Diffraction Effects on the Meteosat Third Generation Infrared Sounder (MTG IRS)

Jochen Grandell and Rolf Stuhlmann European Organisation for the Exploitation of

Meteorological Satellites (EUMETSAT) 64205 Darmstadt, Germany

Email: Jochen.Grandell@eumetsat.int

Abstract—Geostationary Infrared Sounding missions offer good temporal coverage, however due to the large distance to the observed Earth targets the effect of diffraction is increased compared to sounding from a low Earth orbit (LEO). Because of the wave-length dependence of diffraction, the spectral channels do not sample the same volume of air, as in general assumed by retrieval algorithms for LEO IR (Infrared) sounder data. This additional error introduced in the retrieval by diffraction limited instruments is called ‘pseudo noise’ throughout the paper. One such diffraction-limited geostationary system is the candidate Infrared Sounding (IRS) mission on EUMETSAT Meteosat Third Generation (MTG) satellites with a planned need date in 2015, due to the expected lifetime of the current Meteosat Second Generation (MSG) satellites. A simplified Point Spread Function (PSF) is applied. To represent the channels within natural conditions, measured spectra from the low-earth orbit Atmospheric Infrared Sounder (AIRS) at ∆X = 15 km, as well as the Moderate Resolution Imaging Spectroradiometer (MODIS) at ∆X = 4 km are used as an underlying scene when integrating over the PSF. The results show that the pseudo noise is highly depending on wavelength, and highest in the window and CO2 regions (within the broader 700-1200 cm-1, or 8.3-14.3 µm, region). The worst case pseudo noise values are approximately 1 K for these regions. The broad-band AIRS results are confirmed by a direct comparison to MODIS data at 4 km resolution, where the worst case pseudo noise is appx. 0.5 K, while the best case pseudo noise is comparable to AIRS data.

I. INTRODUCTION High spectral resolution IR sounding missions will play

important role in future geostationary meteorological systems, through the provision of Atmospheric Motion Vectors (AMV), to be extracted from tracking of horizontally and vertically resolved water vapor patterns, retrieved from the hyperspectral radiances, or by direct assimilation of the radiances e.g. [1].

Going to the geostationary orbit at about 36000 km will affect the size of volumes of air sampled by the instrument as diffraction becomes a more prominent feature. The dependency of the integrating footprint on Earth on the wavelength is enhanced by a factor of roughly 45, when placing the same instrument in the geostationary position instead of a polar orbit.

While retrieving temperature and humidity from hyperspectral sounding data, a standard assumption in the retrieval process is that all channels involved do sample the

same volume of air, e.g. that the integrating footprint does not change with frequency. As diffraction does introduce frequency dependence, this simplifying assumption is not valid for the spectral measurements taken from the geostationary orbit. The requirement on ‘sampling same volume of air’, however, is only violated in case the observed scene is inhomogeneous, e.g. does have strong gradients in temperature/humidity or is partly cloudy. Thus, applying in these cases retrieval algorithms not specifically designed to address the diffraction problem will degrade the quality of the retrieved atmospheric profiles. The magnitude of the degradation is linked to the so called ‘pseudo noise’, which depends on the scale and strength of the TOA radiance gradients in combination with the strength diffraction changes the instrument field of view with frequency. This pseudo noise can be characterized as the difference of measured radiance spectrum at the top of the atmosphere (TOA) compared to a hypothetical radiance spectrum derived from a ‘diffraction free’ instrument [2], [3].

The objective of this study is to simulate and characterize the magnitude of the pseudo noise expected for the IR Sounder (IRS) mission currently being proposed for the Meteosat Third Generation (MTG). As the pseudo noise depends on the spatial heterogeneity meteorological situation, underlying scenes are modeled from spectra taken from the low-earth orbit AIRS and MODIS instruments. To use this data on spatial scales characteristic to the IRS mission, it is assumed that the horizontal variability provided by the AIRS data is fractal such that it can be downscaled to be representative for the MTG IRS scales of about 4 km [4]. On the other hand, data from MODIS is acquired at a 1 km spatial resolution in 15 out of 36 spectral bands, which coincide with the MTG IRS bands. With an averaging to 4 km, the MODIS data thus provide a direct comparison to the AIRS based results, but with a directly comparable spatial resolution to the MTG IRS.

II. METEOSAT THIRD GENERATION (MTG) IR SOUNDER MISSION

The Meteosat Second Generation (MSG) system has become the primary European source of geostationary observations over Europe and Africa with the start of nominal operations in January 2004. It is one of the key contributions to the Global Observing System (GOS) of the World

Meteorological Organisation (WMO). Considering the typical development cycle for a new complex space system, it has already become necessary to plan for the Meteosat Third Generation (MTG) system. MTG needs to be available around 2015, before the end of the nominal lifetime of MSG [5].

One of the MTG candidate observation missions is a hyperspectral Infrared Sounding (IRS) mission focused on operational meteorology, with some relevance to atmospheric chemistry.

Taking IR soundings with high spectral resolution from the geostationary orbit at a high temporal (30 min) and spatial (4 km) sampling will provide the capability to retrieve Atmospheric dynamic variables (e.g. water vapor flux, wind profiles, transport of pollutant gases). Thus, the focus of the IRS mission is to derive the time evolution of vertically resolved water vapor structures to allow the extraction of three dimensional wind fields with a vertical resolution in the order of 2 km. The spectral bands of the MTG IRS cover the range 700-1200 cm-1 and 1600-2175 cm-1. The main requirements of the IRS mission can be found in [4].

III. METHODOLOGY In general, the instantaneous field of view (IFOV) of a

sounder is characterized by the system Point Spread Function (PSF), which defines the weight of the electromagnetic radiation emerging from a point source propagating to the instrument detector. The total energy (Integrated Energy – IE) received from any but fixed area covered by the IFOV is characterized by the integration of the PSF over the area normalized by the PSF, integrated over an infinite area.

The PSF in its simplest form, when no pupil apodization, numerical filtering or other methods are applied, is determined by the size and shape of the detector, the diffraction pattern known as the Airy disc, optical aberrations, and stray lights. Depending on how the earth is scanned, i.e. in a step and stare or a continuous scan mode, the PSF will additionally account for a “smear” in the later case. However, the amount of image “smear” is also a function of the scan speed.

In the attempt to quantify the pseudo noise for the MTG IRS, a sampling distance of 4 km, defined by the rectangular shape and size of the IRS detector elements within the detector arrays, is analysed. Pseudo noise contributions were calculated in relation to a reference channel at 6.7 µm, meaning that a deviation from the PSF (size and shape) at 6.7 µm is contributing to the pseudo noise.

A. Point Spread Function (PSF) of IR sounder A simplified Point Spread Function (PSF) model was used

to model the system PSF, with only contributions from the detector and diffraction, and was approximated as the convolution of two individual contributions.

According to this approach, the PSF due to diffraction of the IR Sounder is defined as:

( )( )

( )

2

1

ndiffractio

,sin

,sin2,

=yx

D

yxD

JyxPSF

aperture

aperture

θλ

π

θλ

π . (1)

A more detailed description of the computing the system PSF due to diffraction of the MTG IRS can be found in [4].

Figure 1 shows the Point Spread Functions for a 4 km detector size for three wavenumbers at the start, middle and end of the MTG IRS band. It can be seen that although the magnitude of the PSF decreases rapidly with distance from its centre, there is still a significant contribution from outside the detector area.

Figure 1. Computed Point Spread Function (PSF) for the MTG IR Sounder for a detector sizes of 4 km. Plots are only shown for four individual

vavenumbers. An aperture of 30 cm is assumed.

B. Selected Scenes of AIRS and MODIS data The Atmospheric Infrared Sounder (AIRS) and the

Moderate Resolution Imaging Spectroradiometer (MODIS) were launched into a sun-synchronous LEO orbit in May 2002. AIRS is a grating spectrometer with originally 2378 channels in the range 3.74 - 15.4 µm (649 - 2665 cm-1). With the spectral coverage and resolution close to MTG IRS, AIRS data are therefore a good source for simulating and characterizing pseudo noise effects of the MTG IRS. On the other hand, MODIS, which acquires data at 36 spectral bands, out of which 15 are within the MTG IRS spectral bands. MODIS thus offers an interesting comparison to the AIRS results, as the original data at 1 km resolution can be averaged to the MTG IRS spatial resolution of 4 km.

The analysis was conducted using AIRS/MODIS measurements taken on 20 September 2004. Both day and night time data were used. In order to ensure that a great variety of surface and meteorological conditions were covered by the analysis, four individual cases were selected for the pseudo noise investigation.

The selected scenes are briefly introduced as follows:

• Broken cloud cover in the Pacific Ocean. This is a typical broken cloud scene with a spatial variability in brightness temperature, and thus expected to be influenced by pseudo noise.

• Clear sky in the Mediterranean, with a mixed scene of land and sea. This is a rather cloud-free spatially homogeneous scene. However, the radiance contrast at the coastlines is expected to be susceptible to pseudo noise.

• (almost) clear sky in the Pacific Ocean. This is a scene with a cloud front separating a relatively cloud free area. The cloud free area is, however, not as clean as the Mediterranean clear sky scene, and thus expected to be more susceptible to pseudo noise.

• Atlantic Low Pressure System. This is a typical Atlantic cloudy scene, with a developing low pressure system with clouds at various altitudes/temperatures. The different clouds provide again plenty of structures with high contrast within the scene expected to contribute to pseudo noise.

Since the pseudo noise calculation is sensitive to radiance contrasts within a scene, the source of this contrast in effectively irrelevant. Therefore, highest average scene pseudo noise values are expected for scenes with non-uniform cloud covers. In clear sky cases the scene pseudo noise would depend on the surface features present.

C. Statistical analysis of results For computing the pseudo noise, the radiance simulated as

hyperspectral IRS measurements at a fixed sample location ij is calculated from the underlying AIRS radiances by weighting them with the PSF calculated from Eq 7:

( ) ( ) ( )∑∑= =

=n

k

m

lklklij LL

1 1

~ υυωυ , (9)

where

( )υωkl = individual weights as derived from the Point

Spread Function model for the channel at frequency , where n×m is a 3×3 matrix of adjacent AIRS or MODIS samples,

( )υklL = AIRS scene radiance of pixel kl (assumed to be representative to resolve MTG scales) at frequency.

The pseudo noise for an MTG IRS simulated measurement is defined as the difference between the simulated measurement and a hypothetical measurement taken by a diffraction free instrument with a spectrally constant PSF as determined at 6.7 µm:

( ) ( ) ( )υυυε ijijij LL ~−= . (10)

IV. PSEUDO NOISE RESULTS Results for the pseudo noise NEdT estimated as discussed

above are presented in this Section. The results of NEdT are shown as a function of wavenumber, for the MTG IRS bands

which are covered by AIRS data. Subsequently, the spatial distribution of the pseudo noise NEdT for a spectral channel at 790 cm-1 (13.2 µm) is shown for the analysed AIRS scenes.

Figure 2 and Figure 3 show the pseudo noise contribution of the MTG IRS relative to 6.7 µm, for the four AIRS/MODIS scenes selected for their varying surface and meteorological conditions. Results in Figure 2 and Figure 3 are based on AIRS data (∆X = 15 km) and MODIS data (∆X = 4 km), respectively.

The maximum pseudo noise in the range covered by the analysis is approximately 1 K in the AIRS based results, while in the MODIS based results the maximum pseudo noise is approximately 0.5 K. These maximum values are recorded at roughly wavenumber 760 cm-1, corresponding to 13.2 µm in wavelength. Interestingly, the lower limit of the pseudo noise results, e.g. in the clear sky cases seem very comparable for the AIRS and MODIS based results.

The spectral structure of the pseudo noise confirms that it is determined by two components, the spatial variability of the observed scene, and the strength in which the spectral PSF deviates from the reference PSF (e.g. PSF at 6.7 µm in our case). For the LWIR MTG band the pseudo noise increases continuously over the atmospheric window from 1210 cm-1 to 770 cm-1. A clear minimum is visible in the ozone band between 1070 cm-1 and 980 cm-1, compliant to the fact that proportional to increasing ozone absorption the spatial variability is damped. The maximum of pseudo noise is reached at the beginning of the CO2 band at approximately 760 cm-1, before the increasing CO2 absorption starts to more completely mask the spatial scene variance at these lower frequencies. The pseudo noise approaches zero in the centre of the CO2 band, where the emission solely stem from the spatially homogeneous stratospheric layers.

Figure 2. IRS pseudo noise contribution based on AIRS data at 15 km spatial resolution, relative to the AIRS channel at 6.7 µm. Due to lacking AIRS

spectral coverage, some IRS bands are not fully covered. The IRS spectral coverage is 700-1200 cm-1 and 1600-2175 cm-1

Figure 3. IRS pseudo noise contribution based on MODIS data at 4 km spatial resolution, relative to the MODIS channel at 6.7 µm. Of the 36 MODIS bands, 15 are located within the MTG IRS spectral region of 700-1200 cm-1

and 1600-2175 cm-1.

V. DISCUSSION AND CONCLUSIONS Geostationary sounding measurements offer good temporal

coverage, but due to the large distance to Earth, a sounder on a geostationary orbit is diffraction limited. The diffraction is also a function of wavelength, hence measurements taken at different spectral bands sample a different volume of air. This additional error in the retrieval by diffraction limited instruments has been called “pseudo noise” throughout the paper, and is clearly manifested when observing targets with a higher degree of scene variability.

The effect of scene variability for the IR Sounder was investigated with the help of AIRS and MODIS data and a simplified model for the Point Spread Function (PSF). Since the PSF is strongly frequency/wavelength dependent, the results were related to what would be obtained with a PSF at 6.7 µm channel, as this was regarded as the most important region of the band for MTG IR soundings. The performance at this region would also most likely dictate the eventual design of the actual instrument, thus the relative performance of the rest of the band would then be of interest to the user of the measured data. The results show that the highest scene variability was observed, as expected, in the window and CO2 regions of the band. The results are in line with other work in reported in literature, e.g. [2], [3]. In [2] both simulated and airborne measured radiances are used, and the results show that the level of scene heterogeneity has a large impact on the results. Zhang et al. [3] employed Moderate Resolution Imaging Spectroradiometer (MODIS) Airborne Simulator (MAS) data and show results for pseudo noise which are well comparable to the results shown in this paper.

Contrary to AIRS, IASI, and other IR sounders on Low Earth Orbit satellites, the main objective of the MTG IRS is not absolute temperature/humidity sounding. The highest priority of MTG IRS is to support dynamics via tracking of vertical water vapour structures. So what the user of MTG IRS data is

mostly interested in is the information on vertical structures, which comes from the fidelity of the spectral information. This fidelity would be destroyed by excessive and spectrally uncorrelated random noise. In case of a spectrally high correlated noise (spectral bias) the information on vertical structure is not equally destroyed, i.e. it will have a lesser impact. The changes in the Point Spread Function, as discussed by the results presented in this paper, could introduce a quite large spectrally correlated bias, which however degrades retrieval results less than the uncorrelated instrument noise. Therefore, one would need to take the spectral bias off before comparing it to the random instrument noise. A way of doing it could be, for example, to analyze the number of independent information with and without such a noise (if it stays the same the vertical information is retained). This however is not an easy task as the error correlation matrix will change between both calculations and would need to be known.

It is important to notice that for the feasibility of the user's applications, the figures presented in the pseudo noise investigation represent a worst case. Only a part of the noise figures are in the end relevant for the tracking of vertical water vapor structures, as manifested as the main objective of the MTG IRS mission.

Various design options do exist to control or at least modify the pseudo noise contribution, such as pupil apodization and numerical filtering. However, such alternatives are never without cost or some sort of radiometric degradation e.g. [6]. Based on the limited simulations and pseudo noise characterization presented above, a decision for MTG IRS was taken that the pseudo noise shall not drive the system design.

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[3] Zhang, P., J. Li, E. Olson, T. J. Schmit, J. Li, and W. P. Menzel, 2006: Impact of point spread function on infrared radiances from geostationary satellites, IEEE Trans. Geosci. Remote Sensing, 44, 2176-2183.

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