Erroneous Relationships among Humidity and Cloud Forcing Variables in Three Global Climate Models

Transcription

1 4190 J O U R N A L O F C L I M A T E VOLUME 21 Erroneous Relationships among Humidity and Cloud Forcing Variables in Three Global Climate Models FLORIAN BENNHOLD AND STEVEN SHERWOOD Department of Geology and Geophysics, Yale University, New Haven, Connecticut (Manuscript received 23 March 2007, in final form 22 January 2008) ABSTRACT Links are examined between time-averaged cloud radiative properties, particularly the longwave and shortwave components of cloud radiative forcing (CRF), and properties of the long-term averages of atmospheric soundings, in particular upper-tropospheric humidity (UTH), lower-tropospheric precipitable water (PW), and static stability (SS). The joint distributions of moisture measures and the composite or conditional mean CRF for different moisture and stability combinations are computed. This expands on previous studies that have examined cloud properties versus vertical velocity and surface temperature. These computations are done for satellite observations and for three representative coupled climate models from major modeling centers. Aside from mean biases reported previously, several departures are identified between the modeled and observed joint distributions that are qualitative and significant. Namely, the joint distribution of PW and UTH is very compact in observations but less so in models, cloud forcings are tightly related to PW in the data but to UTH in the models, and strong negative net CRF in marine stratocumulus regions occurs only for high SS and low UTH in the data but violates one or both of these restrictions in each of the models. All three errors are preliminarily interpreted as symptoms of inadequate dependence of model convective development on ambient humidity above the boundary layer. In any case, the character of the errors suggests utility for model testing and future development. A set of scalar metrics for quantifying some of the problems is presented; these metrics can be easily applied to standard model output. Finally, an examination of doubled-co 2 simulations suggests that the errors noted here are significantly affecting cloud feedback in at least some models. For example, in one model a strong negative feedback is found from clouds forming in model conditions that never occur in the observations. 1. Introduction Global climate models (GCMs) are a key tool for predicting future climate change and among other things must explicitly predict cloud cover and convective transports of heat and moisture throughout the troposphere. How to accurately represent these processes remains an unsolved problem (e.g., Arakawa 2004; Stephens 2005). Differences in cloud behavior are the dominant source of differences in how models predict overall climate sensitivity (Cess et al. 1996; Colman 2003; Bony et al. 2006), and inadequate convective parameterizations have also been blamed for poor prediction of other phenomena such as the Madden Julian Corresponding author address: S. Sherwood, Dept. of Geology and Geophysics, Yale University, P.O. Box , New Haven, CT Steven.Sherwood@yale.edu oscillation (e.g., Grabowski and Moncrieff 2004). More recent studies have specifically identified low cloud cover in the tropics and middle-latitude storm tracks, which has a strong net cooling effect on climate, as the dominant source of intermodel variability in climate sensitivity (Webb et al. 2006; Bony and Dufresne 2005). Miller (1997) argued that low-level clouds would stabilize climate via a strong negative albedo feedback, if the relationship to low-level static stability reported by Klein and Hartmann (1993) held up. Since the 1970s, satellite observations have offered the possibility of assessing the performance of GCM present-day climate simulations using measured quantities on a global scale. Among those quantities measured are radiative forcings, water vapor in different layers of the atmosphere, and air and sea temperatures. These variables are all likely to influence the physical processes that control cloud cover, type, and radiative impact (e.g., Ramanathan 1987). DOI: /2008JCLI American Meteorological Society

2 1 SEPTEMBER 2008 B E N N H O L D A N D S H E R W O O D 4191 Many studies have used such data to test models and have found systematic errors in simulated water vapor and cloud feedbacks. Current models generally simulate too little clouds in the midtroposphere and too much high cirrus (Wyant et al. 2006), show little consensus on upper-tropospheric ice content (Su et al. 2006), and simulate excessively bright clouds overall (e.g., Eliseev et al. 2003; Zhang et al. 2005). Though a realistic variety of cloud types is often reproduced, their characteristics tend to differ from those observed (Williams and Tselioudis 2007). Water vapor biases vary among models or even versions of the same model but are often too dry in areas that should be wet and too wet in areas that should be dry (e.g., Chen et al. 1996; Gettelman et al. 2006; Salathe and Chesters 1995). All models show strong correlations in the tropics between surface temperature, tropospheric humidity, and cloud cover that are qualitatively realistic; such correlations have occasionally been used to make various arguments about climate feedbacks, but do not show any relationship to the actual feedback strengths in models (John and Soden 2006). Model biases often change when convective or cloud schemes are changed (e.g., Chen et al. 1996). Previous studies have made the problem clear but have not led to consensus as to exactly how model parameterizations need to be changed. One avenue is to pursue more highly directed statistical analyses of model and observational data. One may, for example, composite cloud data according to dynamical regimes defined in some objective way, typically using analyzed vertical velocity as the dynamical index (Weaver and Ramanathan 1997; Norris and Weaver 2001; Bony et al. 2004; Williams et al. 2003, 2006). Compositing normally refers to the averaging of a set of target variables, conditional on a discrete predictor or set thereof, to produce a composite picture for each possible value of the predictor. This general approach has recently been expanded to two dimensions using more than one predictor variable [e.g., sea surface temperature (SST) and maximum SST advection] in composite analyses of cloud radiative forcing (CRF; Ringer and Allan 2004; Norris and Iacobellis 2005). Norris and Iacobellis (2005) inferred from composite analysis of cloud observations, surface winds, and SST measurements how a mainly stratus (St) cloud layer advected over warmer water develops into stratocumulus (Sc) and other convectively more active clouds. In evaluating GCM simulations, Norris and Weaver (2001) found an unrealistic sensitivity of low-level clouds to circulation changes that implied significant errors in cloud feedback arising from low-level clouds. In another bivariate predictor analysis, Ringer and Allan (2004) found strong underestimation of marine stratocumulus (MSc) in one version of the Hadley Center model. Beyond the question of how to represent clouds in models lies the question of how they will change in the real world as climate warms. Bony et al. (2004) proposed using the techniques above to discriminate between cloudiness changes arising from dynamics versus thermodynamic mechanisms on the basis of local SST and, the idea being that the former dominates natural variations while the latter would dominate any climate feedback. Whether this intriguing idea will actually work remains to be seen; a necessary test is if it will be able to predict the forced behavior of coupled climate models. While is attractive for this purpose owing to the useful constraint that it must average globally to zero in any climate, alternatives are worth pursuing for other reasons. First, direct measurements of are far too rare to be of any use and one must use fields indirectly inferred from other data through the use of a model. These fields are unavoidably noisy and inaccurate, at least in the tropics, especially in regions where is highly variable and/or large in absolute magnitude (Newman et al. 2000); this may account for quantitative differences from models that have been reported under these conditions (Stowasser and Hamilton 2006). Second, since the laws of physics governing cloud development are Galilean invariant, any connection between cloud properties and the rate of large-scale vertical translation of the air mass containing them must result indirectly from either the influence of that motion on temperature and humidity or the influence of condensational heating on the ascent rate itself (see Emanuel et al. 1994). Relationships with more proximate predictors should stand a better chance of yielding clear signals in the present climate and of remaining similar in a changed climate. Previous studies have found that, notwithstanding some quantitative differences noted above, relationships between, SST, and cloud properties are qualitatively consistent between models and observations (Williams et al. 2006). In analyzing different variables, we have found several instances where this is not the case. Below, we describe these instances and propose some simple metrics to quantify them. We hope these discrepancies and metrics will be useful to future model development efforts. 2. Data We have used several satellite observation datasets, the output of five coupled GCMs from three modeling centers, and some reanalysis data. We first present a

3 4192 J O U R N A L O F C L I M A T E VOLUME 21 general analysis of cloud forcing over tropical and midlatitude oceans, then a second one focused on the subtropical and midlatitude regions of maritime low cloud cover noted by Klein and Hartmann (1993, see Table 3). Only maritime regions (which dominate feedback in models) are included here to avoid complications associated with orography, and polar regions are omitted because of uncertainties in data quality. Both restrictions have been common in previous studies. All data shown, unless otherwise indicated, come from longterm averages (2 10 yr, over all months, for observations and models, respectively). This is not common. We have applied our analysis to monthly data as well, but found that the long-term average shows the discrepancies between models and observations more clearly. This suggests a particular relevance of our findings to climate rather than just short-term weather phenomena. a. Observations Our general approach will follow that of previous studies mentioned above; the principal innovation is to use different predictor variables, and to focus on longterm rather than monthly means. The relevant quantities for this study are CRF [as defined in Ramanathan (1987)], upper-tropospheric humidity (UTH), lowertropospheric dry static stability (SS), and precipitable water (PW). 1) CLOUD RADIATIVE FORCING We employ the usual definition of cloud radiative forcing (or CRF) as the difference between actual and cloud-cleared outgoing radiant fluxes at the top of the atmosphere. The observations come from Earth Radiation Budget Experiment (ERBE) data obtained from the National Aeronautics and Space Administration (NASA) Langley Research Center. We are using the monthly scanner data product (E-9), available on a horizontal grid. The shortwave (SW) and longwave (LW) components of the CRF are reported separately. The errors for the different sensors for reflected and emitted radiances on a grid are estimated to be about 10 W m 2 (Barkstrom 1984). The dataset has also been found to underestimate the negative SW CRF and overestimate the LW CRF because the clear-sky measurements are contaminated by partial cloud cover (Stubenrauch et al. 2002). This bias has been found to be of the order of 5 10Wm 2 for SW CRF and approximately 4 W m 2 for the LW CRF in the tropics. Overall, this clear-sky bias reduces some of the mean discrepancies with models evident here and in previous studies. The LW CRF caused by a cloud of given area is controlled primarily by the height of the cloud top above the surface (or more specifically, the temperature difference between the level of unit optical depth and the surface), though it is also affected by the amount of water vapor present since this reduces the clear-sky radiance. The SW CRF on the other hand is controlled mainly by the total water content of the cloud, the incident solar flux, and the surface albedo. Thus, both components of the CRF depend not only on what kind of cloud occurs, but where. This effect is particularly severe for SW CRF: the same middlelatitude cloud will reflect much more radiation in summer just because of increased insolation (about 20 W m 2 ). For the LW CRF, this effect is not as important, especially over the oceans where the temperature does not vary as significantly with the seasons. To eliminate the influence of location and season on the SW CRF, we consider a normalized SW CRF that depends only on the cloud s own properties. Following the definition of SW CRF (Ramanathan 1987), we replace S(x, y, t), the solar irradiation at the top of the atmosphere, with an average insolation of S W m 2 S 0 /4 (with S 0 being the solar constant ) and define a normalized SW CRF: C SW,norm S C, where C and are the albedos of clear skies and all skies, respectively; C SW,norm is the SW CRF that would have been exerted with average insolation everywhere on the globe and only carries the time and location information from the albedo measurements. For the computation of the net forcing (sum of both components), we used the true C SW rather than this normalized value. 2) UPPER-TROPOSPHERIC HUMIDITY Channel 12 of the High Resolution Infrared Sounder (HIRS) on board the Television Infrared Operational Satellite (TIROS) Operational Vertical Sounder (TOVS), located around 6.7 m, is sensitive to temperature and humidity in the upper troposphere. Through the radiance to humidity transformation (Soden and Bretherton 1993; Stephens et al. 1996; Lanzante and Gahrs 2000; Jackson and Bates 2001; Bates et al. 2001) the RH from a thick layer mainly between 200 and 500 hpa (with respect to ice), commonly referred to as UTH, can be obtained from the HIRS data. The dataset used in this work is described in Bates et al. (2001). Like the ERBE data, it is on a horizontal grid and averaged monthly. We have only used data from the same years as ERBE. 1

4 1 SEPTEMBER 2008 B E N N H O L D A N D S H E R W O O D 4193 During the analysis, overcast pixels have to be discarded since clouds are opaque in the infrared and thus obstruct the retrieval. This process is known as cloud clearing (Soden and Bretherton 1996). A necessary but not sufficient condition for clouds to form is supersaturation of the air with water vapor. This means that generally RH and clouds are positively correlated where clouds exist, RH is high. Unfortunately, because of this dependence, the cloud clearing introduces a dry bias. In the tropics this clear-sky bias may reach 15% RH but generally it is of the order of 5% 10% RH, lower when RH itself is lower because of reduced cloud formation (Lanzante and Gahrs 2000; Jackson and Bates 2001). In presenting the data we will remind readers of this using arrows when presenting the results (see section 3). The random error from diverse sources is estimated to be of the order of 10% of the RH value (not 10 percentage points of RH) (Soden and Bretherton 1996). 3) STATIC STABILITY Static stability is defined as the difference in potential temperature between two layers. It is an important factor in regulating the vertical humidity transport in the atmosphere. Klein and Hartmann (1993) found the potential temperature difference between 700 hpa and sea level to be a good predictor of MSc and low cloud cover, although Weaver (1999) reported little difference if 500 hpa was used. We therefore rely on satellite data, which represent broadly variations in lowertropospheric temperature but give important global coverage not available from radiosondes. We again use data only from the ERBE time period. Since we are constructing a proxy from a bulk measurement, absolute values of SS are not necessarily comparable to those reported by Klein and Hartmann (1993) and others based on a temperature at a particular level. For the above purpose we used the lowertropospheric temperature (TLT) product derived from Microwave Sounder Unit (MSU) measurements (Christy et al. 2003; Spencer and Christy 1992). Previous comparisons of the monthly product with data from radiosondes at several U.S. stations revealed that the error at the 95% confidence level in a 2.5 pixel was less than 1.3 K (Christy et al. 2003). The TLT is sensitive to the temperature of a broad layer in the atmosphere lying mostly below 600 hpa, so it should serve adequately as a rough proxy for the 700-hPa temperature albeit with some influence from surface and mixedlayer emissions that will slightly reduce the range of the estimated stabilities. For SST we use National Oceanic and Atmospheric Administration s (NOAA s) blended monthly SST analysis (Reynolds et al. 2002), version OI.v2. We linearly interpolated this dataset from its native 1 grid to the 2.5 grid used for the ERBE data. Computing a potential temperature from SST requires the surface pressure, which was obtained from the National Centers for Environmental Prediction National Center for Atmospheric Research (NCEP NCAR) monthly reanalysis (information online at The surface pressure is the only variable in our analysis that did not come from satellite observations, but its influence on estimated static stability is not large, with a 1-hPa error producing approximately a 0.1-K error in SS. 4) PRECIPITABLE WATER Precipitable water is the vertically integrated mass of water vapor in the atmosphere in kilograms per square meter. Because water vapor mixing ratios drop so much above the planetary boundary layer (PBL), PW is determined primarily by the absolute humidity and thickness of the PBL. This distinguishes it from UTH, which reflects the relative humidity above the PBL. We have obtained precipitable water from the NASA Water Vapor Project (NVAP) reanalysis (Randel et al. 1996), a blend of measurements from the Special Sensor Microwave Imager (SSM/I) and in situ observations gathered primarily from radiosondes. The NVAP product discriminates water vapor in several layers. We include here only the precipitable water below 700 hpa, designated PW. This typically constitutes the bulk of the total precipitable water, but by eliminating any overlap with UTH, we fully ensure the independence of the two observables. The NVAP data were obtained from the NASA Langley Research Center and bilinearly interpolated to the ERBE grid. Unfortunately, the product does not start until 1989, which gives an overlap of only 24 months with the ERBE data. However, the amount of data proved to be more than sufficient to reveal key results, as will be seen below. Recently, Trenberth et al. (2005) analyzed different precipitable water datasets from satellite observations, reanalyses, and blended products including the NVAP product. They found that especially over mountain areas and coastal areas the NVAP dataset shows some erroneous behavior. Trenberth et al. also noted that for trend analysis a change in data treatment in 1993 created a discontinuity. Neither inconsistency affects our results since we only use data over oceans and before 1990 and are not looking at trends. To summarize, Fig. 1 shows climatological maps of each variable over the retrieval period. The maps are

5 4194 J O U R N A L O F C L I M A T E VOLUME 21 FIG. 1. Averaged plots of CRF, UTH, SS, and PW from the respective retrieval periods. discussed in the next section along with scatterplots of the data. b. Models We have chosen three models that have been run for the Intergovernmental Panel on Climate Change s (IPCC s) Fourth Assessment Report (AR4) and archived for the Coupled Model Intercomparison Project round 3 (CMIP3) and/or the Cloud Feedback Model Intercomparison Project (CFMIP), as indicated in Table 1. Our choice was motivated by a preference for a subset of models that have a broad range of climate sensitivities (Boer and Yu 2003) that are relatively well known, and for which all needed simulations were available. The climate sensitivities are based on slabocean model versions of the respective GCMs. The sensitivity ranges by somewhat less than a factor of 2, compared to nearly a factor of 3 for all AR4 models. he Community Climate System Model (CCSM) by NCAR, the Hadley Center Coupled Model (HadCM) and the Hadley Center Slab Ocean Model (HadSM) by the Hadley Center, and the Canadian Global Climate Model (CGCM) by the Canadian Climate Center (CCC) are fully coupled atmosphere ocean models. Coupled runs are used for the comparison with the satellite data, whereas some of the runs for the climate change analysis use slab oceans. The IPCC specified certain predefined runs that all participating modeling groups were asked to perform. Table 2 summarizes the runs used in this study. The Community Climate System Model developed by NCAR (Collins et al. 2006) at the lower (T42) resolution (CCSM3) is among the least sensitive to climate forcings. We also considered coupled and slab versions of the CGCM, a model of moderate climate sensitivity (Kim et al. 2002; Flato and Boer 2001). Finally, we used two versions of the relatively sensitive Hadley Centre climate model: the HadCM3 (Gordon et al. 2000), a fully coupled version from CMIP3, and the HadSM4, a 50-m slab-ocean development version used in CFMIP. The output from these models was obtained from the following sources: for CCSM3, the Earth System Grid (information online at for CGCM and HadCM4, the PCMDI archival site (information online at esg.llnl.gov:8443/index.jsp); and for HadSM4, the CFMIP Web site.

6 1 SEPTEMBER 2008 B E N N H O L D A N D S H E R W O O D 4195 TABLE 1. Model resolution and sensitivity. Model Module Horizontal resolution (at equator) Vertical levels Climate sensitivity CCSM3 Atmosphere T42 ( ) 26 Ocean K m 2 W 1 CGCM3 Atmosphere T47 ( ) 31 Ocean K m 2 W 1 HadCM3 Atmosphere Equivalent T47 ( ) 19 HadSM4 Ocean K m 2 W 1 Our study is concerned primarily with comparisons between present-day atmospheric behavior in models and observations. For this purpose, we used 10-yr mean climatologies, from a present-day (1990) run for CCSM3 and from a preindustrial run for each of the other models. Results were not sensitive to the length of the run (not shown). Toward the end of the paper we also briefly consider the sensitivity of cloud forcing in a climate change scenario. For this we compare equilibrium runs at a low CO 2 concentration (280 or 355 ppmv depending on the model; see Table 2) with those at double these initial CO 2 concentrations. To obtain the latter, we averaged the last 10 yr of the relevant high-co 2 simulation (which for the coupled version of CGCM was a 1% yr 1 to doubling run). Among the two Hadley Centre models, only the slab-ocean HadSM4 was available at doubled CO 2. To compare with the observational data, we have estimated quantities from models in a manner similar to that used by the observation systems to measure the real atmosphere. We have not gone so far as to apply the satellite data treatment algorithms on radiative transfer output from the model runs, which would be optimal. More simply, to estimate SS we applied the static (i.e., only dependent on pressure) weighting function for TLT (provided by RSS on their Web site; see section 3) to the model temperature, SST, and surface pressure data. Estimating UTH is less straightforward since the weighting profile depends on the mixing ratio and temperature profile of the troposphere. To approximately capture this effect, we applied a temperature-dependent weighting function (Soden and Bretherton 1996) to model the relative humidity (with respect to ice). While in principle a specific humidity dependent profile would be even better, model biases make this problematic. The key results changed little even if a static weighting function was used (not shown). 3. Analysis and results a. 1D distributions and composites We begin by examining the distributions [probability density functions (PDFs) or densities] of individual environmental variables in isolation. Figure 2 shows distributions (left panels) of UTH and PW from the observations and the models. The distributions are of the long-term mean over all ocean horizontal grid locations within 40 N 40 S. Striking biases are immediately evident, though not unexpected. The observed UTH is much drier than in any of the models. A bias of up to 10% 15% in this direction in cloudy and moist regions is expected because of clear-sky sampling biases (see section 2, indicated by the black arrow in the upper-left panel), but should diminish significantly at low UTH; compensating for this would make the observed distribution wetter and broader. Even considering this bias, however, all models appear too wet and their distributions too wide: in CCSM3, where the bias is strongest, mean UTH values of up to 60% are common while in the observations the distribution declines rapidly above 35%. This is consistent with the conclusions of Iacono et al. (2003), who reported that for the CCSM3 the discrepancy in UTH remains very striking even when using a radiative transfer model considering only clearsky radiances and comparing brightness temperatures. Looking at dry regions (dominant in the midlatitudes), where the clear sky bias is weak, the wet bias persists, although it is less strong than for high UTH values. Biases are less extreme in HadCM3 and CGCM3 and may be reconcilable with the data in the CGCM3 model if one makes very generous allowances for clear-sky sampling biases. For PW, on the other hand, the observations indicate a wetter lower atmosphere than the models predict. Now, the CCSM3 consistently the wettest model is TABLE 2. Model runs and CO 2 concentrations. Runs CO 2 properties Present-day climate 355 ppm Preindustrial 280 ppm CO 2 doubling 560 ppm CO2 doubling for CCSM 710 ppm 1% increase yr 1 in CO 2 to doubling 280 ppm plus 1% until 560 ppm 1% increase yr 1 in CO 2 to doubling for CCSM 355 ppm plus 1% until 710 ppm

7 4196 J O U R N A L O F C L I M A T E VOLUME 21 FIG. 2. (left) Normalized distributions (PDFs) of PW and UTH and (right) average CRF as a function of each, from observed and model data within 40 N 40 S. Simulations are preindustial for HadCM3 and CGCM3, and 1990 control for CCSM3. Each dot represents a sample of equal size. The error bars represent one standard deviation of the entire set for the PDFs and one standard deviation of each bin for the distributions. The arrow in the top-left panel indicates the anticipated bias at high UTH. closest to the observations, while CCMA is farthest away with biases of about 10 kg m 2 in PW. As with UTH, the worst biases are about as big as the spread of the observed values. We know of no systematic observation errors in PW that could explain the differences between the models and the observations. All models show a distribution with two pronounced maxima (one at kg m 2 and another at kg m 2 ) whereas in the observed distribution the two peaks are less pronounced and much closer together (28 and 35 kg m 2 ). This error in the models could indicate weak horizontal moisture transport between low- and high-pw regions. Also shown in Fig. 2 (right panels) are the composite projections of the net CRF onto these two moisture variables. The first thing to note is the overall negative bias in model net CRF, with model clouds cooling the climate system by at least 10 W m 2 more on average than indicated by ERBE. Allowing for ERBE s clearsky bias makes the discrepancy smaller, but since the biases from SW and LW CRF work against each other, a significant difference remains. Interestingly, the maximum net CRF is similar in the models and observations at 30 40Wm 2 and similarly occurs under the driest conditions; the main difference arises because this

8 1 SEPTEMBER 2008 B E N N H O L D A N D S H E R W O O D 4197 TABLE 3. Selection of relevant MSc regions and types (based on Hanson 1991; Klein and Hartmann 1993). Region with subtropical MSc over cold ocean currents Peruvian Namibian Californian Australian Canarian Location 5 35 S, W 5 35 S, 12 W 18 E N, W S, E N, 4 34 W FIG. 3. Scatterplot of UTH and PW for observational data averaged over 24 months. Red dots are used within 20 N and 20 S, blue dots within N and S, and black dots within N and S. maximum is attained rarely in the observations but commonly in the models. This also argues against ERBE biases being the main problem. The models vary somewhat in the relationship of net CRF to moisture, with CCSM showing relatively little relationship between net CRF and PW, and CCMA showing a particularly strong one between net CRF and UTH. It is well known that UTH, PW, and SST, as well as cloud amount and height, all vary similarly in the tropics (see Fig. 1). Strongly negative net CRF indicates low-level clouds, whose (warming) LW CRF is weak but whose (cooling) SW CRF can still be considerable if the cloud cover and water content are sufficient. High and persistent coverage by such clouds tends to coincide with low SST and subsiding (hence dry) freetropospheric air. This certainly contributes to the tendency of negative net CRF to occur at low UTH. Moreover, low SST tends to produce low PW because of a lower saturation mixing ratio, providing a plausible explanation for the negative relationship between the net CRF and PW. As is evident from Figs. 1 and 3, the regions of marine Sc (Table 3) show very low values of UTH. In fact, a negative net CRF appears to become significant below a certain UTH threshold (approximately 20% 25%), a nonlinearity less evident in the models. CCSM and HadCM3 show a slight increase in the lowest UTH regimes but stay practically stable after that, in contrast to the observations. b. Joint distributions and bivariate composites We now move to the central results, which involve the joint distributions of pairs of environmental variables and the composite projection of net CRF onto such pairs. In comparing models to data we now overlook the biases identified above and concentrate on the shapes of the distributions, examining in effect whether relative extrema of different variables have the right relationships. In the spirit of overlooking mean biases, we will plot each dataset on axes shifted so as to recenter the data. 1) TROPICAL AND MIDLATITUDE OCEANS: ALL CLOUDS In the observations, the two humidity variables UTH and PW exhibit a compact, sickle-shaped distribution (Fig. 3). As evident in the figure, points on the handle of the sickle (PW 25 kg m 2 but UTH 25%) come from midlatitudes and show a negative correlation between UTH and PW, while points on the curved blade come from the tropics and show the wellknown positive correlation between PW and UTH (each also highly correlated with SST; not shown). The section in the bottom-left corner (low UTH and low PW) corresponds to the subtropics. Subtropical points tend to straddle the two parts of the distribution. The same data are plotted in a binned form in the top-left panel of Fig. 4. Compositing of net CRF according to these two variables (remaining panels in Fig. 4) reveals much that was hidden in the univariate composites. Highly reflective clouds (strongly negative SW CRF) occur in the ERBE data at both extremes of the PW range, but mostly for midlatitude clouds at low PW. The subtropics (low UTH and low PW) do not show such a pronounced strong negative forcing and especially the PDF reveals that strong forcing does not occur consistently here. Clouds exert stronger LW forcing as UTH increases, but for UTH above 30% this forcing becomes almost entirely dependent on PW rather than UTH. The strongest forcing, at the highest PW, is for deep convective

9 4198 J O U R N A L O F C L I M A T E VOLUME 21 FIG. 4. (top left) Normalized joint distribution of UTH and PW, and average net CRF for each combination of these variables: (top right) net, (bottom left) normalized SW, and (bottom right) LW. Data are climatological means from 60 N to 60 S over ocean pixels. anvil-type clouds, which are also highly reflective. The net forcing ends up being surprisingly simple, depending almost exclusively on PW rather than UTH per se (i.e., gradients of the net forcing are nearly everywhere horizontal in the plot). In other words, net CRF is nearly conditionally independent of UTH given PW. An exception occurs for middle-latitude clouds for UTH between 35% and 55%, where the lowest values of both UTH (locally) and PW seem to favor the strongest net CRF. Furthermore, the net forcing is remarkably weak for PW 20 kg m 2, as has been noted in many other studies (see, e.g., Ramanathan et al. 1989). Conversely, strong negative forcing ( 35Wm 2 ) coincides with low PW (20 kg m 2 ; Fig. 4). Since these PW values occur mainly in midlatitudes (Fig. 3), midlatitude clouds are exerting the most net cooling on today s climate, and this effect (unlike that in the tropics) does correlate with UTH. Three subsequent figures (Figs. 5, 6, and 7) show the same quantities calculated from the models. The first thing that strikes the eye is the much broader joint distributions of the two moisture variables. While the maxima in the joint distributions occur at roughly similar places in the models and the observations, combinations of the two variables far from these maxima occur much more often in the models than in the observations. CCSM (Fig. 5) in particular shows a plentiful population of points at combinations of low UTH and high PW that never occur in the observed data. While the scatter in the other models is slightly less drastic, no model comes close to producing the compact distribution seen in the data. While biases have been noted in the observational data, it is unlikely that these have much to do with the model data differences noted here. For one thing, some of the clearest discrepancies are seen where the data show only high UTH while the models show some low UTH; known observational biases should, if any-

10 1 SEPTEMBER 2008 B E N N H O L D A N D S H E R W O O D 4199 FIG. 5. As in Fig. 4 but for CCSM3. thing, lead to the opposite problem. Second, while all models show broader distributions than do the data, they do not agree as to how much broader and where. Thus, it is unlikely that the problem here lies in the data. The simplicity of the net CRF behavior in the data is not reproduced by any model either. The most striking systematic difference (aside from the excessive SW CRF overall; previously noted) is that UTH has an exaggerated impact on the appearance of high thick clouds. This is evident in both the LW and SW plots of all three models, where forcing gradients are nearly vertical while in the observations they were nearly horizontal. Thus, in the models, deep cloud characteristics are seen to be tightly related to UTH while in reality they are evidently tightly related to PW. The unrealistic combinations of high PW and low UTH noted earlier, particularly in CCSM, become a greater cause for concern when net CRF is examined. There is a strong negative forcing for these points (often in excess of 50 W m 2 ), indicating that clouds from bogus states, which are forming under unrealistic conditions, are cooling the planet in the model. 2) LOW CLOUD COVER REGIONS Because of the obvious importance of low-level clouds, we also show some results for regions identified by Hanson (1991) and Klein and Hartmann (1993). The regions that we used are derived mainly from the former study and are similar to the MSc regions over cold ocean currents examined in Klein and Hartmann (1993). The considered regions are summarized in Table 3. These regions support persistent low stratiform cloud layers (generally referred to as MSc in this paper) of high coverage and relatively low altitude. Because of these characteristics, the net CRF is strongly negative in these regions (see Fig. 1). While low clouds outside these regions (e.g., trade cumulus or the northern and southern oceans) may be equally or even more

11 4200 J O U R N A L O F C L I M A T E VOLUME 21 FIG. 6. As in Fig. 4 but for HadCM3. important for climate sensitivity, we have not yet considered broader areas. Cloud cover in these regions is widely thought to be regulated mainly by dry static stability (SS) (Klein and Hartmann 1993). We thus expect the net CRF to become increasingly negative with increasing SS. We examined the relation between net CRF, SS, and UTH (Fig. 8) from the defined MSc regions. The expected trend does occur but only for low to moderate UTH. At high UTH, the net CRF is small regardless of SS. There are again marked differences between the models and observations, although in this case the models depart from each other in a unique way. Only the CCSM3 reproduces the observed relationship between SS and net CRF at low UTH, with one model actually producing a trend in the opposite direction. The success of CCSM3 in this regard may be a consequence of its use of a parameterization based on the empirical relationship between low-level cloud cover and SS as documented by Klein and Hartmann. Only the CCMA model shows the observed small net CRF at high UTH, with the others sometimes showing strong cooling at high UTH. Thus, no model gets both features of the data right. Williams et al. (2006) recently found that all available CFMIP models showed some low stratiform clouds in the observed MSc regions. This will presumably occur as long as the cold SSTs are roughly reproduced. We thus do not believe these discrepancies result from a geographical misplacement of the low-level cloud but, rather, from errors in the cloud and moisture processes. c. Feedback analysis Following the general strategy of Bony et al. (2004), we may calculate for any given predictor the anticipated change in the net cloud forcing in a new climate given the change in the distribution of. First note that the average in a given climate can be written as

12 1 SEPTEMBER 2008 B E N N H O L D A N D S H E R W O O D 4201 FIG. 7. As in Fig. 4 but for CGCM3. E P d, where E( ) is the conditional expectation (mean) value of given, P is the probability density of, and the integral is over all. Bony et al. (2004) decomposed the climate-induced change in into an induced part arising from changes in P given fixed E( ), an internal part arising from changes in E( ) given fixed P, and the remaining covariation part due to the nonlinear interaction of these terms when both change (employing as the predictor variable, Bony et al. used the terms dynamic, thermodynamic, and covariation, respectively, for the three terms). Thus, if the net CRF intrinsically increases with (say) SS, and SS increases in a warmer climate, an induced increase in net CRF is predicted as noted by Miller (1997). On the other hand, if the relationship between net CRF and SS itself were to shift, this would produce harder-to-predict internal and covariation changes. 2 In Table 4 we present the calculations of each component of change in net CRF with respect to SS for the three models in the region 40 N 40 S. The stabilizing, induced component is present in each model and is especially strong in CGCM3, where in terms of net CRF it is roughly equal (and opposite) to the applied greenhouse forcing. Interestingly, however, the only model in which this predicted feedback actually prevailed was the CCSM; in the two other models, it was canceled by the other two components. The CCSM behavior is not unexpected, given that the model physics strictly enforces a relationship between SS and cloud cover, unlike the other two models. Based on the findings in the previous section we examined the changes in net CRF in the CCSM model more closely. First, we computed relative (normalized) values of each variable, scaled to the range occurring in the particular dataset; for example, for UTH, UTH min UTH UTH rel max UTH min UTH

13 4202 J O U R N A L O F C L I M A T E VOLUME 21 FIG. 8. Joint distributions of UTH and SS and composite projection of net CRF onto these, for observations and models, within MSc regions as defined in Table 3. We then defined by the relationship A b ( R 2 UTH rel PW rel 40%) the main region of UTH PW space not inhabited by observations but sometimes inhabited in models (see Figs. 4 and 5, shaded area in the top-left panel). To quantify the feedback importance of the clouds from bogus states forming in A b, we recalculated the change in net CRF with only this region included specifically : pre A b E pre P pre d A b E CC P CC d, where the superscripts pre and CC indicate the control and climate change runs, respectively. For CCM3 this yields 0.74 W m 2. Comparing this figure to 4 the overall change of 1.75 W m 2 (see Table 4), we conclude that 40% of the negative cloud feedback in CCSM3 coming from the tropics and subtropics over oceans can be attributed to clouds forming under moisture conditions that should not exist. This analysis is crude but indicates that the problems noted here are important for the climate sensitivity of the models. TABLE 4. Different components of the cloud forcing sensitivity to doubling of CO 2 with respect to SS in W m 2 from 40 N to 40 S. (Note: Values for HadSM4 are from a slab model run to equilibrium, while CCSM3 and CGCM3 data are from fully coupled model versions, which are not fully equilibrated.) SS CRF CCSM3 HadSM4 CGCM3 Total Induced Internal Covariation

14 1 SEPTEMBER 2008 B E N N H O L D A N D S H E R W O O D 4203 d. Proposed simple proxy metrics We have identified several qualitative errors that persist in the climatologies of all three models examined, and we have shown their potential importance. We argue in the final section that all of these errors may be symptoms of a single problem in the model physics. Whether or not this proves correct, the qualitative nature of these differences demands attention. The fact that they appear in relationships between different moisture and cloud variables (rather than mean values) suggests a relatively direct connection to moist processes in models that we hope can be exploited. To facilitate this, we propose a few easy-to-compute scalar metrics for quantifying the errors. For the models we used the 1990 (CCSM) and preindustrial runs and we used long-term averages for the calculations. 1) COHERENCE METRIC To measure the compactness of the PW UTH relation, we propose the simple linear correlation coefficient [ln(uth), P] applied to tropical (20 S 20 N) data. Since the locus of tropical points (see Fig. 3) is curved, to better measure the scatter about this relation with a linear correlation analysis, we first take the logarithm of UTH, whose relation to PW is nearly linear (not shown). Both ln(uth) and PW have then been averaged over the respective analysis periods for the models and observations. For ease of computation we also calculated the measures using a simpler proxy of UTH: RH^ 0.5[RH(300hPa) RH(500hPa)]. The correlation coefficients for the observations and the three models are listed in Table 5, and show that this simpler-to-calculate proxy behaves very similarly to UTH. The metrics are significantly higher in the observations than in the three models, especially CCSM, quantifying the characteristics noted earlier. 2) CRF MOISTURE-DEPENDENCE METRIC r 50 To measure the way in which the CRF components depend on moisture, we have derived another simple metric, r 50. We are focusing on the convectively active regions in the tropics and subtropics by examining the slope of the bivariate distribution over UTH and PW. To single out the areas of deeper convection, we used LW and examined in particular the slopes for the 50 W m 2 level in LW CRF (thus, r 50 ). First, we define two LW intervals A [30Wm 2,50Wm 2 ] and B [50 Wm 2,70Wm 2 ]. For the models we have once more used the proxy RH^ instead of UTH. Here, r 50 (W m 2 % 1 ) is defined as follows: TABLE 5. Correlation coefficient for UTH and PW and RH^ and PW in the tropics (20 N 20 S) and moisture dependence metric r 50. Source (UTH, PW) RH^, PW PW B PW A r 50 UTH, PW UTH B UTH A, where is the averaging operator. The calculated values of r 50 are listed alongside the values in Table 5. The much greater r 50 in the observations indicates the mentioned stronger dependence on PW versus the models for deeper cloud regions. At this time we do not propose a simple metric for quantifying the behavior in the MSc regions because the divergent model behavior and possible dependence of the result on the region definitions suggests that this should await further study. 4. Summary and discussion r 50 RH^, PW * (W m 2 % 1 ) Observation CCSM HadCM CGCM * For observations, r 50 uses ln(uth) in RH^. As a primary result of this work, we have documented the mean biases between models and products derived from satellite observations, namely, uppertropospheric humidity, precipitable water, and net cloud radiative forcing, which are too high, too low, and too strong, respectively, in all models. In addition, we have documented several significant and systematic discrepancies between modeled and observed relationships among cloud- and moisture-related variables. These discrepancies are documented here using longterm averages (10 yr for the models and 2 4 yr for the observations). This may seem to be an unconventional way of examining the data, but it accentuates biases by averaging out the synoptic and seasonal variability. The analysis turns out to reveal most clearly the important features, although these also appear in monthly data (not shown). The appearance of the discrepancies in the long-term average fields highlights their likely importance for climate, as well as making it easier for modeling groups to replicate the analyses. The first discrepancy is that UTH and PW are not nearly as tightly connected in the models as in the observations. This represents a disconnect between the boundary layer and the upper-tropospheric water vapor in the models. We propose the linear correlation of 5

15 4204 J O U R N A L O F C L I M A T E VOLUME 21 ln(uth) and PW [where ln(uth) and PW are longterm means] as a proxy that quantifies this error. Furthermore, model locations exhibiting unrealistic combinations of high PW and low UTH tended also to contain clouds with a particularly strong net cooling effect. With a crude calculation, we found that these clouds from bogus states have a strong impact on the climate sensitivity and substantially increase the negative cloud feedback in at least one model. A second problem is that in the models the tropical cloud properties did not vary correctly with respect to moisture, especially in the case of thick, high clouds. While models produced these clouds in a manner more tightly related to UTH, observations show the proximate relationship being to PW. This applies to both the longwave and shortwave forcing properties. This discrepancy was quantified using a simple finite-difference parameter ratio. The final problem was documented in the particularly interesting marine stratocumulus (MSc) regions. Here, observations show that strongly negative cloud forcing (indicating low cloud cover) occurs only when UTH is relatively low and SS is relatively high. In each model at least one of these two conditions was violated, with the SS requirement holding only in CCSM3 and the UTH requirement holding only in CCMA. Wood and Bretherton (2006) and Williams et al. (2006) have recently shown that vertical gradients of es predict low cloud better than does, on which our SS measure is based; Wood and Bretherton (2006) argued that this was caused by increasing specific humidity at higher temperatures decreasing the effective stability near the cloud layer. If this moisture dependence were incorporated into a modified SS predictor of low-cloud amount, most of the induced negative feedback documented here would vanish. Our finding from Fig. 8 that high UTH inhibits (or, at least, does not coincide with) negative net CRF in the observations may be related to this. We offer here a hypothetical, unified explanation for the three errors in the covariance noted above: the model convective and/or boundary layer schemes are underestimating the role of midtropospheric moisture in regulating the depth of the convection. Many studies have investigated the role of moisture above the boundary layer, and some have already proposed its importance to climatic phenomena (e.g., Grabowski and Moncrieff 2004). A failure to heed this by a model would lead to the failure of boundary layer clouds to grow into a moist layer in the upper troposphere, explaining the simulated cases of strongly cooling clouds with high UTH in the models but not the observations (Fig. 8). Another result would be an unrealistic ability of the deep convection to bypass a dry lower and midtroposphere. This could explain the loose connection noted above between PW and UTH in the models, compared to a tight relationship in the observations, suggesting that moisture at all levels must be high for vigorous deep convection to occur in the real atmosphere. Finally, it would explain the noted lack of a sufficiently strong relationship between high cloud and PW, which was particularly evident in the most convectively active regions (high PW and UTH, or top-right panels in Figs. 4 7). The strong observed connection suggests the importance of moisture near and above the boundary layer top in the real atmosphere. An alternative explanation for the relatively strong connection between UTH and thick, deep cloud cover could, however, be excessive moisture detrainment in the upper troposphere or associated errors in the diabatic circulation, raising the UTH of deep convective areas too high relative to others. Most deep convective schemes today include entrainment of ambient air into updrafts, which allows dry air to inhibit to some extent the development of deep convection. Recognition of the potential importance of this has increased, particularly with respect to the correct simulation of the diurnal cycle, and several modeling centers are now changing their schemes to increase the role of entrainment (C. Senior and A. Gettelman 2007, personal communication). However, even the entrainment of dry air in such a calculation can be overcome by sufficient convective available potential energy (CAPE), while the observations cast significant doubt on the ability of real-world deep convection to develop in dry environments even with substantial CAPE (Sherwood 1999; Jensen and Del Genio 2006). Further, the entrainment mechanism has been found to be quantitatively inadequate to explain the large impact of midtropospheric moisture on convective penetration (Sherwood et al. 2004), indicating other microphysical or turbulent mechanisms. While our hypothesis is not original, we hope that the new evidence presented here will be sufficient to spur further modifications of model physics in the appropriate direction. As our results make clear, this problem (if our explanation is indeed correct) affects not only the details of storm development and the diurnal cycle, but also the water climatology and cloud feedbacks in the model. Acknowledgments. We thank Mark Webb of the U.K. Met Office for generously providing output from the HadSM4 model, for calculations of climate sensitivity for different GCMs, and for useful discussions. The provision of MSU data by Remote Sensing Systems (information online at was spon-

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