2.1 Reanalysis products

Our intercomparison focuses mainly on five relatively recent atmospheric reanalyses: the fifth-generation European Centre for Medium-range Weather Forecasts (ECMWF) reanalysis (ERA5; Hersbach et al., 2020); the ECMWF Interim Reanalysis (ERA-Interim; Dee et al., 2011); the Japanese 55-year Reanalysis (JRA-55; Kobayashi et al., 2015); the Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2; Gelaro et al., 2017); and the Climate Forecast System Reanalysis (CFSR; Saha et al., 2010) and its extension via the Climate Forecast System Version 2 (CFSv2; Saha et al., 2014). The earlier MERRA reanalysis (Rienecker et al., 2011) is included in selected comparisons. All six of these products are “full-input” reanalyses in that they assimilate both conventional and satellite data (Fujiwara et al., 2017); however, they differ from each other with respect to their atmospheric models, assimilation techniques, and assimilated data sets. Summary information on the forecast models and variables used are provided in Table 1. We document additional details of the cloud, convection, and radiation schemes in Appendix A. Readers interested in these technical details may wish to consult this appendix before proceeding to the results. With the exception of ERA5, other relevant aspects have recently been reviewed by Fujiwara et al. (2017). An expanded review (including ERA5) is provided in Chapter 2 of the forthcoming SPARC (Stratosphere–troposphere Processes And their Role in Climate) Reanalysis Intercomparison Project (S-RIP) report (Wright et al., 2020; digital version available at https://jonathonwright.github.io/S-RIPChapter2E.pdf, last access: 15 July 2020). Further details on assimilated observations and model treatments have been provided by Long et al. (2017) for temperature, Davis et al. (2017) for water vapour, and Tegtmeier et al. (2020) for the structure of the tropical tropopause layer (TTL), among others.

Table 1Summary of reanalysis products. HCC stands for high-cloud fraction; CC stands for cloud fraction; CWC stands for cloud water content; I/LWC stands for separate ice and liquid water contents; TOA stands for top-of-atmosphere fluxes (short-wave and long-wave and clear-sky and all-sky); and RHR stands for radiative heating rates (short-wave and long-wave and all-sky). We use CFSR products for 1980–2010, CFSv2 for 2011–2014, and all other reanalysis products for 1980–2014. IFS: Integrated Forecast System. JMA GSM: Japan Meteorological Administration Global Spectral Model. NCEP CFS: National Centers for Environmental Prediction Climate Forecast System.

^* Climatological means of HCC, CC, CWC (or I/LWC), and TOA fluxes from all reanalyses are calculated from monthly-mean products.

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The full intercomparison period covers January 1980 through December 2014 and includes all five reanalyses. We also conduct a more detailed intercomparison of daily co-variations among selected variables from January 2001 to December 2010. Results for the full intercomparison are presented in Sects. 3, 4, and 6, while results based on daily co-variability are presented in Sects. 4 and 5. Our intercomparison period includes the CFSR–CFSv2 transition in January 2011 and the intermediate year 2010 (as discussed by Fujiwara et al., 2017, among others). We show in Sect. 6 that both transitions involved changes in the cloud fields that were much larger than the discontinuities at other production stream transitions. The January 2011 transition to CFSv2 also involved changes in the atmospheric-model formulation governing interactions between clouds and radiation. A brief summary of differences in tropical cloud and radiation fields between CFSR and CFSv2 is provided in Appendix B.

2.2 Observational data

We use several observationally based data products to supply context, including TOA radiative fluxes, cloud fraction, cloud ice water content, and atmospheric thermodynamic state variables (Table 2). Observations of these variables are subject to a number of uncertainties, including lack of sensitivity to optically thin clouds or clouds composed of small particles (e.g. Dessler and Yang, 2003), uncertainties caused by overlapping cloud layers (e.g. Zhang et al., 2005), errors in cloud top height (e.g. Sherwood et al., 2004), and diurnal or spatial sampling biases (e.g. Fowler et al., 2000; Hearty et al., 2014). As our primary focus is on the intercomparison of reanalysis products, we have not applied a satellite cloud observation simulator (e.g. Bodas-Salcedo et al., 2015; Stengel et al., 2018) to the reanalysis outputs. Use of a satellite simulator could address sensitivity and sampling biases for easier comparison with observations; however, it could also obscure inter-reanalysis differences in cloud types that are not well observed and complicate analysis of cloud radiative effects in each reanalysis. Accordingly, comparisons between reanalysis products and satellite cloud observations in this paper should be interpreted with care.

Table 2Summary of observational data sets, listed in alphabetical order by project. TOA stands for the top of the atmosphere, and UT stands for upper troposphere, where the latter comprises pressures less than 500 hPa for CERES SYN1Deg and pressures less than 440 hPa for ISCCP and MODIS. Other abbreviations are defined in the text. n/a: not applicable.

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The International Satellite Cloud Climatology Project (ISCCP) has produced observationally based descriptions of clouds and their attributes using geostationary and polar-orbiting satellite measurements (Rossow and Schiffer, 1991). We use the H-series Global Monthly (HGM) product for January 1984–December 2014 (Rossow and Schiffer, 1999; Rossow et al., 2017). As a supplement to the ISCCP cloud data, we use all-sky and clear-sky fluxes of long-wave (LW) radiation at the TOA from the NASA Global Energy and Water Cycle Experiment (GEWEX) Surface Radiation Budget (SRB) project covering January 1984 through December 2007 (Stackhouse et al., 2011; Zhang et al., 2015). These data are based on radiative calculations that combine observed fluxes and ozone with Goddard Earth Observing System Data Assimilation System, Version 4 (GEOS-4) analyses of temperature and water vapour. Pixel-level data from ISCCP are used to estimate cloud radiative effects in SRB.

We use several products from the Clouds and the Earth's Radiant Energy System (CERES) experiment (Wielicki et al., 1996). First, we use time-mean TOA fluxes calculated from Energy Balanced and Filled (EBAF) monthly-mean products at 1^∘ × 1^∘ spatial resolution (Doelling, 2019). We use CERES EBAF Edition 4.1, which provides clear-sky TOA fluxes that are specifically intended for comparison with model outputs (Loeb et al., 2020). Second, we use daily-mean Synoptic Radiative Fluxes and Clouds (SYN1Deg) products at 1^∘ × 1^∘ spatial resolution (Doelling, 2017). The SYN1Deg data set represents an intermediate step in the production of the monthly EBAF data set. SYN1Deg provides several estimates of TOA radiative fluxes, including direct measurements, outputs from initial “untuned” radiative transfer model simulations, and outputs from a second set of radiative transfer simulations in which the model input variables are adjusted to bring the simulated fluxes into better agreement with the observed fluxes. The initial atmospheric state for radiative computations is taken from the GEOS-5 data assimilation system, a different version of that used for MERRA-2. Only the final adjusted fluxes are discussed, as these products are most appropriate for computing cloud radiative effects for comparison with reanalysis estimates. The results are qualitatively similar when the direct measurements are used instead. Along with TOA radiative fluxes, the SYN1Deg data set includes estimates of cloud fraction retrieved using measurements collected by the Moderate-Resolution Imaging Spectroradiometer (MODIS) and geostationary satellites (Minnis et al., 2011; Doelling et al., 2013). We also use high-cloud fraction (HCC) data from Collection 6 of the Terra MODIS Level 3 Atmosphere Product (MOD08; Platnick, 2015).

For observations of the thermodynamic state of the atmosphere, we use level 3 data from the Atmospheric Infrared Sounder (AIRS) version 6 “TqJoint” collection (AIRS Science Team and Teixeira, 2013). This data set provides gridded representations of temperature, moisture, and other fields based on a consistent set of initial retrievals in each grid cell (Tian et al., 2013). As the finest temporal resolutions of other data examined in this study are daily means, we average data from ascending and descending passes together. Variables taken from AIRS TqJoint include temperature, water vapour mass mixing ratio, and geopotential height between January 2003 and December 2014.

Finally, we examine three products derived from CloudSat and Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) measurements. These include two monthly estimates of cloud fraction vertical profiles, one based on combined information from CloudSat and CALIPSO (Kay and Gettelman, 2009) and one based on CALIPSO alone (Chepfer et al., 2010). We use the combined CloudSat–CALIPSO product for the 4 years of 2007–2010 and the GCM-Oriented CALIPSO Cloud Product (general circulation model; GOCCP) for the 8 years of 2007–2014. The first product was discontinued after CloudSat switched to sunlit-only observations in early 2011. We also use ice water content (IWC) measurements from CloudSat and CALIPSO based on the 2C-ICE (CloudSat and CALIPSO Ice Cloud Property Product) retrieval algorithm (R05; Deng et al., 2015), averaged for all tropical profiles (10^∘ S–10^∘ N) over 2007–2010. CloudSat- and CALIPSO-based data sets are provided on height grids, which we convert to pressure using the barometric equation with a constant scale height of 7.46 km. This approach introduces uncertainty in the precise vertical location (in pressure coordinates) of features observed by CloudSat and CALIPSO, which should be taken into consideration when comparing these features to those produced by the reanalyses.

2.3 Derived variables and statistical treatments

Variables directly related to tropical high clouds include HCC and vertical profiles of cloud fraction and cloud water content, while variables used to explore the impacts of differences in high clouds include TOA radiative fluxes and vertically resolved radiative heating rates within the upper troposphere, tropopause layer, and lower stratosphere. All vertically resolved variables are evaluated on pressure levels, interpolated from height or model levels when necessary.

Cloud radiative effects (CREs) are computed as clear-sky minus all-sky fluxes using positive-upward fluxes at the TOA so that LWCRE (long-wave) is generally positive (the presence of clouds reduces outgoing long-wave radiation – OLR) and SWCRE (short-wave) is generally negative (the presence of clouds increases the planetary albedo). CREs are sensitive to differences in both all-sky and clear-sky fluxes (e.g. Soden et al., 2004); accordingly, we report differences in both all-sky and clear-sky TOA fluxes below.

Variables used to diagnose the potential origins of differences in high clouds include SST; vertical velocity at 500 hPa; and vertical profiles of temperature, specific humidity, and geopotential height between 1000 and 100 hPa. The latter three variables are used to compute moist static energy:

where g is gravitational acceleration in Earth's lower atmosphere, z is geopotential height, c_p is the specific heat capacity for dry air, T is temperature, L_v is latent enthalpy of vapourization at 0 ^∘C, and q is specific humidity. Temperature and specific humidity are also used to calculate equivalent potential temperature (θ_e), which is then used to diagnose the potential instability of the lower troposphere as the difference in equivalent potential temperature between the lower troposphere (850 hPa) and the middle troposphere (500 hPa):

Equivalent potential temperature is computed according to the formula proposed by Bolton (1980) using the MetPy software package (May et al., 2008–2020). Relative humidity (RH) is calculated with respect to liquid water using MetPy. This approach avoids inconsistencies in the implementation of the liquid–ice transition among the different data sets (see Appendix A1). Ratios between saturation vapour pressures with respect to ice and with respect to liquid water are calculated using the empirical formulas suggested by Emanuel (1994).

The level of zero radiative heating (LZRH) is determined for all profiles for which the daily-mean net radiative heating rate is positive at 100 hPa. All-sky total radiative heating rates (LW + SW; short-wave) are linearly interpolated onto a 1000-level grid between 100 and 500 hPa with equal spacing in ln (p). The LZRH is then defined as the largest pressure for which all net radiative heating rates are positive between 100 hPa and that level (inclusive).

Statistical treatments mainly consist of composite averages or distributions conditioned on ranked quartiles of LWCRE (i.e. four bins separated by the 25th percentile, the median, and the 75th percentile). We focus in particular on the largest values of LWCRE (denoted as Q₄) in the inner tropics (10^∘ S–10^∘ N) as a proxy for strong convective activity. Results are very similar for ranked quartiles of all-sky OLR, with OLR reversed so that Q₄ corresponds to the smallest values of OLR. Using HCC instead of LWCRE produces more substantial differences, particularly for MERRA-2. Given discrepancies in the precise definition of HCC across reanalyses (Table 1) and the difficulty of defining an appropriate observational benchmark for HCC, we judge HCC less suitable for this purpose. We select LWCRE rather than OLR for convenience of presentation. Averages taken in the horizontal dimension are weighted by relative area; 2-dimensional kernel density estimates are computed using the k-dimensional tree-based implementation in scikit-learn (Pedregosa et al., 2011) with a Gaussian kernel. Optimal bandwidths for kernel density estimates are identified using a 20-fold grid-search cross-validation on randomly selected subsets of the data and consistently converge to values near 1 (0.8–1.3) for LWCRE and values near 2 (1.5–2.4) for SWCRE.

4.1 Top-of-atmosphere radiation budget

Figure 5 shows spatial distributions of all-sky and clear-sky OLR based on CERES EBAF during 2001–2014, along with differences between the five individual reanalysis products and CERES. Rather than direct observations (with clear-sky fluxes taken only from cloud-free columns), the CERES EBAF fluxes discussed in this section are estimates for the entire column with clouds removed and are suitable for direct comparison with model-generated clear-sky fluxes (Loeb et al., 2020). CERES EBAF estimates a time-mean tropical-mean OLR of 260.3 W m⁻² over 2001–2014, smaller than in any of the reanalyses except for MERRA-2. Better agreement is found for clear-sky OLR, with tropical-mean values from all reanalyses within ±2.5 W m⁻² of the CERES EBAF estimate. Accordingly, the time-mean tropical-mean LWCRE based on CERES EBAF (27.3 W m⁻²) was larger than that produced by any of the reanalyses except for MERRA-2 (31.6 W m⁻²). ERA-Interim, ERA5, and CFSR/CFSv2 underestimate clear-sky OLR even as they overestimate all-sky OLR so that negative biases in the tropical-mean LWCRE are approximately twice as large as positive biases in tropical-mean OLR in each of these three reanalyses. Comparison with observationally based estimates with longer durations further indicates that most of the reanalyses overestimate OLR and underestimate LWCRE in the tropics. NASA/GEWEX SRB indicates tropical-mean values of 259.4 W m⁻² for all-sky OLR and 27.7 W m⁻² for LWCRE over 1984–2007, while the NOAA Interpolated OLR product indicates a tropical-mean value of 250.7 W m⁻² for all-sky OLR over 1980–2014.

Figure 5Climatological mean spatial distributions of all-sky outgoing long-wave radiation (OLR; shading) and clear-sky outgoing long-wave radiation (CLR; contours at intervals of 10 W m⁻²) for (a) CERES EBAF over 2001–2014. Differences relative to CERES EBAF for the same period are shown for (b) ERA5, (c) ERA-Interim, (d) JRA-55, (e) MERRA-2, and (f) CFSR/CFSv2 (abbreviated CFSR/v2). Contours in (c) through (f) cover the range within ±10 W m⁻² at intervals of 4 W m⁻². Tropical-mean (30^∘ S–30^∘ N) values of OLR and CLR based on each product are shown at the upper-right and upper-left corners, respectively, of the corresponding panel. Tropical-mean values for the long-wave cloud radiative effect (LWCRE = CLR − OLR) are listed above those for OLR.

Many differences among the reanalyses indicate an inverse relationship between relative biases in OLR and those in HCC. For example, JRA-55, which has the smallest HCCs in the tropics among the reanalyses, likewise produces the largest tropical-mean OLR and the smallest tropical-mean LWCRE. Conversely, MERRA-2, with the largest HCCs among the reanalyses, produces the smallest tropical-mean OLR and the largest tropical-mean LWCRE. ERA5 produces a slightly smaller OLR and a slightly larger LWCRE than ERA-Interim and again shows maximum differences over tropical land areas with strong convection. As with HCC, ERA-Interim and CFSR/CFSv2 produce similar tropical-mean values of both OLR and LWCRE (within ±0.5 W m⁻²). Most differences between these two reanalyses obey the same type of inverse relationship: ERA-Interim produces smaller values of OLR in the Indo–Pacific domain (consistent with larger HCCs in this region), while CFSR/CFSv2 produces smaller values of OLR over tropical mountain ranges (consistent with relatively large HCCs in these locations). There are some notable exceptions though, such as over Africa. ERA-Interim produces slightly larger HCCs in this region (Fig. 1), but CFSR produces smaller values of OLR (this difference is mitigated somewhat in CFSv2; cf. Fig. B2g). This type of inconsistency, in which biases in HCC and OLR do not align with simple expectations, may reflect systematic differences in the depth of convection (and thus cloud top temperature) or the water paths associated with convective anvil clouds. Although we do not directly evaluate differences in cloud top height here (owing in part to the lack of vertically resolved cloud fraction profiles in CFSR/CFSv2), we note that CFSR/CFSv2 produces a more pronounced peak in cloud water content extending to relatively higher altitudes than ERA-Interim in the tropical mean (Fig. 4f).

Figure 6 shows spatial distributions of all-sky net radiation based on CERES EBAF and the five reanalyses, with positive values indicating time-mean energy fluxes into the tropical climate system. Mean values across the tropics are positive (incoming solar radiation exceeds OLR), as indicated here by CERES EBAF (net gain of 45.0 W m⁻²). This excess of incoming energy in the already energy-rich tropics is essential to the “heat engine” model of the atmospheric circulation and is contributed primarily by imbalances in the clear-sky fluxes (e.g. Stephens and L'Ecuyer, 2015, and references therein). Net clear-sky fluxes into the tropics are typically somewhat larger in the reanalyses than in CERES, with overestimates as large as 7 W m⁻² (in ERA-Interim). The closest match in the tropical mean is provided by JRA-55, which is within 0.1 W m⁻² of CERES (this good agreement does not extend to the all-sky net radiation flux, as detailed below). Cloud effects reduce the energy excess provided by clear-sky radiation, as the negative SWCRE outweighs the positive LWCRE. However, most of the reanalyses greatly overestimate the magnitude of this reduction relative to CERES. Such overestimates have implications for atmospheric energy transport and could result at least in part from the lack of two-way coupling between cloud fields and SST in the reanalyses (e.g. Kolly and Huang, 2018; Wall et al., 2019). For JRA-55, which overestimates the net CRE by 22.5 W m⁻² relative to CERES, a little more than half of the bias in the net CRE is attributable to the bias in LWCRE. The remainder is due to overestimated cloud albedo effects. Similar ratios hold for ERA5 and ERA-Interim, with biases in LWCRE contributing approximately 55 % of the overall biases in each case. For MERRA-2, overestimated cloud albedo effects more than compensate for the stronger LWCRE, producing a net CRE similar to that in ERA5 (approximately 9 W m⁻² stronger than that from CERES). CFSR/CFSv2 produces a net CRE very similar to that indicated by CERES, implying compensating biases in SWCRE and LWCRE. However, the horizontal gradients of net radiation are much sharper in this reanalysis than in any of the other data sets included in Fig. 6.

Figure 6Climatological mean spatial distributions of all-sky net incoming radiation (ALL; shading) for (a) CERES EBAF, (b) ERA5, (c) ERA-Interim, (d) JRA-55, (e) MERRA-2, and (f) CFSR/CFSv2 during 2001–2014. Tropical-mean (30^∘ S–30^∘ N) values of ALL and clear-sky net incoming radiation (CLR) based on each product are shown at the upper-right and upper-left corners, respectively, of the corresponding panel. Tropical-mean values for the net cloud radiative effect (CRE = CLR − ALL) are listed above those for ALL.

Figure 7Joint distributions of daily-mean HCC against (a) LWCRE and (b) SWCRE based on CERES SYN1Deg using gridded data from 2001 to 2010. Corresponding joint distributions are shown for (c, h) ERA5, (d, i) ERA-Interim, (e, j) JRA-55, (f, k) MERRA-2, and (g, l) CFSR. The 75th percentile of LWCRE is marked in (a) and (c–g). Sub-distributions of HCC against SWCRE associated with the values of LWCRE that exceeded the corresponding 75th percentile threshold are then shown as purple contours in (b) and (h–l). Distributions of LWCRE, SWCRE, and total CRE are shown in the upper right (in which ERA-Interim is abbreviated ERA-I), with SWCRE multiplied by −1 for convenience of presentation. The thickest boxes mark the interquartile ranges, with the medians marked as horizontal lines and the means marked as stars. The narrower extended boxes indicate the 5th, 10th, 90th, and 95th percentiles.

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Relationships between tropical HCC and TOA radiation fluxes are examined in more detail in Fig. 7, which shows joint distributions of HCC against the LW and SW cloud radiative effects. The joint distributions shown in Fig. 7 are 2-dimensional frequency distributions analogous to scatterplots, where the shading indicates the density of the points and outliers are omitted. The data used to construct these distributions are daily-mean gridded values within 10^∘ S–10^∘ N during the period 2001–2010 and thus reflect both spatial and temporal covariability of TOA radiative fluxes and HCC. For this and other analyses that do not span the CFSR/CFSv2 transition (1 January 2011), we omit any reference to CFSv2 and refer to this reanalysis only as CFSR. Data have been interpolated when necessary to 1^∘ × 1^∘ spatial grids. The abscissa is reversed for plots of SWCRE so that larger absolute magnitudes of both LWCRE and SWCRE are located toward the right. Distributions of daily-mean gridded values of LWCRE, SWCRE, and total CRE are included at the upper right of Fig. 7.

The joint distribution of HCC against LWCRE based on CERES SYN1Deg indicates a tight, nearly linear relationship between these two variables, in which a large value of HCC corresponds to a large LWCRE. The 75th percentile value of LWCRE based on CERES SYN1Deg is 51.0 W m⁻², which corresponds to an HCC of roughly 0.57. Among the reanalyses, CFSR is most similar to CERES SYN1Deg in its joint distribution of HCC against LWCRE. However, the CFSR distribution has a stronger curvature so that the 75th percentile of LWCRE corresponds to a smaller value of LWCRE (37.6 W m⁻²) despite a similar value of HCC (0.58). JRA-55 has the smallest 75th percentile value of LWCRE (23.7 W m⁻²). This value of LWCRE corresponds to an HCC value of around 0.56 in JRA-55, whereas it corresponds to an HCC of only 0.27 in CERES SYN1Deg, implying that the relatively small mean HCC in JRA-55 is not the only reason behind relatively weak LWCRE in this reanalysis. Joint distributions based on ERA5, ERA-Interim, and MERRA-2 are qualitatively more distinct, with secondary modes at large values of LWCRE. In ERA-Interim, there is a clear distinction in both variables between the primary mode (associated with small values of both HCC and LWCRE) and the secondary mode (associated with large values of HCC and LWCRE). HCCs associated with the latter mode are almost exclusively greater than 0.9. The 75th percentile value (37.1 W m⁻²) falls between the two modes and corresponds to an HCC of 0.65. The distribution based on ERA5 is similar to that based on ERA-Interim but with a greater fraction of the data (and greater variability) in the large-LWCRE mode. The 75th percentile value is thus substantially larger in ERA5 (47.0 W m⁻²) than in ERA-Interim, as is the mean cloud fraction associated with this value (0.75). Bimodality in MERRA-2 takes a different form. The first mode corresponds to small values of LWCRE. Although the peak of this distribution is at small values of HCC, this small-LWCRE mode still exhibits relatively large occurrence frequencies at values of HCC approaching 1. The mean HCC associated with this mode is around 0.35. The second mode peaks at relatively large values of both LWCRE (∼88 W m⁻²) and HCC (∼0.7). The 75th percentile of LWCRE (72.1 W m⁻²) is contained within the second mode, meaning that the large-LWCRE mode contains more than 25 % of the inner-tropical data points in MERRA-2. An LWCRE of 72.1 W m⁻² corresponds to an HCC of approximately 0.68 in MERRA-2, slightly less than that associated with the same value of LWCRE in CERES SYN1Deg (0.73).

The unique bimodality of the HCC–LWCRE distribution in MERRA-2 is a consequence of the separation of cloud condensate in the prognostic cloud scheme into “large-scale” and “anvil” cloud types. Of these two types, anvil clouds are assigned higher number densities that translate into greater values of optical thickness when the radiation calculations are performed (Bacmeister et al., 2006). The model used to produce MERRA-2 also uses different procedures to relate the evolution of cloud fraction to autoconversion between the large-scale and anvil cloud types, which appears to result in relatively large values of cloud fraction persisting even as CWC declines (the small-LWCRE mode in Fig. 7f). Although the treatment of prognostic cloud fraction used in MERRA-2 is conceptually similar to that used in JRA-55 (Appendix A1), JRA-55 and MERRA-2 produce very different relationships between cloud fraction and condensate. Tuning efforts to increase the amount of cloud ice in the upper troposphere in MERRA-2 were motivated by a desire to improve OLR (recognizing that convective detrainment altitudes are too low in GEOS-5, the developers accepted overestimating cloud ice to get OLR right) and upper-tropospheric humidity (Molod et al., 2015). The anvil cloud fraction was then kept small relative to the cloud ice content to prevent a worsening of SWCRE as LWCRE was increased.

Joint distributions of HCC against SWCRE are consistent with SWCRE being less tightly linked than LWCRE to HCC in the tropics. However, large HCCs are typically associated with both large LWCREs and large SWCREs. CERES SYN1Deg and four of the five reanalyses show extensive overlap between large values of LWCRE and large values of SWCRE. CFSR is a notable exception, with large values of LWCRE often corresponding to small values of SWCRE. As a consequence, the distribution of total CRE based on CFSR is broader than that based on CERES or the other reanalyses, with the middle 90 % spanning from less than −100 W m⁻² to approximately +40 W m⁻². The weaker SWCRE associated with large HCCs results in a more positive total CRE on average, with the median value in CFSR close to zero. These differences can also be seen in the CFSR/CFSv2 climatology, which has sharper spatial gradients of net TOA radiation (Fig. 6f) and a smaller tropical-mean net CRE than any other reanalysis. Although LWCRE is weakest in JRA-55 among the data sets evaluated here, the tropical-mean SWCRE is larger in JRA-55 than in any data set except MERRA-2. The total CRE is thus substantially more negative in JRA-55 than in any other reanalysis (see also Fig. 6d). Fewer than 5 % of gridded values of total CRE in the tropics are positive in JRA-55. This latter statement also holds for ERA-Interim; however, greater compensation between LWCRE and SWCRE in ERA-Interim leads to a narrower distribution and a smaller negative bias in the tropical-mean total CRE relative to CERES. MERRA-2 tends to overestimate both LWCRE and SWCRE, especially for anvil clouds. However, compensation between these two biases produces a distribution of total CRE that is comparable to (though slightly broader than) that based on CERES SYN1Deg. Among the five reanalyses, ERA5 shows the closest agreement with CERES SYN1Deg across all three flavours of CRE. LWCRE in ERA5 is slightly weaker on average than that based on CERES, while SWCRE is similar on average but with a narrower distribution. The total CRE is thus slightly more negative in ERA5 than indicated by CERES, with a narrower distribution but good agreement in the mean value.

4.2 Radiative heating in the tropical UTLS

In addition to altering top-of-atmosphere radiative fluxes, differences in tropical high clouds may influence radiative heating rates locally within the UTLS. Among the reanalyses considered in this study, neither JRA-55 nor CFSR provide vertically resolved estimates of radiative heating under clear-sky conditions. To skirt this limitation, we construct composite mean profiles of radiative heating rates conditional on the four quartiles of LWCRE in an adaptation of the approach employed by Zhang et al. (2017). Figure 8 shows these composite profiles for the period 2001–2010, separated into total, LW, and SW radiative heating. Here, Q₁ represents daily gridded heating rates for which LWCRE (at TOA; Fig. 7a and c–g) is in the smallest 25 % of all daily gridded values. Q₂ and Q₃ represent the lower-middle and upper-middle quartiles, respectively, while Q₄ represents heating rates for which the associated LWCRE exceeds the 75th percentile value marked in Fig. 7. The impact of clouds on heating rates is then estimated as the difference between the Q₄ and Q₁ profiles. Results are very similar for ranked quartiles of all-sky OLR, with OLR reversed so that Q₄ corresponds to the smallest values of OLR.

Figure 8Composite mean profiles of daily-mean radiative heating rates as a function of pressure for the first through fourth quartiles (Q₁–Q₄) of LWCRE in the inner tropics (10^∘ S–10^∘ N; see also Fig. 7) based on (a) ERA5, (b) ERA-Interim, (c) JRA-55, (d) MERRA-2, and (e) CFSR during 2001–2010. Here Q₁ refers to the bottom quartile (weak long-wave CRE) and Q₄ to the top quartile (strong long-wave CRE). Total radiative heating rates (upper row; a–e) are separated into (f–j) long-wave and (k–o) short-wave components in the lower two rows.

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Among these five reanalyses, cloud effects on radiative heating rates are generally smallest in ERA-Interim and largest in MERRA-2. Results for these two reanalyses are consistent with those reported for ERA-Interim and MERRA by Wright and Fueglistaler (2013), who found that cloud impacts on radiative heating in MERRA are qualitatively opposite to those in ERA-Interim through much of the upper troposphere. The response in ERA-Interim is largest in the 100–200 hPa layer, where radiative heating rates are enhanced when LWCRE is large. At lower altitudes in the upper troposphere (200–400 hPa), cloud-induced increases in SW heating are effectively offset by cloud-induced increases in LW cooling. By contrast, ERA5, JRA-55, and CFSR show only weak cloud impacts on total radiative heating at pressures less than 175 hPa. In all three cases, the insensitivity in total radiative heating rates at these altitudes traces back to a near-complete compensation between enhanced LW cooling and enhanced SW heating. Substantial cloud-related perturbations in the LW and SW components extend upward to around 100 hPa in ERA5 and CFSR but only to around 150 hPa in JRA-55. MERRA-2 produces the largest cloud impacts on radiative heating rates. Indeed, direct comparison of cloud radiative effects between MERRA and MERRA-2 (not shown) indicates that cloud effects in MERRA are further amplified in MERRA-2, consistent with the increase in CWC in the tropical upper troposphere between MERRA and MERRA-2 (Fig. 4f). High-cloud effects in MERRA-2 reduce radiative heating rates in the 100–200 hPa layer (largely due to enhanced LW cooling, partially offset by enhanced SW heating) and increase radiative heating rates at pressures greater than 200 hPa. The latter results from enhanced SW heating near the top of the anvil layer (200–250 hPa) and enhanced LW heating near the base of the anvil layer (300–350 hPa), taking the MERRA-2 profile of tropical-mean cloud water content (Fig. 4f) as a guide. Cloud effects in ERA5 are intermediate between those in CFSR and MERRA-2. This is consistent with the pronounced convective anvil in the ERA5 profile of tropical-mean CWC (Fig. 4f), which better matches the profiles produced by CFSR and MERRA-2 than that produced by ERA-Interim.

Differences in the radiative impacts of tropical high clouds are linked to differences in transport through the TTL and lower stratosphere (Fueglistaler and Fu, 2006; Yang et al., 2010). Relevant metrics include the level of zero net radiative heating (LZRH) and the rate of diabatic ascent at the base of the “tropical pipe”, which defines the upward branch of the Brewer–Dobson circulation (e.g. Fueglistaler et al., 2009; Dessler et al., 2014). The LZRH marks the boundary between negative all-sky radiative heating rates (corresponding to net descent) in the tropical troposphere and positive radiative heating rates (corresponding to net ascent) in the TTL and lower stratosphere (Sect. 2.3; see also Folkins et al., 1999; Gettelman et al., 2004). To represent ascent at the base of the tropical pipe, we use the vertical velocity in potential temperature coordinates (${\dot{\mathit{\theta }}}_{\mathrm{rad}}$) at the 420 K isentropic level, near the top of the TTL. We evaluate distributions of LZRH pressure (Fig. 9a) and ${\dot{\mathit{\theta }}}_{\mathrm{rad}}$ (Fig. 9b) at 420 K based on ERA5, ERA-Interim, JRA-55, MERRA-2, and CFSR during 2001–2010. Distributions conditional on the top quartile of LWCRE (Q₄) for each reanalysis are shown in colour.

Figure 9Histograms of (a) the vertical location of the level of zero net radiative heating (LZRH) and (b) the vertical velocity in isentropic coordinates ($\dot{\mathit{\theta }}$ on the 420 K isentropic surface). Data are based on daily-mean products from (left to right and top to bottom) ERA5, ERA-Interim, JRA-55, MERRA-2, and CFSR during 2001–2010. Colour histograms show distributions for the top quartile of long-wave cloud radiative effect in each reanalysis (see Fig. 7).

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The largest differences in LZRH distributions are between ERA-Interim and MERRA-2 (Fig. 9a). Neglecting the influence of clouds, the primary mode of the ERA-Interim distribution (p∼140 hPa) is located at slightly higher altitudes than that in MERRA-2 (p∼150 hPa). These primary modes match the vertical locations of the clear-sky LZRH in each system well (not shown). The more striking distinction between ERA-Interim and MERRA-2 is in the impacts of clouds on the LZRH altitude. Whereas clouds tend to lower the LZRH in ERA-Interim (to around 170 hPa on average), clouds raise the LZRH significantly in MERRA-2 (to around 110 hPa). This difference has important implications for the efficiency of mass and constituent transport from the deep convective detrainment level (200–300 hPa) into the tropical lower stratosphere. In MERRA-2, the cloudy and clear-sky modes of the distribution are almost completely distinct. By contrast, the breadth of the LZRH distribution based on ERA-Interim (and especially the breadth of the distribution associated with the largest values of LWCRE) indicates that ERA-Interim produces a broad spectrum of cloudy states. This diagnostic thus helps to clarify the environmental conditions associated with the two very different tropical-mean CWC profiles in Fig. 4f, with the pronounced anvil layer in MERRA-2 in sharp contrast to the gradual decrease of CWC with height in ERA-Interim. Distributions of the LZRH location based on ERA5, JRA-55, and CFSR are more consistent with each other. Each distribution has one major mode, although the altitude of the LZRH tends to be highest in CFSR (median: 134 hPa), followed by ERA5 (144 hPa) and JRA-55 (148 hPa). All three reanalyses indicate slight upward shifts toward lower pressures (by around 5 hPa) in the median LZRH location associated with the largest values of LWCRE, but these shifts are much less pronounced than that suggested by MERRA-2.

Distributions of ${\dot{\mathit{\theta }}}_{\mathrm{rad}}$ at 420 K (Fig. 9b) are more consistent among the reanalyses. Differences in the mean value are consistent with previous assessments (Schoeberl et al., 2012; Abalos et al., 2015; Tao et al., 2019), with ERA-Interim (average: 0.82 K d⁻¹) and JRA-55 (0.80 K d⁻¹) having stronger lower-stratospheric ascent than MERRA-2 (0.56 K d⁻¹) or CFSR (0.49 K d⁻¹). The mean value in ERA5 (0.49 K d⁻¹) is consistent with that in MERRA-2 and CFSR but with a much broader distribution. Our focus here is on the cloud effects and the role they play in the overall differences. All five reanalyses indicate weaker lower-stratospheric radiative heating rates in atmospheric columns with large values of LWCRE. As with many of the diagnostics examined in this study, this effect is least pronounced in JRA-55, with the mean for Q₁ (smallest LWCREs) only 0.13±0.03 K d⁻¹ larger than that for Q₄ (largest LWCREs). This relatively small cloud influence may contribute to the relatively narrow distribution of ${\dot{\mathit{\theta }}}_{\mathrm{rad}}$ in JRA-55. By contrast, the much broader distributions of ${\dot{\mathit{\theta }}}_{\mathrm{rad}}$ in ERA5 and ERA-Interim are accompanied by large cloud effects, with differences of 0.49±0.12 K d⁻¹ between Q₁ and Q₄ in ERA5 and 0.45±0.06 K d⁻¹ in ERA-Interim. These large cloud effects reflect sharper spatial gradients in HCC (Fig. 1c) and LWCRE (Fig. 5c) between tropical deep convective regions and surrounding areas in the ECMWF reanalyses relative to JRA-55. The cloud influence on ${\dot{\mathit{\theta }}}_{\mathrm{rad}}$ in MERRA-2 is comparable to that in ERA-Interim, with a difference of 0.39±0.03 K d⁻¹ between Q₁ and Q₄. However, the distribution based on MERRA-2 is compressed toward the mean relative to that based on ERA-Interim, with fewer extreme values and shorter tails. Only 8 % of ${\dot{\mathit{\theta }}}_{\mathrm{rad}}$ values in MERRA-2 fall outside the interval [0, 1] K d⁻¹, as opposed to 36 % of values in ERA-Interim (33 % in ERA5). This pairing of large cloud effect and narrow distribution implies a strict stratification of lower-stratospheric heating rates with respect to LWCRE, with values of ${\dot{\mathit{\theta }}}_{\mathrm{rad}}$ in MERRA-2 approaching those in JRA-55 as the effects of clouds are reduced. The mean difference between these two reanalyses is ∼0.4 K d⁻¹ in Q₄ (where the mean LWCRE in MERRA-2 is more than double that in JRA-55) but only ∼0.1 K d⁻¹ in Q₁ (where mean values of LWCRE are 3.1 W m⁻² in both systems). Our results thus support the suggestion by Tao et al. (2019) that differences in climatological HCC in the tropics can explain much but not all of the difference in lower-stratospheric ascent rates between these reanalyses. The cloud effect on lower-stratospheric heating rates is 0.31±0.09 K d⁻¹ in CFSR. The uncertainty is relatively large in CFSR because of large variance in distributions of ${\dot{\mathit{\theta }}}_{\mathrm{rad}}$ within each LWCRE quartile (primarily due to higher occurrence frequencies of negative values in all four quartiles). Approximately 4 % of ${\dot{\mathit{\theta }}}_{\mathrm{rad}}$ values associated with the relatively cloud-free Q₁ and Q₂ groupings in CFSR are negative, an order of magnitude larger than the fraction in ERA-Interim and several orders of magnitude larger than the fractions in JRA-55 and MERRA-2. However, the largest variance in ${\dot{\mathit{\theta }}}_{\mathrm{rad}}$ is produced by ERA5. Although variance decreases with decreasing LWCRE, the fraction of negative ${\dot{\mathit{\theta }}}_{\mathrm{rad}}$ values in Q₁ and Q₂ (9 %) is still more than double that in CFSR. The broader distribution of diabatic heating rates in this reanalysis may be related to improved consistency between diabatic and kinematic vertical motion in the lower stratosphere in ERA5 relative to ERA-Interim (Hoffmann et al., 2019).

5.1 Convection and its environment

Tropical deep convection tends to cluster over the warmest SSTs. This behaviour is captured by all five of the reanalysis systems, with the largest LWCREs systematically associated with the largest SSTs. Tropical-mean SSTs prescribed during the 2001–2010 analysis period are very similar among the reanalyses (Table 3). Note that OISST v2 (Optimum Interpolation Sea Surface Temperature; Reynolds et al., 2007) was used as an atmospheric lower boundary condition during portions of this intercomparison period by ERA-Interim (July–December 2001) and MERRA-2 (through March 2006), and as the primary input to SST analyses by CFSR (Fujiwara et al., 2017, their Table 4). The observational benchmark distribution of SST is therefore not strictly independent. This benchmark, using CERES SYN1Deg for daily-mean LWCRE and OISST v2 for daily-mean SST, suggests that the mean SST for Q₄ is 1 K warmer than the tropical mean. Q₄ in CFSR exhibits the weakest difference relative to tropical-mean SST (0.7 K), with values in the other reanalyses ranging from 0.9 K (JRA-55) to 1.2 K (ERA-Interim and MERRA-2). CFSR is the only coupled atmosphere–ocean data assimilation system among these five reanalyses, giving it the potential for two-way interactions between high clouds and SST (although analysed SST is still pegged quite tightly to observations; Saha et al., 2010).

Table 3Mean values of the distributions shown in Fig. 10 for all data points in the inner tropics (All; 10^∘ S–10^∘ N) and for the top quartile of LWCRE in the same region (Q₄). The row labelled “Observed” summarizes the results when LWCRE is taken from CERES SYN1Deg, SST from OISST v2, and potential instability and mid-tropospheric RH from AIRS.

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Figure 10b summarizes distributions of lower-tropospheric potential instability (defined as the difference in θ_e between 850 and 500 hPa; Eq. 2) for all tropical points and for points associated with Q₄ of LWCRE. Values of potential instability in the tropics tend to be positive in all five reanalyses. However, this tendency is weaker for MERRA-2 and CFSR than for ERA5, ERA-Interim, or JRA-55, indicating systematic differences in the moist thermodynamic state of the tropical atmosphere (see also Table 3). Moreover, while ERA5, ERA-Interim, and JRA-55 indicate larger potential instabilities associated with Q₄ of LWCRE than in the tropical mean; MERRA-2 and CFSR indicate the opposite. The latter is in better agreement with AIRS. For ERA-Interim, these differences may be linked to the convective closure (Appendix A2). The convection scheme in ERA-Interim specifies an adjustment timescale that, in practice, often exceeds the model time step (especially at coarser resolutions; Bechtold et al., 2008, their Fig. 1). Potential instability in convective locations (Q₄) may thus be shifted toward larger positive values in ERA-Interim (Fig. 10b). The new closure (Bechtold et al., 2014) and finer model resolution used in ERA5 reduce the difference between the Q₄ and tropical-mean values of potential instability by about 50 % (Table 3). The discrepancy between JRA-55 and the other reanalyses has a different origin. Figure 11a shows vertical profiles of MSE averaged over the upper and lower quartiles of daily gridded LWCRE within the inner tropics (10^∘ S–10^∘ N). A “kink” is evident in the vertical profile for JRA-55 between 900 and 850 hPa but not in any of the other profiles. This kink arises because the Q₄ profile in JRA-55 has a warm bias at 850 hPa (+0.4 kJ kg⁻¹ relative to ERA5; Fig. 11b, lower row) but a cool and dry bias at 900 hPa (total −1.0 kJ kg⁻¹; not shown). The convective scheme in JRA-55 restricts cloud base to the model level at ∼900 hPa (JMA, 2013). Thermodynamic instabilities that develop at higher levels (such as the 850 hPa level used to compute potential instability) are thus difficult for the convection scheme to eliminate.

Figure 10Histograms of (a) sea surface temperature (SST), (b) potential instability (${\mathit{\theta }}_{\mathrm{e},\mathrm{850}}-{\mathit{\theta }}_{\mathrm{e},\mathrm{500}}$), (c) grid-scale vertical velocity in the middle troposphere (ω₅₀₀), and (d) relative humidity in the middle troposphere (RH₅₀₀). Data are based on daily-mean products at 1^∘ × 1^∘ resolution from (top to bottom) ERA5, ERA-Interim, JRA-55, MERRA-2, and CFSR during 2001–2010 in the inner tropics (10^∘ S–10^∘ N). Observational estimates are shown along the top axis where available, with data from CERES SYN1Deg (LWCRE), OISST v2 (SST), and AIRS (potential instability and RH₅₀₀). Distributions that include AIRS data are for 2003–2010 rather than 2001–2010. Colour histograms show distributions for the top quartile of LWCRE in each data set (see Fig. 7). Mean values for each distribution are listed in Table 3.

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Figure 11(a) Composite vertical profiles of moist static energy (MSE) for ERA5 (cyan), ERA-Interim (blue), JRA-55 (purple), MERRA-2 (red), and CFSR (green) averaged for the upper (Q₄; thick lines) and lower (Q₁; thin lines) quartiles of daily-mean LWCRE during 2001–2010. Profiles calculated from AIRS observations (September 2002–December 2010; grey dashed lines) are conditioned on quartiles of daily-mean LWCRE from CERES SYN1Deg. At the right are distributions of the (b) temperature (c_pT), (c) moisture (L_vq), and (d) geopotential (gz) components of MSE for Q₄ from each reanalysis at the levels marked by yellow dashed lines in (a): 850 hPa (lower row), 500 hPa (centre row), and 300 hPa (upper row). Mean values are marked as vertical lines; biases in these mean values relative to the mean value from ERA5 are colour-coded at the upper left of each panel (each list from top: ERA-Interim, JRA-55, MERRA-2, and CFSR).

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Decomposing differences in moist static energy into contributions from temperature, specific humidity, and geopotential (Fig. 11b–d), we find that the largest spreads result from differences in moisture content at both 850 and 500 hPa. At 850 hPa, latent energy (L_vq) based on CFSR and MERRA-2 is 1–2 kJ kg⁻¹ less than that based on JRA-55, ERA5, or ERA-Interim (Fig. 11c, lower panel). Meanwhile, at 500 hPa, latent energy based on MERRA-2 is nearly 3 kJ kg⁻¹ larger than that in JRA-55 and more than 1 kJ kg⁻¹ larger than that in ERA5, ERA-Interim, or CFSR (Fig. 11c, middle panel). Biases in c_pT are on the order of ±0.5 kJ kg⁻¹ at both levels (Fig. 11b, lower two panels). For JRA-55 and MERRA-2, temperature biases compensate for humidity biases at 850 hPa but exacerbate the effects of humidity biases at 500 hPa. The relationship between potential instability and LWCRE in CFSR is most similar to that based on observations in terms of mean values, with AIRS estimates 0.4–0.5 K larger than those based on CFSR for both the tropics as a whole and the top quartile of LWCRE (Table 3). However, the distribution of potential instability based on AIRS is broader than that based on CFSR and in that sense is more reminiscent of the distributions based on MERRA-2 or ERA5 (Fig. 10b).

We briefly highlight two other features of the MSE profiles shown in Fig. 11a. First, lower-tropospheric values of MSE associated with Q₄ are evidently larger in the reanalyses than in the AIRS observations. This may indicate that the reanalyses are systematically too moist or too warm in the lower troposphere but may also reflect systematic errors or sampling biases (e.g. cloud clearing) in the AIRS observations. Second, MERRA-2 shows much larger values of MSE in the upper troposphere of convective regions relative to other reanalyses. This bias results from both greater humidity (perhaps due to greater detrainment of cloud water and subsequent condensate evaporation; Fig. 4) and systematic warm biases (possibly linked to more intense cloud radiative heating at anvil level; Fig. 8). At 300 hPa, the excess Q₄ MSE in MERRA-2 relative to ERA5 is on average 61 % attributable to differences in temperature (c_pT; upper panel of Fig. 11b) and 33 % attributable to differences in moisture content (L_vq; Fig. 11c). The remainder (∼6 %) arises from differences in geopotential (Fig. 11d). This bias in upper-tropospheric MSE is systematic throughout the tropics (e.g. the Q₁ profile in Fig. 11) but with smaller magnitudes and temperature biases contributing more outside of deep convective regions. Greater upper-tropospheric MSE in MERRA-2 implies stronger gross moist stability and specifically a stabilization of the upper troposphere that may suppress the average depth of convection. The lower, more extensive anvil deck in MERRA-2 contributes to both strong cloud top radiative cooling around 200 hPa (Fig. 8) and the inability of convective heating to compensate for this cooling. As noted previously for MERRA, this combination yields a physically implausible layer of time-mean zonal-mean diabatic descent centred near 200 hPa that extends across the entire tropics (Wright and Fueglistaler, 2013).

Figure 10c shows distributions of grid-scale vertical velocity (ω) in the middle troposphere (500 hPa). Distributions for the whole tropics are qualitatively similar across the five reanalyses, with peaks at small positive values (subsidence) and long tails toward large negative values (ascent). Larger values of LWCRE in ERA-Interim and JRA-55 are associated almost exclusively with grid-scale ascent in the middle troposphere. This relationship is less pronounced in MERRA-2 and CFSR, although the strongest mid-tropospheric ascent rates are associated with Q₄ in all five reanalyses. These differences may be understood in terms of differences in the convective triggers (Appendix A2), which explicitly consider large-scale convergence in ERA-Interim and JRA-55 but not in MERRA-2 or CFSR. Dependence of the convective trigger on large-scale vertical velocity was eliminated from the ECMWF atmospheric model between the version used for ERA-Interim and that used for ERA5 (Bechtold et al., 2008). No observational benchmark is available for evaluating these distributions.

Figure 12Composite distributions of daily-mean CWC as a function of radiative heating rate and grid-scale relative humidity (RH) in (a, f) ERA5, (b, g) ERA-Interim, (c, h) JRA-55, (d, i) MERRA-2, and (e, j) CFSR on the 100 hPa (upper row; a–e) and 150 hPa (lower row; f–j) isobaric surfaces. RH is calculated with respect to liquid water. Grey shaded regions in each panel mark ranges of ice saturation ratios ($e_{\mathrm{i}}^{*}/e_{\mathrm{\ell }}^{*}$) at these levels, with light shading marking the minimum and maximum and dark shading marking the interquartile range. Solid pink contours mark paired values of radiative heating and RH that are more commonly associated with cloudy conditions (Q₄ of the daily-mean LWCRE) than with clear-sky conditions (Q₁ of LWCRE); dashed orange contours mark the opposite (values more commonly associated with Q₁ than Q₄). Composite mean CWCs are masked for bins containing fewer than 200 samples.

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Distributions of mid-tropospheric RH (Fig. 10d; defined here with respect to liquid water) are bimodal in all five reanalyses, with peaks at both very small values (<10 %) and relatively large values (>50 %). The largest values of LWCRE tend to be associated with large values of mid-tropospheric relative humidity, although this relationship is tighter for MERRA-2 and CFSR than for ERA5, ERA-Interim, or JRA-55. The largest differences among the distributions are at the upper end of the range and can be at least partially explained by differences in the treatment of the liquid–ice transition (Appendix A; Fig. A1). As JRA-55 has the strictest transition from liquid to ice, mid-tropospheric RH with respect to liquid water is generally less than 75 %. ERA-Interim and ERA5 prescribe more gradual transitions from liquid to ice and thus produce larger relative humidities with respect to liquid water. Another potentially important parameter is the critical RH at which large-scale cloud formation (or evaporation of cloud water) is assumed to occur. This value is more than 90 % in MERRA-2 at 500 hPa as opposed to around 80 % in ERA5 and ERA-Interim, leading MERRA-2 to produce a larger frequency of very high relative humidities at this level. Tighter distributions of mid-tropospheric RH associated with the largest values of LWCRE (Fig. 10d) also suggest that deep convection may be more sensitive to mid-tropospheric entrainment of dry air in MERRA-2 and CFSR than in ERA5, ERA-Interim, or JRA-55. For MERRA-2 this is consistent with the application of a Tokioka-type entrainment condition (Bacmeister and Stephens, 2011): entrainment rates smaller than a randomly selected minimum (the Tokioka parameter) are disallowed. For small values of RH, entrainment is efficient in diluting the updraught so that plumes can only reach the upper troposphere when the entrainment rate is small. The Tokioka condition thus tightens the preference for deeper convection to occur in more humid environments. Entrainment rates are also relatively large in CFSR, which uses a base entrainment rate equal to the maximum rate in JRA-55 and about an order of magnitude larger than the base rate in ERA-Interim (Appendix A2). Among the reanalyses, the distribution of mid-tropospheric RH in JRA-55 is most consistent with that based on AIRS. However, as for lower-tropospheric MSE, caveats concerning sampling and cloud-clearance biases apply when interpreting the AIRS distribution.

5.2 Clouds in the TTL

Tropical high clouds in the reanalyses may also originate via the parameterized effects of grid- or subgrid-scale saturation. In the TTL, such in situ cloud formation is often associated with adiabatic cooling linked to wave activity or slow ascent (Massie et al., 2002; Schoeberl et al., 2019). Figure 12 summarizes relationships among CWC, radiative heating rates, and RH at isobaric levels near the base of the TTL (150 hPa) and near the tropopause (100 hPa). The TTL is located above the typical levels of convective detrainment (200–300 hPa; Fig. 4), with a lower boundary near the LZRH (140–150 hPa; Fig. 9a). Clouds in this layer are often associated with slow radiatively balanced ascent and occasionally with very deep convection that penetrates into the TTL (e.g. Fueglistaler et al., 2009). These two cloud populations may be distinguished by their CWCs (smaller for in situ cirrus; larger for convective anvil clouds) and associated radiative heating rates (weak radiative heating for slow ascent; strong cloud top cooling for most anvil clouds, possibly supplanted by strong warming for clouds reaching very high altitude). The essential radiative signature of cloud top cooling and cloud base warming can be seen by comparing the radiative heating profiles in Fig. 8a–e and the vertical locations of the anvil cloud layers in Fig. 4f. Radiative heating thus helps to distinguish different types of clouds in the lower part of the TTL: (1) in situ cirrus clouds, which are associated with weak positive heating rates balancing large-scale ascent (i.e. close to the “spine” of the plot); (2) deep convection that detrains near the base of the TTL, which is associated with large CWCs and negative radiative heating (the “left wing”); and (3) deep convection that detrains inside the TTL, which is associated with large CWCs and positive heating rates (the “right wing”). The latter two types are distinguished by both the depth and water content of the anvil cloud (Fig. 13), and the third type grows progressively rarer with increasing altitude. Compositing on RH in addition to radiative heating helps to highlight some differences and unrealistic features among the reanalyses, as discussed below.

Figure 13Composite mean profiles of cloud water content (CWC) from (a) ERA5, (b) ERA-Interim, (c) JRA-55, (d) MERRA-2, and (e) CFSR associated with different ranges of radiative heating rates at 150 hPa: negative rates less than −1 K d⁻¹ (blue), neutral rates within ±1 K d⁻¹ (grey), and positive rates greater than +1 K d⁻¹ (red). Note different x axis ranges for CWC.

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At 150 hPa, the distributions based on ERA5 (Fig. 12f) and MERRA-2 (Fig. 12i) show wings of large CWCs at large negative and large positive radiative heating rates bracketing a central axis in which radiative heating is weak and CWC depends mainly on RH. The largest values of LWCRE are associated with strong radiative cooling at 150 hPa (the left wing), while strong radiative heating (the right wing) is more often associated with Q₂ or Q₃ rather than Q₄. This difference is consistent with composite mean profiles of CWC (Fig. 13): large negative heating rates at 150 hPa are associated with shallower anvils and larger CWCs, while large positive heating rates are associated with deeper anvils and smaller CWCs. The distribution based on JRA-55 (Fig. 12h) is similar to those based on ERA5 and MERRA-2 but with a smaller range of radiative heating rates, consistent with smaller anvil water contents (Fig. 4c). The distribution based on CFSR (Fig. 12j) also shows similarities but with additional variance in radiative heating linked to the occasional occurrence of extremely large daily-mean CWCs (up to 1408 mg kg⁻¹) at this level. Approximately 1 % of daily-mean CWCs at 150 hPa in CFSR exceed 100 mg kg⁻¹, far more than in any other reanalysis (maximum: 0.1 % in ERA5). The ERA-Interim distribution (Fig. 12g) is more distinctive, with CWC (and LWCRE) more tightly linked to RH and an asymmetry toward positive heating rates. ERA-Interim produces few instances of large negative heating rates, as clouds are associated with enhanced radiative heating at 150 hPa in this reanalysis (Fig. 8).

At 100 hPa, ERA5 and ERA-Interim (Fig. 12a and b) show similar distributions of composite mean CWC, as the largest values are associated with positive radiative heating and supersaturation with respect to ice. However, these two systems show different relationships with LWCRE. Whereas large values of LWCRE often correspond to positive heating rates at 100 hPa in ERA-Interim, the largest values of LWCRE typically correspond to negative heating rates at this level in ERA5. ERA5 and ERA-Interim are the only models considered here that explicitly consider supersaturation with respect to ice. Figure 12a and b indicates that, owing to different radiative signatures of deep convection within the TTL, in situ cirrus clouds form preferentially above strong convective regions in ERA-Interim but outside of these regions in ERA5. The distribution based on MERRA-2 is also bimodal (Fig. 12d), but in this reanalysis the most prominent mode is a leftward-facing wing with relatively large CWCs, negative radiative heating rates, and large LWCREs. This mode is consistent with cooling at the tops of anvil clouds near the tropical tropopause. The second mode features positive radiative heating rates and saturation with respect to ice and is thus consistent with expectations for thin high clouds near the tropopause (e.g. Fusina et al., 2007).

With the exception of ERA-Interim, the largest CWCs at 100 hPa are associated with very large water paths through the UTLS and large negative radiative heating at 100 hPa. The smallest CWCs at 100 hPa correspond to near-zero radiative heating. Mean CWCs associated with positive radiative heating ($>+\mathrm{0.5}$ K d⁻¹) are significantly larger but still more than a factor of 10 smaller than those associated with strong negative radiative heating. Taking strong negative radiative heating ($<-\mathrm{0.5}$ K d⁻¹) and large CWCs (>10 mg kg⁻¹) at 100 hPa as a crude indicator of overshooting convection that reaches the tropopause, these events occur around 0.2 % of the time in MERRA-2 and 0.1 % of the time in CFSR and ERA5. These criteria are never met in JRA-55 or ERA-Interim. Conversely, taking large positive radiative heating ($>+\mathrm{0.5}$ K d⁻¹) and above-average CWCs (>0.01 mg kg⁻¹) as indicative of in situ cirrus in air rising through the TTL, this regime covers 35 % of the tropics in ERA-Interim; 24 % in JRA-55; and around 10 % in ERA5, MERRA-2, and CFSR.

The distribution based on CFSR at 100 hPa (Fig. 12e) indicates severe problems with humidity fields around the tropopause. Values of RH in CFSR at this level cluster around three values: zero (7 % of samples), saturation with respect to ice (6 %), and saturation with respect to liquid water (77 %). Values between zero and saturation with respect to ice account for the remaining 10 % of samples. Saturation with respect to liquid water occurs occasionally at 150 hPa in CFSR as well (Fig. 12j), although these instances differ from those at 100 hPa in that they are associated mainly with small values of LWCRE and negligible CWCs and only represent a small fraction of samples (1.5 %). Humidity fields in the stratosphere are unrealistically small in CFSR (Davis et al., 2017); Fig. 12 shows that unrealistic behaviour often extends downward into the TTL. In Appendix B, we show that the situation is much improved in CFSv2.

Although MERRA-2 contains no explicit representation of ice supersaturation, RH in this reanalysis exceeds saturation with respect to ice in around 33 % of gridded daily means at 150 hPa and 20 % of gridded daily means at 100 hPa. This decrease with height differs from the parameterized behaviour in ERA-Interim and ERA5, in which daily-mean supersaturation frequencies increase from 15 %–25 % at 150 hPa to 30 %–40 % at 100 hPa. The occurrence of ice supersaturation in MERRA-2 can result from the partitioning of liquid and ice and subsequent gradual relaxation of liquid condensate to ice as implemented in the model's prognostic cloud scheme (Appendix A1), but it is surprising that it remains so prevalent in the TTL. This feature may result from temporal truncation: the model limits the water vapour content at grid-scale saturation; the temperature is then modified by some other process; and output is written without further adjustment to the water vapour field. All of the supersaturated points in MERRA-2 have non-zero CWCs, and CWC tends to increase with increasing supersaturation (r=0.24). Liquid water is present in trace amounts for almost all supersaturated points at 150 hPa (93 %) and a substantial fraction of supersaturated points at 100 hPa (31 %). This persistence of positive liquid water contents at very low temperatures will be addressed in a forthcoming version of the GEOS-5 model.