Satellite passive microwave observations around the 183.311 GHz water-vapour line can provide accurate monitoring of water-vapour profiles with good temporal and spatial sampling for operational numerical weather prediction (NWP). They represent a good complement to infrared sounding measurements, which are limited to cloud-free regions. Over the ocean, passive microwave measurements are now routinely assimilated in NWP systems and they provide interesting atmospheric profiling capabilities. Over land, however, they are not fully exploited. Firstly, land-surface microwave emissivities are usually much higher than ocean emissivities, with the consequence that the surface contribution to the measured signal is much larger. Secondly, the land-surface emissivities have a higher spatial heterogeneity than their oceanic counterpart. In addition, they are much more difficult to model, being dependent upon a large number of variables (e.g. soil moisture, vegetation and snow properties). However, efforts are under way to use, invert and assimilate microwave radiances over land (Aires et al., 2001; Karbou et al., 2005), thanks essentially to the development of land-surface emissivity databases, directly calculated from satellite observations (Prigent et al., 1997, 2006; Aires et al., 2011a).
The objective of the French–Indian Megha-Tropiques (MT) mission is to study the water cycle in the intertropical region and to evaluate its influence on the energy budget, with a specific focus on the analysis of the life cycle of tropical convection. MT is a mini-satellite that was successfully launched on 12 October 2011 using the Indian Polar Satellite Launch Vehicle. The duration of the mission is three years. MT has been placed in a circular orbit at 800 km with a 20° inclination, covering the tropical belt between 23°N and 23°S. One of the main features of the MT mission is its time sampling of the Tropics, with a 20° inclination of its orbit that allows some locations to be observed up to five times a day.* MT flies three instruments mounted on an Indian platform. They observe simultaneously three related components of the atmospheric water cycle, as detailed below:
Sondeur Atmosphérique du Profil d'Humidité Intertropicale par Radiométrie (SAPHIR), a cross-track microwave sounder developed by the Centre National d'Etude Spatiales (CNES) to estimate water-vapour atmospheric profiles;
Microwave Analysis and Detection of Rain and Atmospheric Systems (MADRAS), a conical microwave radiometer developed by CNES and the Indian Space Research Organization (ISRO)) to measure precipitation and cloud characteristics;
Scanner for Radiation Budget (ScaRaB), a cross-track broad-band optical radiometer developed by CNES and the Laboratoire de Météorologie Dynamique (LMD) for the estimation of radiation fluxes at the top of the atmosphere.
A processing chain for satellite microwave observations is developed in this study for the retrieval of the atmospheric humidity, along with some surface products. This algorithm operates over both ocean and land, for clear and cloudy/non-precipitating situations. The theoretical assessment of the SAPHIR/MADRAS retrievals will be presented in this article, but since no real observations are available yet the algorithm will be tested on two other platforms that include a water-vapour microwave sounder: the AQUA mission with very similar instruments (the Advanced Microwave Scanning Radiometer for the Earth Observing System (AMSR-E) and Humidity Sounder for Brazil (HSB), though HSB had a short lifetime), and the METeorological OPerational (MetOp) platform with different companion instruments (the Advanced Microwave Sounding Unit (AMSU-A) and the Microwave Humidity Sounder (MHS)), on which a near-real-time scheme is tested. The results will be presented for the tropical region (±30° in latitude) that is covered by the Megha-Tropiques mission, although the algorithms are very general and can be applied globally.
Section 2 introduces the microwave instruments from the three satellite platforms considered in this study and provides a preliminary assessment of their sounding capabilities based on their main characteristics. Section 3 presents the various datasets used in this work. The retrieval scheme is described in section 4 and the theoretical results are discussed in section 5 and compared with the results from the AQUA and MetOp platforms. Conclusions are drawn in section 6.
2. The microwave instruments
The water-vapour sounders from the three satellite missions are described, along with the other microwave radiometers available on the same platforms. A preliminary analysis of the sounding capabilities of the instruments is conducted, based on the calculation of the weighting function and the Jacobians and on considerations on the instrument noise. Table 1 summarizes the main characteristics of the instruments.
Table 1. Instrument characteristics for the three satellite missions considered in this study: Megha-Tropiques, AQUA and MetOp.
10 km at nadir
13.5 km at nadir
16 km at nadir
Frequencies in GHz (left), bandwidth in MHz (centre) & noise in K (right)
40×67 km (lower freq) to 6×10 km (higher freq)
60 to 5 km
48 km at nadir
in GHz (left)
& noise in K
57.290344 (= FLO)
SAPHIR is a passive microwave sounder with six channels around the 183.31 GHz absorbing line at ±0.2, ±1.1, ±2.8, ±4.2, ±6.8 and ±11 GHz (Table 1). Compared with the currently flying water-vapour microwave instruments, it has more sounding channels for a theoretically better vertical description of the water-vapour profile. Note that it does not include window channels around 90 and 150 GHz, such as the Advanced Microwave Sounding Unit-B (AMSU-B), but these frequencies are available on the MADRAS companion instrument described below. SAPHIR has a cross-track viewing geometry, with 130 pixels per scan line from nadir to ±42.96°. This means that the pixel size of 10 km at nadir increases with the scanning angle. It can be noted that SAPHIR has larger instrument noise (NEΔT) than MHS, but it is expected that the additional channels in SAPHIR will allow for better description of the vertical distribution of water vapour.
MADRAS is a passive microwave imager that measures the radiation at nine frequency bands: 18.7, 23.8, 36.5, 89 and 157 GHz at vertical and horizontal polarizations, except for 23.8, which is vertical-only. It has a conical viewing geometry: the incidence angle of the measure has a constant angle of 53.5° (i.e. about 45° on-board angle), which makes it easier to exploit the polarization information. The size of the pixels is constant but the difference in the scan geometry makes the merging of the data with the cross-track measurements from SAPHIR more complex. The scan coverage is ±65° and the swath is about 1700 km wide.
It is expected that the L1B1 products from the Megha-Tropiques ground segment will provide collocated SAPHIR and MADRAS observations. The SAPHIR measurements will be projected on to the 89 GHz MADRAS pixels (10 km cross-track × 16.8 km along-track resolution).
The passive microwave measurements from the AQUA platform are composed of collocated observations from two radiometers: HSB (only operated from May 2002–February 2003) and AMSR-E. The HSB cross-track sounder is a nearly identical copy of AMSU-B with four moisture-sounding channels (instead of five for AMSU-B). Three out of four are located around the strong water-vapour absorption line at 183.31 GHz (±1.0, ±3.0 and ±7.0) and the fourth channel is a window channel at 150 GHz (Lambrigtsen and Calheiros, 2003). During one scan, HSB samples 90 scenes of 1.1° between ±49.5°, with a footprint size of 13.5 km at nadir. AMSR-E is a dual-polarized radiometer operating at frequencies of 6.9, 10.7, 18.7, 23.8, 36.5 and 89 GHz designed for the retrieval of surface and atmospheric variables including water vapour, cloud liquid water, precipitation, sea-surface temperature, near-surface wind speed and soil moisture. The instrument has a conically scanning antenna that provides multichannel observations at a constant incidence angle of 55° across a 1445 km swath. The spatial resolution of AMSR-E varies from approximately 60 km at 6.9 GHz to 5 km at 89 GHz (Kawanishi et al., 2003).
Launched on 19 October 2006, MetOp is the first European polar-orbiting satellite dedicated to operational meteorology. MetOp carries two passive microwave sounders, MHS and AMSU-A (1 and 2) for temperature sounding.
Similar to the historical intruments on board the Defense Meteorological Satellite Program (DMSP) and National Oceanic and Atmospheric Agency (NOAA) orbiters, MHS provides measurements in the 183.31 GHz water-vapour absorption line at ±1, ±3 and ±7 GHz, plus at two window channels at 89 and 150 GHz, which enable deeper penetration through the atmosphere down to the Earth's surface. Each swath is made up of 90 contiguous individual pixels and scanned every 2.67 s. MHS pixels at nadir have a diameter of approximately 16 km.
AMSU-A is dedicated to the retrieval of atmospheric temperature profiles, with 12 sounding channels between 50 and 60 GHz O2 bands and three other channels at 23.8, 31.4 and 89 GHz. It is a cross-track scanning radiometer, with ±48.3° from nadir and a total of 30 Earth fields of view of 3.3° per scan line, providing a nominal spatial resolution of 48 km at nadir. The swath is approximately 2000 km and the instrument realizes one scan in 8 s. The MHS and AMSU scans are synchronized. Each AMSU-A pixel is covered by 3 × 3 MHS pixels; this facilitates their synergetic use (Aires et al., 2011c).
2.4. Preliminary evaluation of the sounding capabilities
The weighting function of an instrument channel is defined as
where ν is the frequency, t is the transmission to the top of the atmosphere (TOA) and P is the pressure. The integration is performed on the vertical, from the bottom to the upper part of the atmosphere. Analyzing this quantity is a standard way to monitor the sounding characteristics of an instrument. Figure 1 represents the water-vapour weighting functions at various frequencies and for different instruments, i.e. SAPHIR (left), HSB (middle) and MHS (right). These results are calculated with a standard tropical atmosphere. The water-vapour weighting function of a particular channel, at a given pressure/altitude, indicates the change of the measured brightness temperature at the TOA for a perturbation of the water vapour at that pressure/altitude. Values are here expressed as change of relative humidity and normalized to one km of atmosphere (K km−1 per unit change of relative humidity). The further the channel from the line centre, the lower the atmospheric layer it sounds. SAPHIR has more channels than the other instruments close to the 183.311 GHz line and the bandwidths of these channels are significantly narrower than for the other instruments. The channel at ±11 GHz from the line centre sees closer to the surface, but still with a limited contribution from the surface itself. As a consequence, it is expected that the lower layer of the atmosphere will not be well described by such an instrument. The bandwidths of the channels have two implications: on one hand, the narrower the bandwidth the narrower the weighting function (up to a certain extent) and the higher the vertical resolution of the profile; on the other hand, the instrument noise is inversely proportional to the square root of the channel bandwidth, with direct consequences for the retrieval accuracy. For drier atmospheres, the weighting function would peak at lower altitudes (less opacity in the atmosphere). Note that there are large overlaps of the weighting functions, meaning that the information from the different channels will not be independent. This can be illustrated by computing the number of principal components in three datasets including observations from the three sounders considered in this study: HSB, MHS and SAPHIR. When performing such principal-component analysis, it can be seen that three (resp. four) principal components represent more than 99% (resp. 99.5%) of the total variability of the satellite observation datasets. These two numbers mean that there are four independent pieces of information out of the six SAPHIR measurements (results are identical for HSB and MHS instruments).
An alternative way to analyze the sounding capacities of an instrument is given by the Jacobians, i.e. the first derivative of the Brightness Temperature (TB) measured for each channel with respect to the geophysical variable of interest (the relative humidity, RH, in this case): ∂TB/∂RH. In practice, since the analytical Jacobians are not available for water vapour when expressed in terms of relative humidity, we estimate them using the ‘input perturbation’ method, in which the RH is perturbed by 10% independently for each atmospheric layer and the resulting perturbations in TB are calculated. Jacobians are a direct measure of the information content of the observations as used in the atmospheric inversion. The Jacobians are related to the weighting function, but integrated on the atmospheric layers on which the inversion is performed. This means that the Jacobian is dependent on the discretization of the atmosphere that is chosen, not the weighting function. Another difference is that the Jacobian can be computed for each atmospheric variable, where the weighting function is traditionally computed for the total transmission, which integrates the contribution of all the geophysical variables at one time (this of course represents less information). Figure 1 (bottom) represents such Jacobians computed using the RTTOV radiative transfer model (Saunders et al., 1999). This code will be used in this study to build the simulated satellite observation datasets. These Jacobians can be interpreted in terms of profile retrieval, compared with the instrument noise of the radiometers: when a first guess in relative humidity RH is close enough to the real profile, the perturbation of TB for each channel is given by the vector ΔTB = (∂TB/∂RH) × ΔRH. This is to be compared with the instrument noise of the radiometer. These computations have been performed using a standard tropical situation over land (with an emissivity equal to 0.9, shown as a dashed line) and over ocean (with an emissivity equal to 0.6, shown as a continuous line). If no continuous line can be seen, it means that the land case is identical to the ocean case. The weighting functions are not sensitive to the surface type (i.e. to the emissivity), in contrast to the Jacobians of the channels sensitive to the surface: it can be seen that for 150 GHz HSB and 89 and 157 GHz MHS results the Jacobians over land surfaces are reduced compared with those over oceanic surfaces. Since SAPHIR does not possess a channel truly sensitive at the surface, there is no impact (but an impact would be observed on the surface-sensitive channels of MADRAS, not shown). Examination of the Jacobians also shows that the SAPHIR instrument would likely provide more information on the upper part of the atmosphere, due to its channel being located closer to the line centre. However, the large radiometric uncertainty of this channel might limit its potential. On the other hand, limited information will be derived from SAPHIR alone about the lower atmospheric layers. As a consequence, SAPHIR observations will have to be combined with MADRAS measurements to estimate water-vapour content in the lower part of the atmosphere. This will be confirmed by the theoretical retrieval statistics in section 5.
3. Datasets and radiative transfer code
In this section, the various datasets used in this study are presented, along with the radiative transfer (RT) model chosen to train the calibration and the inversion algorithms.
3.1. ECMWF operational analyses
A dataset of surface and atmospheric situations is developed in order to allow RT simulations of the satellite observations. We use the atmospheric profiles and surface properties from the six-hourly operational global analyses (Uppala et al., 2005) from the Integrated Forecasting System of the European Centre for Medium Range Forecasting (ECMWF) provided on a regular 1.125° grid (hereafter referred to as the ANA database). In order to run accurate RT simulations, the following information is kept: the temperature, water vapour and ozone profiles on 21 pressure levels ranging from 1000 to 1 hPa, the cloud profiles (cloud cover, liquid and ice water) and surface properties (10 m horizontal wind, 2 m pressure and temperature, surface skin temperature, convective and large-scale precipitation and total cloud cover).
In the following, only non-precipitating situations are considered to limit possible biases in the simulation due to the scattering of the upwelling radiation by droplets: a threshold of 0.1 mm in the precipitation fields is used to detect precipitation. Scenes above 1000 m are avoided to minimize topographic effects and pixels closer than 100 km from the coast are discarded to reduce inconsistencies between the different frequency channels with different fields of view.
In order that the ECMWF data and the real satellite observations coincide, the analysis fields are interpolated using a bilinear spatial interpolation scheme. For each satellite observation, only the neighbours in the ECMWF grid with the same surface type (ocean or land) are considered to calculate the bilinear interpolation. The coincidence is accepted only if the time difference is less than one and a half hours.
3.2. Global land-surface microwave emissivities
For atmospheric profiling, surface-sensitive microwave observations have so far essentially been used over ocean. Over land, the surface emissivity is difficult to estimate: it is usually high, limiting the contrast with the atmospheric contribution, very variable in space and complex to model.
A parametrization of the land-surface microwave emissivities has recently been developed (Prigent et al., 2008). For each location and time of the year, it provides realistic first-guess estimates of the land-surface microwave emissivities from 19–100 GHz for all scanning conditions, incidence angles and polarizations. It is anchored to climatological monthly mean maps of the emissivities at 19, 37 and 85 GHz, calculated from SSM/I (Prigent et al., 1997; 2006). It was originally designed for frequencies between 19 and 85 GHz but tests proved it beneficial down to 5 GHz and up to 190 GHz (Aires et al., 2011a). The nominal spatial resolution of the emissivity estimates is 0.25°×0.25°. The results have been thoroughly evaluated and the root-mean-square (RMS) errors are usually within 0.02, with the noticeable exception of snow-covered regions, where the high spatial and temporal variability of the emissivity signatures is difficult to capture. A tool based on this parametrization has been developed for the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) NWP Satellite Application Facility (SAF) (Aires et al., 2011a). This tool is interfaced with the Radiative Transfer for TIROS Operational Vertical Sounder (RTTOV) radiative transfer code.
3.3. Satellite observation datasets
The evaluation of the retrieval method will be based on existing observations from AMSR-E/HSB and AMSU-A/MHS. In addition, to perform accurate retrievals, the observations have to be calibrated and we adopt here an innovative calibration procedure based on a learning database. Datasets of collocated AMSR-E/HSB and AMSU-A/MHS are created and they are large enough to be used for both calibration and evaluation, the learning dataset for calibration accounting for less than 5% of the total database.
The collocation procedure between AMSR-E and HSB footprints is described in Aires et al. (2010). It assumes that for both sensors the footprints are co-registered. Observations for AMSR-E are extracted from the level 2A data, which provide a resampling of the nominal resolution observations into coarser resolution fields of view. In the present study, the chosen resolution is 21 km. The level 1B dataset provides the calibrated and geolocated HSB observations, along with scene information. The collocation method averages all the HSB scenes that fall into each AMSR-E elliptical footprint, accepting a maximum time difference of 70 s and assuming that the information for each HSB scene is concentrated at its centre. The final AQUA satellite database is composed of two full months of observations (September 2002 and January 2003) containing the 16 collocated brightness temperatures and the scene information (land fraction) from the MHS dataset.
The collocation procedure between AMSU-A and MHS is much simpler, thanks to the similarity in the scanning mechanisms of both instruments (section 2.3). The final MetOp satellite database is composed of two full months of observations (July 2007 and January 2008) containing the 20 collocated brightness temperatures.
3.4. The RTTOV radiative transfer
Our retrieval scheme is based on a radiative transfer model. The model that is chosen is really a part of the retrieval scheme, which is used directly in the retrieval algorithm in a iterative inversion; it is used to create the learning datasets (for inversion and calibration) in statistical algorithms. The RTTOV-9.3 radiative transfer model can simulate the microwave instrument on board Megha-Tropiques, AQUA and MetOp platforms. This model, originally developed at ECMWF (Eyre, 1991) and now supported by the EUMETSAT NWP-SAF (Saunders et al., 1999; Matricardi et al., 2001), allows for rapid simulations of radiances for satellite infrared and microwave radiometers for a given atmospheric state vector.
In order to compare real satellite observations and RT simulations, RTTOV is run using all the analysis information (section 3.1) together with the surface emissivity database over land (section 3.2), while over ocean the emissivities are computed by the FASTEM-3 (Deblonde and English, 2001) surface emissivity model. To keep the spatial variability of the land-surface emissivities, the 1.125° grid point ANA database is interpolated for each pixel of the 0.25° emissivity database. Based on these inputs, RTTOV is used to perform simulations of the brightness temperatures (TB) for each microwave instrument. For comparison purposes and to build up the calibration learning database, the RT is calculated for each real observation in coincidence with the ANA database and the surface emissivity dataset.
For convenient and efficient use in an interoperable platform, an RTTOV interface has been written. The interface library is written in c++ and can call the RTTOV code directly. This library can be linked to any fortran or c program.
4. Retrieval scheme
The retrieval scheme presented in this study is composed of a classification procedure to identify the type of scene being treated and two processing steps. The first processing step uses a statistical neural network (NN) model to calibrate the satellite observations. The second step is based on another NN that performs the actual retrieval, using the calibrated datasets (Figure 2). The choice for this approach is described in the following section.
4.1. General strategy
In order to train the NN for remote sensing purpose, two strategies can be used, Firstly, the training can be done using a learning database composed of real satellite observations and collocated water-vapour profiles from, for example, the ECMWF operational analysis. This type of scheme is said to be an ‘empirical’ inversion because no RT model is used to solve the inverse problem. Secondly, the training can also be done using a learning database composed of the same water-vapour profiles from the ECMWF operational analysis with its simulated satellite observation, provided by a RT model, instead of real observations. This type of inversion is said to be a ‘physical’ inversion because a RT model is being used. The first approach involves only one transformation of the real observations: it mixes the calibration and the retrieval in a unique procedure. The second approach explicitly involves two transformations: The calibration of the data and the actual retrieval. The calibration of the real satellite observations is necessary because systematic differences exist between RT simulations (used in the training of the retrieval scheme) and the real observations. Both methods could lead to similar results, but the second one is preferred here (Aires et al., 2010). In this approach, there is no introduction of coincidence or resolution errors, in contrast to the empirical approach, which needs to put the ECMWF profiles and the satellite observations in coincidence. Note that the empirical approach could not be used, since the MT data were not available at the time of this development.
The choice of the NN for the retrieval of water vapour has been made for various reasons. One of them is that weighting functions tend to sound higher in the atmosphere when the water-vapour content increases. This means that the dependences between the satellite observations and the water-vapour content at a given altitude vary with the actual atmospheric situation. The NN is a nonlinear method, meaning that its output/input relationships are state-dependent. The training will teach the NN to adapt its retrieval to the water-vapour content.
4.2. A priori classification
The retrieval chain is based on four distinct configurations: (1) cloud-free over ocean scenes, CF/O; (2) cloud-free over land scenes, CF/L; (3) cloudy over ocean scenes, CL/O; (4) cloudy over land scenes, CL/L. Only non-precipitation scenes are considered. This means that the chain needs two classification processes: one to determine whether a situation is cloudy or clear and one to eliminate precipitating scenes.
Three options have been studied to identify clear and cloudy scenes in our retrieval scheme: (1) using the cloud cover from the ECMWF operational analysis as an a priori flag, (2) using an independent classifier derived from visible/infrared (VIS/IR) observations on board geostationary satellites and (3) developing a dedicated cloud classifier based on the microwave observations. The third option has been investigated in Aires et al.(2011b): a microwave cloud classifier has been designed to find whether a scene is clear or has low, middle or high cloud cover. The training for this statistical method has been performed using a Meteosat Third Generation-Spinning Enhanced Visible and Infrared Imager (MSG-Seviri) cloud classification. In the present study, the cloud cover from the ECMWF operational analysis has been chosen, although we are aware of its limitations. The use of the microwave dedicated cloud classifier will be considered in the future. Each atmospheric situation is classified as being clear (cloud cover below 2%) or cloudy (cloud cover over 2%). No partial coverage is considered.
Various options are also considered for the precipitation flags: (1) using the precipitation estimates of the ECMWF operational analysis (i.e., short-range prediction); (2) using microwave precipitation flags from the literature such as Alishouse et al.(1990), Ferraro et al.(1996), Weng et al.(2003) or Hong and Heygster (2005); (3) using the precipitation retrieved by other instruments on board the same satellite platform (such as the Brain algorithm from MADRAS for the Megha-Tropiques mission). Preliminary tests showed that the quality of the ECMWF a priori precipitation analysis is sufficient for this purpose. In the following, the scenes will be eliminated if the ECMWF precipitation estimate (for both large-scale and convective precipitation) is higher than 0.1 mm.
4.3. NN calibration scheme
We will only comment briefly on this step, since this calibration methodology has been described in Aires et al.(2010). The procedure has been developed for AQUA (AMSR-E/HSB) and MetOp (AMSU-A/MHS) data. A similar methodology can be applied to the Megha-Tropiques instruments, when enough observations become available.
4.3.1. Calibration model
Neural networks (NN) have been widely used to perform nonlinear transformations from one space to another by following some particular statistical constraints. In this calibration procedure, a multi-layered perceptron (MLP) model (Rumelhart et al., 1986; Hornik et al., 1989) is used as a nonlinear mapping model. It is composed of three layers of neurons: the first layer codes the inputs (i.e. observed brightness temperatures), the third layer codes the outputs (i.e. the calibrated brightness temperatures) and the second layer, called the hidden layer, is used to increase the complexity of the NN model. The higher the number of neurons in this hidden layer, the more complex the NN becomes. The NN is trained to reproduce the behaviour described by a database of samples, i.e. the learning dataset composed of the real observations TB and their associated calibrated TBs. The real AMSRE/HSB (respectively AMSU-A/MHS) observations and the coincident TB RTTOV simulations presented in section 3 constitute the learning dataset here. The NN is designed to ‘project’ or calibrate the actual real observations into the space of the RTTOV simulations.
Four NNs have been derived corresponding to the four cases previously described: CF/O; CF/L; CL/O; CL/L. Each one of these four learning datasets includes about 100 000 situations, which is largely sufficient to train the four respective NNs. Each one of these calibration cases will be associated with a different retrieval model (see section 4.4). The goal of the calibration procedure is to reduce the RT errors (e.g. bias, range of variability, structure, saturation) but it should be kept in mind that other sources of discrepancies are still present in the learning database and the calibration procedure cannot suppress them all by building a perfect bridge between real and simulated satellite TB.
4.3.2. Comparison of real and simulated satellite observations
RMS error differences between simulated TB and the initial real observations and the calibrated observations are represented in Figure 3 for the four configurations (CF/O, CF/L, CL/O and CL/L) and for the AQUA and MetOp platforms. All the situations in which the differences between the simulated and calibrated TB are larger than three standard deviations of these TB differences are filtered out (corresponding to less than 0.5% of the situations). Most of these situations correspond to precipitating scenes, missed by the precipitation filter. The impact of the calibration can be directly measured by comparing the continuous (calibrated) and dashed (non-calibrated) lines. The calibration often reduces the discrepancies between the simulated and observed satellite measurements by a few degrees. This is true for land scenes, for both cloud-free and cloudy situations, and for every channel of all instruments. For ocean scenes the impact is also very interesting for cloud-free and cloudy situations, except for lower frequencies (≤ 10 GHz) in clear scenes, where the impact is close to zero. The calibration procedure never degrades the statistics. Note that a large part of the discrepancy between the simulated and the initial observations is likely due to the RT simulations and not to instrument calibration problems. The simulation errors can arise from errors in the input parameters (e.g. ECMWF analysis, land-surface emissivities), as well as from deficiencies of the RT code. For instance, initial errors at low AMSR-E frequencies (at 6 and 10 GHz, especially in H polarization) over land are likely due to extrapolation errors in the emissivities (the land-surface emissivities are derived from satellite observations between 19 and 85 GHz). Over the ocean, the errors with AMSR-E in H polarization before and after calibration could be related to limitations of the radiative transfer model in its simulation of sea-surface emissivities that are particularly sensitive to H polarization.
Other statistical results were analyzed (not shown) to check the quality of the calibration: (1) the distribution of the errors is narrower when using the calibrated data, (2) the correlation is only slightly increased when the real observations are calibrated, meaning that the calibration transformation is statistically close to linear for most of the samples, and (3) the scatter plots of differences showed that the quality of the calibration procedure is satisfactory for all TB ranges. The angle dependence of the calibration has been checked and is very limited (not shown): the same calibration procedure is adopted regardless of the scanning angle.
4.4. NN retrieval scheme
NN techniques have been very successful in developing computationally efficient algorithms for remote sensing applications. For example, a NN algorithm is applied to retrieve simultaneously the atmospheric temperature and humidity atmospheric profiles from 1000–1 hPa over the sea using AMSU-A and -B observations (Aires etal., 2007). In this section, such a NN retrieval algorithm is used in association with the NN calibration scheme.
4.4.1. NN model
The retrieval scheme is composed of a MLP neural network, similar to the one in section 4.3. The NN model is composed of three layers: the first layer codes the inputs of the retrieval scheme (i.e. satellite observations and a priori information), the third layer represents the outputs (i.e. the retrieved products) and again the hidden layer is used to control the complexity of the model. As in section 4.3, different retrievals need to be considered for the four configurations (CF/O, CF/L, CL/O and CL/L) and for the Megha-Tropiques, AQUA and MetOp platforms.
The inputs of the NN models are as follows:
the calibrated TB in the RT simulation space from Megha-Tropiques, AQUA and MetOp microwave instruments (section 3.3);
a priori information on the atmospheric temperature profile given by the ECMWF operational analysis (section 3.1);
a priori surface emissivities from a microwave emissivity climatology (see section 3.2) and surface skin temperature from the ECMWF analysis, for land surfaces.
No a priori information on the water-vapour (WV) profile is used directly in the retrieval, in order better to assess the information content of the satellite observations independently of other related information. Nevertheless, the ECMWF operational analysis is used to provide some a priori information on the water vapour, by classifying the situation according to the total column water vapour (TCWV): TCWV ≤ 20 kg m−2, 20 kg m−2 < TCWV ≤ 35 kg m−2 or 35 kg m−2 > TCWV. This limits the reduction of the dynamical range of the retrieval compared with the learning database, which is often observed with statistical mapping. A dedicated NN is used for each of these categories and for each of the NNs considered earlier for the various retrieval configurations. In addition, the retrievals are trained for different scanning angles (5, 15, 25, 35, 45 and 55°): the actual retrieval of real data at a particular scanning angle will linearly interpolate the result of the two NNs with the closest scanning angles. The total number of NNs is composed of four configurations (clear/cloudy and land/ocean) × three platforms × three humidity ranges × six incidence angles, for a total of 216 NNs.
The intermediate outputs of the retrieval scheme are the 43 water-vapour contents of the atmospheric profile from the surface to the top of the atmosphere and the TCWV, in addition to the surface temperature and emissivities over land and to the surface wind speed over ocean. Note that the surface skin temperature is not retrieved over ocean, as Megha-Tropiques and MetOp do not provide low-frequency observations sensitive to this parameter. The architecture of the NNs for the Megha-Tropiques data consists of 15+43+15+1=74 (resp. 15+43=58) neurons in the first layer, 50 neurons in the hidden layer and 43+1+15+1=60 (resp. 43+1+1=45) for the land (resp. ocean) retrieval. For practical reasons, the WV retrieval is performed on the 43 atmospheric layers defined by RTTOV (in particular in order to facilitate the a posteriori test described in the following paragraph). However, MADRAS/SAPHIR, AMSR-E/HSB or AMSU-A/MHS instruments cannot provide such high vertical resolution (see section 2.4) and the final retrieval of our inversion scheme is defined on six thicker layers delimited by the surface: 920, 750, 560, 400 and 250 hPa and the top of the atmosphere. The mapping from 43 to 6 layers is an integration of the water-vapour content of each of the finer layers into the thicker layer. The number and the limits of these thicker layers have been optimized to minimize the retrieval uncertainty: all possible combinations of the 43 original layers into 6 thicker layers have been considered, the retrieval results have been estimated for each one and finally the six coarse vertical layers associated with the lowest uncertainties have been selected. In the retrieval statistics, all the results will be presented in these six layers.
Following the retrieval, an a posteriori test is performed. It uses the retrieval results and the ECMWF a priori information as inputs to the RTTOV model. These simulated TB are compared with the observations, and when the differences are larger than a fixed threshold (corresponding to three standard deviations of a statistic previously performed) the results are discarded. This is a standard procedure in operational retrieval schemes.
4.4.2. Learning and testing datasets
One year of ECMWF operational analysis (section 3.1) is used to build the learning dataset. Using a RT model in all of these surface and atmospheric situations would be too demanding computationally and also inefficient, because there would be redundancies in this dataset. Instead, the full year's worth of data are reduced using a uniform sampling procedure. For the RT simulations, the cloud flag described in section 4.1 is used and all the precipitation scenes are suppressed. The RT simulations are performed for MADRAS/SAPHIR, AMSR-E/HSB and AMSU-A/MHS instruments.
The resulting dataset is divided into a learning dataset (representing 80% of the situations) and a generalization dataset (corresponding to the remaining 20%). Results presented in following section will use the generalization dataset. The training is performed using a back-propagation algorithm (Rumelhart et al., 1986).
5. Theoretical evaluation
In this section, the information content of the microwave instruments on board the Megha-Tropiques, AQUA and MetOp platforms is evaluated using two approaches: firstly measuring directly the performance of the retrieval scheme on simulated observations and secondly using the classical information-content analysis (Rodgers et al., 1990). The first approach provides uncertainty estimates that are generally too optimistic (reasons will be provided in the next section); the information-content analysis is also a simplification of the real world but it is generally used as a tool to compare instrument configurations. The advantage of performing these theoretical evaluations is that the quality of the Megha-Tropiques instruments, real observations not yet being available, can be compared relatively with that of AQUA and MetOp instruments. In a companion article (Bernardo etal., 2012, hereafter Paper II), the same retrieval scheme will be evaluated using real observations from AQUA and MetOp and this will provide a good assessment of the performance that is to be expected from the Megha-Tropiques instruments.
5.1. Theoretical retrieval uncertainties using simulated observations
The full NN retrieval scheme has been applied to the testing dataset (not to the learning dataset), for the three platforms (Megha-Tropiques, AQUA and MetOp), including the four configurations (cloud-free/cloudy situations over land/ocean). Figure 4 represents the RMS errors as % of relative humidity for the retrieval of the profile over the six atmospheric layers. There is no bias for any configuration and any platforms (not shown). As expected, land retrievals are more difficult than those over the ocean, especially for the lower atmospheric layers where the error is increased by a factor of two (retrieval errors remain identical for layers higher than 500 hPa). For all cases, results are similar under clear and cloudy conditions. MetOp retrievals are more precise than AQUA and Megha-Tropiques ones. This can be explained by the lower instrument noise of MHS channels compared with HSB or SAPHIR (Table 1). Megha-Tropiques and AQUA results are similar. They both include a water-vapour sounding instrument and an imager with window channels. The improvement related to additional channels for the SAPHIR instrument is balanced by an instrument noise, which is higher than for HSB. This is in agreement with the results in Figure 5(b).
It should be noted here that theoretical retrieval errors underestimate the real retrieval uncertainties because not all possible sources of uncertainties that could appear in real-world conditions are considered.
No coincidence errors between the two considered instruments or with the a priori information from the ECMWF operational analysis are introduced.
No RT errors have been used, as this is a difficult quantity to measure.
The Gaussian nature of the a priori information (such as the temperature profile from the ECMWF analysis) is a simplification.
The statistics are performed on a diverse and large dataset, but these atmospheric situations come from the ECMWF operational analysis, meaning that the profiles are smoother than real profiles or can be biased if the analysis is not correct.
Furthermore, the a priori is considered, in this study, to have the same statistics for all situations, which is a simplification. For example, the apriori uncertainty of the water vapour should be different for dry and humid situations.
Overall, the dataset used to make these statistics is completely coherent with the dataset used to train the NN; this is less true, of course, when using real-world observations.
These theoretical uncertainty assessments are representative of perfect inversion conditions, but any additional source of uncertainty will degrade them toward realistic estimates. In particular, the impact of the calibration errors is expected to be very significant. The important point about these theoretical uncertainty estimates is that it is possible to compare the retrieval capacities of the Megha-Tropiques instruments with existing instruments. Since the uncertainty estimations performed on real observations can be obtained for MetOp and AQUA instruments (see Paper II), it will become possible to extrapolate the real retrieval uncertainties that can be expected during operational use of the Megha-Tropiques instruments. Based on these statistics, it is expected that Megha-Tropiques retrievals will have similar statistics to AQUA retrievals.
Table 2 provides the theoretical RMS errors of the retrievals for the TCWV over ocean and land, the surface skin temperature and microwave emissivity at 23.8 GHz over the continents (19 GHz would be more interesting, since this is a window channel, but it is not present in the AMSU-A instrument) and the wind speed over the ocean. These statistics are estimated for the three platforms. They are compared, when possible, with the uncertainties of the first guess used as inputs of the retrieval scheme and specified in the development of the NN. Over ocean, the TCWV is retrieved with 1.6–1.7 kg m−2 for both clear and cloudy cases and the three platforms have a similar accuracy. For land surfaces, the AQUA retrievals are slightly better than the Megha-Tropiques and MetOp retrievals with similar characteristics.
Table 2. Theoretical retrieval errors for Megha-Tropiques, AQUA and MetOp platforms, along with the specified first-guess errors over ocean and land surfaces for TCWV, oceanic wind speed, surface temperature (Ts) and emissivity at 23.8V GHz.
Wind speed (m s−1)
Emis 23.8V GHz
For all cases, the retrieval errors are better than the first-guess errors, which means that the retrieval did bring additional useful information. The wind speed over the ocean is more precise for AQUA and Megha-Tropiques than when using MetOp observations, as expected, because of the higher number of channels sensitive to surface and lower frequencies in these two platforms (see Table 1). The surface temperature is retrieved with an uncertainty lower than 2 K, which is a decrease of the uncertainty of the a priori by 50%. The accuracy of the retrieval of the emissivities is related to the retrieval of the surface temperature (Ts) (English, 2008). It ranges from 0.007–0.009, which is a very good improvement of the a priori that had uncertainties equal to 0.025. It will be seen in Paper II that, beyond this global theoretical uncertainty statistic, the spatial structure of the emissivities and surface temperature is preserved in the retrievals.
5.2. Information content analysis
In the classical information-content analysis (Rodgers et al., 1990), the RT is linearized around a first-guess solution f0:
where f is the geophysical variable to be retrieved (atmospheric WV profile in our case), f0 is a first guess, TBε is the brightness temperature observed by the microwave instrument, TB0 is the brightness temperature corresponding to the first-guess solution f0, A is the Jacobian of the RT model (section 2.4), and ε the instrument noise (other sources of uncertainties can also be included in this term). If the hypothesis that the variables considered in the problem are Gaussian is valid, the Bayesian retrieval can use an iterative procedure:
where T is the transpose, Sε is the covariance of the instrument noise and Sf is the covariance matrix of the first-guess error. The iteration starts with the first-guess solution f0, which is updated sequentially using Eq. (3) until convergence is reached. This is a traditional retrieval method used in NWP centres.
It is always very important to have an uncertainty estimate for any retrieval that is made. In the retrieval method of Eq. (3), the uncertainty in the retrieval is given by the retrieval-error covariance matrix:
It is possible to use this expression to measure the quality of retrievals based on the instrument noise information, the Jacobian of the RT for the considered channels and the a priori information provided by the first guess.
Important information required on the right-hand side of Eq. (4) is Sf, the covariance matrix of the first-guess error. This represents the a priori information about the variables to retrieve, before the inversion. In this experiment, 30% of apriori uncertainty is chosen for the water vapour, with no correlation between the atmospheric layers. Given the range of variability of water vapour in the Tropics, this means that actually no a priori information is considered, so the estimated uncertainty will describe the retrieval errors from the satellite observations only.
Another necessary piece of information is the linearization A of the radiative transfer, which is equal to the Jacobian presented in section 2.4. In Figure 1, the sensitivities of the water-vapour sounding channels are provided for a standard tropical situation. Note that here only the Jacobians in water vapour are considered, assuming that the other variables are already known.
The term Sε in Eq. (4) represents the instrument noise provided in Table 1. The RT errors could also be considered and introduced in this covariance matrix, but they are difficult to characterize and they have been neglected in the following. The calibration errors could also be introduced, but in order to compare the various instrument configurations and to assess the intrinsic retrieval-scheme capacities, it has been decided not to include them. Since we are interested here in the comparison of the sounding capacities of the instruments, the introduction of these additional terms would not change our conclusions.
Figure 5(a) (left) presents the theoretical RMS error of the retrieval, in % of RH, for the three sounders MHS, HSB and SAPHIR over ocean (grey lines) and land (black lines) surfaces. The land/ocean differences are only present for the lower layers (pressure 600 hPa). As expected from the preliminary analysis of the Jacobians and from the respective instrument uncertainties, MHS provides the most accurate retrieval of the atmospheric profile in most atmospheric layers. SAPHIR is extremely performant for pressures higher than 400 hPa because of its 183.31 GHz ±0.2 channel (see Figure 1): the uncertainty can reach 5%, which is probably too optimistic and dependent upon over-simplified hypotheses. In contrast, SAPHIR does not have surface-sensitive channels and its uncertainties for the lower atmospheric layers are close to 30%, which means that it has no information (the a priori information has a specified uncertainty of 30% in this experiment). Although SAPHIR has more channels than the other sounders, the lack of surface-sensitive channels and the receiver noises limit the capability of the SAPHIR instrument alone. However, once combined with observations from their companion instruments (Figure 5(b)), the three missions provide similar information content for water-vapour profiling, with an advantage for Megha-Tropiques for higher layers (pressures > 400 hPa) and for the lower atmospheric layers over the ocean. The information provided by the MADRAS instrument for the lower atmosphere significantly improves the retrieval of water vapour up to ∼ 600 hPa and justifies the combination of SAPHIR/MADRAS in our retrieval chain.
An algorithm has been developed for microwave instruments, in particular for the Megha-Tropiques mission, to retrieve water-vapour atmospheric profiles over both ocean and land for clear and cloudy conditions (precipitation cases are not treated). A preliminary version of this algorithm is ready to be used as soon as the mission is launched, in autumn 2011. The retrieval is based on a neural network inversion. The initial algorithm has been extended to the retrieval of water-vapour profiles from the microwave instruments on board AQUA and MetOp. The retrieval chain includes a calibration scheme, as well as a tool to obtain a first guess for the land-surface emissivity. Other parameters also retrieved by the algorithm include surface temperature and microwave emissivities over the continents and surface wind speed over the ocean.
The retrieval shows similar theoretical performance over both ocean and land, even for the description of the lower atmosphere. This is very encouraging, given the traditional difficulty in using surface-sensitive channels in assimilation procedures, for the retrieval of the lower atmospheric layers. The uncertainty estimates have been assessed using simulated data and traditional information-content analysis. The real retrieval uncertainties are expected to be higher, in particular because of the impact of calibration errors. Comparison of the theoretical capabilities of the different microwave instruments on the three platforms shows that the combination of SAPHIR observations with MADRAS measurements provides better results over ocean and similar theoretical performance to the other missions over land for water-vapour profiling and for surface by-products (ocean wind speed, continental surface emissivities and temperature). However, Megha-Tropiques should perform better for higher atmospheric layers (i.e. pressures > 400 hPa).
In Paper II, the retrieval method is tested on real observations from AQUA and MetOp instruments and compared with ECMWF operational analysis and in situ measurements. Along with the theoretical results presented here, this will make it possible to evaluate the real retrieval capabilities to be expected from Megha-Tropiques.
We thank Nicolas Viltard and Sonia Labetoule for providing a cross-track/conical coincidence code. We thank Rémy Roca for discussions linked to the Megha-Tropiques mission. We also thank Hélène Brogniez for her collaboration on the calibration step. We are grateful to Didier Renault, Anne Liefermann and more generally the Centre National des Études Spatiales (CNES) agency, to support part of this study in the context of the development of the Megha-Tropiques algorithms.