Abstract

The main purpose of this study is to underline the sensitivity of cloud liquid water content (LWC) estimates purely to 1) the shape of computationally simplified temperature-dependent thermodynamic phase and 2) the range of subzero temperatures covered to partition total cloud condensate into liquid and ice fractions. Linear, quadratic, or sigmoid-shaped functions for subfreezing temperatures (down to −20° or −40°C) are often used in climate models and reanalysis datasets for partitioning total condensate. The global vertical profiles of clouds obtained from CloudSat for the 4-yr period June 2006–May 2010 are used for sensitivity analysis and the quantitative estimates of sensitivities based on these realistic cloud profiles are provided. It is found that three cloud regimes in particular—convective clouds in the tropics, low-level clouds in the northern high latitudes, and middle-level clouds over the midlatitudes and Southern Ocean—are most sensitive to assumptions on thermodynamic phase. In these clouds, the LWC estimates based purely on quadratic or sigmoid-shaped functions with a temperature range down to −20°C can differ by up to 20%–40% over the tropics (in seasonal means), 10%–30% over the midlatitudes, and up to 50% over high latitudes compared to a linear assumption. When the temperature range is extended down to −40°C, LWC estimates in the sigmoid case can be much higher than the above values over high-latitude regions compared to the commonly used case with quadratic dependency down to −20°C. This sensitivity study emphasizes the need to critically investigate radiative impacts of cloud thermodynamic phase assumptions in simplified climate models and reanalysis datasets.

1. Introduction

Given their importance in the water and energy cycle, cloud properties are recognized as one of the essential climate variables (ECVs) by the Global Climate Observing System (GCOS; Mason et al. 2004). From the observational perspective, international initiatives such as the International Satellite Cloud Climatology Project (ISCCP), the Global Energy and Water Cycle Experiment Cloud Assessment (GEWEX CA), and the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) Satellite Application Facility for Climate Monitoring (CM-SAF) (Rossow and Schiffer 1999; Schulz et al. 2009; Stubenrauch et al. 2009) have substantially helped and continue to help in understanding the statistical characteristics of most cloud properties. Cloud water is one of those key properties tightly linked to microphysical as well as dynamical processes. In spite of the considerable progress over the recent years, cloud ice and liquid water still remain major sources of intermodel differences (Li et al. 2008; Waliser et al. 2009). One of the least understood and most elusive microphysical properties of clouds is its liquid water content (LWC). Considering its key role in atmospheric radiative transfer, further information about LWC is useful to evaluate climate models and study relevant processes.

Knowledge of the processes governing the thermodynamic phase of cloud condensate is central to partition total condensate into liquid and ice fractions, which differ substantially in their radiative properties and consequently impact on the cloud–precipitation interactions and radiation budget in climate models. However, the explicit representation of the cloud thermodynamic phase can be quite challenging and some kind of simplified temperature dependency is, therefore, often used. At present, there is no general consensus on (a) the shape of temperature-dependent probability function of liquid or ice phase occurrence and (b) the temperature range to be used to scale total cloud condensate. Apart from the linear dependency on temperature, quadratic functions or some types of sigmoid functions are also often used (or observed) for subzero freezing temperatures to partition total condensate into liquid or ice phase (Dee et al. 2011; Doutriaux-Boucher and Quaas 2004; Hu et al. 2007, 2010; Naud et al. 2010; Uppala et al. 2005; Wood 2008). The subzero temperature range from 0° to down to −20° or −40°C is often used to scale the total cloud condensate. For example, in the current versions of the EC-EARTH model (up to version 3.0) and the 40-yr and interim European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analyses (ERA-40 and ERA-Interim, respectively), the quadratic dependency is assumed to be in the range of −23° to 0°C (Hazeleger et al. 2010; Uppala et al. 2005; Dee et al. 2011). The different temperature dependencies, especially with respect to the shape of an assumed function, could be a significant source of intermodel differences in the estimates of LWC. More importantly, it would lead to different estimates of downwelling radiation at surface. Thus, it is imperative to investigate sensitivity of LWC estimates to these different shapes of temperature-dependent probability functions of liquid or ice phase occurrence and the range of subzero temperatures covered for partitioning total condensate.

For the first time, it is possible to obtain estimates cloud LWC globally using the Cloud Profiling Radar (CPR)/CloudSat data (Stephens et al. 2002; Wood 2008). So far, there are very few observational studies that characterize cloud LWC globally (Hogan et al. 2004; Hu et al. 2007, 2010; Lee et al. 2010). In particular, Hu et al. (2010) present comprehensive global statistics of supercooled water clouds combining Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) and Moderate Resolution Imaging Spectroradiometer (MODIS) data and also examine the relationship between temperature and cloud phase. However, virtually no study exists that provides information on the expected spread in the global estimates of LWC solely due to assumptions on the shape of temperature-dependent cloud thermodynamic phase.

2. The CloudSat datasets

We use the standard 2B-CWC-RVODproduct for the present study (Wood 2008). In this product, for every cloudy profile, both liquid-only and ice-only retrievals are provided in addition to combined cloud water content. The liquid-only retrievals are obtained assuming that the entire cloudy profile consists of only liquid phase cloud, while the same cloudy profile is then assumed to be in only ice phase and the ice-only estimates of water content are retrieved. For cloudy bins with temperatures warmer than 273.15 K, original liquid-only estimates are kept unchanged as LWC. For each CloudSat bin that falls into the temperature range of 253.15–273.15 K, the liquid-only and ice-only water content estimates are scaled linearly adjusting number concentration. The liquid and ice water content (IWC) are computed using the following equations:

 
formula

where NT is droplet number density, rg is geometric mean radius, and w is the distribution width parameter; and

 
formula

where NT is ice particle number concentration, Dg is geometric mean diameter, and w is the distribution width parameter.

Following the approaches of Marks and Rodgers (1993), Austin and Stephens (2001), Austin et al. (2009), the forward model is used to estimate the number density, radius, and the width parameter required to compute LWC and IWC. Using an optimal estimation technique, the forward model relates a state vector of known quantities (i.e., radar reflectivities and visible optical depth) to a state vector of unknowns (i.e., number density, radius, and the width parameter). The a priori values of unknowns together with their covariance matrix (representing variability) are initially assigned based on climatology, temperature, and other criteria. The measurement error covariance matrix provides estimates of uncertainties in the measurements (noise, calibration, etc.). By minimizing a cost function that represents a weighted sum of the measurement vector–forward model difference and the state vector–a priori difference, the retrieval algorithm obtains the optimal solution. The visible optical depth information is ingested from the 2B-TAU product (Polonsky et al. 2008). This product makes use of MODIS reflectivities (as a function of observational geometry) from the level 1B data to retrieve estimates of optical depth and effective radius. Further in-depth details of the retrieval procedure can be obtained from the process description and interface control document by Wood (2008).

To avoid contamination from precipitation, we further make use of the precipitation flag from the standard 2C-PRECIP-COLUMN product (Haynes 2008). This flag is, however, only available over the oceans and we rely on the precipitation flag provided in the 2B-CWC-RVOD product over land. Further details on the algorithm theoretical basis and retrieval framework of these flags can be obtained in Haynes (2008) and Wood (2008).

The data for the 4-yr period from June 2006 to May 2010 are analyzed. The data are further partitioned for day and night conditions. The analysis is carried out for four seasons, namely December–February (DJF), March–May (MAM), June–August (JJA), and September–November (SON) months. For quality control, the retrievals are not used if bad GEOPROF input or bad ECMWF temperature input or large χ2 values are reported by the RVOD_CWC_Status flag as recommended by the CloudSat Science Team. Furthermore, the retrievals of LWC are used only if χ2-based scaled uncertainty (see Wood 2008) is less than 100%. Note that these data products from CloudSat are under continuous development. Nevertheless, they are mature and validated enough to investigate the large-scale statistics of LWC and to use for the sensitivity studies. The temperature profiles from the ERA-Interim reanalysis data (Dee et al. 2011) are additionally used for the same time period.

It is important to keep the few limitations of CloudSat retrievals in mind, while interpreting the results presented in the next section. The retrievals below 800 m are not quantitatively useful because of the influence of ground clutter, and hence they are not used. This has an implication for regions such as the Arctic and the parts of the southeast Atlantic, where very low-level clouds will not be included in the analysis. Estimating a fraction of vertical distribution missed as a result of this limitation is difficult since it is a function of region, season, and local processes as well as of atmospheric transport of heat and moisture, etc. But one can certainly provide a range based on the previous studies. For example, Shupe et al. (2011) provide the most up-to-date description of cloud vertical structure over the Arctic at six measurement stations. Their study shows that the cloud fraction in the boundary layer varies considerably across different stations and throughout the year. In the Surface Heat Budget of the Arctic Ocean (SHEBA), the majority of clouds (>50%) are within the lowermost 1 km of the troposphere and show a distinct bimodal seasonal cycle, whereas in Eureka less than 30%–40% of all clouds are below the lowerest kilometer. Using CALIPSO data covering nearly the entire Arctic, Devasthale et al. (2011) show that roughly 35% of all thin water clouds are observed below 800 m in spring and about 25% in other seasons. It is, however, to be noted that even if CloudSat cannot fully sample all cloud regimes over the Arctic, these clouds remain highly susceptible to the assumptions regarding the temperature range and the relationship shape (as shown later in the present study) because of their mixed-phase nature (Shupe 2011). Another inherent limitation is that, in mixed-phase clouds, the radar reflectivity is not an exact representative of either liquid-only or ice-only cloud condensate. Assuming only one phase for retrieval in such clouds may lead to biases in LWC estimates. Unfortunately, it is extremely difficult to estimate such bias. Assuming that the liquid fraction dominates in mixed-phase clouds (based on the few previous studies) and considering the fact that we used median rather than mean LWC values for analysis, we hope that this bias is partly alleviated. Nevertheless, it is to be noted that in spite of these limitations, CloudSat still provides the most faithful description of global cloud vertical structure hitherto among the datasets available for research.

3. Results and discussions

From the radiation budget perspective, it is important to understand which cloud regimes are likely to show high sensitivity to assumptions on thermodynamic phase. Figure 1 shows various types of clouds typically observed zonally in the northern hemispheric summer that likely hold liquid water. The rising branch of the Hadley cell manifests itself into convective cloud systems in the tropics. The large vertical extent of these clouds entails that the ice phase predominantly occurs above freezing level (typically around 5 km) and liquid phase below. The baroclinic disturbances in midlatitudes leading to frontal systems often set conditions for the spectrum of clouds vertically extending across the freezing level. A growing body of evidence suggests that, in the Arctic, thin clouds consisting of supercooled liquid water are often present during the winter half of the year and precipitate ice crystals (Intrieri and Shupe 2004).

Fig. 1.

The schematic diagram showing a simplistic zonal view of different cloud regimes that contain liquid water.

Fig. 1.

The schematic diagram showing a simplistic zonal view of different cloud regimes that contain liquid water.

The footprints of these major cloud regimes and their zonal features are evident in Fig. 2, which shows zonal histograms of LWC for different seasons and for the land–ocean and day–night conditions. In general, the median LWC shows decreasing tendency from the tropics to poles and the probability density functions (PDFs) become narrower. Note that the shapes of PDFs vary zonally and thus are functions of cloud regime or type. The signatures of summer monsoons are also visible in the distributions of LWC (refer to the plots for JJA months). The convective systems associated with Indian, East Asian, and African monsoons harbor clouds with a wide range of liquid water. This is visible in the broadest PDFs of LWC in the 0°–40°E latitude band during the JJA months. The day–night differences in the PDFs are also strongest during these months over the oceanic areas. The signatures of seasonal shifts in the intertropical convergence zone and monsoonal clouds are prominently visible in these figures.

Fig. 2.

The zonal histograms of liquid water content (2006/07–2009/10). Each bin is 1 mg m−3 by 1° latitude and is normalized along the y axis by the total number of observations summed at particular latitude bin.

Fig. 2.

The zonal histograms of liquid water content (2006/07–2009/10). Each bin is 1 mg m−3 by 1° latitude and is normalized along the y axis by the total number of observations summed at particular latitude bin.

In the present study, we investigate the three most commonly used shapes of temperature-dependent cloud thermodynamic phase, linear, quadratic, and sigmoid, in the temperature range from 0° to −20°C.

  • Linear assumption: It is assumed that the fraction of liquid phase decreases linearly as a function of subfreezing temperature. This assumption is used in the current version of the CloudSat 2B-CWC-RVOD data. The fraction of water phase (p) would be 
    formula
    where T is temperature at a particular level, Tmin = 253.15 K, and Tmax = 273.15 K.
  • Quadratic assumption: It is assumed that the relationship between the fraction of liquid phase and subfreezing temperature is quadratic. This assumption is commonly used in the climate models that do not have separate explicit ice and liquid water prognostics and in reanalysis datasets (e.g., EC-EARTH, ERA-40, and ERA-Interim). The fraction of water phase p in this case would be 
    formula
  • Sigmoid assumption: The recent studies that mainly use observational data show that the relationship is most likely to be some form of the sigmoid function. We use the following form to represent the sigmoid family: 
    formula
    where Tr = 20 K (total temperature range; i.e., 273.15 K − 253.15 K) and Td is the discretized temperature range between 253.15 and 273.15 K in intervals of 1 K.

These fractions for partitioning total condensate into liquid phase as a function of temperature based on the above three assumptions are shown in Fig. 3. It can be clearly seen that the quadratic assumption will lead to underestimation of LWC and the sigmoid assumption to overestimation when compared to the linear function. In practice, the estimates of LWC under these three assumptions are calculated as follows:

  • For each cloudy profile, the quality control as mentioned in section 2 is applied.

  • It is then checked if both ice and liquid water content retrievals are reported for the profile (using variables RVOD_liq_water_content and RVOD_ice_water_content in the 2B-CWC-RVOD product) and if the temperature in the cloudy bins is in the range from 253.15 to 273.15 K using ERA-Interim temperature profiles.

  • If the above conditions are satisfied, then the liquid-only retrievals of water content for these cloudy bins are scaled according to the three probability functions (at the corresponding temperatures).

  • The liquid-only retrievals are kept unchanged for cloudy bins with temperature greater than 273.15 K.

  • To clearly demonstrate the sensitivity of LWC estimates to these assumptions, we express the percentage change in median LWC estimates in the quadratic and sigmoid cases with respect to the linear case.

The results of this analysis are shown in Fig. 4 for the nighttime conditions. Note that all 4-yr data are used in the analysis. It is observed, as expected, that the percentage deviation in the mean values of LWC is negative for the quadratic assumption and positive for the sigmoid assumption. The calculated percentage deviation varies from season to season and for land–ocean and day–night conditions. The maximum absolute deviations with respect to the linear case are observed over the deep convective regions (20%–40%) in the tropics and over the stratus, stratocumulus, and altocumulus regions in the middle and high latitudes (≥50%). The maximum differences vary seasonally and spatially following the ITCZ and mesoscale convective regions in the tropics. The persistent altocumulus clouds over the southernmost parts of the Southern Ocean (around 60°–70°S) show very high sensitivity with differences greater than 40%. The midlatitude clouds have differences in LWC estimates on the order of 10%–30%. The clouds in the extratropics have the least sensitivity.

Fig. 3.

The temperature-dependent probability of water phase clouds. The black line indicates the linear function used in the standard CloudSat 2B-RVOD-CWC product. The blue and red lines indicate quadratic and sigmoid functions, respectively.

Fig. 3.

The temperature-dependent probability of water phase clouds. The black line indicates the linear function used in the standard CloudSat 2B-RVOD-CWC product. The blue and red lines indicate quadratic and sigmoid functions, respectively.

Fig. 4.

The percentage change in LWC in the quadratic and sigmoid cases with respect to the linear case for the daytime data. The spatial grid size is 5° × 5°.

Fig. 4.

The percentage change in LWC in the quadratic and sigmoid cases with respect to the linear case for the daytime data. The spatial grid size is 5° × 5°.

Figure 5 shows the spatial locations where clouds with subzero temperatures (supercooled liquid water) up to −20°C, analyzed above, were encountered. Their occurrence is normalized with respect to the highest frequency to facilitate comparison in different seasons. It can be clearly seen that the majority of these clouds are observed over middle and high latitudes but also, to some extent, over the convective regions in the tropics where they follow seasonality in the ITCZ and monsoons. These clouds are persistent over the Southern Ocean in all seasons, while during the winter half of the year they are present over the northeast Atlantic and northern Pacific where winter storms are typically observed. It is interesting to note that the spatial pattern in Fig. 5 looks similar to the one observed by Hu et al. (2010) for supercooled water clouds studied using combined CALIPSO–MODIS data over the middle and high latitudes, with the difference that we additionally observe these clouds over the tropics. This may be due to the fact that the Cloud–Aerosol Lidar with Orthogonal Polarization (CALIOP) cloud phase can be retrieved only for the uppermost part of deep convective clouds, the tops of which could be in ice phase and hence not considered in their analysis. CloudSat, on the other hand, provides the entire vertical cross section of clouds and thus enables us to additionally consider those mixed-phase parts (based purely on temperature criteria) within deep convective clouds.

Fig. 5.

The seasonal normalized frequency of occurrence of clouds in the CloudSat vertical bin in the range of 253.15–273.5 K.

Fig. 5.

The seasonal normalized frequency of occurrence of clouds in the CloudSat vertical bin in the range of 253.15–273.5 K.

Figure 6 shows normalized frequency of the number of data bins (each ~240 m in depth) in the 2B-CWC-RVOD product that fall into the temperature range of 253.15–273.15 K as a function of latitude in different seasons, while Fig. 7 shows the vertical location of these bins in the atmosphere. These figures essentially provide statistics on depth and height of the part of the cloudy profile that would be influenced by the assumption on thermodynamic phase. This part of the cloudy profile is hereafter denoted as the mixed-phase profile (MPP). Over the high-latitude regions, about 50% of MPPs have geometrical depth less than 500 m and are found mostly below 2 km. Toward the low-latitude regions, the distribution of MPPs is broader, suggesting the existence and sampling of more geometrically thicker clouds from the convective systems. The arch-like structure of maximum distribution in Fig. 6 mainly reflects the zonal variation of freezing height. Figures 5 and 6 also indirectly confirm the above interpretation that convective, stratus, and altocumulus clouds are most sensitive to these assumptions.

Fig. 6.

The seasonal and night, normalized zonal frequency distribution of the number of cloudy CloudSat bins (y axis) in the vertical profiles that fall into the temperature range of 253.15–273.15 K.

Fig. 6.

The seasonal and night, normalized zonal frequency distribution of the number of cloudy CloudSat bins (y axis) in the vertical profiles that fall into the temperature range of 253.15–273.15 K.

Fig. 7.

The seasonal and night, normalized zonal frequency distribution of the height of cloudy bins in the vertical profile that fall into the temperature range of 253.15–273.15 K.

Fig. 7.

The seasonal and night, normalized zonal frequency distribution of the height of cloudy bins in the vertical profile that fall into the temperature range of 253.15–273.15 K.

There is growing evidence that the cloud condensate is sustained in liquid phase even down to −40°C [e.g., the most recent studies by Hu et al. (2010) and Shupe (2011), and references therein]. Although many state-of-the-art models do take into account this wider range of temperature when partitioning total condensate, it is, however, not yet reflected in the mainstream reanalyses such as ERA-Interim, ERA-40, and the National Centers for Environmental Prediction (NCEP) reanalysis. Therefore, in order to understand sensitivity to this wider subzero temperature range, we investigated the percentage difference in median LWC for two cases: when the sigmoid relationship for temperatures down to −40°C is applied and when the quadratic relationship for temperatures down to −20°C is applied. The choice of these two cases was based on the fact that the first relationship is most recently observed by Hu et al. (2010) based purely on observational data and close to the latter (−23°C) is used in reanalyses such as ERA-40 and ERA-Interim. The CloudSat data processing in these two cases is in principle similar to as explained above in steps (a)–(e). The result of this analysis is shown in Fig. 8. As expected, much wider range of subzero temperatures in one case compared to the other (−40° vs −20°C) and the differences in the shapes of the temperature-dependent partitioning function (sigmoid vs quadratic) have an amplifying effect on the percentage differences in median LWC as shown in Fig. 7. The spatial pattern and seasonality, however, resemble those in Fig. 4. Over the convective regions in the tropics, the differences could reach 50%–80%, while over high-latitude regions they can be even higher, reaching and exceeding 100%.

Fig. 8.

The seasonal percentage change in LWC in the sigmoid case with temperature down to −40°C with respect to the quadratic case with temperatures down to −20°C for the nighttime data.

Fig. 8.

The seasonal percentage change in LWC in the sigmoid case with temperature down to −40°C with respect to the quadratic case with temperatures down to −20°C for the nighttime data.

4. Conclusions and implications

The CPR/CloudSat data offer unique insight into the global distribution of cloud liquid water content, an important variable that hitherto has remained elusive. The information on this microphysical property of clouds is extremely useful not only for process studies but also to evaluate climate models in order to understand their strengths and improve weaknesses. Here, a global view of LWC using four years of data from the standard 2B-CWC-RVOD product is presented and the sensitivity of LWC estimates purely to 1) the shape of temperature-dependent thermodynamic phase and 2) the range of subzero temperatures used for partitioning total cloud condensate into liquid and ice fractions is investigated. These simplifications are often used in climate models and reanalysis datasets. We tested the three most common shapes of temperature dependency functions, namely, linear, quadratic, and a form of sigmoid, and investigated two subzero temperature ranges, down to −20° and −40°C.

The need for bracketing this sensitivity has been understood in the scientific community for a while, and based on the definitions of three functions it was expected that positive differences would be observed for the sigmoid case and negative ones for the quadratic case with respect to the linear case. However, the novelty of the present study lies in that, given the availability of realistic information on layer-by-layer cloud verticality from the active CloudSat cloud profiling radar, we were able to precisely quantify these differences for the first time and highlight cloud regimes that are most sensitive to thermodynamic assumptions.

It is found that particularly three cloud regimes—convective clouds in the tropics, low-level clouds in the northern high latitudes, and middle-level clouds over the midlatitudes and Southern Ocean—are most sensitive to assumptions about the thermodynamic phase. The LWC estimates based purely on quadratic or sigmoid functions in these cloud types can differ by up to 20%–40% over the tropics (in seasonal means), 10%–30% over the midlatitudes, and up to 50% over high latitudes compared to a linear assumption. When the temperature range is extended down to −40°C, LWC estimates in the sigmoid case can be much higher than above values over high-latitude regions compared to the commonly used case with quadratic dependency down to −20°C.

From the radiation budget perspective, it is important to understand how much impact these different assumptions have on the downwelling fluxes (also via cloud–precipitation processes). It is to be noted that the highest differences are observed over three distinct cloud regimes and over two key geographical regions, the one mainly acting as an energy source (e.g., convective regimes in the tropics) and the other as a heat sink (stratus and stratocumulus regimes in the high latitudes). Another important implication is that the broadly similar differences (in absolute amounts) would also be evident in the estimation of ice water content due to these assumptions. An underestimation (overestimation) of LWC in the quadratic (sigmoid) case would lead to the overestimation (underestimation) of IWC with respect to the linear case. The third implication is that we need to be cautious in comparing cloud properties from climate models and reanalysis data with different assumptions on cloud phase. Finally, it is worthwhile to point out that the observed differences are reported for LWC averaged over the entire cloudy profiles and with respect to the linear case. These differences would be even higher only for those parts of cloudy profiles that fall into the temperature range of 253.15–273.15 K and for the sigmoid versus quadratic cases. Although many state-of-the-art climate models have improved and have separate prognostics for liquid and ice water, temperature and height still remain the deciding factors in determining cloud phase. More experimental or aircraft measurements over different cloud regimes are needed to better understand the probability function that is most likely to represent reality and the role of microphysical and dynamical processes therein. Detailed comparisons with other global satellite datasets (e.g., Hu et al. 2010) and recent data from phase 5 of the Coupled Model Intercomparison Project (CMIP5) will be attempted in future. The present study is a good example of the usefulness of an active satellite sensor in studying the impact of different parameterizations in global climate models.

Acknowledgments

The authors thank the CloudSat Science Team and CloudSat DPC for the data. The ERA-Interim data were obtained from the ECMWF data server. We would also like to thank two anonymous referees and the editor (Robert Wood) for their constructive suggestions and help during the review process. This study was funded by Swedish National Space Board.

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