CloudSat radar reflectivities are simulated in the Met Office global forecast model in a manner which is consistent with the CloudSat observations. The method is described and applied in an evaluation study of the model's performance over the period December 2006 to February 2007. The study uses both statistical and case study approaches and examines the model's simulation of cloud systems globally and in three regions of contrasting weather and cloud regimes: the tropical warm pool, the North Atlantic Ocean, and the stratocumulus region off the west coast of California. In general, the model shows a good representation of the vertical structure of clouds systems, although a lack of midlevel cloud is ubiquitous. The model shows a nondrizzling cloud mode and a clearly separated drizzling mode that is not seen in the observations, independent of the geographical region. The comparisons suggest that the intensity of drizzle is too high, confirming on a global basis what recent ground-based measurements have also shown. They also suggest that the parameterization of ice cloud fraction as a monotonic function of the grid box mean ice water content is not consistent with the observations.
 In common with forecasting centers around the world, the Met Office is constantly seeking to improve the representation of cloud systems in its numerical weather prediction models. A key aspect of this effort is the evaluation of model performance against the best available and most useful observational data from satellites. Recent studies using both narrowband radiances [Ringer et al., 2003] and broadband radiative fluxes [Allan et al., 2005] have highlighted important strengths and deficiencies of the current generation of models. For example, the location and basic characteristics of large-scale midlatitude systems is generally well represented, although the precise positions and detailed structures, which may both be crucial to improving forecast accuracy, still indicate potential for some improvement. In the tropics, however, the situation is far more challenging: here, errors in the location, timing, and evolution of convection and its associated cloud systems leads to much greater divergence between the observed and simulated cloud fields.
 While such studies are clearly very useful for identifying model weaknesses, the lack of a three-dimensional view makes it difficult to translate the results into information that can be specifically used to improve cloud parameterizations, in particular the relationships between cloud water and ice and the physical and radiative properties of the clouds. The CloudSat mission [Stephens et al., 2002] provides such a 3D view, and as the first global survey of the vertical structure of cloud systems it should allow us to both evaluate models in more detail and, perhaps even more importantly, improve the representation of cloud processes through more physically based parameterizations.
 For these reasons we have developed a system which allows us to make full use of CloudSat data for the evaluation of clouds in the UK Met Office Unified Model (MetUM). We adopt the model-to-satellite approach; that is, we simulate as closely as possible the data produced by CloudSat, including taking into account the orbital path of the satellite. The benefit of this approach is that it allows a truly like-for-like comparison, in this case between simulated and observed radar reflectivities, taking into account processes that affect the radar signal and removing the effect of inconsistent assumptions in the modeled and retrieved cloud properties. This is the approach commonly taken in numerical weather prediction and data assimilation [Eyre and Lorenc, 1989], and is now increasingly used in climate model evaluation [Webb et al., 2001; Ringer et al., 2003]. Williams and Brooks  define cloud regimes as principal clusters of joint cloud top pressure-optical depth histograms. They show that regime properties are found to be similar in the MetUM at all forecast times, including the climatological mean. This suggests that weaknesses in the representation of fast local processes in the MetUM are largely responsible for errors in the simulation of the cloud regimes. As the Met Office uses the same model for both weather forecasting and climate prediction the global forecast model is a useful framework in which to analyze cloud representation errors that are relevant for both numerical weather prediction and climate time scales.
 Here we use this approach to evaluate the performance of the Met Office global forecast model over the period December 2006 to February 2007. The primary aims of this study are to demonstrate the use of simulated CloudSat reflectivities using a state-of-the-art forecasting system and to suggest ways in which such an approach, and the chosen analysis methods, may be applied to other models. The remainder of this paper is organized as follows: section 2 describes the simulation of the radar reflectivities; section 3 describes the model, methodology and observations; global and regional comparisons of the CloudSat data and the model are presented in section 4; sensitivity tests are carried out in section 5 and conclusions are presented in section 6.
2. Simulation of CloudSat Radar Reflectivities
 This section details the methods employed to compute the different contributions to the total reflectivity and attenuation terms of the radar signal. We have followed as closely as possible the assumptions made in the model microphysical scheme. The gamma distribution function is used for the representation of the cloud particle size distribution, its mathematical expression being:
where D is the diameter of the particle, N0 is the intercept parameter, and ν and Λ are free parameters.
 This form of the size distribution allows us to obtain the ith statistical moment of the distribution analytically:
2.1. Reflectivity Due to Liquid Clouds
 The radar effective reflectivity factor, Ze, is given by:
where a Khrgian-Mazin distribution is used for water droplets (ν = 2). The use of ν = 2 is somewhat arbitrary, as neither the cloud nor the radiation schemes use an explicit particle size distribution. We choose this value because it is used in the MetUM sulphur cycle. Typical values for ν range from 1 to 15 [Miles et al., 2000]. Using ν = 10 decreases Zel by 4.5 dBZ. The factor ∣Kl(f, T)∣2/0.93 is a calibration factor, Kl(f, T) being the dielectric factor of liquid water at temperature T for a frequency f. This calibration factor ensures that at centimeter wavelengths the reflectivity reduces to the familiar form Z = μ6 [Hogan et al., 2006].
 Two additional equations are needed to obtain Zel, namely expressions for the total cloud droplet number concentration, N,
and the liquid water content (LWC),
 Using (4) and (5) in (3), the radar reflectivity of water clouds can be obtained as:
 In order to express Ze in the more common units of dBZ, it first has to be converted to [mm6m−3].
2.2. Reflectivity by Ice Clouds
 In the case of ice clouds, the particle size distribution used in the microphysics scheme [Wilson and Ballard, 1999] is exponential (ν = 0), the intercept parameter being a function of temperature:
with N0i(T) = N0i exp(−0.122 T), N0i = 2.0 × 106 m−4, and T is in °C.
 In the case of ice clouds, using the Debye approximation [Debye, 1929] the radar reflectivity factor is expressed as:
where the mass is parameterized as mi(D) = aD2 (a = 0.069 kg m−2) [Wilson and Ballard, 1999]. Therefore, only one additional moment of the distribution is needed to compute Zei. This is obtained from the definition of ice water content (IWC):
 The dielectric factor of solid ice, ∣Ki∣2, is independent of the frequency and temperature with a value of 0.174. A non-Rayleigh scattering correction is applied following the methodology proposed by Benedetti et al. .
2.3. Reflectivity by Precipitation
 For large particles, the radar reflectivity factor no longer follows the sixth power law in (3), and therefore a different approach must be followed. For a given frequency, the reflectivity factor is proportional to the reflectivity η, which is the total backscatter cross section of all scatterers in unit volume. We have used a lookup table of scattering cross sections for spherical particles to develop a parameterization of η = η(P; T), where P is the precipitation water content (liquid or ice). Although parameterizations for both rainfall and snowfall were derived, only that for rainfall is used in this study because the falling ice is treated as cloud in the MetUM. The lookup table for f = 94 GHz was computed using the Mie codes of Barber and Hill , integrated over a Marshall-Palmer distribution for different rain rates and temperatures (M. Rogers, personal communication, 2005). The model uses a diagnostic representation of rain and does not assume a particle size distribution. We have chosen the Marshall-Palmer distribution, which is commonly used to characterize rainfall. The parameterizations have been obtained from nonlinear least squares fits to equations of the form η = E1(T) and E2(T) being fitting parameters obtained for 19 temperature values between 200 and 300 K.
 The reflectivity factors described above are derived under the assumption that the space between the radar antenna and the target is a vacuum. However, at millimeter wavelengths the radar signal can be attenuated because of the interaction by several atmospheric components: absorption by gases (H2O and O2), and extinction by water droplets and precipitation. Therefore, the reflectivity factor corrected by attenuation will be:
where Ai =σei(s) ds is the integral extinction along the portion of atmosphere between the antenna and the target for component i. The factor 2 accounts for the two-way attenuation as the signal travels twice through the same atmospheric mass. Gaseous attenuation is accounted for by using the model proposed by Liebe . In the lower troposphere, attenuation by gases ranges from ≈1 dB in cold and dry atmospheres to ≈6 dB in tropical atmospheres.
 For the computation of the attenuation by precipitation, we have followed an approach similar to that used in the computation of the reflectivity. The extinction coefficient σeprecip is modeled from the data of lookup tables. Attenuation by rainfall is very strong, and can be of the order of tens of dBZ in heavy precipitation.
 Attenuation by clouds is mainly caused by absorption by liquid droplets, and can be of the order of 5 dBZe. The scattering effects are much smaller at radar wavelengths. The extinction coefficient is obtained by its Rayleigh approximation, neglecting scattering,
2.5. Subgrid Sampling
 Cloud structure at the subgrid scale is parameterized by large-scale models. Models show large biases if only vertical profiles of grid box mean cloud values are used in radiation calculations [Cahalan et al., 1994; Barker and Räisänen, 2005]. To overcome this, large-scale models employ cloud overlap assumptions, which influence the fluxes of radiation and precipitation through the atmosphere [e.g., Ritter and Geleyn, 1992]. When simulating satellite data in large-scale models, this subgrid-scale variability has to be included and treated in a consistent manner.
 The scheme that we use to introduce subgrid variability in the computation of the radar reflectivity is the Subgrid Cloud Overlap Profile Sampler (SCOPS), a technique developed for the International Satellite Cloud Climatology Project (ISCCP) simulator [Klein and Jakob, 1999; Webb et al., 2001]. Each grid box is divided into a number of vertical columns (of the order of tens to a few hundred, depending on the particular application) and a subgrid distribution of clouds is generated within the model grid box [Klein and Jakob, 1999]. SCOPS [Webb et al., 2001] uses a pseudorandom sampling process, fully consistent with the maximum, random and maximum/random cloud overlap assumptions used in many models [e.g., Pincus et al., 2005]. Maximum overlap is applied to the convective cloud, and maximum/random is used for large-scale cloud. At a given level, the convective and large-scale cloud water contents are distributed evenly in the subcolumns that are occupied by convective and large-scale cloud, respectively. This implies that the subgrid distribution only accounts for the cloud overlap assumptions, but not for the subgrid probability density function of condensate itself. As rain drops and snow particles produce a strong signal at radar frequencies, they also have to be taken into account in the subgrid sampling algorithm. We have developed a simple algorithm that provides subgrid distribution of precipitation fluxes compatible with the cloud distribution output by SCOPS and the grid box mean precipitation fluxes simulated by the model. The amount of precipitation at a particular level is distributed horizontally in proportion to the amount of cloud above each particular subcolumn. This makes the subcolumns with a larger proportion of cloud above them to have larger precipitation fluxes.
 Once this subgrid sampling has been carried out, the outputs can be aggregated to produce a final product at the original (grid box) resolution for visualization. Because of this subgrid vertical structure and the fact that radar reflectivity is a nonlinear function of cloud/precipitation condensate, the aggregated reflectivity will not be the same as that calculated from grid box mean profiles. All the statistical analysis in this paper uses the reflectivities at subgrid resolution.
3. Description of Model, Methodology, and Observations
 The model used in this study is the MetUM global forecast model at cycle G42, operational from December 2006 to May 2007. The horizontal resolution is 0.5625° longitude by 0.375° latitude, corresponding to approximately 40 km in midlatitudes. There are 50 vertical levels with the model top at around 63 km (0.01 hPa). The dynamical core is a two-time level semi-implicit, semi-Lagrangian (SISL) formulation and is also nonhydrostatic [Davies et al., 2005]. A summary of the physical parameterizations is given in Table 1. The formulation of the global NWP model outlined here is similar to the atmospheric component of the coupled climate model HadGEM1 [Martin et al., 2006] and also includes developments from the next generation coupled climate version.
Table 1. Summary of Physical Parameterizations
Cloud microphysical scheme
Wilson and Ballard ; models the transitions between water vapor, liquid, ice and rain with the cloud ice content a prognostic variable
Met Office Surface Exchange Scheme (MOSES II [Essery et al., 2003]); NWP model soil moisture initialized using a soil nudging technique
 The methodology is similar to that used in previous comparisons of the NWP model with Geostationary Earth Radiation Budget (GERB) data [Allan et al., 2005]. Model diagnostics are produced every 3 h from a two–time step forecast run from each of the four analyses per day at 0000, 0600, 1200 and 1800 UTC and from each of subsequent forecast states at T+3. These analyses are generated using the scheme of Rawlins et al.  from the previous T+3 forecast states using a 6 h assimilation window. Using short-range NWP forecasts has the advantage, for the purpose of evaluating the model parameterizations against observations, that the large-scale atmospheric circulation is represented as accurately as possible within the limits of a modern data assimilation system. This enables a less ambiguous attribution of any discrepancies found to the model parameterizations rather than their inputs. Model outputs are sampled along the orbit track, choosing the model time that is closest to the observation time. As the model output frequency is 3-hourly, the time mismatch between model and observations is less than 1.5 h. A sensitivity test increasing the output frequency up to 30 min of model data to minimize the mismatch was carried out. We looked at the impact on cloud amount and found no significant difference.
 CloudSat and the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) fly in nearly identical Sun-synchronous orbits at 705 km altitude within the A-Train [Stephens et al., 2002]. CloudSat carries the first millimeter wavelength cloud profiling radar (CPR) in space, which operates at a frequency of 94 GHz [Im et al., 2005]. The CPR points in the nadir direction, and its pulses sample a volume of 480 m in the vertical, with a horizontal resolution of 1.4 km across track. The primary instrument on board CALIPSO is the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP), the first polarized lidar in space, operating at 532 nm and 1064 nm [Winker et al., 2007]. CALIPSO is able to detect thin cloud layers with optical depths of 0.01 or less, provided that the signal is averaged along track [McGill et al., 2007]. We use the CloudSat 2B-GEOPROF data set [Mace et al., 2007] and the CALIPSO Vertical Feature Mask (VFM) [Vaughan et al., 2004]. The 2B-GEOPROF data set provides the radar reflectivity, in dBZ, and identifies where hydrometeors occur (“cloud mask”). The CALIPSO VFM provides a target classification that gives information on the location and properties of aerosol and cloud layers. The ISCCP D1 cloud products [Rossow and Schiffer, 1999] are also used, along with radiative fluxes from the Clouds and the Earth's Radiant Energy System (CERES) Edition2D SRBAVG [Wielicki et al., 1996] and the Earth Radiation Budget Experiment (ERBE) S-4 [Barkstrom and Smith, 1986] data sets.
 We construct joint height-reflectivity histograms in 2.5° longitude by 2.5° latitude regions. We divide the vertical axis of these histograms into bins of 1 km, and the horizontal axis into bins of 2.5 dBZe. The value of the CPR cloud mask of the 2B-GEOPROF product gives a measure of the confidence on the cloud identification. We consider a positive identification when the value of the cloud mask is greater or equal than 20, which gives an estimated false detection rate smaller than 5% [Marchand et al., 2008]. Hydrometeor fraction in each layer is then defined by the number of positive identifications with reflectivity greater than or equal to −27.5 dBZe divided by the total number of measurements in that layer. The −27.5 dBZe threshold is also applied to compute cloud fraction from the model reflectivities, which makes the comparisons more consistent by accounting for the sensitivity of the instrument.
4.1. Global Perspective
 The geographical pattern of the vertical distribution of hydrometeors simulated in the model is generally similar to the CloudSat observations (Figure 1), although there are notable differences. At midlatitudes, for example, hydrometeor fraction is underestimated below 5 km in both hemispheres. In tropical deep convection regions hydrometeors are underestimated at lower levels, overestimated above 8 km and underestimated once again in the upper troposphere. This latter discrepancy indicates that convection does not reach the altitudes suggested by the observations. The model appears to conform well to the spatial pattern of clouds above 7 km. The zonally averaged hydrometeor distributions (Figure 2) show a marked underestimate below 5 km in the midlatitude storm track regions. CloudSat shows a clear asymmetry in hydrometeor fraction between the two descending branches of the Hadley circulation. In the winter hemisphere descending branch, where the Hadley circulation and its associated subsidence strength is stronger [Peixoto and Oort, 1992; Kållberg et al., 2005], the presence of hydrometeor is negligible in almost the entire vertical column, with only values near 0.1 below 3 km. The model seems to capture this asymmetry in the circulation, although because of its inability to produce midlevel cloud, this asymmetry is not so evident in the cloud distribution. On the other hand, the convection scheme detrains too much moisture at high levels (A. V. Maidens and S. H. Derbyshire, Improving mass flux profiles in the Gregory-Rowntree convection scheme using adaptive detrainment, submitted to Quarterly Journal of the Royal Meteorological Society, 2008), and therefore produces too much cloud at these levels in the tropics.
 Area-weighted joint height-reflectivity histograms are shown in Figures 2c and 2d. The observations sample a triangular region in this 2-D space. This region is limited on its left-hand side by the sensitivity limit of the CPR (approximately −30 dBZ). There seems to be a linear relationship between maximum reflectivity and height that we shall analyze in more detail below. Low levels, below 3 km, seem to show a slightly bimodal distribution, with a peak around −25 dBZ, and a second maximum near 5 dBZ. A very light drizzle flux of 0.001 mm h−1 can dominate the radar reflectivity at 94 GHz and produce a reflectivity of −20 dBZ [O'Connor et al., 2005]. The LWC needed to produce a reflectivity of −20 dBZ is around 0.3 g m−3, so −20 dBZ can be considered as an approximate threshold to define a drizzling cloud. The transition in the observations is smooth (nondrizzle-drizzle-rainfall), with highly populated bins in between. The lowest 1-km layer is not shown in the CloudSat plot because of the effect of the contamination by ground clutter. The model shows a completely different picture, sampling three main preferred regions of the height-reflectivity space. In the mid and high levels, the model explores a much smaller range of reflectivities, with the majority of points clustered around a much tighter height-reflectivity relationship. At lower levels, the model seems to operate in two regimes, one with nonprecipitating cloud (reflectivities ≈−30 dBZ), and the other for precipitating cloud (reflectivities ≈0 dBZ).
 We now look in more detail at three oceanic regions: the tropical warm pool (70–150°E, 5°S–20°N), North Atlantic (300–350°E, 40–60°N), and Californian stratocumulus (220–250°E, 15–35°N). These regions are of particular interest because they show different weather and cloud regimes, with a region where convection is a dominant feature, a midlatitude region where synoptic storms are frequent, and a subtropical region with boundary layer cloud.
4.2. Tropical Warm Pool
 The reflectivity-height histograms (Figures 3a and 3b) share some common characteristics with the global ones. The observations show two different modes at low levels with two distinct maxima for reflectivities ≈−27 and 0 dBZ, although the disjoint character of these two low-level distributions is still more pronounced in the model simulations. The strength of the signal grows as height decreases because of aggregation that produces larger particles. Once the falling ice reaches the freezing level, located at ≈5 km in the tropical atmosphere, it melts and falls as rain. This relationship is also present in the observations, although they also show smaller reflectivities at those levels. This region of the histogram that is not sampled by the model is the region that Zhang et al.  label as cumulus congestus in their clustering analysis of CloudSat data. Attenuation in rainfall is significant, and explains the decrease in reflectivity as we move downward below the freezing level. The frequency of occurrence increases below 5 km (Figure 3e), which seems to be consistent with the existence of a second precipitation mode from clouds with tops below 5 km [Haynes and Stephens, 2007]. A lack of hydrometeors below 7 km is also seen in Figure 3e, underestimating their occurrence by a factor of 3. Between 8 and 10 km, the model overestimates the hydrometeor occurrence, although the location of the maximum (≈11.5 km) is well captured. Above 13 km, the model hardly produces any cloud, whereas CloudSat still observes significant amounts.
Figures 3c and 3d show cloud top pressure versus cloud optical thickness histograms from the ISCCP-D1 data set and MetUM. MetUM results are computed using the ISCCP simulator [Klein and Jakob, 1999; Webb et al., 2001] applied to the atmosphere-only version of the Hadley Centre Global Environmental Model version 2, HadGEM2-A, because these diagnostics were not available from the global forecast model. Top of atmosphere (TOA) shortwave and longwave cloud forcings (SCRF and LCRF) from observations (CERES and ERBE) and MetUM are displayed in the embedded table. The data are for the following DJF climatologies: 1985–2004 for ISCCP, 2000–2004 for CERES, 1985–1989 for ERBE, and 1978–1997 for HadGEM2-A. The use of climate model ISCCP histograms is justified on the basis of the results from [Williams and Brooks, 2008]. The ISCCP histograms also show the lack of midlevel top cloud in the model, although we cannot tell from ISCCP how much midlevel cloud there is under any thick high-top cloud. The CloudSat simulator indicates that there really is very little cloud simulated at midlevels, and the model tends to produce shallow cumulus only. Both the lack of cloud with tops at midlevel and the fact that deep convective clouds do not reach high enough (Figure 3e) contribute to make the longwave cloud radiative forcing (LCRF) a little low. The model simulates a substantial amount of thin cirrus, consistent with ISCCP. It is reassuring that CloudSat does suggest there should be a lot of cirrus here as there is believed to be a large uncertainty in the amount of thin cirrus observed by ISCCP [e.g., Zhang et al., 2005; Williams and Webb, 2008].
4.3. North Atlantic
 The overall structure of the height-reflectivity histograms (Figures 4a and 4b) shares some features with the tropical warm pool: there are three (less distinct) main clusters, and a height-reflectivity relationship for ice clouds, with the model showing less spread in the reflectivity values. The split into two regimes at lower levels is still visible in the model histogram, with a very small contribution from nondrizzling cloud. This implies that basically all the low-level cloud produced by the model precipitates, and that the intensity of this precipitation is too large compared with the observations.
Figures 4c and 4d show that the model does not produce thick cloud with tops above 300 hPa, whereas ISCCP shows a substantial amount of cloud with tops at those levels that CloudSat does not seem to observe. The ISCCP simulator gives a local minimum in cloud with tops at around 5 km compared with the ISCCP observations, although this lack of midlevel cloud is not as apparent as in the tropical warm pool. The CloudSat simulations suggest the model actually produces a substantial amount of cloud around 5 km (Figure 4e), which implies the model is producing midlevel cloud as part of frontal systems and it is specifically cloud with tops at midlevels which is lacking.
 A more detailed understanding of the differences in the height-reflectivity histograms can be achieved by analyzing a case study. Figure 5a shows the Met Office surface analysis chart for the North Atlantic and part of Europe for 26 February 2007 at 1200 UTC. A depression (966 mbar) is located east of Labrador and south of Greenland, between 50°N and 60°N. The system is in its mature stage, with an occluded front in the core, the cold front extending southward from 60°N, with the warm front ahead reaching the Bay of Biscay. The large-scale cloud distribution is fairly well captured with respect to MODIS (Figures 5b and 5c), except for the lack of cloud behind the cold front. The A-Train passed over this system at 1415 UTC, and the red line in Figure 5a shows the approximate track followed by CloudSat in its ascending node.
 The radar reflectivities as simulated from the model variables along that transect are shown in Figures 6a (sub–grid box resolution) and 6b (grid box resolution). The observations from CloudSat are shown in Figure 6c, and Figure 6d shows the target classification as provided by the CALIPSO VFM. Overall, the model represents the 3D structure reasonably well, although there are noticeable differences from the observations. From 0 to 500 km, the model simulates a cloud deck that is not seen by CloudSat. As CALIPSO is able to detect thinner clouds than CloudSat, Figure 6d helps to identify whether these cirrus clouds are spuriously generated by the model or present in reality. Although CALIPSO (Figure 6d) sees high cloud in this first part of the transect, it is thinner than the cloud simulated by the model and higher, above 10 km. The sector from 500 to 1000 km is characterized by a multilayered cloud structure, with a high cloud layer between 9 and 12 km. Underneath this layer, is a second layer, between 5 and 7 km that is clearly visible by both CloudSat and CALIPSO. This midlevel cloud shows radar reflectivity factors between −20 and 0 dBZe, and attenuates the lidar signal most of the time. These two effects combined are an indication of mixed phase cloud [Hogan et al., 2003]. Although the model produces cloud in this part of the system, it does not capture the multilayered structure seen in reality. The model also shows a strong signal in the radar reflectivity factor below the freezing level that is not seen in the CloudSat measurements. This signal comes from spurious drizzle generated by the model from boundary layer clouds. We cannot be certain whether or not these clouds are present in reality as the ability of CloudSat to detect nonprecipitating boundary layer cloud is limited [Stephens et al., 2002], and the CALIPSO signal at these levels has been attenuated by the mixed phase cloud above. The sector from 1000 to 1400 km is characterized by the presence of hydrometeors from around 13 km (seen by CALIPSO) down to the ground. The CloudSat signal below 7 km seems to be dominated by precipitation, which sometimes causes strong attenuation at low levels. The freezing level can be clearly seen in the CloudSat signal in this part of the transect dominated by precipitation, with a significant increase in reflectivity with respect to the values just above the freezing level (bright band). The origin and characteristics of the 94 GHz radar bright band (or its nonexistence in nonprecipitating clouds) is a topic of research currently under discussion in the literature [Sassen et al., 2005, 2007; Kollias and Albrecht, 2005]. The simulations show a more abrupt jump caused by the phase change from falling ice above the freezing level, to rainfall below it. This discontinuity is also caused by the different forward models used for these two hydrometeors.
 The simulated reflectivity values are significantly smaller than the observations for temperatures between −40°C and −20°C. The Cloudnet project provides systematic evaluation of cloud profiles in seven forecast models using ground observations (radar, lidar and microwave radiometer) [Illingworth et al., 2007]. Cloudnet results for December 2006 over Chilbolton, UK, show that the MetUM global forecast model generally underestimates IWC by approximately a factor of 2 or more. Despite the fact that the mean uncertainty of current retrievals of IWC using radar is large (±66% as reported by Heymsfield et al.  in an intercomparison study), the underestimation of simulated IWC seems to be the most likely explanation for the low bias in the reflectivities. This is also supported by recent comparisons of model IWC against aircraft measurements [Baran, 2008].
Figure 7 shows the reflectivity-height histograms for this case study. Comparisons against the histograms in Figure 4 show that the case study is representative of the average DJF histograms over the whole region. The model clearly shows a strong height-reflectivity relationship, which is more diffuse in CloudSat. When CloudSat explores the left-hand side region of the main ice cloud branch in Figure 7a (clouds between 500 and 1000 km in Figure 6c), the model still produces reflectivities in the main branch but less cloud cover (Figure 6a). There are several factors that contribute to this behavior. The N0ice = N0ice(T) relationship that the particle size distribution function uses implies a unique size distribution for a given water content and temperature. In reality there is considerable variation in the particle size distribution for a given ice water content and temperature [Field, 1999; Field et al., 2005], and representing this would diffuse out the relationship seen in the model. In order to get this variation from the model a dual moment scheme would be needed, that is, a scheme that predicts ice number concentration as well as ice water content. An additional factor that contributes to this lack of spread is the parametrization of ice cloud fraction as a monotonically increasing function of the grid box mean IWC that is used in the model, which prevents small IWCs from having large cloud fractions. This makes the average values shown in Figure 6b more reasonable in the regions between 500 and 800 km. However, the smaller reflectivities and hence the better agreement with the observations in that region are due to the small model cloud fractions, which do not seem to be consistent with the observations.
4.4. Californian Stratocumulus
 CloudSat shows a reflectivity-height histogram with only two clusters (Figure 8a), one that comprises clouds above 5 km height, and another for hydrometeors (cloud and drizzle) below 3 km, with the rainfall cluster almost missing. The average profile of hydrometeor fraction as function of height (Figure 8e) clearly shows the two modes observed in this region. The upper cluster corresponds to cirrus clouds, which are common in that region during DJF [Wylie and Menzel, 1999], while the clusters at lower levels corresponds to the stratocumulus deck and associated drizzle, characteristic of the eastern basins of the subtropical oceans. The model also shows the upper level cluster (Figure 8b), although with less spread in the reflectivities for a given height, as in the other regions. Again, the model produces two clusters in the lower levels, confirming the binary transition between nondrizzling and drizzling cloud. The fact that the reflectivities for drizzling cloud span a small range of high values implies that the intensity of drizzle in the model is too high, even though the frequency of drizzling cloud might be underestimated. Hogan et al.  show that the overestimation of drizzle flux at cloud base is a common feature in several models.
 The ISCCP comparisons (Figures 8c and 8d) show an excess of simulated thick cloud, particularly at low levels, which causes the SCRF to be too strong in the model. However, the fact that the drizzle intensity is too large implies that any attempt to reduce the drizzle intensity by reducing the autoconversion rate may have a negative impact on the radiation budget by increasing the SCRF. The ISCCP simulator suggests a similar relationship between height and optical thickness to the one observed in the model height-reflectivity histogram. The radiation code uses a parameterization of the effective diameter with temperature [Kristjánsson et al., 2000; Edwards et al., 2007] that is less sensitive to temperature than the one implied by the exponential particle size distribution used in the microphysics scheme [Wilson and Ballard, 1999], and used in this study. This, and the fact that larger effective diameters at lower levels tend to reduce the optical thickness, implies that the lack of spread in the reflectivity-height branch is probably caused by the ice cloud fraction parameterization.
5. Sensitivity Tests
 We have conducted several sensitivity studies to assess the robustness of our comparisons. Figure 9 shows reflectivity-height histograms for the tropical warm pool region, computed using two different reflectivity models for ice cloud, namely, the Rayleigh approximation (equation (10)), and the 94 GHz empirical formula with unbiased variance of Hogan et al. [2006, Table 2]. Using colocated aircraft IWC measurements and reflectivities from the Chilbolton radar, Hogan et al.  develop empirical relationships IWC = IWC(Z,T) for several radar frequencies, which can be inverted to express Z = Z(IWC,T). The Rayleigh approximation breaks down in the region between 5 and 10 km, where it gives very large reflectivities. This is caused by the large particles implied by the parameterization of aggregation in the particle size distribution used for ice clouds. The intercept parameter N0i is a function of temperature (N0i(T) = N0i exp(−0.122 T), T in °C), decreasing as T increases, which implies that a cloud with given IWC will have a greater proportion of large particles at warmer temperatures. Therefore, the non-Rayleigh effects become more relevant as T increases, and it is in this region where the results from the empirical formula differ most from the Rayleigh approximation. The theoretical correction by Benedetti et al.  that we apply to our computations (Figure 3b) seems to perform well as compared to the empirical formula of Hogan et al.  used in Figure 9b, although it tends to produce smaller reflectivities between 5 and 7 km. With the ice particle size distribution used, the effective diameter, De, is proportional to (IWC/N0i(T))1/3. That means that high IWC and temperatures close to 0°C will produce large De. Indeed, high IWC values occur in this range of temperatures, so both terms contribute to this effect. At those levels, the effective diameters produced by the particle size distribution are large, greater than 3 mm, making the polynomial expansion on the effective diameter used in the correction for Mie effects less accurate. These changes only affect the histogram, whereas the vertical profile of frequency of occurrence remains unchanged as the differences occur in the region with Z > −27.5 dBZ. In spite of these differences with respect to the empirical formula, the main conclusions from the analysis of the histogram remain unchanged.
 The impact of the shape of the particle size distribution in the reflectivity computations has also been tested by multiplying or dividing by five the intercept parameter and the exponent that accompanies temperature in the ice cloud particle size distribution, which we define as C0 in this discussion, as shown in Figure 10. The changes in the histogram can be interpreted taking into account equation (10) and the impact of the correction for Mie effects presented above. When the intercept N0i is divided by 5 (Figure 10a), the PSD is skewed toward larger particles, and the Rayleigh reflectivity increases by 4.5 dBZ. This is seen at high levels, where the histogram is shifted 2 boxes to the right. Below 10 km, the correction for Mie effects is stronger than in the original simulation. When the intercept N0 is multiplied by 5 (Figure 10b), the effects are the opposite in the Rayleigh scattering regime, and the correction for Mie effects are less intense as the ice PSD moves toward smaller particles. Figures 10c and 10d can be qualitatively interpreted in a similar manner. Decreasing C0 acts in the same way as decreasing N0i, but with the additional complexity of increasing its impact with height, as T decreases. Figure 10c shows how the ice branch moves toward a Mie scattering regime, whereas in Figure 10d the entire branch has moved toward a Rayleigh scattering regime. In summary, changes in C0 have a huge impact in the reflectivity. Hogan et al.  compute the best estimates for N0i and C0 on the basis of observations of Z and IWC, obtaining 4.4e6 and 0.115, respectively. Our results are consistent with these values, as any change in C0 seems to worsen the simulation, and an increase in N0i would produce smaller effective diameters, improving the simulation between 5 and 10 km.
 In order to test the impact of large-scale rainfall on the bimodality in the histogram below 4 km, a sensitivity study with large-scale rainfall set to zero has been carried out (Figure 11). Most of the low-level mode with reflectivities around 0 dBZ disappears, with only the contribution from convective precipitation remaining.
 We also tested the impact of the poor spatial sampling provided by CloudSat. We computed the height-reflectivity histograms for December, January and February independently (both for model and observations) in this region (not shown), and compared them against DJF. All the histograms show the same main features, which indicate little impact of sampling over this large region on monthly means. February is the month which differs most (particularly in the observations), with a lack of falling ice associated with anvils in midlevels. These differences are probably not due to sampling to but real changes in the meteorology.
 The impact of the overlap assumptions on the results has been tested by comparing the max/random overlap results (standard configuration) with those of using maximum or random overlap (not shown). Only random overlap produces significant differences in the rainfall mode (lower right corner of the histogram), increasing slightly the hydrometeor frequency of occurrence below 2 km. This is due to the fact that attenuation by clouds is small (liquid) or negligible (ice), and therefore it is not relevant for the reflectivity at a particular level how clouds are distributed above that level. This is not the case for rainfall, which attenuates the signal strongly, and therefore the overlap assumption is important.
 We have developed a system that allows us to make full use of CloudSat data for the evaluation of clouds and precipitation in numerical models, and have applied it to the UK Met Office global forecast model. We simulate as closely as possible the data produced by CloudSat, consistent with the microphysical assumptions used in the model, and taking into account the spatiotemporal sampling of the satellite orbit.
 This study illustrates our approach and documents some aspects of the behavior of UK Met Office global forecast model:
 1. The model shows a good overall representation of the vertical structure of midlatitude systems, with high cloud top height very well captured.
 2. The low-level distribution of hydrometeor reflectivities is strongly bimodal, with a nondrizzling cloud mode and a drizzling mode clearly separated, independent of the geographical region. This suggests that the intensity of drizzle is too high, confirming on a global basis what recent ground-based measurements have shown [Hogan et al., 2007].
 3. The model shows a general underestimation of hydrometeor occurrence below ≈7 km. The underestimation is greater at midlevels in deep convective cloud, consistent with the lack of detrainment of moisture by the convection scheme at midlevels. This probably has the side effect of producing too much cloud at high levels, where most of the moisture is detrained (Maidens and Derbyshire, submitted manuscript, 2008).
 4. The model underestimates deep convective cloud top height in the tropics, where cloud top heights are 1–2 km lower on average than CloudSat.
 5. The strong height-reflectivity relationship in the model simulations indicate that the parameterization of ice cloud fraction as a monotonic function of the grid box mean IWC is not consistent with the observations, which show much more spread in this relationship.
 6. The results suggest that the model underestimates the ice water content in frontal systems.
 This study is a demonstration of a possible way to use CloudSat data to evaluate numerical models, and we plan to extend this analysis to other regions/seasons and also to our climate model. There are also other topics that deserve attention. For instance, many microphysical process rates are dependent on the moments of the particle size distribution, and the radar reflectivity is a measure of one of those moments [Field et al., 2007]. Therefore, CloudSat can provide information about microphysical processes on a global basis [e.g., Stephens and Haynes, 2007] and their relation to the dynamics through their impact in the radiative heating profiles. Another aspect in which CloudSat may play an important role is in the study of subgrid variability of cloud condensate, which may be used to develop new parameterizations that treat overlapping assumptions and subgrid distribution of condensate in a consistent manner.
 This approach can also be extended to the evaluation of climate models. In the context of the Cloud Feedback Model Intercomparison Project (http://www.cfmip.net), several climate modeling centers (Hadley Centre, LMD/IPSL, LLNL, CSU) have joined together to develop a community ISCCP/CloudSat/CALIPSO simulator designed to be easily plugged in to numerical models, from high-resolution models to climate models. This community simulator has a similar structure to the one presented here, but uses QuickBeam [Haynes et al., 2007] to simulate the radar signal. The code used to simulate the lidar signal is an evolution of the one developed by Chiriaco et al. , and subsequently used by Chepfer et al. . A new precipitation overlapping algorithm is being developed by Y. Zhang and S. Klein at LLNL, and A. Bodas-Salcedo.
 This work was supported by the Joint Defra and MoD Programme, (Defra) GA01101 (MoD) CBC/2B/0417_Annex C5. We thank Richard P. Allan and William J. Ingram for providing comments on an early draft of the paper. We thank Matt Rogers, from Colorado State University, for providing the lookup tables used to parameterize reflectivity and attenuation by precipitation. We also thank Angela Benedetti for providing us with the coefficients needed to implement the correction by Mie effects. CloudSat data were obtained from the CloudSat Data Processing Center (http://cloudsat.cira.colostate.edu). CALIPSO, ISCCP, CERES, and ERBE data were obtained from the NASA Langley Research Center Atmospheric Sciences Data Center (http://eosweb.larc.nasa.gov). MODIS images were obtained from the NASA Goddard Space Flight Center Level 1 and Atmosphere Archive and Distribution System (LAADS) (http://ladsweb.nascom.nasa.gov). The program sam2p (http://www.inf.bme.hu/pts/sam2p) was used to convert images to different formats. We thank the three anonymous reviewers from comments that helped to improve the quality of the paper.