad, especially near the surface, sounders alone cannot detect the atmospheric temperature inversion in the lower atmosphere, a significant parameter for nowcasting. We have chosen to use T1000 rather than a temperature of the air at 2m because the latter depends on altitude, which might have caused another error.

Each library profile is documented with an air mass. The sub-set corresponding to the air mass of the situation considered is used for computing the covariance matrix of the brightness temperatures CovTb for the N+1 channels and its inverse, as well as the standard deviations vector S_tb.

Inter-channel correlation in the CovTb matrix is very strong due to the serious overlapping of the weight functions. It is very difficult to perform a matrix inversion in such conditions. Besides, if the correlation is too strong, profiles are selected according to their shape rather than their value. To solve the problem, an 0.8 factor is currently applied onto the non-diagonal terms of the matrix before inversion.

2. Selecting the initial profile

The mean squares distance, weighted by the variability of each channel thanks to the CovTb matrix, is computed for each p profile as follows:
dist(p) = [ (Tb_mes - Tbcal(p))t CovTb-1 (Tb_mes - Tbcal(p)) ] 1/2
Tb_mes : observations vector for N+1 channels
Tbcal(p) : brightness temperatures vector computed for each profile

CovTb : covariance matrix of brightness temperatures

Exponents t and -1 respectively mean transposed matrix and its inverse.

Note that: the CovTb covariance matrix is set for the air mass in the actual situation. However, dist(p) is computed for all library profiles. Indeed, practice has shown better results if all profiles are considered, which leads us to think that the definition of the air mass types is not optimized.

The initial profile is defined as follows :

1. "the closest" profile corresponding to the shortest distance dmin is selected.
2. this selection is applied to other profiles by increasing the search distance: up to 3 iterations are allowed (to avail of at least 4 profiles) by selecting all profiles with a distance shorter than dist_i+1= C0*dist_i
3. if more than 10 profiles are extracted, only the 10 closest are retained.
The initial profile (temperature, moisture, ozone profile, surface air parameters) is the mean of these information items for the selected profiles. Skin surface parameters (surface temperature, pressure, surface emissivity, wind) are the observation parameters (see paragraph 6.4.4). Associated synthetic brightness temperatures are the means of the selected profiles brightness temperatures.

Guard rails and error flags are placed so as to avoid any incorrect initialization of the inversion:

• distance is not computed with profiles for which

Tbmes(imw)- Tbcal(p,imw) > C1*S_fw(imw)                 imw = MSU2 or AMSU6
                                                                                            S_fw = error standard deviation of the forward model
• if dmin exceeds a reference distance dst, then flag= 7

        dst = C2 * [ S_tbt CovTb-1 S_tb ] ½                                        S_tb vector of standard deviations for the library?s Tbs.
• if there is no profile in the selection ball, then flag= 6 or 8
• if the number of channels such as [ Tb_mes(i)- Tbcal(i) > C1*S_fw ] is > Nb for the closest profile or for the guess profile (in which case, Tbcal = mean of the Tb for the 4 to 10 selected profiles), then flag= 4 or 5.
Error flags are processed as follows:
• 0 = OK
• if < or =5 : warning but inversion is allowed .
• if > or =6 : situation rejected. Move to the next one.
C0, C1, C2, Nb values are given in an "include" file, described in [4].
• Inversion

Once an initial atmospheric profile has been found, inversion consists of perturbing this profile under certain limits (so as not no move too far away from it) in order to minimize the error between the measurement and the synthetic brightness temperature of the final profile.

1. Cost function:

Trying to invert the (possibly cleared) observations consists of finding the most probable atmospheric profile Ta taking account of the observations Tb_mes, i.e. maximizing the conditional probability of Ta for Tb_mes (bold characters correspond to vectors) :

P( Ta | Tb_mes) = maximum

According to the Bayes theorem:

P( Ta | Tb_mes ) = P(Tb_mes | Ta) . P( Ta )

P(Tb_mes | Ta) : probability of measuring Tb_mes when the atmosphere is Ta.

P( Ta) : probability of obtaining Ta before inverting.

Gaussian errors are supposed and probabilities are expressed using the Gauss law (matrix notation):

P(Tb_mes | Ta) = exp { -1/2 (Tb_mes - Fw(Ta))t . (O + F)-1 . (Tb_mes - Fw(Ta)) (1)

P( Ta ) = exp { -1/2 (Ta - Tag)t . G-1 . (Ta - Tag) }

O error covariance matrix of satellite Observations

F error covariance matrix of the forward model

G error covariance matrix of the guess.

Tag guess.

Fw(Ta) brightness temperatures computed with the RTTOV direct model for the Ta profile.

exponents t and -1 respectively mean transposed and inverse matrix.

The most probable solution is the function which minimizes the cost function J:

J(Ta) = (Ta - Tag)t . G-1 . (Ta - Tag) + (Tb_mes - Fw(Ta))t . (O + F)-1 . (Tb_mes- Fw(Ta) (2)

To find the most probable value for Ta, we can either minimize the equation (2) by supposing that there are no multiple minimum values or look for Ta so that the J(Ta) gradient in relation to Ta is null:

J'(Ta) = G-1 . (Ta - Tag) - K(Ta)t . (O + F)-1 . (Tb_mes - Fw(Ta)) = 0 (3)

K(Ta): partial derivatives of Fw(Ta) according to Ta elements.

Linear case

When the problem is linear, the matrix K is unrelated to the Ta profile:

Fw(Ta) = Fw(Tag) + K . (Ta - Tag) (4)

By substituting the equation (4) in (3), the following result is obtained:

Ta = Tag + G . Kt . (K . B . Kt + (O + F) )-1 . (Tb_mes - Fw(Tag)) (5)

For further details on the mathematical formula, refer to item [18].

The linearity hypothesis is rather well confirmed in clear situations. In the slightly non-linear case (e.g.: cleared observations), K varies a little with Ta and the equation (4) is used, in which K = K(Tag).

The inverse operator G Kt [ (K G Kt + O) ]-1 is used by several inversion software programs. In this case, the inversion operator can be pre-computed off-line and stored for each profile of the initial library.

Non-linear case

Inverting the water vapor sensitive channels (moisture profile) or using the sounding observations polluted by clouds directly no longer allows for the linearity hypothesis because matrix K quickly varies according to certain variables of Ta. Moreover, some studies have revealed that cleared radiance often contains non gaussian errors that are correlated between channels. Non-linear algorithms also make it possible to take account of different types of parameters in the Ta profile vector : temperature, moisture, cloud amount, cloud top pressure, micro-wave surface emissivity.

The cost function (equation 2) is then reduced to a minimum by using an ``iterative descent algorithm''. Various algorithms can be used. J. Eyre [18] has suggested a method based on Newton iterations with a calculation of the second derivative J" for the cost function. For the iteration n:

Tan+1 = Tan - J"(Tan)-1 . J(Tan) (6)

The derivative of J'(Ta), equation (3), in relation to Ta is as follows:

J"(Tan)-1 = (G-1 + Knt . (O + F)-1 . Kn)-1 with Kn = K (Tan)

When the size of Ta is larger than that of Tb_mes, it is more effective to compute the equivalent form:

J"(Tan)-1 = G - G .Knt .( Kn .G. Knt + (O + F) )-1 . Kn.G (7)

After manipulations on matrixes, this final formula is obtained:

Tan+1 = Tan + (Tag -Tan) + Wn { (Tb_mes - Fw(Tan) - Kn ( Tag - Tan) } (8)

Wn = G Knt ( Kn G Knt + (O + F) )-1

The convergence of the iteration on equation (8) ends when the increment (Tan+1 - Tan) is small enough and when (Tb_mes - Fw(Tan+1)) is in the order of the measurement error in all channels.

Note that the first iteration corresponds to the linear solution (equation 5).

This type of algorithm is used by the Arpège and IFS models (European Center).

2. Inversion procedure in ICI

The ICI software is programmed for processing the non-linear case by means of the equation (8) with an iteration loop. However, in release 2, only one iteration is performed (which brings us back to the linear solution) for running time purposes. Since water vapor channels are not all used at present and the channels involved in the inversion are ?non-polluted? by clouds, experiments have shown that a single iteration is sufficient for (Tb_mes - Fw(Ta)) to be in the order of the measurement error.

Non-linear programming was chosen to "prepare" release 3. The iteration loop will probably be required for the water vapor channels AMSU-B and HIRS11-12.

The operator W is computed for each inversion by using the direct RTTOV model for computing Fw(Ta_g) and its adjoint model for computing K(Ta_g), partial derivatives of the forward model according to the profile.

Matrix O + F is replaced by S_fw , standard deviations for the direct model?s errors (Tbcal(observed profile) - Tb_mes). This means that the non-diagonal terms of the matrix are reset, as it is very difficult to find out whether an error comes from the radio sounding measurement, from the co-location or from the radio sounding extrapolation onto the upper atmospheric levels of the direct model.

The Gauss law P(Ta) supposes that the initial profile is not biased. This applies to the models for which the initial profile originates from a forecast. In the case we are dealing with, with a search in a profile base, "a posteriori" validations show that the initial profile is slightly biased. The initial profile of this bias are corrected before inversion:

Tag = Tag - DTag

Error covariance matrixes G and (O+F) as well as the DTag bias are computed off-line in the MONITORING module (see chapter 6.8) for the 3 types of cloudy conditions (clear/partly cloudy/cloudy) and the 2 types of surface (sea/land).

The channels implied in the inversion process are described in chapter 6.3.

Differences (Tb_mes - Fw(Ta)) between measurements and brightness temperatures computed for the inverted profile are used for computing the distance:

dist =(1/N) S_{i=1,N [ ( Tbmes - Fw(Ta) ) / Sfw] 2}

If dist > value, the inversion is rejected into code 1.

The retrieval is computed over the 40 atmospheric pressure levels of the RTTOV model (0.1hpa to 1000hpa) for temperature, on the 25 low levels (50 to 1000hpa) for moisture and for surface temperature and humidity values.

Output data
The ICI module writes the results of the inversion into a binary, sequential file, with 1 record per situation, containing :
satellite data (level1d) and data resulting from processing.
environment data (numbers corresponding to the secant, pressure level, air mass, cloud type, surface type, rejection code)
forecast data
cleared satellite data
information on the guess (profile, associated brightness temperatures, identification data)
retrieved profile.
The detailed format of the result file is specified in [4].
Transmitting the information from one variable to the next
As different variables contain the same type of information, it can be difficult to determine its source or the processing applied on. This chapter tries to help the user for that purpose.

Satellite data:

Skin surface temperature: from the cloud mask

Air mass type: from the search for the closest (chapter 6.4.7)

Micro-wave emissivity: depends on the surface type (chapters 6.5.5 and 6.4.6)

Land/sea identifier: from level1d (AAPP atlas)

Cloud top pressure: for cloudy cases, from the guess profile together with the cloud top temperature (from level1d)

guess profile: Information on identification and surface is given by the satellite data (Ts, ps, land/sea, lat, lon, altitude, date)

profile: mean of the selected profiles (temperature, moisture, ozone) on each levels

Surface pressure: from the forecast

information on air on the surface: interpolation of the guess profile (temperature, moisture, ozone) at the surface pressure ps

additional information computed after defining the initial profile: type of air mass by minimizing the distance, geopotential, tropopause, total water vapor and ozone contents

?associated satellite data? = satellite measurements data except for brightness temperatures that are the Tbcal mean of profiles used in the formation of the initial profile. We then substract the forward model bias to the values (to look like observations).

identification information: that of ?the closest? profile

retrieval: information of the guess except :

profile: retrieved profile (temperature, moisture). For ozone, it is the same profile than for the guess

information on air on the surface = temperature and moisture of the retrieval at 1000hpa

additional information computed after initial profile definition: type of air mass by computing the distance, geopotential, tropopause, total water vapor and ozone contents

two emissivity values (for AMSUA and AMSUB channels) are computed in clear conditions, by using the retrieved profile and the satellite observations together.
 

 

Result coding

Depending on their requirements, users avail of four result coding routines that can read the binary result file and are activated on request :

ASCII coding: this routine can read inversion or co-location files and codes the satellite data and the profile on the RTTOV levels. The profile is a retrieval in the case of inversion files or an observation (radio sonde, analysis) in the case of co-location files.

AAPP level2 format coding: this coding was developed for potential integration of inversion in the AAPP system. It is then possible to compare the results of various sounding models.

SATEM coding: it is currently used for transmitting thicknesses onto some layers to the numerical weather prediction model. It is systematically activated at the CMS.

GRIB coding: this coding is particularly useful to display the inversion fields in terms of temperature and moisture on some levels onto the Synergie meteorological terminals. It is systematically activated at the CMS.

ASCII format is detailed in [3] and AAPP level2 format in [4]. SATEM and GRIB formats are meteorological standards, refer to the relevant documents [19].

 

 
 

Spooling: the next 3 modules (chapters 6.6, 6.7, 6.8) are run outside any real-time flow at different times of the day.

1. THE BASE_METEO MODULE

This module consists of acquiring meteorological information (profiles, surface parameters) observed, analyzed and forecasted, meant to be available for inversion. At the CMS, this data is extracted from the Diapason data base which contains the radio soundings conveyed through the GTS as well as analyses and forecasts related to the Arpège French numerical models and to the European center. The ATOUR10 grid of Arpège (100E,65W ; 0N,80N), centered on Western Europe, was chosen as analysis and forecasting grid for processing the observations of Lannion Acquisition Area. The grid pitch is 1*1 degrees. Analyses are extracted on 20 pressure levels from 1000 à 0.1hpa, for temperatures and moisture. Diapason files are in the GRIB format. They were in release 1 in ASCII format, also described in [4].

Release 3 is very likely to be used on the ATOUR10 grid of the European Center. Indeed, as early as this fall, analyses will reach 1hpa, which may solve the profile extrapolation problem.

Extracted profiles are checked (particularly important for radio sounding) and formatted to the input format of the direct RTTOV model, which then becomes the format used for all profiles to the end of inversion.

This input parameterization makes it possible to sample the fields of analysis in latitude and longitude, in order to reduce the size of the BASE_METEO files. At present, it is worth 2*2 at the CMS.

1. Quality tests

Quality tests are carried out on radio soundings and analyses. Profiles are dismissed if one of the following tests is confirmed:

for T : lowest pressure > 50Hpa, highest pressure < 850Hpa, number of levels of T, Td <value, lowest pressure of Td > 400Hpa

with, in addition, for radio soundings:

no surface level, incoherence between computed and read geopotential, no tropopause level, number of geopotential levels < value, deviation in T between 2 successive levels > 25K, deviation in P between 2 successive levels > value

2. Profiles: setting to RTTOV input format

Analyzed profiles and radio soundings are formatted to the ?profil40? format, compatible with the RTTOV input:

A climatological ozone profile (currently US Standard 76) is associated with each profile.

The water vapor content (in g/g) is computed for each level from the dew point temperature for radio soundings and from relative moisture for analyses.

Profiles in temperature, moisture and ozone are interpolated (in log of p) and extrapolated on 40 fixed levels, from 0.1Hpa to 1000Hpa. The temperature extrapolation retained at present is the MSIS software, even though it is far from satisfactory. It provides a temperature value for a pressure, a position (latitude, longitude) and a given instant. MSIS is used for stratospheric pressures that are not covered by radio sounding (above 50 - 30Hpa) and analysis (above 10Hpa). Connection between the real profile and the MSIS profile is brutal. Moisture extrapolation is as follows:

if p <70Hpa h2o(p)= constant

if 70<= p < 350Hpa h2o(p)= h2o(p=350) *(p/350)**3

Other information is associated with the profile: surface pressure (1000hpa for analysis, read value for radio sounding), temperature, moisture and ozone values at the surface pressure, an air mass (by computing the distance for average profiles of 5 different types), an evaluation of the tropopause level, water vapor and ozone integrated contents, geopotential computed on the 40 levels.

The air mass is determined as follows: average profiles for 5 air masses (winter polar, summer polar, wintermid-latitude, summermid-latitude, tropical) have previously been defined using the TIGR library classification. The air mass allocated to the profile is that which reduces most the distance in space of the pressures between the profile considered and each one of the 5 profiles.

The format associated with profiles p40 is specified in [4].

3. Forecasting

Forecast GRIB files on Diapason machine contain the same information as the analyses. However, the present ICI release only retains the sea pressure, the temperature at 1000Hpa and the wind module at 10m. The names of the files, when extracted, are reset in order to correspond to the date of the forecast.
 
 
2. THE BASE_PROFILE MODULE

The purpose of this module is to avail, on input of the sounding scheme, of the profiles representing atmospheric conditions for the acquisition area and the date considered. Up and down radiance and total transmittance are computed for each profile. For each satellite, profiles, radiance and transmittances are stored in 3 distinct files.

1. Profiles

With input parameterization, the profiles retained are analyses (in the profil40 format) of the fields at 00H archived in BASE_METEO and sampled at the 10*10-degree resolution so that a minimum of independence is possible between profiles. Each one of these daily ?sub-fields? is stored in a file, the name of which includes the name of the satellite and the date of the day. The file containing the BASE_PROFIL profiles for the d day is then compiled by linking the files from day d-10 to d-1. Radio soundings have not been retained for the creation of the BASE_PROFIL because they are mainly on land or on the coast and do not represent sea situations very well. The BASE_PROFIL is reviewed every day so as to avail of a rolling library as representative as possible of the meteorological situation for d day.

The number of days of the rolling library and the type of selection (1 N/profile or every N degree) is a processing option.

In the future, it would be suitable to place 2 profile files on a parallel level, one for clear situations, the other for cloudy situations. This would provide more coherent water vapor profiles under cloudy conditions.

For users who do not have a regular source of analyses at their disposal, this rolling base can be replaced by a worldwide static climatological library in the ?profil40? format. Two libraries are available with the ICI package: TIGR of the LMD [13] and NESDISPR of the NOAA/CIMSS [11] .

2. Radiance and transmittance

For each profile of the daily files, the up and down radiance E_up and E_do of each channel are computed with RTTOV for 10 incidence angle and 10 surface pressure conditions (from 1020 to 500hpa). Radiance values are stored in some daily files. Total ground-satellite transmittance ts(i) is also computed and stored in a third daily file type. Similarly, for profiles, radiance and transmittance files are linked up to constitute a 10-day rolling library. The concatenation is done by unix command for profile files. A fortran program is needed for radiances and transmission files because the record lenght of these files depends on the situation number.

3. Air mass covariance matrix

All BASE_METEO profiles have an air mass. This way, Tb covariance matrixes are allocated to the BASE_PROFIL for 5 air masses, 10 scanning secants, 10 surface pressures in channels space. The channels used are for Noaa14: HIRS 2,3,4 MSU 2,3,4, for Noaa15 : HIRS 2,3,4 AMSU 6,7,8,9. Matrixes are weighted by a coefficient on non-diagonal terms (since the channels are very much correlated) and then inverted. Inverse matrixes are archived.

 
3. Monitoring

The purpose of this module is on the one hand to re-adjust the inversion model to make sure that the retrieved profiles remain stable and intact with time, by periodically re-computing software statistic coefficients (tuning), on the other hand to perform a regular follow-up of the results quality (validation). Both actions are carried out by using co-located data files (co-location). This module is activated off-line 4 times a day for the co-location routine and at the end of the night for tuning (in order to prepare files for the following day) and validation.

We have noticed that the guess profile can be selected from a worldwide climatology without affecting the quality too much, which is not the case if the model is not regularly re-adjusted. To obtain a good inversion, it is then necessary to acquire regularly observed profiles.

In the document, you will find a description of what is being achieved at the CMS thanks to the input parameterization retained for computing all coefficients on a daily basis. Another time-division frequency can be used for co-location and tuning (especially for centers which do not systematically receive digital forecast model outputs).

1. Co-location

Co-location collects, for a given situation, satellite information of the level1d input file, guess and retrieval results, the forecast information used, the environment data for running the inversion and the closest observed atmospheric profiles.

Co-location is supplied with satellite data, forecast data and retrieved profiles from the binary inversion output files (see chapter 6.4.12) and in the BASE_METEO with two types of observed profiles: analyses and radio soundings. Co-location is performed at the end of each 00, 06, 12 and 18-H cycles, after supplying the BASE_METEO. The orbits considered are the orbits acquired at +/- 3 hours in relation to the time of observed profiles.

The program loops on the observed profiles and searches for all the closest inverted situations on sea. Distance is limited to 100 kilometers. If the search on sea is unsuccessful (no situation selected), the search is resumed on land. The co-location retained among the closest is then selected according to 3 hierarchical criteria: cloud amount, distance and time related deviation. The cloud amount is used for searching the clearest data in priority.

For each co-located situation, a test computes the departure on all channels, between the brightness temperatures computed for the observed profile by means of the radiative transfer model and the sounder?s measurements. The channels used in the inversion (see chapter 6.3) for which the departure is more than 3 times S_fw(i) are counted. If their number exceeds a maximum value (which depends on the cloudy type), the situation is flagged with an error code (but not suppressed from the file). The values for S_fw(i) are that used for the ICI module for the orbits considered of the considered day.

Four co-location files are generated per day, for 00, 06, 12 and 18-H cycles. The name of each file contains the satellite?s name as well as the date and time of the cycle.

2. Tuning

This routine is determining to obtain high quality and stable inversions in time. Its purpose is to compute the statistic parameters used in the ICI module on a regular basis. These parameters vary with the season, the type of meteorological situation and the age of the satellite.

Statistics on the mean and the standard deviation are performed on a daily basis (at the end of the day in order to prepare the following day) on the basis of all the co-location files available on the 10 preceding days. This way, all parameters change on a regular basis and they are constant values for the day. In some centers, the computation is carried out once or twice a month (e.g.: European Center). The result of these statistics is stored in two different files the name of which includes the satellite?s name as well as the starting and finishing dates considered. The first file is binary and contains the covariance matrix G whereas the second file is a text file with all other coefficients. Files are then copied with a generic name related to the satellite only.

The re-adjusted coefficients in ICI are the following:

direct model errors :

The following coefficients are set in the Tb space with clear co-locations on land and on sea separately from the Tbcal (observed profile) -Tbmes  differences. They are:

polynomial regression coefficients a₀(i), a_k(i) for all the channels required for computing the direct model biases in real time (see paragraph 6.4.7)

mean values of biases (delta). They are used in the ICI module if there is no regression coefficient.

error standard deviations S_fw used instead of the O+F matrix and to determine the error flag when selecting the guess profile as well as to compute the reference distance in the inversion routine.

Guess error:

Coefficients are set in the pressure space, on land and on sea separately, for the different cloud conditions, from the Tag - Tao differences.

DTag  guess bias

G guess error covariance matrix
 

3. Validation

The quality of inversions is followed up in a routine by means of a systematic output of graphs in the postcript format. The routine reads the statistic files described in the tuning chapter. Diagram 7 and 8 are an example of an output showing the quality of the inversion.

Both diagrams show the error statistics concerning the mean and standard deviation of the inversions compared to the analyses and radio soundings for Noaa14 (diagram 7) and Noaa15 (diagram 8), on the 40 RTTOV working levels. Statistics have been performed for  the last 10 days period and 3 cloud types. Statistics for land are on left figure and for sea on right.

Diagram 8 : Noaa15 : Quality of the retrieved profiles as compared to the observed profiles
 

Other statistics on the mean and standard deviation are compiled for two main cycles per day, so as to avail of a sufficient number of co-locations to have representative statistics:

Noaa14 : at 00H (00 and 06-H co-location files) and at 12H (00 and 06-H co-location files)

Noaa15 : at 06H (06 and 12-H co-location files) and at 18H (18 and 00-H co-location files)

By this way, a daily follow-up of the results quality is possible.

At present graph routines are generated using the PvWave software, they are not part of the ICI package we are distributing and are not described here. We are now developing a set of graph routines with a standard ?freeware? graphic software which could be implemented in the next ICI release.