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  • View in gallery

    Projected instantaneous and effective antenna pattern functions for AMSU-B scan positions 1 (scan edge) and 45 (scan center), respectively. The curves are derived from synthetic antenna pattern functions with 3-dB beamwidth as specified in Table 1. For the scan center the instantaneous field of view in the along-track direction equals the instantaneous field of view in the cross-track direction

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    Sizes of the EFOVs of AMSU-A and AMSU-B in both the along-track and cross-track direction as function of scan position. Shown are the calculated EFOVs from the scan center (positions 15 AMSU-A and 45 AMSU-B) to the scan edge (positions 30 for AMSU-A, 90 for AMSU-B). The functional behavior is symmetrical for the lower scan positions 1–15 of the AMSU-A and scan positions 1–45 of the AMSU-B

  • View in gallery

    Scan geometry of AMSU-A and AMSU-B in along-track/cross-track coordinates. The large ellipse in the middle depicts the 3-dB size of the AMSU-A footprint. The small ellipses show the AMSU-B footprints. The AMSU-B footprints shown as solid lines are those of the first AMSU-B scan after the synchronization pulse

  • View in gallery

    Error characteristics of the application of the BG method. The value ΔG is defined in Eq. (2) and gives a measure of the difference between the target and the matched antenna pattern functions. The noise amplification is defined as the rms over the BG coefficients ai

  • View in gallery

    Cross sections through the AMSU-A’s target (thin lines) and the BG-convolved AMSU-B antenna patterns (thick lines) for AMSU-A scan positions 1, 5, 10, and 15. The left panels show the cross sections in the cross-track direction, while the right panels show the cross sections in the along-track direction

  • View in gallery

    Image of AMSU-B 89-GHz channel of the NOAA-15 overpass over northern Europe on 22 May 1999 at 1815 UTC. The lines indicate the positions of the four transects that are plotted in Fig. 8

  • View in gallery

    Scatterplot of AMSU-A 89-GHz brightness temperatures vs convolved AMSU-B 89-GHz brightness temperatures for BG convolution and equally weighted averages using different sizes of a square window of AMSU-B data

  • View in gallery

    The left images show AMSU-A 89-GHz brightness temperatures along the transects shown in Fig. 6. The right images show the corresponding differences between the convolved AMSU-B brightness temperatures and AMSU-A at 89 GHz. The thick lines show results for the BG estimate, and the thin lines show the 5×5 equally weighted averages

  • View in gallery

    AMSU-B BG convolution bias and rms errors as function of the AMSU-A scan position

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Optimal Convolution of AMSU-B to AMSU-A

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  • 1 Institut für Weltraumwissenschaften, Freie Universität Berlin, Berlin, Germany
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Abstract

In order to find an optimal convolution of the Advanced Microwave Sounding Unit (AMSU) -B to AMSU-A resolution the scan characteristics of AMSU-A and AMSU-B on board NOAA-15 are examined. A set of coefficients for this degradation is derived using the Backus–Gilbert technique. A 7 × 7 set of adjacent AMSU-B pixels is used where the center pixel is the one closest to a given AMSU-A observation. The error characteristics of the convolution are investigated and except for the two outermost footprints a good reproduction of the spatial sensitivity of the AMSU-A by the convolved AMSU-B is obtained. For a NOAA-15 overpass over inhomogeneous terrain AMSU-A data at 89 GHz were compared to convolved AMSU-B data at the same frequency. The root-mean-square deviation between the so-convolved AMSU-B data and the AMSU-A data was on average 1.7 K, including a systematic deviation of −1 K of AMSU-B to AMSU-A. In comparison, simple, equally weighted averages of AMSU-B data produce rms errors in the order of 4 K and large deviations in regions where gradients in the brightness temperatures occur.

To apply the Backus–Gilbert technique the AMSU’s effective field of view (EFOV) as a function of the scan position was determined. For the continuously scanning AMSU-B the integration time of 18 ms per observation in conjunction with the sensors rotation leads to a considerable broadening of the antenna pattern in cross-track direction and thus to an increase of the EFOV as compared to the instantaneous field of view (IFOV). This does not occur for the stepwise scanning AMSU-A where the IFOV equals the EFOV (neglecting the second-order effects induced by the ∼1-km movement of the subsatellite point during AMSU-A integration). Analytical expressions to calculate the AMSU-A and AMSU-B footprint sizes as functions of their respective scan positions were derived. These expressions exhibit rms deviations to the actual footprint size of 0.5 km with maximum deviations of less than 1 km.

Corresponding author address: Dr. Ralf Bennartz, Freie Universität Berlin, Institut für Weltraumwissenschaften, Fabeckstr. 69, 14195 Berlin, Germany.

Email: bennartz@zedat.fu-berlin.de

Abstract

In order to find an optimal convolution of the Advanced Microwave Sounding Unit (AMSU) -B to AMSU-A resolution the scan characteristics of AMSU-A and AMSU-B on board NOAA-15 are examined. A set of coefficients for this degradation is derived using the Backus–Gilbert technique. A 7 × 7 set of adjacent AMSU-B pixels is used where the center pixel is the one closest to a given AMSU-A observation. The error characteristics of the convolution are investigated and except for the two outermost footprints a good reproduction of the spatial sensitivity of the AMSU-A by the convolved AMSU-B is obtained. For a NOAA-15 overpass over inhomogeneous terrain AMSU-A data at 89 GHz were compared to convolved AMSU-B data at the same frequency. The root-mean-square deviation between the so-convolved AMSU-B data and the AMSU-A data was on average 1.7 K, including a systematic deviation of −1 K of AMSU-B to AMSU-A. In comparison, simple, equally weighted averages of AMSU-B data produce rms errors in the order of 4 K and large deviations in regions where gradients in the brightness temperatures occur.

To apply the Backus–Gilbert technique the AMSU’s effective field of view (EFOV) as a function of the scan position was determined. For the continuously scanning AMSU-B the integration time of 18 ms per observation in conjunction with the sensors rotation leads to a considerable broadening of the antenna pattern in cross-track direction and thus to an increase of the EFOV as compared to the instantaneous field of view (IFOV). This does not occur for the stepwise scanning AMSU-A where the IFOV equals the EFOV (neglecting the second-order effects induced by the ∼1-km movement of the subsatellite point during AMSU-A integration). Analytical expressions to calculate the AMSU-A and AMSU-B footprint sizes as functions of their respective scan positions were derived. These expressions exhibit rms deviations to the actual footprint size of 0.5 km with maximum deviations of less than 1 km.

Corresponding author address: Dr. Ralf Bennartz, Freie Universität Berlin, Institut für Weltraumwissenschaften, Fabeckstr. 69, 14195 Berlin, Germany.

Email: bennartz@zedat.fu-berlin.de

1. Introduction

In May 1998 the first Advanced Microwave Sounding Unit (AMSU) was launched on board NOAA-15. AMSU consists of two instruments, AMSU-A and AMSU-B. The main dedication of the former is temperature soundings of the atmosphere, whereas the latter provides information mainly about atmospheric humidity. Both instruments will be flown on at least two subsequent National Atmospheric and Oceanic Administration (NOAA) satellites (NOAA-L and NOAA-M). Similar instruments (AMSU-A and the Microwave Humidity Sounder) will be on board the European METOP satellite, currently scheduled for launch in 2002. Therefore, these instruments will continue to play an important role in data assimilation as well as for nowcasting and forecasting issues.

This paper deals with issues related to the AMSU’s observation geometry and the possibility to optimally degrade the AMSU-B’s resolution to the AMSU-A’s field of view. An optimal degradation would average the AMSU-B data in a way that the spatial sensitivity of the AMSU-A is perfectly reproduced so that observations at the same frequency but with different spatial resolution will become identical after the higher resolution is degraded to the lower resolution. Although keeping the high resolution of AMSU-B is advantageous for many applications (e.g., cloud liquid water or precipitation retrieval) and a degradation is thus not a priori useful for all purposes, the benefits of this type of mapping are obvious in cases where combined products from AMSU-A and AMSU-B are to be derived. Such products could, for example, be combined water vapor/temperature profiles for use in operational data assimilation or simple calibration cross checks of the different instruments.

A way to perform such degradation is provided by the Backus–Gilbert (BG) technique (Backus and Gilbert 1970), which has been used extensively in passive microwave remote sensing to convolve, deconvolve, and map channels of passive microwave radiometers onto other resolutions (Poe 1990; Farrar and Smith 1992; Robinson et al. 1992; Bauer and Bennartz 1998). Other, more computationally expensive methods such as Fourier filtering have been applied to the problem as well (e.g., Atkinson and McLellan 1998). A comprehensive overview of different techniques can, for example, be found in Burns et al. (1994), who compare various techniques for image restoration and resolution matching in passive microwave remote sensing. While the BG method is not necessarily optimal with respect to its noise features (which are of minor importance in the context of degrading spatial resolution), the advantage of the BG method is its simplicity and computational efficiency, which easily allows near-real-time processing of large data streams. A necessary prerequisite for the application of the BG method is accurate knowledge about the scan characteristics and the spatial sensitivity of the sensors. Before applying the BG method we therefore focus on the AMSU’s scan properties in order to derive the necessary input data for the BG method.

2. AMSU-A/B scan characteristics

a. AMSU-A

The AMSU-A scan characteristics relevant here are listed in Table 1. During one scan AMSU-A performs 30 measurements of the earth. Its scan concept is cross track and stepwise, meaning that the antenna’s rotation is stopped at a fixed position for the integration time. The time needed for a complete scan of 30 pixels is approximately 6 s; the constant full scan period of 8 s is maintained via an increased rotation velocity during the phase of the rotation, in which the instrument does not perform earth or calibration measurements. The step angle equals the instantaneous field of view (IFOV). The lag between adjacent pixels in the along-track direction is 52.8 km, which can be derived from scan period times subsatellite velocity (see Table 1). The subsatellite point velocity is approximately 6.6 km s−1 presuming an average earth radius of 6371 km and an orbital period of 6081 s. The integration time of one AMSU-A observation is 165 ms, during which the subsatellite point and hence the center of the footprint move about 1 km or roughly 2% of AMSU-A’s footprint size at nadir.

b. AMSU-B

The AMSU-B has a full scan period of 8/3 s, so that three full scans are performed during one AMSU-A scan. Both instruments are synchronized via a pulse at the beginning of each AMSU-A scan. AMSU-B’s 90 pixels per scan are separated by 1.1° in the cross-track direction and 17.6 km in the along-track direction. One complete AMSU-B measurement takes 19 ms, with 18-ms integration time and 1-ms dump time. Its IFOV is three times smaller than AMSU-A’s IFOV. During integration time (18 ms), the subsatellite point moves about 125 m, whereas the main reflector of AMSU-B’s antenna rotates about 1.04°. This rotation causes a shift of the footprint center equivalent to the size of the IFOV itself and hence leads to a significant broadening of the EFOV in cross-track direction.

c. Determination of the EFOV

In the subsequent discussions we distinguish between four different representations of the respective antennas spatial sensitivity. The term antenna pattern function refers to the antenna pattern that is usually measured prelaunch. This function is expressed in terms of the zenith angle relative to the antenna’s boresight and an azimuth angel. Laboratory measurements of the antenna pattern functions of the AMSU-B have been published by Hewison and Saunders (1996). Mo (1999) has published antenna pattern functions for the AMSU-A. The term IFOV is used for the 3-dB points of the antenna pattern function projected onto the earth’s surface. This projection leads to IFOVSs that, for off-nadir observations, are broadened more in the cross-track than in the along-track direction. In order to obtain the actual spatial sensitivity of a given sensor, the effects of the movement of the platform and the possible rotation of the antenna during integration time have to be considered as well. For continuous scanners, such as the AMSU-B, the antenna rotation during integration time causes a nonnegligible broadening of the field of view. This is obviously not the case for the stepwise scanning AMSU-A. The sample integration and antenna rotation effects are accounted for in the effective antenna pattern function (Ge). We use the term effective field of view (EFOV) for the 3-dB distances of what is the actual field of view of the spaceborne sensor (including effects of antenna rotation). Necessary information about the relevant scan characteristics of both AMSU-A and AMSU-B are available from the NOAA-KLM User’s Guide (Goodrum et al. 1999).

The method used to determine the EFOV is described in detail in Bennartz (1999), where it was applied to the Special Sensor Microwave/Imager (SSM/I). This method allows one to project a given antenna pattern function G(λ,ϕ) onto the earth surface and to account for time integration effects. The variables λ and ϕ are the azimuth angle with respect to the relative elevation angle of the antenna pattern function in its native, radial coordinate system. The method was applied to all AMSU-A and AMSU-B pixels, and the resulting projected and time-integrated EFOV is expressed in kilometers in cross-track and along-track directions of the satellite. Instead of the actual antenna pattern functions, we used synthetic antenna pattern functions for the subsequent considerations. These functions are simple, rotationally invariant Gaussians with half-width value equal to the 3-dB elevation angle as presented by Hewison and Saunders (1996) and Mo (1999), respectively. Thus G(λ,ϕ) simplifies to G(ϕ). This essentially means that sidelobe effects and azimuthal variations in the antenna response are neglected. Bennartz (1999) shows that, for the similar case of the SSM/I, neglecting the sidelobes does not have a significant effect on the projected and time-integrated EFOV (as compared to other possible sources of error). Since the antenna pattern presented by Hewison and Saunders (1996) as well as Mo (1999) indicates even lower sidelobe contributions for the AMSU than those for the SSM/I (presented by Hollinger et al. 1987) the aforementioned simplification appears reasonable for the AMSU as well.

Figure 1 shows the projected instantaneous and effective antenna pattern functions for the AMSU-B scan positions 1 (scan edge) and 45 (scan center). The calculations were done using NOAA-15’s nominal altitude of 833 km (see Table 1) and an earth radius of 6371 km. The AMSU-B’s antenna rotation results in an increase of the EFOV at position 1 of about 13 km from 51.5 to 64 km. At the scan center the effect is less pronounced; the EFOV in the cross-track direction increases by 4 km from 16.0 to about 20 km. In the along-track direction the EFOV equals the IFOV.

In Fig. 2 we plot the EFOVs at all AMSU-A and AMSU-B scan positions. Both along-track and cross-track values are shown. The EFOV of the nth pixel at the one side of the scan equals the EFOV of the nth pixel from the other side. We derived analytical expressions that allow one to calculate the EFOV as function of scan position. These are given in Table 2 and allow us to calculate the EFOV of AMSU-A and AMSU-B with an accuracy of better than 1 km with respect to the projected EFOVs shown in Fig. 2.

3. Convolution of AMSU-B to AMSU-A

a. The Backus–Gilbert method

The AMSU-B data are convolved to the AMSU-A’s resolution by means of the BG method (Backus and Gilbert 1970). Since the method is well described in the aforementioned literature (Poe 1990; Farrar and Smith 1992; Robinson et al. 1992; Bauer and Bennartz 1998), we only give a general overview on the method without discussing its details. In the following we adapt the notation of Bauer and Bennartz (1998).

Given a set of i = 1, ..., N brightness temperature observations TBi with known effective fields antenna patterns GE,i for each observation, the BG method allows us to estimate a set of coefficients ai, so that a synthetic brightness temperature TB can be derived from
i1520-0426-17-9-1215-e1

The characteristic of the BG method is that it allows us to a priori specify a target effective antenna pattern GT to which the synthetic brightness temperature corresponds. This is done by minimizing the rms deviation between the weighted sum of the effective fields of view of the source data and the target effective antenna pattern. In addition to the fit of the target antenna pattern, the BG method further allows us to adjust the derived ai with different degrees of emphasis on noise amplification. Under the assumption that the noise components of the TBi vary independently, the noise amplification can be derived from Eq. (1) by error propagation laws as Σa2i. Noise amplification is of major importance when over-sampled low-resolution data are deconvolved (e.g., Bauer and Bennartz 1998). Deconvolution realizes a high-pass filter on the data, where some of the ai are larger than unity and hence the noise of the target temperature TB is amplified. In the present case, we wish to degrade the high-resolution AMSU-B data to the low-resolution AMSU-A data and hence perform a low-pass filtering on the data. Therefore, noise amplification is of minor importance, since all ai will be well below one and thus the target noise is reduced. This statement is subsequently confirmed.

b. Derivation of coefficients

Transferring the general explanations of section 3a to the special problem of the convolution of AMSU-B to AMSU-A leads to the following steps.
  1. Calculate the observation geometry and the relative orientation of the AMSU-B with respect to a given AMSU-A observation. This essentially means that a simple swath model had to be implemented, where the relative positions of the AMSU-B center coordinates are given in the coordinate system of the AMSU-A, with orthogonal along-track/cross-track directions. Since AMSU-A and AMSU-B are synchronized at the beginning of each AMSU-A scan, the relative position of the pixels is a function of the scan line and scan position (as shown in Fig. 3). In order to validate the swath model, we compared the distances between the pixels in our model to distances derived from an actual NOAA-15 overpass, where the geolocation was done using the Advanced ATOVS [Advanced TIROS (Television Infrared Observation Satellite) Operational Vertical Sounder] Processing Package [AAPP; Klaes (1997)] and differences of less than 1.5 km in the relative orientation between the two methods were found. Note that as indicated in Table 1 we used a spherical model of the earth surface instead of an ellipsoidal model as done in the AAPP. The usage of a spherical model instead of a more complicated elliptical model is justified by the scale invariance of the BG method;that is, as long as the relative orientation of the different footprints and the relative size of the different footprints remains constant, the estimate of the ai is invariant against changes in the absolute scale.

  2. Once the relative position of all pixels is known, the AMSU-B observation closest to the AMSU-A observation has to be found. For the first pixel of an AMSU-A scan, this is the second AMSU-B pixel of the first scan line after the synchronization pulse (see Fig. 3). Since AMSU-B scans three times faster than AMSU-A, the closest AMSU-B observation moves to subsequent scan lines as the end of the AMSU-A scan is approached. Once the closest AMSU-B observation is found, a rectangular box surrounding this observation is chosen for the convolution. In our case a box of 7 × 7 AMSU-B observations is used for all scan positions. This box is sufficiently large at all scan positions to enclose the AMSU-A effective antenna pattern up to two times the EFOV. Figure 3 visualizes two more scan properties that impact the convolution. First, the oversampling of the AMSU-B in the along-track direction is largest at the scan edge, whereas at scan center the AMSU-B is slightly undersampled with respect to the EFOV. We can therefore expect that the convolution will work better in regions close to the scan edges. Note that in the cross-track direction there is a small but constant relative oversampling of the AMSU-B (which is due to the effects of sensor rotation; see section 2c). The second finding is that for the outermost AMSU-A pixels the outer part of the footprint is not covered by AMSU-B (see Fig. 3, upper left panel). Therefore, we cannot expect the BG result to resemble the outermost footprints of the AMSU-A, simply because AMSU-B does only cover the inner parts of the AMSU-A footprint. The same holds to a less extent for the AMSU-A scan positions 2 and 29. Although for these the EFOV is covered by AMSU-B observation, 50% of the received energy emerges from regions outside the 3-dB footprint, which lay outside the AMSU-B scan as well.

  3. Once the correct 7 × 7 region of interest has been selected, the effective antenna patterns of the AMSU-B and the target effective antenna pattern of the AMSU-A have to be determined at high resolution on the along-track/cross-track plane. We used a horizontal spacing of 1 km in either direction. These data form the direct input for the BG formalism (see, e.g., Bauer and Bennartz 1998) and coefficients ai can be derived for the input observation geometry. Since observation geometry changes with scan position, the ai have to be calculated separately for each AMSU-A scan position. Thus, the final set of coefficients for all AMSU-A scan positions is of the size 7 × 7 × 30.

As integral measures of the accuracy of the BG method we define the noise amplification e = Σa2i and the value ΔG defined as
i1520-0426-17-9-1215-e2

This value is a measure for the maximum deviation between the target and the matched effective antenna pattern functions. A value ΔG = 0% means that both functions are identical, whereas ΔG = 100% means that both observe completely different scenes. Note that the value ΔG gives a theoretical upper limit for the expected error. The actual error of convolved brightness temperatures strongly depends on the homogeneity of the observed scene. For example, for an idealized horizontally homogeneous cloud field, the resulting convolved brightness temperature does not depend on the convolution method at all. As shown below, the actual convolution error is much smaller than ΔG even for horizontally inhomogeneous scenes such as, for example, coastlines with strong brightness temperature gradients.

The noise amplification and the ΔG values for the AMSU-B to AMSU-A convolution are given in Fig. 4. The values of ΔG range between 25% and 2%, where values higher than 6% only occur for the two outermost AMSU-A scan positions. This is due to the aforementioned nonoptimal coverage of the AMSU-A’s outermost pixels by AMSU-B. Cross sections through the true and BG convolved effective antenna pattern functions for AMSU-A pixel 1 are shown in Fig. 5 (upper panels). One can clearly identify the underrepresentation of the left side of the cross-track effective antenna pattern function in the region between −150 and −50 km, where no AMSU-B data are available. As can further be seen in Fig. 5, the BG convolved effective antenna pattern at scan position 5 fits the target effective antenna pattern almost perfectly, which translates to the smallest ΔG values of about 1%. For the scan positions 10 and 15 the deviation between the target and the matched effective antenna pattern increases to values of ΔG ∼ 6%, which is caused by oscillations of the fitted effective antenna pattern in along-track direction. These oscillations are caused by the undersampling of the AMSU-B at near-nadir scan positions (see Fig. 3); they are strongest at scan positions 15 and 16, where the undersampling is strongest.

Although the effective antenna pattern of the AMSU-A cannot be perfectly matched by the BG convolution, the results imply a good agreement between the convolved AMSU-B and the AMSU-A observations. The validity of this statement will be justified in the next section, where we apply the BG convolution to AMSU data and quantify its accuracy by comparing the 89-GHz AMSU-A data with convolved AMSU-B data at the same frequency.

4. Validation

a. Data description

The data used for validation of the method were received via high resolution picture transmission from the Swedish Meteorological and Hydrological Institute from a NOAA-15 overpass over northern Europe on 22 May 1999 at 1815 UTC. Figure 6 shows an image of the AMSU-B channel at 89 GHz. The synoptic situation was governed by a low pressure system with a center west of Norway. At the time of the overpass its cold front was passing Sweden and the eastern part of Germany. The rain bands can be identified as dark stripes where scattering of precipitation-sized ice particles leads to a decrease in the observed brightness temperature at the high-frequency channels. In addition to the precipitation features the overpass includes several coastlines, so that it is well suited to evaluate the capability of the BG convolution.

b. Comparison of AMSU-B and AMSU-A

After application of the BG convolution the convolved 89-GHz AMSU-B data can be compared to the AMSU-A data at 89 GHz. Ideally, if both instruments are well calibrated and the above-outlined presumptions about the EFOVs and observation geometry are right, the convolved brightness temperatures of the AMSU-B should equal those of the AMSU-A. Figure 7 shows scatterplots of the results for the aforementioned NOAA-15 overpass. Besides the BG convolved values we also used equally weighted averages over a square area of AMSU-B pixels surrounding the AMSU-A observation. These equally weighted averages represent a simple, straightforward averaging strategy that does not account for the effective antenna pattern of the different instruments. The size of the square was varied among 3 × 3, 5 × 5, and 7 × 7. At the low and high ends of the range of brightness temperatures (i.e., homogeneous water respective land surfaces) all methods produce similar results with very little scatter. This reflects the fact that if homogeneous scenes are observed the averaging does not have any effect. In the intermediate range, however, strong deviations between the equally weighted averages of the AMSU-B and the AMSU-A data occur. These deviations sometimes exceed 30 K. Obviously, these intermediate brightness temperatures occur mainly over inhomogeneous terrain such as coastlines or close to the edge of precipitation systems. In contrast to the equally weighted averages the BG convolution exhibits significantly less scatter; maximum deviations are around 5 K. Table 3 shows the overall rms error and bias characteristics of the four different averaging techniques. While rms errors for the equally weighted averages are above 4 K, the BG method shows an rms error of 1.7 K. The bias component between AMSU-B and AMSU-A is −1.1 K. Note that this negative bias does not depend on the averaging and is also apparent for the other averaging techniques. These show rms deviations between AMSU-A and AMSU-B of around 4 K that are thus on average a factor of 2 higher than for the BG method. The best results for equally weighted averages are obtained for the 5 × 5 box with an rms deviation of 3.5 K. Figure 8 shows the AMSU-A brightness temperatures along the transects shown in Fig. 6. The right figures show the differences between the AMSU-A and the AMSU-B temperatures for the BG convolution and for the 5 × 5 equally weighted averages. Figure 8 shows that if the observed scene is homogeneous, the averaging technique is not of importance (e.g., transect 4, pixels 10–20). However, if gradients in the observed brightness temperature field occur, the BG convolution yields more stable results.

From Fig. 8 it can also be seen that for the along-track transects (TS 3 and 4) systematic deviations between the AMSU-A and degraded AMSU-B data occur. Therefore, in Fig. 9 we show the bias and rms deviations between the AMSU-A and the BG-convolved AMSU-B data as function of the AMSU-A scan position. One can see that the bias between AMSU-A and AMSU-B has a pronounced dependence on the scan position. While at the center of the scan positive biases are found, the bias decreases to values of about 2.5 K close to the scan edge. This structure can also be found in the rms deviation, which indicates that the rms is governed by the bias component. In fact, the bias-corrected root-mean-square deviation (≡rmse2 − bias2) is almost independent on the scan position and has values smaller than 1.5 K for most scan lines with a maximum value of 2.4 for scan line 30. The correlation coefficient between the convolved AMSU-B data and the AMSU-A data is better than 0.995 except for the highest scan position.

5. Discussion

The method presented here allows us to optimally convolve high-resolution AMSU-B observations to low-resolution AMSU-A footprints. The method is based on a weighted average over a set of 7 × 7 AMSU-B pixels, surrounding the AMSU-A pixel under consideration. Since only a weighted sum over AMSU-B pixels has to be calculated, the method is fast and can be used in real-time applications as well as in global climate studies, where huge amounts of data have to be reprocessed. Weighting coefficients were generated using the Backus–Gilbert method. For the test cases presented in this study, the bias-corrected rms deviation between AMSU-A and convolved AMSU-B observations at 89 GHz is in the order of 1.5 K, depending on scan position. They are thus about a factor of 2 smaller than the rms deviation when a set of 5 × 5 AMSU-B pixels are equally weighted averaged to the AMSU-A resolution. The two outermost scan positions of the AMSU-A cannot completely be recovered, since the AMSU-B does not cover the whole 3-dB range of the footprint. In situations where high coincidence between both sensors is needed, it might therefore be worthwhile to exclude the convolved AMSU-B data at AMSU-A scan positions 1 and 30 from the data analysis. The proposed convolution method will be of interest for all applications requiring a common resolution of AMSU-A and AMSU-B. Such applications could be simultaneous humidity and temperature profiling, precipitation retrieval, and calibration cross-checks at channels that are available for both instruments (89 GHz).

As a by-product of the convolution, analytical formulations to calculate the AMSU-A’s and AMSU-B’s effective fields of view in cross-track and along-track direction were derived. The accuracy of these expressions is about 1 km in either direction. These formulations may also be of interest for several applications, where exact knowledge about the spatial resolution is required. This is, for example, the case for precipitation retrievals where visible/near-infrared data are matched to the AMSU resolution in order to gain information about the subscale cloud structures within an AMSU field of view.

The implementation of the convolution is done in C where the interface to the AMSU data is kept consistent with the data field definitions of the Advanced ATOVS processing package (Klaes 1997). The software package and data to apply the convolution can be obtained from the author or directly downloaded from the Institute for Space Sciences Web site (http://www.fu-berlin.de/iss).

Acknowledgments

The AMSU data were kindly provided by Anke Thoss, who is with the Swedish Meteorological and Hydrological Institute (SMHI). The author would also like to thank Nigel Atkinson and Tim Hewison, both with the U.K. Met. Office, for many constructive comments on this paper. I would further like to thank Barbara Burns from Aerojet for her thorough and constructive review.

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Fig. 1.
Fig. 1.

Projected instantaneous and effective antenna pattern functions for AMSU-B scan positions 1 (scan edge) and 45 (scan center), respectively. The curves are derived from synthetic antenna pattern functions with 3-dB beamwidth as specified in Table 1. For the scan center the instantaneous field of view in the along-track direction equals the instantaneous field of view in the cross-track direction

Citation: Journal of Atmospheric and Oceanic Technology 17, 9; 10.1175/1520-0426(2000)017<1215:OCOABT>2.0.CO;2

Fig. 2.
Fig. 2.

Sizes of the EFOVs of AMSU-A and AMSU-B in both the along-track and cross-track direction as function of scan position. Shown are the calculated EFOVs from the scan center (positions 15 AMSU-A and 45 AMSU-B) to the scan edge (positions 30 for AMSU-A, 90 for AMSU-B). The functional behavior is symmetrical for the lower scan positions 1–15 of the AMSU-A and scan positions 1–45 of the AMSU-B

Citation: Journal of Atmospheric and Oceanic Technology 17, 9; 10.1175/1520-0426(2000)017<1215:OCOABT>2.0.CO;2

Fig. 3.
Fig. 3.

Scan geometry of AMSU-A and AMSU-B in along-track/cross-track coordinates. The large ellipse in the middle depicts the 3-dB size of the AMSU-A footprint. The small ellipses show the AMSU-B footprints. The AMSU-B footprints shown as solid lines are those of the first AMSU-B scan after the synchronization pulse

Citation: Journal of Atmospheric and Oceanic Technology 17, 9; 10.1175/1520-0426(2000)017<1215:OCOABT>2.0.CO;2

Fig. 4.
Fig. 4.

Error characteristics of the application of the BG method. The value ΔG is defined in Eq. (2) and gives a measure of the difference between the target and the matched antenna pattern functions. The noise amplification is defined as the rms over the BG coefficients ai

Citation: Journal of Atmospheric and Oceanic Technology 17, 9; 10.1175/1520-0426(2000)017<1215:OCOABT>2.0.CO;2

Fig. 5.
Fig. 5.

Cross sections through the AMSU-A’s target (thin lines) and the BG-convolved AMSU-B antenna patterns (thick lines) for AMSU-A scan positions 1, 5, 10, and 15. The left panels show the cross sections in the cross-track direction, while the right panels show the cross sections in the along-track direction

Citation: Journal of Atmospheric and Oceanic Technology 17, 9; 10.1175/1520-0426(2000)017<1215:OCOABT>2.0.CO;2

Fig. 6.
Fig. 6.

Image of AMSU-B 89-GHz channel of the NOAA-15 overpass over northern Europe on 22 May 1999 at 1815 UTC. The lines indicate the positions of the four transects that are plotted in Fig. 8

Citation: Journal of Atmospheric and Oceanic Technology 17, 9; 10.1175/1520-0426(2000)017<1215:OCOABT>2.0.CO;2

Fig. 7.
Fig. 7.

Scatterplot of AMSU-A 89-GHz brightness temperatures vs convolved AMSU-B 89-GHz brightness temperatures for BG convolution and equally weighted averages using different sizes of a square window of AMSU-B data

Citation: Journal of Atmospheric and Oceanic Technology 17, 9; 10.1175/1520-0426(2000)017<1215:OCOABT>2.0.CO;2

Fig. 8.
Fig. 8.

The left images show AMSU-A 89-GHz brightness temperatures along the transects shown in Fig. 6. The right images show the corresponding differences between the convolved AMSU-B brightness temperatures and AMSU-A at 89 GHz. The thick lines show results for the BG estimate, and the thin lines show the 5×5 equally weighted averages

Citation: Journal of Atmospheric and Oceanic Technology 17, 9; 10.1175/1520-0426(2000)017<1215:OCOABT>2.0.CO;2

Fig. 9.
Fig. 9.

AMSU-B BG convolution bias and rms errors as function of the AMSU-A scan position

Citation: Journal of Atmospheric and Oceanic Technology 17, 9; 10.1175/1520-0426(2000)017<1215:OCOABT>2.0.CO;2

Table 1.

NOAA-15 satellite characteristics and AMSU-A and AMSU-B instrument characteristics taken from the NOAA–KLM user’s guide (Goodrum et al. 1999). The initial offset from synchronization pulse refers to the beginning of the integration of the first AMSU-A and AMSU-B pixel

Table 1.
Table 2.

Analytical expressions for the effective field of view of AMSU-A and -B as functions of the scan position n. For AMSU-A n ∈ {1, 15} and for AMSU-B n ∈ {1, 45}. The scan positions 16–30 of AMSU-A and 46–90 of AMSU-B are symmetrical to 1–15 and 1– 45, respectively [for the higher scan positions use n′ instead of n with n′ = 31 − n(AMSU-A) or n′ = 91− n(AMSU-B)]

Table 2.
Table 3.

Summary of the error characteristics of the BG methods compared to equally weighted averages using different sizes of a square window of AMSU-B data. The values are derived from convolved AMSU-B data at 89 GHz with the AMSU-A channel at 89 GHz being the reference

Table 3.
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