This article was corrected 2014. See end of the on 13 AUG the full text for details.
Corresponding author: K. Suzuki, Jet Propulsion Laboratory, California Institute of Technology, Mail Stop 233‒300, 4800 Oak Grove Dr., Pasadena, CA 91109, USA. (firstname.lastname@example.org)
 This study examines the validity of a tunable cloud parameter, the threshold particle radius triggering the warm rain formation, in a climate model. Alternate values of the model's particular parameter within uncertainty have been shown to produce severely different historical temperature trends due to differing magnitude of aerosol indirect forcing. Three different threshold radii are evaluated against satellite observations in terms of the statistics depicting microphysical process signatures of the warm rain formation. The results show that the simulated temperature trend best matches to observed trend when the model adopts the threshold radius that worst reproduces satellite‒observed microphysical statistics and vice versa. This inconsistency between the “bottom‒up” process‒based constraint and the “top‒down” temperature trend constraint implies the presence of compensating errors in the model.
 Climate models contain various uncertain parameters in the formulations of parameterizations for physical processes. These parameters represent “tunable knobs” that are typically adjusted to let the models reproduce realistic values of key‒observed climate variables. The water conversion from cloud to rain is one particular process that is often tuned to reproduce a reasonable top‒of‒atmosphere radiation budget. The liquid water conversion rate is typically parameterized as a function of liquid water mixing ratio and number concentration, and its formulation involves a set of parameters determining how the conversion rate depends on the cloud properties. One of the most influential parameters contained in some parameterization schemes, among others, is a threshold particle radius below which the precipitation is not assumed to form [e.g., Kessler, 1969]. The threshold radius is introduced to simply mimic a distinct behavior of rain formation that tends to occur only when cloud particles grow large enough to activate the coalescence process. The threshold radius serves as a switch triggering the rain formation, thereby largely controlling the suspended cloud water content after the precipitation occurs: a larger threshold radius prohibits the rain formation and increases cloudiness. There is a long history in tuning this parameter in climate models [e.g., Rotstayn, 2000].
 Given that the threshold radius is a strong modulator of the precipitation formation, choice of its value has a significant impact on representation of aerosol effects on precipitation. Golaz et al.  explored this sensitivity using Geophysical Fluid Dynamics Laboratory (GFDL) Atmospheric Model version 3 (AM3) to find that the radiative flux perturbation induced by anthropogenic aerosol changes is closely correlated to the assumed value of the threshold radius. Their results show that the radiative impact reaches nearly 1 Wm−2 when changing the threshold radius from 6.5 to 10.2μm, which is a range narrower than reviewed by Rotstayn . This significant sensitivity of the radiative flux perturbation to alternate configuration of the particular parameter also implies a substantial effect on climate simulation from preindustrial to present days. This is indeed demonstrated by Golaz et al.  who build two alternate configurations (CM3w and CM3c) of GFDL Coupled Climate Model version 3 (CM3) with different values of autoconversion threshold and additional cloud retuning to maintain radiation. The twentieth century temperature trend is severely affected by the choice of the threshold radius as shown in Figure 1 as a result of its significant impact on the aerosol indirect effect. These results also show that the temperature trend best matches to observations when the smallest value of the threshold radius is assumed and vice versa. It is critical for more reliable climate predictions to constrain which threshold value is more plausible than others based on a bottom‒up observational evidence.
 This study proposes to evaluate these particular model configurations on the global scale using satellite observations. A series of recent studies by the authors [Suzuki et al., 2010, 2011, 2013] has developed new methodologies for analyzing multisensor satellite observations to characterize the warm rain formation process and applied them to cloud‒resolving models. Given the capability of the methodologies to diagnose the model biases for this particular process, the methodologies are applied to evaluate the alternate model configuration in Golaz et al.  in an attempt to constrain the threshold radius.
2 The Data
 We use satellite observation data from CloudSat R042B‒Geoprof [Marchand et al., 2008] and Moderate Resolution Imaging Spectroradiometer (MODIS) collection 5.1 level 2 MYD06 cloud product [e.g., Platnick et al., 2003] for the period of January–March in 2008. The former provides the vertical profile of the radar reflectivity factor at 94 GHz, and the latter provides effective particle radius (re) and cloud optical thickness (τc) of warm‒topped liquid clouds. The warm‒topped clouds are determined using the MODIS cloud phase flag and the CloudSat echo top characterization. We use the CloudSat data with the cloud mask showing high confidence of hydrometer detection (>30). The analysis is restricted to global ocean.
 This study also analyzes climate model simulation data obtained from GFDL AM3w, AM3, and AM3c, whose configurations are the same as CM3w, CM3, and CM3c in Golaz et al. . The effective particle radius diagnosed at the cloud top and the cloud optical depth are used for analysis. The simulation is also equipped with the Cloud Feedback Model Intercomparison Project Observation Simulation Package satellite simulator [Bodas‒Salcedo et al., 2011] to simulate the radar reflectivity factor at the CloudSat wavelength. The radar reflectivity simulated at subcolumn within model grids accounting for subgrid‒scale variability are output and analyzed. The data for the lowest 1 km layer are removed from analysis for consistency with CloudSat that suffers from ground cluttering. The analysis uses the 6‒hourly instantaneous output for the 3 month period of 2008 corresponding to satellite observations. Although the model output is not sampled at the same local time as satellites, we speculate that the statistics shown would not be substantially sensitive to sampling method since the analysis examines the interrelationship between simultaneously observed cloud and precipitation that is not likely to be influenced by sampling method.
3 Microphysical Statistics
 We analyze vertical profiles of CloudSat radar reflectivity in the manner that is combined with MODIS cloud properties as proposed by Suzuki et al. . The profiles of radar reflectivity are rescaled as a function of in‒cloud optical depth (ICOD) that is determined by vertically slicing the total cloud optical thickness (τc) from MODIS with the aid of adiabatic profile assumption [Suzuki et al., 2010]. The probability density function of the radar reflectivity normalized at each ICOD bin is shown in the form of contoured frequency diagram and classified according to different ranges of cloud‒top effective particle radius (re) which is also obtained from the MODIS cloud product. The statistics derived in this manner are shown in Figures 2a–2c. The satellite‒derived statistics clearly depict that the vertical microphysical structure tends to transition from nonprecipitating clouds (Figure 2a) through drizzling clouds (Figure 2b) to precipitating clouds (Figure 2c) as a monotonic function of the cloud‒top effective radius (re), as has been reported by Suzuki et al. .
 Corresponding statistics are obtained from the climate model simulations with alternate configurations of the threshold radius (rthresh) and are shown in Figures 2d–2f (rthresh=6.0μm), 2g–2i (rthresh=8.2μm), and 2j–2l (rthresh=10.6μm), respectively. It should be noted that the statistics constructed are generally more robust over smaller ICOD values that are more frequent than larger ICOD values (Figure S1 in the supporting information). Figure S1 also illustrates that the model ICODs are systematically larger than satellite observations, a feature consistent with recent studies [e.g., Nam et al., 2012]. The comparisons of re (Figure S2) also show that the modeled revalues tend to be smaller than MODIS, underscoring the importance of further investigations of cloud properties themselves.
 It is found in Figure 2 that the joint ICOD‒reflectivity statistics are systematically different among differing assumptions of rthresh. The statistics for AM3w (rthresh=6.0μm) indicate much faster rain formation compared to satellite observations: the majority of the reflectivity profile is found to have a clear characteristic of downward increase even for the smallest particle size range of re=6.5–10μm (Figure 2d). This is a distinct discrepancy from satellite observations (Figure 2a) that indicate nonprecipitating characteristics as illustrated by the majority of reflectivity values smaller than −20dBZ.
 Similar characteristics are also found in the case of AM3 (rthresh=8.2μm) (Figures 2g–2i), which shows essentially the same behavior of the microphysical transition as a function of re: the reflectivity profiles tend to increase downward regardless of re. It should, however, be noted that the statistics for re=6.5−10μm (Figure 2g) tend to have a weaker peak of the downward‒increasing characteristics with another small peak of the nonprecipitating reflectivity value (<−20dBZ) hinted in the vicinity of the cloud top. This indicates that nonprecipitating clouds tend to exist more frequently in the case of AM3 (rthresh=8.2μm) compared to AM3w (rthresh=6.0μm).
 AM3c (rthresh=10.6μm) shows a clear contrast to the other two cases: the reflectivity profiles for the smallest range of re have a distinct population of nonprecipitating clouds (Figure 2j). This characteristic is much closer to satellite observations (Figure 2a) than those for other threshold values (Figures 2d and 2g). The nonprecipitating branch in Figure 2j tends to transition into the drizzling range covering Ze=−15∼0 dBZwhen re=10−15μm as shown in Figure 2k. These drizzling clouds tend to have smaller reflectivity values than smaller threshold cases (Figures 2e and 2h) and to be closer to satellite observations (Figure 2b).
 Overall comparisons of the microphysical statistics shown in Figure 2 suggest AM3c to be the most plausible configuration among the three, in terms of the reproducibility of the nonprecipitating characteristic and its transition into precipitating clouds with the increasing cloud‒top particle size. Although the satellite simulator is somewhat sensitive to assumptions (e.g., subgrid‒scale characteristics and drop size distributions) [e.g., Di Michele et al., 2012], the overall differences among alternate configurations and observations tend to be larger than can be explained by the forward simulation uncertainty. It is also worth noting that the statistics broken down into different latitudes (Figure S3) show more complicated pictures. The model statistics, particularly for AM3c, have substantial dependency on latitudes, highlighting the importance of further investigation over different regions.
4 Single‒column Model Analysis
 To further understand behaviors of the statistics in Figure 2 in terms of model representation of microphysical processes, a simple theoretical analysis is performed. This is the same approach as Suzuki et al.  using a simplified single‒column model (SCM) that isolates the liquid cloud microphysical processes from their full coupling to other processes in 3‒D models. The SCM is described by a pair of prognostic equations for mixing ratios of cloud water (qc) and rain water (qr) given as
where ρ denotes atmospheric density, τrepis a time scale over which the cloud water content is replenished to its adiabatic value (qadb), and Vt is terminal fall velocity of the rain water. Cloud water is formed by replenishment and depleted by autoconversion (Raut) and accretion (Racc) processes. Detailed description of the SCM is documented in Suzuki et al. .
 In this study, the autoconversion rate (Raut) is parameterized in the same way as in GFDL AM3 based on the scheme of Tripoli and Cotton  that triggers the autoconversion only when qc exceeds its threshold value (qthresh). qthresh is related to the threshold radius (rthresh) as , where ρwand Ncdenotes the liquid water density and the droplet number concentration, respectively.
 Equations (1) and (2) are numerically solved for steady state solution under various assumed values of Nc. The solutions are then expressed in the form of the radar reflectivity profile as a function of in‒cloud optical depth for different ranges of the cloud‒top effective radius (re) that is closely correlated to the differing Ncvalues. The radar reflectivity is obtained by a forward calculation from qc and qr[Suzuki et al., 2013]. Figure 3 shows the results for three different values of rthresh=6.0, 8.2, and 10.6μm, which are used in AM3.
 It is clearly found in Figure 3 that the radar reflectivity profiles vary with rein a systematically different manner for different assumptions of rthresh as in the AM3 results. For the case of rthresh=6.0μm (Figure 3a), the reflectivity increases downward for all the ranges of re, indicating a rain formation regardless of re. The variation of the reflectivity with regard to differing re is also limited to a range that is as narrow as AM3w (Figures 2d–2f) and is substantially narrower than satellite observations (Figures 2a–2c). The reflectivity range becomes wider for larger values of rthresh. In the case of rthresh=8.2μm (Figure 3b), the smallest “edge” of the reflectivity profile reaches to the value smaller than −20dBZ. Although this is qualitatively more similar to the observed characteristic found in Figure 2a, the reflectivity profiles for re=6.5–10μm still contain substantial rain formation (increasing downward), which is in clear contrast to the nonprecipitating characteristic in satellite observations (Figure 2a). The observed nonprecipitating characteristic is reproduced with rthresh=10.6μm (Figure 3c): the reflectivity variation for re=6.5–10μm, in particular, is limited to the range within the nonprecipitating values. This is also consistent with the characteristic in AM3c (Figure 2j) that has a pronounced nonprecipitating branch. This further suggests that the assumption of rthresh=10.6μm is more plausible than the other two configurations (rthresh=6.0 and 8.2μm) in terms of microphysical process representations in the SCM. The similarities found between the SCM results (Figure 3) and the GFDL AM3 statistics (Figure 2) also suggest that the behavior of the original model is attributed to the autoconversion process representation through choices of the threshold radius.
 The results described above suggest that alternate configurations of the autoconversion threshold radius provide systematically different microphysical characteristics in the statistics directly comparable to satellite observations. The comparisons of the statistics among different choices of the threshold radius as well as between the models and observations identify which configuration is more realistic than others. The results show that the assumption of rthresh=10.6μm (AM3c), the largest threshold radius among the three cases, is most plausible in terms of reproducibility of microphysical transitions from nonprecipitating to precipitating clouds. This is consistent with a previous aircraft observation study [Pawlowska and Brenguier, 2003] that shows that precipitation forms when the maximum mean volume droplet radius exceeds 10μm. The smallest threshold value of rthresh=6.0μm (AM3w), in contrast, produces much narrower variation of precipitation and is biased to form rain too frequently. These results contradict the fact that the smallest threshold radius (CM3w, rthresh=6.0μm) best reproduces the historical temperature trend and CM3c (rthresh=10.6μm) produces almost no significant warming for most of the twentieth century (Figure 1) [Golaz et al., 2013]. This contradiction implies the presence of compensating model errors. If this behavior is not a peculiarity of GFDL CM3, the contradiction may be occurring in other climate models as well.
 This study was carried out at Jet Propulsion Laboratory, California Institute of Technology, under a contract with National Aeronautics and Space Administration (NASA) and supported by NASA grants NNN13D771T and NNN13D968T. The CloudSat data products were provided by CloudSat Data Processing Center at CIRA/Colorado State University.
 The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.
In the originally published version of this article, the author's Acknowledgments had inaccurate funding information. The following correction has been made, and this version may be considered the authoritative version of record. In the Acknowledgments (paragraph ), “NASA grants NNX07AR11G and NNX09AJ45G” should read “NASA grants NNN13D771T and NNN13D968T.”