a. Experiments and numerical setup

The use of numerical data from CRMs can now be considered a standard tool for evaluating and developing cloud parameterizations for GCMs (Moncrieff et al. 1997). The strategy consists in forcing CRMs with observed domain and time-averaged tendencies of temperature and water vapor, and in utilizing the ensemble CRM data as pseudo-observations of small-scale processes (Grabowski et al. 1996; Xu and Randall 1996; Wu et al. 1999; Guichard et al. 2000). In the present study the numerical data are obtained from the CRM version of the nonhydrostatic mesoscale model Méso-NH (Lafore et al. 1998) including in particular a 1.5-order turbulence scheme, an interactive radiation parameterization and a prognostic microphysical scheme for five precipitating and nonprecipitating liquid and solid water categories. The model was run on a large domain including 256 × 256 horizontal grid points with a spacing of 2 km, and 47 vertical levels between the surface and the model top at 25 km; the model time step is 5 s. The case studies include (i) a tropical oceanic case observed during the Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE), that is, a 2-day period from 1200 UTC 10 December 1992 to 1200 UTC 12 December 1992 (Lin and Johnson 1996; Guichard et al. 2000), and (ii) a continental midlatitude convective case observed during the Atmospheric Radiation Measurement (ARM) experiment, that is, a 36-h period from 1200 UTC 29 June 1997 to 0000 UTC 1 July 1997 (Cederwall et al. 2000; Zhang et al. 2001). For each case study the model is forced with observed large-scale tendencies for temperature and moisture; however, the wind profile is relaxed toward observed values; for the ARM case the surface fluxes are also prescribed from observations. Boundary conditions are periodic. The model's initial conditions are horizontally uniform, but a small random temperature perturbation of 0.2 K is applied at the first model level in order to initiate convection.

The evolution of the domain-averaged surface precipitation as simulated by the CRM are depicted in Fig. 1. The ARM and TOGA COARE case studies include a strong convective period with maximum surface precipitation rates of 65 and 54 mm day⁻¹, respectively. In the following, cloud layer statistics are computed from 3-hourly snapshots of the simulations.

b. Fractional cloudiness and cloud condensate

The CRM-derived cloud fraction N and the normalized cloud condensate content r_l/σ_s are displayed in Figs. 2a,b as a function of Q₁ (the data came from all model levels). Here, N is defined at every vertical model level as the number of grid points with r_l = r_c + r_i > 0 divided by the total number of horizontal grid points. The corresponding analytical cloud relations as suggested by CB are also illustrated in Fig. 2, where

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Interestingly, the analytical results derived for boundary layer clouds also fit the present CRM results for deep precipitating convective situations, suggesting a broad application of these relations. Note that, in the definitions (1)–(2), the precipitating species are not included, otherwise the cloud relations (7)–(8) are not satisfied (not shown). The results for Q₁ > −1 are close to the Gaussian cloud relations discussed in Mellor (1977). The spread in the CRM results for TOGA COARE for positive values of Q₁ (i.e., the ensemble average values are oversaturated) is attributed to the insufficient statistical representation of upper-tropospheric cirrus clouds due to the relatively low vertical model resolution of 700 m above the 12-km level.

Next, the possibility of using Q₂ [see (6)] instead of Q₁ is checked in Fig. 3. The results are similar to that discussed in Fig. 2, especially for N. However, concerning the normalized condensate content a more rapid decrease to zero is observed for Q₂ < 0. Therefore, for actual model applications one would prefer using (7)–(8) as a function of Q₁, however the fractional cloudiness can be reasonably represented using either Q₁ or Q₂.

c. Parameterization of σ_s

The practical application of the cloud relations (7) and (8) in meteorological models requires the knowledge of the second-order moment σ_s. Here, a simple parameterization is suggested based on first-order turbulence closure and the stationarity assumption of the second-order moments:

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where C⁻¹_pm∂h_l/∂z = ∂T_l/∂z + g/C_pm(1 + r_w), l is a length scale, and c_σ is a constant of value 0.2 (Cuxart et al. 2000). Equation (9) only includes quantities that are known in any model. However, an alternative formulation based on the convective mass flux might be obtained following Lenderink and Siebesma (2000). The time-averaged vertical profiles and respective standard deviations of σ_s for the TOGA and ARM experiments are displayed in Fig. 4. All profiles exhibit a quasi-monotonic decrease of σ_s with height between the top of the boundary layer (located at z = 500 m for TOGA and at 1500 m for ARM) and the tropopause level; a typical order of magnitude for σ_s is 4 × 10⁻⁴ (see also CB). The larger time variability for ARM is associated with the passage of a midlatitude disturbance. Furthermore, the small discontinuity in the σ_s profiles corresponds to the 0°C isotherm, but might be exaggerated by the model's microphysical scheme. The parameterized profiles are also plotted in Fig. 4, using a constant free tropospheric length scale l = 900 m, a value that has been determined experimentally as the best fit of (9) to the CRM results. Inside the boundary layer (z < l), l is simply set equal to z, the height of the model layer, but more sophisticated formulations might be more appropriate (e.g., Bougeault and Lacarrère 1989; Holtslag and Nieuwstadt 1986). The results show that (9) gives a reasonable approximation of σ_s provided that the variances are computed from gradients of conserved variables.

Finally, the usefulness of the cloud parameterization is checked by comparing in Fig. 5 the time-averaged vertical profiles of the cloud fraction and the condensate mixing ratio obtained from the CRM to the corresponding profiles obtained using (i) the cloud relations (7)–(8) together with the CRM derived values of σ_s, and (ii) the cloud relations (7)–(8) together with the parameterized values of σ_s using (9). The results show that the parameterization closely reproduces the cloud fraction profiles for both the TOGA COARE and ARM case. However, the condensate profiles are more sensitive to the choice of σ_s. The parameterization slightly overestimates the cloud condensate for TOGA and underestimates the values for ARM, indicating that the length scale l in (9) might vary as a function of stability.

a. Mesoscale simulations

In the following, the cloud parameterization is applied in a mesoscale model and its impact is evaluated based on model simulations of midlatitude and subtropical cloud systems, and subsequent comparisons with satellite observations. The model is the nonhydrostatic mesoscale model Méso-NH, previously described. The free tropospheric vertical grid length is set to 700 m for the midlatitude case and 300 m for the subtropical case. Horizontal grid lengths are 40 and 30 km, respectively. Therefore the model includes a parameterization for shallow and deep subgrid-scale convective transport and precipitation (Bechtold et al. 2001).

The midlatitude case is from the Fronts and Atlantic Storm-Track Experiment (FASTEX) intensive observing period 16 (IOP16). The simulation covers 6480 × 4800 km over the North Atlantic Ocean, is initialized by Météo France/ARPEGE reanalyses at 0000 UTC 17 February 1997, and is integrated forward for 12 h. The subtropical case is taken from the PICO3 (subtropical ozone peaks) experiment. The PICO3 simulation covers 5400 × 5400 km in the subtropical North Atlantic sector. It is also integrated for 12 h starting with European Centre for Medium-Range Weather Forecasts (ECMWF) analyses at 1200 UTC 20 October 2000. The fields included in the initial and boundary conditions of the numerical experiments are only temperature, winds, and water vapor. No cloud initialization of the numerical experiments is performed; that is, the mixing ratio of the liquid and ice water species build themselves during the course of the simulations.

For the two control simulations (CTRL), the cloud scheme is the explicit five-categories microphysical parameterization already used for the CRM simulations. For both the midlatitude and subtropical cases the statistical cloud scheme is applied diagnostically to the fields predicted by the corresponding CTRL simulation after 12 h. However, for the subtropical case an additional simulation (PROG) is run using the statistical cloud scheme in prognostic mode. A prognostic application of the scheme is achieved by replacing the condensation/evaporation tendencies in the prognostic equations for r_c, r_i, r_υ, and T by the following tendencies

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where r_l is diagnosed from (8), χ is the fraction of liquid and solid condensate defined previously, Δt is the model time step, and the asterisks denote values at the previous time step.

b. Synthetic observations

Synthetic radiances corresponding to the Meteosat IR channel, in the thermal infrared window (10.5–12.5 μm), were computed by the narrowband radiative transfer code designed by Morcrette and Fouquart (1985) with 10 spectral bands as described in Chaboureau et al. (2000, 2002). Radiances are then converted to brightness temperatures (BTs), taking into account the filter function of the IR channel. The cloud radiative properties for liquid water are parameterized following Stephens (1978), whereas the radiative properties for cloud ice are based upon Kristjánsson et al. (1999). The maximum-random cloud overlap assumption is assumed.

Synthetic radiances corresponding to the Meteosat visible (VIS) channel, were computed by the large-band radiative transfer code designed by Fouquart and Bonnel (1980) and used by the model to compute the shortwave radiative tendencies. The cloud optical properties are derived from Fouquart (1987) for the cloud water droplets, and from Ebert and Curry (1992) for the cloud ice crystals. This large-band code has been roughly modified to take into account the viewing angle of the satellite. However, the resulting synthetic radiances are sufficiently realistic to be compared with the observations.

In the next subsections, synthetic observations are labeled (i) explicit when obtained from the CTRL simulation using the cloud condensates determined by the explicit microphysical cloud scheme, (ii) diagnostic when obtained from the CTRL simulation using the cloud condensates diagnosed by the statistical cloud parameterization, and (iii) prognostic when obtained from the PROG simulation. Biases between model and observation are also given for either infrared BTs or visible radiances. They are obtained by averaging the differences between simulated and observed radiative quantities over the domains shown in Figs. 6 and 7.

c. Midlatitude case

Figure 6 shows the results of the model-to-satellite approach applied to the midlatitude case at 1200 UTC 17 February 1997, both in the VIS and the IR Meteosat channels. Only the southeastern part of the simulation domain, most illuminated by the sun, is displayed. Several synoptic cloud features, with radiances larger than 60 W m⁻² sr⁻¹ can be observed on the Meteosat images (Figs. 6a,b). First, the cloud system of IOP16 over the British Isles, with BTs less than 255 K, is characterized by a warm front ahead, a cloud head to the northwest of Ireland, and a trailing cold front. Second, the cirriform cloud pattern lying along 45°N between 40° and 20°W, which is associated with the jet stream and the warm front of a secondary low, displays low BTs of less than 235 K and moderate radiances, between 60 and 70 W m⁻² sr⁻¹. Third, the convective cloud fields located in the rear of the Irish low (north of 45°N) and off the Portuguese coast (between 20° and 10°W) are clearly distinct in the visible image (Fig. 6b). These cumulus clouds that developed in convectively unstable areas exhibit moderate BTs between 245 and 275 K.

These synoptic key patterns are also present at the same locations in the two synthetic BT images (Figs. 6c,e) with or without the use of the subgrid-scale cloud parameterization. Indeed, as these cloud systems are largely a result of the dynamical forcing, the good agreement found in the location and the BT intensity of the cloud systems between the observed and explicit IR BTs reflects the quality of the dynamical fields in the Méso-NH simulation. The subgrid-scale cloud parameterization is able to correctly diagnose the condensate mixing ratios at the stratiform cloud tops and slightly improves the representation of BTs in the convective cloud fields. Thus, the domain-averaged bias is reduced to −0.9 K compared to 2.0 K for the explicit experiment.

But the effect of the cloud parameterization has a much larger impact in the visible spectral range where the presence of reflectors such as clouds dramatically modifies the radiances observed from space. In the explicit VIS image (Fig. 6d) only the frontal areas of the cloud system of IOP16 display radiances over 60 W m⁻² sr⁻¹. These large values are also present at the same location in the observed and diagnostic images (Figs. 6b,f). But outside these ascending frontal areas, the explicit VIS image exhibits low radiances of less than 50 W m⁻² sr⁻¹, where large values are observed. This results in a domain-averaged bias of −24 W m⁻² sr⁻¹. This default in representing optically thick clouds is corrected by the use of the cloud parameterization and its ability to realistically diagnose subgrid-scale condensate over the whole tropsopheric column (see discussion in the next subsection). Thus, the diagnostic VIS image shows a larger spatial cloud signature in the ascending stratiform frontal areas but also in the jet stream region. This results in a better overall agreement with the observations, with a bias that is reduced to −4 W m⁻² sr⁻¹. Another improvement given by the cloud parameterization can be seen in the cumulus cloud areas, where the radiances are increased to values above 30 W m⁻² sr⁻¹. However, the spatial variability of the broken clouds as observed in the VIS channel is underestimated by the cloud parameterization, which gives more uniform radiances.

To summarize, the use of the cloud parameterization in calculating synthetic observations leads to a better agreement with the Meteosat images, particularly in broken cloud areas both in the VIS and IR channels, and also in the stratiform frontal zones when looking at the VIS channel.

d. Subtropical case

The results for the subtropical Atlantic case are shown in Fig. 7. The displayed snapshot corresponds to 1200 UTC, after 12 h of simulation. Low observed BTs, less than 255 K, are associated with a frontal system extending from France to the north of the Canary Islands, and with deep convective systems over the ocean south of 25°N and over Algeria (Fig. 7a). Medium BTs around 270 K correspond to a midlatitude cloud system entering the northwestern part of the domain. The cold sector in the rear of the front over western Europe is characterized by cumulus cloud fields with BTs between 275 and 285 K.

In the resulting explicit IR image, the main cloud systems appear at the right location revealing the quality of the simulated dynamical fields (Fig. 7b). However, the cloud patterns generally have a smaller spatial extent with larger BT than the observed ones. Moreover, large oceanic areas of high and homogeneous BTs appear to be typical for clear sky in the explicit simulation, whereas broken cloud fields are observed at the same locations. These discrepancies result in a domain-averaged bias of 11 K.

The differences between the observation and the CTRL simulation are significantly reduced with the aid of the cloud parameterization, as shown by the diagnostic synthetic IR image (Fig. 7c). As already seen for the midlatitude case, the areas with BTs less than 255 K exhibit a larger spatial extent than in the explicit IR image, in particular the frontal system over Western Europe, the northwestern cloud system, and the oceanic and African deep convective systems. Furthermore, shallow and deep convective cloud systems now appear in the North Atlantic cold sector and over parts of the tropical and subtropical ocean. With the aid of the diagnostic cloud parameterization, the domain averaged bias is reduced to 7 K.

Finally, the prognostic synthetic IR image obtained from the PROG simulation (Fig. 7d) is similar to the synthetic IR image diagnosed from the CTRL simulation, in spite of the fact that the modified cloud field now interacts with the dynamics and thermodynamics of the model. Furthermore, the PROG simulation produces an overall smoother cloud field, (avoiding, for example, the unphysical oscillations near 40°N, 25°W in Figs. 7b,c) and more realistically represents the cold frontal band and the southeasterly propagating cloud field in the nortwestern part of the domain. As a consequence, the domain-averaged bias is further reduced to 5 K.

The vertical structure of the simulated cloud fields is examined with the aid of a vertical cross-section along 20°W from 7° to 48°N across the tropical deep convective cloud systems, the trailing cold front, and the post-frontal shallow convective region (Fig. 8). The CTRL simulation represents the tropical convective system (located between 0 and 900 km) by a lower and upper tropospheric cloud layer (Fig. 8a). In contrast, the PROG simulation produces a more homogeneous vertical structure of the convective cloud systems (represented by the sum of the liquid+ice condensate mixing ratios) with cloud bases at 500 m and cloud tops that attain 15 km. Furthermore, the PROG simulation produces a second deep convective system at 1800 km and a shallow convective cloud field north of the cold frontal band located at 2700 km. All these features are missing in the CTRL simulation. However, it is possible that the PROG simulation overestimates the subtropical low-level cloud fields between 900 and 2500 km due to the simple mixing formulation in (9).