a. Characteristics of the Méso-NH model

The nonhydrostatic mesoscale cloud model Méso-NH jointly developed by Météo-France and the Centre National de la Recherche Scientifique (CNRS) is used to simulate the atmospheric state for the selected precipitation cases. A detailed description of the Méso-NH is given in Lafore (1998). See the Méso-NH scientific documentation available online at http://mesonh.aero.obs-mip.fr/mesonh for a complete description of the model.

The mixed-phase microphysical scheme developed by Pinty and Jabouille (1998) essentially follows the approach of Lin et al. (1983): a three-class ice parameterization is used with a Kessler (1969) scheme for the warm processes. The scheme predicts the evolution of the mixing ratios of six water species: r_υ (vapor), r_c, and r_r (cloud droplets and rain drops), and r_i, r_s, and r_g (pristine ice, snow aggregates, and frozen drops graupel defined by an increasing degree of riming). The concentration of the pristine ice crystals is diagnosed. The concentration of the precipitating water drops, snow, and graupel is parameterized according to Caniaux et al. (1994), with the total number concentration N given by

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where λ is the slope parameter of the size distribution, and C and x are empirical constants derived from radar observations. The size distribution of the hydrometeors is assumed to follow a generalized γ law:

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where g(D) is the normalized form which reduces to the Marshall–Palmer law when α = ν = 1 (D is the diameter of the drops or the maximal dimension of the particles). Finally, simple power laws are taken for the mass–size (m = aD^b) and for the velocity–size (υ = cD^d) relationships to perform useful analytical integrations using the moment formula:

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where M(p) is the p^th moment of g(D). A first application of Eq. (3) is to compute the mixing ratio r_x as

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Table 1 provides the characterization of each ice category and cloud droplets/raindrops.

Méso-NH outputs include a full description of the atmospheric parameters (pressure, temperature, and mixing ratios for the water vapor, and the five hydrometeor categories). The multiple interactions operating between the different water categories are accounted for through the parameterization of 35 microphysical processes (nucleation, conversion, riming, sedimentation, etc.). More detailed information can be found in Wiedner et al. (2004).

b. The case studied: A light precipitation at Hoek van Holland

This case occurred on 19 September 2001 over northeastern France and Netherlands. It was a long lasting precipitation event produced by a quasi-stationary low pressure system. Maximum rainfall of 100 mm has been measured over the whole event at Hoek van Holland, Netherlands, with intensities of a few millimeters per hour.

Temperature, wind, surface pressure, water vapor, and sea surface temperature taken from the ECMWF 6-hourly analysis are used as initial and boundary conditions. The vertical grid has 50 levels up to an altitude of 20 km, with layer thickness varying from 60 m close to the surface up to 600 m. The horizontal grid spacing is 10 km and the domain cover 1600 km × 1600 km.

The model is initialized on 0000 UTC 19 September 2001 and is integrated forward for 24 h. Outputs at 1800 UTC are analyzed in this study. A representation of the total columns of liquid cloud, rain, ice, graupel, snow, and water vapor, as simulated by Méso-NH at 1800 UTC is shown in Fig. 1.

a. The microwave satellite observations: SSM/I and AMSU

Two different microwave instruments are used for this study: (i) SSM/I hosted by the Defense Meteorological Satellite Program’s satellites and (ii) AMSU on board National Oceanic and Atmospheric Administration (NOAA) satellites. SSM/I is a conical scanning instrument with a constant viewing angle of 53°. It operates at frequencies between 19 and 85 GHz with both horizontal (H) and vertical (V) polarizations detected. The elliptical fields of view decrease in size proportionally with frequency, from 43 × 69 km at 19 GHz to 13 × 15 km at 85 GHz. In contrast, the AMSU is a cross-track scanning instrument with viewing zenith angles varying between 0° and 58.5°. The frequency channels range from 23.8 to 89 GHz (AMSU-A) and from 89 to 190 GHz (AMSU-B). The spatial resolution at nadir is 48 km for AMSU-A and 16 km for AMSU-B. For a given instrument (A or B), the spatial resolution is fixed regardless of the frequency but it changes with the zenith angle. The polarization is variable and results from a combination of two orthogonal linear polarizations (V and H), and so depends on the scanning angle.

For the analysis of window channels, SSM/I presents the advantages of constant viewing angle and constant spatial resolution at a given frequency, as compared to the AMSU cross-track instrument. This facilitates the comparison between simulations and observations: the variability and uncertainty related to viewing angle and spatial resolution are suppressed. In addition, two orthogonal polarizations are available from SSM/I, making it easier to separate potentially polarized surface effects from the atmospheric contribution. Although this study focuses primarily on high frequency evaluation, comparison with SSM/I observations helps analyze the atmospheric situation and the differences between AMSU simulations and observations.

b. The observed and simulated fields

At first, observations from SSM/I at 1941 UTC and AMSU at 1755 UTC are compared to the simulated TB fields at 1800 UTC, along with the IR observed and simulated images (Fig. 2). A few qualitative remarks can be stated: 1) the global spatial structures are fairly well represented in the microwave and in the IR meaning that the mesoscale cloud model is able to reproduce the thermodynamic nature of the precipitating system, 2) the overall agreement between simulated and measured TBs in the microwave is reasonable, 3) a closer look at the figures in the microwave and in the IR reveals small displacements in the cloudy structures and discrepancies in the intensity of the radiative signatures. The microwave simulations show scattered cloud fields across the North Sea but the observations do not. In addition, the strong scattering signatures (TB depression) observed over central Germany/east France or south Norway appear in the simulations but with significantly less intensity, especially at higher window frequencies that are particularly sensitive to scattering by frozen particles.

c. The observed and simulated TB distributions

For a more quantitative comparison of the simulated and observed TBs, their statistical distributions (histograms) are compared in Fig. 3 for selected SSM/I channels. The data are divided according to the surface type (land and sea, coastal data being excluded). It is anticipated that the TB comparison would be less informative for the AMSU instruments because of their varying incidence angle. At all frequencies, the distributions of the TBs are significantly broader over ocean, because of the lower emissivity of the ocean surfaces. Hence, clouds cause a significant warming and therefore a widening of the TB distribution.

The 19-GHz channels are highly responsive to surface emissivities, especially under clear sky conditions. A reasonable agreement of measured and simulated TB distributions at this frequency is found in Fig. 3. Differences of TB (hereafter noted ΔTB) between observations and simulations are further separated into cloudy (flagged by the simulated clouds in Méso-NH) and clear pixels in Fig. 4. This confirms that the agreement is especially good under clear conditions and that surface emissivity estimates for land and sea are reliable, at least at low frequencies. Note that a nonnegligible dispersion of the ΔTBs are expected due to a nonperfect coincidence between the atmospheric structures observed by the satellite and those of Méso-NH (on which the RT simulations are based). The 22-GHz channel is sensitive to the total water vapor column over ocean. For this channel as well, good agreement is obtained.

Over ocean and land, an overestimation of the simulated TBs is apparent at 37 and 85 GHz. Emission from liquid clouds is significant at 37 GHz and increases with the frequency. Low clouds simulated by the atmospheric model emit radiation therefore increasing the TBs as compared to a colder and cloud-free sea surface. For clear conditions (as flagged by Méso-NH; Fig. 4), the differences between simulations and observations do not show significant bias except at 85-GHz vertical polarization. From Fig. 2, one can also notice that especially at 85 GHz, the impact of the cloud fields east of the U.K. coast seems overestimated as compared to the observations.

At 85 GHz over land, a significant population of pixels has simulated TBs exceeding those of the observations (see Fig. 4). We checked that most of these pixels are located in central Germany/eastern France and southern Norway, where we already noticed (Fig. 2) too-high simulated TBs. The largest differences between observed and simulated TBs are located in regions where significant quantities of snow are present in the clouds. Other differences in regions where warm clouds are present have similar counterparts in the IR and it appears that these differences are due to expected slight mislocations of the cloud structure by the cloud model. To further evidence the critical importance of frozen particles in the simulations, histograms are presented at 89 and 150 GHz separating the pixels according to the amount of snow total column, over land (Fig. 5). Small snow concentrations result in moderate ΔTBs centered close to zero. For a deeper column of snow the distributions shift toward larger ΔTBs. At 183.31 ± 1 the distributions are narrower and are centered on the same range of values. The explanation is that the channel weighting function peaks above the snow cloud and it is therefore not sensitive to the underlying layer of snow.

d. Detailed analysis for a representative transect

A closer look at the differences between simulated and observed TBs is presented along a transect of constant latitude of 50° (Fig. 6). This cross section includes both liquid cloud and rain over the English Channel and over land and the presence of significant frozen quantities over Germany. The vertically integrated masses of the hydrometeors as calculated by Méso-NH are also displayed.

Over the Channel, west of 2°, it appears that the cloud and rain structure simulated by Méso-NH is translated westwards by ∼2° with respect to the observations. This can be observed from both microwave channels (SSM/I and AMSU-B) and IR observations, although their overpass times differ slightly. It is also seen on Fig. 2, in the comparison between the observations and the simulations. Because of saturation effects, high frequencies (150-GHz channel and the IR observations) are less sensitive compared to the low frequency window channels. The spatial consistency between the microwave and the IR differences confirms that in this region, discrepancies between simulations and observations in the microwave are essentially related to a mislocation of the cloud structure, not to inaccurate RT simulation in the microwave.

East of ∼5°E, there is an overestimation of the simulated microwave TBs that increases strongly with frequency in the window channels. The frequency and angular dependencies of the discrepancy is consistent with an underestimation of the scattering efficiencies of frozen particles. Here, TB errors are quite low (of the order of 2 K) at 19 GHz while they reach 40 K at 85 GHz as observed by SSM/I at a constant 53° incidence. The discrepancy observed at 89 GHz with AMSU-B is more limited: with close to nadir incidence in this area (from 15° at 7°E to 1° at 12°E), AMSU-B TB depression due to scattering are expected to be weaker. At 150 GHz, the difference observed by AMSU-B is larger than at 89 GHz, as expected. The stronger the water vapor absorption in the 183 GHz channels, the smaller the discrepancy: first, the TBs being already rather cold in the most absorbing channels, the effect of scattering by the frozen particles is less obvious; second, the frozen particles can be at least partly located below the peak of the weighting function and will thus have a more limited impact. On the thermal IR signal, no significant difference is found in this region meaning that the cloud top temperature is correctly estimated by Méso-NH.

a. Particle size and density

For each layer and each hydrometeor category, Méso-NH provides the mixing ratio r_x and the size distribution of the maximum dimension of the particle [Eq. (2) and Table 1]. The intrinsic mass of the particles is specified (m = aD^b) but the shape of the particles or in other words their volume and density, which are not explicitly needed in the microphysical scheme but which are indeed crucial parameters affecting the scattering properties, are free parameters. Liquid drops are spheres (b = 3; Table 1). Graupel and small ice crystals are not strictly spheres (b = 2.8 and b = 2.5, respectively), but are approximated so in the RT code because there is no real justification for a more complicated treatment. With b = 1.9, snow particles are the most challenging particles because they are clearly not spherical. In this work, two shape approximations are tested: the sphere case and the randomly oriented oblate spheroids. The oblate spheroid shape for snow is favored by polarimetric radar studies (Vivekanandan et al. 1994; Ryzhkov et al. 1998). Figure 7 displays the particle size distributions, as given by Méso-NH for three mixing ratios. For comparison purpose, the equivalent size distributions used in Skofronick-Jackson et al. (2002) are also drawn. It is emphasized that in the Méso-NH scheme, the diameter D corresponds actually to the largest dimension of the (falling) particle and not to a melted diameter of the drop of same mass. Two Méso-NH size distributions are shown for snow. The first one considers D as the largest dimension of the particle, the second one considers D as the diameter of the sphere of equivalent volume, the particles being oblate spheroids with an aspect ratio of 2 (the largest axis being twice the smaller one).

The largest variability in Fig. 7 is observed for the snow size distributions (note that the mass concentration of 5.10⁻³ kg m⁻³ is not realistic for snow and is just shown for comparison with the others). In the tropical cases explored by Wiedner et al. (2004), the graupel mixing ratios were usually high compared to those of snow and microwave scattering was dominated by the graupel. In midlatitude cloud systems, snow mixing ratios in precipitating clouds are comparable or sometimes larger than the graupel ones and the accurate treatment of the snow in the RT simulations is required.

The particle density is a critical parameter that determines the dielectric properties, and as a consequence the scattering efficiency of the particles. As introduced above, the density of snow particles is an opened microphysical parameter in Méso-NH until a hypothesis is made on the shape of the particle. Figure 8 shows the density of the graupel and of the snow particles as calculated with different assumptions.

The graupel are rimed particles for which it is reasonable to assume a spherical shape with diameter and mass given by Méso-NH (see Table 1). Their density is below 0.3 g cm⁻³, lower than the values used by Burns et al. (1997; 0.6 g cm⁻³) and Skofronick-Jackson et al. (2002; 0.4 g cm⁻³). The snow density is calculated considering spheres and oblate spheroids with an aspect ratio of 2. The density modeled by Matrosov et al. (1996) is also presented (density = 0.07 D⁻¹ g cm⁻³) with D the equivolume particle diameter (the sphere and the spheroid with aspect ratio of 2 are shown). Regardless of the model, the snow density falls abruptly from the ice density (0.917 g cm⁻³) to very low densities, well below the 0.1 g cm⁻³ density value that is often selected (e.g., Burns et al. 1997; Skofronick-Jackson et al. 2002).

For the snow, another approach is suggested by Liu (2004). By analyzing accurate discrete dipole approximation (DDA) modeling, Liu observes that snow has scattering and absorption properties between those of a solid ice equal-mass sphere of diameter D₀ and a ice–air mixed sphere with a diameter equal to the maximum dimension of the particle D_max. For each frequency and particle shape, a softness parameter [SP = (D − D₀)/(D_max − D₀)] is derived that gives the diameter of the best-fit equal-mass sphere. For each particle shape, this is actually equivalent to use a frequency dependent effective density along with modified diameters.

b. Refractive index of the hydrometeors

The refractive index for liquid water is rather well established (although measurements are very limited at high frequencies and low temperatures) and is taken from Manabe et al. (1987) for rain and cloud droplets. Mätzler (2006) recently reviewed the works performed on the ice and snow refractive index at microwave and millimeter wave frequencies. This study includes among others the results from Jiang and Wu (2004). The model preferred by Mätzler (2006) and by Jiang and Wu (2004) is compared to the Warren (1984) parameterization (used in Wiedner et al. 2004). Differences between models are limited, although they are slightly larger at lower frequencies for the real part of the index. For the imaginary part, the new model predicts a frequency dependence, whereas Warren (1984) considered it fixed “over a large region of the microwave and radiowave spectrum.”

Snow and graupel are considered heterogeneous media, made of ice and air. The permittivity can then be calculated from the permittivity of ice, knowing the density of the particles. A large number of mixing formulas are available in the literature. The most common one is the Maxwell–Garnett formula that gives the effective dielectric constant of a mixture as a function of the dielectric constants of the host material and inclusions. For snow and graupel, the host is the air and the inclusion is the ice. Other mixing formulas can be found in the literature and several have been tested (Ulaby et al. 1986; Matrosov et al. 1996; Mätzler 2006) for snow for different densities. For a given snow density, the differences essentially come from the modeling of the ice permittivity. The tested mixing formulas give very similar results, being all derived from the same theory. In the following, we will use the Maxwell–Garnett formula itself, with the Mätzler (2006) ice model.

The impact of potential snow wetness has also been tested. The wetness percentage (W) of Skofronick-Jackson et al. (2002) is adopted: it predicts the increase of wetness with temperature [W(%) = 0 for T < 258.15 K; W(%) = T − 258.15 for T < 258.15K; W(%) = 15 for T > 273.15 K]. The percentage of air, ice, and water are adjusted by converting air into water following the above relations. The Maxwell–Garnett mixing formula is used twice, first for the mixing of ice in an air matrix and second for the mixing of water in the air–ice matrix. The wetness has a strong influence on the refractive index (not shown) that will translate in stronger absorption.

It is to be stressed that these refractive index estimates are based on a very limited number of experiments (Mätzler 2006) at very few frequencies, and under laboratory conditions where the ice/snow properties can significantly differ from those in the cloud environment.

c. Frozen particle concentration

To assess the range of variability related to the mesoscale cloud model, simulations from the Méso-NH and the German Lokal-Modell are compared. This comparison does not intent to evaluate one model with respect to the other, but to point out the differences in the simulated frozen quantities depending on the microphysical parameterization, and thus to have an idea of the uncertainty of these quantities.

The Lokal-Modell (LM; Steppeler et al. 2003) of the German Meteorological Service (DWD) is a fully compressible nonhydrostatic model, currently in operation with a horizontal resolution of 7 km. In this study, model integrations are performed on a finer grid with 2.8 km resolution, which covers 440 km × 440 km centered over the Netherlands. The configuration of LM has been adapted accordingly: at first, parameterized moist convection is switched off since it is assumed that most features of deep convection are resolved. Second, the numerical treatment is improved to ensure accurate and positive definite advection of hydrometeors and to reduce numerical diffusion. A two-level time integration scheme based on a Runga–Kutta method (Wicker and Skamarock 1998) is applied and advection of hydrometeors is calculated by a semi-Lagrangian algorithm. Prognostic model variables are the same as for Méso-NH and are vertically discretized on 35 hybrid levels. The LM comprises a state-of-the-art package of parameterizations of all nonresolved processes, for example, for subgrid-scale turbulence, radiative fluxes, and a one moment bulk scheme. More details are available in Doms and Schättler (1999).

The spatial structures of the clouds generated by the two simulations are similar. However, significantly larger frozen quantities are generated by the German mesoscale scheme (see Fig. 9), giving an idea of the uncertainty to be expected from the cloud simulations.

d. TB simulations with different assumptions

Our objective in this section is to analyze the sensitivity of the radiative transfer simulations to the different hypothesis, in the presence of significant amount of scattering particles and to recommend the most realistic set of scattering parameters. Our selection criteria are based on simulations at 89 and 150 GHz because these frequencies are the most sensitive to scattering by hydrometeors as shown above. As previously discussed, the main discrepancies between observations and simulations occur in regions where snow dominates in the atmospheric column. Our analysis of tropical situations showed that good agreements were obtained in areas where graupel contents were much more important than snow ones (Wiedner et al. 2004). Thus, we will essentially test the influence of the snow parameters on the radiative transfer. We concentrate here on the results along a representative transect for the Hoek case (Figs. 6 and 9).

Figure 10 shows simulations at 89, 150, and 89–150 GHz for this transect for various hypotheses, compared to the AMSU-B observations for the same locations. The observations being performed at different angles, the simulations will be presented for two incidence angles (8° and 19°).

The first simulation (black curves) corresponds to the initially selected parameters for snow. The dielectric properties are calculated from the Maxwell–Garnet mixing formula, using Mätzler (2006). The particles are spheres and for each particle type, the nominal size distribution of Méso-NH is used. There is almost no scattering simulated, both at 89 and 150 GHz.

Multiplying the snow content by 1.5 or by 0.5 in each layer does not change the result by more than 1 K along the transect. Switching from the Maxwell–Garnet mixing formula to the Ulaby et al. (1986) one for the snow dielectric properties does not improve the results (not shown). Considering snow, with a wetness degree depending on the temperature of the layer, the TBs decrease by a few kelvin (see the yellow curves in Fig. 10). Changing the snow size distribution to the one used for the graupel does not change the TBs much either (not shown). All these experiments lead to the conclusion that the selected snow parameters are such that even with a column-integrated content higher than 1 kg m⁻², the snow particles are transparent to the microwaves. The snow particle sizes that are likely to scatter radiation at 89 and 150 GHz have a very low density (see Fig. 8). Hence, it seems that probably the too-low density of the largest flakes is responsible for the poor dielectric properties that result in only very weak scattering.

Calculations are then performed, assuming that the snow particles are randomly oriented oblate spheroids (not shown). Slightly more scattering is produced, but a closer examination of the results shows that it is not essentially due to the change in particle shape but to its impact on the snow density and as a consequence on the snow dielectric properties: when changing from spheres to spheroids with the same maximum diameter D, the volume of this particle decreases for the same mass (m = _aD^b in Méso-NH) and as a consequence its density increases.

A density of 0.1 g cm⁻³ is then applied to the snow particles, a value that is often selected for snow (light blue curves in Fig. 10). For consistency purposes, a minimum threshold of 0.1 g cm⁻³ is also applied to the graupel density. Changing the density of snow leads to a significant decrease of the TBs. Setting the graupel density to 0.4 g cm⁻³ regardless of the graupel particle size yields TBs that are very low, much lower than the AMSU-B observed values for this case, confirming our previous study of tropical cyclones (Wiedner et al. 2004). These results suggest that a constant density of 0.1 g cm⁻³ for the density of snow is a good compromise to describe the snow density, as this clearly improves the scattering by large snow particles. The density of graupel is kept at its initial value calculated from Méso-NH assumptions but with a minimum of 0.1 g cm⁻³: this is consistent with the physical sense that for a given particle size, graupel is growing denser than snow.

Under these assumptions (light blue curves in Fig. 10), the magnitude of the TBs depression related to the scattering is of the same order, for both 85 and 150 GHz. Examination of Fig. 2 shows that the observed scattering at 150 GHz is significantly larger than at 85 GHz, and the simulations should reproduce this spectral dependence. The purple curves in Fig. 10 represent RT simulations with the size distribution of snow taken identical to the graupel one, thus assuming fewer large particles and more abundant smaller ones. The simulation shows a slightly improved frequency gradient but still much weaker than the observed one.

The sensitivity to the snow content is then analyzed. The German LM model has been shown to predict more frozen quantities than Méso-NH so additional RT simulations are performed, multiplying the snow content by 1.25 in each atmospheric layer (the density of snow is 0.1 g cm⁻³ and the original snow size distribution is reset). The TBs are significantly depressed for both frequencies (green curves in Fig. 10).

Finally, the method developed by Liu (2004) is also tested, using the averaged softness parameters of 0.33 and 0.27 for 89 and 150 GHz, respectively, as suggested in Liu (2004; dark blue curves). The results are very encouraging: not only the magnitude of the scattering is close to the observations, but the frequency gradient also agrees with the measurements. The softness parameters are frequency sensitive and have been tuned by Liu (2004) to obtain an optimal agreement with the discrete dipole approximation calculations. This solution is selected as the optimum one. In the last simulation (red curves), the method by Liu is also adopted, but with a multiplication factor of 1.25 on the snow quantities in Méso-NH. As compared to the previous simulation, the improvement is not significant.

The complete Méso-NH field for the Hoek case is then simulated for AMSU and SSM/I conditions using the initial Méso-NH outputs and assumptions for all quantities, along with the Liu (2004) softness parameter for snow. Figure 11 shows the results for the AMSU-B channel at 150, 89, and 89–150 GHz, as compared to the observations and to the previous original simulations. The new simulations show enhanced scattering (lower TBs) at 150 GHz in the convective region where snow is present. It also shows an improved simulation of the frequency gradient (89–150 GHz) as compared to the satellite measurements. Similar simulations have been performed for the four other cases and for example a light precipitation event over the Rhine River, 10 February 2000, is shown. The AMSU instrument at 150 GHz observes significant scattering over east France and Germany. With the original snow parameterization, very limited scattering is simulated, whereas the new simulations show more scattering, closer to the observed values. One can notice that the surface emission over the snow-covered Alps is very well reproduced by our simulations.

For the five cases, the satellite-observed TBs have been compared to simulations with the old and new treatments of snow in the RT, with consistent better agreement with the new simulations. There are still differences between the simulated and the observed fields over cloud structures at these high frequencies, as expected due to their large sensitive to the detailed microphysics of the hydrometeors, but a better agreement is systematically observed for midlatitude cases when changes are applied to the snow treatment.