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 A detailed grid-point-based comparison of the cloud top phase derived from the 40-year reanalyses (ERA40) of the European Centre for Medium-Range Weather Forecasts (ECMWF) with satellite measurements is presented. For this purpose an algorithm is implemented to extract a two-dimensional “satellite-like” field of the cloud top phase from ERA40 data. This field is compared with cloud top phase data from the Polarization and Directionality of the Earth Reflectances (POLDER-1) instrument which was in orbit from November 1996 to June 1997. The thermodynamic cloud phase in ERA40 data is parameterized as a function of temperature with pure liquid clouds above 0°C, pure ice clouds below −23°C and mixed clouds in between. The matching performance of clouds derived from ERA40 with clouds observed by POLDER-1 is best in the extratropical storm track regions and over the tropical continents. Detailed comparison of the cloud top phase for grid points where both data sets indicate a cloud shows a relatively good agreement for warm (T > 0°C) and cold (T < −30°C) clouds. In the intermediate temperature range, ERA40 contains too many ice clouds compared to POLDER-1. The comparison reveals only small seasonal variations. A slightly revised parameterization for the phase partitioning of condensed cloud water is suggested (shifting the thresholds by −10°C), which leads to a generally improved agreement between cloud top phases derived from ERA40 and POLDER-1.
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 Clouds are one of the most important factors that impact weather and climate. They have a strong effect on the radiative balance (both in the terrestrial and solar spectrum) and the atmospheric water cycle. Because processes that influence the formation and life cycle of clouds cover a scale range from microphysics to mesoscale and synoptic-scale systems, the correct formation of clouds in numerical weather prediction and climate models is a very challenging topic. A comparison of the frequencies of high-, medium- and low-level clouds in ten atmospheric general circulation models with satellite observations revealed substantial differences [Zhang et al., 2005]. There are several reasons why not only the correct representation of cloudy and cloud-free regions, and of cloud altitude are of major interest. Physical processes such as precipitation formation and the net radiative balance are basically related to the cloud phase and the phase transition in the clouds. The influence of the cloud phase on radiation has been quantified with model simulations which lead to a difference in brightness temperature of about 10°C by changing the cloud phase from ice to liquid [Sun and Rikus, 2004].
 So far the representation of clouds especially in global-scale weather prediction models is highly simplified. The thermodynamic phase of clouds does typically only depend on grid point temperature. Such a standard parameterization neglects processes that impact the phase transitions within clouds like subgrid-scale temperature fluctuations and the influence of aerosols. Experimental data reveal a more complicated picture with the existence of ice clouds, liquid and mixed phase clouds in the temperature range between 0 and −30°C [e.g., Rogers and Yau, 1989; Mazin, 2006]. This raises the question about the reliability of the cloud phase in numerical models, calculated with a simple temperature depending parameterization. Another frequent simplification is the lack of supersaturated regions. For instance, in the ERA40 data cloud formation starts at grid-point-averaged relative humidity values of 80% and humidity values cannot exceed 100% (relative to ice at temperatures below 0°C). In contrast, several independent data sets reveal the frequent existence of supersaturation up to 120% relative humidity in the upper troposphere (e.g., Spichtinger et al.  and Gettelman et al.  based upon satellite data, and Vaughan et al.  inferred from vertical soundings). It is important to mention that in some climate models efforts have been made to include more physically based parameterizations in particular of cirrus cloud formation [e.g., Lohmann and Kärcher, 2002; Lohmann et al., 2004]. Also, for instance the ECMWF very recently introduced ice supersaturation in their forecast system [Tompkins et al., 2007]. However, most global model cloud data sets, including the frequently used ECMWF and NCEP reanalyses are based upon the aforementioned simplifications.
 Nevertheless, previous statistical validations of simulated cloud cover provided fairly good results. A study based on a comparison of high cloud climatologies from ERA40 and satellite data by Chevallier et al.  showed that more than 60% of observed high cloud anomalies in large oceanic basins are captured by the ERA40 data. A good agreement of ice clouds in operational analyses from the ECMWF and satellite observations was also found by Li et al. , but the ice water content (IWC) was by a factor of 3 higher in the satellite data than in ECMWF analyses. The global verification of the cloud phase in global model data sets is not straightforward and has not been performed so far. It requires reliable measurements of this parameter over an extended time period.
 This study uses data from the POLDER-1 instrument [Parol et al., 2004] to “validate” the thermodynamic phase of ERA40 cloud tops. Since the thermodynamic phase is not directly measured by POLDER-1, we regard our study as a comparison between quantities derived from observations and the ERA40 data set, and not as a strict validation. Cloud top phases in both data sets will be compared with relatively high spatial and temporal resolution (∼100 km and 6 h, respectively). Statistics of matching frequencies of clouds and cloud top phases at individual grid points will be presented. In order to compare the two data sets with differing resolutions and parameters, a combined observation-to-model and model-to-observation approach is implemented. The resolution of the satellite data is adapted to the resolution of the model both in space and time (observation-to-model), while a two-dimensional “satellite-like” field is extracted from the three-dimensional ERA40 fields of cloud ice and cloud liquid water (model-to-observations, as described in section 2.3). Section 2 presents the two data sets and the implemented algorithm. In section 3 the statistical results of the comparison of the data sets will be presented and in section 4 sensitivity studies will be shown to check the robustness of the algorithm. In section 5 it will be analyzed whether different parameterizations for the partitioning of condensed cloud water between the liquid and ice phase in ERA40 could lead to an improved agreement of cloud top phases with POLDER-1 observations.
2. Data Sets
2.1. POLDER-1 Data Set
 The POLDER-1 (Polarization and Directionality of the Earth Reflectances) instrument was launched on board the Japanese ADEOS-1 satellite. The data set covers the time period from 30 October 1996 to 30 June 1997. The spatial resolution of the two-dimensional cloud parameters is approximately 19 km corresponding to about 1/6 degree at the equator. Since POLDER-1 measures the reflected sun light, the data domain is a function of the time of the year and excludes regions of polar night.
 POLDER-1 is an instrument with multispectral, multidirectional and multipolarization capabilities. One special feature of POLDER-1 is its capability to observe one target from up to 14 different angles during a single overpass. The reflectance measurements are taken in eight different wavelength bands between 443 and 910 nm. The behavior of the scattered polarized radiance in dependence of the scatter angle varies with the shape of the scattering object. Spherical particles that are assumed to be liquid show a strong maximum in the polarized reflectance at a scattering angle of 140°. Nonspherical particles (ice) do not produce such a maximum, which is the basis to distinguish between clouds that consist of mainly spherical (liquid) particles, mainly nonspherical (ice) particles or both of them (mixed). Therefore, the POLDER-1 cloud top phase parameter can take on 4 different values, denoting ice, mixed and liquid clouds, and cloud-free conditions. For a detailed description of the algorithms for cloud detection and derivation of cloud properties see Buriez et al.  and Goloub et al. .
 The second parameter in the POLDER-1 data set that is used in this study is the cloud top pressure, obtained by the “Rayleigh” method. This method determines the cloud top height from the polarization measurements at 443 nm. At this wavelength the reflected radiance essentially corresponds to the light scattered by the layer above the clouds. For a complete description of the determination of cloud top pressure see Buriez et al. . Chepfer et al.  compared the POLDER-1 cloud height derived from the “Rayleigh” method with lidar measurements. Their result was that the cloud top height is underestimated by POLDER-1 for optically thin clouds. Further comparisons with radiative transfer model calculations showed that the “Rayleigh” method delivers fair results for clouds with optical depth larger than 3.
 In several studies the capability and reliability of POLDER-1 observations concerning cloud detection and determination of the cloud top phase and cloud pressure level have been tested. The algorithm for cloud detection was validated with surface synoptic observations by Breon and Colzy . The results of this global validation showed that POLDER-1 cloud detection works well apart from situations with small cloud cover. The detection works better for low-level and midlevel clouds than for high clouds which may be due to the lower optical thickness of high clouds. This might be important in tropical regions where large areas are covered by cirrus clouds.
 A first validation of the cloud top phase derived from POLDER-1 with lidar measurements was done by Chepfer et al.  and Goloub et al. . They detected a discrepancy of 6% for high clouds. In addition, Goloub et al.  compared the POLDER-1 cloud phase with a cloud classification applied to Meteosat data. This method showed that low-level and midlevel clouds are correctly identified as liquid clouds. Limitations were found for some classes of high clouds, especially for cirrus overlapping low-level/midlevel clouds and heterogeneous high clouds. A more extensive validation of the thermodynamic cloud phase in the POLDER-1 data was done by Riedi et al. . The cloud boundaries were determined from a combination of radar, lidar and ceilometer data, and the temperature and pressure at the cloud top have been derived from rawinsonde measurements. The results confirmed the other studies and thereby the reliability of the POLDER-1 cloud top phase product.
 In 2005 the data of the POLDER-1 instrument have been reprocessed using the improved algorithms developed for the POLDER-2 mission. This improved version of POLDER-1 data with a higher spatial resolution has been used in this study.
 An example of the POLDER-1 cloud top phase and pressure over parts of Europe is shown in Figures 1a and 1b. Obviously there are several regions where a cloud top phase was observed by POLDER-1 but the cloud pressure level could not be defined (e.g., African coast, south of Italy). This will impact the results of the comparison which are shown in the following sections.
 For the comparison with model data, POLDER-1 data have been transformed into a data set with 1 degree horizontal and 6 h temporal resolution. Therefore, the POLDER-1 measurements have been attributed to the ERA40 data times (0000, 0600, 1200, and 1800 UTC) within a ±3 h time window. For the spatial regridding, the 36 pixels of the original high-resolution data set that fall within a 1 × 1 degree grid box have been considered. The POLDER-1 cloud top phase which occurs most frequently in each box is assigned to that grid point. For this procedure, all cloud free pixels have been taken into account, whereas cloudy pixels were only considered if cloud top pressure information was available. This method to determine the predominant cloud phase on the scale of an ERA40 grid box turned out to be unambiguous in most cases. For more than 72% of the investigated grid boxes one cloud phase occurred at more than 75% of the considered high-resolution pixels. Also, in every grid cell, from all pixels that belong to the predominant cloud top phase category, the mean cloud pressure and its standard deviation, pcl and σp, respectively, have been determined. These values will be important for the cloud top phase determination in the ERA40 data, as explained in section 2.3.
 With this approach we obtain the POLDER-1 cloud top phase with the same temporal and spatial resolution as the ERA40 data. Figure 1c shows an example. White regions denote missing data. For instance in eastern Spain no cloud top phase could be determined on the coarse grid because POLDER-1 cloud top phase pixel values were all cloudy (Figure 1a) and none of them contained a cloud top pressure value (Figure 1b). In contrast, just to the east of these pixels, over the Mediterranean, cloud top pressure information was also completely missing, but since at least one phase information pixel indicated cloud-free conditions, the entire grid box was set to no cloud. This indicates that our gridding procedure has a small bias toward no cloud conditions in situations where POLDER-1 cloud top pressure information is missing.
2.2. ERA40 Data Set
 The 45-year (1958–2002) ERA40 reanalyses data set from the ECMWF [Uppala et al., 2005] has a resolution of T159L60 which corresponds to a horizontal grid point distance of about 100 km and 60 levels in the vertical. Observations are assimilated with the three-dimensional variational approach. Note that several satellite products are assimilated since 1979, but POLDER-1 data are not included and therefore serve as an independent comparison data set. ERA40 includes three-dimensional fields of Liquid Water Content (LWC) and Ice Water Content (IWC). Clouds are formed in the ECMWF model when the grid-cell-averaged relative humidity is higher than a certain threshold. This threshold is height dependent and ranges from 80% relative humidity in the tropopause region and free troposphere to 100% relative humidity near the surface. All relative humidity values are with respect to water at temperatures above 0°C and with respect to ice at colder temperatures. This means that no supersaturation is allowed in the model data. The parameterization of the thermodynamic cloud phase is done in a simple way. At temperatures higher than T0 = 0°C the condensed water is purely liquid (LWC) while at temperatures below Tice = −23°C the water is purely ice (IWC). In the temperature range between Tice and T0 both phases occur and the cloud is a mixed phase cloud. The fraction α of liquid water between Tice and T0 is increasing with increasing temperature, according to:
 In this study the ERA40 data are used with a 6-h time resolution (0000, 0600, 1200, and 1800 UTC) for the time period from October 1996 until June 1997. The fields have been interpolated onto a regular 1 × 1 degree longitude-latitude grid. For the comparison with the POLDER-1 cloud top phase, the three-dimensional fields IWC and LWC have to be converted at every time instant into a “satellite-like” two-dimensional field of ERA40 cloud top phase.
2.3. Estimation of a Two-Dimensional Field of ERA40 Cloud Top Phase
 Instead of applying a radiative transfer model as a forward operator on ERA40 profiles to simulate radiances measured by POLDER-1 we choose a more heuristic approach to determine the thermodynamic cloud top phase. The algorithm is based on vertical scans of IWC and LWC at every model grid point (see schematic in Figure 2).
 To get a starting level for the scan, the mean cloud pressure level derived from POLDER-1 (pcl, see section 2.1) is used, however the value is reduced by 150 hPa since the POLDER-1 cloud pressure level does not exactly correspond to the cloud top pressure. For most clouds, this level pcl-150 hPa should be above the cloud. The model level below this pressure level, ktop, is the starting level to integrate the IWC and LWC in the ERA40 data downward until the model level K to derive the vertically integrated mass of hydrometeors per area:
 Here qijkice represents the grid box averaged IWC at the grid point (i, j, k), g is the earth acceleration, Δpk is the thickness of the model level, and k denotes the index of the model level. The same equation holds for the vertical integration of the liquid cloud phase, Qijliq. These integrations are conducted downward until a threshold Q* for either the liquid or the ice phase or both is exceeded. This might occur before the vertical scan reaches the bottom of the cloud. At this level K the vertical scan is stopped and the cloud top phase at this horizontal ERA40 grid point is set to mixed if both Qijice and Qijliq exceed Q*, it is set to liquid if only Qijliq ≥ Q* and to ice if only Qijice ≥ Q*. If a maximum pressure pcl + 150 hPa is reached and none of the integrated hydrometeor classes exceed the threshold, the ERA40 grid point is assumed to be cloud free. Now a “satellite-like” field of the cloud top phase derived from ERA40 data is available with the same resolution in time and space as the modified POLDER-1 data set, and both data sets are ready for a detailed grid-point-based comparison every 6 h during the time period from 30 October 1996 to 30 June 1997.
 The number of clouds identified in the ERA40 data set depends upon the choice of the threshold value Q*. As a simple “best choice,” the threshold value has been determined such that the percentage of cloudy ERA40 grid points is approximatively equal to this percentage in the POLDER-1 data set (if averaged over the globe and the entire time period). This yields a value of Q* = 10−2 kg m−2. According to Lin and Rossow  this is close to the water path of a cloud with an optical depth of 3 and an effective particle radius of 10 μm. Although the chosen value for Q* is not based on physical reasoning, it corresponds roughly to the minimum optical depth for a reliable cloud detection by POLDER-1 [Chepfer et al., 2000]. In section 4 the sensitivity of the results to the choice of the threshold value Q* will be discussed.
 Two minor technical issues should be mentioned at this point. First, no value for pcl is available if POLDER-1 most frequently observed no cloud within a grid box. Then, the scan in the ERA40 data starts at the highest model level and is continued down to the lowest model level as long as no threshold is exceeded. Second, if the standard deviation of the POLDER-1 cloud top pressure values within a grid box is very large (σp > 100 hPa), then the lowest pressure value of these pixels is taken as starting level for the ERA40 scan. A possible reason for a large standard deviation might be an inhomogeneous cloud layer.
Figure 1d shows an example of the cloud top phase derived from the ERA40 data with the introduced algorithm at the same time and in the same area as for the POLDER-1 examples (Figures 1a–1c). Some features agree well with the gridded POLDER-1 data (compare with Figure 1c), for instance the area covered by ice clouds to the west of Ireland, liquid clouds to the west of Spain and a large cloud free region over the Mediterranean. This snapshot yields the impression that the ERA40 data contain considerably more ice clouds than observed by POLDER-1, while mixed clouds are very rare in both data sets.
 We now turn to a systematic grid-point-based comparison of the two global data sets for the entire time period considered.
 First, results from a two-category cloud/no cloud comparison of the ERA40 and POLDER-1 data sets are presented (section 3.1). The identified cloud-cloud matches are then used for the three-category cloud phase comparison (section 3.2).
3.1. Geographical Distribution of Cloud Matches
 In both data sets, a grid point is considered as cloudy, if the cloud top phase is either liquid, mixed or ice. Figure 3 shows the geographical distribution of the frequency bias and the percentage correct (PC) value (averaged over the entire time period). The bias corresponds to the ratio of the number of clouds identified from ERA40 with the number of clouds observed by POLDER-1. The PC is the fraction of the ERA40 pixels where the binary information about cloud or no-cloud agrees with POLDER-1. Optimum values would be equal to one for both bias and PC. In order to eliminate small-scale features, the fields have been aggregated on a 3 × 3 degree grid.
 The bias (Figure 3a) indicates a significant overestimation (values >1) over the tropical ocean. Apart from these regions, i.e., in the extratropics and over tropical continents, no significant overestimations and underestimations in the cloud frequency occur. An exception is Greenland and parts of Antarctica, where again high bias values are found, which might also indicate a problem of the POLDER-1 cloud retrieval over ice covered surfaces [Riedi et al., 2000]. It is notable that in regions with pronounced synoptic activity, e.g., the Southern Hemisphere near 50°S, the North Atlantic and North Pacific storm tracks [see, e.g., Wernli and Schwierz, 2006] the bias values are close to 1. In the same areas, also the PC is close to its optimum value (∼0.8, see Figure 3b). Together, this indicates a reasonably good performance of the ERA40 data set in terms of cloud cover in synoptically active regions. In the tropics, the PC is largest over the continents, where convection occurs typically with a clear diurnal cycle. Over the Sahara, the PC is probably very high because of the very high frequency of no-cloud conditions in both data sets. The lowest PC values (even below 0.2) are found over the tropical oceans.
 Since in the following only grid points with cloud-cloud matches will be considered, it is important to infer from this statistical analysis that clouds are best captured in the ERA40 data set in the extratropical storm tracks and over the tropical continents.
3.2. Conditional Comparison of Cloud Top Phase
 In this section results are presented of the quantitative comparison of the cloud top phase in the two data sets. Only those grid points where both data sets indicate a cloud are considered for this comparison. For instance in the northern extratropics (20–90°N) the number of data points that enter the comparison varies between about 5,000 per day in December (no data in polar night area) and more than 10,000 per day in June.
 In both data sets, three categories of the cloud top phase are distinguished: ice (I), liquid (L) and mixed (M). Conditional comparisons will be performed for grid points where POLDER-1 observed a certain cloud top phase, and vice versa, for grid points where a certain cloud top phase was diagnosed from the ERA40 data set. In the former case, the considered events will be denoted by label P and the appropriate phase label, e.g., PI for ice clouds observed by POLDER-1. Analogously, for instance EL denotes liquid cloud tops in the ERA40 data set. Finally, the terminology PIEL will be used to denote the conditional comparison category where POLDER-1 observed an ice cloud and ERA40 data contained a liquid cloud. Events where both data sets reveal the same phase are called matches (e.g., PIEI, ELPL), and if the phases differ the events are called mismatches (e.g., PIEL, ELPM).
Figure 4 presents the monthly mean probabilities of those cloud top phase comparison categories where POLDER-1 observed an ice cloud or a liquid cloud (Figures 4a and 4b), and where ERA40 data contained one of these cloud types (Figures 4c and 4d). The values are averages over all grid points in the extratropical Northern Hemisphere (20–90°N). Matching probabilities are very high in two cases: 85–95% for PIEI (Figure 4a) and about 90% for ELPL (Figure 4d). This shows that almost all of the ice cloud tops observed by POLDER-1 are reproduced in the ERA40 data set; and almost all of the simulated ERA40 liquid cloud tops are confirmed by POLDER-1. At this point it should be mentioned again that just cases where both data sets indicate a cloud contribute to the statistics. Matching probabilities are distinctively lower for the other two categories: 30–50% for EIPI (Figure 4c) and 20–45% for PLEL (Figure 4b). Here, mismatches between the ice and liquid cloud phase are as frequent as matches (EIPL) or even larger (40–70% for PLEI, Figure 4b). Very rare are mismatches associated with mixed phase cloud tops, except for PLEM, where 10–15% of the observed liquid cloud tops are diagnosed as mixed phase cloud tops in the ERA40 data (Figure 4b). As discussed later, the main reason for the strongly different matching probabilities of the reverse cases PIEI and EIPI is the occurrence of too much ice at temperatures above −25°C in the ERA40 data set.
 For the two categories PLxx and EIxx there is a moderate seasonal variation. Matches between the two data sets are more frequent during the winter months and have a minimum in April–June (recall that no data are available for the summer and early autumn season). In the southern extratropics (20–90°S) the results (not shown) are very similar except for the seasonal variations. Highest matching probabilities occur in April and May. This indicates that in the extratropics ERA40 agrees better with POLDER-1 during the cold season. A hypothesis for this seasonal behavior is that ERA40 simulates cloud top phases associated with synoptic-scale weather systems (that dominate during the winter season) with higher accuracy than those produced by small-scale convection.
 Finally, in the tropics (20°S–20°N, see Figure 5) the results for observed ice and liquid clouds (PI and PL) differ substantially compared to the extratropics, whereas for EI and EL there is no striking difference between the regions. Month-to-month variations are generally very weak in the tropics. For ice clouds observed by POLDER-1 (PI) the matching probability is about 5–20% lower than in the extratropics. This decrease is associated with enhanced probability for the mismatch PIEL (15–30%, see Figure 5a). Largest differences between tropics and extratropics occur for liquid clouds within the POLDER-1 data, i.e., for the category that scored poorest in the extratropics (Figure 4b). In the tropics matching probabilities for PLEL are between 65 and 80% while mismatches of the type PLEI occur in less than 30% of the cases.
 In summary, this quantitative conditional comparison revealed a very good agreement for observed ice cloud tops and simulated ERA40 liquid cloud tops in both the extratropics and the tropics, and a good agreement for observed liquid cloud tops in the tropics. The agreement between the two data sets is less satisfying for observed liquid cloud tops as well as for simulated ice cloud tops in the extratropics, and for simulated ice cloud tops in the tropics. In the next section it will be investigated whether cloud temperatures provide additional insight into the comparison results, and in particular to what degree the simple temperature relationship of the ERA40 phase partitioning (equation (1)) might be responsible for the occurring mismatches.
3.3. Temperatures of ERA40 Ice Clouds
 In this section the focus is on one of the comparison categories (ice cloud tops simulated by ECMWF, i.e., EI) where the statistical results globally revealed rather poor agreement. Figure 6 presents the percentage of matches EIPI and mismatches EIPL as a function of ERA40 temperature at the level where Q* is exceeded, separately for the time periods from November to February (Figures 6a–6c) and March to June (Figures 6d–6f), and for the regions northern extratropics (Figures 6a and 6d), southern extratropics (Figures 6b and 6e) and tropics (Figures 6c and 6f). Also shown as a function of temperature is the total number of identified ERA40 ice cloud top grid points (right y axis).
 In agreement with the results from the last section, there are remarkable differences between the extratropics and the tropics and between the two investigated time periods in the extratropics. Most conspicuous is the strong temperature dependence of the matching frequency EIPI. In all diagrams, the frequency of ice cloud tops in POLDER-1 observations is larger than the one for liquid cloud tops at temperatures below −20 to −25°C. At warmer temperatures, mismatches (observed liquid clouds) dominate and reach frequencies of 90% at −5°C in the southern extratropics. This clearly indicates that in the extratropics most of the EIPL mismatches occur at relatively warm temperatures (−25°C < T < 0°C), while very good agreement exists at cold temperatures around −40°C. A very likely reason for this behavior is that ERA40 data contain a too large fraction of cloud water as ice at temperatures above −25°C. The main reason for the seasonal behavior of the EIPI matches in the extratropics (see Figure 4c) appears to be the temperature distribution of ice cloud tops in the ERA40 data. In both extratropical regions (but in particular in the Southern Hemisphere) the fraction of cold ice cloud tops during winter is larger than during spring/autumn and therefore matching frequencies are highest during the cold season. This is also indicated by the median values of the temperature distributions of ice cloud tops, which are slightly lower during the colder season in the northern extratropics (−21.8°C versus −21.2°C) and distinctively lower in the southern extratropics (−20.6°C versus −18.2°C).
 In the tropics the temperature distribution of ice cloud tops in ERA40 is completely different. Cold ice cloud tops at temperatures below −30°C are more frequent compared to the extratropics, as indicated by the median values. This explains the slightly higher frequencies of EIPI in the tropics (see Figure 5c). Similar to the extratropics, EIPL mismatches become more frequent than matches at temperatures above ∼−25°C.
4. Sensitivity Studies
 The introduced algorithm for the determination of the ERA40 cloud top phase (section 2.3) depends on several parameters that have to be specified. These are the thresholds for the vertical integration of IWC and LWC and the vertical pressure interval used for the vertical scan. In this section, the default values will be varied in order to assess the sensitivity of the results to these parameters. In addition, the influence of the cloud optical thickness observed by POLDER-1 will be investigated. POLDER-1 cloud top phase observations should be more reliable for clouds with higher optical thickness as already mentioned in section 2.1. To learn how the integration threshold Q* for the cloud phase determination in ERA40 data impacts upon the results of the comparison, Q* has been increased step by step from 10−5 to 1 kg m−2 (recall that a value of Q* = 10−2 kg m−2 has been chosen as the default value).
Figure 7a shows the frequency bias and PC value for the existence of clouds averaged over the northern extratropics during January 1997. Since Q* controls the number of clouds that are determined by the vertical scan algorithm, the bias decreases if the threshold is increased. A rapid decrease of the bias occurs if Q* is increased to values above the default value. The optimum value (bias equal 1) is obtained close to the default value, and overestimations result for smaller thresholds. The PC reveals a similar tendency with a marked decrease for large thresholds. For thresholds smaller than the default value, the PC is rather insensitive to changes of Q*.
 In addition, the probabilities of the four cloud top phase matching categories are shown in Figure 7b for different thresholds Q*. Whereas matches in the categories EIPI and ELPL are fairly constant for different thresholds, the number of matches for PIEI and PLEL is highly sensitive to Q* if it is increased above the default value of 10−2 kg m−2. While the probability for PIEI tends to 0 for Q* = 1 kg m−2, PLEL increases up to 100%. This is due to the fact that liquid clouds occur at relatively warm temperatures and therefore, they can contain high amounts of LWC required to exceed Q*.
 This brief analysis confirms the suitability of the chosen threshold of Q* = 10−2 kg m−2, because it combines a high cloud hit rate between POLDER-1 and ERA40, fairly insensitive matching probabilities (in particular for PIEI and PLEL) and robust statistics based on a large number of considered grid points.
 A decrease of the starting pressure level for the vertical scan (the default value is the POLDER-1 cloud pressure minus 150 hPa) does not strongly change the results. The main effect is to decrease the number of ERA40 no cloud events and to increase the number of cloud tops in ERA40, mainly of ice clouds. This is no surprise since now the vertical scans start at higher altitudes. Considering the cloud top phase, only the matches PLEL decrease slightly (about 5–10% in the extratropics and up to 15% in the tropics). Although the chosen pressure reduction of 150 hPa is rather subjective, a larger pressure reduction would essentially lead to the same results.
 To assess the uncertainties which are associated with POLDER-1 measurements of optically thin clouds, the comparison procedure has been repeated considering only those cloudy pixels in POLDER-1 where the optical depth τ as observed by POLDER-1 was larger than a certain threshold. The threshold has been increased step by step from 0 (the default value) to 50. This leads to a reduction of the number of cloud grid points to about 3000 per month but according to Breon and Colzy  increases the reliability of the POLDER-1 data set. Taking into account only optically thicker clouds did not lead to an overall improvement of the matching frequencies. For clouds with τ > 20, the frequencies of the two categories who scored best in the comparison, PIEI and ELPL, increase close to 100%. In contrast, for observed liquid clouds and ice clouds indicated by ERA40 the mismatches PLEI and EIPL, respectively, increase for optically thicker clouds and exceed the probabilities for a match in these two categories. The reason for this is that for optically thick clouds the fraction of clouds that exist between −20°C and 0°C increases (as verified with scatter plots of τ versus T, not shown) and therefore, as discussed with Figure 6, the mismatches exceed the matches in these two categories.
5. Comparison With Different Parameterizations
 The main result from the comparison presented in the previous sections is that the ERA40 data contain too high fractions of IWC at temperatures above −30°C. This could be due to two main reasons: (1) the neglect of supersaturation and (2) a wrong partitioning of the condensed phase between ice and liquid. Here the second issue is further investigated by modifying the phase partitioning (see equation (1)). The comparison procedure with POLDER-1 observations can then be repeated to see whether the modified parameterizations perform better or not. The effect of supersaturation is not examined here because it is technically not possible to diagnostically determine ERA40 fields of IWC and LWC if supersaturation was allowed.
 In order to modify the phase partitioning, the total cloud water amount has been determined at every grid point by adding IWC and LWC, and then the two quantities have been recalculated based upon different formulations of α (equation (1)). This procedure ignores that in the ERA40 data set the formation of precipitation is calculated separately for pure ice clouds and for mixed/liquid clouds and that therefore a modified partitioning would lead to changes in precipitation and eventually in the total cloud water content. It is assumed that the quantitative effect of this inconsistency can be neglected.
 Four different parameterizations have been considered. CTL denotes the standard parameterization used at the ECMWF with Tice = −23°C and T0 = 0°C in equation (1). The three others aim at producing the phase transition from liquid to ice at lower temperatures. For LOW, only the parameter Tice has been changed and set to the probably unrealistically low value of −63°C. LOW indicates the maximum difference (compared to CTL) that can be obtained by only changing Tice. For CLD, both parameters are lowered by 10°C compared to CTL. Similar values have been used previously by Del Genio et al. . Finally, DBQ denotes the parameterization suggested by Doutriaux-Boucher and Quaas , who compared POLDER-1 observations with output from the LMDZ general circulation model. In addition to changing the lower threshold (Tice = −32°), also the exponent in equation (1) has been modified from 2 to 1.7. Figure 8 illustrates the four different parameterizations of the partitioning parameter α as a function of temperature. One can see that DBQ and LOW allow mixed clouds in a broader temperature range compared to CTL and CLD. Temperature distributions for the three cloud top phases (not shown) reveal that both CLD and LOW produce more liquid clouds than CTL at temperatures between −20 and 0°C. The frequency of mixed clouds is about equal for CLD and CTL, however for CLD shifted to 10°C colder temperatures. Accordingly, the number of ice cloud tops is significantly reduced in CLD and LOW compared to CTL at T > −20°C.
Figure 9 shows the matching probabilities for the different parameterizations as a function of time of year in the northern extratropics. First we pay attention on how the different parameterization influence PIEI (Figure 9a). The largest values occur for CTL and DBQ; values for CLD and LOW are lower, by about 10% and 20–25%, respectively. This result is as expected since CTL and DBQ produce more IWC compared to the other parameterizations (see Figure 8). In contrast, for PLEL (Figure 9b) CLD and LOW lead to strongly increased values compared to CTL (by 30–50%). For CLD and LOW matching probabilities for PLEL are approximately in the same range as for PIEI, in clear contrast to CTL. For EIPI (Figure 9c) the situation is quite similar to PLEL. The matching probabilities of LOW and CLD are 10–35% higher than for CTL and DBQ scores in between. Finally, for ELPL (Figure 9d) the variations are smallest with almost equal values for all different parameterizations. This is expected since most liquid cloud tops diagnosed from ERA40 data occur at temperatures above 0°C.
 Overall, one can conclude that the parameterization CTL performs poorest (except for PIEI and ELPL) and that LOW and in particular CLD reveal much better results if compared with POLDER-1 observations. For CLD, the loss in matching probability for PIEI (about 10% on average) is compensated by an improvement in two other categories (30% for PLEL and 10–15% for EIPI).
 Note that a parameterization with an even more rapid transition from the liquid to the ice phase would lead to larger matching probabilities with POLDER-1, because the observations contain only very few mixed phase cloud tops. However, it is questionable whether this low number is reliable. For instance, Mazin  estimated the frequency of mixed clouds between −30 and 0°C to 30–40%. It is not straightforward to infer the expected number of mixed phase cloud tops, however it seems reasonable to consider a parameterization with a fairly large interval between T0 and Tice.
6. Discussion and Conclusions
 First we briefly discuss the limitations of the data sets and of our comparison approach. The POLDER-1 cloud top phase observations provide a data set for a global almost-annual comparison of clouds in meteorological models. The general reliability has been documented in previous studies and further improved because of the reprocessing of the data in 2005. Nevertheless there remain some uncertainties about the data quality in case of thin clouds and the low number of mixed phase cloud tops awaits further confirmation. The situations where no POLDER-1 cloud pressure value could be determined are problematic for our approach since this value is very useful for constraining the vertical scan in the ECMWF data to the relevant layer. When this parameter is not available, it can occur that the determined ECMWF cloud top phase pertains to a different cloud layer than observed by POLDER-1. A systematic uncertainty stems from the time difference between observations and model data. We compared the ECMWF clouds at 6 h time intervals with observations that have been taken within 3 h from the analysis time. In particular in situations with rapidly moving small-scale clouds this must lead to mismatches in the grid-point-based comparison. Some tests have been performed where POLDER-1 observations have been considered only within 1 h from the analysis time. This enhances the probability that a cloud observed by POLDER-1 is represented in the ERA40 data by about 5% (from about 75% to 80%) but does not affect the results of the comparison of the thermodynamic cloud top phases. Therefore, we decided to use the POLDER-1 observations within a 3 h time window, which yields the maximum number of grid points that enter the comparison. Another point is that POLDER-1 data are available for less than a year. This prevents us from looking at a full seasonal cycle (in particular, the potentially interesting Asian Monsoon phase is missing) and aspects of interannual variability. Some of the comparison values and the interhemispheric differences might be seasonally biased since the analyzed time period mainly covers Northern (Southern) Hemispheric winter (summer). Finally, it should be emphasized that our comparison approach only considers the phase of the cloud top and not the ice and liquid water content. The relatively good agreement in the POLDER-1 and ERA40 cloud phase does not imply that the ERA40 liquid and ice water contents are realistic. Microphysical studies indicate that the detailed structure of ice clouds (e.g., the ice particle number density) depends strongly on processes that are not or at least not well represented in most global models, such as gravity wave induced temperature and vertical velocity perturbations and aerosol (in particular ice nuclei) concentrations [Kärcher and Ström, 2003; Haag and Kärcher, 2004; Hoyle et al., 2005]. It is therefore expected that a comparison of for instance IWC would lead to significantly larger discrepancies between ERA40 and observations, compared to the model errors in the cloud top phase diagnosed here.
 To our knowledge, the presented comparison is a first effort toward a global comparison of the cloud top phase in the ERA40 data set with satellite observations. A forward operator algorithm has been introduced that determines a two-dimensional field of the cloud top phase from the ERA40 data which is comparable to the observations. However, this algorithm is not based upon physical laws, it rather constitutes a heuristic approach that involves some subjectively chosen threshold parameters. The influence of these parameters on the comparison results has been discussed in section 4. It was shown that the method provides robust and meaningful results.
 A comparison of cloud representation within the two data set shows that best agreement occurs in the extratropical storm tracks where more than 70% of clouds observed by POLDER-1 are represented by the ERA40 data. In these regions, the frequency bias of clouds is close to the optimum value of 1, and percentage correct values are about 0.8. In the tropics, the comparison shows relatively good agreement of the two data sets over the continents, but poor agreement over the oceans with a significant positive bias. This points to possible problems associated with thin clouds in the upper troposphere that might be overestimated in the ERA40 data (because of the neglect of supersaturation) and underestimated by the POLDER-1 instrument. Note however, that the large differences found between the tropics and extratropics could also indicate that our approach to identify clouds and the cloud top phase from ERA40 data is not equally suitable in all geographical areas.
 In the extratropics thermodynamic phase matching probabilities were very high (larger than 80%) for ice cloud tops observed by POLDER-1 and for liquid cloud tops diagnosed from ERA40. Much lower matching probabilities were found for observed liquid cloud tops and for diagnosed ice cloud tops. It was shown that this asymmetry is due to a systematic overestimation of ice clouds at temperatures above −30°C in the ERA40 data set. In the tropics the comparison results differ from the extratropics: POLDER-1 cloud tops were generally well captured by ERA40 (∼70%), whereas only 50% of ERA40 ice cloud tops were correctly identified by POLDER-1.
 As a final result beyond comparison, a modified parameterization of the cloud phase partitioning has been suggested that leads to a better agreement of the top cloud phase with POLDER-1 observations. The best comparison results have been obtained with the parameterization CLD where both temperature thresholds in equation (1) were lowered by 10°C. Still, this parameterization is extremely simple and it might be useful only in situations where computational efficiency is an issue. The significant shift of the phase transition to cooler temperatures (CLD compared to CTL) is in qualitative agreement with recent observations in mixed phase Arctic clouds. Sandvik et al.  report temperatures of −23 to −20°C for an ice fraction of 50%. The same fraction is reached at about this temperature in the parameterization CLD (at −17°C), and therefore at clearly too high temperatures in CTL. It would be of interest to include the CLD parameterization in the recently introduced parameterization of supersaturation at the ECMWF [Tompkins et al., 2007] and to compare different model versions with cloud top phase information from POLDER instruments, in particular from POLDER-3 on board the satellite PARASOL which is in orbit since December 2004. In addition, the MODIS instrument (on board the TERRA satellite since February 2000, and on board AQUA since May 2002), which is also able to determine the thermodynamic cloud phase offers the possibility for a longer-term comparison of model clouds with observations. A combined observational data set of cloud thermodynamic phase has been recently constructed using measurements from MODIS and POLDER-3 [Riedi et al., 2007] providing a semicontinuous confidence index ranging from confident liquid to confident ice instead of the usual discrete classification.
 We are very grateful to the POLDER team, in particular Catherine Proy, for the delivery and help with the analysis of the POLDER-1 data. We thank the German Weather Service (DWD) and ECMWF for granting access to the ERA40 data set. We thank Daniel Lüthi at ETH Zürich for hosting the POLDER-1 data in the early phase of this project. The comments of the anonymous referees were very helpful to improve the presentation of our results. Part of this work has been funded by the German Research Foundation (DFG) as part of the Collaborative Research Centre 671 “Tropospheric ice phase.”