These authors contributed equally to this work.

In the frame of Earth observation remote-sensing data analysis, synergistic retrieval (SR) and complete data fusion (CDF) are techniques used to exploit the complementarity of the information carried by different measurements sounding the same air mass and/or ground pixel. While more difficult to implement due to the required simultaneous access to measurements originating from different instruments, the SR method is sometimes preferred over the CDF method as the latter relies on a linear approximation of the retrieved states as functions of the true atmospheric and/or surface state.

In this work, we study the performance of the SR and CDF techniques when applied to simulated measurements of the Far-infrared Outgoing Radiation Understanding and Monitoring (FORUM) and the Infrared Atmospheric Sounding Interferometer – New Generation (IASI-NG) missions that will be operational in a few years, from two polar-orbiting satellites. The study is based on synthetic measurements generated for the two missions in clear-sky atmospheres. The target parameters of the inversion are the vertical profiles of temperature, water vapor and ozone mixing ratios, surface temperature, and spectral emissivity.

We find that for exact matching of the measurements, the results of the SR and CDF techniques differ by less than

Synergistic retrieval (SR) and complete data fusion (CDF) are two methods used to combine remote-sensing measurements acquired by independent instruments, simultaneously probing the same air mass and/or surface area. Measurements in different parts of the electromagnetic spectrum (e.g., ultraviolet, visible, infrared), adopting different acquisition geometries (e.g., nadir and limb sounding), have different sensitivities to the vertical distribution of atmospheric and surface variables. For this reason, combining complementary information from different spectral regions and different sensors can significantly improve the performance of the determined vertical profiles and surface parameters, in terms of both enhanced spatial resolution and error reduction.

In the last few decades, the need to advance the knowledge of tropospheric and stratospheric chemical/physical processes stimulated the development of new techniques to fully exploit the synergy of the great number of existing satellite measurements. Recent studies demonstrated the benefits of combining measurements from different sensors operating in different spectral ranges and/or with different observation geometries, by using simulated

The approaches for the combined use of two or more observations of the same portion of atmosphere and/or surface to determine the atmospheric and/or surface state could be divided into two main classes

The SR is commonly used, as it rigorously combines complementary information of the measurements (see, e.g.,

The a posteriori techniques, such as data fusion

FORUM will be the ninth Earth Explorer mission of the European Space Agency

When FORUM- and IASI-NG-simulated measurements are combined, usually, the differences between the SR and the CDF solutions are not larger than the retrieval error due to measurement noise. For this reason, to accurately characterize these differences, we base the results of our study on statistically significant sets of test retrievals from simulated observations. A first set of test retrievals uses perfectly matching FORUM and IASI-NG measurements, while a second set uses realistically mismatching measurements. All the synthetic measurements used in this paper refer to a clear-sky Antarctic winter scenario, with Earth's surface covered by snow. A dry atmosphere is in fact a prerequisite to retrieve surface spectral emissivity in the FIR region, a key target for the FORUM mission

The statistics of the differences between the SR/CDF products and the true state parameters allow us to quantify the possible biases and the random errors of the two solutions. For verification purposes, these ex post statistical error estimates can also be compared to the related ex ante predictions provided by the error covariance matrices (CMs) of the two solutions. Finally, the statistics of the differences between the SR and CDF solutions quantify the discrepancies between the two methods for realistic forward model linearity and mismatch between the measurements.

The structure of the paper is as follows. In Sect.

We first recall the equations of the SR and CDF approaches. The formalism adopted is based on that of

The minima of these cost functions are found using the Gauss–Newton iterative formula:

We indicate with

The SR is obtained by simultaneously fitting the radiances acquired by the two instruments with the forward model simulations, i.e., by minimizing the cost function:

As in the case of the inversion of a single measurement, the minimum of this cost function is found using the Gauss–Newton iterative formula that, in the case of the SR, takes the following form:

If the two measurements do not refer to the same atmosphere because of temporal and/or spatial mismatches, then the two state vectors

The CDF uses the results of the individual retrievals, and its solution is obtained by minimizing the following cost function

From Eq. (

If the two measurements do not exactly coincide both in space and time, we allow for this mismatch by introducing a coincidence error according to the approach described in

First, let us consider the case of perfectly matching measurements. If, on the one hand, in the range of variability of the solutions of the individual retrievals and of the SR, the linear approximation can be applied to the forward model of both measurements, then the two methods are equivalent, as demonstrated in the appendix of

Now, let us consider the case of measurements not perfectly matching. In the SR, the CM

As mentioned in Sect.

The key instrument of the FORUM mission will be an FT spectrometer measuring the spectrum of the upwelling Earth's outgoing longwave radiation (OLR) by looking at nadir

Like FORUM, IASI-NG will also measure the upwelling spectral radiance; however, its focus will be on the MIR region, with a coverage from 645 to 2760 cm

Figure

FORUM and IASI-NG NESR and ARA requirements. The ARA errors, originally given in brightness temperature, are converted to radiance units assuming a scene temperature of 280 K. The plotted curves refer to

To generate a synthetic measurement, we proceed as follows. The atmospheric state is first defined by setting the vertical profiles of temperature and constituent's volume mixing ratio (VMR) at a set of fixed pressure levels. The surface is then defined by setting the values of surface pressure, temperature, height above sea level and spectral emissivity (on a 5 cm

The measurement error covariance matrices

Pseudorandom noise extracted from a multi-variate Gaussian distribution consistent with the measurement error CM is finally added to the simulated apodized spectral radiances.

The FORUM orbit will be adjusted to match the MetOp-SG-1A orbit; however, the matching between the two orbits will not be perfect. Necessarily, there will be a time lag between the two satellites. Currently, this lag is specified to be smaller than 1 min. Secondly, the ground tracks of the two satellites will not coincide exactly. The maximum distance between the FORUM and MetOp-SG-1A ground tracks is however required to be smaller than 300 km. These conditions are usually referred to as the requirements for the two satellites to fly in loose formation.

Since FORUM will measure only a single ground pixel in the nadir-looking geometry, its measurements will match only the IASI-NG pixels closest to satellite ground track. The distance between the centers of IASI-NG pixels ranges from

When dealing with mismatching measurements, we always assume the worst case of 1 min time lag and 26 km distance between the closest FORUM and IASI-NG soundings. At these temporal and spatial scales, the inconsistency between the spectra measured by the two instruments may be assumed to arise mainly from the different temperature and H

The objective of both SR and CDF is to get the best estimate of the atmospheric and surface state corresponding to the air mass and the ground pixel sounded by FORUM, with the help of the IASI-NG measurement. If IASI-NG is not probing the same air mass or ground pixel as FORUM, a

We estimate the error covariance matrices,

In

We illustrate the results of two main sets of tests. The first set is based on the assumption of perfectly matching FORUM and IASI-NG measurements. In the second set, this assumption is dropped and the matching errors described in Sect.

Another feature common to all the presented test retrievals is the method used to build the error CMs of the a priori estimates of the state vector. The a priori errors of vertical distribution profiles and of surface temperature coincide with the background errors assumed at the UK Met Office when the current IASI measurements are assimilated in their numerical weather prediction (NWP) system. The specific values of a priori errors are shown in the figures presented later. Regarding the a priori error of surface emissivity, this is set equal to 0.1 in the spectral range covered by the measurements included in the inversion and equal to an arbitrarily small value (10

As shown in

To reinforce the conclusions of our analysis, additional test experiments were also carried out at mid-latitudes and tropical latitudes. Although at these latitudes the retrieval of FIR surface emissivity is more challenging due to the increased opacity of the atmosphere, the behavior of the SR and CDF methods is actually very similar to that observed with the polar atmospheres considered here. Thus, the results of those experiments are supplied only as a Supplement.

In the first part of the study, we carried out a set of test retrievals emulating an idealized situation in which both FORUM and IASI-NG measure, with perfect matching, for 900 times, the same area over the Antarctic Plateau, covered by snow with coarse grains. In each occasion of the measurements, surface temperature and the atmospheric state change stochastically with respect to the reference

More in detail, we repeat for

After these 900 runs, we evaluate both the average and the standard deviation of the differences between the synergistic/fused results and the true values used for the generation of synthetic observations. The average differences quantify the product's bias, while the standard deviation of the differences is an (ex post) estimate of the product error which, in principle, should equal the product error estimated (ex ante) with the error CMs (see Eqs.

Case of perfectly matching measurements. Average on the 900 trials of a priori (green), true (blue), CDF (black) and SR (magenta) profiles. Panel

Figure

Case of perfectly matching measurements. Average differences between CDF and true profiles (black), and between SR and true (magenta) profiles. Dashed lines represent the average error of CDF (black) and of SR (magenta) as evaluated from the error CMs of Eqs. (

Case of perfectly matching measurements. Average differences between CDF and SR profiles (red). Dashed lines represent the average error of CDF (black) and of SR (magenta) as evaluated from the error CMs of Eqs. (

Figure

Case of not perfectly matching measurements. Average differences between CDF and true profiles (black), and between SR and true profiles (magenta). Dashed lines represent the average error of CDF (black) and SR (magenta) as evaluated from the error CMs of Eqs. (

In the second part of the study, we proceed with the same approach adopted for the first set of tests; however, we also introduce a space and time mismatch between the measurements of FORUM and IASI-NG. In this case, we reproduce an idealized scenario in which both instruments measure, for 900 times, a limited area of the Antarctic Plateau surface. The matching of the measurements is not perfect: according to the requirements mentioned earlier, FORUM and IASI-NG measurements are acquired within 1 min from each other and sound, randomly, air masses and surface areas located within a horizontal distance of 26 km from each other. In each of the measurements, the sounded atmosphere and the surface temperature change stochastically with respect to the reference

Note that, even if the atmospheres and the surface pixels sounded by the two measurements are different, we still assume as homogeneous the individual fields of view (FOVs) of the two instruments. This assumption is motivated by the fact that so far, at least for the FORUM sensor, the response to a non-uniformly illuminated FOV is not known. Moreover, the simulation of FOV inhomogeneities would require an atmospheric model with a spatial resolution on the order of

In detail, for

Figure

Case of not perfectly matching measurements. Average differences between CDF and SR profiles (solid red lines). Dashed lines represent the average error of CDF (black) and SR (magenta) as evaluated from the error CMs of Eqs. (

Figure

In this work, we characterize the differences between synergistic retrieval (SR) and complete data fusion (CDF) techniques that may be used to generate synergistic products from independent remote-sensing measurements of the same air mass and/or ground pixel.

Our assessment is based on synthetic upwelling spectral radiance measurements of the Far-infrared Outgoing Radiation Understanding and Monitoring (FORUM) and the Infrared Atmospheric Sounding Interferometer – New Generation (IASI-NG) missions that will be operational in a few years from two different polar-orbiting satellites. The analysis is limited to clear-sky conditions that are expected to be the most favorable to exploit the complementarity of the measurements considered.

The presented results rely on solid statistics of 900 simulated observations (and related test retrievals) with perfect matching and of 900 simulated observations with a realistic time and space mismatch. The simulated spectral radiances are based on a winter atmospheric scenario over the Antarctic Plateau. The extremely dry atmosphere makes the far-infrared (FIR) region (100–620 cm

For perfectly matching measurements, we find that the differences between the SR and CDF solutions are as small as

As a conclusion, we confirm that SR and CDF provide equivalent results when applied to FORUM and IASI-NG complementary measurements. The final choice of which of the two approaches should be preferred for routine operations will depend on the actual architecture of the ground processors of the two missions. The SR approach requires the FORUM ground processor to also access the calibrated spectral radiances measured by IASI-NG with their error CMs; thus it implies a quite relevant throughput of data to be exchanged between the ground processors of the two missions. Conversely, the CDF technique is easily applied a posteriori using state vectors and diagnostic data derived from independent inversions of the individual measurements of the two missions. Despite its simplicity, a drawback of the latter technique originates from the fact that the two combined state vectors, being retrieved by two different mission processors (likely using different forward models), will be affected by different model error components. Some of these components may be correlated; thus specific studies may be required to establish a reliable total error estimate of the fused state vector.

The used reference atmospheres, the surface states and their variability, as well as the mismatch error variance data and the noise error covariance matrices associated with the FORUM and IASI-NG measurements can be freely downloaded from Zenodo at

The supplement related to this article is available online at:

MR implemented the (synergistic) inversion code and carried out the test retrievals presented. CT implemented the CDF algorithm in a computer program and computed the CDF solution for all the presented test cases. SC developed the theoretical background for the CDF. MR, CT and SC equally contributed to the design of the test scenarios and to the interpretation of the results, as well as to writing and revising the text of the paper. CB computed the atmospheric variability from ERA5 data and contributed to writing the paper. UC was the principal investigator of the AURORA H2020 project and the task coordinator of the OT4CLIMA project; both projects significantly supported the development of the CDF method. LP is the principal investigator of the FORUM mission and of the FORUM science project that supported the presented studies. All the authors have revised and checked the text of the paper.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The development of the CDF method was supported by the AURORA and OT4CLIMA projects.
The AURORA project (

This research has been supported by the Horizon 2020 (AURORA (grant no. 687428)), the Agenzia Spaziale Italiana (grant no. 2019-20-HH.0) and the Ministero dell'Università e della Ricerca (grant no. OT4CLIMA).

This paper was edited by Martin Riese and reviewed by Joern Ungermann and one anonymous referee.