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					    Kalpana water vapour channel radiances; their inclusion into 
        a fast radiative transfer model and subsequent use in the 
                                      ECMWF IFS forecast model 
                                                                  

                                                                            
 
 
 
 
 
                                              

                       Randhir Singh1, Graeme Kelly2, Roger Brugge3 

 
 
 
                                              


                                              


      1   Atmospheric Sciences Division, Meteorology and Oceanography 
           Group, Space Applications Centre, ISRO, Ahmedabad, India  

                                              

     2   UK Met Office, University of Reading, Reading, United Kingdom  

                                              


           3   The National Centre for Earth Observation, Department of 
          Meteorology, University of Reading, Reading, United Kingdom 

 

 

 

MAY 2009 
 
              The use of Kalpana water vapour channel radiances in a weather forecast model                                   2009    


                                              TABLE OF CONTENTS
ABSTRACT

1. Introduction ......................................................................................................................... 1

2. Overview of the Kalpana VHRR ........................................................................................ 5

3. Radiative transfer model: RTTOV .................................................................................... 7

3.1 General description of the model ………………………………………………………. 7

3.2 Radiative transfer equation .............................................................................................. 7

3.3 Transmittance parameterization ....................................................................................... 9

3.4 Line-by-line transmittance database ................................................................................ 10

3.5 Generation of transmittance coefficients ......................................................................... 12

4. Assessment of the accuracy of RTTOV for the Kalpana VHRR ...................................... 15

4.1 Comparison with line-by-line model computed transmittances and radiances .............. 15

4.1.1 Transmittances comparisons ........................................................................................ 15

4.1.2 Radiance comparisons .................................................................................................. 16

4.2 Comparison with the Kalpana observed clear sky WV radiances ….............................. 17

5. Comparison of performance of Kalpana and Meteosat-7 clear sky WV radiances
   in the ECMWF IFS Model ............................................................................................... 22
5.1 Introduction ..................................................................................................................... 22

5.2 Kalpana and Meteosat-7 WV radiance observations ...................................................... 23

5.2.1 The clear sky WV radiance products ........................................................................... 23

5.2.2 Bias correction of Kalpana clear sky WV radiances .................................................... 23

5.3 Assimilation methodology .............................................................................................. 25

5.3.1 The ECMWF model .................................................................................................... 25

5.3.2 The ECMWF operational 4D-Var scheme ................................................................... 26


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             The use of Kalpana water vapour channel radiances in a weather forecast model                                  2009   


5.3.3 Experimental setups ..................................................................................................... 27

5.4 Assimilation results ......................................................................................................... 28

5.4.1 Impact of Kalpana and Meteosat-7 clear sky WV radiances on the analysis .............. 28

5.4.2 Impact of the Kalpana and Meteosat-7 clear sky WV radiances on the forecast …..... 35

5.5 Conclusions .................................................................................................................... 38

6. Generation of transmittance coefficients for future Indian meteorological satellites ...... 39

6.1 Introduction .................................................................................................................... 39

6.2 GOES-11 channel characteristics ................................................................................... 39

6.3 Megha Tropiques channel characteristics ....................................................................... 43

6.4 Transmittance coefficients for GOES-11 ........................................................................ 45

6.5 Transmittance coefficients for Megha Tropiques ........................................................... 46

6.6 Accuracy of RTTOV for GOES-11 and Megha Tropiques ............................................ 46

6.6.1 Transmittance comparisons .......................................................................................... 47

6.6.2 Radiance comparisons .................................................................................................. 49

7. Overall conclusions and Future Possibilities ................................................................... 52

Acknowledgements ………………………………………………………………………... 55

References …………………………………………………………………………………. 57




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                                                                                               2009




                                           ABSTRACT


       A fast radiative transfer model (RTM), to compute emitted infrared radiances for a

Very High Resolution Radiometer (VHRR) onboard the operational Indian geostationary

satellite Kalpana, has been developed and verified. This work is a step towards the

assimilation of Kalpana water vapor (WV) radiances into numerical weather prediction

models. The fast RTM uses a regression-based approach to parameterize channel-specific

convolved level to space transmittances. A comparison between the fast RTM and the line-

by-line RTM demonstrated that the fast RTM can simulate line-by-line radiances for the

Kalpana infrared channels to an accuracy better than that of the instrument noise, while

offering more rapid radiance calculations. A comparison of clear sky radiances of the

Kalpana WV channel with the ECMWF model first guess radiances is also presented, aiming

to demonstrate the fast RTM performance with the real observations. In order to assimilate

the radiances from Kalpana, a simple scheme for bias correction has been suggested. In

addition to Kalpana, the RTM has also been developed and verified for the soon-to-be-

launched (Megha Tropiques) Indian meteorological satellite. Another planned Indian satellite

(INSAT-3D) will have channels similar to that of GOES-11 and, since at present the INSAT-

3D sensors response functions (SRFs) are not available, GOES-11 SRFs have been used in

order to access the accuracy of the fast RTM for INSAT-3D. To this end, the fast RTM has

also been developed and verified for GOES-11.


       The Kalpana VHRR (Very High Resolution Radiometer) water vapour channel is

very similar to the water vapour channel of MVIRI (Meteosat Visible and Infrared Radiation

Imager) on Meteosat-7 and both satellites observe the Indian subcontinent. Thus it is possible

to compare the performance of VHRR and MVIRI in NWP (Numerical Weather Prediction)
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                                                                                              2009




models. In order to do so, the impact of Kalpana- and Meteosat-7-measured water vapour

radiances were evaluated using analyses and forecasts of moisture, temperature, geopotential,

and winds using the ECMWF (European Centre for Medium Range Weather Forecast) IFS

NWP model. Using Kalpana WV radiances instead of                  observations from Meteosat-7

improves the fit of radiosonde data; in particular, the differences from both the background

and analysis fields are reduced for upper level temperature, geopotential and winds, and low-

middle level moisture. The fit of temperature and moisture sensitive channels in IASI, AIRS,

HIRS, and MHS is also improved using Kalpana WV radiances in place of Meteosat-7 ones.

Using Kalpana radiances appears to improve the prediction of the mid-upper tropospheric

geopotential in the tropics and moisture and winds over the Indian region. The results show

that, had Kalpana WV radiances been used in the ECMWF model instead of Meteosat-7, the

analysis and forecast during July 2008 would have been slightly better.




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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




                                      1 INTRODUCTION


       The complex nature of errors associated with retrieved information can lead to difficulties in

assimilating satellite retrievals of temperature and moisture in numerical weather prediction (NWP)

models (Andersson et al., 1991; Eyre et al., 1993). As an alternative, Eyre (1989) proposed a

method to use radiances directly via 3D-Var/4D-Var techniques. The basis of this method is that the

model maps conventional meteorological parameters into satellite radiance space using a radiative

transfer (RT) model in order to calculate the misfit between the model and observations quantified

by a scalar cost function. The value of this cost function is then used, along with the adjoint of the

forecast and RT models, to minimize the fit to the observations to find the optimal initial

conditions.

       RT models, which simulate observed satellite radiances for a given atmospheric state, can be

categorized into physical models and fast models. Physical (line-by-line) models calculate

absorption coefficients from atmospheric variables using line-by-line calculations, and are

computationally expensive. To assimilate satellite radiances into an NWP model without delaying

the forecast production, this calculation must be made in a few milliseconds. Fast RT models

usually achieve this goal by parameterizing the absorption stage. RTTOV (Radiative Transfer for

TIROS Operational Vertical Sounder) is an example of a fast model where the layer optical depth is

parameterized (Rayer 1995; Saunders et al., 1999; Matricardi et al., 2004) using linear combinations

of profile-dependent predictors. Presently most of the operational weather centres (e.g. METO

(United Kingdom Met Office), ECMWF (European Centre for Medium-Range Weather Forecasts),

NCEP (National Centers for Environmental Prediction) and Météo-France) assimilate radiances into

their NWP models. This approach has led to a significant improvement in the quality of the NWP

analyses and forecasts (Eyre et al., 1993; Andersson et al 1994; Kelly, 1997; Andersson et al., 1998;




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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




Derber and Wu, 1998; English et al., 2000; Bouttier and Kelly 2001) particularly in the southern

hemisphere and tropics.

       Infrared and microwave radiance data such as those from the Advanced TIROS Operational

Vertical Sounder (ATOVS) have been shown to be beneficial to NWP global model forecasts

because they provide valuable information on atmospheric temperature and humidity (English et al.,

2000; Bouttier and Kelly, 2001). At present, these data are far more useful over the oceans than

over land, since information about emissivity and surface temperature over land is not very accurate

and induces the removal of low-peaking channels in the assimilation process. Improvements in both

assimilation techniques and instruments will push the benefit of radiances further. In particular,

sounders such as the Advanced Infrared Sounders (AIRS) and the Infrared Atmospheric Sounding

Instrument (IASI) show more potential than ATOVS observations through their much finer spectral

and vertical resolution (Prunet et al., 1998). Despite their lower spectral resolution, radiometers on

geostationary satellites are particularly well adapted to weather forecasting, since they allow almost

continuous (i.e. approximately hourly temporal resolution) access to information about the

evolution of temperature and humidity fields at a high horizontal resolution.

       Owing to the sparseness of in situ moisture observation most of the NWP centres assimilate

water vapour radiances from satellite observations (McNally and Vesperini, 1996; Peubey and

McNally, 2009) to improve the upper tropospheric moisture analysis. In contrast to polar orbiting

satellites, data from geostationary radiometers/imagers have mainly been used for NWP either in

the form of atmospheric motion vectors (AMVs) derived from tracking features in the imagery or in

the form of cloud-top information (Macpherson et al., 1996). The assimilation of water vapour

radiances from geostationary satellites is quite recent, for example Geostationary Operational

Environmental Satellite (GOES) imager data at the Canadian Meteorological Centre (CMC;

Garand and Wagneur, 2002), at NCEP (Derber et al., 2003), and Meteosat-7 data at the ECMWF

(Köpken et al., 2004; Szyndel et al., 2004; Munro et al., 2004). Currently there are two Indian

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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




geostationary satellites, Kalpana at 74°E and INSAT-3A at 93.5°E, which provide mid-upper

tropospheric moisture information. Kalpana and INSAT-3A images are being extensively used in

conjunction with other available conventional meteorological data for analysis and weather

forecasting. The atmospheric motions vectors (AMVs) computed from the images from these

satellite are disseminated operationally on the Global Telecommunication System (GTS) for

international use.

       Although no systematic validation studies of AMVs computed from these satellites have

been carried out, limited studies made in this regard indicate that the quality of this product has led

to some improvement in NWP analyses and forecasts. In contrast, the assimilation of moisture

information, particularly in the form of raw radiances, from these satellites has not been attempted.

This is because a fast RT model is not available for these satellites, and, the raw radiance

measurements from these satellites are not disseminated operationally on GTS.

       In this study, we intend to exploit Kalpana water vapour radiances in the ECMWF 4D-Var

assimilation system. In order to do this, RTTOV has been selected as the fast RT model for use.

Applications of RTTOV to Kalpana require the generation of new regression coefficients for the

transmittance parameterization, specific to the spectral characteristics of the sensors on Kalpana

satellite. In this study the fast transmittance coefficients for sensors on Kalpana satellite have been

generated, verified, and implemented in RTTOV. The accuracy of RTTOV for the simulation of the

Kalpana VHRR transmittances and radiances is assessed by comparing the RTTOV simulated

transmittances profiles and top of the atmosphere radiances with the corresponding values from

line-by-line model.

       The Kalpana VHRR water vapour channel is very similar to the water vapour channel of

MVIRI (Meteosat Visible and Infrared Radiation Imager) on Meteosat-7 and both satellites observe

the Indian subcontinent. Thus it is possible to compare the performance of VHRR and MVIRI in

NWP models. In order to do so, the impact of the Kalpana and Meteosat-7 WV radiances were

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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




evaluated using analyses and forecasts of moisture, temperature, geopotential, and winds from

extensive (~30 days; July 2008) ECMWF 4D-Var assimilation cycles. The present study is, to our

knowledge, the first where radiance assimilation from a sensor onboard an Indian satellite has been

attempted.

       In addition to Kalpana, the fast transmittance coefficients for sensors on future Indian

meteorological satellite (e.g. Megha Tropiques) have also been generated, verified and implemented

in RTTOV. Fast transmittance coefficients have also been generated and verified for GOES-11 in

order to access the accuracy of RTTOV for INSAT-3D (another future Indian satellite).

       In the following section, an overview of the Kalpana VHRR is given. In section three we

outline the RTTOV radiative transfer model, transmittance parameterization used in RTTOV and

the generation of the transmittance coefficients for Kalpana VHRR. Section four describes the

performance of the fast RT model, for Kalpana VHRR, evaluated with the line-by-line model and

real observation. Section five details the Kalpana water vapour radiances, bias correction, and the

results of Kalpana water vapour radiance assimilation experiments. Section six describes the details

of the future Indian meteorological satellites and the generation of the transmittance coefficients for

these satellites. Section seven provides a summary of the work shown here as well as discussion of

the future work.




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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




                          2 OVERVIEW OF THE KALPANA VHRR


       METSAT (METeorological SATellite), launched in 2002 by an upgraded, four- stage

PSLV-C4 rocket from Sriharikota on the southeast coast of India, is the first exclusively

meteorological satellite built by ISRO (Indian Space Research Organisation). Previously,

meteorological services had been combined with telecommunication and television services in the

INSAT (Indian National SATellite) system. METSAT was developed by ISRO Satellite Centre,

Bangalore, while the meteorological payloads were developed by Space Applications Centre (SAC)

Ahmedabad. The triaxially-stabilized, 1,050 kg (including 560 kg of propellant), 550 W satellite

carries a VHRR scanning radiometer for three-band images: one in visible (VIS; 0.55-0.75 µm), the

second in the thermal infrared window (WN; 10.2–13.0 µm) and the third in the water vapour

infrared band (WV; 5.4–7.8 µm), to obtain atmospheric cloud cover, water vapour and temperature.

It carries also a Data Relay Transponder (DRT) to provide data from fixed/mobile ground level

weather platforms. On 5 February 2003 METSAT was renamed Kalpana to honour the late Indian

born astronaut Kalpana Chawla, who died in the Columbia STS-107 accident.


       Fig-2.1 shows the normalized spectral response (Fig-2.1a) and normalized weighting (Fig-

2.1b) functions of Kalpana infrared window (WN) and water vapour (WV) channels. The

normalized weighting functions shown in Fig-2.1b are computed from line-by-line radiative transfer

model using U.S. Standard Atmosphere. The weighting function, the derivative of transmittance

with respect to height (pressure), specifies the relative contribution each atmospheric layer makes to

the radiation emitted to space and thereby determines those regions of the atmosphere which are

sensed from space at this wavelength. The WN channel contains weak absorption line of water

vapour, CO2 and ozone and has a peak weighting function at the surface (Fig-2.1b), while the water

vapour (WV) channel is dominated by strong water vapour absorption lines and measured


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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




emanating (Fig-2.1b) from typically around 200-700 hPa, although in extremely dry atmosphere the

emission can originate from the lower layers.




Figure 2.1 (a) The spectral coverage of the Kalpana VHRR infrared bands plotted with Earth–
emitted spectra calculated from the U.S. Standard Atmosphere. (b) The normalized weighting
functions of the Kalpana VHRR infrared bands. The weighting functions are calculated from the
U.S. Standard Atmosphere using the line-by-line Radiative transfer model (LBLRTM).




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                      3 RADIATIVE TRANSFER MODEL: RTTOV


3.1 General description of the model


       RTTOV was originally developed (Saunders et al., 1999) and maintained by ECMWF but

the improvement and updates are now implemented through the EUMETSAT NWP Satellite

Applications Facility (SAF) by the METO, Météo-France and ECMWF. RTTOV does not perform

monochromatic radiative transfer (RT) calculations, but computes channel-specific convolved

transmittances for a particular satellite channel. RTTOV can simulate a range of different infrared

and microwave sensors. Prior to our study, RTTOV did not have coefficients to parameterize the

optical depths for any Indian satellite.


3.2 Radiative transfer equation


       For a plane-parallel atmosphere in local thermodynamic equilibrium with no scattering and

assuming specular reflection at Earth’s surface, the clear sky upwelling monochromatic radiance

(Saunders et al., 1999) at the top of the atmosphere can be written as

                                                1

        R(υ, θ) = ϒs (υ, θ)εs (ν, θ)B(υ,Ts ) + ∫ B(υ,T )d ϒ +
                                                ϒs
                                           1                                       (3.1)
                     [1 − εs (υ, θ)]ϒs (υ, θ)∫ (B(ν,T ) /ϒ2 )d ϒ
                                     2

                                           ϒs




where R(ν, θ) are monochromatic radiances at wave number ν and zenith angle θ, B(ν,Ts) is

Planck’s function for scene temperature T, ϒs and ϒ are surface-to-space and level-to-space

monochromatic transmittances, and εs (ν, θ) is the surface emissivity; here subscript s refers to the

surface. To represent the outgoing radiance as viewed by the satellite sensor, the spectrum of the

monochromatic radiance given by Eq. (3.1) must be convolved with a particular satellite sensor

response function (SRF).
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        The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




            R(θ) =
                       ∫ R(ν, θ)φ(ν )d ν
                                                                                                                    (3.2)
                          ∫ φ(ν )d ν

where φ(ν ) is the normalized SRF and the circumflex denotes convolution. The most accurate (line-

by-line) method of obtaining these monochromatic radiances R(ν,θ) is by summing the absorption

coefficients in very narrow spectral interval over each contributing line followed by integration over

the atmospheric path.


         By assuming that the convolved monochromatic (Matricardi et al., 2004) radiance can be

replaced with a radiance calculated using convolved transmittances, we can rewrite Eq. (3.1) in

discrete layer notation for J atmospheric layers (level j =1 to js from the top to the layer above the

surface) and for a nadir view to simplify the notation:


                                  js    u                      js      u   2
      Ri = ϒi,s εi,s Bi (Ts ) + ∑ R i, j + (1 − εi,s ){∑ Ri, j (ϒi,s / (ϒi, j ϒi, j −1 ))}+ Li             (3.3)
                                 j =1                        j =1




where Ri is the convolved radiance for the ith radiometer channel and ϒi, j is the convolved

transmittance from level j to space integrated over the ith radiometer channel spectral response. Li

is a small atmospheric contribution (Saunders et al., 1999) from the surface to the first layer above
                         u
the surface and R i , j is defined as


            u                                                 d i, j
         R i , j = Bi (T j ) + [ Bi (T j +1 ) − Bi (T j )]                                                (3.4)
                                                             d i , j +1


where d i , j ( d i , j = − log( ϒ i , j ) ) and d i , j +1 ( d i , j +1 = − log( ϒi , j +1 )) are the convolved optical depths

from space to the top and the bottom of the layer, respectively. This final RT equation (Eq.3.3) for

clear sky conditions used in RTTOV involves convolved layer-to-space transmittances (instead of

monochromatic transmittances), which are calculated from profile-dependent predictors and fast

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           The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




transmittance coefficients. The generation of fast transmittance coefficients is a one-off procedure;

once generated, they are simply read by RTTOV during the model integration, thereby drastically

reducing the computation time needed.


3.3 Transmittance parameterization


             RTTOV deals separately with gases of constant mixing ratio (Saunders et al., 1999) and

with each gas of variable (H2O and O3 in this study) mixing ratio. The combined transmittances

     Fix +H 2O +O3
( ϒi , j               ) of all the gases are obtained as the product of the individual transmittances. However,

Beer’s law is not obeyed for convolved transmittances, thus convolution of the transmittances of all

the gases is not equivalent to the product of each gas convolved individually.

                 Fix +H 2O +O3          Fix   H 2O   O3
              ϒi, j               ≠ ϒi , j ϒi , j ϒi , j                                                   (3.5)

                Fix +H 2O +O3                                                              Fix   H 2O           O3
where ϒi, j                      is the convolved transmittance of all the gases and ϒi, j , ϒi, j , and ϒi, j are the

transmittances of single gases convolved individually. To reduce the error introduced by separation

of the gas transmittances after convolution, the ratios of the convolved transmittances are taken so

that product of the individual component terms would produce the desire total transmittance

(Bormann et al., 2005). In ratio form the total transmittance can be written as:


                                                                           ⎞
                                              ⎛ Fix +H 2O ⎞⎛ Fix +H 2O +O3 ⎟
                                                          ⎟ ⎜ ϒi, j
                 Fix +H 2O +O3     ⎛ Fix ⎞ ⎜ ϒi, j
                                            ⎟⎜⎜           ⎟⎜               ⎟
              ϒi , j             ≡ ⎜ ϒi , j ⎟ ⎜
                                   ⎜                      ⎟⎜
                                                          ⎟ ⎜ Fix +H O ⎟   ⎟
                                                                           ⎟                            (3.6)
                                   ⎜
                                   ⎝        ⎟⎜
                                            ⎠⎜     Fix    ⎟
                                                          ⎟⎜               ⎟
                                              ⎝ ϒi , j ⎟ ⎜ ϒ i , j         ⎟
                                                                      2
                                                          ⎠⎝               ⎠


where the superscripts indicate which gases are taken in each transmittance calculation. The three

factors on the right-hand side (Eq. 3.6) thus serve as ‘effective level-to-space transmittances’ for the

fixed gases, water vapour, and ozone, respectively. The convolved effective layer optical depths can

be defined as:



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          The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




      Fix      Fix             ⎛ Fix     Fix ⎞
    d i, j − d i, j −1 = − log ⎜ϒi, j ÷ ϒi, j −1 ⎟
                               ⎜                 ⎟
                                                 ⎟                                   (3.7)
                               ⎜
                               ⎝                 ⎠


                                ⎛ Fix +H 2O     Fix +H 2O ⎞
       H 2O     H 2O            ⎜ ϒi , j       ϒi, j −1 ⎟ ⎟
     d i, j − d i, j −1 = − log ⎜
                                ⎜
                                ⎜            ÷            ⎟
                                                          ⎟
                                                          ⎟                                  (3.8)
                                ⎜
                                ⎜ ϒi, j
                                         Fix        Fix
                                                          ⎟
                                                          ⎟
                                ⎝               ϒi, j −1 ⎠



                                ⎛ Fix +H 2O +O3  Fix +H 2O +O3 ⎞
                                                               ⎟
     O3        O3               ⎜ ϒi , j
                                ⎜               ϒi, j −1       ⎟
   d i, j − d i, j −1           ⎜
                        = − log ⎜ Fix +H O ÷                   ⎟
                                                               ⎟                    (3.9)
                                                     Fix +H 2O ⎟
                                ⎜
                                ⎜ ϒi , j   2                   ⎟
                                                               ⎟
                                ⎝                ϒi, j −1      ⎠

           The transmittance parameterization in RTTOV is based on a linear regression model for the

above convolved effective layer optical depths. The convolved effective layer optical depth (Rayer

1995; Saunders et al., 1999; Matricardi et al. 2004) from level j to space for the ith radiometer

channel can be written as:

                                                 M
                          d i , j = d i , j −1 + ∑ ai , j ,k X k , j               (3.10)
                                                k =1




where Xk,j constitute the profile-dependant predictors, M is the number of predictors, and ai,j,k are

the regression coefficients for each layer.


3.4 Line-by-line transmittance database


           The line–by-line monochromatic transmittance database (LBL database) used to derive the

regression coefficients (ai,j,k) was generated using LBLRTM_v_11.3 (hereafter LBLRTM).

LBLRTM is a physical radiative transfer model (Clough et al., 1981) that is publicly available. The

LBLRTM has been developed at Atmospheric Environmental Research (AER) and is derived from

the Fast Atmospheric Signature Code (FASCODE). It has been extensively validated against

atmospheric radiance spectra by Matricardi (2007), who recommended that LBLRTM should be

used as the line-by-line model for the generation of an LBL database to train the fast RTMs for

infrared region.

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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




       LBL transmittance calculations are very expensive and so LBLRTM uses an optimum

number of diverse profiles for the training and validation of the fast RTMs. The ‘ECMWF 52’ set of

atmospheric profiles (Chevallier, 2002), representing the range of variation in temperature and

absorber amount found in the real atmosphere, is used to compute the LBL database - they contain

temperature, moisture, and ozone at 43 (1013 - 0.1 hPa) pressure levels. The ‘ECMWF 52’ profiles

were sampled from a large profiles dataset generated using an operational suite of the ECMWF

forecasting system (the IFS). The characteristics of the ‘ECMWF 52’ profiles used here are

summarised in Fig-3.1.




Figure 3.1 The vertical distribution of the (a) temperature profiles, (b) water vapour profiles, and

(c) ozone profiles in the “ECMWF 52” training dataset. The thick solid black line indicates the

mean profile.


       For the LBL calculations we included 15 atmospheric constituents; while the concentration

of H2O and O3 was allowed to vary, the other ‘fixed’ gases (CO2, N2O, CO, CH4, NO2, SO2, NO,


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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




N2, O2, CCl4, NH3, CF4, and CCl3F) were held constant. The line parameters were obtained from the

2004 edition of the HITRAN molecular database. The monochromatic transmittances were

computed for each of 52 profiles from space to each of 43 pressure levels (1013 - 0.1 hPa) and at

six viewing angles (θ) measured from the zenith, namely those angles for which secθ has the values

1.00, 1.25, 1.50, 1.75, 2.00, 2.25. LBL calculations were performed at full resolution, and the

resulted spectra were subsequently convolved with Kalpana VHRR channels response functions.


3.5 Generation of transmittance coefficients


        The monochromatic transmittances ( ϒi , j = exp(−di , j ) ) provided by LBLRTM were

convolved over the Kalpana SRF to produce polychromatic transmittances ( ϒi, j ). In order to apply

                                                                                      Fix +H 2O          Fix +H 2O +O3
                                                                             Fix   ϒi , j             ϒi , j
Eq. (3.6), the convolved transmittances were grouped into three { ϒi, j ,                   Fix
                                                                                                  ,        Fix +H 2O
                                                                                                                         } sets.
                                                                                      ϒi, j             ϒi, j

These convolved transmittances computed for the ‘ECMWF 52’ profiles then became the data

points in the regression (Eq. 3.10). The effective layer optical depths from the LBL database were

then used to compute the regression coefficients by multiple linear regression (MLR) of d i , j − d i , j −1

against the predictor values Xk,j. The predictors used to parameterize the layer optical depths are

functions of temperature, absorber amount, pressure and viewing angle. The MLR is performed on

the layer optical depths instead on the level to space optical depths; the former gives significantly

more accurate (Matricardi and Saunders 1999) results than the latter. The fast transmittance

coefficients are generated for H2O, O3, and the fixed gases. The predictors used (Tables-3.1 & 3.2)

in Eq. (10) are those given by Matricardi et al., (2004). For mixed gases there are 10 predictors, for

water vapour 15, and for ozone 11.


        Fast transmittance coefficients for Kalpana (only the WV channel) were also generated by

Singh et al. (2009), who used the ‘ECMWF 83’ profiles at 101 pressure levels (1100 - 0.005 hPa).

     12
         The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




Currently, the RTTOV used in operational assimilation system at ECMWF uses only 43 pressure

levels. In order to assimilate the Kalpana radiances in ECMWF IFS model, the fast transmittance

coefficients for Kalpana VHRR (WV & WN channels) are generated again (in this study) for

‘ECMWF 52’ profiles at 43 levels (1013 – 0.1 hPa). The accuracies of the fast model are same for

both datasets.


Predictors          Fixed gases            Water vapour                         Ozone
X1,j                sec(θ )                sec (θ )W ( j )
                                               2
                                                        r
                                                         2
                                                                                sec(θ )Or ( j )
X2,j                sec (θ )
                          2
                                           (sec(θ )Ww ( j ))2                     sec(θ )Or ( j )
X3,j                sec(θ )Tr ( j )        (sec(θ )Ww ( j ))4                   sec(θ )Or ( j )δ T ( j )
X4,j                sec(θ )T ( j )
                               r
                                2
                                           sec(θ )Wr ( j )δ T ( j )             (sec(θ )Or ( j ))2
X5,j                Tr ( j )                 sec(θ )Wr ( j )                      sec(θ )Or ( j ) δ T ( j )
X6,j                T ( j)
                     r
                      2
                                           4 sec(θ )Wr ( j )                    sec(θ )Or ( j )2 Ow ( j )
X7,j                sec(θ )Tw ( j )        sec(θ )Wr ( j )                      Or ( j )
                                                                                         sec(θ )Or ( j )
                                                                                Ow ( j )
X8,j                          Tw ( j )     (sec(θ )Wr ( j ))3                   sec(θ )Or ( j )Ow ( j )
                    sec(θ )
                              Tr ( j )
X9,j                  sec(θ )              (sec(θ )Wr ( j ))4                   Or ( j ) sec(θ ) Ow ( j ) sec(θ )
X10,j                 sec(θ ) 4 Tw ( j )   sec(θ )Wr ( j )δ T ( j ) δ T ( j )   sec(θ )Ow ( j )
X11,j                               0        sec(θ )Wr ( j ) δ T ( j )          (sec(θ )Ow ( j ))2
X12,.j                              0      sec(θ )(Wr ( j ))2                                     0
                                                 Ww
X13,j                               0        sec(θ )Wr ( j ) Wr ( j )                             0
                                                   Ww ( j )
X14,j                               0                Wr2 ( j )                                    0
                                           sec(θ )
                                                     Tr ( j )
X15,j                               0                Wr2 ( j )                                    0
                                           sec(θ )
                                                     Tr4 ( j )


Table 3.1. Predictors used for the parameterization of the optical depths for the fixed gases, water
vapour and ozone.




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        The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




Tl = (Tl +1 + Tl profile ) / 2
         profile
                                             Tl * = (Tl +1
                                                        reference
                                                                  + Tl reference ) / 2   Tr (l ) = Tl / Tl *

Wl = (Wl +1 + Wl profile ) / 2
         profile
                                             Wl * = (Wl +1
                                                        reference
                                                                  + Wl reference ) / 2   Wr (l ) = Wl / Wl *

Ol = (Olprofile + Olprofile ) / 2
        +1                                   Ol* = (Olreference + Olreference ) / 2
                                                       +1                                Or (l ) = Ol / Ol*

P = ( P+1 + P ) / 2
 l     l     l


           l
Tw (l ) = ∑ ( p (i) − p (i − 1))Tr (i − 1)
          i =2



          ⎛ l                                  ⎞ ⎛ l                                ⎞
Ww (l ) = ⎜ ∑ p (i )( p(i ) − p (i − 1))W (i ) ⎟ ÷ ⎜ ∑ p(i )( p (i) − p(i − 1))Wi * ⎟
          ⎝ i =2                               ⎠ ⎝ i =2                             ⎠

          ⎛ l                                  ⎞ ⎛ l                               ⎞
Ow (l ) = ⎜ ∑ p (i )( p (i ) − p (i − 1))O(i ) ⎟ ÷ ⎜ ∑ p(i )( p(i ) − p(i − 1))Oi* ⎟
          ⎝ i =2                               ⎠ ⎝ i =2                            ⎠



Table 3.2. Definition of the profile variables used in predictors defined in Table 3.1. The Pl is the
value of pressure at each level. Tl profile , Wl profile , Olprofile are the temperature, water vapour mixing
ratio, and ozone mixing ratio profiles. Tl reference , Wl reference , Olreference are the corresponding reference
profile. For these variables l refers to the lth level; otherwise l is the lth layer, i.e., the layer above
the lth level.




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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




 4. ASSESSMENT OF THE ACCURACY OF RTTOV FOR THE KALPANA VHRR

4.1 Comparison with line-by-line model computed transmittances and radiances

       The transmittance coefficients generated for the Kalpana VHRR infrared channels were

implemented in the RTTOV, thereby enabling us to simulate the transmittances and radiances, for

Kalpana, for a given temperature, moisture and ozone profile along with surface temperature and

winds. The accuracy of RTTOV in simulating Kalpana channel transmittances and radiances was

assessed by comparing the RTTOV simulated transmittance profiles and top of the atmosphere

radiances with the corresponding values from the line-by-line models; these simulated values were

computed for an independent set (i.e. a set not used in the training of RTTOV) of profiles. The

independent dataset used in this study comprises 117 diverse profiles generated from the ECMWF

IFS model (Chevallier, 2001). The transmittance comparison is more useful in understanding how

the fast model performs and to see where it needs to be improved, but radiances need to be accurate

as they will be used in the assimilation.


4.1.1 Transmittances comparisons


       Fig 4.1(a) shows the RMSD between LBLRTM and RTTOV simulated transmittances for

Kalpana VHRR channels. These statistics are for 6 different viewing angles in the range 0° to 63.6°.

The infrared window channel (WN) shows the minimum RMSD, while the channel sensitive to

water vapour (WV) shows the maximum (0.007) RMSD. In both the channels maximum RMSD are

found near the peaks of the weighting function (where the instrument sensitivity to the variation in

moisture or temperature is largest).




    15
      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




Figure 4.1 (a) Root mean square of the difference (RMSD) between RTTOV and LBLRTM layer to
top of the atmosphere transmittances for the independent 117-profile set for 6 viewing angles, for
Kalpana VHRR infrared channels. (b) RMSD and bias of RTTOV top of atmosphere brightness
temperature differences from LBLRTM model for the same profiles and angles for the Kalpana
VHRR channels. Also shown is the instrument noise, NeDT.

4.1.2 Radiances comparisons


       The ability of the fast model to reproduce the line-by-line (LBL) radiances in terms of the

bias and RMSD between the fast model and LBL computed radiances is shown in Fig 4.1(b). Also

plotted in Fig 4.1(b) are the instrument noise values (NeDT) for each channel. The radiances are

plotted in units of equivalent black body brightness temperature. The brightness temperatures have

been computed using the radiative transfer formulation within RTTOV and the LBL model

transmittances to ensure any differences are only due to the LBL and fast model transmittances and

are not a result of the integration of the radiative transfer through the atmosphere. So, errors in the

brightness temperature were computed by using the fast model transmittances, as opposed to those

computed by using the LBL transmittances in Eq. (3.3). Radiances for all 6 viewing angles are

    16
      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




included in the statistics. Fig 4.1(b) demonstrates that the RTTOV errors (WV channel RMSD =

0.15 K; WN channel RMSD=0.07 K) are well below the instrument noise (WV channel NeDT =

0.23 K; WN channel NeDT= 0.18 K) for Kalpana VHRR channels.


4.2 Comparison with the Kalpana observed clear sky WV radiances

       An end to end evaluation (Saunders et al., 1999) of the fast model can be done by comparing

the radiances computed from the NWP model first guess field (the first guess radiances) with the

measured radiances. The limitation of this comparison is that errors in the fast model, errors in the

instrument calibration and errors in the NWP model first guess profiles add uncertainties to the

comparison. Nevertheless, the comparison is very important as the differences between these

radiances, after bias correction, will be presented to the NWP model for the direct radiance

assimilation.


       RTTOV has been employed to compute the first guess radiances for the comparison with the

Kalpana observed WV channel radiances. The comparison is not performed for the WN channel

(surface peaking channel) due to the uncertainty in the surface emissivity and surface temperature.

The atmospheric profiles of temperature, moisture, and ozone along with surface temperature and

winds used for the calculation of first guess radiances are produced by ECMWF. The ECMWF

dataset has a maximum horizontal grid spacing of about 125 km with 91 vertical levels. The

Kalpana raw radiances (given in terms of equivalent black body brightness temperatures) are

available at a resolution of 8 x 8 km2 at the sub-satellite point. The brightness temperatures used in

this study are clear sky brightness temperatures (CSBTs) and represent averages over those pixels

of a 6 x 6 pixel sub-segment that are found cloud free (cloud flagging is based on the window

channel radiances). Thus the resolution of the CSBTs product corresponds to about 50 x 50 km2 at

the sub-satellite point. CSBTs for the Kalpana WV channel were simulated by RTTOV using the

ECMWF profiles at the main synoptic hours (0000, 0600, 1200, and 1800 UTC) from 1st to 31st

    17
      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




July 2008 over the area covered by the Kalpana disk (approximately 50ºS-50ºN; 20ºE-120ºE). The

observed CSBTs are interpolated to 125 x 125 km2 to match the first guess CSBTs. The RMSD

values and the bias between the Kalpana-observed and the RTTOV-simulated CSBTs are analysed

for the month of July 2008.




Figure 4.2 The geographical distribution of RMSD values between the Kalpana-observed and the
ECMWF first guess CSBTs (K). These statistics are computed from 6-hourly data during 1st -31st
July 2008. The white gaps in the figure are due to the non-availability of CSBTs due to persistent
clouds.

          Fig 4.2 shows an example of the geographical distribution of the RMSD values during July

2008. Over a significant portion of the domain the RMSD are below 1 K. Slightly higher

differences are seen over the Himalayan and surrounding elevated regions. The surface emissivity

and land surface temperature used in RTTOV for the forward calculation may be the reasons for

these large differences. Over the Himalayan region the Kalpana WV channel weighting function

peaks near the surface and hence the surface radiance contributes significantly to the measured

radiances. The surface radiances are strongly influenced by the surface emissivity and the land


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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




surface temperature. The model surface emissivity is a constant value of 0.98 which is not a good

assumption for many surfaces. Also, the model land surface temperature is not accurate over the

higher orography. Overall it appears that first guess radiances produced by RTTOV from ECMWF

atmospheric profiles are consistent with the Kalpana-observed radiances.




Figure 4.3 Geographical distribution of mean difference (bias) between Kalpana-observed and
ECMWF first guess CSBTs (K), at (a) 0000 UTC, (b) 0600 UTC, (c) 1200 UTC, and (d) 1800
UTC, during July 2008. The white gaps in the figure are because of unavailability of the Kalpana
CSBTs due to the persistent clouds.
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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




       The mean differences pattern of the observed minus first guess CSBTs at 0000, 0600, 1200

and 1800 UTC averaged for July 2008 are displayed in Fig 4.3. For most of the time, except 1800

UTC and at 0000 UTC over the equatorial Indian Ocean, the CSBTs from the ECMWF IFS model

are lower than those observed by Kalpana over the whole disk. Thus the observations are warmer

than the first guess at 0000, 0600 and 1200 UTC, while the observations are cooler than the first

guess at 1800 UTC.


       Fig 4.4 shows the temporal evolution (at 6-hourly intervals) of the mean differences (bias)

(Fig 4.4(a); grey line) and RMSD (Fig 4.4(b); grey line) between the first guess CSBTs and those

from Kalpana, averaged over the whole disk of Kalpana. In addition to the whole disk, the statistics

for land and sea surfaces were also analysed separately. From Fig 4.4, a diurnal cycle in the bias

and RMSD can be seen. The whole Kalpana disk mean bias varies from -0.2 to 0.8 K and the

RMSD from 0.65 to 1.2 K. It was found that a diurnal variation in the mean bias and RMSD with a

magnitude similar to that of the whole Kalpana disk values are present (not shown) over both land

and sea. Fig 4.4(c) shows the temporal evolution of the Kalpana observed (black line) and ECMWF

first guess (grey line) domain-averaged CSBTs. It is quite clear that the ECMWF IFS shows large

diurnal variations in the CSBTs in comparison to the Kalpana observations. The absence of large

diurnal variations in the Kalpana observed CSBTs is responsible for the diurnal variation in the

differences between the observed and first guess CSBTs. The temporal evolution in the whole

Kalpana disk mean bias and RMSD is similar to the finding of Szyndel et al. (2004), who studied

the differences between ECMWF first guess CSBTs and SEVIRI (Spinning Enhanced Visible and

Infrared Imager) on Meteosat-8. However, the magnitude of the bias and RMSD for Kalpana (bias

-0.2 to 0.8 K; RMSD 0.65 to 1.2 K) is smaller than SEVIRI (bias -1.7 K; RMSD 1.5 to 2 K).




    20
      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




Figure 4.4 (a) Temporal evolution of the whole Kalpana disk mean bias with respect to the
ECMWF first guess CSBTs; (b) as (a) but for the RMSD values. The grey lines are before the
application of a bias correction and the black lines are after the bias correction. (c) Kalpana-
observed CSBTs (black) and ECMWF first guess CSBTs (grey). The discontinuities in the time
series are due to the non availability of Kalpana data.




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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




       5 COMPARISON OF THE PERFORMANCE OF KALPANA AND
     METEOSAT-7 CLEAR SKY WV RADIANCES IN THE ECMWF IFS
                                            MODEL

5.1 Introduction


       The Kalpana VHRR water vapour channel is very similar to the water vapour channel of

MVIRI on Meteosat-7. The Meteosat-7 WV radiances have been operationally assimilated at the

ECMWF (Köpken et al., 2004) since 2002, having a small positive to neutral impact on the

prediction of upper level winds and geopotential (Köpken et al., 2004; Szyndel et al., 2004; Munro

et al., 2004). Köpken et al. (2004) have monitored the difference between Meteosat-7 and ECMWF

first guess WV radiances and found that Meteosat-7 observations were on average 3.8 K warmer,

while the RMSD was of the order of 2 to 2.5 K. These large differences were believed to be due to

the calibration of the Meteosat-7 instrument, and to biases in the radiative transfer (RT) model and

the ECMWF water vapour fields. Another striking feature in the Meteosat-7 monitoring time series

were regular spikes in the first guess departures. These were caused by stray solar radiation

intruding into the radiometer close to local midnight. A comparison of Kalpana WV radiances with

the corresponding ECMWF model first guess radiances shows (Singh et al., 2009) that the Kalpana

radiances exhibit a small difference (Kalpana minus model of -0.2 to 0.8 K) with RMSD values of

the order of 0.65 to 1.2 K. The monitoring results thus indicate that Kalpana is less noisy than

Meteosat-7.

       The objective of this study, therefore, is to compare the performance of the Kalpana and

Meteosat-7 WV radiances in the ECMWF 4D-Var assimilation system in order to see if there are

any advantages to using Kalpana rather than Meteosat-7 WV radiances.




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       The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




5.2 Kalpana and Meteosat-7 WV radiance observations


5.2.1 The clear sky WV radiance products


          Like the Meteosat-7 WV channel (Munro et al., 2004), the spectral response function (Fig

2.1(a)) of the Kalpana WV channel is significantly broad. Raw Kalpana WV channel radiances are

produced by the Space Applications Centre, SAC, and are available at pixel resolution of 8 x 8 km2

at the sub-satellite point. The radiances used in this study are clear sky radiances (expressed in

terms of equivalent black body brightness temperature; CSBTs) and represent averages over those

pixels of a 6 x 6 pixels sub-segment that are found cloud-free. Thus the resolution of the Kalpana

clear sky radiances corresponds to about 50 x 50 km2 at the sub-satellite point.

        The Meteosat-7 clear sky radiance data used in this study are produced by EUMETSAT and

available via the Global Telecommunications System (GTS). The clear sky radiances are calculated

by averaging radiances from cloud free pixels over a segment of 16 x 16 pixel square. The

resolution of the clear sky radiance product of Meteosat-7 corresponds to 80 x 80 km2 at the sub-

satellite point.

5.2.2 Bias correction of the Kalpana clear sky WV radiances


        Before a new observation is introduced to the assimilation system, initial monitoring of the

first guess departures (representing the difference between the observations and the model first

guess in observation space) is undertaken. In an optimal system, the distribution of these departures

should be centered on zero (e.g. model and observation should be unbiased) and Gaussian in shape.

In section 4, we saw that observation and model are slightly biased and the biases vary with time.

Hence, in order to assimilate the Kalpana CSBTs in the ECMWF assimilation system, bias

correction is essential. Before removing this bias, it is important to understand whether the biases

are caused by the observations or the model. The inaccuracies in the fast RTM, the error in the

calibration of the satellite instrument and the error in the first guess model profiles of temperature
     23
      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




and humidity are three possible sources for the differences between the observed and first guess

CSBTs. RTTOV was shown (section 4) to reproduce line-by-line calculations with very good

accuracy (RMSD 0.15 K; bias -0.03 K). This indicates that the fast RTM may not be the source of

the bias. A comparison of the Kalpana observed CSBTs with RTTOV-simulated CSBTs using

spatially and temporally coincident radiosonde profiles of temperature and moisture can help to

decide whether the biases are attributable to the model or to the observation. To check this, the

Kalpana-observed CSBTs have been compared (Singh et al., 2009) to CSBTs computed from

pseudo-profiles extracted from ECMWF analyses at 0000 and 1200 UTC during July 2008. Singh et

al., (2009) concluded that that the diurnal pattern in the bias and RMSD may not be due to the

ECMWF first guess; rather it is probably due to the calibration of the VHRR instrument.


       The geographical distribution (Fig 4.3) of the biases of Kalpana is relatively homogenous

and does not show any variation with airmass or scan angle. Therefore, no scan or airmass

correction is required for the Kalpana data. The global mean biases are 0.30 K, 0.73 K, 0.68 K, and

-0.1 K at 0000, 0600, 1200, and 1800 UTC, respectively. For the assimilation of CSBTs from

Kalpana, it was decided to apply a simple bias correction that was simply a function of the time.

The above mentioned values were subtracted from the observed CSBTs during July 2008. In most

cases, the whole Kalpana disk mean differences after the bias correction are within ± 0.1 K (Fig

4.4(a); black line). The RMSD values (black line; Fig 4.4(b)) are also reduced after the bias

correction. Fig 5.1 shows the histogram of the differences (observation minus first guess) before

(Fig 5.1(a)) and after (Fig 5.1(b)) bias correction during July 2008. In Fig 5.1(a) the distribution of

the differences before bias correction is not Gaussian (note the tail on the right hand side of the

histogram and a non-zero mean). The bias-corrected differences (Fig 5.1(b)) have a zero mean and

the shape of their distribution is Gaussian. This simple time-dependent bias correction procedure is

thus successful in reducing the whole Kalpana disk mean biases.


    24
      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




Figure 5.1 Histogram of Kalpana observed minus ECMWF first guess CSBTs, (a) before and (b)
after applying the bias correction.




5.3. Assimilation Methodology

5.3.1 The ECMWF model


       The ECMWF IFS global model and its four-dimensional variational (4D-Var) assimilation

scheme (Mahfouf and Rabier 2000; Rabier et al., 2000) are used for the assimilation of Kalpana and

Meteosat-7 observed clear sky WV radiances. The assimilation experiments described in this paper

were carried out with version 32r2 of the model (http://www.ecmwf.int/products/data/technical

/model_id/index.html) run at a truncation of T159 (approximation 125 km at the equator). In the

vertical, a hybrid coordinate of 91 levels between the surface and the top (90 km) of the atmosphere

is used. The model includes a semi-Lagrangian advection scheme together with a linear Gaussian

grid (Hortal 1999). The physics package is an improved version of that described by Gregory et al.

(2000), with the main modifications summarized by Jakob and Klein (2000) and Morcrette (2002).



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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




5.3.2 The ECMWF operational 4D-Var scheme


       The variational approach to the assimilation of the data into NWP models has been

described by number of authors (e.g. Lorenc 1986; Le Dimet and Talagrand 1986). It relies on the

minimization of an objective cost function, J(x), with respect to an atmospheric state x. The

ECMWF 4D-Var systems is based on an incremental formulation that guarantees a good agreement

between operational practicability and a physically consistent four-dimensional analysis (Courtier et

al. 1994). The objective cost function in the incremental approach is formulated as follows:


           J (δ x0 ) = J o + J b + J c                                                    (5.1)


                  1 n
           Jo =     ∑ (di − H ilδ xi )T Ri−1 (di − H ilδ xi )
                  2 i =0
                                                                                         (5.2)




                1
           J b = (δ x0 )T B −1 (δ x0 )                                                    (5.3)
                2


       In this formulation, J 0 is the observation cost function measuring the distance between the

model trajectory and corresponding observations; J b is the background cost function which

                                                                                    b
measures the distance between the initial state of the model x0 and the background x0 obtained

from short-range forecast valid at the initial time of the assimilation period. An additional cost

term, J c , is added in Eq. (5.1) to further constrain the fast modes of the estimated state (Gauthier

and Thepaut 2001). In Eq. (5.2), δ xi = xi − xib is the analysis increment and represents the departure

of the model state ( x) with respect to background ( xb ) at any time ti ; H l is the tangent linear form

of the full non-linear observational operator ( H ) and di = yi − H i ( xib ) is the departure of the model

background equivalent from observation ( yi ) . In the case of radiance assimilation, H includes the


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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




RTTOV. The matrix Ri is the combined error covariance of the observations and the observational

operator, while B represent the background error covariance matrix. The background covariances

matrix is formulated according to the “wavelet- J b ” method of Fisher (2003). The observation

errors are assumed to be uncorrelated in space and time. Since observation errors are assumed

uncorrelated, the matrix R is simple diagonal matrix with observation errors variances as the

element.


5.3.3 Experimental setups


       Analyses are produced at nominal times of 0000 and 1200 UTC (during 1-31st July 2008) by

the 4D-Var system described, with an assimilation window of 12 h (i.e. observations between 0600

and 1800 UTC are used for the 1200 UTC analysis, while the observation window of 1800 to 0600

UTC applies for the 0000 UTC analysis). From both (0000 and 1200 UTC) analyses, a 10-day

forecast is made at T159 resolution. Two sets of experiments were conducted daily (1-31st July

2008) from the 0000 and 1200 UTC analyses, a control or reference simulation (REF) and the

Kalpana experimental simulation (KAL).


       For REF, conventional and satellite data used operationally (Kelly and Thepaut 2007) were

assimilated. It should be noted here that in the ECMWF assimilation system the mid-upper

tropospheric humidity (over the Kalpana disk) is controlled by radiosondes, Meteosat-7 and polar

orbiting satellite (e.g. NOAA, Aqua, and METOP-A) observations. The KAL run is similar to the

REF run, except that the Meteosat-7 WV radiances were replaced by Kalpana WV radiances. In

both REF and KAL the temporal resolution of the observations was hourly. The performance of

each experiment was verified against its own analysis.




    27
      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




       Prior to assimilation, Kalpana and Meteosat-7 clear sky radiances underwent a quality

checking process in order to reduce the possibility of assimilating bad observations. First, data with

scanning angle greater than 60° and above high orography were excluded (Peubey and McNally,

2009). The data over high orography were excluded because channel “sees” the surface when the

surface elevation is high, and the surface contribution to the measurement is significant and

uncertain. The WV channel in Kalpana and Meteosat-7 is sensitive to the surface over higher

orography and the surface contribution to the radiances is poorly (because of the large error in

model first guess land surface temperature) defined. Secondly, a gross error quality control was

performed, the observations being rejected (Köpken et al., 2004) when the first guess departures

were more than 2.5(σ OBS + σ FG )0.5 with σ OBS and σ FG being the expected observation and first-guess
                     2       2




errors in radiation space, respectively. The observation error ( σ OBS ) for Kalpana and Meteosat-7

clear sky radiances is 2 K, while σ FG depends on the profile of background errors in specific

humidity on the model levels.


5.4. Assimilation Results


5.4.1 Impact of Kalpana and Meteosat-7 clear sky WV radiances on the analysis


a. Overview of the fit to Kalpana and Meteosat-7 clear sky WV radiances


       The first comparison that we made can be described as a sanity check; the O-A

(observations minus analysis) and O-B (observations minus background [sometimes known as the

first guess]) values SD (standard deviation) and bias values, averaged for the northern hemisphere

(> 20° N), tropics (20º S -20 º N) and the southern hemisphere (> 20° S), were plotted as a function

of time. In a successful assimilation, the analysed SD and bias are smaller than in the first guess,

hence the analysis matches the observations better than does the first guess.



    28
      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




       Comparison between Kalpana observed and first guess radiances indicates that these two

products differ (Fig 5.2; solid grey lines) with an SD of the order of 1 to 1.7 K. The bias (Fig 5.2;

dashed grey lines) between the Kalpana observed and the first guess radiances are within ± 0.4 K.




Figure 5.2 Time series of mean difference (bias; dashed lines) and standard deviation (SD; solid
lines) of Kalpana observed CSBTs minus the corresponding model first guess (grey) and analysis
(black) CSBTs during July 2008, for (a) northern hemisphere, (b) tropics, and (c) southern
hemisphere. The discontinuities in the time series are due to the non availability of the Kalpana
data for some times.

       The first guess bias and SD seen in Fig 5.2 are slightly higher than the bias-corrected

differences and RMSD mentioned in section 4. This may be due to the following reasons. Firstly, in

offline monitoring (section 4), the ECMWF analyses had Meteosat-7 WV radiances in them, while

    29
      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




during the assimilation of Kalpana radiances the Metosat-7 WV radiances were not used. Hence the

ECMWF first guess is slightly different here from in the offline monitoring and as a result the bias

of the order of ± 0.4 K are still seen (Fig 5.2; dashed grey lines) in the first guess departures.

Secondly, in section 4 we discussed the whole-disk Kalpana mean bias and not northern

hemisphere, tropics and southern hemisphere biases separately. However, these biases are corrected

before assimilation with the online bias correction scheme (Auligne et al., 2007) in the ECMWF

assimilation system.


       The SD of the analysis departures (Figs 5.2; solid black lines) varies from 0.7 to 1.1 K as

opposed to 1 to 1.7 K for the first guess departures. The mean bias of the first guess (Fig 5.2;

dashed grey lines) differences were also significantly reduced (Fig 5.2; dashed black lines) in the

analysis. This suggests that online bias correction has worked effectively in reducing the bias.


       When Meteosat-7 WV radiances are assimilated, the analysis (Fig 5.3; solid black lines) fit

has an SD of about 0.6 to 0.9 K, while the first guess (Fig 5.3; solid grey lines) fit varies from 0.9 to

1.5 K. The mean bias of the first guess (-0.1 to 0.6 K; Fig 5.3; dashed grey lines) differences are

also significantly reduced (0 to 0.2 K; Fig. 5.3; dashed black lines) in the analysis. The first guess

SD for Meteosat-7 seen in Fig 5.3 is less than those mentioned by Köpken et al. (2004). Also, the

SD for Meteosat-7 is smaller than that for Kalpana. This is because the assimilation experiments are

initialized with an operational analysis which contains Meteosat-7 WV radiances. The first guess

SD would have been large if the operational analysis used for initializing the experiments had no

Meteosat-7 radiances. Overall, Figs 5.2 and 5.3 confirm that the analysis is closer to the

observations than it is to the background.




    30
      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




Figure 5.3 Time series of mean difference (bias; dashed lines) and standard deviation (SD; solid
lines) of Meteosat-7 observed CSBTs     minus the corresponding model first guess (grey) and
analysis (black) CSBTs    during July 2008, for (a) northern hemisphere, (b) tropics, and (c)
southern hemisphere.

b. Overview of the fit to other assimilated observations


       Fig 5.4 shows comparisons of first guess and analysis departures averaged over the whole

month with respect to observed brightness temperature from the Infrared Atmospheric Sounding

Interferometer (IASI) on METOP-A. These IASI observations are from temperature sensitive

channels near 15 µm CO2 bands. The details about the IASI channels number (Fig 5.4; y-axis),




    31
      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




used in the ECMWF assimilation system and corresponding wave number are given by Collard,

(2007).




Figure 5.4 Standard deviation (SD; left) and mean difference (bias; right) of the background (solid
line) and analysis (dotted line) departures from METOP-A IASI brightness temperature (K)
observations in the northern hemisphere (upper panel), tropics (middle panel), and southern
hemisphere (lower panel). For the background, the REF run is in red and KAL in black. For the
analysis, the REF run is in cyan and KAL is in green.


    32
      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




       Both the background and analysis bias with respect to IASI observations are lower (Fig 5.4)

in KAL than in REF. The reductions in bias are seen over all three regions of the globe. This

reduction is more significant for southern and northern hemispheres in the case of KAL when

compared to REF. This indicates that the model run with assimilation of Kalpana radiances had a

lower bias with respect to the IASI observations than the reference run. The SD with respect to IASI

observations is also improved, particularly in the northern hemisphere (Fig 5.4; upper panel).

Similar comparisons have been done for the Microwave Humidity Sounder (MHS) on METOP-A,

the High Resolution Infrared Radiation Sounder (HIRS) on METOP-A and NOAA, the Advanced

Microwave Sounding Unit (AMSU-B) on NOAA, and the Atmospheric Infrared Sounder (AIRS)

on board Aqua. The biases with respect to MHS, HIRS, and AMSU and AIRS observations are

lower (not shown) in KAL, particularly for water vapour sensitive channels, than in REF.


       The performance of these two experiments was also compared in term of relative humidity,

temperature, winds, and geopotential to radiosonde (TEMP) observations. Fig 5.5 (upper panel)

shows the fit to radiosonde humidity observations for the southern hemisphere. It is clear that biases

against both background and analysis are reduced, particularly in mid-troposphere when Kalpana

radiances are assimilated. However the biases are slightly higher in upper troposphere when

Kalpana radiances are assimilated. Radiosonde observations of humidity have to be taken with care,

particularly in upper troposphere (Gaffen, 1991). In the northern hemisphere and tropics the

improvement due to the assimilation of Kalpana radiances is very small (not shown) but positive

compared with the REF run. The assimilation of Kalpana radiances also improves the fit of

radiosonde temperature and geopotential. The biases of sonde temperature (not shown) and

geopotential (Fig 5.5; middle panel; for the southern hemisphere) against both background and

analysis are reduced, particularly in the middle and upper levels, over all the latitude bands. In

terms of influence on wind fields, a significant improvement is found in the first guess zonal wind


    33
         The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




in the upper troposphere with radiosonde for the northern hemisphere (Fig 5.5; lower panel)

observations, while the statistics for other (tropics and southern hemisphere) latitude bands are

unchanged. The statistics are also unchanged for meridional winds (not shown) for all latitudes

bands.




Figure 5.5 Standard deviation (SD; left) and mean difference (bias; right) of the background (solid
line) and analysis (dotted line) departures from radiosonde relative humidity observations in the
southern hemisphere ( %; upper panel), geopotential in the southern hemisphere (m; middle
panel), and zonal winds in the northern hemisphere (ms-1; lower panel). The REF run is in red and
the KAL run in black.




    34
      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




       Overall these results show that the assimilation of Kalpana radiances observations tends to

affect the moisture, temperature, winds, and geopotential analyses in a positive way. The effect of

using Kalpana radiances is neutral or positive with respect to the REF run when compared with

other assimilated observations from moisture sensitive instruments, except for some negative

impact in the upper troposphere moisture when compared with radiosonde humidity. The effect on

temperature and geopotential is mostly positive in mid-upper levels and neutral in the lower levels.

The assimilation of Kalpana radiances observations tends to affect upper level zonal winds in a

positive way when compared with radiosonde observed winds. However, both the background and

analysis SD with respect to radiosonde and satellite observations are similar (except for IASI

observations over the northern hemisphere) in the REF and KAL runs.


5.4.2 Impact of the Kalpana and Meteosat-7 clear sky WV radiances on the forecast


       The RMSD computed with respect to analysis is used as a measure to quantitatively

compare the 1 to 5 day forecasts from the REF and KAL runs. Fig 5.6 shows the RMSD averaged

over the whole month of July 2008, at different pressure levels for geopotential for day one, day

three and day five forecast for tropics. Compared with Meteosat-7, the impact of the Kalpana WV

radiances is positive in the tropics while neutral to positive in the northern and southern

hemispheres (not shown).




    35
      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




Figure 5.6 Forecast of geopotential for tropics, verified against analysis for the KAL run (black
line) and the REF run (grey line), (a) for the day two forecast, (b) the day three forecast, and (c)
the day five forecast.

       The impact of the Kalpana WV radiances on relative humidity and winds is neutral (both

REF and KAL runs show similar RMSD; not shown) over all the three regions, with the two lines

almost overlapping at all the levels. Similar statistical quantities have been calculated for the Indian

(5° N- 32°N; 75° E - 100° E) region; here, the impact of the Kalpana WV radiances on relative

humidity is neutral to positive. The positive impact is seen (Fig 5.7) in mid-upper troposphere,

particularly on day 3 and day 5 forecasts. A lightly negative impact in the KAL run is seen (Fig

5.7(a)) at 200 hPa in the day 2 forecast. The statistics for geopotential are similar (not shown) to

those for the tropics. The assimilation of Kalpana WV radiances also impacted winds positively

(Fig 5.8), particularly in the lower-middle troposphere on the day 5 forecast.




    36
      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




Figure 5.7 Forecast of relative humidity for the Indian region, verified against analysis for the
KAL run (black line) and the REF run (grey line), (a) for the day two forecast, (b) the day three
forecast, and (c) the day five forecast.




Figure 5.8 Forecast of winds for Indian region, verified against analysis for the KAL run (black
line) and the REF run (grey line) for the day five forecast.



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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




5.5 Conclusions


       This study concentrates on the use of clear sky water vapour radiances from the Kalpana

satellite. We have used the ECMWF 4D-Var system to assimilate, for the first time, WV radiances

from an Indian satellite. The performance of Kalpana WV radiances was compared with that of

Meteosat-7 WV radiances, which are operationally assimilated at ECMWF. Results for the month

of July 2008 show a positive impact of the Kalpana WV radiances on the analysis of temperature

and water vapour sensitive channels, as shown by comparisons with IASI, HIRS, MHS, AIRS, and

AMSU-B. Also, with respect to conventional radiosonde temperature and geopotential, a slight

improved first guess fit is noticed, particularly in the mid-upper levels, when Kalpana WV

radiances are assimilated.


       The assimilation of Kalpana WV radiances data also improves the fit of radiosonde

humidity data; in particular, biases of sonde humidity data against both background and analysis are

reduced in the southern hemispheric middle troposphere. Changes in the zonal wind field do also

occur through the use of 4D-Var. The impact of using Kalpana WV radiances on the 1 to 5 day

forecasts, as investigated using the RMSD, appears to be positive for mid-upper level geopotential

in the tropics and Indian region. Assimilation of Kalpana WV radiances also shows a positive

impact on the mid-upper level moisture and lower–middle levels winds over the Indian region. Thus

the findings of this study suggest that NWP should assimilate Kalpana WV radiances, if they were

to be available via the GTS, instead of Meteosat-7 radiances.




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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




 6.0 GENERATION OF TRANSMITTANCE COEFFICIENTS FOR FUTURE

                    INDIAN METEOROLOGICAL SATELLITES


6.1 Introduction


       Advanced, multispectral (visible, IR, and passive microwave) imagers, sounders (infrared

and microwave) and scatterometers are planned for launch in the near future to support the

operational data needs and ongoing research efforts. The forthcoming meteorological satellites

INSAT-3D and Megha Tropiques are due to be launched later in 2009. INSAT-3D will carry

improved VHRR and the vertical sounders for temperature and humidity profiles. The Megha-

Tropiques satellite will be a joint mission between ISRO and CNES, France, with the objective of

studying the water cycle and energy exchanges in the tropics. In addition to the modifications made

for Kalpana, the fast transmittance coefficients have been generated, verified and implemented in

RTTOV for Megha Tropiques. The channel selection of INSAT-3D is patterned after GOES-11 and

the satellite will be placed over the Indian Ocean. The accuracy of fast the RTM of INSAT-3D will

be very similar to that of GOES-11 because INSAT-3D will have channels similar to that of GOES-

11. At present the INSAT-3D SRFs are not available and hence the fast transmittance coefficients

applicable to GOES-11 were used in order to access the accuracy of INSAT-3D.


6.2 GOES-11 channel characteristics


       Channel No          1            2            3           4            5             6

       Wavelength     0.55 - 0.75   1.55 - 1.70   3.8 - 4.0   6.5 - 7.1   10.2 - 11.3   11.5 - 12.5
         (µm)



                        Table 6.1: GOES-11 Imager channel specification.




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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




       Fig-6.1 shows the normalized spectral response (Fig 6.1(a)) and normalized weighting (Fig

6.1(b)) functions of the GOES-11 (http://cimss.ssec.wisc.edu/goes/g11_report/) imager infrared

channels (Table 6.1, channels 3 to 6).




Figure 6.1 (a) The spectral coverage of the GOES-11 imager infrared bands plotted with Earth–
emitted spectra calculated from the U.S. Standard Atmosphere. (b) The normalized weighting
functions of the GOES-11 imager infrared bands. The weighting functions are calculated from the
U.S. Standard Atmosphere using the line-by-line radiative transfer model (LBLRTM).




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     The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




      Channel     Central Wavelength      Channel Types                        Purpose
        No               (µm)

           1             14.7                                      Stratospheric Temperature

           2             14.4                                      Tropopause Temperature

           3             14.1          Longwave Channels           Upper-level Temperature

           4             13.9                                          Mid-level Temperature

           5             13.4                                          Low-level Temperature

           6             12.7                                          Total Precipitable Water

           7             12.0          Atmospheric Window        Surface Temperature/Moisture

           8             11.0                                           Surface Temperature

           9             9.7                  Ozone                               Ozone

           10            7.4                                             Low-level Moisture

           11            7.0              Water Vapour                   Mid-level Moisture
                                           Channels
           12            6.5                                            Upper-level Moisture

           13            4.57                                          Low-level Temperature

           14            4.52           Shortwave Channels             Mid-level Temperature

           15            4.45                                      Upper-level Temperature

           16            4.13                Nitrogen             Boundary Layer temperature

           17            3.98                                           Surface Temperature

           18            3.7           Shortwave Channels        Surface Temperature/Moisture

           19            0.69                 Visible                          Clouds


                          Table 6.2: GOES-11 sounder channel characteristics.

      Most of the sounder channels of GOES-11 (Table 6.2) cover Earth–emitted spectra in the

carbon dioxide, water vapour and ozone bands. Figs 6.2 and 6.3 show the normalized spectral

response        and     normalized        weighting         function         of           the     GOES-11




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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




(http://cimss.ssec.wisc.edu/goes/g11_report/) sounders infrared channels. The weighting functions

have been computed for U.S Standard Atmosphere using a line-by-line radiative transfer model.




Figure 6.2 The spectral coverage of the eighteen GOES-11 sounders infrared bands plotted with
Earth–emitted spectra calculated from the U.S. Standard Atmosphere.




Figure 6.3 The normalized weighting functions of the eighteen GOES-11 sounder infrared bands.
The weighting functions are calculated from the U.S. Standard Atmosphere using the line-by-line
radiative transfer model (LBLRTM).

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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




6.3 Megha Tropiques channel characteristics


       Megha-Tropiques, with a unique combinations of scientific payloads and its special near-

equatorial orbit (offering improved data sampling of the ITCZ), is expected to provide valuable data

for climate research. Data gathered by the mission will be used to study the tropical climate system.

The goals are the study of 1) the life cycle of convective systems and their interaction with

environment, 2) cloud properties and precipitation, 3) horizontal and vertical distributions of water

vapour, 4) radiative fluxes.


       The Megha-Tropiques satellite will carry three payloads namely


           •   MADRAS (Microwave Analysis and Detection of Rain and Atmospheric Structure),

               a microwave imager operating in the frequency range from 18 to 157 GHz for

               measuring rain, atmospheric water vapour content, liquid water content and ocean

               surface wind speed;


           •   SAPHIR, a multi-channel microwave sounder operating at 183 GHz to measure

               vertical profiles of atmospheric humidity over land and ocean, and


           •   ScaRab, operating in the optical region for estimating earth radiation budget over

               tropical convective region.


       Megha-Tropiques will additionally be equipped for GPS based radio-occultation

measurements. The mission has been planned specifically for the coverage of the tropical region

(±20º) with a large sampling frequency. The swath width is 1700 km for MADRAS and SAPHIR.

Tables 6.3 and 6.4 show the channels specification for MADRAS and SAPHIR, respectively. Fig-

6.4 shows the normalized weighting function of the SAPHIR channels for U.S. standard

atmosphere. The weighting functions shown in Fig 6.4 are computed from transmittance data base


    43
      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




generated using MPM-89/92 (Millimeter Wave Propagation Model; Liebe et al., 1989; Liebe et al., 1993)

line-by-line radiative transfer model. ScaRab is not used in the present study.


     Channel        Central       Polarization        Maximum           Spatial Resolution
       No         Frequencies                         Bandwidth               (Km)

         1         18.7 GHz          H&V              ± 100 MHz                   40

         2         23.8 GHz            V              ± 200 MHz                   40

         3         36.5 GHz          H&V              ± 500 MHz                   40

         4          89 GHz           H&V              ± 1350 MHz                  10

         5          157 GHz          H&V              ± 1350 MHz                  6



                  Table 6.3: Megha Tropiques MADRAS channels characteristics




     Channel          Central          Polarization     Maximum         Spatial Resolution
       No           Frequencies                         Bandwidth             (Km)

         1       183.31 ± 0.2 GHz           H            200 MHz                  10

         2       183.31 ± 1.1 GHz           H            350MHz                   10

         3       183.31 ± 2.8 GHz           H            500 MHz                  10

         4       183.31 ± 4.2 GHz           H            700MHz                   10

         5       183.31 ± 6.8 GHz           H           1200 MHz                  10

         6        183.31 ± 11 GHz           H           2000 MHz                  10



                   Table 6.4: Megha Tropiques SAPHIR channels characteristics




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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




Figure 6.4 The normalized weighting functions of the six Megha Tropiques SAPHIR sounder bands.
The weighting functions are calculated from the U.S, Standard Atmosphere using the line-by-line
radiative transfer model (MPM-89/9).

6.4 Transmittance coefficients for GOES-11


       The method of generation of the fast transmittance coefficients for the GOES-11 imager and

sounder infrared channels is the same as that used for the Kalpana VHRR described in section 3.

The line-by-line transmittances (LBL database, section 3.4) were convolved with the GOES-11

SRFs shown in Figures 6.1a and 6.2. These convolved transmittances become the data points in the

regression (Eq. 3.10). As with the Kalpana VHRR, the fast transmittance coefficients are generated

for H2O, O3, and the fixed gases. The predictors used in Eq. (10) are those given in Table 3.1.




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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




6.5 Transmittance coefficients for Megha Tropiques


       Except for the line-by-line transmittances data (LBL database), the methodology of

generation of the fast transmittance coefficients for Megha Tropiques channels is the same as that

for Kalpana and GOES-11. For the microwave channels (MADRAS and SAPHIR), the LBL

transmittances database is generated using MPM-89/92 line-by-line model (Liebe et al., 1989 and

Liebe et al., 1993). The MPM model used here is a modified version of the original MPM-89/92

model. The modification has been done (Saunders 2008) to include ozone among the mixed gases

(instead of it being variable gas) using a climatological profile. Therefore, the prediction of the

mixed gas transmittance includes, when appropriate, the effect of the ozone at the concentration

found in the climatological profile. The half-width of the 22 GHz water vapour line also has been

updated based on the more recent value given in the HITRAN molecular line database. This has

removed systematic differences between the measured and calculated brightness temperature near

centre of the line (Saunders 2008). The “ECMWF 52” profiles described in section 3 were used to

generate the LBL database. The transmittance database was generated at 43 levels (1013 - 0.1 hPa).

The monochromatic transmittances were computed for each of the 52 profiles from space to each of

43 pressure levels and at six viewing angles (θ) measured from the zenith, namely those angles for

which secθ has the values 1.00, 1.25, 1.50, 1.75, 2.00, 2.25. The line-by-line transmittances were

convolved with the MADRAS and SAPHIR spectral response function. These convolved

transmittances then become the data points in the regression (Eq. 3.10). The fast transmittance

coefficients are generated for H2O and the fixed gases. The predictors used in Eq. (10) for H2O and

fixed gases are those given in Table 3.1.


6.6 Accuracy of RTTOV for GOES-11 and Megha Tropiques


       The fast coefficients generated for GOES-11 and Megha Tropiques were implemented in the

RTTOV. This enabled us to simulate the transmittances and radiances for GOES-11 and Megha
    46
      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




Tropiques, for a given temperature, moisture and ozone (only for infrared channels) profile. The

accuracy of RTTOV for the simulation of GOES-11 and Megha Tropiques channels transmittances

and radiances was assessed by comparing the RTTOV simulated transmittances profiles and top of

the atmosphere radiances with the corresponding values from the line-by-line models. The fast

model transmittances profiles and top of the atmosphere radiances computed for the independent

(not used in the training of RTTOV) set of profiles were compared with the corresponding LBL

values to test the robustness of the fast model.    The independent dataset used in this study

comprises 117 diverse profiles generated from the ECMWF atmospheric model (Chevallier, 2001).


6.6.1 Transmittance comparisons




Figure 6.5 Root mean square of the difference (RMSD) between RTTOV and LBLRTM layer to top
of the atmosphere transmittances for independent 117 profile set at six viewing angles, for GOES-
11 imager infrared channels.




    47
      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




       The RMSD values of (LBLRTM minus RTTOV) were calculated at each level for

independent datasets. Figs 6.5 and 6.6 show these RMSD values for the simulated transmittances

for the GOES-11 imager and sounder channels, respectively. These statistics are for 6 different

viewing angles. Most of the channels show RMSD values less than 0.003 over all altitudes. The

shortwave channels show the minimum RMSD values, while channels sensitive to ozone and water

vapour shows the maximum (0.004 to 0.007) RMSD values. In all the channels the maximum

RMSD is to be found near the peaks of the weighting function (where the instrument sensitivity to

the variation in moisture or temperature is largest). Fig 6.7 shows the RMSD of (MPM-89/92 minus

RTTOV) for MADRAS and SAPHIR on Megha Tropiques. Most of the channels show a RMSD

less than 0.0015. As in infrared channels, the maximum RMSD values are found near the peaks of

the weighting function. It should be noted here that accuracy of RTTOV will be very similar for

GOES-11and INSAT-3D channels.




    48
      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




Figure 6.6 Root mean square of the difference (RMSD) between RTTOV and LBLRTM layer to top
of the atmosphere transmittances for independent 117 profile set at six viewing angles, for GOES-
11 sounders infrared channels.




Figure 6.7 The RMSD values between RTTOV and MPM-89/92 for the layer to top of atmosphere
transmittances for independent 117 profile set, at six viewing angles, (a) for MADRAS, and (b) for
SAPHIR.

6.6.2 Radiances comparisons

       The ability of the fast model to reproduce the line-by-line (LBL) radiances in term of the

bias and RMSD (between the fast model and LBL computed radiances) is shown in Figs 6.8 and

6.9. Also plotted in Figs 6.8 and 6.9 are the instrument noise values (NeDT) for each channel.

Radiances are in units of equivalent black body brightness temperature. The brightness

temperatures have been computed using the radiative transfer formulation within RTTOV and LBL

model transmittances to ensure any differences are only due to the LBL and fast model

transmittances and are not due to the integration of the radiative transfer through the atmosphere.

    49
      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




So, errors in the brightness temperature were computed by using the fast model transmittances as

compared with those computed by using the LBL transmittances in Eq. (3.3). Radiances for all 6

viewing angles are included in the statistics. Figs 6.8 and 6.9 demonstrate that the RTTOV errors

are well below the instrument noise for most (except ozone channel) of the channels.




Figure 6.8 RMSD (upper panel) and bias (lower panel) of RTTOV top of atmosphere brightness
temperature differences from the LBLRTM model for the 117 independent profile set and 6 viewing
angles. Channels 1-4 are GOES-11 imager channels and channels 5-22 are GOES-11 sounders.




    50
     The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




Figure 6.9 RMSD (upper panel) and bias (lower panel) of RTTOV top of atmosphere brightness
temperature differences from the MPM-89/92 model for the 117 independent profile set and 6
viewing angles. Channels 1-6 are those of SAPHIR and channels 7-11 are those of MADRAS.




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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




            7. OVERALL CONCLUSIONS AND FUTURE POSSIBILITIES

       The objective of this study was to generate fast transmittance coefficients for the infrared

channels on the Kalpana satellite, in preparation for the assimilation of Kalpana WV radiances into

an NWP model using a variational assimilation scheme. The fast transmittances coefficients for the

Kalpana infrared channel were generated and implemented in RTTOV and it was shown that the

fast model can simulate the line-by-line radiances to a degree of error that is below the level of

instrumental noise. The results indicate that the fast model is adequate for operational use in data

assimilation. In addition to Kalpana, the fast transmittance coefficient were also generated and

implemented in RTTOV for Megha Tropiques. The fast transmittance coefficients were also

generated and verified for GOES-11 in order to access the accuracy of RTTOV for INSAT-3D.

The accuracy of RTTOV for INSAT-3D will be very similar to that of GOES-11 because INSAT-

3D will have channels similar to that of GOES-11.


       Data assimilation schemes assume bias free observations, thus a bias correction has to be

applied in order to reduce any systematic deviation between the observed and first guess radiances.

The comparison of the first guess radiances with that of the Kalpana observed radiances shows

good agreement (RMSD 0.65 to 1.2 K; bias -0.2 to 0.8 K). The mean biases exhibit a diurnal cycle

which is probably due to the VHRR calibration. A simple time dependent bias correction scheme

has been suggested; when applied the comparison of the first guess radiances with that of bias

corrected Kalpana radiances shows only a very small differences (Kalpana disk mean biases are

within ± 0.1 K; RMSD 0.75 K).


       The ECMWF 4D-Var IFS system has been used to assimilate, for the first time, WV

radiances from an Indian satellite. The performance of Kalpana WV radiances was compared with

that of Meteosat-7 WV radiances, which are operationally assimilated at ECMWF. Results for the


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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




month of July 2008 show a positive impact in the use of Kalpana WV radiances on the analysis of

temperature and water vapour sensitive channels, as shown by comparisons with IASI, HIRS, MHS,

AIRS, and AMSU-B. Also, with respect to conventional radiosonde temperature and geopotential, a

slight improved first guess fit is noticed, particularly in the mid-upper levels, when Kalpana WV

radiances are assimilated. The assimilation of Kalpana WV radiances data also improves the fit of

radiosonde humidity data; in particular, biases of sonde humidity data against both background and

analysis are reduced in the southern hemispheric middle troposphere. Changes in the zonal wind

field do also occur through time sequence information and the balances used in 4D-Var. The impact

of the Kalpana WV radiance assimilation on 1 to 5 day forecasts, as investigated using the RMSD,

appears to be positive for mid-upper level geopotential in the tropics and Indian region.

Assimilation of Kalpana WV radiances also has a positive impact on the mid-upper level moisture

and lower–middle levels winds over Indian region. Thus findings of this study suggest that NWP

models should assimilate Kalpana WV radiances, if they were to be made available via the GTS,

instead of Meteosat-7 radiances.


       In the future, a sounder with several additional channels in the visible, infrared, and water

vapour bands will become available on the Indian INSAT-3D satellite, to be launched by ISRO.

The information of three humidity and more than seven temperature sounding channels of the

INSAT-3D sounder will provide more vertical information - useful for the definition of the

humidity and temperature fields. The forthcoming Megha Tropiques satellite will carry SAPHIR, a

multi-channel microwave sounder operating at 183 GHz to measure vertical profiles of atmospheric

humidity over land and ocean. The SAPHIR channels are similar to channels of the Advanced

Microwave Sounding Unit A (AMSU-A) instrument abroad the NOAA series of satellites.

Assimilation of AMSU-A radiance data into NWP models has provided a tremendous positive

impact at all the major weather centres. The usefulness of the radiance data from SAPHIR in NWP


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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




will be assessed by conducting similar assimilation experiments. Both INSAT-3D and Megha

Tropiques will provide the observation with high spatial (~10-30 km) and temporal resolution.

Hence in future, in addition to the global NWP model, more rigorous assimilation experiments will

be carried out with a mesoscale model in to order to make better use of the higher temporal and

spatial resolution of these observations.




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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




                                 ACKNOWLEDGEMENTS

       Firstly, I (Randhir Singh) would like to thank the Department of Science and Technology

(DST), of the Government of India, for awarding me the BOYSCAST Fellowship. I would like to

express my heartiest appreciation and gratitude to Prof. Alan O’ Neill for all the support he has

given me during my tenure of the award at the University of Reading. His guidance was invaluable

in accomplishment of this work. I am also very grateful to Dr. Roger Brugge for his extensive

support. In addition, I would like to thank the other members of the National Centre for Earth

Observation at the University of Reading for providing assistance throughout my work. Special

thanks go to Dr. Ross Bennister and Dr. Stefano Migliorini, for their patience in answering my

queries regarding data assimilation. I want to thank my roommate Dr. Andrea Kaiser-Weiss for her

constant support. Very special thanks go to Mrs. Jan Fillingham for being so supportive throughout

my time at the University of Reading.


       At the Met Office, I would like to thank Dr. Graeme Kelly for his countless hours of help

and his keen interest in the assimilation of Kalpana WV radiances, and Dr. Roger Saunders and Dr.

Peter Rayer for their kind help in generating and implementing the fast transmittance coefficients

for Indian satellites. The frequent discussions with Dr. Marco Matricardi of ECMWF, Dr. Pascal

Brunel of Météo-France, and Dr. Hal Woolf of the University of Wisconsin-Madison, regarding the

development of the fast radiative transfer model, are also gratefully acknowledged.


       I would also like to thank my colleagues at the Space Applications Centre (SAC), especially

Dr. P. K. Thapliyal, Dr. P. K. Pal and Dr. P. C. Joshi. Their encouragement and moral support was

vital throughout this work.

       The LBLRTM used in this study was made publicly available (ftp.aer.com) and supported

by Atmospheric and Environmental Research Inc. I sincerely acknowledge the help and cooperation

received from Mark Shephard, of Atmospheric and Environmental Research, Inc. in implementing
    55
     The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




LBLRTM for line-by-line transmittance calculation. Kalpana raw radiances were obtained online

(ftp.mosdac.gov.in). The provision of the RTTOV software by the NWP-SAF is also

acknowledged.




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      The use of Kalpana water vapour channel radiances in a weather forecast model  2009 




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