1. Introduction
Clouds play important roles in large varieties of weather and climate phenomena (e.g., Liou and Ou 1989; Lynch 1996; Mueller et al. 2011). The impact of clouds on weather and climate is due to the linkage between clouds and radiation processes. The interaction between clouds and radiation, especially cloud overlap in radiation process, is also related to long-term global climate precipitation (e.g., Bechtold et al. 1993; Jakob and Klein 2000). Clouds can change the local and global radiation balances and, in turn, variations of radiation can affect the formation and dissipation of clouds (Rybka and Tost 2014). Therefore, in aspects of numerical weather prediction and climate change, it is important to resolve realistic cloud fractions. To simulate realistic cloud fractions, a large number of cloud fraction schemes have been developed over the past several decades. These were developed by employing two types of methods based on diagnostic and prognostic approaches.
Cloud fractions parameterized by the diagnostic approach are simply expressed as a function of relative humidity (e.g., Slingo 1987; Slingo and Slingo 1991) or as a function of both relative humidity and cloud water contents (e.g., Xu and Randall 1996) and can also use a probability density function (PDF) of moisture variability within a grid box (Smith 1990). Prognostic cloud fraction schemes are based on a prognostic equation composed of source and sink terms of cloud area (e.g., Tiedtke 1993; Tompkins 2002; Wilson et al. 2008a). Because of the need to represent various sources and sinks, prognostic cloud fraction schemes are relatively complex compared with diagnostic cloud fraction schemes (Franklin et al. 2012). For this reason, diagnostic cloud fraction schemes [in particular, the scheme proposed by Xu and Randall (1996)] have been used in several weather and climate models such as the Canadian Climate Model (CCM) (von Salzen and McFarlane 2002), the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5), and the International Pacific Research Center (IPRC)-RegCM model (Wang et al. 2004). However, significant uncertainties related to diagnosed cloud fractions were reported by Wetzel and Bates (1995). Moreover, observed cloud fractions are strongly dependent on cloud water, while diagnosed cloud fractions mostly depend on relative humidity (Shimpo et al. 2008). Therefore, diagnostic cloud fraction schemes were replaced with prognostic cloud fraction schemes in the Met Office Unified Model (UM) (e.g., Wilson et al. 2008a,b) and in the European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecast System (IFS) (e.g., Klein and Jakob 1999; Hogan et al. 2001). As a result of this change, it was reported that the simulations conducted via prognostic cloud fraction scheme had slightly better agreements with observations than those conducted via diagnostic cloud fraction scheme (e.g., Delanoë et al. 2011).
The source and sink terms in a prognostic cloud fraction scheme involve planetary boundary layer (PBL) mixing, convection, advection, condensation, and evaporation (Tiedtke 1993). Recently, the importance and variability of convection schemes in relation to cloud fraction schemes have been emphasized (e.g., Teixeira 2001; Franklin et al. 2012; Rybka and Tost 2014). Based on Rybka and Tost (2014), global model simulations with different convection schemes significantly differ in the transport of trace gases and precipitation patterns due to the assumptions and formulations of convection schemes. Franklin et al. (2012) argued that interactions between cloud schemes and convection schemes play an important role in temperature and moisture errors. It was also reported that in order to obtain a realistic cloud fraction, a coupling with the convection parameterization is important (Teixeira 2001). Therefore, the formation of cloud area by convection in a prognostic cloud fraction scheme should be treated carefully. For the above reasons, in this study, a prognostic cloud scheme has subsequently been modified with respect to coupling with convective parameterization. Additionally, this prognostic cloud scheme has been evaluated in a global forecasting system.
2. Prognostic cloud scheme
It has been well established that cloud fraction is proportional to the quantities of cloud water contents. The various relations between cloud fractions and condensed cloud water contents have been suggested based on observations (e.g., Wood and Field 2000; Gultepe and Isaac 2007; Shimpo et al. 2008). In particular, Gultepe and Isaac (2007) developed formulas considering the subgrid-scale variability using data measured from the Alliance Icing Research Study (AIRS) field campaign over the region in Ontario during the winter of 1999/2000. However, the formulas suggested by Gultepe and Isaac (2007) were made with the observations of stratiform clouds, and, therefore, new formulas for convective clouds were devised in this study.
Relations between cloud water content and cloud fraction for (a) 100- and (b) 50-km scales using CloudSat data during July 2010. The N represents the number of data used to make formulas describing the relations between cloud water contents and cloud fractions for convective clouds. (c) The dashed lines and solid lines indicate the relations between cloud water contents and cloud fractions for stratiform clouds and convective clouds, respectively.
Citation: Monthly Weather Review 144, 3; 10.1175/MWR-D-15-0273.1
Horizontal distribution of temporally and vertically averaged cloud water contents formed via cumulus parameterization scheme in our global forecasting model during July 2013.
Citation: Monthly Weather Review 144, 3; 10.1175/MWR-D-15-0273.1
Vertical profiles of horizontally averaged (over 10°S–20°N, 180°–180° during July 2013, shown as a rectangle in Fig. 2) (a) temperature, (b) cloud water contents formed by cumulus parameterization scheme, and (c) cloud fractions calculated using Eq. (5). Cloud water contents were obtained from a global model simulation and were averaged only when cumulus convection occurred. The atmosphere was divided into warm, mixed, and cold phases depending on temperature in (a). In (b), the solid line, the dashed line, and the chain line indicate total cloud water mixing ratio, cloud liquid water mixing ratio, and cloud ice water mixing ratio, respectively. In (c), the solid and dashed lines represent cloud fraction with and without consideration of the difference of ice and liquid water densities in clouds.
Citation: Monthly Weather Review 144, 3; 10.1175/MWR-D-15-0273.1
3. Experimental setup
To evaluate the impact of the prognostic cloud fraction scheme on our global forecasting system, comparative studies were conducted via a diagnostic cloud fraction scheme and the prognostic cloud fraction scheme (these will hereafter be referred to as DIAGC and PROGC, respectively). Details of the physics package including DIAGC and PROGC are presented in Table 1. The performance of diagnostic or prognostic cloud fraction schemes depends on the models used, and, therefore, the comparative studies were conducted using a same modeling system, Global/Regional Integrated Model system (GRIMs). GRIMs is a multiscale atmospheric/oceanic model system with unified physics that is used in numerical weather prediction, seasonal simulations, and climate research projects, with applications ranging from global to regional scales (Hong et al. 2013). The experiments have been conducted only in the global version and no regional modeling has been done. The 1-month simulations during July 2013 were carried out for the comparison of cloud fractions via DIAGC and PROGC. Additionally, in order to investigate the impact of PROGC on our global modeling systems, 10-day simulations were also conducted for a specific event and the case of heavy rainfall event over the Korean Peninsula [1200 UTC 25 July–1200 UTC 4 August 2011, details are described in Jang and Hong (2014)], was selected. The horizontal resolution was a T254 resolution, with approximately 50-km grid spacing, and the vertical resolution was defined by 42-layer hybrid sigma-pressure coordinates (Koo and Hong 2013).
The GRIMs physics packages used in the comparative study presented in this study. Physics packages for DIAGC and PROGC are identical to the GRIMs physics package V3.3 excepting for cloudiness, and the current GRIMs physics package V3.3 is identical to PROGC.
4. Results and discussion
To evaluate the performance of the prognostic cloud fraction scheme, cloud fractions calculated from GRIMs simulations for the cases of DIAGC and PROGC were compared with combined data from Cloud–Aerosol Lidar with Orthogonal Polarization (CALIOP) and CloudSat. Recently, the effectiveness of coincident CALIOP and CloudSat observations has been emphasized (e.g., Hogan et al. 2006; Stein et al. 2011; Naud et al. 2013) because of the reduced sensitivity of CloudSat observations to thin cirrus (e.g., Im et al. 2007; Liu et al. 2010) and to low clouds (e.g., Stephens et al. 2002). The combined CALIOP and CloudSat dataset was created by combination of two CloudSat standard products and CALIOP Level-2 Vertical Feature Mask (VFM) data (Kay and Gettelman 2009), and monthly cloud fractions collected during the month of July from 2006 to 2009 were used for evaluation. The horizontal distributions of low-, mid-, and high-level cloud fractions calculated via PROGC and DIAGC were evaluated via comparison with satellite data in Fig. 4. Here, low-, mid-, and high-level clouds from simulation results were defined as maximum cloud fractions between surface–700, 700–400, and 400–0 mb, respectively, and, therefore, the comparison with satellite observation could have uncertainty because algorithms used to calculate low-, mid-, and high-level clouds from simulation results and satellite observations are different. Cloud fractions via PROGC were greater than those via DIAGC. The relatively small cloud fractions via DIAGC were previously cited by Lazarus et al. (1999), who reported that the cloud fractions diagnosed from Xu and Randall (1996) tended to be underestimated, compared with data from the Atlantic Stratocumulus Transition Experiment (ASTEX). A large volume of high-level clouds via PROGC appears to be partly caused by cloud formation under the cold phase because cloud fractions under this phase are slightly high compared with those under the warm phase (as mentioned in section 2). Moreover, distinct patterns of low- and midlevel clouds over the equatorial region were effectively captured in results via PROGC; these are also shown in the combined CALIOP and CloudSat datasets. The low- and midlevel clouds over the equatorial region via PROGC reflect the vertical distribution of cloud water formed by subgrid cumulus convection, shown in Fig. 3. Cloud fractions determined via PROGC appear to be more realistic than those generated via DIAGC when they are compared with satellite data according to aspects of horizontal distributions and horizontal mean values. The horizontally averaged values of low-, mid-, and high-level cloud fractions via PROGC were similar to those of satellite data, while those via DIAGC were found to be relatively small, having values that were roughly half of those corresponding to satellite data and PROGC cloud fractions. In particular, it was remarkable that cloud fractions over the ocean for DIAGC were shown to be relatively small, compared with those for PROGC and satellite data (see the white areas, where cloud fractions are less than 0.1). In reality, we can easily observe the cloudy atmosphere over the ocean from satellite images (e.g., King et al. 2013), but the diagnostic cloud fraction scheme does not appear to be able to capture this feature. Moreover, a large volume of clouds near the Antarctic region during the austral winter via PROGC showed good agreement with satellite data, as previously mentioned by Hines et al. (2004), who reported that a large mass of clouds near the Antarctic region was primarily composed of midlevel cloud. On the other hand, a large volume of low-level clouds over the Arctic region, commonly shown in DIAGC and PROGC, was not observed in the satellite data. Based on the evaluation presented in Fig. 4, cloud fractions determined via PROGC appear to be more realistic than and highly preferable to those determined via DIAGC although there are some discrepancies between the simulated cloud fractions and satellite observations over Artic region.
Horizontal distributions of cloud fractions of (a)–(c) high-, (d)–(f) mid-, and (g)–(i) low-level clouds obtained from GRIMs simulations (DIAGCS and PROGC) and a combination of CALIOP and CloudSat data. The mean values of low-, mid-, and high-level cloud fractions are represented at the top right of each panel.
Citation: Monthly Weather Review 144, 3; 10.1175/MWR-D-15-0273.1
In the radiation process, cloud radiative forcing is mainly decided by cloud optical depth and cloud fraction, and cloud optical depth is proportional to the cloud water path. Before passing the radiation process, the grid-mean cloud water path is divided by the cloud fraction to estimate the real cloud water path in the cloud, and the cloud water path in the cloud decreases for the same cloud water contents when the cloud fraction increases. If the cloud water contents via DIAGC and PROGC are the same, the cloud water path in the cloud via PROGC could be smaller than that via DIAGC because the cloud fractions via PROGC are larger than those via DIAGC, and this could partly affect the reduction of cloud forcing. However, cloud forcing increases with large cloud fraction because it is also proportional to the cloud fraction through the radiation process. Again, if cloud water contents via DIAGC and PROGC are the same, clouds via DIAGC could be smaller but denser than those via PROGC. To estimate the impact of PROGC on radiation, the solar radiation fluxes scattered by large (and coarse) clouds via PROGC and small (and dense) clouds via DIAGC with the same cloud water contents were compared in an ideal test and we found that the solar radiation flux scattered by large (and coarse) clouds is slightly greater than that by small (and dense) clouds with the same cloud water contents. Therefore, it can be expected that the cloud forcing via PROGC in radiation process will increase, compared to those via DIAGC, if cloud water contents are not changed for both cases of DIAGC and PROGC.
To investigate the impact of PROGC on radiation, radiation budgets for the cases of PROGC and DIAGC at the surface were compared (Table 2). All variables were temporally and horizontally averaged over global and tropical (20°S–20°N) areas during the period of July 2013. The downward shortwave radiation flux for the case of PROGC is slightly higher than that for the case of DIAGC, implying that the cloud forcing (scattering or reflecting) via PROGC is weaker than that via DIAGC. This weak cloud forcing could result from the smaller amount of cloud water contents via PROGC than that via DIAGC (see Fig. 5b), as discussed above. The weak cloud forcing via PROGC induces the surface warming (see Fig. 5a). The increased temperature near the surface favors triggering the moist precipitating convection owing to the cumulus parameterization scheme. It is noted that precipitation in the microphysics process (total precipitation minus convective precipitation) via PROGC is less than that via DIAGC in our simulations (see Table 2). In addition, the overall reduction of the precipitation in the case of PROGC seems to be balanced with the weakened moisture transport toward the rainfall area. It was confirmed that the wind speed over the trade wind regions is weakened (not shown). The mean surface wind speed over the tropical area via PROGC was less than that via DIAGC by 0.18 m s−1, which is associated with the reduction in the sensible and latent heat fluxes from the surface. In summary, total precipitation is roughly proportional to the amount of condensed water in convection and microphysics processes and, therefore, the smaller cloud water contents via PROGC can result from: 1) weak cloud forcing, 2) high downward solar radiation, 3) surface warming and strong convection, 4) weak condensation in microphysics process, and 5) low cloud water formation in the overall physics process (mainly convection and microphysics processes). The low cloud water formation can results in low latent heat and can be inferred from low temperature at mid- and high altitudes via PROGC, compared to DIAGC (see Fig. 5a).
Summary of radiative fluxes and precipitation rates for the cases of DIAGC and PROGC. The values were averaged over the global and tropical areas (20°S–20°N, 180°–180°) during July 2013.
Vertical profiles of (a) the temperature difference (PROGC − DIAGC) and (b) cloud water contents via DIAGC and PROGC over the tropical area. Temperature and cloud water content were temporally and horizontally averaged over 20°S–20°N, 180°–180° during July 2013.
Citation: Monthly Weather Review 144, 3; 10.1175/MWR-D-15-0273.1
In sequence, the impacts of the improved cloud fractions determined via PROGC on temperature, mean sea level pressure, and geopotential height were investigated, focusing on these effects over the global area, Northern Hemisphere, the tropical region, and Southern Hemisphere, because temperature is directly affected by the interaction between clouds and radiation. As mentioned in section 3, 10-day simulations for the heavy rainfall event were conducted for DIAGC and PROGC. Temperature via DIAGC has a negative bias from the surface to about 600 mb and a positive bias from about 600 mb to the top of atmosphere until the fifth day over the whole area, compared to NCEP FNL (final) analysis data (NOAA/National Centers for Environmental Prediction 2000) (see Figs. 6a–d). During the last period, a negative bias of temperature was dominant for all layers. The global pattern of temperature bias for the case of PROGC was similar to that for DIAGC (Fig. 6e) but was slightly reduced at high latitudes except for over the Southern Hemisphere (Fig. 6h). In particular, the reduction of warm bias (from 0 to 5 days) and increase of cold bias (from 6 to 10 days) at the high altitude over the tropical region was distinguished and this is due to the decreased cloud forcing via PROGC as mentioned previously. Geopotential height and mean sea level pressure via DIAGC and PROGC were also compared in Table 3. The statistical values (bias and RMSE) were calculated from the comparison between simulation results via DIAGC/PROGC and FNL analysis. Globally, both the mean sea level pressure and the geopotential height at each layer via PROGC were slightly improved except for over the Southern Hemisphere and the improvement was also distinguishable at the high altitude over the tropical region.
Pressure–time cross sections of globally averaged bias (shading) and root-mean-square error (contour) of temperature over (a),(e) the global area; (b),(f), the Northern Hemisphere; (c),(g) the tropical region; and (d),(h) the Southern Hemisphere via (top) DIAGC and (bottom) PROGC compared with FNL data.
Citation: Monthly Weather Review 144, 3; 10.1175/MWR-D-15-0273.1
Bias and RMSE between GRIMs-simulated results via PROGC and FNL analysis data of mean sea level pressure and geopotential height at 0000 UTC 27 Jul 2011 (forecast hour: 24 h). The values in parentheses indicate the statistical value between GRIMs-simulated result via DIAGC and FNL analysis data for comparative analysis.
5. Summary and conclusions
The prognostic cloud fraction scheme described in this paper was based on the work by Tiedtke (1993) and revised in terms of the formation of cloud area by a cumulus parameterization scheme. The diagnostic cloud fraction scheme (DIAGC) was substituted with this prognostic cloud fraction scheme (PROGC) in our global forecasting system (GRIMs). Cloud fractions calculated from PROGC showed better agreements with the combined CALIOP and CloudSat data than those calculated via DIAGC. In particular, over the tropical region, distinct mid- and low-level clouds, which are not shown in the results generated via DIAGC but are represented in satellite data, were effectively captured via PROGC. Horizontal and vertical distributions of cloud fractions calculated via PROGC appeared to be more realistic than those estimated via DIAGC, based on comparisons with satellite data. In an aspect of radiative effect, we found that the cloud forcing of large and coarse clouds via PROGC is smaller than that of small and dense clouds via DIAGC because the cloud water contents via PROGC were slightly smaller than that via DIAGC. The difference of cloud forcing between PROGC and DIAGC seems to induce the difference of convection intensity, which indirectly affects the condensation in the microphysics process. Large cloud fractions but small cloud water contents via PROGC result in the reduction of downward solar radiation and owing to the surface warming, evaporation of water vapor and convection over the ocean surface via PROGC seems to be rather stronger than those via DIAGC. Consequently, the above process in PROGC affects the reduction of condensation in the microphysics process and the cooling of mid- and upper atmosphere due to less latent heat. In addition, the improved cloud fractions estimated via PROGC result in the reductions of biases and root-mean-square errors of temperature, geopotential height, and mean sea level pressure in our global forecasting system, especially at high altitudes over tropical regions.
The prognostic cloud fraction scheme is difficult to be realized in a numerical forecasting model because of the complexity owing to the need to represent both source and sink terms (Franklin et al. 2012). Nevertheless, the prognostic cloud fraction scheme that was implemented in our global forecasting system showed more realistic cloud fractions. Moreover, the modification of the prognostic cloud fraction scheme by changing the formation process of the cloud area by cumulus convection is valuable because coupling between the cloud scheme and the convection scheme is characterized by substantial uncertainty (e.g., Teixeira 2001; Franklin et al. 2012).
Acknowledgments
This work has been carried out through the R&D project on the development of global numerical weather prediction systems of the Korea Institute of Atmospheric Prediction Systems (KIAPS) funded by the Korea Meteorological Administration (KMA).
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