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  • View in gallery

    (left) Cloud fraction and (right) cloud-top height distributions for all CALIPSO samples classified as trade cumulus for the months of July (top) 2006, (middle) 2007, and (bottom) 2008. The percentage of samples classified as TCu (out of all ocean grid points between 30°N and 30°S) is shown in the right figures, as well as the percentage of TCu samples that fully attenuate the lidar signal.

  • View in gallery

    As in Fig. 1, but for samples identified as trade cumulus from model cycles (top) CY31R1, (middle) CY32R3, and (bottom) CY32R3 using the DualM parameterization. Only results from July 2008 are shown. For easier comparison, the observed cloud-top height distribution from CALIPSO for the same month is shown in gray.

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    (left) Cloud fraction and (right) cloud top height histograms of all samples classified as trade cumulus for January 2007 from (top) CALIPSO and (bottom) model cycle CY32R3. Shown in gray is the observed cloud-top height distribution.

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    (left) Cloud fraction and (right) cloud top height distributions for trade cumulus samples from model cycle CY32R3 during July 2008. Sample distributions from even days of the month, corresponding to model forecast hours 24–48, are shown in black, while distributions from odd days (forecast hours 48–72) are shown in gray.

  • View in gallery

    Hourly output of the model’s cloud fraction from one grid point at 10.11°S, 139.05°W (left) from IFS with Tiedtke parameterization for shallow convection (the highest cloud fractions can be found in the upper half of the cloud) and (right) from the IFS with DualM parameterization (cloud fractions tend to be lower overall, with the highest values near cloud base; the cloud field is less noisy).

  • View in gallery

    Maps of trade cumulus sample frequency of occurrence from (top) CALIPSO, and from model cycles (middle) CY32R3 and (bottom) CY32R3-DM for July 2008.

  • View in gallery

    Maps of monthly mean total cloud cover from (top to bottom) CALIPSO, Aqua MODIS, ISCCP, and the model for the month of July 2006. The white solid contour marks the 50% level.

  • View in gallery

    Cloud fraction distributions for MODIS cloud mask sampled within a grid box (gray, 2D) and along the CALIPSO track (black, 1D) from 1–8 July 2008. Only ocean samples between 30°N and 30°S are considered. Samples where CALIPSO detects high clouds are excluded. The difference between 1D and 2D distributions provides an empirical estimate of the sampling error for low clouds in the tropical and subtropical oceans.

  • View in gallery

    Cloud fraction distributions from (left) CALIPSO and (right) CY32R3 of the IFS. The leftmost bin includes samples that are cloud-free below 4 km. Shown in gray is the CALIPSO distribution corrected for the sampling error, based on 1D vs 2D cloud fraction comparison performed with MODIS cloud mask.

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Evaluation of Trade Cumulus in the ECMWF Model with Observations from CALIPSO

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Abstract

Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) are used to assess trade cumulus cloudiness in three versions of the Integrated Forecasting System of the European Centre for Medium-Range Weather Forecasts. The observations are recast onto the model grid, and two simple threshold criteria for cloud-top height and cloud fraction are used to identify grid points containing trade cumulus clouds. The cloud fraction and cloud-top height distributions of the sample populations are then compared. Results show that all versions of the model overestimate the frequency of occurrence of trade cumulus clouds but underestimate their cloud fraction when present. These effects partially compensate. Cloud-top heights are overestimated in model cycles using the modified Tiedtke parameterization for shallow convection, but are in very good agreement with observations when the dual mass flux parameterization is introduced.

Corresponding author address: Maike Ahlgrimm, European Centre for Medium-Range Weather Forecasts, Shinfield Park, Reading RG2 9AX, United Kingdom. Email: maike.ahlgrimm@ecmwf.int

Abstract

Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) are used to assess trade cumulus cloudiness in three versions of the Integrated Forecasting System of the European Centre for Medium-Range Weather Forecasts. The observations are recast onto the model grid, and two simple threshold criteria for cloud-top height and cloud fraction are used to identify grid points containing trade cumulus clouds. The cloud fraction and cloud-top height distributions of the sample populations are then compared. Results show that all versions of the model overestimate the frequency of occurrence of trade cumulus clouds but underestimate their cloud fraction when present. These effects partially compensate. Cloud-top heights are overestimated in model cycles using the modified Tiedtke parameterization for shallow convection, but are in very good agreement with observations when the dual mass flux parameterization is introduced.

Corresponding author address: Maike Ahlgrimm, European Centre for Medium-Range Weather Forecasts, Shinfield Park, Reading RG2 9AX, United Kingdom. Email: maike.ahlgrimm@ecmwf.int

1. Introduction

Satellite observations have been routinely used for cloud evaluation in general circulation models (GCMs). The International Satellite Cloud Climatology Project (ISCCP) dataset in particular has been well explored. Previous studies suggest that many GCMs have difficulties in modeling sufficient low cloud cover and relative amounts of low clouds with high and low optical depths (Jakob 1999; Webb et al. 2001; Zhang et al. 2005).

The advent of the ISCCP products constituted a step forward, beyond the evaluation of top-of-the-atmosphere radiative balances toward an assessment of vertically resolved cloud radiative effects. Further separation by cloud optical depth allowed some differentiation of cloud types, though solely based on the clouds’ radiative effect. However, the ISCCP products have some inherent limitations. Vertical resolution is limited to three levels, and height determination is prone to errors. Each pixel with approximate size of 5 km is treated as either clear or cloudy. Thus, optical properties for each pixel are radiatively weighed averages (Rossow and Schiffer 1999). For partially cloudy pixels, the retrieved optical depth is therefore not necessarily representative of the in-cloud optical depth.

The Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellite provides direct measurements of cloud-top height with very good accuracy and high vertical resolution. While cloud amount derived from CALIPSO is not without its limitations either (as will be discussed in detail), the lidar’s small footprint of 100-m diameter is much more suitable for observing broken cloud cover, as is found in the trade cumulus (TCu) regions. Previous studies (Chepfer et al. 2008; Wilkinson et al. 2008) have shown the value of these observations for model assessment but did not take full advantage of the high vertical resolution available from the lidar.

Over 10 years ago, Jakob (1999) determined that the Integrated Forecasting System (IFS) as used in the first European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (Gibson et al. 1997) underestimates marine stratocumulus cloud cover by 15% but overestimates the cloud cover in the trade cumulus regions by 10%–15%. The current cloud scheme in the IFS is based on the same prognostic Tiedtke scheme (Tiedtke 1993) with some modifications over time (Jung et al. 2008). While the representation of stratocumulus clouds improved markedly with the introduction of the eddy diffusivity mass flux (EDMF) parameterization (Köhler 2005; Tompkins et al. 2004; Ahlgrimm et al. 2009), ongoing in-house evaluation with observations from the Clouds and the Earth’s Radiant Energy System (CERES) still shows evidence of a shortwave bias in the trade cumulus regions. A new parameterization, which treats boundary layer processes and shallow convection in one framework, is being tested as possible future replacement for the Tiedtke shallow convection treatment. Thus, further evaluation of trade cumulus in the IFS is warranted and particularly timely.

In the study presented here, global observations from CALIPSO are recast onto the model grid. Using simple threshold criteria, samples containing trade cumulus clouds are identified, and the properties of observed and modeled sample populations are compared. We take advantage of CALIPSO’s highly accurate cloud-top height detection and aim to separate contributions to model error from cloud frequency of occurrence and cloud amount when present. While reproducing the observed cloud radiative forcing is arguably one of the benchmarks for good performance of a GCM, our approach starts to separate error contributions from cloud amount, frequency, vertical location, and cloud optical properties.

Section 2 describes the observations used for this evaluation, while section 3 introduces the model cycles and briefly summarizes the changes implemented from one cycle to the next. The methods used to compare model results with observations are explained in section 4. The use of profiler observations with a narrow footprint to estimate cloud cover over an area is always subject to a sampling error. In section 5, the impact this and other errors may have on the results of this study is explored. Section 6 concludes this article.

2. CALIPSO observations

CALIPSO observes cloud and aerosol layers with very high vertical and along-track resolution. In the lower troposphere, individual footprints are spaced 333 m apart, and vertical bins measure 30 m. Full signal attenuation occurs in features with an optical depth greater than approximately 3. Thus, the signal is frequently attenuated in marine boundary layer clouds, and a cloud-base retrieval is unreliable. For this study, the level-2 cloud layer product at 1-km horizontal resolution is used. For this product, three individual backscatter profiles with footprint diameters of about 100 m are averaged before searching for cloud layers. This improves the signal-to-noise ratio while still maintaining a high along-track resolution (Vaughan et al. 2005). Each 1-km average profile is flagged for full signal attenuation. Data from six months (January 2007, 2008, 2009 and July 2006, 2007, 2008) are compared to model results from three versions of the IFS.

3. Model cycles

The three model cycles in this comparison were chosen because they mark changes in the model physics with potential impact on the low cloud cover. Table 1 lists the model cycle names and periods during which the cycles were operational. The oldest cycle considered, CY31R1, is the cycle just previous to the model version used in the ECMWF interim reanalysis (Simmons et al. 2007) and uses the same physics package. Changes in the model physics from the 40-yr ECMWF Re-Analysis (ERA-40) to CY31R1 are described in Beljaars et al. (2006). It uses the EDMF parameterization to model boundary layer processes and stratocumulus clouds. Shallow and deep convection are parameterized using Tiedtke’s method (Tiedtke 1989).

In CY32R3, the Monte Carlo independent column approximation (McICA) is implemented and the model’s shortwave radiation is replaced by the rapid radiative transfer model RRTM-SW (Iacono et al. 2008). In addition, the convection parameterization for deep convection is updated and vertical diffusion in the free atmosphere is reduced (Bechtold et al. 2008).

The last cycle considered is a modified version of CY32R3. The EDMF dry and stratocumulus-topped boundary layer parameterization operational at ECMWF since April 2005 is now under development to be upgraded to include shallow cumulus. Neggers et al. (2009) proposed a dual mass-flux description (DualM) to allow the freedom to describe nonlocal parcels reaching cloud base and cloud top separately, but in an integral framework. Work toward implementation has required a few upgrades to the published work, which are summarized in the appendix. The dual mass flux parameterization replaces the Tiedtke scheme for shallow convection originating in the surface layer. The Tiedtke scheme is still used to represent shallow convection originating above the surface layer, allowing multilevel triggering.

In all cases, the IFS is run at T399 (approximately 50 km) resolution with 91 vertical levels. The forecasts are initialized at 0000 UTC every other day and run for three consecutive days. The first 24 h of each forecast are discarded, and days 2 and 3 of each forecast are stitched together to provide a month-long continuous record. All forecasts are initialized from the operational analysis current for the year and month of the run (Table 2). No appreciable spinup of the forecasts is apparent in the trade cumulus cloud fields after the first 12–24 h, as will be shown in the results section.

4. Method

Two simple threshold criteria for cloud fraction and cloud-top height are used to independently identify samples containing trade cumulus clouds in model and observations. The search area is restricted to the ocean between 30°N and 30°S. The frequency of occurrence, cloud-top height, and cloud fraction of these samples is then compared.

For an equitable comparison of CALIPSO observations with the model, the observations are first recast onto the model grid. The level-2, 1-km layer products used here provide the cloud-top and cloud-base height for each observed cloud layer and indicate whether the cloud fully attenuated the lidar signal. The strategy for determining vertically resolved cloud fraction on the model grid and a column-representative cloud-top height follows the steps outlined in Ahlgrimm et al. (2009). To summarize, in each model layer, the ratio of cloudy lidar shots to the total number of shots falling into the model column provides an along-track cloud fraction. The column-representative cloud-top height is an average of all observed cloud tops associated with the lowest cloud feature in the column. If this cloud-top height does not exceed 4 km, and the cloud fraction remains below 50%, the sample is considered to contain trade cumulus clouds. Over a month, the lidar samples about 96 000 ocean grid points within the prescribed region.

In the model, cloud fraction is a prognostic variable and readily available. To calculate a cloud-top height representative of the lowest modeled cloud feature in the column, the generalized overlap assumption (Räisänen et al. 2004) is used to create binary subcolumns. The number of subcolumns is equal to the number of lidar shots within the grid box. The column-representative cloud-top height is calculated equivalent to the observations from the “cloud tops” of the subcolumns. Cloud edges always fall onto model layer interfaces, consistent with the assumption that clouds fill model layers homogenously in the vertical.

A lidar simulator is used to determine whether the clouds in the subcolumns fully attenuate the lidar signal. This simulator is based on Chiriaco et al. (2006) with modifications. Particle effective radii are calculated from cloud liquid and ice water contents consistent with the IFS shortwave code of cycle CY32R3. Where the model does not provide guidance, constants and parameters are chosen as in the Cloud Feedback Model Intercomparison Project (CFMIP) Observation Simulator Package version 1.0 (available from www.cfmip.net). The simulated level of signal attenuation is used to adjust the subcolumn cloud base to an apparent cloud base where full attenuation occurs. However, the simulated backscatter signal is not used to identify cloud layers from the model. In the absence of aerosol and artificial noise (which are not included in the simulator), the simulated backscatter for lower tropospheric clouds always exceeds the molecular background such that the resulting cloud field is identical to the binary subcolumns used as input for the simulator. Parallel to the observations, the model samples, using the attenuation-corrected cloud fraction, are compared to the critical values for cloud fraction and cloud-top height and labeled TCu when appropriate.

5. Results

a. Distributions

Figure 1 shows distributions of (left) cloud fraction and (right) column-representative cloud-top height of CALIPSO samples classified as TCu for the three months of July. The sample distributions are very similar for all three Julys. In all cases, around 45% of samples fulfill the cloud fraction and top-height criteria for trade cumulus. Out of those samples, approximately 30% of individual 1-km profiles are fully attenuated (i.e., contain clouds with optical depths of more than approximately 3). The panels in the left column show that along-track cloud fractions are most frequently observed in the 10%–20% range, with slightly decreasing sample numbers for higher and lower fractions. The right panel shows the cloud-top height distribution of the TCu samples as a sample density. Since cloud boundaries in the model always fall onto model layer interfaces, irregular bins whose width corresponds to the model layer thickness are used in this distribution. The vertical axis shows the sample density within each bin as number of samples per width of the bin (m−1). The peak of this distribution is located around 850 m with a skewed tail toward higher cloud tops; shallow clouds topping out around 850 m are observed most frequently, while deeper clouds occur less often.

Figure 2 (top) shows the corresponding distributions for IFS cycle CY31R1. From here on, only July 2008 is shown, as all months look very similar and percentages do not differ by more than 1%. The cloud-top height distribution from CALIPSO is plotted in gray in the background of the right panel for easier comparison. About 70% of the samples are classified as TCu in the model, significantly more than the 45% observed. Samples with less than 10% cloud fraction are most common, with sample numbers decreasing with increasing cloud fraction. Compared to CALIPSO, it appears that most of the additional samples found in the model have small (<20%) cloud fraction. The peak in the cloud-top height distribution can be found near 1500 m, and the distribution is less skewed. The lidar simulator determines 63% of the subcolumns to be fully attenuated in the TCu samples.

The picture is similar for CY32R3 (Fig. 2, middle). In this cycle, slightly fewer samples are classified as TCu (65%), but still significantly more than observed. The cloud fraction distribution has a similar emphasis on small fractions, and cloud tops are too high. The cloud-top height distribution has a slightly lower peak than previously and is more skewed, overestimating the occurrence of deeper clouds.

The cloud-top height distribution is improved markedly by the introduction of the DualM parameterization (Fig. 2, bottom). The low-level peak agrees very well with the CALIPSO observations, though the occurrence of deeper clouds is still overestimated. Unfortunately, the occurrence of clouds with very low fraction increases again to 71%.

Results for January 2007 (Fig. 3) are very similar to the other Januarys and the months of July. Trade cumulus clouds are found with the same frequency and characteristics in observation and model, albeit in slightly different areas of the globe. The similarity of the distributions between months and seasons suggests that sample classification reliably identifies clouds with similar characteristics, regardless of season or exact location.

To ensure that clouds from forecast days 2 and 3 do not differ because of model spinup, samples have been split according to model forecast day in Fig. 4. Half the samples (from model forecast day 2) are shown in the black curve, while the other half (from forecast day 3) are shown in gray. No systematic shift in the curves or number of samples is apparent, confirming that sample populations are similar for forecast days 2 and 3. It also shows that even half a month of observations is a sufficiently long time to collect a robust sample population. These results also apply to the other months not shown here.

The shift in the cloud-top height distribution from CY32R3 to CY32R3-DM can be traced back to aspects of the Tiedtke scheme for shallow convection and the dual mass flux parameterization. In the modified Tiedtke formulation as used in CY32R3, the volume of the updraft is conserved, and the updraft mass is detrained in the upper half of the cloud. The detrained cloud volume appears as a source term in the model’s prognostic equation for cloud fraction. Almost invariably, this leads to “top heavy” clouds in the trade regions. The greatest cloud fractions in the model column are found in the upper half of the cloud, with small cloud fractions at cloud base (Fig. 5). The DualM parameterization was developed and tested based on observational campaigns such as Barbados Oceanographic and Meteorological Experiment (BOMEX; Siebesma et al. 2003), which suggest that cloud cover and mass flux are greatest at cloud base and decrease with height in the undisturbed trade wind regime. The DualM parameterization reproduces this profile well and indeed places the greatest cloud fractions at cloud base. When the model column is divided into subcolumns, the difference in the cloud fraction profiles translates into a greater number of low cloud tops for the DualM case and more numerous high cloud tops for the Tiedtke clouds.

b. Maps

Figure 6 shows maps of the observed and model frequency of occurrence of trade cumulus samples on a 2° × 2° latitude–longitude grid. The darker shades in the model figures clearly show the higher frequency of occurrence, but patterns are similar to the observations. Areas with low frequency of occurrence generally correspond to the stratocumulus regions or regions where deep convection frequently obscures the view of the lidar. Maps for the other Julys look very similar, while the maps for January reflect the seasonal shift of the ITCZ and the changes in the extent of the stratocumulus regions (not shown).

While the total number of TCu samples in the region is sufficient for robust distributions as shown in the previous figures, the noisy nature of the maps indicates that a month of observations is not sufficient for reliable statistics at any given grid point on the map.

To summarize: all versions of the model heavily overestimate the frequency of occurrence of TCu samples but underestimate sample cloud fraction. With the Tiedtke parameterization for shallow convection, cloud-top heights are often too high by several hundreds of meters, whereas the DualM scheme produces cloud tops in much better agreement with observations. The modeled clouds are optically thick, such that twice as many samples are fully attenuated in the model compared to observations.

The question remains whether the model overall over- or underestimates the cloud cover in the trade cumulus regions. A simple multiplication of the sample cloud fractions with their frequency of occurrence will not yield a satisfactory answer, since it is unknown what, if any, cloud is present when the sample does not meet the trade cumulus criteria. Figure 7 shows monthly mean total cloud cover from Moderate Resolution Imaging Spectroradiometer (MODIS) Aqua, ISCCP, CALIPSO, and the IFS. The level-3 Aqua MODIS monthly global product is used for this figure, as well as the ISCCP D2 climatological summary product (Rossow and Schiffer 1999). Comparing the model to CALIPSO, the model actually appears to be lacking cloud cover in the subtropical highs, particularly in the South Indian and Atlantic Oceans. The additional clouds that CALIPSO observes could well be subvisible high clouds, but MODIS, which does not have the same sensitivity to optically thin clouds as the lidar, also observes a higher total cloud cover in the trade cumulus regions. The ISCCP product has a lower cloud cover than the model and either of the other observational datasets in the Pacific Ocean but similar cloud cover in other areas. Cycles CY31R3 and CY32R3 have very similar total cloud cover, while the DualM parameterization produces a slightly reduced total cloud cover. This comparison of monthly mean maps is rather superficial, but the fact that the model’s cloud cover falls within the range of various observational datasets is encouraging and suggests that model’s overestimated frequency of occurrence must in large part be compensated by the low cloud fractions of the trade cumulus samples. The modeled clouds also appear to have a greater radiative impact (due to larger optical depth) than observed, which may further compensate for a lack of cloud, if the CALIPSO and MODIS figures are to be trusted. The model is well tuned to produce realistic radiative fluxes in the time mean.

c. Error sources

While the lidar can very accurately observe the vertical location of clouds, it is less than ideal for estimating the cloud fraction of an area (grid box). When using the lidar observations to estimate cloud fraction, the following error sources should be considered:

1) Attenuation error

Part of the atmosphere cannot be observed because of signal attenuation. This is a limitation of the instrument, and the areas that cannot be observed must be excluded from the comparison with model data. By using the lidar simulator to correct for signal attenuation, this error component has been addressed. Nevertheless, there are many parametric choices to be made in the simulator (explored in Chiriaco et al. 2006, Wilkinson et al. 2008, and Chepfer et al. 2008, among others), all of which have the potential to introduce inaccuracies. Also, a systematic error in either cloud occurrence or optical thickness of high clouds will have an impact on the amount of low cloud that is excluded from the comparison based on the level of full attenuation calculated by the simulator. The number of samples excluded because of upper-level optically thick clouds is slightly greater (by 3.27%) in the observations than in the model. This percentage is very consistent across months, varying by only half a percent. The difference is insufficient to explain the large discrepancy in TCu sample numbers between model and observations.

2) Averaging error

In the CALIPSO level-2 cloud layer product, three individual backscatter profiles are averaged before the algorithm searches for cloud or aerosol layers. Each footprint has approximately 100-m diameter, and the centers of footprints are spaced 333 m apart. If a layer is optically thin, the additional averaging in the 1-km product may improve the signal-to-noise ratio such that a cloudy layer can be distinguished from the background when it would otherwise have been missed in the individual profiles. But this averaging also leads to an overestimation of cloud fraction when only one or two out of the three individual profiles are cloudy, but their backscatter signal dominates the averaged profile.

To quantify the possible error in the TCu cloud fraction estimate due to averaging, we have compared each 1-km cloud layer record with the three corresponding 333-m cloud layer records for July 2008. To eliminate the influence of upper clouds, only records containing either no cloud or a cloud with top below 4 km were considered. Instead of using cloud fraction, which is unavailable from individual records, we choose a region in the central South Pacific (0°–30°S, 120°–150°W,) to restrict samples to mostly trade cumulus. The entire month of July 2008 provides roughly 780 000 1-km records in this area, and triple the number of 333-m records.

Table 3 shows the percent occurrence of clear and cloudy (with regards to clouds below 4 km) 1-km and 333-m records. In 18.8% of cases, the 1-km record detects a cloud, but fewer than three 333-m records are cloudy. The resulting difference between low cloud fractions of 42.63% (1 km) versus 31.75% (333 m) is quite considerable at 10.88%. What remains unclear is what portion of this difference is genuine additional cloud found by the improved detectability at 1 km and how much is erroneous overestimation. Barring outright errors in the algorithm, one might argue that at least the 2.88% of cloudy 1-km profiles with corresponding clear 333-m profiles would be such cases where the 1-km product is truly superior in its detection skill. The fact that this percentage rises slightly when only daytime cases are considered (and drops for nighttime) supports this interpretation, as detection in the single shot is more likely to fail in a noisier background. This leaves a remaining 8% difference in low cloud fraction that is partially an outright cloud fraction overestimate and partially a result of better signal detection in the 1-km product. This percentage is likely dependent on the nature of the cloud field—small individual clouds leading to greater errors than larger clusters. The same exercise repeated for a typical stratocumulus region (southeast Pacific) results in a potential cloud fraction overestimate of only approximately 4%.

A repetition of the sample classification described in section 4 for a worst-case scenario, where cloud fraction is overestimated in all samples by 8%, leads to only 3.1% additional TCu samples. This is insufficient to resolve the >20% difference between detected TCu samples in observations and model. The observed cloud fraction distribution (as shown in Fig. 1, bottom left) shifts toward lower values (not shown) such that the maximum between 10% and 20% cloud fraction is lost. Thus, the worst-case scenario cloud fraction distribution from CALIPSO more closely resembles the model distributions. Still, sample numbers in the lower cloud fraction bins remain smaller than for any of the model versions. Hence, the statement that all model versions overestimate the occurrence of TCu samples, and that additional samples have primarily low cloud fractions compared to observations, remains valid.

3) Sampling error

The lidar only observes along a narrow track, rather than sampling the full area covered by a grid box. In the absence of a conceptual method to quantify this error, imaging observations from Aqua MODIS can provide an empirical estimate. From the 1-km-resolution MODIS cloud mask, all points falling into a T399 model grid box are identified. A grid box has dimensions of approximately 50 km × 50 km. The ratio of cloudy to total pixels within this box provides a two-dimensional (2D; area) cloud cover estimate. By identifying those pixels within the box closest to the lidar track, a one-dimensional (1D; along-track) cloud cover can also be calculated. Since both 1D and 2D cloud cover are based on the same 1-km MODIS cloud mask, a comparison will show purely the error introduced by sampling the cloud fraction in a grid box along a track. Eight days of observations are used to produce Fig. 8 (1–8 July 2008), corresponding to just over 6000 grid points with good MODIS data. Only ocean grid points between 30°N and 30°S were used, and grid points with high clouds present were excluded based on CALIPSO cloud tops. Thus, while the area considered is the same as for the CALIPSO evaluation, all low cloud samples are included regardless of cloud fraction.

Figure 8 shows that for the 1D cloud fraction estimate, more samples fall into the lowest and highest cloud fraction bins. Most of these samples are either cloud free or are overcast. Fewer samples fall into the midrange of the distribution compared to the 2D observations. For each calculated cloud fraction sample, the 2D estimate uses many more pixels (approximately 502) compared to the along-track estimate (approximately 50). This alone will make it less probable that completely clear or cloudy grid boxes will be observed in the 2D case.

Shown in Fig. 9 (left, solid black bars) is the CALIPSO cloud fraction distribution from Fig. 1 for July 2008. While cloud-free samples were excluded previously, this figure includes all samples that are cloud free below 4 km in the lowest bin. The right panel shows the equivalent distribution for CY32R3 of the IFS. In both cases, adding the cloud-free samples does increase sample numbers in the lowest cloud fraction bin, but both the total sample number and the sample numbers at the low end of the cloud fraction range remain higher in the model compared to the CALIPSO observations.

Even though care was taken to choose MODIS samples similar to the CALIPSO trade cumulus samples, the two instruments will observe slightly different cloud fields. CALIPSO’s 1-km shots in fact represent the average of three individual lidar footprints rather than coverage of a 1-km square area. While the MODIS cloud mask shows vertically integrated cloud cover, CALIPSO’s TCu cloud fraction is based on low clouds only. Consequently, the relation of the observed 1D CALIPSO cloud fraction distribution to the unknown “true” distribution if the lidar where to sample the full area will likely differ slightly from what is shown in Fig. 8 for MODIS. Still, it seems reasonable that CALIPSO will also overestimate cloud-free and overcast occurrences and underestimate the occurrence of cloud fractions in the midrange.

Shown as gray bars in Fig. 9 (left) is the CALIPSO cloud fraction distribution corrected for the sampling error based on the quotient of 2D MODIS samples to 1D MODIS samples. This correction is not accurate, but it indicates the direction in which the CALIPSO distribution would be likely to shift if the sampling error were removed: fewer samples in the lowest bin but more samples with higher cloud fractions.

While we can still not properly quantify the sampling error, the comparison of MODIS 1D to 2D cloud fractions indicates that, qualitatively, the sampling error will shift the trade cumulus cloud fraction distribution toward higher values. Thus, the discrepancies between model and CALIPSO cloud fraction distributions cannot be explained by the sampling error. In fact, the sampling error would act to lessen the differences, but it may also be partially compensated for by the averaging error discussed above.

6. Conclusions

CALIPSO observations prove to be highly useful in the assessment of the vertical location of trade cumulus clouds. The IFS with the physics package as used in the interim ECMWF reanalysis overestimates the typical cloud-top height of trade cumulus clouds by 500 m and more. Updates to the Tiedtke convection parameterization and to the vertical diffusion do not have much impact on the trade cumulus clouds. The introduction of the DualM parameterization, however, leads to a dramatic improvement in the location of cloud-top heights and to a more realistic profile of cloud fraction.

The components of the model important for radiative balance in the trade cumulus areas are well tuned. Three of these components—cloud frequency of occurrence, cloud amount when present, and cloud optical depth—do not agree well with CALIPSO observations individually, but together they compensate to produce reasonable mean cloud cover and radiative fluxes at the top of the atmosphere. In particular, all model versions tend to underestimate the gridbox cloud fraction when trade cumulus is present, but they compensate with a higher frequency of occurrence. This compensation illustrates the difficulties in updating individual components of the model’s parameterization: all parts contributing to the balance must be addressed simultaneously or the model performance will suffer.

By classifying clouds from a large area and considering the population’s characteristics, a single month of observations is sufficient to provide a robust sample size. Cloud-top height and fraction distributions for these populations do not differ appreciably from year to year or for different seasons.

This evaluation is limited to the frequency and extent of trade cumulus clouds in the model, as these are the aspects of shallow convection that the lidar can observe. Clearly, cloud amount and occurrence are not the only benchmarks for evaluating shallow convection parameterizations, and additional evaluations of convective transport and state of the atmosphere are necessary to assess the overall performance of a parameterization. A manuscript addressing these aspects of the DualM’s performance in the IFS is in preparation.

Acknowledgments

The development and testing of the DualM parameterization in the IFS model is supported by a fellowship from the Atmospheric Radiation Measurement program at ECMWF (Grant DE-FG02-07ER64400). The ISCCP D2 data were obtained from the International Satellite Cloud Climatology Project web site (http://isccp.giss.nasa.gov) maintained by the ISCCP research group at the NASA Goddard Institute for Space Studies, New York, NY, in May 2009. The CALIPSO 1-km cloud layer product, versions 2.01 and 2.02, was retrieved from the Atmospheric Science Data Center at the NASA Langley Research Center. MODIS data were obtained through the Level 1 and Atmosphere Archive and Distribution System (LAADS) web service.

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APPENDIX

Modifications to the Dual Mass Flux Parameterization

The Dual Mass Flux parameterization as documented in Neggers et al. (2009) and Neggers (2009) is modified in the following way for the IFS CY32R3-DM discussed in this article:

  1. Wind errors are reduced and model scores improve when momentum transport by shallow cumulus convection is accounted for (Tiedtke 1989). This transport is approximated using the conventional entraining parcel–mass-flux approach without pressure gradient term.
  2. The eddy diffusivity component within layers containing shallow cumulus clouds is written as a function of stability using a Richardson number formulation just as in the statically stable atmosphere (Bechtold et al. 2008).
  3. The modified Tiedtke scheme, as used in the operational IFS, permits triggering above the surface layer (Bechtold et al. 2004), which is most commonly found in frontal convection. Currently, the DualM scheme only replaces the Tiedtke convection for shallow clouds originating in the surface layer, while the Tiedtke scheme continues to address convection trigged above.
  4. Derbyshire et al. (2004) demonstrate the large impact of environmental humidity on cumulus activity. The concept of convective premoistening suggests a mechanism whereby earlier convective updrafts moisten the environment locally, which favors the growth of later updrafts. Since such small-scale moisture variations are not explicitly resolved on the model grid, we can take advantage of the prognostic total water variance equation in the DualM shallow convection scheme to implement premoistening. The parcel entrainment is then written as
    i1520-0493-138-8-3071-eqa1
    where qenv corresponds to the mean of the top tail of a Gaussian moisture distribution with total water variance σqt2. The tail limit is currently chosen as the top 10%. Further testing with LES is needed to validate this limit.

The DualM parameterization uses large entrainment rates in agreement with LES simulations and observations (Nitta 1975; Siebesma et al. 2003). However, through convective preconditioning, we manage to maintain sufficiently strong convective transport, which is conventionally only achieved through unrealistically small entrainment rates.

Fig. 1.
Fig. 1.

(left) Cloud fraction and (right) cloud-top height distributions for all CALIPSO samples classified as trade cumulus for the months of July (top) 2006, (middle) 2007, and (bottom) 2008. The percentage of samples classified as TCu (out of all ocean grid points between 30°N and 30°S) is shown in the right figures, as well as the percentage of TCu samples that fully attenuate the lidar signal.

Citation: Monthly Weather Review 138, 8; 10.1175/2010MWR3320.1

Fig. 2.
Fig. 2.

As in Fig. 1, but for samples identified as trade cumulus from model cycles (top) CY31R1, (middle) CY32R3, and (bottom) CY32R3 using the DualM parameterization. Only results from July 2008 are shown. For easier comparison, the observed cloud-top height distribution from CALIPSO for the same month is shown in gray.

Citation: Monthly Weather Review 138, 8; 10.1175/2010MWR3320.1

Fig. 3.
Fig. 3.

(left) Cloud fraction and (right) cloud top height histograms of all samples classified as trade cumulus for January 2007 from (top) CALIPSO and (bottom) model cycle CY32R3. Shown in gray is the observed cloud-top height distribution.

Citation: Monthly Weather Review 138, 8; 10.1175/2010MWR3320.1

Fig. 4.
Fig. 4.

(left) Cloud fraction and (right) cloud top height distributions for trade cumulus samples from model cycle CY32R3 during July 2008. Sample distributions from even days of the month, corresponding to model forecast hours 24–48, are shown in black, while distributions from odd days (forecast hours 48–72) are shown in gray.

Citation: Monthly Weather Review 138, 8; 10.1175/2010MWR3320.1

Fig. 5.
Fig. 5.

Hourly output of the model’s cloud fraction from one grid point at 10.11°S, 139.05°W (left) from IFS with Tiedtke parameterization for shallow convection (the highest cloud fractions can be found in the upper half of the cloud) and (right) from the IFS with DualM parameterization (cloud fractions tend to be lower overall, with the highest values near cloud base; the cloud field is less noisy).

Citation: Monthly Weather Review 138, 8; 10.1175/2010MWR3320.1

Fig. 6.
Fig. 6.

Maps of trade cumulus sample frequency of occurrence from (top) CALIPSO, and from model cycles (middle) CY32R3 and (bottom) CY32R3-DM for July 2008.

Citation: Monthly Weather Review 138, 8; 10.1175/2010MWR3320.1

Fig. 7.
Fig. 7.

Maps of monthly mean total cloud cover from (top to bottom) CALIPSO, Aqua MODIS, ISCCP, and the model for the month of July 2006. The white solid contour marks the 50% level.

Citation: Monthly Weather Review 138, 8; 10.1175/2010MWR3320.1

Fig. 8.
Fig. 8.

Cloud fraction distributions for MODIS cloud mask sampled within a grid box (gray, 2D) and along the CALIPSO track (black, 1D) from 1–8 July 2008. Only ocean samples between 30°N and 30°S are considered. Samples where CALIPSO detects high clouds are excluded. The difference between 1D and 2D distributions provides an empirical estimate of the sampling error for low clouds in the tropical and subtropical oceans.

Citation: Monthly Weather Review 138, 8; 10.1175/2010MWR3320.1

Fig. 9.
Fig. 9.

Cloud fraction distributions from (left) CALIPSO and (right) CY32R3 of the IFS. The leftmost bin includes samples that are cloud-free below 4 km. Shown in gray is the CALIPSO distribution corrected for the sampling error, based on 1D vs 2D cloud fraction comparison performed with MODIS cloud mask.

Citation: Monthly Weather Review 138, 8; 10.1175/2010MWR3320.1

Table 1.

ECMWF model cycles.

Table 1.
Table 2.

Operational analyses that were used to initialize model runs.

Table 2.
Table 3.

Frequency (%) with which clear and cloudy 1-km profiles coincide with clear and cloudy individual 333-m profiles in the central South Pacific (0°–30°S, 120°–150°W) during July 2008. The category “other cloud” contains all samples with upper-level clouds.

Table 3.
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