Constraining the low-cloud optical depth feedback at middle and high latitudes using satellite observations
Abstract
The increase in cloud optical depth with warming at middle and high latitudes is a robust cloud feedback response found across all climate models. This study builds on results that suggest the optical depth response to temperature is timescale invariant for low-level clouds. The timescale invariance allows one to use satellite observations to constrain the models' optical depth feedbacks. Three passive-sensor satellite retrievals are compared against simulations from eight models from the Atmosphere Model Intercomparison Project (AMIP) of the 5th Coupled Model Intercomparison Project (CMIP5). This study confirms that the low-cloud optical depth response is timescale invariant in the AMIP simulations, generally at latitudes higher than 40°. Compared to satellite estimates, most models overestimate the increase in optical depth with warming at the monthly and interannual timescales. Many models also do not capture the increase in optical depth with estimated inversion strength that is found in all three satellite observations and in previous studies. The discrepancy between models and satellites exists in both hemispheres and in most months of the year. A simple replacement of the models' optical depth sensitivities with the satellites' sensitivities reduces the negative shortwave cloud feedback by at least 50% in the 40°–70°S latitude band and by at least 65% in the 40°–70°N latitude band. Based on this analysis of satellite observations, we conclude that the low-cloud optical depth feedback at middle and high latitudes is likely too negative in climate models.
Key Points
- We examine low-cloud optical depth sensitivity to surface temperature and EIS
- Compared to satellites, optical depth in models is too sensitive to temperature
- Associated feedback in middle and high latitudes is likely too negative in models
1 Introduction
Current state-of-the-art climate models predict a wide range of estimates for the cloud feedbacks, which leads to a wide range in the projected increase in temperature due to a doubling or a quadrupling of carbon dioxide concentrations [IPCC, 2014]. However, some cloud feedbacks are consistently found across models, such as an increased reflection of solar radiation to space in middle and high latitudes brought on by increases in cloud optical depth with warming [Zelinka et al., 2013]. Because the radiative effect of increased reflection on the Earth's radiation budget is larger than the effect of increased longwave emission, the increase in the optical depth of low clouds leads to a negative cloud feedback. The models agree on the sign but not on the magnitude of this response at middle and high latitudes, and we ask in this study whether observations support this negative cloud feedback and if observations can constrain its magnitude.
An increase in the cloud optical depth with global warming is supported by a number of mechanisms based on local cloud processes. First, given the Clausius-Clapeyron relationship, an increase in temperature leads to an increase in the adiabatic lapse rate of the saturated water vapor; for the same increase in height from cloud base, a greater amount of water vapor condenses to form clouds, leading to an optically thicker cloud [Betts and Harshvardhan, 1987; Tselioudis et al., 1998; Gordon and Klein, 2014]. Second, if the cloud contains ice, then the change in the liquid/ice partitioning in the cloud with warming can also lead to a brightening of the cloud. Even without a change in the total water content of the cloud, the cloud will brighten, because liquid drops have smaller effective radii than ice particles, causing an increase in surface area and a greater optical depth [McCoy et al., 2014]. The total water content can also increase from a suppression of precipitation through a slowdown of the Wegener-Bergeron-Findeisen process. Because ice particles increase the efficiency of precipitation, the replacement of ice with liquid slows down the precipitation formation process, which leads to a smaller sink of cloud water and a thickening and brightening of the cloud [Senior and Mitchell, 1993; Tsushima et al., 2006; Ceppi et al., 2016a].
Aircraft- and satellite-based observations also support an increase in optical depth with warming at middle and high latitudes. Feigelson [1978] combined in situ aircraft measurements to find that the cloud liquid water content increased with temperature and estimated the resulting increase in optical depth. Using satellite retrievals from the International Satellite Cloud Climatology Project, Tselioudis et al. [1992] found that optical depth of low clouds increases with warming in continental clouds with cloud top temperatures below approximately −8 °C. They, however, found that optical depth decreases with warming for all oceanic clouds, in agreement with the findings of Norris and Iacobellis [2005]. The differences between land and ocean responses have yet to be explained.
Thus, theory and observations support an increase in optical depth with warming in clouds at colder temperatures. However, recent studies hint at a bias in the cloud feedback strength in climate models in the middle and high latitudes. Studies comparing model-simulated clouds and satellite retrievals from active sensors, such as Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO), have shown that at temperatures below 0°C, models tend to overestimate the relative occurrence of ice clouds, particularly over the Southern Ocean [Cesana and Chepfer, 2013; McCoy et al., 2016; Bodas-Salcedo et al., 2016; Kay et al., 2016]. Similarly, comparisons between in situ aircraft observations and model-simulated clouds reveal a large underestimate of liquid water path in mixed-phase clouds in models [Klein et al., 2009]. When model parameters are adjusted to improve the representation of the phase partitioning of these clouds, the simulations show a weaker negative cloud feedback in the middle and high latitudes [Tan et al., 2016]. Note that these studies focus on the feedback related to the phase partitioning of clouds, whereas this study considers the total feedback related to changes in optical depth, which would capture any competing mechanisms.
Because the proposed processes that connect an increase in cloud optical depth to warming (e.g., cloud-phase partitioning or increase in adiabatic cloud water) occur over timescales of hours, the sensitivity of cloud optical depth to temperature variations on timescales of days to months might inform us about the optical depth sensitivity to temperature on the global warming timescale. The argument is that these cloud processes are timescale invariant in both models and in nature [Klein and Hall, 2015]. This method of constraining cloud changes due to global warming using cloud sensitivities in our observational record has been used by previous studies examining the low-cloud cover feedbacks over the subtropical oceans [e.g., Qu et al., 2014; Myers and Norris, 2015].
(1)We have two goals in this study. First, we use multiple global satellite retrievals of cloud optical depth to quantify the optical depth sensitivity in the current climate and attempt to constrain the models' optical depth feedback. Second, we use the observationally constrained optical depth responses to estimate an observationally constrained shortwave cloud feedback.
(2)Section 2 describes the climate model and satellite data used in the analysis. Section 3 compares the sensitivity of cloud optical depth to surface temperature and EIS changes arising from monthly and interannual variability in the climate models and in the satellite retrievals. The comparison reveals biases in the sensitivities of many models. Using the sensitivities from section 3, we determine the extent to which the observable sensitivities can be used to predict optical depth changes due to global warming and assess the agreement between models and satellites and quantify the impact of model biases in optical depth sensitivity on shortwave cloud feedback in section 4. We find that biases in the models' temperature sensitivities lead to negative biases in the shortwave cloud feedback. In section 5, we discuss the observational uncertainties and the agreement of our results with existing studies and provide conclusions to the analysis in section 6.
2 Data
2.1 Satellite and Reanalysis Data
We use three passive satellite retrievals summarized in Table 1. They are retrievals from the International Satellite Cloud Climatology Project (ISCCP) [Rossow and Schiffer, 1999], the Moderate Resolution Imaging Spectroradiometer (MODIS) [Pincus et al., 2012], and the Pathfinder Atmospheres Extended data record (PATMOS-x) [Heidinger et al., 2014]. The monthly, gridded satellite products that we analyze from all three data sets share the characteristic of reporting the relative frequencies of cloud for specified bins of cloud top pressures and the optical depths. Because the Multi-angle Imaging SpectroRadiometer (MISR) data set only provides retrievals of clouds over oceans, we do not include it in our analysis. Differences between the three data sets in Table 1 include, but are not limited to, the period of satellite observations, the satellite viewing angle, the number of spectral bands used, how cloud edges are treated, and how cloud top pressure is estimated. The different instruments and algorithms retrieve different cloud optical depths and cloud top pressures, even from the same scene [Marchand et al., 2010]. Therefore, the use of all three data sets provides a measure of the observational uncertainty, albeit a lower limit.
| Satellite | Period of Retrievals | Reference |
|---|---|---|
| ISCCP | Jan 1983 to Dec 2009 | Rossow and Schiffer [1999] |
| MODIS | Jan 2001 to Dec 2014 | Pincus et al. [2012] |
| PATMOS-X | Jan 1982 to Dec 2010 | Heidinger et al. [2014] |
- a Also listed are time period over which the retrievals are available and the associated references.
We limit our analysis to low-level clouds with cloud top pressures greater than 680 hPa, because compared to higher clouds, they are better connected to surface air temperature changes and their optical depths are not as influenced by changes in large-scale vertical motions [Norris and Iacobellis, 2005]. To arrive at a monthly mean low-cloud optical depth (τ), we compute the cloud fraction weighted mean ln(τ) at each grid point from monthly mean frequencies in each bin of optical depth and cloud top pressure. Then to aid the comparison across different data sets, we regrid the monthly and grid mean ln(τ) to a common, coarse 2.5° × 2.5° grid. With each data set we filter for instances where the satellite-retrieved frequency of clouds with tops with pressure greater than 680 hPa is greater than 0.1 to ensure that enough low clouds are sampled to retrieve a monthly mean τ. Because frequencies are not reported for clouds with optical depths lower than 0.3 in some satellite retrievals (e.g., ISCCP), we disregard frequencies reported in those bins [Pincus et al., 2012]. Ignoring these optically thin clouds in the analysis has minimal effect on our results.
For temperature, humidity, and surface pressure retrievals necessary to calculate monthly surface air temperature (T) and estimated inversion strength (EIS), we use the European Center Medium-range Weather Forecasting interim reanalysis product (ERA-Interim) [Dee et al., 2011]. Previous studies have used cloud-level temperatures to compare against cloud changes [Tselioudis et al., 1992; Gordon and Klein, 2014; Ceppi et al., 2016a, 2016b]. Because we are mainly examining low-level clouds and because the cloud level changes within a month and from month to month, we use the surface air temperature. The surface air temperature is directly taken from the 2 m temperature reported in ERA-Interim, whereas the EIS is calculated using the 700 hPa and 1000 hPa geopotential heights, the surface relative humidity, and the 700 hPa, 850 hPa, and 1000 hPa temperatures, based on the method of Wood and Bretherton [2006]. The surface temperature and EIS values are also regridded to the common 2.5° × 2.5° grid. Because high correlations between T and EIS are problematic when computing multiple linear regressions, sensitivities of optical depth to T and EIS computed only when the r2 between T and EIS is less than 0.8. We examine the impact of the correlation between T and EIS on our analysis in Appendix A and conclude that the correlations do not adversely affect the calculation of the predictors in section 3.2.
2.2 Climate Model Data
To obtain the optical depths of low-level clouds from the climate models, we use the output from the International Satellite Cloud Climatology Project (ISCCP) cloud simulator [Klein and Jakob, 1999; Webb et al., 2001]. The ISCCP simulator output from the model simulates what the ISCCP satellite would retrieve given the model's cloud field and hence provides a way to more accurately compare model output with satellite retrievals [Bodas-Salcedo et al., 2011]. The ISCCP simulator output also allows us to use the cloud radiative kernels of Zelinka et al. [2012a] to connect the cloud optical depth changes to radiative flux changes between the control and perturbed climate.
Whereas Gordon and Klein [2014] compared the responses between the preindustrial control run and abrupt 4 × CO2 run of the coupled simulations or 2 × CO2 run of slab ocean models, we examine simulations from the Atmosphere-only Model Intercomparison Project (AMIP) experiment and compare them with simulations from the AMIP4K experiment where the same CO2 forcing is prescribed, but where the sea surface temperature is uniformly increased by 4 K. By comparing the optical depths from AMIP with AMIP4K experiment, we are able to quantify the temperature-only mediated response of cloud optical depth. We compare the optical depth feedback across the AMIP and AMIP4K experiments, because our goal is to constrain aspects of the optical depth feedback that we are able to using satellite observations, without the confounding effects of increased CO2, which exist in the abrupt 4 × CO2 and other CO2-induced warming scenarios.
Output of the ISCCP cloud simulator from the AMIP and AMIP4K experiment only exists as monthly output and restricts our analysis to eight models. We use 30 years of output from the AMIP and AMIP4K simulations. The surface temperature and EIS are calculated in both the AMIP and AMIP4K simulations for each model using the surface air temperature and surface humidity. The models that we analyze are summarized in Table 2.
| Model | Modeling center | Reference |
|---|---|---|
| CanAM4 | Canadian Centre for Climate Modelling and Analysis | von Salzen et al. [2013] |
| CCSM4 | National Center for Atmospheric Research | Gent et al. [2011] |
| GFDL-CM3 | US Dept. of Commerce/NOAA | Donner et al. [2011] |
| Geophysical Fluid Dynamics Laboratory | ||
| CNRM-CM5 | National Centre for Meteorological Research | Voldoire et al. [2013] |
| HadGEM-2A | Hadley Centre for Climate Prediction and Research/ | Martin et al. [2011] |
| Met Office | ||
| MPI-ESM-LR | Max Planck Institute for Meteorology | Stevens et al. [2013] |
| MIROC5 | Atmosphere and Ocean Research Institute | Watanabe et al. [2010] |
| (The University of Tokyo), | ||
| National Institute for Environmental Studies, | ||
| and Japan Agency for Marine-Earth Science and Technology | ||
| MRI-CGCM3 | Meteorological Research Institute | Yukimoto et al. [2012] |
- a Also listed are the institutions that develop and produce the models and the models' associated references.
3 Calculating the Predictor
3.1 Optical Depth Sensitivity to Temperature (T) and Estimated Inversion Strength (EIS)
Whereas many studies have focused on the sensitivity of optical depth to temperature [Tselioudis et al., 1992; Somerville and Remer, 1984; Gordon and Klein, 2014], others have shown that the strength of the boundary layer capping inversion, quantified by the estimated inversion strength (EIS), has a substantial effect on the cloud cover [Wood and Bretherton, 2006; Eitzen et al., 2011] and the cloud optical depth over the subtropical regions [Eitzen et al., 2011; Bretherton et al., 2013]. Even over the midlatitude regions, the seasonal cloud cover is controlled by EIS [Wood and Bretherton, 2006]. Norris and Iacobellis [2005] also point out that the cloud optical depth is controlled by the lower tropospheric stability, which the EIS captures. If we compute the optical depth sensitivity to temperature without considering the effect of EIS, we might unknowingly incorporate the optical depth sensitivity to EIS into the sensitivity to temperature. We therefore incorporate EIS with temperature into a two-parameter model to explain and predict changes in optical depth (τ) as in equation 2.
We first examine the extent to which monthly mean EIS and temperature control monthly mean τ in the models and in observations. We focus our analysis on the Northern Hemisphere (NH) and Southern Hemisphere (SH) middle latitudes between 40° and 70°, where studies have found a robust increase in optical depth with warming [Zelinka et al., 2012b] and a timescale invariance of optical depth response to temperature [Gordon and Klein, 2014]. We limit our analysis to regions equatorward of 70° due to limits in satellite retrievals at high latitudes, where high solar zenith angles and viewing angles severely compromise the accuracy of cloud optical depth retrievals [Marchand et al., 2010].
We compare the extent to which surface temperature (T) and EIS explain variations in optical depth in the models and in the satellite observations (Figures 1a and 1b). The monthly variability in ln(τ) explained by variations in EIS, T, and the linear combination of the two are shown for the NH and SH regions (40°–70°). For each combination of model or satellite retrieval and region, the variance explained is first calculated at each grid point, then weighted by the cloud fraction and grid box area, and then the variances are averaged over each region to obtain a regionally averaged variance explained by each component. The sensitivities (∂ln(τ)/∂T and ∂ln(τ)/∂EIS), which are computed using a first order multiple linear regression model, are also regionally averaged in this way. The combination of EIS and T can explain 7 to 36% of the variance in ln(τ) in the satellite retrievals, whereas they can explain 18 to 61% of the variance in models. Whereas EIS plays an equal role or more important role in explaining ln(τ) variations in the observations, we see that in five models, T alone explains a quarter or more of the variability in ln(τ). Because T explains such a large amount of the ln(τ) variance in models, the combination of EIS and T explains more of the variance in models than they do in observations.
In models where T has a tight control on cloud optical depth (Figures 1a and 1b), the sensitivity of optical depth to temperature (∂ln(τ)/∂T) is much also larger than satellite estimates (Figure 1c). The model's ∂ln(τ)/∂T can be greater than 0.1, a 10% increase in the optical depth for 1 K of surface warming. Most models also underestimate ∂ln(τ)/∂EIS compared to observational estimates (Figure 1d), where half do not capture the correct sign of the sensitivity. The comparison between models and observations shows that no model correctly captures both ∂ln(τ)/∂T and ∂ln(τ)/∂EIS.
3.2 Optical Depth Sensitivity Calculated From Interannual Anomalies
Although we can use the sensitivities from Figures 1c and 1d to make predictions of optical depth feedbacks, the entire data set includes both seasonal and interannual variability. For the following three reasons, we use the sensitivities estimated from interannual variations alone for our predictors of the optical depth feedback. First, although corrections have been made to try to correct for the overestimate in the cloud optical depth retrievals at high solar zenith angles, the optical depth retrievals are likely still affected by this issue [Marchand et al., 2010]. By restricting our analysis to interannual variations separately for each month, we reduce seasonally varying solar zenith angle as a contaminant in inferring the sensitivity of optical depth to meteorological parameters. Second, previous studies have shown that ∂ln(τ)/∂T in both observations and models vary as a function of T [Tselioudis et al., 1992; Gordon and Klein, 2014]. These studies find that ∂ln(τ)/∂T typically decreases with T. Seasonal T swings, which are larger than interannual T variations and, in many areas, larger than the warming expected from anthropogenic global warming, can be large enough to mask this T dependence of ∂ln(τ)/∂T. Finally, by calculating the interannual sensitivities for each calendar month, we are able to make 12 different predictions of optical depth change to assess how the sensitivities in models and satellites agree across the seasonal cycle. To obtain the regional and monthly mean sensitivities, the sensitivities are calculated in each 2.5° × 2.5° grid box for each month of the year. They are then spatially averaged, weighting by the low-cloud fraction in each box.
The interannual sensitivities of optical depth to T and EIS in each calendar month are shown in Figure 2. As in Figure 1c, Figure 2 reveals that in both hemispheres, ∂ln(τ)/∂T is overestimated in models, compared to the observational estimates (Figures 2a and 2b). Compared to Figure 1c, they show a greater disagreement between the satellite and model estimated ∂ln(τ)/∂T, mainly because ∂ln(τ)/∂T is more negative than that calculated with the annual cycle included. The comparison between models and satellite estimates also reveals that ∂ln(τ)/∂EIS is underestimated in five of eight models (Figures 2c and 2d).
We also find that in both models and satellites ∂ln(τ)/∂T exhibits a seasonal cycle in the NH. This seasonal cycle in ∂ln(τ)/∂T exists over land and ocean (not shown). All satellite retrievals show larger ∂ln(τ)/∂T in the winter but not all models. The seasonal changes in ∂ln(τ)/∂T in the satellite retrievals are consistent with results from Tselioudis et al. [1992], who found ∂ln(τ)/∂T to decrease in clouds with temperature above −12°C. In the NH satellite observations, ∂ln(τ)/∂T flips sign from positive to negative in the summer, which suggests a positive optical depth feedback in the summer. In the SH, a seasonal cycle in ∂ln(τ)/∂T is less apparent, possibly due to a smaller amplitude in the seasonal temperature variations. The models all show a positive ∂ln(τ)/∂T throughout the year, and the satellite observations suggest no change or a slight decrease in optical depth throughout the year, except in PATMOS-X, where we see an increase in the optical depth with warming in the SH winter. The spread in satellite ∂ln(τ)/∂T is much larger in the SH winter than in other seasons or in the NH.
Although previous studies find that the optical depth sensitivity to EIS (∂ln(τ)/∂EIS) is positive, there are no real expectations as to whether ∂ln(τ)/∂EIS should vary with seasons. Satellite observations suggest that ∂ln(τ)/∂EIS does not vary seasonally. However, some models show that the ∂ln(τ)/∂EIS varies seasonally, which calls into question whether the same physical mechanisms that relate optical depth variations to EIS variations in the observations are correctly represented in those models. With the interannual sensitivities ∂ln(τ)/∂T and ∂ln(τ)/∂EIS, we are equipped to see how well they capture the actual optical depth change seen between the present day (AMIP) and global warming (AMIP4K) simulations.
4 Predicted and Actual Optical Depth Changes With 4 K Sea Surface Warming
4.1 Actual Δln(τ), Predicted Δln(τ), and Their Intermodel Correlation
We examine whether equation 2 and the interannual sensitivities (∂ln(τ)/∂T and ∂ln(τ)/∂EIS) can accurately predict the low-cloud optical depth changes found between the AMIP and AMIP4K simulations in Figure 3. Figure 3a shows the multimodel mean, actual optical depth differences (Δln(τ)act) between the AMIP4K and AMIP simulations. Consistent with previous studies [Zelinka et al., 2013], a robust increase in the optical depth of low clouds at middle and high latitudes exists in both hemispheres. Figure 3b shows Δln(τ)pred from equation 2, using the difference in temperature (ΔT) and EIS (ΔEIS) found between the AMIP and AMIP4K experiments in each individual model. Although there is disagreement between the actual and predicted responses in tropical regions with deep convection, the predictions show an increase in optical depth at middle and high latitudes that is consistent with the actual optical depth changes. Finally, Figure 3c shows the intermodel correlation between Δln(τ)act and Δln(τ)pred in each grid box, essentially asking whether models with higher Δln(τ)pred also have higher Δln(τ)act. Consistent with the findings of Gordon and Klein [2014], there is a strong correlation between Δln(τ)pred and Δln(τ)act at middle and high latitudes. From Figure 3, we also verify that in the latitudes between 40° and 70° in both hemispheres, there is a consistent increase in low-cloud optical depth, where predicted changes based on interannual variations are consistent with the changes that accompany a 4 K increase in SSTs. Over the subtropical eastern ocean basins, the optical depth slightly decreases in the AMIP4K experiment, which the multimodel mean predictions also capture. However, because our focus is the optical depth feedback over the middle and high latitudes, the rest of this analysis will focus on the predicted and actual changes found in the 40° to 70° latitude bands in the Northern and Southern Hemispheres.
4.2 Middle- and High-Latitude Optical Depth Change and Observational Constraint
Although Figure 3 shows that the predicted and actual optical depth changes are well correlated in the middle and high latitudes and that their model mean response look similar to each other, it does not ensure that the predictions equal the actual changes in low-cloud optical depth. Figure 4 shows the region-mean predicted and actual changes in cloud optical depth between 40° and 70° latitudes in the Northern and Southern Hemisphere (NH and SH) from each model. Regional means are computed with cloud fraction and grid box area weighting. The filled markers represent the total predicted response from both the changes in surface temperature and EIS (Δln(τ)pred in equation 2), whereas the open markers note the response predictions based solely on the surface temperature changes (∂ln(τ)/∂T × ΔT). From how close the total predicted responses are to those predicted from just the surface temperature, we conclude that the optical depth differences between the AMIP4K and AMIP simulations are dominated by the response to surface temperature in both hemispheres. This is mainly because ΔEIS is small compared to ΔT between the AMIP and AMIP4K experiments; ΔEIS ranges from 0 to 0.6 K, compared to approximately 4 K for ΔT. The distance of the filled markers from the one-to-one line denotes how well the predictions are able to capture the actual response. Despite a large range in predicted and actual optical depth changes across the models, in both hemispheres the predicted values are mostly able to capture the actual response. However, the slope is less than one, and the y intercept is larger than zero. Gordon and Klein [2014] also found a slope less than one and hypothesized that the rapid adjustments from the CO2 affected the slope. Because there is no increase in CO2 in the AMIP4K experiments, the slopes of less than one are likely due to other factors. Because uncertainties exist in both Δln(τ)pred and Δln(τ)act, the slopes are calculated by using the total least squares method, based on minimizing the perpendicular distance between the fit and the data, as discussed by Reed [1992]. Slopes between predicted and actual values that are reported in subsequent sections of this study are also calculated using the total least squares method, unless otherwise noted.
In Figure 4, we have also plotted out the predictions based on the satellite observations as arrows denoting the range along the x axis. We have used ∂ln(τ)/∂T and ∂ln(τ)/∂EIS from the satellite observations at each grid box and multiplied them by each of the model's ΔT and ΔEIS due to the 4 K SST warming to arrive at an observation-based predicted optical depth change. The uncertainties represented by the horizontal arrows include the 95% confidence intervals in the slopes of the temperature and EIS sensitivities, which are scaled by the effective number of degrees of freedom in the optical depth field of each satellite data set, and uncertainties arising from the range in ΔT and ΔEIS found across the eight models. Much of the uncertainty arises from the uncertainties in the slopes, rather than uncertainties in ΔT or ΔEIS. The details of the calculation can be found in Appendix B. In both hemispheres, most models overestimate the increase in cloud optical depth with warming. In the SH, five of eight models predict optical depth changes that lie outside of the observational estimate, while seven of eight models predict changes in the NH that lie outside of the observational estimate. Based on the dominant effect that temperature has in controlling the optical depth, we also conclude that the difference between the model and satellite-based predictions are due to a higher ∂ln(τ)/∂T in the models.
Whereas the satellites disagree on whether the optical depth increases or decreases in the SH, there is consistent agreement across satellites that the optical depth decreases with warming in the NH. Because we include both land and ocean regions, there might be concerns that the decrease in the optical depth with warming in the satellite retrievals, particularly in the NH, is contaminated by surface radiative properties driven by the amount of snow on the ground. We have, therefore, examined how the optical depth properties change when we only look at clouds over the (ice-free) oceans, and we find that although the magnitudes are smaller, the satellite predictions over the NH still show a decrease in optical depth with warming. By examining the optical depth relationship in each month of the year in the following analysis, we also verify that the decrease in optical depth with warming is not related to snow cover on the ground.
Because we have calculated the optical depth sensitivities to T and EIS for each month of the year, we can determine whether the timescale invariance holds in every month and whether the predicted optical depth changes vary by seasons. We first examine the correlations between the predicted and actual optical depth changes (Δln(τ)pred and Δln(τ)act) in each month across the eight models in Table 3. As we found with the annual average response, in most months Δln(τ)pred correlate well with Δln(τ)act. The correlations are below 0.7 only in July and August over the NH. The correlations tend to be higher in the SH. Table 3 also lists the total least squares regression slope between Δln(τ)pred and Δln(τ)act, which is an indicator of the timescale invariance across models. The slopes are typically less than one in all months and in both hemispheres. If we remove one of the models (MPI-ESM-LR), the slopes are substantially closer to one (not shown). We do not find a similar improvement in Figure 4 when we remove MPI-ESM-LR.
| 40°–70°N | 40°–70°S | |||
|---|---|---|---|---|
| Correlation | Slope | Correlation | Slope | |
| January | 0.88 | 0.73 | 0.94 | 0.97 |
| February | 0.89 | 0.68 | 0.94 | 0.67 |
| March | 0.88 | 0.70 | 0.94 | 0.67 |
| April | 0.94 | 0.69 | 0.97 | 0.56 |
| May | 0.87 | 0.63 | 0.93 | 0.52 |
| June | 0.71 | 0.40 | 0.87 | 0.45 |
| July | 0.35 | 0.30 | 0.86 | 0.49 |
| August | 0.37 | 1.4 | 0.85 | 0.54 |
| September | 0.72 | 0.62 | 0.88 | 0.54 |
| October | 0.95 | 0.75 | 0.93 | 0.59 |
| November | 0.82 | 0.92 | 0.94 | 0.67 |
| December | 0.75 | 0.55 | 0.95 | 0.80 |
- a The actual Δln(τ) are obtained from taking the difference in ln(τ) between AMIP4K and AMIP experiments, whereas the predicted Δln(τ) are estimated with the current-climate sensitivities from the AMIP experiment and equation 2.
Whereas Table 3 shows that timescale invariance largely holds across months, Figures 5a and 5b show how Δln(τ)pred varies with the seasons in the two hemispheres. In the NH, the seasonal cycle is evident in both the model and satellite estimates. In the SH, the seasonal cycle of model and satellite Δln(τ)pred is weaker or nonexistent, although some models indicate that the optical depth increases more in the austral summer. PATMOS-X also has a Δln(τ)pred that increases in the austral winter, but we note that the uncertainty also increases during the winter.
Despite the wide range in response predicted by the models and satellite retrievals, the model-predicted Δln(τ) is consistently more positive than the satellite-predicted Δln(τ). The range of satellite estimates overlaps most of the model-predicted values only in the SH winter months. The disagreement between models and satellites is most evident in the summer months, where the satellite estimates show good agreement among each other. The sensitivity of downwelling shortwave radiation to a unit logarithmic change of low-cloud optical depth (∂SW/∂ln(τ)—gray shading in Figures 5a and 5b) and low-cloud fraction (Figures 5c and 5d) also increase in the summer. ∂SW/∂ln(τ) varies as a function of solar insolation and mean ln(τ), and its value during the summer is at least double that of the winter. The low-cloud fraction increases by approximately 5% during the summer months. Thus, the discrepancy between the model and satellite estimates in the summer is likely to have a substantial radiative impact, which we quantify next.
4.3 Radiative Impact of the Optical Depth Change
To quantify the radiative impact of the changes in low-cloud optical depth and determine the impact of the discrepancy between the model-based and observation-based predictions on the total SW cloud feedback, we use shortwave (SW) cloud radiative kernels [Zelinka et al., 2012a]. SW cloud radiative kernels quantify the impact on top of atmosphere SW fluxes of unit changes in cloud fraction segregated by cloud top pressure and optical depth, at all latitudes, longitudes, and months. Multiplying the SW cloud radiative kernel histograms by the temperature-mediated change in cloud fraction histograms provides the radiative impact of the change in each cloud type. Summing over all cloud types yields the SW cloud feedback at every location. The SW cloud feedback can further be decomposed into amount, altitude, and optical depth components using the methods of Zelinka et al. [2012b, 2013]. Here we present a modified method that allows us to compute the low-cloud optical depth feedback from the change in low-cloud ln(τ) and to estimate the bias in SW cloud feedback due to the bias in low-cloud ln(τ) sensitivity to environmental conditions. The modified method is necessitated by the fact that a single scalar Δln(τ) value is used rather than the full distribution of changes in cloud fraction as a function of ln(τ).
(3)The SW low-cloud optical depth feedback derived from equation 3 agrees closely with that derived from the full cloud fraction and radiative kernel histograms in all models. Statistics of the point-by-point comparison between annual mean maps of the two estimates are shown in Table 4. The best fit slopes between the two estimates are within 9% of 1:1 in all models, the root-mean-square error is less than 10% in all models except MPI-ESM-LR (RMSE =10.6%) and MRI-CGCM3 (RMSE =12.8%), and the spatial correlations exceed 0.95 in all models except CCSM4 (r = 0.88).
| Model | Slope | RMSE | Correlation |
|---|---|---|---|
| CanAM4 | 0.96 | 7.43% | 0.96 |
| CNRM-CM5 | 0.98 | 5.55% | 0.99 |
| MPI-ESM-LR | 1.06 | 10.59% | 0.97 |
| HadGEM2-A | 1.06 | 5.75% | 0.97 |
| CCSM4 | 0.99 | 4.88% | 0.88 |
| MIROC5 | 1.04 | 3.18% | 0.98 |
| MRI-CGCM3 | 0.91 | 12.80% | 0.96 |
| GFDL-CM3 | 0.93 | 4.16% | 0.98 |
- a Both Northern Hemisphere and Southern Hemisphere areas are combined here.
In Figure 6, we plot the radiative impact of the predicted optical depth changes to the radiative impact of the actual low-cloud optical depth changes, alongside those based on the satellite predictions. All calculations are performed using equation 3, and each model's regional means are cloud fraction and grid box area weighted. As in Figure 4, we find that the predictions correlate well with the actual feedback strength arising from the low-cloud optical depth changes, although like the optical depth response, we find that the predictions tend to overestimate the strength of the negative cloud feedback. If we compare the model predicted feedbacks with the satellite-based predictions, the multimodel mean local discrepancy between the model and satellite estimates range from 0.21 to 0.33 W m−2 K−1 in the NH and from 0.56 to 0.95 W m−2 K−1 in the SH. For context, the local radiative impact of the total SW cloud feedback ranges between −0.93 and 0.02 W m−2 K−1 (mean of −0.39 W m−2 K−1) in the NH and between −1.62 and 0.22 W m−2 K−1 (mean of −0.86 W m−2 K−1) in the SH.
Zonal mean SW low-cloud optical depth feedbacks predicted using both model- and satellite-derived interannual ln(τ) sensitivities in equation 3 are shown in Figure 7. As was implied by the Figure 3, the magnitude of the multimodel mean SW low-cloud optical depth feedback is largest over the middle and high latitudes. Whereas the multimodel means predict a negative low-cloud optical depth feedback in these regions, the feedbacks based on the ln(τ) from the satellite retrievals mostly show a positive cloud feedback. Although there is a substantial amount of observational uncertainty in the Southern Hemisphere, they do not overlap the multimodel mean feedback.
The total SW cloud feedback arises primarily due to changes in both cloud amount and optical depth, and these changes occur not only in low-clouds with optical depths greater than 0.3 considered here but also in higher clouds and in clouds with optical depth less than 0.3. Thus, it is important to place the magnitude of the biases in low-cloud optical depth feedback into proper context. To do so, we compute observationally constrained total SW cloud feedbacks by summing the optical depth feedback for low clouds with τ>0.3 with (1) the amount, altitude, and residual feedbacks for low clouds with τ>0.3, (2) the feedback from “thin” low clouds with τ<0.3, and (3) the feedback from “non low” clouds with cloud top pressures less than 680 hPa. Optical depth feedbacks for low clouds with τ>0.3—whose multimodel means are shown in Figure 7—are computed as described above. The amount, altitude, and residual feedback components for low clouds with τ>0.3 are computed by performing the decomposition of Zelinka et al. [2013] only for the relevant portion of the histogram (CTP > 680 hPa, τ>0.3). Thus, all cloud feedbacks except those due to changes in optical depth of low clouds with τ>0.3 are taken from the model and left unchanged in the hypothetical SW cloud feedbacks shown below.
To provide some context of the contribution of the low-cloud optical depth feedback to the total SW cloud feedback, the low-cloud optical depth feedback, averaged over 40°–70°S is −0.46 W m−2 K−1, whereas the total SW low-cloud feedback is −0.21 W m−2 K−1 (the positive amount feedback in low-clouds partially counteracts the negative optical depth feedback). The total SW non-low cloud feedback is −0.64 W m−2 K−1 and hence contributes more to the total SW cloud feedback in this region than low clouds in these simulations.
We plot in Figure 8 the total SW cloud feedback, along with observationally constrained estimates of the SW cloud feedback in which each model's low-cloud optical depth feedback has been set to the value predicted from satellite-derived interannual ln(τ) sensitivities. Swapping the model-derived low-cloud optical depth feedbacks with the observationally constrained low-cloud optical depth feedbacks shown in Figure 8 results in a large reduction in the magnitude of the large negative SW cloud feedback over the Southern Oceans, with a slightly smaller effect in the NH midlatitudes. The feedback constrained using PATMOS-X observations nearly entirely removes the negative lobe of the feedback in the SH. Though exhibiting substantial disagreement in the magnitude of the bias, all observationally constrained estimates exhibit a substantially weaker negative SW cloud feedback at high SH latitudes than what the models are currently producing.
5 Discussion
5.1 Observational Uncertainties
By incorporating three different satellite retrievals that use different platforms, instruments, and retrieval algorithms, we have attempted to provide an estimate of the observational uncertainty. Indeed, the spread among the three satellites can sometimes be comparable to the intermodel spread (Figures 4 and 5). Even within one observational data set, the uncertainties in optical depth response arising from uncertainties in calculating the optical depth sensitivities to temperature and estimated inversion strength (EIS) (∂ln(τ)/∂T and ∂ln(τ)/∂EIS) can be substantially large (Figure 4). These challenges hamper our efforts to constrain the low-cloud optical depth feedback to a narrower range. The large observational uncertainty in ∂ln(τ)/∂T and ∂ln(τ)/∂EIS is possibly due to the temperature and EIS only being able to explain about 30% of the variance in optical depth.
We have limited our analysis to clouds with τ > 0.3, because some of the satellite retrievals cannot capture those thin clouds. However, the models do simulate and output the cloud fraction for clouds with τ < 0.3. Its effect on the models' current-climate τ sensitivities are minimal, leading to an RMSE of 0.02 for ∂ln(τ)/∂T and an RMSE of 0.01 for ∂ln(τ)/∂EIS. Similarly, the effect of thin clouds on the total SW cloud feedback is also small. Therefore, we do not expect the exclusion of those clouds in our analysis to affect our main conclusions.
Another aspect of the observations that we are unable to reconcile in this study is the disagreement in ∂ln(τ)/∂T and ∂ln(τ)/∂EIS between those obtained using month-to-month variability and those obtained using only the interannual variability. Because ∂ln(τ)/∂T is a function of T, we do not expect a one-to-one correspondence, but the disagreements in ISCCP ∂ln(τ)/∂T in the SH (Figure 2a) and the ISCCP and PATMOS ∂ln(τ)/∂EIS in the NH (Figure 2c) are substantial. However, despite the large range of observational estimates depending on the choice of timescale, the observational estimates are inconsistent with the models that indicate a large increase in τ with warming and a decrease in τ with increasing EIS.
5.2 Our Findings in Context of Existing Literature
Is our finding that τ should decrease with warming at middle and high latitudes at odds with previous observations? Although climate models have consistently shown an increase in cloud optical depth with warming over middle and high latitudes, the observational evidence for increases in optical depth with warming have only been found over land and only at colder temperatures [Feigelson, 1978; Tselioudis et al., 1992; Del Gelnio and Wolf, 2000]. We also find with our analysis of satellite retrievals (Figure 2a) that ∂ln(τ)/∂T can be positive in the winter over the NH, which is approximately 40% covered by land. Over the ocean, results from Norris and Iacobellis [2005] and Figure 4b of Tselioudis et al. [1992] indicate that ∂ln(τ)/∂T is either indistinguishable from zero or negative. This is also what we find with our satellite estimates. Therefore, the observational estimates of ∂ln(τ)/∂T in this study are consistent with those reported in previous studies. Our results indicating positive ∂ln(τ)/∂EIS values are consistent with the findings of Eitzen et al. [2011], who examined cloud sensitivities over the subtropical oceans, and with Norris and Iacobellis [2005], who found optical depth to increase with increasing lower tropospheric stability. Although EIS has previously been found to explain changes in cloud properties over the ocean, we find that the EIS also explains as much of the variability in the optical depth over land (Figure 1a).
We find that the low-cloud optical depth feedback appears to be too negative in climate models. Is this consistent with previous studies? Gordon and Klein [2014], based on the models' optical depth sensitivity to temperature and satellite-based estimates from Tselioudis et al. [1992], suggested that the optical depth feedback is likely too negative. Other studies have suggested that in the latitudes that we study, climate models produce clouds with too much ice, with respect to liquid [Tsushima et al., 2006; Cesana et al., 2015; McCoy et al., 2016; Bodas-Salcedo et al., 2016; Kay et al., 2016]. If too much ice indeed exists in modeled clouds, particularly in the summer months, this will be consistent with the models overestimating the increase in optical depth with warming due to an unrealistic increase in liquid with warming and associated smaller particle size and reduced precipitation sink (as discussed in section 1). Furthermore, the modeling results of Tan et al. [2016] show that if cloud microphysical parameters are adjusted in version 5.1 of the National Center for Atmospheric Research's Community Atmosphere Model so that they better represent the observed supercooled liquid fraction in mixed-phase clouds, then the cloud optical depth feedback in our region of study, which is negative in the default version of the model, becomes positive.
The results in this study, however, appear at first hand to disagree with Ceppi et al. [2016b], who suggest that the cloud feedback in models and satellites are in agreement in the middle and high latitudes. After demonstrating that the LWP changes in the models correlate well with cloud shortwave (SW) changes in Ceppi et al. [2016a], Ceppi et al. [2016b] extended the study to examine the total SW cloud feedback in models. They reported an observable negative SW cloud feedback in middle and high latitudes that agreed with most model estimates, whereas our results indicate that the low-cloud optical depth feedback is likely too negative in most models. There are a number of methodological differences between the two studies (e.g., the spatial scales over which cloud properties are averaged, the latitude limits to compute regional means, whether to use monthly or interannual variations to compute regressions), but one possible source of discrepancy is that we limit our study to the low-cloud optical depth feedback, whereas Ceppi et al. [2016b] examined the total SW cloud feedback, which include other cloud changes that can lead to a negative SW cloud feedback. Indeed, Figure 8 reveals that the total predicted shortwave feedback remains negative even when the low-cloud optical depth sensitivities from the models are replaced with those from the satellite retrievals. This shows that the negative shortwave cloud feedback in the middle and high latitudes is not solely determined by the low-cloud optical depth feedback. For example, Figures 1d and 2b of Ceppi et al. [2016b] show that in addition to an increase in optical depth, many models also show an increase in cloud fraction with warming in the region. However, despite the differences between this study and that of Ceppi et al. [2016b], they both agree that the models with the largest negative SW cloud feedbacks are not consistent with observational estimates.
A substantially weaker negative SW cloud feedback at high SH latitudes likely implies a smaller poleward jet shift [e.g., Ceppi et al., 2014] and likely has implications for changes in midlatitude baroclinicity and storm tracks, for the magnitude of polar amplification and sea ice loss at high latitudes, and for the increase in poleward heat transport under global warming [Zelinka and Hartmann, 2012].
6 Conclusions
The first part of our analysis compares the sensitivity of low-cloud optical depth to temperature (T) and estimated inversion strength (EIS) in CMIP5 models and satellite retrievals. We assess the ability of T and EIS to explain the monthly and interannual variations in cloud optical depth. At these timescales, the models inaccurately capture the optical depth dependence on EIS; either the EIS explains a relatively small fraction of the optical depth variability compared to T or the optical depth sensitivity to EIS (∂ln(τ)/∂EIS) is the opposite sign as that in the satellites. Whereas the linear combination T and EIS explains on average 36% of the month-to-month variance in the SH in models (46% in the NH), in satellite estimates, the linear combination only explains on average 15% in the SH (29% in the NH). This discrepancy between the models and satellite estimates appears to be connected to the models overestimating the sensitivity of optical depth to T (∂ln(τ)/∂T), but it might also reveal that mechanisms are inadequately represented in models. In other words, errors in model physics, such as in the cloud-phase transition, are leading to an overestimate in ∂ln(τ)/∂T within many of the models.
We find that in the models, the optical depth sensitivity is largely timescale invariant (Figure 4), which allows us to use observed sensitivities to help constrain the models' low-cloud optical depth feedback. Although the models do not accurately capture the observed ∂ln(τ)/∂EIS, its effect on the models' predicted low-cloud optical depth feedback are small due to the small change in EIS predicted with warming in the middle and high latitudes (Figure 4). Indeed, our general conclusions about the low-cloud optical depth feedback would have remained the same if we had excluded EIS from our analysis, but given that EIS explains more of the variance in monthly low-cloud optical depth in observations, we have kept EIS in our analysis.
Because the models overestimate ∂ln(τ)/∂T compared to satellite retrievals, we find that most models likely overestimate the increase in optical depth with large-scale global warming. The discrepancy between models and satellites appears in most months of the year, but it is particularly evident in the summer, when a majority of the models predict an increase in optical depth with warming but where satellites predict a decrease. The robust discrepancy between models and satellites and the increased solar insolation and cloud cover in the summer season have radiative implications. The multimodel mean SW cloud feedback in the SH region (40–70°S) is −0.86 W m−2 K−1. If we replace the models' optical depth sensitivity with the satellites' sensitivities, the total SW cloud feedback in the region increases between 0.48 and 0.86 W m−2 K−1.
Although substantial uncertainty exists in the observations, we find that the observations all suggest that the SW cloud feedback in the 40–70° latitude band is too negative in many models. The low-cloud optical depth feedback is one of several SW cloud feedbacks in the middle and high latitudes, but given the magnitude of the apparent discrepancy reported in this study, the effects will likely increase the equilibrium climate sensitivity and potentially affect the jet location [e.g., Ceppi et al., 2014]. Future research examining the actual changes in cloud properties are needed to connect cloud process changes with the optical depth sensitivities, so that we might better understand the sources of model spread and the discrepancy between models and observations.
Acknowledgments
We thank the climate modeling groups for producing and making available their model output. For CMIP, the U.S. Department of Energy's (DOE) Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. The model output can be obtained from the Earth System Grid Federation. The satellite observations were obtained from CFMIP-OBS, hosted at http://climserv.ipsl.polytechnique.fr/cfmip-obs/. The ECMWF Interim Reanalysis fields are publicly available from http://www.ecmwf.int/. The data used to generate the figures and tables in this study can be obtained by contacting the corresponding author. We thank Steve Ghan, Jonathan Jiang, and two anonymous reviewers for providing comments and feedback that have helped to improve the manuscript. The efforts of the authors are supported by the Regional and Global Climate Modeling Program of the United States Department of Energy's Office of Science. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. IM-Release: LLNL-JRNL-688437.
Appendix A: How the Correlation Between T and EIS Affects the Calculation of Sensitivities
Strong correlations between T and EIS are potentially problematic when computing the sensitivities (∂ln(τ)/∂T and ∂ln(τ)/∂EIS) with multiple linear regression. Indeed, the magnitude of the correlation between T and EIS in the monthly reanalysis data of ERA-Interim is high over Northern Hemisphere middle- and high-latitude land areas and over parts of the Southern Hemisphere middle- and high-latitude oceans (Figure A1). However, most of our analysis is conducted using the sensitivities derived from interannual variations in T, EIS, and ln(τ) (see section 3.2), where the magnitude of the correlation is substantially lower, particularly in the 40°–70° region that we study (see Figure A2 for interannual correlations in January and July).
Furthermore, in Figure A3, we examine whether the correlation between T and EIS affects interannual ∂ln(τ)/∂T and ∂ln(τ)/∂EIS by plotting the sensitivities derived from ISCCP as a function of the correlation. Our conclusions are the same if we use ln(τ) from the other two satellites (not shown). All grid boxes between 40°–70°N and 40°–70°S for all calendar months are combined and binned into 0.1 bins of correlation in Figure A3. The distribution of data is shifted to negative correlations (Figure A3c). There are instances when the correlation between T and EIS are too strong, such that the slopes cannot be computed. Therefore, we have not calculated the sensitivities when r2 between T and EIS exceed 0.8. Such cases are rare, however, and we do not expect them to have a substantial impact on our results.
Although outliers exist when the magnitude of the correlation is high, between correlations of −0.9 and 0.5, where 95% of the data reside, the range of median values across the correlation bins is 0.038 for ∂ln(τ)/∂T and 0.043 for ∂ln(τ)/∂EIS. For context, the range of values across models in Figure 2 is approximately 0.10 for ∂ln(τ)/∂T and 0.07 for ∂ln(τ)/∂EIS. The range across correlation bins is on the order of, but certainly smaller than the cross-model range in ∂ln(τ)/∂T and ∂ln(τ)/∂EIS. And although ∂ln(τ)/∂EIS decreases when the magnitude of the correlation increases, no discernible relationship between ∂ln(τ)/∂T and the correlation exists. Figures A3a and A3b also show that the width of the distribution of the sensitivities increases when the magnitude of the correlation is high, but increases in the width are most apparent for ∂ln(τ)/∂T when the correlation is greater than 0.5. The width of the distribution shows that there is a fair amount of scatter in the grid box values of ∂ln(τ)/∂T and ∂ln(τ)/∂EIS, but there is no evidence that the correlations between T and EIS lead to significant biases in ∂ln(τ)/∂T and ∂ln(τ)/∂EIS.
Appendix B: Calculating Confidence Intervals on Observations
) from σTslope and σEISslope using the equation
(B1)From
values at each grid box, we then obtain the regional mean value by taking the area and cloud fraction weighted mean.
(B2)
(B3)| Scaling Ratio S (×10−3) | ||
|---|---|---|
| 40°–70°N | 40°–70°S | |
| ISCCP | 3.2 | 2.4 |
| MODIS | 9.4 | 7.0 |
| PATMOS-X | 2.4 | 1.3 |
(B4)Finally, after the 95% confidence intervals are calculated for each model, we take the maximum and minimum extents from all the models' confidence intervals to arrive at the limits shown in Figure 4. The uncertainties in Figures 5 and 6 are similarly computed.
