Resolution enhancement for microwave-based atmospheric sounding from geostationary orbits

Authors


Abstract

[1] The purpose of this study is to develop and evaluate techniques that improve the spatial resolution of the channels already selected in the preliminary studies for Geostationary Observatory for Microwave Atmospheric Soundings (GOMAS). Reference high resolution multifrequency brightness temperatures scenarios have been derived by applying radiative transfer calculation to the spatially and microphysically detailed output of meteorological events simulated by the University of Wisconsin–Nonhydrostatic Model System. Three approaches, Wiener filter, Super-resolution and Image-fusion have been applied to some representative GOMAS frequency channels to enhance the resolution of antenna temperatures. The Wiener filter improved resolution of the largely oversampled images by a factor 1.5–2.0 without introducing any penalty in the radiometric accuracy. Super-resolution, suitable for not largely oversampled images, improved resolution by a factor ∼1.5 but introducing an increased radiometric noise by a factor 1.4–2.5. The Image-fusion allows finally to further increase the spatial frequency of the images obtained by the Wiener filter increasing the total resolution up to a factor 5.0 with an increased radiometric noise closely linked to the radiometric frequency and to the examined case study.

1. Introduction

[2] The vertical profile of the temperature and the humidity of the air constitutes a primary data for weather forecasting. Its measure must be available on the whole globe, and therefore the satellite constitutes the most suitable base of observation. The infrared (IR) measure guarantees the best possible quality in terms of accuracy, spatial resolution and vertical resolution, but it quickly becomes unusable with increasing presence of clouds in the satellite filed of view. Using the microwaves (MW) instead, in the absorption bands of the O2 at 54 GHz, 118 GHz and 425 GHz (for the temperature sounding) and of the H2O at 183 GHz and 380 GHz (for the humidity sounding) we can, even though with smaller vertical resolution, effect the survey even in presence of clouds, at least until clouds are not associated to precipitation. The greatest obstacle to the observation in the microwaves frequencies from Geosynchronous Earth Orbit (GEO) is constituted by the low spatial resolution of the remotely sensed data. Possible convective cells or frontal systems appear in the MW too smooth making impossible the exact identification of the contours of a possible structure associated to precipitation, in which the retrieval of the vertical profiles cannot be effected.

[3] Within the post-MSG (Meteosat Second Generation) studies, the possibility to integrate with the Meteosat Third Generation (MTG) the use of the MW additionally to the VIS/IR observation is under evaluation. In Table 1 are brought the selected channels for this study, the relative characteristics of resolution expressed as Instantaneous Field of View (IFOV) at subsatellite point (s.s.p.) for 3-dB contours, the sampling (pixel) and the noise equivalent (NE) ΔT for the satellite GEO in MW [Dietrich et al., 2006]. The above characteristics depending on the antenna diameter (3 m for this study) and the state of the art, both of them defined in the GOMAS project [Bizzarri et al., 2002]. For the strongly oversampled data, at least with Nyquist (100% oversampling, i.e. double sampling rate respect to IFOV), it is possible to increase the resolution through techniques of deconvolution [Poe, 1990; Farrar and Smith, 1992]. In this condition are the channels of the bands at 54 GHz (IFOV 81 km, sampling 10 km), 118 GHz (IFOV 37 km, sampling 10 km) and 183 GHz (IFOV 24 km, sampling 10 km).

Table 1. GOMAS Channels to Be Simulateda
ν (GHz)Δν (MHz)IFOV (km)Pixel (km)NEΔT at Pixel Level (K)Peak of Weighting Function
  • a

    The integration time corresponding to one 10-km pixel is 6 ms; the IFOV dimension is referred to a s.s.p. for a 3 m antenna diameter.

53.84519081100.485 km
50.30018081100.48Surface
118.750 ± 2.10080037100.335 km
118.750 ± 5.000200037100.21Surface
183.310 ± 5.000200024100.345 km
183.310 ± 17.000400024100.36Surface
380.197 ± 18.000200012100.725 km
424.763 ± 4.000100010101.025 km

[4] The bands at 380 GHz (IFOV 12 km, sampling 10 km) and 424 GHz (IFOV 10 km, sampling 10 km) are not oversampled. In this case it is possible to increase the resolution by increasing contemporarily the sampling by means of the Super-resolution technique. A further increase of spatial resolution is possible by means of the Image-fusion technique, by joining the results obtained by deconvolution with Wiener filter and Super-resolution.

[5] It is important to underline that the initial resolution of GOMAS channels are within a factor of two of similar frequency microwave observations from Low Earth Orbit (LEO), even though the geostationary satellite is stationed at altitudes over 40 times higher than satellites in LEO. Using some resolution enhancement techniques, like the ones we have tested in this paper, this value can be further reduced, making the MW remote sensing from GEO comparable to that from LEO, but with the advantage of being updated much more frequently. In this perspective it is also possible to review the basic issues of possible GOMAS design features, such as the expected numbers of channels that might be used for sounding applications which could be reduced, as to the twenty some channels that will be used for the NPOESS ATMS.

2. Simulating the MW Measurement by GEO Satellite

2.1. Simulated Reference Scenario

[6] In order to simulate the upwelling brightness temperatures (TB) that would be observed by the geostationary radiometer, we apply to the University of Wisconsin–Nonhydrostatic Model System (UW-NMS) simulated events a 3D-adjusted plane-parallel radiative transfer model (RTM) [Roberti et al., 1994; Liu et al., 1996; Bauer et al., 1998; Tassa et al., 2003]. The RTM-generated upwelling TB values over simulated satellite footprints has been calculated at the model resolution (higher than the radiometer resolution) and with observation at the nadir.

[7] For this study two reference scenarios have been simulated: a winter frontal system over Piedmont region (Italy) at 12:00 UTC on 24 November 2002 (141 × 261 spots/pixel) (see TB panels in Figures 123456and 1314) and a convective system characterized by snow on the Adriatic Sea (Italy) at 12:00 UTC on 28 February 2004 (200x200 spots/pixel) (see TB panels in Figures 789101112 and 1516). The first scenario has a resolution and a sampling of 2.34 km and the second has a resolution and a sampling of 3.00 km.

Figure 1.

Brightness temperature (TB), antenna temperature (TA) and reconstructed brightness temperature (T′B) for Piemonte case at 50.300 GHz.

Figure 2.

Brightness temperature (TB), antenna temperature (TA) and reconstructed brightness temperature (T′B) for Piemonte case at 53.845 GHz.

Figure 3.

Brightness temperature (TB), antenna temperature (TA) and reconstructed brightness temperature (T′B) for Piemonte case at (118.750 ± 5.000) GHz.

Figure 4.

Brightness temperature (TB), antenna temperature (TA) and reconstructed brightness temperature (T′B) for Piemonte case at (118.750 ± 2.100) GHz.

Figure 5.

Brightness temperature (TB), antenna temperature (TA) and reconstructed brightness temperature (T′B) for Piemonte case at (183.310 ± 5.000) GHz.

Figure 6.

Brightness temperature (TB), antenna temperature (TA) and reconstructed brightness temperature (T′B) for Piemonte case at (183.310 ± 17.000) GHz.

Figure 7.

Brightness temperature (TB), antenna temperature (TA) and reconstructed brightness temperature (T′B) for Adriatico case at 50.300 GHz.

Figure 8.

Brightness temperature (TB), antenna temperature (TA) and reconstructed brightness temperature (T′B) for Adriatico case at 53.845 GHz.

Figure 9.

Brightness temperature (TB), antenna temperature (TA) and reconstructed brightness temperature (T′B) for Adriatico case at (118.750 ± 5.000) GHz.

Figure 10.

Brightness temperature (TB), antenna temperature (TA) and reconstructed brightness temperature (T′B) for Adriatico case at (118.750 ± 2.100) GHz.

Figure 11.

Brightness temperature (TB), antenna temperature (TA) and reconstructed brightness temperature (T'B) for Adriatico case at 183.310 ± 5.000) GHz.

Figure 12.

Brightness temperature (TB), antenna temperature (TA) and reconstructed brightness temperature (T'B) for Adriatico case at (183.310 ± 17.000) GHz.

2.2. Simulated Radiometric Antenna Temperature

[8] A microwave image aims at reconstructing the brightness temperature distribution of a given scenario. By means of the antenna beam scanning it is possible to record the TB angular distribution as seen from the radiometer system. Then it is practical to consider the antenna system (antenna + scanning system) as a transducer that operates on the TB distribution. The observed brightness distribution (antenna temperature, TA) can be considered as the convolution of the antenna pattern with the true brightness distribution, to which is added radiometric noise.

equation image

In equation (1), (x, y) represent spatial coordinates, TA represents the MW measurement by GEO satellite, TB is the simulated reference scenario, H the antenna pattern having full width half maximum (FWHM) equal to the correspondent IFOV, × denotes the linear convolution operator, [•]decimation denotes the decimation process necessary to reduce the image sampling at 10 km (see Table 1) and N the correspondent radiometric noise NEΔT. The antenna pattern H has not yet been defined, so it will be modeled with a two-dimensional Gaussian. This choice is not particularly binding: in facts, it is possible demonstrate [Bizzarri et al., 2005] that a different choice of H does not involve great changes in the final results. The decimation process consists in extracting one pixel every 4 × 4, for the Piedmont case (1 px = 2.34 km), and one pixel every 3 × 3 to the Adriatic case (1 px = 3.00 km). For all cases and all frequencies the decimation process has been done in according to Nyquist theorem. The radiometric noise N(x,y) is simulated by a random generation of noise values having Gaussian distribution with standard deviation equal to the expected NEΔT of the specific frequency channel. Equation (1) has been resolved by making the Fourier transform of each term (equation (2)), so that the operation of convolution becomes a simple product:

equation image

In which (u, v) represent the coordinates spatial frequency.

3. Resolution Enhancement

[9] The Resolution enhancement is done with two techniques: one for strongly oversampled images, at least with Nyquist (100% oversampling, i.e. double sampling rate in respect of what would be needed to have adjacent IFOVs) and one for images with sampling lower than the Nyquist's (lower than 100%).

3.1. Deconvolution With Wiener Filter for Heavily Oversampled Images

[10] Since all GOMAS channels are sampled at 10 km intervals, the 100% oversampling applies to 54 GHz (81 km IFOV), 118 GHz (37 km) and 183 GHz (24 km). The reconstructed brightness temperatures (T'B (x,y)) can be calculated by means of the Wiener filter W(u,v):

equation image

where [•]IDTF denote the Inverse Discrete Fourier Transform. The general Wiener filter formula [Vaseghi, 2000] is:

equation image

where the symbol * denotes the complex conjugate, PNN(u, v) and PTBTB(u,v) are the power spectrum respectively of N(u, v) and TB(u, v). For white additive noise the power spectrum PNN(u, v) is equal to the variance of the noise:

equation image

PTBTB(u, v) is not known and is estimated with:

equation image

where PTATA(u, v) are the power spectrum of TA(u, v). With this approximation the reconstructed T'B in spatial frequency coordinates becomes:

equation image

However, the previous formula may not be stable if the denominator tends to zero, for this reason is introduced a threshold value γ:

equation image

where α is a tuning parameter used to optimize the deconvolution performance, and FPRA is the Floating-Point Relative Accuracy of a calculation software. Introducing the above threshold value we have:

equation image

We will see that in some cases, especially at lower MW frequencies (54 GHz), where the content of the high spatial frequencies is low, α = 1 is a good value. On the contrary, at higher microwave frequencies (183 GHz), we have better results for higher α values (α = 10).

[11] The method produces a positive result if the correlation coefficient between T′B and TB (RT′B) is greater than the correlation coefficient between TA and TB (RTA). In addition to the correlation coefficient is necessary to evaluate if the radiometric noise of T′B (NEΔT′) is not excessively amplified. For its evaluation, we used the Immerkær Method [Immerkær, 1996], based on a 3 × 3 linear filter that removes the structure of image and then estimate the variance from the residuals. This filter is the weighted difference of two Laplacian filters [Gonzalez and Woods, 1992], L1 and L2, which estimate the second derivative of the image signal. The effect of L is to reduce constant, planar and quadratic 3 × 3 facets to zero plus a linear combination of the noise.

equation image

Once the image has been filtered to remove structure, the filtered pixel values can be used to compute the estimated standard deviation σ:

equation image

This method is designed specifically for the case of zero mean additive Gaussian noise.

[12] For a statistically significant evaluation, we processed 1000 occurrences of TA, each characterized by a different random occurrence of the radiometric noise matrix, to which we applied the deconvolution technique with Wiener filter. Table 2 shows the result of this assessment in terms of RT′B and NEΔT' mean. The reconstruction of the image is always good (RT′B > RTA) and the noise is always attenuated (NEΔT′ < NEΔT). This result is typical of the denoising action of the Wiener filter and is the result of the oversampling. For evaluating the performance of the Wiener filter in terms of resolution (IFOV′), each deconvolved image T'B has been confronted with different antenna temperature comparison TAcom, obtained by convolution between TB and different antenna patterns having a different FWHM, variable in the range (5 ÷ 100) km with 0.5 km of step. The TAcom more similar to T′B in terms of correlation coefficient identifies, by means the related FWHM, the searched IFOV′. IFOV′ is an indicative quantity of the spatial resolution of TA showing an increase of the resolution by a factor of ∼1.5 ÷ 2.0. The results show that the Wiener filter allows to increase the resolution and to lower at the same time the radiometric noise of the image. Figures 112 show the TB, TA and T′B maps for the selected case studies and channels. It is evident from the visual inspection how the T′B images resemble the original TB more than TA as numerically assessed in Table 2 and a very careful analysis confirms the reduction of the noise (NEΔT′ < NEΔT) as expected following the description of Wiener filter in Vaseghi [2000] and in Bizzarri et al. [2005]. The denoising effect obtained by applying the Wiener filter is a consequence of the large oversampling of the simulated sensors. As a matter of fact, many samples have information concerning the same point, since the IFOV is much larger than the sampling distance. So, this “over-information” can be used to reduce the radiometric noise as well as a set of measurements, affected by any random error, can be used to calculate the mean value, which approximates the truth more than one single measurement.

Table 2. Wiener Filter Performance for 1000 Simulations
RegionFrequency (GHz)SNR (dB)RTAαReconstructed Value
NEΔT′ (K)RT’BIFOV′ (km)
Piemonte50.30036.50.61 ± 0.01 0.180.711 ± 0.00144
Adriatico51.00.81 ± 0.01 0.180.862 ± 0.00139
Piemonte53.84525.60.55 ± 0.02 0.160.626 ± 0.00149
Adriatico23.10.61 ± 0.02 0.160.666 ± 0.00145
Piemonte118.750 ± 5.00070.90.75 ± 0.0110.090.816 ± 0.00126
Adriatico80.40.74 ± 0.01 0.090.866 ± 0.00118
Piemonte118.750 ± 2.10063.70.77 ± 0.01 0.120.830 ± 0.00121
Adriatico71.60.75 ± 0.01 0.120.858 ± 0.00118
Piemonte183.310 ± 17.00063.20.84 ± 0.02 0.120.869 ± 0.00116
Adriatico73.20.90 ± 0.03100.140.922 ± 0.00115
Piemonte183.310 ± 5.00063.70.85 ± 0.0210.130.879 ± 0.00116
Adriatico76.10.92 ± 0.04100.140.935 ± 0.00115

3.2. Super-Resolution for Nonstrongly Oversampled Images

[13] The Super-resolution is a technique to reconstruct a high quality image from standard sampled (i.e. not oversampled) image, so in our case this technique can be applied to 380 GHz (12 km) and to 424 GHz (10 km). Super-resolution includes two steps: the resampling of the original image on a finer regular grid, and the application of an Inverse Filter to deconvolve the resampled images.

3.2.1. Resampling

[14] In order to resample the original image we have applied the spline cubic interpolation. This kind of interpolation involves the spline cubic interpolation between adjacent points along the two main axes of the grid, followed by the linear interpolation along the same two axes between the new points as well. The spline cubic interpolation, in the mathematical subfield of numerical analysis, is a form of interpolation where the interpolant is a special type of piecewise polynomial called a spline. Generally, in one dimension, for a data set {xi} of n + 1 points, we can construct a cubic spline with n piecewise cubic polynomials between the data points. If

equation image

represents the spline function interpolating the function f, we require: (1) the interpolating property, S(xi) = f(xi), (2) the splines to join up, Si-1(xi) = Si(xi), i = 1,…,n−1, and (3) twice continuous differentiable, Si1(xi) = Si(xi) and Si1(xi) = Si(xi), i = 1,…,n−1.

[15] For the n cubic polynomials comprising S, this means to determine these polynomials, we need to determine 4n conditions (since for one polynomial of degree three, there are four conditions on choosing the curve). However, the interpolating property gives us n + 1 conditions, and the conditions on the interior data points give us n + 1 − 2 = n-1 data points each, summing to 4n−2 conditions. We require one other condition: the interpolating property, S(x0) = S(xn) = 0 resulting in the natural cubic spline: this forces the spline to be a straight line outside of the interval, while not disrupting its smoothness. Natural cubic spline yield the least oscillation about f than any other twice continuously differentiable function.

3.2.2. Inverse Filter

[16] The Inverse Filter method derives from the fact that TA(x, y) is the results of the convolution process of TB(x, y) with antenna pattern H(x, y). Neglecting the radiometric noise we have:

equation image
equation image

with I(u, v):

equation image

However, in most cases, this procedure is not stable since it happens that for certain values of (u,v), the denominator equals to zero. This problem can be solved by introducing a threshold value γ so that I(u, v) becomes:

equation image

Examining different cases we have observed that the optimal value for γ parameter is around 2.5, value that we have used.

[17] In order to evaluate the resolution enhancement performance obtainable by using the Super-resolution method, as we did for Wiener filter based on 1000 simulations. For each simulation we generate a random occurrence of the radiometric noise, computing one TA occurrence over which we apply the Super-resolution techniques. Table 3 shows the results for these simulations in terms of correlation coefficient. The Super-resolution shows an improvement of the image that highlights both by the largest value RT′B respect to RTA both by the lower value of IFOV′ when compared with IFOV. The noise amplification NEΔT′ is acceptable. Figures 13141516 show the TB, TA and T′B maps for the selected case studies and frequencies.

Figure 13.

Brightness temperature (TB), antenna temperature (TA) and reconstructed brightness temperature (T′B) with Super-resolution method for Piemonte case at (380.197 ± 18.000) GHz.

Figure 14.

Brightness temperature (TB), antenna temperature (TA) and reconstructed brightness temperature (T′B) with Super-resolution method for Piemonte case at (424.763 ± 4.000) GHz.

Figure 15.

Brightness temperature (TB), antenna temperature (TA) and reconstructed brightness temperature (T′B) with Super-resolution method for Adriatico case at (380.197 ± 18.000) GHz.

Figure 16.

Brightness temperature (TB), antenna temperature (TA) and reconstructed brightness temperature (T′B) with Super-resolution method for Adriatico case at (424.763 ± 4.000) GHz.

Table 3. Super-Resolution Performance for 1000 Simulations
RegionFrequency (GHz)SNR (dB)RTASuper-Resolution
NEΔT’ (K)IFOV’ (km)RT’B
Piemonte380.197 ± 18.00059.70.85 ± 0.091.81∼7.50.9565 ± 0.0001
Adriatico 76.70.95 ± 0.031.53∼7.00.9767 ± 0.0001
Piemonte424.763 ± 4.00051.50.86 ± 0.081.41∼7.00.9489 ± 0.0002
Adriatico 68.20.96 ± 0.021.85∼7.00.9792 ± 0.0001

3.3. Image-Fusion

[18] The Image-fusion consists in using the high spatial frequencies content of high resolution images (namely the 118.750 ± 5.000, 118.750 ± 2.100, 380.197 ± 18.000 and 424.763 ± 4.000 GHz) to improve the spatial resolution of the lower frequency channels (namely 50.300, 53.845, 118.750 ± 2.100, 183.310 ± 5.000 GHz). The input to the Image-fusion technique are images already reconstructed by applying the Wiener Filter or the Super-resolution (depending on the channel). Also this operation is executed in the spatial frequencies domain by means of the Fourier transform of the two images [Chen and Staelin, 2002].

[19] The first step is to fix a threshold value γ in Fourier transform of the highly resolved image in order to extract only the information related with the high spatial frequencies, namely the small scale variability. Generally, this value depends on the characteristics of the image (i.e. pixel number, pixel dimension, etc.), but for our cases we have observed that the optimal threshold value is something like γ = 103. The second operation is to select a weight β in order to estimate the amount of high spatial frequencies content to be transferred to the low resolution image.

equation image

where TB(u,v)IF' is the Fourier transform of the image reconstructed with Image-fusion, TB(u,v)LOW′ is the image at low spatial resolution (i.e. obtained using the Wiener filter) and TB(u,v)HIGH is the image at high spatial resolution (derived from Wiener filter or Super-resolution, depending on the selected frequency). β is a tuning parameter, selectionable depending on spatial features of high frequency image. The application of the method to our simulated images shows that β = 0.33 if the high frequency image is reconstructed by Wiener filter (like 54–118 GHz). Instead, smaller β values are suggested if the high frequency image is obtained by Super-resolution (54-424 GHz and 183-380 GHz). Having high spatial frequency contents (Adriatic case), the best reconstruction is obtained using β = 0.10, otherwise β = 0.20 is enough. Obviously, it makes more physical sense to apply the Image-fusion technique to bands having similar physical information, i.e. 54 GHz, 118 GHz and 424 GHz for O2 channels and 183 GHz and 380 GHz for H2O, choosing channels peaking approximately at the same altitude. The peaks of weighting function in clear-air conditions are in Table 1.

[20] As we did to evaluate the Wiener filter, the performances provided by the Image-fusion method is assessed making use of a Monte Carlo technique, based on 1000 simulations. For each simulation we generate a couple of random occurrences of the radiometric noise both for the high and low frequency channels involved in the fusion process, generating in this way 1000 couples of TA occurrences. Then, we apply the Image-fusion technique to each couple. Table 4 shows the results of these simulations expressed in terms of correlation coefficient. The first five columns indicate the region, the radiometric frequencies and the performance results from resolution enhancement with Wiener filter or Super-resolution. The last column, RT'B indicates the correlation coefficient between the Image-fusion result and the TA. When this value is greater than the corresponding RT′B value under “low spatial frequency” it means that the technique has made a further reconstruction of the image obtained by Wiener filter or Super-resolution. Table 5 shows the performance obtainable using Image-fusion method in terms of IFOV' and noise amplification NEΔT′. Figures 171819202122 show an example of Image-fusion application.

Figure 17.

Brightness temperature (TB), reconstructed brightness temperature (T'B) with Wiener filter and reconstructed brightness temperature (T′B) with Image-fusion for Piemonte case at 50.300 GHz, using (118.750 ± 5.000) GHz channal for data fusion.

Figure 18.

Brightness temperature (TB), reconstructed brightness temperature (T′B) with Wiener filter and reconstructed brightness temperature (T′B) with Image-fusion for Piemonte case at 53.845 GHz, using (118.750 ± 2.100) GHz channal for data fusion.

Figure 19.

Brightness temperature (TB), reconstructed brightness temperature (T′B) with Wiener filter and reconstructed brightness temperature (T′B) with Image-fusion for Piemonte case at 53.845 GHz, using (424.763 ± 4.000) GHz channal for data fusion.

Figure 20.

Brightness temperature (TB), reconstructed brightness temperature (T′B) with Wiener filter and reconstructed brightness temperature (T′B) with Image-fusion for Adriatico case at 50.300 GHz, using (118.750 ± 5.000) GHz channal for data fusion.

Figure 21.

Brightness temperature (TB), reconstructed brightness temperature (T′B) with Wiener filter and reconstructed brightness temperature (T′B) with Image-fusion for Adriatico case at 53.845 GHz, using (118.750 ± 2.100) GHz channal for data fusion.

Figure 22.

Brightness temperature (TB), reconstructed brightness temperature (T′B) with Wiener filter and reconstructed brightness temperature (T′B) with Image-fusion for Adriatico case at 53.845 GHz, using (424.763 ± 4.000) GHz channal for data fusion.

Table 4. Image-Fusion Performance for 1000 Simulations in Terms of Correlation Coefficient
RegionLow ResolutionHigh ResolutionImage-Fusion
Frequency (GHz)RT′BFrequency (GHz)RT’Bequation imageRT′B
Piemonte50.3000.711118.750 ±5.0000.8160.330.776 ± 0.002
53.8450.626118.750 ± 2.1000.8300.330.775 ± 0.001
424.763 ± 4.0000.9490.200.758 ± 0.004
118.750 ± 2.1000.830424.763 ± 4.0000.9490.200.851 ± 0.001
183.310 ± 5.0000.878380.197 ± 18.0000.9770.200.890 ± 0.001
Adriatico50.3000.862118.750 ± 5.0000.8660.330.877 ± 0.001
53.8450.666118.750 ± 2.1000.8580.330.719 ± 0.001
424.763 ± 4.0000.9790.100.690 ± 0.001
118.750 ± 2.1000.858424.763 ± 4.0000.9790.100.861 ± 0.001
183.310 ± 5.0000.935380.197±18.0000.9760.100.943 ± 0.001
Table 5. Image-Fusion Performance for 1000 Simulations in Terms of NEΔT and IFOV
RegionLow ResolutionHigh Resolution Frequency (GHz)Image-Fusion
Frequency (GHz)Enanched Resolution
NEΔT′ (K)IFOV′ (km)NEΔT′ (K)IFOV′ (km)
Piemonte50.3000.18∼44118.750 ± 5.0000.12∼26
53.8450.16∼49118.750 ± 2.1000.11∼26
424.763 ± 4.0001.06∼30
118.750 ± 2.1000.12∼21424.763 ± 4.0001.10∼19
183.310 ± 5.0000.13∼16380.197 ± 18.0002.04∼13
Adriatico50.3000.18∼39118.750 ± 5.0000.11∼30
53.8450.16∼45118.750 ± 2.1000.12∼16
424.763 ± 4.0000.61∼30
118.750 ± 2.1000.12∼18424.763 ± 4.0000.69∼16
183.310 ± 5.0000.14∼15380.197 ± 18.0001.04∼11

4. Conclusion

[21] An overall statement of the assessment exercise is offered as follows.

[22] 1. For the 54 GHz band the 81 km resolution can be reduced to ∼(40 ÷ 50) km simply by deconvolution and ∼30 km by additional Image-fusion with 118 GHz or 425 GHz bands; no degradation of NEΔT is observed: on the opposite, the radiometric accuracy improves because the Wiener filter is noise-reducing.

[23] 2. For the 118 GHz band, the 37 km resolution can be brought to ∼20 km simply by deconvolution and ∼18 km by additional fusion with the 425 GHz bands; however, whilst deconvolution improves the NEΔT, the Image-fusion process degrades NEΔT significantly.

[24] 3. For the 183 GHz band, the 24 km resolution can be brought to ∼15 km simply by deconvolution and ∼12 km by additional fusion with the 380 GHz bands. Deconvolution improves the NEΔT, fusion degrades NEΔT significantly.

[25] 4. For the 380 GHz band, the 12 km resolution can be brought to 8 km by Super-resolution. The NEΔT degrades significantly.

[26] 5. For the 425 GHz band, the 10 km resolution can be brought to 7 km by Super-resolution. The NEΔT degrades significantly.

[27] As a whole, these results are better than expected. At 54 GHz, that constitute the main case for the study, the 30 km resolution after deconvolution + Image-fusion is better than the SSM/I resolution at 37 GHz and the same as the 54 GHz band in the MW sounder of NPOESS (ATMS). Even stopping at deconvolution level, we have 40 km, that is better than AMSU-A, that is currently used for estimating precipitation. It is important to note that the deconvolution process improved resolution by a factor 1.5–2 without introducing any penalty in the radiometric accuracy. On the contrary, the radiometric accuracy substantially improved because of the noise-suppressing characteristics of the Wiener filter.

[28] One main result of this study is to support the case for the 54 GHz band that is the most interesting for liquid precipitation, the one better penetrating clouds and the most informative of the atmospheric temperature profile.

[29] In future working, we are planning to conduct additional, more sophisticated simulation tests that generate simulated soundings in order to examine the adequacy of these geostationary soundings to enhance the accuracy of operational weather forecasting models as compared to models that only make use of traditional observations and microwave soundings from LEO. Future studies will also include the examination of the limitations to broad-scale coverage normally expected from geostationary orbit due to the degradation in resolution that will come into play for areas offset from nadir due to oblique viewing angles and earth curvature.

Acknowledgments

[30] This work has been carried out in the framework of EUMETSAT study contract EUM/CO/04/1386/KJG. We wish to thank David H. Staelin for helpful advice and suggestions.

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