High-Repetition Millimeter-Wave Passive Remote Sensing of Humidity and Hydrometeor Profiles from Elliptical Orbit Constellations

a. Background on Flower constellation theory

The theory of FCs is a new methodology to design satellite constellations (Mortari et al. 2004; Mortari and Wilkins 2008). They are a natural consequence, and an extension to n satellites, following the theory of compatible orbits (also called resonant or repeating ground track). Compatible orbits constitute a set of special orbits whose orbital period T_r is synchronized with the period T_r = 2π/ω_r of a rotating frame (Mortari and Wilkins 2008),

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where N_p and N_d are two arbitrary integers, T_r is the orbital period, a is the orbit semimajor axis, and ω_r is the angular frequency of a rotating frame with μ as Earth’s gravitational parameter (i.e., the product of gravitational constant and Earth mass). For different values of N_p and N_d, there is a value of ω_r providing the same orbital period. This means that a compatible orbit is also compatible with an infinite set of rotating reference frames. Once N_p and N_d are chosen, the orbital period of the satellite can be computed from (1), whereas the semimajor axis a is derived from the inversion of the third Keplerian law as in the second term of (1).

The Earth-fixed Earth-centered (ECEF) rotating frame is particularly (or the most) important. However, the “compatibility” concept is a relative concept (relative to a rotating frame); hence any orbit can be seen as compatible. An important aspect of a satellite on a compatible orbit is that its trajectory in the rotating reference frame constitutes a closed loop with assigned repetition time. The FC theory explains how to place satellites on the same relative trajectory so that the whole constellation is made of satellites that fly along relative trajectories, one after another. Repeating ground track is not a unique property of Flower constellations, but the innovative concept of the Flower constellations is based on two main properties: compatibility and phasing (Mortari and Wilkins 2008). As previously introduced, compatibility property rules satellite dynamics synchronization with respect to a set of rotating reference frames, while the phasing determines satellite distribution along 3D “space track” (with respect to the rotating reference frames).

To meet the constraint of commonly repeating space tracks, all the satellites of an FC have common values of the semimajor axis a, ellipticity e, inclination i, and argument ω of the perigee, while the argument Ω_k of right ascension of the ascending node (RAAN) and mean anomaly M_k of the kth satellites must satisfy proper phasing rules. This means that FCs are characterized by six integers and five Keplerian orbit parameters. The first two integers (N_p, N_d) of the previous list define the semimajor axis (or the period), whereas the other three integers (N_s, F_n, F_d) define the satellite distribution along the relative path. The Keplerian parameters define the orbit shape, orientation, and synchronization with Earth (note that h_p is equivalent to ellipticity e). The number of orbits is determined by the N_p parameter and all the orbits have identical shape, inclination, and argument of perigee. They are only rotated in RAAN to obtain an even distribution about the central body. Flower constellations are a very ductile and useful tool, allowing an “optimized design” of satellite constellations; genetic algorithms can be exploited to optimize FCs with respect to given mission requirements (e.g., Marzano et al. 2009).

b. Analysis of incremental Flower constellations

The optimal design of an FC is a complex task. Further constraints on FC design come from the sensor specifications, in particular the orbit height range and sensor swath (that affect the spatial resolution and observation repeat time). The orbit height has been set within the range 650–1270 km and sensor swath to about 2500 km (depending on the scanning system here fixed to ±50° around the antenna boresight), in agreement with the previous study (Marzano et al. 2009). Another major concern is the choice of the inclination angle i, which might be chosen either to be a generic freedom parameter or to satisfy sun-synchronicity or to keep a constant perigee argument by imposing the orbit inclination angle i = 63.4°. Indeed, a safety constraint might be also considered: when launching from specific sites (i.e., Korou in New Guinea), the inclination must be larger than 70° to avoid risks of overpassing highly populated areas.

To extend previous analyses, the design of the FC has been focused on the incremental feature concept by analyzing the following configurations:

1. incremental FCs at i = 63.4°, having moderately elliptical orbits with perigee/apogee ratio equal to about 650/1270 km, with either two satellites (IFC-ME2) or four satellites equally distributed in two different orbit planes (IFC-ME4) or six satellites equally distributed in three different orbit planes (IFC-ME6),

2. Walker Constellation of Circular Orbits (WK-CO6) with six minisatellites in different orbital planes with i = 63.4°, following the design concept of Walker (having the same “average distance” from Earth as the FC, 1060 km), and

3. Sun-Synchronous Circular Orbit (SS-CO6) constellation with six minisatellites equally distributed along the same orbit plane at an altitude of about 1000 km.

Two target regions of interest have been identified: (i) the Mediterranean Scale Basin (MSB) windows, defined between 25°–45° latitude and −10°–35° longitude [this area is larger than the corresponding one used by Marzano et al. (2009)]; (ii) the Regional Scale European (RSE) window, delimited by the following latitude–longitude corners, respectively: 23° to −10°, 64° to −40°, 64° to 66°, and 23°to 36° [this area is identical to that used by Marzano et al. (2009)]. As a metric of space–time coverage we have again adopted the target area revisit time interval or gap time ΔT_rev as the time interval between two satellite overpasses over the target area, counted when the sensor swath of any constellation satellite partially intersects the target area (to have a useful observation, a connection time threshold of 5 min has been considered). To compare the various satellite constellations, we have compared them in terms of the cumulative distribution function (CDF).

Figure 1 shows the gap time CDF for IFC-ME6 and WK-CO6 and SS-CO6 constellations over the MSB area. Figure 2 shows the same as in Fig. 1, but for the RSE area. The deployment of six minisatellites with a large swath sensor allows revisit time gaps less than 1 h, almost comparable to a geostationary platform. It can be noticed how FC provides better revisit time performance for every time percentage with respect to WK performance.

The incremental features of FCs can be appreciated in Fig. 3, which shows the comparison among the gap time CDFs for IFC-ME2, IFC-ME4, and IFC-ME6 constellations for the MSB area. Figure 4 shows the same as in Fig. 3, but for the RSE area. As shown in the figures, IFC becomes very efficient since the second batch of satellites is operative (IFC-ME4); as a matter of fact, revisit time interval performance reaches a very high level, being lower than 1 h for 70% of the total time for the MSB window.

Table 1 shows the orbit elements for the incremental Flower constellation with six satellites distributed within three different orbit planes.

A further analysis has been performed for the evaluation of constellation performance over single sites located within the Mediterranean basin; in this frame the gap time is the time interval between two satellite overpasses over a single point on Earth. It is worthwhile to underline that single sites’ gap time performance is clearly lower than the one obtained for regional coverage (being the regional access calculated considering a large number of sites). Table 2 provides the median value of the gap time ΔT_rev of IFC-ME6 and WK-CO6 constellations for specific sites within the Mediterranean basin such as Rome (Italy), Madrid (Spain), Athens (Greece), Ankara (Turkey), Belgrade (Serbia), Cairo (Egypt), Algiers (Algeria), and Rabat (Morocco). For SS-CO6 the median value gap is about 11 h for every site. It is worth noting that IFC performances are better with respect to WK one for every site; the performance increase ranges from a few minutes to 1 h (the median value gap is 5.5 h for WK-CO6 while it is 5 h for IFC-ME6).

a. Background on linearized Bayesian analysis and inversion

The problem of the inversion of observations from space is not fully constrained, in particular in the presence of clouds and precipitation. The application of statistical principles is therefore fundamental for solving the inverse problem (Rodgers 1976, 2000), and to estimate the strongly state-dependent uncertainty associated with a given retrieval. In the following, the state of the atmosphere (i.e., temperature, humidity, and hydrometeor profiles) is denoted as a vector x and the multiple-channel observations from a hypothetical microwave radiometer are indicated by a vector y. The statistical link between y and x is expressed by means of Bayes’ theorem, which denotes p(x|y), the a posteriori probability density function (pdf) of x when y is observed, in terms of the likelihood pdf p(y|x) and a priori pdf p(x). In our context the link between x and y is described by the radiative transfer observation operator, H, which may be strongly nonlinear and characterized by an error distribution ε, summarizing both observation errors and forward modeling errors with an overall error covariance matrix 𝗖_ε.

For linear problems the Bayesian theory reduces to the optimal estimation theory (Rodgers 2000). The latter requires a priori information on the state vector x_b (and its error covariance matrix 𝗕_ε) that is close enough to the true state so that the forward model behaves linearly. While this is realistic for clear-sky applications, it may be generally questionable for applications to clouds and precipitation. If we suppose the problem to be only weakly nonlinear around x_b, the forward model simulation can be written as

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which corresponds to the first-order Taylor development with the tangent-linear approximation 𝗛 of the forward model H. By definition in a Bayesian context, a solution is optimal when the posterior pdf p(x|y) is maximized. It can be shown that in the linear case, the optimal analysis state x has the following expression:

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with 𝗛^T (T is the matrix transpose) being the adjoint of the observation operator, the angular superscript (^) denotes an estimated state, and 𝗔_ε is the so-called analysis error covariance matrix. The improvement of estimation error depends on the sensitivity of the observation y to the state x and on the accuracy of the measurement and modeling [i.e., on 𝗛 and 𝗖_ε, their respective magnitudes, and finally on the accuracy of the a priori information (through 𝗕_ε)]. The optimal estimation formulation of the inversion problem furnishes a number of useful diagnostics to measure the quality of the results. The most important of these is the 𝗔_ε, which provides a direct estimate of the uncertainty in the retrieved rain-rate profile due to uncertainties associated with the a priori profile, forward model, and measurements themselves.

The optimal estimation theory, previously described, can be adopted to perform information content analysis (Rodgers 2000). One figure of merit for the information content is the entropy reduction (ER), reflecting the improvement given by each channel to the retrieval error and measuring the reduction of entropy in a posteriori pdf. The entropy reduction is defined as the difference between the entropy of the a priori PDF p(x) and that of the a posteriori probability p(x|y). The log with basis 2 is usually chosen for expressing ER in units of bits. The channel selection is an iterative procedure proposed by Rodgers (1996) in which the contribution of each channel is sequentially quantified based on the hypothesis of error non correlation among channels (i.e., that 𝗖_ε is diagonal). Iterative methods loop over channels and sort them by decreasing information content given a priori information (from the model background 𝗕_ε) and information from the ones previously selected.

Given a set of candidate channels, the iterative selection method starts with no channels selected and sequentially chooses the channel with the highest information content, taking into account the information provided by previously selected channels (Bauer and Di Michele 2007). Therefore at each iteration (3) requires an update to 𝗔_ε (initially, 𝗔_ε,0 = 𝗕_ε). The difference of 𝗔_ε between two iteration steps k and k − 1 determines the information gain or reduction of ER (ΔER):

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The iteration procedure may be terminated when all channels have been selected or the information content of additional channels reaches a certain threshold. Details on this procedure are given by Di Michele and Bauer (2006). Depending on the application the radiometer is designed for, the different geophysical variables contributing to the measured radiation can be considered either sources of information or sources of uncertainty (see Di Michele and Bauer 2006).

The previous theoretical framework can be also used to introduce the one-dimensional variational data assimilation (1D-Var) inversion technique (Rodgers 2000; Bauer et al. 2006a). Employing a 1D-Var technique for the solution of a retrieval problem has several advantages: (i) handling of nonlinear problems (i.e., state dependent Jacobians are dealt with through the multiple iterations of the linear 1D-Var); (ii) more flexibility in handling non-Gaussian errors; and (iii) the ability to target specific problems through carefully designed simulation studies. As already mentioned, given an observation y, the best (optimal) estimate of x is the value maximizing p(y|x). It can be shown that, under the hypothesis of Gaussian error distributions, this corresponds to minimizing the following cost function J:

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In (5), J(x) quantifies the penalty arising from the difference between the estimated state (x) and the background state (x_b) as well as the observations (y), each weighted by their error covariance matrices. Equation (4) can be solved numerically by iterative procedures. We refer to as this as a variational retrieval. In general, the minimization of Eq. (4) requires the evaluation of the gradient of J(x), given by

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From (3), we deduce that the optimal estimate, derived from a Newtonian iteration, at the (n + 1)th step can be expressed as

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where 𝗔_ε is given by (3), y_n = H(x_n) is the simulated measurement vector at the nth step, and 𝗛_n^T is the observation-operator adjoint or kernel (weighting) function computed at the nth step, representing the sensitivity of the model to the parameter being retrieved. It is clear from (7) that a forward model H that is very sensitive to x is desirable since the Kernel functions weight the measurement portion of the retrieval as a strong function of state. Details on the implementation of the 1D-Var retrieval algorithm will be given in section 3c.

b. Millimeter-wave information content analysis

Atmospheric profiles were extracted from Cycle31R2 of the European Centre for Medium-Range Weather Forecasts (ECMWF) forecasting system (e.g., Bauer et al. 2006a,b). The spectral model was truncated at wavenumber 799, which corresponds to a horizontal resolution of 25 km. Vertical resolution is achieved using 91 pressure levels between 0.01 hPa and the surface. Forecasts for the to 36-, 42-, 48- and 54-h range of days 1, 10, and 20 of every month between July 2006 and June 2007 were chosen to give a total of 144 global snapshots of the atmosphere, each composed of 843 490 profiles (i.e., dimension of the global grid), altogether providing 121 462 560 profiles. To avoid excessive computation, the original samples were reduced by a random resampling into uniform distributions to prevent biasing the results of channel selection toward profiles with less intense clouds and precipitation. To ensure global coverage this sampling was separately performed over profiles located in 15° × 10° latitude–longitude grid boxes. The sampling was repeated for profiles with different times of day and months to maintain the meteorological representativeness. Figure 5 shows the geographical distribution of the selected profiles.

The observation operator consists of a radiative transfer model that accounts for multiple scattering at microwave frequencies in clouds and precipitation (Matricardi et al. 2004; Bauer et al. 2006b). The model is part of the Radiative Transfer Model for the Television and Infrared Observation Satellite (TIROS) Operational Vertical Sounder (RTTOV), e.g., Saunders et al. 2001). Since RTTOV aims at applications in NWP, the code is designed for optimal computational efficiency and makes available the forward, tangent-linear, adjoint, and k versions of the model. The k version refers to the code that can be used for calculating the model Jacobian matrices that contain the partial derivatives of brightness temperatures due to perturbations in input parameters. While the relative contribution of temperature and water vapor profiles to the total signal in clouds and precipitations is small, surface emissivity largely affects the observations in thin and semitransparent clouds. For an ocean surface, emissivity is modeled according to the fast emissivity model FASTEM-2 (Ellison et al. 2003) that is part of RTTOV. Land surface emissivity is particularly difficult to simulate because of the complex interaction of electromagnetic radiation with soil, vegetation, and snow cover as a function of a large number of unknown state variables. Therefore, land emissivity was modeled based on climatologies derived from SSM/I observations and integrated NWP and satellite products (Prigent et al. 1997). Surface emissivity maps retrieved from all seven SSM/I channels were employed to interpolate SSM/I emissivities to the frequencies of the channels under investigation. The parametric fit developed by Grody (1988) was used for this purpose, as described in O’Dell and Bauer (2007). This procedure, which only provides values of land emissivity at 53°, was complemented by the approach proposed by Karbou (2005) to model the emissivity scan dependence. The classification defined in the Biosphere–Atmosphere Transfer Scheme land cover classification was used for this purpose, obtained using AMSU data for the period from 15 August to 15 September 2005.

The formulation of the methodology for channel selection in section 3a clearly showed that the results not only depend on the background error covariance statistics, but also on the definition of observation plus modeling errors. These are difficult to estimate because they contain uncertainties in microphysical and radiative transfer modeling that are impossible to measure directly. The errors are therefore expected to be larger than common radiometric noise contributions in those channels that are most sensitive to clouds, precipitation, and surface emission. In this study, the values estimated in Bauer and Di Michele (2007) were used that were derived from real SSMI/S observations and model simulations. The definition of the background error covariance matrix of temperature, water vapor, and for hydrometeor contents is also required and an uncertainty needs to be assigned to surface temperature and surface emissivity. For this purpose the operational analysis error fields (Andersson et al. 2005) that correspond to each sampled profile were extracted to serve as background errors for temperature and specific humidity.

If z_i are the altitude discrete levels with i = 1 − N_z, the atmospheric state vector x is then represented by a water vapor vertical profile V(z_i), a nonprecipitating (cloud) water content vertical profile W_c(z_i), a precipitating (rain) water content vertical profile W_r(z_i), a nonprecipitating (ice crystals and aggregates) water content vertical profile W_i(z_i), and a precipitating (snow and graupel) solid water content vertical profile W_s(z_i). The measurement vector y is, in general, represented by the set of T_Bp(v_j, θ) at prescribed frequencies ν_j, polarization p, and incidence angle θ.

The ER-based channel selection methodology has been applied choosing a starting set of frequency channels between 23.8 and 230 GHz at vertical and horizontal polarization based on a channel set that has been optimized for future microwave sounders and imagers as part of the post–European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) Polar System (post-EPS) program (Schlüssel et al. 2008). The final ranking of the considered frequency set is done by evaluating an average ΔER over all the profiles of the dataset. Table 3 summarizes the results for each tropospheric parameter of interest (i.e., humidity, clouds, and precipitation). Moreover, both land and ocean surfaces are distinguished, whereas humidity results are also separated for cloudy and clear sky. Only results for the conically scanning radiometer at 53° off-nadir angle are also considered, as those for the cross-track linear scanning are similar. Dual-side band channels are also considered in Table 3, even though the bandwidth effect has been neglected.

Frequencies below 52.8 GHz are valuable for clouds and precipitation together with channels located in the far wings of the 118-GHz absorption line, as expected, while 23.8 GHz contributes strongly to the water vapor profiling over ocean. Over both land and ocean the role of the 118-GHz frequency band for cloud and precipitation observation is more obvious than 89 GHz, whereas the 183-GHz frequency band is essential for humidity profiling over both land and ocean.

Restricting the frequency range to 89–229 GHz (to reduce antenna size; see section 3a), Fig. 6 shows the channel ranking for humidity profiling at each iteration k (see equation within the optimization procedures over entire globe using average results over boxes of 3° × 3°). Figure 7 shows the same as Fig. 6, but for hydrometeor profiling. Each channel is color coded and its ranking is shown for each successive iteration of the ER procedure over the entire globe (see Fig. 5). This means that for each grid box, Figs. 6 and 7 show the geographically distributed information content priority of each channel. It is worth noting that colors are not uniform over each panel meaning that the priority ranking will vary with latitude and longitude. This indicates that different channels dominate in different cloud conditions and underlines the fact that a large number of channels is required to optimize the observation of clouds and precipitation under all weather conditions. However, since only the channels above 89 GHz were included in this study, less spatial and spectral variability is found than expected if channels between 10 and 89 GHz were also included. The variability is generally more pronounced over the poles and around the intertropical convergence zone, especially for humidity after iteration 4.

c. Retrieval numerical results

From Table 3 we have derived a large set of channels in the millimeter-wave range that is able to provide humidity and hydrometeor profile information. If our aim is to keep the overall size of the radiometric payload small, we will restrict our analysis to frequencies above 89 GHz as shown in Figs. 6 and 7. Moreover, if more than 10 channels are considered, size and weight of the passive sensor will exceed what is compatible with a minisatellite bus (Marzano et al. 2009). Our choice for the radiometer configuration was based on an analysis comparing retrieval performances of a variety of subsets of the channels ranked in Table 3 (Marzano et al. 2009). The channel combination that provided the best performances is used in this paper, which is given by the following set: (89H GHz, 89V GHz, 166.0V GHz, 118.75V ± 0.7 GHz, 118.75V ± 2.1 GHz, 118.75V ± 3.0 GHz, 183.31V ± 1.0 GHz, 183.31V ± 3.0 GHz, 190.3V GHz, 229.0H GHz), where V and H stand for vertical and horizontal linear polarization, respectively. This means that T_Bp(v_j, θ) is a vector of 10 elements assuming a conically scanning radiometer with a 53° incidence angle at the surface. This configuration is called the Florad Millimeter-Wave Imaging Sounder (FLOMIS) and is the same one used by Marzano et al. (2009).

The 1D-Var methodology has been implemented using the 1D-Var perturbation approach (1D-VarP) described in Bauer and Di Michele (2007). 1D-VarP represents a self-consistent testing environment to evaluate the performance of a given instrument configuration. This is because all ingredients are defined, that is, state variables, observables, as well as their error characteristics, and based on realistic estimates of errors and meteorological representativeness. Retrieval accuracy can be determined, for instance, as a function of instrument noise, biases, channel cross correlation, and other parameters. It is based on a similar approach as already applied to clear-sky retrieval studies (e.g., Deblonde and English 2003). The procedure for evaluating the retrieval accuracy is briefly described by the following points:

1. The control vector x (state) contains vertical profiles of temperature and humidity, surface skin temperature, and 10-m wind speed (u and υ components) relative to a single atmospheric state. In the case of profiles over land, wind speed is replaced by emissivity parameters. Profiles of temperature, humidity, surface temperature, and additional variables, obtained from the short-range ECMWF model forecasts, are extracted from the global database described in section 3b.

2. The covariance 𝗕_ε represents the uncertainty associated with each of the components of x. In 1D-VarP, the first guess covariance statistics from the operational forecasts are used as the background error covariance matrix for temperature and humidity. Values relative to the corresponding time and location are associated with each profile of the database. For surface skin temperature and ocean wind speed, average values of background errors are used. In the case of profiles over land, the errors of surface emissivity are assumed to be equivalent to the spatial/temporal variability of emissivity that is included in the emissivity climatology at the location of interest.

3. The forecast (“true”) profiles and background error covariances are used to generate the first guess needed for the 1D-VarP. The first guess is obtained from adding random perturbations to the forecast profiles. The random perturbation δx_i of the ith element of x is determined through an eigenvalue analysis and a Gaussian random number generator whose distribution has zero mean and unity variance.

4. Hydrometeors associated with the true profiles can be created by applying cloud and convection models to temperature and humidity and additional input variables (e.g., tendencies and surface fluxes). Observations, y_true, are simulated by processing the true profiles with the RTTOV model as described above. To produce realistic observations (y_o), noise is added to y_true. The noise corresponds to the radiometric noise that has been specified by Schlüssel et al. (2008). The observation error covariance matrix 𝗖_ε is assumed to be diagonal and derived from the observation statistics in Bauer and Di Michele (2007).

5. The (perturbed) first guess profiles and the simulated observations (from the unperturbed profiles) are then fed into the 1D-VarP retrieval block. The minimization module that is employed in 1D-VarP to compute (5) is the limited-memory quasi-Newton software developed by Gilbert and Lemarechal (1989). The retrieval error estimates are derived from the comparison of retrieved and unperturbed (true) profiles in terms of biases and error standard deviations. In our current configuration, 350 perturbations are performed per profile. This ensures a good compromise between accuracy of the results and computational efficiency.

The 1D-VarP method was applied to the global dataset described in the previous paragraph, but results are shown here just for the midlatitude region (latitude ranging from −70° to −35° and from 35° to 70°). This region denotes the target area of the designed FLORAD mission.

The retrieval performance is quantified in terms of statistics of the residual error between the true profiles and the profiles retrieved from the simulated observations using 1D-Var (analysis). The retrieval performance is also compared to the variability of the respective geophysical variable in the true dataset. This demonstrates the improvement of the retrieval over an estimate based on the mean climatological profile and its variability. In addition, the statistics of the residual error between the true profiles and the first guess profiles used for initializing the 1D-Var are computed corresponding to the a priori knowledge. It is worth a reminder that the first guess profiles were generated by random perturbation of the true temperature and humidity profiles using the background error covariance from the operational forecast model. Therefore, any improvement of the analysis with respect to the first guess residual error demonstrates the FLOMIS observational contribution. Of course, it is expected that the improvement with respect to the operational forecast is substantially smaller than the improvement with respect to an estimate based on the mean climatological profile only. This is because the operational forecast has much higher skill than climatology.

Statistics were computed separately for cases over ocean and over land. Moreover, the dataset was further fractioned into clear-only, cloudy, and precipitating cases. Results for all of these combinations are presented in Figs. 8 –13. In Fig. 8 the vertical profiles of bias and error standard deviation (std) for temperature and humidity estimates in clear-sky conditions over ocean are shown. Our analysis shows that the bias of the analysis resembles the bias of the first guess, and is negligible for both temperature and humidity. The error std statistics demonstrate that the FLOMIS contribution to the forecast is rather small but consistently positive in the troposphere for temperature and substantial for humidity with up to 30% near the surface. Note also that, as expected, the std error for the forecast is already substantially less than the variability of the atmospheric profiles (expressed here in terms of the std of the midlatitude subset). Similar results are shown for clear-sky conditions over land in Fig. 9, although in this case the FLOMIS contribution for the humidity profile is limited to 10% while for temperature it is slightly greater than over ocean. The reduction in humidity retrieval accuracy over land is explained by the much reduced radiometric sensitivity to moisture over surfaces with high emissivity.

Figures 10 –11 show the results for the cloudy cases (ocean and land, respectively) including the retrieval errors for cloud liquid and ice water. The vertical profiles of error bias and std for temperature, humidity, rain, and snow retrievals over ocean are shown in Fig. 12. With respect to the clear-sky cases, we note an increase in error reduction for temperature profiles throughout the troposphere, reaching 20%. This may be explained by the strong cloud contribution to emission that enhances the radiometric sensitivity to the temperature of liquid water. The fact that both temperature and liquid water error statistics are improved suggests that there is little aliasing and that the chosen channels are able to distinguish between the signal contribution from temperature and hydrometeors, respectively. However, the increased biases show that some aliasing is present because of the ambiguity of signal contributions. The reduction of the humidity profile retrieval error is largely reduced in the presence of liquid water. This may be explained by the strong sensitivity of the 183-GHz channels to liquid water, which causes these channels to become sensitive to temperature rather than humidity in the presence of liquid water.

Over land (Fig. 11) the observations add a little skill to the a priori knowledge for moisture and cloud liquid water and similar skill for temperature. The main observational impact is seen for temperature, which matches the impact over ocean, and cloud ice. The latter is expected to be mainly contributed by the 183-GHz channels. The comparison of a priori and climatology standard deviations shows that for cloud variables the short-range forecast has less skill over land than over ocean and that the substantial skill of moisture prediction over both land and ocean is not fully propagated into cloud variables.

If precipitation is included (Fig. 12) the FLOMIS contribution to the estimation accuracy reaches 10% for rain profiles while it increases to up to 50% for snow profiles. Figure 13 shows the results for the precipitation dataset over land. Here, the broad picture is unchanged, although we note a small increase of the FLOMIS contribution to both rain and snow profiling accuracy. Again, a small aliasing effect is visible expressed as increased biases in lower-level temperatures and humidity. This is a common problem of underconstrained retrievals, here amplified because of the limited sensitivity of microwave radiances over high emission surfaces and the ambiguity of signal contributions by temperature, moisture, liquid water (cloud and rain), and surface emission. The largely different spectral signature of frozen particle scattering reduces the ambiguity, which explains why the snowfall retrieval accuracy is so much superior to the rainfall retrieval accuracy, in particular given the FLOMIS channel selection.