What Are the Main Causes of Positive Subtropical Low Cloud Feedbacks in Climate Models?

We investigate positive subtropical low cloud feedback mechanisms in climate models which have performed the CMIP6/CFMIP‐3 AMIP and AMIP uniform +4K experiments while saving CFMIP‐3 process diagnostics on model levels. Our analysis focuses on the trade cumulus/stratocumulus transition region between California and Hawaii, where positive low cloud feedbacks are present in the JJA season. We introduce a methodology to test various positive cloud feedback mechanisms proposed in the literature as the main causes of the low cloud responses in the models. Causal hypotheses are tested by comparing their predictions with the models' responses of clouds, cloud controlling factors, boundary layer depth and temperature/humidity tendencies to climate warming. Changes in boundary layer depth, relative humidity in the cloud layer, convective moistening rate and large‐scale humidity advection at the top of the boundary layer are shown to be crucial for identifying the main causes of the low cloud reductions in the models. For the cases examined, our approach narrows down the seven mechanisms considered to between one and three remaining candidates for each model. No single mechanism considered can explain the feedback in all of the models at the locations examined, but the surface latent heat flux/convective entrainment mechanism remains a candidate for BCC‐CSM2‐MR, IPSL‐CM6A‐LR, and MRI‐ESM2.0, while the surface upwelling longwave mechanism remains for CESM2, HadGEM3‐GC3.1‐LL, and MIROC6.

3 of 25 mechanisms from the literature are then considered in turn, and are ruled out in cases where their predictions are incompatible with changes in boundary layer properties, near-surface properties and surface fluxes, radiative fluxes, convective and boundary layer heating and moistening rates, moist static energy (MSE) tendencies and/or changes in vertical velocity and large-scale advection.We conclude by summarizing our findings and discussing the implications for future work in Section 3.

Choice of Locations and Cloud Profiles
Figure 1 shows maps of changes in the climatological JJA mean shortwave Cloud Radiative Effect (CRE) (Arking & Ziskin, 1994;Coakley & Baldwin, 1984) between the CMIP6/CFMIP-3 amip and amip-p4K uniform +4K SST perturbation experiments described in M. J. Webb et al. (2017).Changes in this quantity can be seen as a simple measure of the cloud feedback, allowing for certain caveats as discussed by Soden et al. (2004) and M. J. Webb and Lock (2013), and noting that the experiments here are subject to a uniform increase in SST.The shortwave cloud feedbacks exhibit different magnitudes and spatial patterns across the region.For this study we are concerned with identifying the main causes of the positive subtropical low cloud feedbacks in these models.
The bands running East/West equatorward of 15°N are associated with changes in high clouds in the East Pacific ITCZ, and can also be seen in changes in the longwave CRE (not shown).As such they are not relevant to the primary question of this study.Locations from the GPCI transect (Teixeira et al., 2011), which sample a range of low cloud regimes, from coastal stratocumulus to fairweather trade cumulus via the stratocumulus-to-trade cumulus transition regime, are marked with circles.The location along the transect with the most positive feedback in each model is marked with a square.This location is (141°W, 23°N) for IPSL-CM6A-LR and MIROC6, and (137°W, 26°N) for the other models.These locations will be the focus for further analysis below.We consider the more weakly positive and occasionally negative low cloud feedbacks at other locations along the transect less relevant to our primary research question.
Figure 2 shows profiles of the low-level cloud fraction in the AMIP experiment and its changes in the AMIP +4K experiments with climate warming at the selected locations.The horizontal lines indicate the σ level at which the low-level cloud fraction reduces the most, σ cl↓ .All models show reductions in the maximum low cloud fraction in the warmer climate.Reductions are more prominent near cloud top in CESM2, HadGEM3-GC3.1-LL,and MIROC6 suggesting a reduction in the mean cloud top altitude, with increases at lower levels in CESM2 and MIROC6 which are suggestive of a reduction in cloud base height.BCC-CSM2-MR, IPSL-CM6A-LR, and MRI-ESM2.0 on the other hand show decreases near cloud base and increases near cloud top suggesting increases in mean cloud base and top heights.In this study we will focus on understanding the low-level cloud reduction at the level σ cl↓ , as we expect it to have the largest impact on the low cloud fraction seen from space and hence on the shortwave low cloud feedback.
Various physical hypotheses have been proposed to explain low-level cloud reductions in the warmer climate, each of which make different predictions for how various cloud-related quantities will change in the warmer climate.Here we consider a number of these hypotheses in turn and assess the likelihood that each one could be the main cause of the low-level cloud reductions shown above for each model.This is done by testing the predictions of each hypothesis against the model changes in cloud-layer properties, cloud controlling factors, near-surface properties, surface fluxes and temperature and humidity budget terms.If the responses for a model are not consistent with the predictions of a given hypotheses, we can rule that hypothesis out as the main cause of the low cloud reduction for that model, at that location.One or more hypotheses may remain as candidates to be the main cause of the low cloud reduction for any given model at the end of this process.This may be because two or more mechanisms contribute substantially to the low cloud reduction in a given model, or because the model diagnostics available are not sufficient to distinguish between the hypotheses.Competing effects which would on their own lead to low cloud increases may also be present, but since we are examining the locations where the largest low cloud reductions are present, such opposing effects must be small compared to those which are the main cause of the low cloud reduction.Wyant et al. (1997) proposed a two-stage mechanism to explain the reduction in cloud fraction observed along the stratocumulus to trade cumulus transition with increasing SST in the present climate, based on LES.Here we focus on the mechanism in the first stage and will consider the mechanism in the second stage in Section 2.3.

Low Cloud Surface Latent Heat Flux Decoupling Mechanism
Their initial state was a shallow, well mixed boundary layer with a positive subcloud buoyancy flux, topped by thin stratocumulus cloud.In the first stage of the transition, warming SSTs and the deepening boundary layer were accompanied by increasing surface latent heat fluxes.This was argued to increase latent heat fluxes, buoyancy fluxes, and turbulence levels within the cloud, increasing the ratio of turbulent entrainment to radiative cooling.The warm entrained air was argued to lead to increasingly negative buoyancy fluxes below cloud base, creating a weak stable layer which prevented all but the strongest cumulus updrafts from penetrating the cloud base.(This argument was also supported by a mixed layer model in Bretherton and Wyant (1997).)The resulting cumulus-under-stratocumulus state was characterized by a well mixed surface layer with stratocumulus layers above which were slightly statically stable but had strong conditional stability with increasing height.The boundary layer became increasingly "decoupled," with distinct circulations in the subcloud layer and cloud  et al., 2004).It is possible that GCMs with coarser vertical resolution might exhibit reduced cloud layer relative humidity in response to increased drying and heating associated with turbulent entrainment, and/or reduced turbulent moistening from below due to decoupling.This could lead to a reduction in large-scale cloud fraction in a GCM in response to decoupling.For example, Zhang et al. (2013) argued that positive cloud feedbacks were caused by enhanced turbulent cloud top entrainment in some single column models (SCMs) run as part of the CFMIP-GASS Intercomparison of Large Eddy Simulations and SCMs (CGILS, Blossey et al., 2013;Zhang et al., 2013).
Turning to climate change, Mitchell et al. (1987) and Richter and Xie (2008) argued that the bulk thermodynamic formulas employed in surface schemes in climate models are generally formulated in such a way that ensures that surface evaporation will increase at 7%/K with increasing surface temperature (in the absence of changes in relative humidity, surface wind speed, and air sea temperature differences).Rieck et al. (2012) used the same argument, and suggested that increases in surface latent heat flux in the warmer climate with a fixed relative humidity could result in a positive trade cumulus feedback, albeit following a different mechanism to the decoupling mechanism above (see below).
The stratocumulus to trade cumulus transition was argued by Wyant et al. (1997) to follow from the systematic deepening of the MBL, driven by the decrease in lower-tropospheric stability and by decreasing mean subsidence.Although weakening subsidence and its effect on boundary layer depth was considered a major factor in decoupling by Bretherton and Wyant (1997) and Wyant et al. (1997) held subsidence fixed in their experiments so as to highlight the effect of the SST on the stratocumulus to trade cumulus transition.They attributed the deepening of the boundary layer to the increase of the SST relative to the temperature of the free troposphere which was held fixed.This would be expected to reduce the strength of the temperature inversion at the top of the boundary layer.Based on the mixed-layer-model arguments of Bretherton and Wyant (1997), this would be expected to lead to an increase in entrainment of air from the free troposphere by turbulent mixing, resulting in an increase in boundary layer depth.
A causal physical hypothesis for reduced cloud fraction inspired by the first stage of the Wyant et al. (1997) mechanism plus the other considerations outlined above is presented in Figure 3.We will refer to this as the surface latent heat flux decoupling mechanism in the subsequent analysis.
We now consider the possibility that the surface latent heat flux decoupling mechanism is the main cause of the positive cloud feedbacks in each of the climate models at the selected locations.Our approach is to consider a number of changes in model variables that would have to be present if this was the case, and to rule this mechanism out as the main cause of the cloud feedback where such changes are absent.First we consider the increase in the surface latent heat flux.Table 2 shows that the models all show increases significantly below the 7%/K which would be expected for an increase in SST without changes in near-surface relative humidity or wind speed.Changes in circulation and near-surface properties can result in increases in surface latent heat fluxes which are considerably smaller than 7%/K, and indeed smaller than the approximately 2%-3%/K increases seen in the global mean (M.J. Webb & Lock, 2013).The increase in surface latent heat flux in MIROC6 is just 0.1%/K.We do not consider it credible that an increase of this magnitude could be the main cause of a reduction of cloud fraction of 11.6%/K, as it is more than a factor of a hundred smaller in percentage terms.For comparison, the LES simulations of Wyant et al. (1997) showed increases in surface evaporation of 15.7%/K (compound) which is more than a factor of two larger than the associated reductions in cloud fraction of about 6%/K seen after 6 days in their simulation.Note that we are not suggesting that the latent heat flux increase with SST seen under climate change in the climate models should be comparable with those in the present-day stratocumulus to trade cumulus transition.Only that the sensitivity of the low cloud fraction change to the increase in latent heat flux under climate change would have to be two orders of magnitude larger than the sensitivity in the present-day stratocumulus to trade cumulus transition if it were to explain the low cloud reduction in MIROC6.For this reason, we consider it extremely unlikely the surface latent heat flux decoupling hypothesis is the main cause of the low cloud fraction reduction in MIROC6, and so we reject it as the explanation in this case with high confidence.(Note that this is a judgment based on our subjective assessment of the evidence.Other reasonable researchers may disagree with this judgment, and we reserve the right to change our judgment if new evidence or better arguments come to light.Note also that we are assuming that our use of long term means of model quantities means that we can safely assume that sampling uncertainties are negligible.)The other models have percentage increases in surface latent heat fluxes which are at least one tenth of their percentage low cloud fraction reductions, so at this point (based on the surface latent heat flux changes alone) we choose to remain open to the possibility that the surface latent heat flux decoupling mechanism is the main cause of the low cloud reduction in these models.
We now turn to the next step in the causal diagram in Figure 3, the increased latent heat flux and buoyancy flux in the cloud layer.Unfortunately the CFMIP experiments do not publish diagnostics for these quantities, or for turbulent cloud top entrainment, convective detrainment of cloud water into stratocumulus or buoyancy fluxes below cloud base.The mechanism does however predict an increase in boundary layer depth in response to increased turbulent entrainment.It should be borne in mind though that the weakening in the overturning circulation commonly seen with warming in climate models is also expected to lead to an increase in boundary layer depth.All of the models show reduced subsidence in terms of weaker vertical pressure velocities at 700 hPa (Table 2).This means that any shallowing of the boundary layer must require a reduction in turbulent entrainment, which would be incompatible with the hypothesis.Similarly weakening subsidence in the absence of any change in boundary layer depth implies a reduction in turbulent entrainment.
The level of the inversion, and hence the boundary layer depth can be estimated from by locating the level of the strongest vertical gradient in the potential temperature θ (Figure 4, Table 2).The σ level of the inversion capping the boundary layer is estimated using a weighted mean of the σ values for the three levels with the most negative values of dθ/dσ, using the values of dθ/dσ as the weights.This method is designed to detect changes in time mean boundary layer depth that may be less than a single full grid level.No evidence of a deepening boundary layer is seen in CESM2, HadGEM3-GC3.1-LL3or MIROC6 (Figure 4, Table 2).The same is the case if we estimate   the boundary layer depth from profiles of relative humidity using the three levels with the largest values of dRH/ dσ (Figure 5, Table 2).Based on this evidence we consider it extremely unlikely that the surface latent heat flux decoupling mechanism is the main cause of the low cloud reductions in these models.
We also consider the possibility that more negative buoyancy fluxes below cloud base stabilize the subcloud layer, reducing turbulent moistening from below.Stabilization of the cloud and subcloud layer would be expected to lead to a larger increase in potential temperature θ in the cloud layer than at the surface.Table 2 shows this effect to be present in most of the models, but not BCC-CSM2-MR or IPSL-CM6A-LR.We therefore conclude that the surface latent heat flux decoupling mechanism is extremely unlikely to be the main cause of the low cloud reduction in BCC-CSM2-MR or IPSL-CM6A-LR at the locations examined.Finally, we look to see if the relative humidity drops in the cloud layer in the models.Table 2 and Figure  In summary, we conclude that the surface latent heat flux decoupling mechanism is extremely unlikely to be the main cause of the low cloud fractions reductions in any of the models at the locations examined.BCC-CSM2-MR and IPSL-CM6A-LR show no stabilization of the boundary layer and an increase in relative humidity in the cloud layer.CESM2, HadGEM3-GC3.1-LL3,and MIROC6 show no deepening of the boundary layer which indicates that BL-top entrainment is decreasing, while MIROC6 shows a very small increase in surface latent heat flux.Finally, MRI-ESM2.0shows no reduction in relative humidity in the cloud layer.

Low Cloud Surface Latent Heat Flux/Convective Entrainment Mechanism
Wyant et al. (1997) argued that during the second stage of the stratocumulus to trade cumulus transition, as SST and surface latent heat fluxes increase further, the decoupled boundary layer allows cumulus convection to become increasingly vigorous and deeper, penetrating the trade inversion and entraining more warm/dry air from above.They argued that this evaporates liquid water in convective updrafts before they detrain, reducing the convective source term for the stratocumulus, causing to dissipate.Their LES experiments supported this argument.Cloud base precipitation was also seen to increase as the cumulus convection became more vigorous.
Although their argument related to entrainment within convective updrafts, it is also possible that warm, dry air entrained from above in areas of compensating subsidence around them might evaporate stratocumulus.Rieck et al. (2012) used the argument that surface latent heat fluxes will increase in the warming climate to motivate LES simulations of the RICO trade cumulus case with increased SSTs, initialized with specific humidities 9 of 25 adjusted to give the same relative humidities as at the start of their control experiment.Surface evaporation increased at approximately 6% per degree surface warming, and trade cumulus occurrence reduced.This was attributed to a deepening and drying of the boundary layer, due to increased entrainment of warm, dry air from above by convection in response to increasing surface fluxes.This mechanism is very similar to second stage of the mechanism proposed by Wyant et al. (1997), albeit starting from a cumulus boundary layer rather than a well mixed stratocumulus boundary layer, and set in the context of climate warming rather than the stratocumulus to trade cumulus transition.Subsequently Zhang et al. (2013) examined positive shallow cloud feedbacks in the CGILS SCMs in cases where the shallow convection schemes were active and made the related argument that active convection could cause larger ventilation of the cloud layer in a warmer climate, leading to a decrease in cloud and a positive cloud feedback.
A causal physical hypothesis for reduced cloud fraction inspired by the second stage of the Wyant et al. (1997) mechanism, Rieck et al. (2012) and other ideas discussed above is presented in Figure 6.We will refer to this as the surface latent heat flux/convective entrainment mechanism in the subsequent analysis.If this was the main cause of the positive cloud feedback in a climate model, then we would expect to see an increase in surface evaporation, a deepening of the boundary layer and an enhanced drying or weakened moistening by parametrized convection in the cloud layer.
Table 3 summarizes the model responses of quantities relevant to the surface latent heat flux/convective entrainment mechanism.We reject this mechanism as the main cause of the positive low feedback in MIROC6 because of the very small increase in surface latent heat flux (the same as for the surface latent heat flux decoupling mechanism discussed above).Also MIROC6 does not exhibit a deepening boundary layer or enhanced convective drying in the cloud layer.HadGEM3-GC3.1-LLshows a reduction in upward convective mass flux in the cloud layer which we consider incompatible with increasingly vigorous shallow convection.It also shows no deepening of the boundary layer, and no evidence of increased convective drying or heating of the cloud layer (Table 3, Figure 7 and Figure S1 in Supporting Information S1).Hence we reject the surface latent heat flux/convective entrainment mechanism as the main cause of the positive low cloud feedback seen here in HadGEM3-GC3.1-LL.
Similarly we reject this hypothesis for CESM2, on the basis of the shallowing of its boundary layer, given also that subsidence isn't increasing, as discussed in Section 2.2.The results from BCC-CSM2-MR, IPSL-CM6A-LR, and MRI-ESM2.0 on the other hand are consistent with what would be expected if the surface latent heat flux/convective entrainment mechanism were the main cause of their low cloud reductions, and so this hypothesis stands as a candidate explanation in these models.Although relative humidity increases in the cloud layer in some of these models, this does not rule out the possibility that stratocumulus cloud fraction reduces because of a reduced source term for large-scale cloud from the convection scheme which is not mediated by the large-scale relative humidity.Diagnostics which could rule this possibility out are not currently available from these experiments.

Low Cloud Vertical Specific Humidity/MSE Gradient Large Scale Advection Mechanism
Brient and Bony (2013) proposed a positive low cloud feedback mechanism based on changes in vertical gradients of specific humidity and conservation of MSE, a thermodynamic quantity which is a function of atmospheric temperature, humidity and potential energy.They argued that the non-linearity of the Clausius-Clapeyron relationship would cause the specific humidity (and thus MSE) to increase more near the surface than at altitude with climate warming, with changes in relative humidity playing a secondary role.This would lead to an enhanced vertical gradient of specific humidity and MSE between the PBL and the lower free troposphere, and so an enhanced import by large-scale subsidence of low-MSE and dry air from the free troposphere into the PBL.This would in turn cause a reduction of low-level cloudiness in the boundary layer, weakening the longwave radiative cooling of the PBL by cloud-radiative effects which would become "less necessary" to balance the MSE budget.
Subsequently, Bretherton et al. (2013) argued that cloud thinning in LES experiments based on the CFMIP-GASS Intercomparison of Large Eddy Simulations and SCMs (CGILS, Blossey et al., 2013) was caused by enhanced vertical humidity gradients between the free troposphere and boundary layer, which allows a thinner cloud to sustain the same turbulent entrainment.
Figure 8 provides a summary of the Brient and Bony (2013) vertical specific humidity/MSE gradient large scale advection mechanism as a causal diagram, and Table 4 summarizes relevant quantities from the models.In the absence of changes in the relative humidity profile, we would expect the difference between the specific humidity in the cloud layer and at 700 hPa (which spans the inversion and approximates the specific humidity jump across it) to increase at approximately 7%/K.Increases of around 4%-5%/K are present in four of the models, but very small increases of 0.1%-0.2%/Kare seen in CESM2 and MIROC6, leading us to reject this hypothesis as the main explanation for the low cloud reductions in these two models (Table 4, Figure 9).Note that while Figure 9 confirms that the gross vertical gradient in specific humidity between the free troposphere and the surface increases consistently in all of the models, the changes in vertical specific humidity gradients across the inversion are considerably more diverse.It is the gradient across the inversion that affects the large-scale vertical humidity advection, not the difference between 700 hPa and the surface.
The hypothesis also predicts increased drying due to vertical large-scale advection at the top of the boundary layer.Unfortunately we do not have diagnostics of the vertical large-scale humidity advection available, but we do have the total (horizontal plus vertical) large-scale specific humidity advection (Figure 10).We argue that if enhanced drying by vertical large-scale advection were to be the main cause of the cloud fraction reduction, then it would have to contribute more than changes in horizontal large-scale advection to the total.This means that in cases where there is no enhanced drying apparent in the total at the top of the boundary layer, we can rule out the hypothesis above.No such enhanced drying is present in the total at the top of the boundary layer in CESM2, HadGEM3-GC3.1-LL,IPSL-CM6A-LR, MIROC6 or MRI-ESM2.0,so we argue that the vertical specific humidity/MSE gradient large scale advection mechanism cannot be the main cause of the cloud reductions in these models (Table 4, Figure 10).This is consistent with the findings of M. J. Webb and Lock (2013), in which we estimated the vertical advection of MSE in HadGEM2-A at a very similar location to the one considered here and found that it was small compared to the total advection term.Note also that care must be taken when interpreting changes in advective moisture tendencies when the boundary layer depth is changing.The PBL depth is increasing in IPSL-CM6A-LR and MRI-ESM2.0which means that the advective drying increases at some levels, even though the advective drying is weaker at the BL top in the AMIP +4K experiment compared to that at the lower BL top in the AMIP experiment (Figure 10).This is a consequence of the change in BL depth, not an increase in vertical specific humidity gradient.
BCC-CSM2-MR does not provide a large-scale temperature advection diagnostic and so we don't estimate the large-scale vertical MSE advection for it.CESM2, IPSL-CM6A-LR, MIROC6 and MRI-ESM2.0exhibit no reduction in the advective MSE tendency in the cloud layer (Table 4, Figure S2 in Supporting Information S1).One of the reasons why the advective MSE tendency and/or advective specific humidity tendency does not reduce in these models may be that the reductions in subsidence will act to reduce the magnitude of the large-scale vertical MSE and specific humidity advection; this effect may compensate for or overwhelm the effects of increased vertical gradients in these quantities.
In summary, we rule out the low cloud vertical specific humidity/MSE gradient large scale advection hypothesis as the main cause of the low cloud changes seen in all of the models except for BCC-CSM2-MR.

Low Cloud Vertical Humidity Gradient Convective Entrainment Mechanism
Subsequent to Brient and Bony (2013), a number of studies have argued that increasing vertical specific humidity gradients with warming might cause enhanced drying of the boundary layer via compensating subsidence associated with parametrized convection (e.g., Brient et al., 2016;S. C. Sherwood et al., 2014;Vial et al., 2016;Vogel et al., 2022).Figure 11 presents a causal hypothesis for a low cloud vertical specific humidity gradient convective entrainment mechanism based primarily on shallow convective arguments (e.g., Vogel et al., 2022).Table 5 shows the relevant model quantities.
We rule out this hypothesis in CESM2 and MIROC6 because the vertical specific humidity gradients between the cloud layer and the free troposphere increase by less than 1%.We do not think that the hypothesis can explain the low cloud reductions in HadGEM3-GC3.1-LLbecause the convection scheme is moistening the cloud layer more rather than less in the warmer climate.None of the remaining models (BCC-CSM2-MR, IPSL-CM6A-LR, and MRI-ESM2.0)show a drop in relative humidity in the cloud layer.Hence we rule out the vertical specific  humidity gradient convective entrainment hypothesis as the main cause of the low cloud reductions in any of the models at the locations examined.

Low Cloud Downwelling Longwave Driven Entrainment PBL Shallowing Mechanism
Boundary layer cloud top longwave cooling depends on the difference between local upwelling and downwelling longwave fluxes.Based on LES experiments, Bretherton et al. (2013) argued that increases in specific humidity in the free troposphere with warming could increase the downwelling longwave radiation and reduce the radiative driving of turbulence in the boundary layer, resulting in reduced cloud top entrainment, a shallowing of the boundary layer and shallowing/thinning of the cloud layer.Additionally it is possible that GCMs with coarser vertical resolution than LES models might exhibit reduced cloud layer relative humidity and cloud amount instead of (or as well as) cloud thinning in response to such boundary layer shallowing.In a situation where saturated cloud layers in an LES model might become thinner than the vertical extent of a GCM grid box, a GCM might represent an increasing ratio of subsaturated to saturated air within a gridbox as a reducing gridbox average relative humidity, leading to a reduced horizontal cloud fraction.Increases in free tropospheric specific humidity would be expected with warming if relative humidity remained constant, but would be larger if it increased.Increases in downwelling longwave fluxes could also occur in response to increasing free tropospheric temperatures, and could additionally be affected by changes in mid-upper level clouds (Christensen et al., 2013).Finally, although not relevant to these experiments, we note that this mechanism is similar to those argued to explain changes in low level cloud in response to increased carbon dioxide which are not mediated by increases in SST (e.g., Bretherton et al., 2013;Kamae et al., 2015;Schneider et al., 2020).
This downwelling longwave driven entrainment PBL shallowing mechanism is summarized in a causal diagram in Figure 12 and relevant quantities from the models are shown in Table 6.All of the models which provide the relevant diagnostics show increases in the downwelling longwave clear-sky flux in the cloud layer, consistent with this hypothesis (Table 6, Figure S3 in Supporting Information S1).Most of the models also show reductions in radiative cooling in the cloud layer, also consistent with the hypothesis (Table 6, Figure S4 in Supporting Information S1); the exception is IPSL-CM6A-LR which shows an increase in radiative cooling at the level of the largest cloud fraction reduction (Table 6, Figure S4 in Supporting Information S1), which is well below the level of maximum radiative cooling near the cloud top (Figure S4 in Supporting Information S1, Figure 2).However we don't feel we can rule out the downwelling longwave driven entrainment PBL shallowing mechanism in IPSL-CM6A-LR on the basis of this fact alone, as radiative cooling is decreasing near the boundary layer top near the σ = 0.8 level (Figure S4 in Supporting Information S1).Crucially however, BCC-CSM2-MR, HadGEM3-GC3.1-LL,IPSL-CM6A-LR, and MRI-ESM2.0show no significant shallowing of the boundary layer (Figures 4 and 5, Table 6).For this reason we rule out the downwelling longwave driven entrainment PBL shallowing hypothesis as the main cause of the low cloud feedback in these models.Note that we do not rule out a reduction in cloud top entrainment driven by reduced longwave cooling in these models.Entrainment may well be reducing, but not by enough to cause a shallowing of the PBL in the presence of the deepening effect associated with weakening large scale subsidence (Table 6).The results available for CESM2 and MIROC6 meanwhile are consistent with the downwelling longwave driven entrainment PBL shallowing hypothesis, and so it remains a candidate to explain the positive low cloud feedback seen in these models.(Note that at the time of writing, the sign of the downwelling longwave clear-sky flux published for IPSL-CM6A-LR appeared to be incorrect-we reversed its sign for the present analysis.)

Low Cloud Downwelling Longwave/Convective Stability Mechanism
Another argument that has been put forward to explain low cloud changes across a range of regimes and timescales (in subtropical trade cumulus in particular) is that changes in cloud radiative cooling affect the stability of the boundary layer, in turn influencing the strength, depth and fractional area of shallow convective clouds (e.g., Vial et al., 2021Vial et al., , 2023;;Vogel et al., 2022; M. J. Webb & Lock, 2013;Wyant et al., 2009).Detrainment of water vapor or condensate from shallow convection may in turn promote large scale cloudiness in climate models, for example, at the convective cloud base (e.g., Brient et al., 2016).Figure 13 presents a summary of a variant of this mechanism that could explain a reduction in low cloud in the warmer climate, where the boundary layer is stabi- lized by increased downwelling longwave radiation from the free troposphere (Vial et al., 2023;Vogel et al., 2022).Relevant quantities from the models are presented in Table 7.
As discussed above, all of the models which provide the relevant diagnostics are consistent with the increases in downwelling longwave clear-sky fluxes predicted by this hypothesis.Also, all of the models show reduced radiative cooling at or (in the case of IPSL-CM6A-LR) above the level of the largest low cloud reduction (Figure S4 in Supporting Information S1).However can we rule the hypothesis out as the main cause of the low cloud reduction in BCC-CSM2-MR and IPSL-CM6A-LR because the potential temperature increases the same amount in the cloud layer as at the surface, indicating that the boundary layer is not stabilizing (Table 7).We can also rule it out in IPSL-CM6A-LR because the convective mass flux and convective cloud fraction both increase at the level of the maximum cloud reduction.We rule it out for HadGEM3-GC3.1-LLbecause the reduction in convective cloud fraction is too small to explain the total response, and convective moistening of the environment is increasing (Figure 7).Similarly, the increase in convective moistening of the environment in MIROC6 leads us to consider it extremely unlikely that this mechanism could be the main cause of the low cloud fraction reduction in that model.Changes in relative humidity in the cloud layer are shown for completeness in Table 7.Although the average relative humidity in the cloud layer does not change in MRI-ESM2.0,the enhanced convective drying at cloud base (Figure 7) and the absence of a convective cloud fraction diagnostic means that we cannot exclude the possibility that this change is mainly due to a reduction in convective cloud amount.In the case of CESM2 the change in convective cloud fraction is too small to explain the change in total cloud fraction, but we cannot rule out the possibility that the low cloud reduction is caused by a reduction in convective moistening of the cloud layer.Hence the downwelling longwave driven convective stability hypothesis remains a potential candidate mechanism to explain the reductions in low cloud fraction in CESM2 and MRI-ESM2.0.

Low Cloud Surface Upwelling Longwave Mechanism
More recently, in Ogura et al. (2023) we proposed a new positive low-cloud feedback mechanism and demonstrated that it explained the positive subtropical low cloud feedback in the AMIP/ AMIP +4K experiments performed with the MIROC5 and MIROC6 climate models.Our hypothesis was that increasing sea surface temperatures can radiatively heat the cloud layer from below, resulting in a drop in relative humidity in the cloud layer and hence a reduction in low-level cloud.This mechanism was demonstrated by  performing uniform +4K SST perturbation experiments where the effects of increasing SST on radiative transfer and surface turbulent fluxes were separated.The low cloud reductions in the warmer climate were present only when the effects of increasing SSTs on the radiation were included.This mechanism is summarized by the blue boxes in the causal diagram in Figure 14.
During the present analysis we noted that the cloud layer in HadGEM3-GC3.1-LL is several model levels thick (Figure 2), and was not immediately clear to us how a radiative heating of the cloud base would lead to a reduction in relative humidity throughout the depth of the cloud.This led us to develop a new variant of the surface upwelling longwave mechanism (green boxes, Figure 14), in which heating of the cloud base by radiation stabilizes the boundary layer, resulting in a partial "decoupling" of the sub-cloud layer and the cloud layer, in turn inhibiting turbulent mixing of moisture between the sub-cloud layer and the full depth of the cloud layer.Relevant quantities from the models are presented in Table 8.Both variants of the surface upwelling longwave mechanism are consistent with the results shown for CESM2, HadGEM3-GC3.1-LL,and MIROC6, so we are unable to rule this out as the main cause of the low cloud reductions in these models (Table 8, Figure 15, Figures S4 and S5 in Supporting Information S1).(Note that the experiments of Ogura et al. (2023) already provide strong evidence to support this for MIROC6).However we rule this mechanism out as the main cause of the cloud reductions in BCC-CSM2-MR, IPSL-CM6A-LR, and MRI-ESM2.0as they do not show the reductions in relative humidity in the cloud layer predicted by this hypothesis (Table 8, Figure 5).Also BCC-CSM2-MR and IPSL-CM6A-LR do not show any evidence to support decoupling as the cloud layer does not warm faster than the surface.Finally, in BCC-CSM2-MR moistening of the cloud layer by the boundary layer turbulence scheme shows an increase rather than the decrease predicted (Table 8, Figure 4 and Figure S5 in Supporting Information S1).
We also note that reductions in cloud fraction initially caused by the mechanism above may in turn reduce longwave cooling of the cloud layer, warming it and reducing relative humidity further, amplifying the reduction in cloud fraction (Brient & Bony, 2012).While this latter effect may amplify the cloud decrease in response to increasing upwelling longwave radiation from the surface, we argue that it cannot be the main cause of a positive low cloud feedback.This is because it requires an initial reduction in low cloud fraction to operate.However we do note that this and other potential amplifying mechanisms may increase the magnitudes of low cloud reductions in response to any mechanism that is the main cause of a positive low cloud feedback.

Summary and Conclusions
We have investigated positive subtropical low cloud feedback mechanisms in six models which saved temperature and humidity budget terms in the CMIP6/CFMIP-3 AMIP and AMIP +4K experiments.Our analysis focuses on the trade cumulus/stratocumulus transition region between California and Hawaii at locations on the GPCI transect, where positive low cloud feedbacks are present in the JJA season.We have tested for dominant contributions from a number of positive cloud feedback mechanisms proposed in the literature by comparing the relative sizes of climatologically meaned changes in clouds, cloud controlling factors, boundary layer depth and temperature/ humidity tendencies with warming.
Our findings are summarized in Table 9.None of the mechanisms considered remain as a candidate for the main cause of the positive low cloud feedback in all of the models at the locations examined.Our approach has been successful in narrowing the seven mechanisms considered down to a single candidate for two of the models, two candidates for three of the models and three candidates for one model.The surface latent heat flux/ Changes in boundary layer depth, relative humidity in the cloud layer, convective moistening rate and large-scale humidity advection at the top of the boundary layer are the crucial factors which enable the list of candidate mechanisms to be reduced.These quantities all require additional diagnostics on model levels requested in the CFMIP-3/CMIP6 experiments.We argue that these quantities, as well as other terms in the models' temperature and humidity budgets should be considered essential for future studies examining low cloud feedback mechanisms.As such we consider it crucial to include these diagnostics in a wider range of experiments in future versions of CMIP, and in other model intercomparisons, for example, those using storm resolving models.In this study we have not attempted to assess the credibility of the cloud feedback mechanisms in the climate models.In this we are hampered by the fact that there is no better agreement in the literature on the causes of positive feedbacks in nature than there is in climate models.However, we note that different mechanisms appear to be important in different models, which suggests that not all can be consistent with whatever mechanism may be the main cause of positive low cloud feedback in the real world.Indeed none may be.We do however consider identifying the mechanisms operating in climate models as a useful step toward identifying candidate mechanisms that may be important in nature.Also, our findings suggest that examination of observed variations in boundary layer depth, cloud layer relative humidity, convective moistening and large-scale humidity advection at the top of the boundary layer could provide information with which to narrow down candidate mechanisms for the causes of positive low cloud feedbacks in nature.Equally, using such observational quantities in the model development process has the potential to lead to improved parametrizations and more credible cloud feedbacks in comprehensive climate models and storm resolving models.
The present approach is not successful in reducing the list of hypotheses considered to a single candidate mechanism in four of the six models examined.One possibility here is that two or more mechanisms contribute equally to the low cloud reduction.The approach we have outlined here is not able to exclude this possibility.We argue that unambiguously identifying the mechanisms responsible for positive low cloud feedbacks in such cases will require intervention experiments designed to test specific hypotheses.A theoretical limitation of the present approach is that it relies on climatological average changes.We have for instance ruled out reductions in relative humidity as the main driver of reductions in cloud fraction in cases where the relative humidity does not decrease on average.It is of course possible that reductions in relative humidity at times when there is more cloud could cause reductions in cloud fraction, but that relative humidity could increase at other times when there is little or no cloud.In such a situation changes in the temporal distribution of relative humidity could lead to a reduction in cloud fraction even though the average relative humidity increases.We consider this possibility unlikely however as we are unable to think of a mechanism which would exhibit such behavior.If it were shown to be the case however, then our present case for ruling out of some mechanisms on the basis of there being no reduction in climatological mean relative humidity in the cloud layer would need to be revisited (e.g., for the surface latent heat flux decoupling, vertical specific humidity gradient convective entrainment and surface upwelling longwave mechanisms in MRI-ESM2.0and other models (see Table 9)).This question could be investigated using high frequency model outputs saved from some CFMIP models (e.g., Vial et al., 2023;Vogel et al., 2022;M. J. Webb, Lock, Bodas-Salcedo, et al., 2015, M. J. Webb et al., 2017).
Another important caveat associated with this work is that while we have demonstrated an approach for testing physical hypotheses proposed to explain the causes of positive low cloud feedbacks, we have in this first instance applied it only to a single location in the Californian stratocumulus/trade cumulus transition region for each model.As with other studies focusing on a small number of locations such as Blossey et al. (2016) or Vial et al. (2023), we should be mindful that our findings might not be robust when applied to other locations or seasons.Clearly it would be of interest to apply this approach to other locations and seasons in these models in future work.We note however that ruling out a given hypothesis as the main cause of the positive low cloud feedback in one location also rules it out as a general explanation that applies to all equivalent locations.
Also we note that some hypotheses can be excluded without reference temperature and humidity budget terms.This suggests that something may be learned about the positive cloud feedback mechanisms in other models using this approach; for instance our analysis has shown that examination of changes in boundary layer depth alone is a powerful approach for ruling out potential low cloud feedback mechanisms.This is an encouraging prospect  as boundary layer depth is relatively easy to constrain observationally compared to temperature and humidity budgets.
Finally, we emphasize that we have not exhaustively tested all positive low cloud feedback mechanisms described in the literature.For the present study we have concentrated on those that we are most familiar with and which we are able to interpret causally.In future work we hope to consider additional hypothesized positive low cloud feedback mechanisms as explanations for stratocumulus/trade cumulus transition cloud feedbacks in climate models, for example, those discussed in Brient and Bony (2012), Blossey et al. (2013), Jones et al. (2014), Blossey et al. (2016), Hirota et al. (2021), Koshiro et al. (2022), andSchiro et al. (2022).We would also like to consider the details of the parametrizations in the models in more detail, to see if any mechanisms can be ruled out because they rely on processes that are not represented.
The processed CMIP6 data required to produce the figures and tables are available in a Zenodo archive available via the DOI in the reference section under M. J. Webb (2023).The code and data in this archive is accessible without restriction, and released under a BSD license (please see the archive for further details.) Software Availability statement: The code to download the CMIP6 data from the ESGF, process it and produce the figures and tables is available in the Zenodo archive listed in the Data Availability statement above (M.J. Webb, 2023).

Figure 1 .
Figure 1.Climatological JJA changes in the shortwave Cloud Radiative Effect between CFMIP-3 amip and amip-p4K experiments in the northeast tropical Pacific (W/m 2 ).Circles show locations along the GCSS/WGNE Pacific Cross-section Intercomparison (GPCI) transect.Squares indicate locations on the GPCI transect with the most positive feedbacks identified for further analysis.

Figure 2 .
Figure2.Cloud fraction profiles for locations indicated by squares on Figure1.The y-axis is defined in terms of σ, the pressure at that level in the atmosphere divided by the surface pressure.The horizontal line indicates σ cl↓ , the level of maximum low-level cloud fraction reduction in the AMIP +4K experiment compared to the AMIP control.

Figure 3 .
Figure 3. Summary of the surface latent heat flux decoupling mechanism.Hypothesized causal relationships where a change in one variable causes a change of the same sign in another are represented using an arrow labeled with + symbol.Those where a change of the opposite sign is caused are labeled with a − symbol.

Figure 4 .
Figure 4.As Figure 2 but for potential temperature (K).The response curve has 270 K added to it so it can be shown on the same scale.The horizontal blue dotted and orange dashed lines indicate the levels of the boundary layer top for the control and +4K experiments respectively, estimated by locating the level of the strongest vertical potential temperature gradient (see text for details).The horizontal black line indicates the level of the largest cloud fraction reduction from Figure 2.

Figure 5 .
Figure 5.As Figure 2 but for relative humidity (%).The horizontal blue dotted and orange dashed lines indicate the levels of the boundary layer top for the control and +4K experiments respectively, estimated by locating the level of the strongest vertical relative humidity gradients in the AMIP and +4K experiments respectively.The horizontal black line here and on all subsequent figures showing profiles indicates the level of the largest cloud fraction reduction from Figure 2.

Figure 6 .
Figure 6.Summary of the surface latent heat flux/convective entrainment mechanism.

Figure 8 .
Figure 8. Summary of the vertical specific humidity/moist static energy gradient large scale advection mechanism.

Figure 10 .
Figure 10.As Figure 2 but for advective moistening/specific humidity tendency (kg/kg/s).The horizontal blue dotted and orange dashed lines indicate the levels of the boundary layer top for the control and +4K experiments respectively, estimated from the vertical potential temperature gradients.

Figure 13 .
Figure 13.Summary of the downwelling longwave driven convective stability mechanism.

Figure 14 .
Figure 14.Summary of the surface upwelling longwave mechanism.Blue boxes represent the hypothesis of Ogura et al. (2023), while the green boxes represent a newer variant of the hypothesis incorporating boundary layer decoupling.

Figure 15 .
Figure 15.As Figure 2 but for clear-sky longwave upwelling radiation (W m −2 ).The response curve has 300 W m −2 added to it so it can be shown on the same scale.(No data available for CESM2).
The terms in brackets in the first column indicate the sign or magnitude of the response predicted by the hypothesis.Values in bold are judged with high confidence to be inconsistent with this mechanism being the main cause of the low cloud reduction in a given model.The bottom row indicates whether or not the hypothesis is rejected for a given model.

Table 2 Table Showing Percentage
Changes per Degree SST Warming in Quantities Relevant to the Surface Latent Heat Flux Decoupling Mechanism

Table 4
As Table 2 but for the Vertical Specific Humidity/Moist Static Energy Gradient Large Scale Advection Mechanism

Table 5
As Table 2 but for the Vertical Specific Humidity Gradient Convective Entrainment Mechanism Figure 11.Summary of the vertical specific humidity gradient convective entrainment mechanism.

Table 6
As Table 2 but for the Downwelling Longwave Driven Entrainment PBL Shallowing Mechanism

Table 7
As Table 2 but for the Downwelling Longwave Driven Convective Stability Mechanismconvective mechanism remains as a candidate to explain the cloud feedbacks in three models, BCC-CSM2-MR, IPSL-CM6A-LR, and MRI-ESM2.0.The surface upwelling longwave mechanism also remains a candidate in the other three models, CESM2, HadGEM3-GC3.1-LL,and MIROC6.The downwelling longwave entrainment mechanism remains a candidate in CESM2 and MIROC6, while the downwelling longwave driven convective stability mechanism remains a candidate in CESM2 and MRI-ESM2.0.The vertical specific humidity/MSE gradient mechanism remains a candidate in BCC-CSM2-MR only, while the surface latent heat flux decoupling and vertical specific humidity gradient convective entrainment mechanisms are ruled out as the main cause of the low cloud reduction for all of the models at the locations examined.
Ogura et al. (2023)ton, et al., 2015)mate model experiments which perturb downwelling longwave fluxes above the top of the boundary layer to test theBretherton et al. (2013)downwelling longwave driven entrainment PBL shallowing mechanism, and experiments which perturb the free tropospheric specific humidity to test the(Brient & Bony, 2013)vertical specific humidity/ MSE gradient large scale advection mechanism.Similarly, experiments with parametrized convection deactivated (e.g., M. J.Webb, Lock, Bretherton, et al., 2015)may be performed to test theWyant et al. (1997)surface latent heat flux/convective entrainment hypothesis, and further experiments separating radiative and turbulent components of SST forcing may be used to test theOgura et al. (2023)surface upwelling longwave mechanism in additional models.

Table 8
As Table 2 but for the Surface Upwelling Longwave Mechanism