Untangling causality in midlatitude aerosol-cloud adjustments

. Aerosol-cloud interactions represent the leading uncertainty in our ability to infer climate sensitivity from the observational record. The forcing from changes in cloud albedo driven by increases in cloud droplet number ( N d ) (the first 10 indirect effect) is confidently negative and has narrowed its probable range in the last decade, but the sign and strength of forcing associated with changes in cloud macrophysics in response to aerosol (aerosol-cloud adjustments) remain uncertain. This uncertainty reflects our inability to accurately quantify variability not associated with a causal link flowing from the cloud microphysical state to cloud macrophysical state. Once variability associated with meteorology has been removed, covariance between the liquid water path averaged across cloudy and clear regions (LWP, here, characterizing the 15 macrophysical state) and N d (characterizing the microphysical) is the sum of two causal pathways linking N d to LWP: N d altering LWP (adjustments) and precipitation scavenging aerosol and thus depleting N d . Only the former term is relevant to constraining adjustments, but disentangling these terms in observations is challenging. We hypothesize that the diversity of constraints on aerosol-cloud adjustments in the literature may be partly due to not explicitly characterizing covariance flowing from cloud to aerosol, and aerosol to cloud. Here, we restrict our analysis to the regime of extratropical clouds 20 outside of low-pressure centers associated with cyclonic activity. Observations from MAC-LWP, and MODIS are compared to simulations in the MetOffice Unified Model (UM) GA7.1 (the atmosphere model of HadGEM3-GC3.1 and UKESM1). are found to be similar between the model and observations. There is also agreement with previous literature on cloud-controlling factors finding that increasing stability, moisture, and sensible heat flux enhance LWP, while increasing subsidence, and sea surface temperature decrease it. A simulation where cloud microphysics 25 are insensitive to changes in N d is used to characterize covariance between N d and LWP that is induced by factors other than aerosol-cloud adjustments. By removing variability associated with meteorology and scavenging we infer the sensitivity of LWP to changes in N d . Application of this technique to UM GA7.1 simulations reproduces the true model adjustment strength. Observational constraints developed using simulated covariability not induced by adjustments and observed covariability between N d and LWP predict a 25-30% overestimate by the UM GA7.1 in LWP change and a 30-35% 30 overestimate in associated radiative forcing.

You bring up a very good point and this section was poorly explained. It might be better to portray 'Nd' in this case as the Nd in the regression of LWP on Nd that is used to characterize covariance between LWP and Nd. In the case where Nd=Nd_cloud we run many simulations where we replace the Nd in the autoconversion, settling, and radiation (ASR) with a constant. The regression analysis is performed using many simulations with constant Nd in the ASR, which is then used as the independent variable in the regression. In the case where Nd=Nd_scav we take one of these simulations where Nd in the ASR is set to a constant and regress on the Nd calculated by the nucleation scheme. In the last case where Nd=Nd_cloud=Nd_scav, this is just the control run where the Nd_cloud (eg the Nd in the ASR) is linked to the Nd calculated by the nucleation. In this case the Nd seen by the ASR, and driven by the scavenging are not distinct entities and Nd_cloud =Nd=Nd_scav so the derivative of one with respect to another goes to one (dy/dx =1 if y=x).
We have added additional text and a flow chart to the paper to try and clarify this calculation.
You nudge winds and temperature down to 1.7km altitude, yet analyse boundary layer clouds up to 3.2km in altitude. Can you be sure that your nudging has no impact on your derived relationships? And why do you nudge different variables for the different model experiments (Table 2)?
Also a great point. In the context of this calculation nudging the large-scale environment should only manifest through the inferred meteorological controls on cloud. Nudging was used in this study for two reasons: 1) because the simulations are relatively short so nudging creates more comparable simulations for a shorter integration in the sense of looking at the same meteorological regimes 2) because we wanted to compare to the observations and wanted to try to sample similar meteorological regimes. You make a very good point about the nudging of U and T in the PI-PD simulations. This was copied from existing suites at the MetOffice used to calculate the aerosol radiative forcing (Yoshioka et al., 2019). Temperature nudging has now been turned off. This shows the same results qualitatively, but shifts the inferred and true ∆LWP between PI and PD closer together. Additional simulations were carried out with nudging starting at level 27 (~5km) instead of level 16 (~1.8km) of the model, and without wind nudging altogether. The results from these simulations are shown in the SM and do not qualitatively change the results of this study.
Equ. 4: Have you performed tests on overfitting? For instance what is the reasoning for fitting both EIS and omega_550? Is there really additional skill added to the fit by including both?
The use of both EIS and omega 550 was based on existing research showing that EIS and subsidence correlate, but have opposing effects in terms of their effect on low cloud cover (Myers and Norris, 2013;Wall et al., 2017). We have tested for overfitting by training our model in the control run and then predicting dLWP/dln(Nd) in simulations with very low and very high Nd (Fig. 8f of the main text).
P8L7ff: I found this sentence confusing (see general comment above). Isn't it rather that precipitation scavenging is the only source of Nd variability? And that this variability is not representative of cloud adjustments?
This is right except that Nd variability is also due to sources of aerosol, advection, and sinks like dry deposition. We have added a new schematic figure illustrating the links between cloud, aerosol, and meteorology and have added text to try and explain this better.
P9L25 & Fig 4. "there is significant variability in LWP associated with Nd". This is only true if the full residual LWP-LWP_fitted is entirely flat and has no remaining functional dependence (i.e. your predictors describe all of the variability, which may not be the case). Have you checked for this?
We have changed this sentence to reflect that we meant that the coefficient in the multiple linear regression is confidently greater than zero. There is no requirement for significance to mean that all variability is explained.
P12L7: It is interesting that you find the settling Nd to have the dominant effect over autoconversion. I would argue that this deserves further comment. Is there any support from this from observations? If it would be specific to the UM model, how would that affect your conclusions?
We also thought this was an interesting effect. Unfortunately it is hard to say how a metric similar to the precipitation probability Spop used in many studies to characterize the response of precipitation to aerosol (Ma et al., 2018) could be created to look at settling of cloud droplets. However, comparison to other model studies does show that in regions of low cloud with less frequent precipitation the process rate associated with settling is large compared to autoconversion (Gettelman et al., 2013), which opens the door to this process being a significant source of aerosol-cloud adjustments.
Overall, our results are insensitive to whether precipitation or settling suppression dominate adjustments as we neglect feedbacks between adjustments and scavenging. We have added text to clarify this. Thank you for suggesting this.
Typos and text edits have been changed as suggested. In regards to acronyms in Table 2 being unclear: the first column is just the unique identifier of the simulation in the MetOffice repository so that they can be requested by people wanting to replicate our analysis. Are these what you were referring to? We added some additional text to the descriptions to make it clearer what the simulation with PI and PD simulations are for. Thank you also for finding these.

R2:
Page 2, line 19-21: The sentence does not read well. The first half of the sentence stated that aerosol-cloud interactions play a minor role, but the second half of the sentence stated the importance of making data volume available. I don't understand the logic here. Moreover, it might be necessary to substantiate the statement "Aerosol-cloud interactions are likely to contribute a relatively small fraction of overall variability in cloud properties" by providing some references.
This was unclearly expressed. What we meant to convey is that detecting aerosol-cloud adjustments above the background of meteorological variability presents us with a signal-tonoise problem with the small amount of variability in LWP that is due to aerosol-cloud adjustments against the large amount of variability driven by dynamics and thermodynamics. To overcome small signal to noise ratio we need to use a lot of data to be able to detect a signal. We have changed the sentence to try and better communicate this. We have added a reference that puts an upper limit on the amount of variance explained by adjustments, and which is generally small.
2. This study focuses on the interstitial regions between cyclones only, but there are many other cloud regimes where aerosols can have similar or different impacts on clouds. It might be helpful to add a paragraph to discuss the applicability as well as limitations of this study.
Great point-we did a previous study in cyclones, which is noted in the introduction and in the conclusions. We have added a few sentences to expand on this and to discuss how adjustments might look in the tropics and subtropics and limitations in our analysis technique.
What is the effect of the degradation of spatial resolution (when all the data is regridded to 1degree) on the covariance analysis? Is ACI derived from the gridded data still representing the physics? Could you discuss if this is an important issue (as discussed in McComiskey and Feingold, 2012) that affects the conclusion of the study? (McComiskey and Feingold, 2012) examined the first indirect effect (the Twomey effect), but it is still important to consider the effects of resolution on our results. It is reasonable to suppose that degradation of the spatial resolution will lead to weakening the multiple linear regression coefficients as a function of decreasing variance in the dataset. However, we validate our projected aerosol-cloud adjustment by comparing the change in LWP inferred from the variance in the PD of the GCM to the change in LWP between the PI and PD calculated by the GCM (Fig. 9b) as well as the response in simulations with prescribed Nd in the cloud microphysics (Fig. 8f). The change inferred by the 1x1° daily-mean UM GA7.1 data in the PD agrees with both these tests, neither of which are sensitive to resolution. We have added text discussing resolution.
5. Page 6, line 13-14: Do you mean aerosol emissions or concentrations are set to PI and PD for the two simulations? If emissions, please provide the reference for the emission data. If concentrations, please provide the reference for the concentration data.
It is aerosol and chemistry emissions. Anthropogenic emissions are the CMIP6 emissions (Eyring et al., 2016). Natural emissions are from MEGAN-MACC (Sindelarova et al., 2014) over land and POET (Granier et al., 2005) over ocean. This has been added to the document. Section 2.5, I understand that you intend to separate the scavenging effect from other microphysical processes. However, these processes of course are nonlinear. Could you provide a discussion on the applicability and limitation of the linear assumption here as well as the use of multiple linear regression?
Additional discussion has been added to the end of Section 2.5 noting that the relationship between LWP and Nd appears to be approximately linear and discussing that in regimes or models with very large adjustments moderated through precipitation our analysis framework will break down.

Introduction
Uncertainty in the radiative forcing due to aerosol-cloud interactions is the leading uncertainty limiting our ability to accurately diagnose the Earth's climate sensitivity from the observational record (Forster, 2016). The best estimate of the radiative forcing due to aerosol-cloud interactions (also called the first indirect effect (Twomey, 1977)) has narrowed to -1.2 to -0.34 Wm -2 in a recent survey of forcing from aerosol-cloud interactions (Storelvmo, 2017;Bellouin et al., 2019), but the 5 sign and strength of the forcing due to changes in cloud macrophysical properties in response to aerosol (aerosol-cloud adjustments) remain uncertain (Bellouin et al., 2019). This uncertainty reflects the difficulty in disentangling the many factors that determine cloud macrophysical properties. Unlike cloud droplet number concentration (Nd), which is primarily driven by the availability of suitable aerosol, cloud macrophysical properties are primarily determined by the state of the atmosphere, but may be modulated by Nd (Stevens and Feingold, 2009). 10 Here, we focus on liquid clouds. Within liquid clouds two main processes are hypothesized to alter cloud liquid content in response to changes in Nd. As Nd is increased there may occur (1) a suppression of precipitation by enhanced Nd (Albrecht, 1989;Pincus and Baker, 1994), and (2) strengthened entrainment of dry air (Ackerman et al., 2004;Bretherton et al., 2007;Wang et al., 2003;Xue and Feingold, 2006). These processes drive the liquid content of cloud in opposite directions following a perturbation in microphysics, further complicating the interpretation of covariability between cloud 15 macrophysical and microphysical properties. Because these processes exist at a time and length scale far below those resolved in climate models they must be parameterized, resulting in substantial uncertainty. Because of this, constraining the cloud macrophysical response to changes in cloud microphysics using observations is an essential step towards constraining aerosol forcing. Aerosol-cloud adjustments are likely to contribute a relatively small fraction of overall variability in cloud macrophysical properties (Bender et al., 2019) -making the data volume available from remote-sensing observations 20 particularly relevant to providing an observational constraint by detecting the small signal from aerosol-cloud adjustements hidden in meteorologically-induced cloud variability. The literature has produced numerous careful analyses of the observational record, but these analyses have produced divergent estimates of the aggregate effect of increased Nd on liquid clouds. These impacts range from increased Nd increasing liquid content in clouds (Chen et al., 2014;Rosenfeld et al., 2019), to almost no response in in-cloud and area-averaged LWP (Toll et al., 2017;Malavelle et al., 2017), to decreasing liquid 25 content (Gryspeerdt et al., 2019;Sato et al., 2018). In contrast, the response in cloud cover to Nd has tended to be consistently inferred as producing a forcing equal or larger than the first indirect effect (Gryspeerdt et al., 2016;Christensen et al., 2017;Andersen et al., 2017). A simulation of deep, open-cellular boundary layers has shown an increase in cloud fraction, and a decrease in in-cloud LWP, ultimately resulting in an increase in reflected shortwave in the simulation (Possner et al., 2018). Given the wide range of potential observational constraints it remains difficult to offer advice on what 30 cloud microphysical parameterizations are the most realistic.
However, the causal link flowing from Nd to clouds is not the only mechanism relating cloud macrophysics to cloud microphysics. As shown in Wood et al. (2012), the spatial pattern in Nd observed in nature is primarily determined by 3 precipitation scavenging. That is to say, Nd may both alter cloud macrophysical properties, and be altered by them and interpreting observations as a constraint on only microphysical to macrophysical causality is erroneous, as discussed in Gryspeerdt et al. (2019). To be able to constrain cloud responses to aerosol-driven changes in Nd we must be able to characterize the effects of cloud macrophysical properties on Nd (by precipitation scavenging) and covariability between Nd and LWP induced by confounding factors such as the relative location of aerosol sources and climatological cloud cover, or 5 meteorological modulation of aerosol and clouds. Bender et al. (2019) proposed utilizing the observed covariance between Nd and LWP as an aggregate measure of aerosol-cloud-radiation behavior across climate models and reanalysis. For a model to be able to realistically reproduce aerosol-cloud behavior one precondition is that covariance flowing from clouds to aerosol, and from aerosol to clouds as well as the non-causal covariance induced by airmass history must result in a total covariance consistent with observations. 10 Similarly, Gryspeerdt et al. (2019) examined covariance between Nd and in-cloud LWP, but proposed to separate variability induced by adjustments from other sources of covariability by using clustering on global data. This study follows on from these earlier studies and attempts to partition covariance between LWP and Nd related to causality flowing from Nd to LWP from other covariance. We utilize empirical analysis of observations and model output to try and disentangle variability driven by meteorological 'cloud-controlling factors' (Stevens and Brenguier, 2009) and variability related to changes in 15 cloud microphysics. Within this framework we focus on the midlatitudes. Previous work has performed similar analysis on cyclonic midlatitude systems, finding a distinct increase in LWP at a fixed precipitation rate (McCoy et al., 2018c). These large synoptic systems account for roughly half the midlatitudes (Bodas-Salcedo et al., 2014). Here, we turn our attention to the remaining interstitial regions between cyclones. This regime tends to be less cloudy, has an overall lower albedo, and lower cloud optical depth (an example is shown in Fig. 1a). Thus, while these regions do not host dramatic fronts and cloud 20 shields, changes in their liquid cloud due to anthropogenic aerosol may contribute strongly to the overall aerosol forcing because cloud areal coverage and cloud optical depth are farther below saturation.

Region and variable selection 25
The empirical analysis on both observational and simulated data in this work follows pioneering studies investigating meteorological controls on subtropical Norris, 2013, 2015;Qu et al., 2015;Klein et al., 2017;Seethala et al., 2015) and midlatitude (Miyamoto et al., 2018) marine boundary-layer cloudiness. The selection of variables used in this study is based on the findings of these earlier studies. The predictors examined here are sea surface temperature (SST), large scale subsidence (!) at 550 hPa, the strength of the inversion at the top of the boundary layer (estimated 30 inversion strength, EIS, as defined in Wood and Bretherton (2006)), the total water vapor path (WVP), and sensible heat flux (SHF). A summary is given in Table 1. A priori we expect that increasing SST should lead to decreasing cloudiness (Myers 4 and Norris, 2015;Qu et al., 2015;McCoy et al., 2017;Bretherton and Blossey, 2014). Increasing subsidence should decrease liquid water path (Myers and Norris, 2013). Increasing inversion strength should lead to increasing cloud fraction (Wood and Bretherton, 2006;Klein and Hartmann, 1993;Qu et al., 2015;Myers and Norris, 2015;Seethala et al., 2015). As shown in Miyamoto et al. (2018) from examination of midlatitude ocean fronts, increased SHF should increase cloudiness. Finally, while less extensively studied, an overall increase in WVP seems likely to lead to increased cloudiness as the atmospheric 5 column moisture increases, holding all else equal (McCoy et al., 2018b).
The central goal of this study is to develop an empirical constraint on aerosol-cloud adjustments. However, direct measurements of the aerosol state to constrain aerosol-cloud adjustments have been found to be sensitive to errors in pristine conditions (Ma et al., 2018). To develop a constraint on aerosol-cloud adjustments we examine the cloud microphysical state in addition to the meteorological parameters listed above. Cloud droplet number concentration is the state variable relating 10 cloud macrophysics to aerosol concentration Grosvenor et al., 2018) and is the predictor used in this study to characterize aerosol-cloud adjustments.
We hasten to note that the list of predictors described above is not intended to be complete (that is to say, we do not anticipate that we will be able to explain 100% of the variability in clouds with these predictors). Our goal is to explain enough variability with these predictors to be able to infer statistically-robust relationships between cloud macrophysical and 15 microphysical properties in the variance unexplained by meteorological variability. The predictive abilitiy of these inferred relationships will be tested within the context of a global climate model (GCM).
Having discussed predictors, we will now discuss predictands. Out of cyclone cloud cover is primarily liquid, boundary layer cloud, which substantially affects shortwave radiation, but has little effect on longwave radiation (Hartmann and Short, 1980). Thus, we focus on liquid water path (LWP) averaged over cloudy and clear regions. This variable allows 20 observations and model output to be compared without needing to simulate output from a passive spectoradiometer (Bodas-Salcedo et al., 2011) or considering cloud overlap, as would be required for in-cloud LWP .
Analysis is carried out in the northern hemisphere (here 30°-60°N) over oceans. This choice has been made for several reasons: First, there is a large variability in Nd across the northern midlatitudes that is not strongly driven by the seasonal cycle. In the Southern Ocean cloud condensation nuclei (CCN) variability is primarily due to biogenic sources and 25 their variability is strongly driven by the seasonal cycle, making analysis in the context of meteorological controls difficult to interpret (Ayers and Gras, 1991;McCoy et al., 2015a;Charlson et al., 1987). Second, Southern Ocean Nd is still poorly represented in the MetOffice Unified Model GA7.1 (discussed in section 2.4) with both too low a mean value and generally too small a seasonal cycle -in contrast to the Northern Hemisphere, which compares well with observations (Mulcahy et al., 2018).  (2007) cyclone compositing algorithm, which uses sea level pressure (SLP) to identify cyclone centers. Here we utilize the same 5 compositing approach, but focus on all data that is 2000 km away from a cyclone center, following Bodas-Salcedo et al.
(2014). This separates the midlatitudes into times when a cyclone is nearby and when there is no cyclone nearby. Once cyclone centers are identified all data within 2000km of an identified cyclone center is masked out of the data set. All data over land is also masked because microwave observations are unavailable (see next section).
A schematic representation of the frequency of occurrence of out-of-cyclone states is shown in Fig. 1b and is 42% 10 in the 30°N-60°N region focused on in this study. All data is regridded to a common 1°x1° spatial resolution before analysis.
All data is daily-mean, except for observed Nd, which is only available for the MODIS Aqua overpass; however the diurnal cycle of Nd is thought to be relatively slight (Dong et al., 2014) and it is unlikely that this retrieval limitation significantly impacts our results. Our choice of resolution is motivated by the natural resolution of the MAC-LWP data set. Performing the analysis with a coarser resolution might change the regression coefficients derived in section 2.5, as has been reported for 15 analysis of the first indirect effect (McComiskey and Feingold, 2012). However, in section 3.4 we validate the adjustments inferred from this resolution against the true adjustments in UMGA7.1 and find agreement which demonstrates that our choice of resolution does not affect our results.

Observations
Cloud liquid water path (LWP) is calculated based on the aggregated observations from multiple satellite 20 microwave sensors following the methodology of the multisensory advanced climatology of LWP (MAC-LWP; Elsaesser et al. (2017)) at daily-mean resolution. Microwave radiometers are sensitive to total liquid. This means that the retrieval must calculate a partitioning between precipitating and non-precipitating liquid. Here, the liquid water path in clouds is calculated following Elsaesser et al. (2017). Previous analysis has shown that the midlatitude partitioning or rain and cloud in MAC-LWP compares favorably with convection-permitting simulations (McCoy et al., 2018c). The MAC-LWP data set estimates 25 that 7% of total liquid path is rain in the NH midlatitudes outside of cyclones. Because of the low fraction of rain water in the midlatitudes outside of cyclones it is unlikely that the need to partition the observations into rain and cloud water substantially affects observational constraints as calculated in section 3.3. Liquid water path is defined as the average of cloudy and clear regions and is insensitive to overlying ice cloud (unlike passive optical retrievals). This definition of LWP is consistent with the definition from GCMs. Microwave retrievals are only available over ocean. 30 Observations of Nd are calculated based on MODIS observations of cloud optical depth and droplet effective radius.
Level-2 swath data (joint product) from MODIS collection 5.1 (King et al., 2003) is filtered by removing pixels with solar Deleted: Fig. 1 6 zenith angles greater than 65° to eliminate problematic retrievals at a pixel-level (Grosvenor and Wood, 2014). The dailymean Nd at 1°x1° resolution is calculated from the filtered level 2 swath data and only low (cloud tops below 3.2 km), liquid clouds were used to calculate Nd. Only 1°x1° regions where the liquid cloud fraction exceeds 80% are considered valid (Bennartz et al., 2011) and the Nd is calculated using effective radius from the 3.7µm MODIS channel. This data set is evaluated in Grosvenor et al. (2018) and in McCoy et al. (2018a), where it shows consistency with measurements from 5 aircraft.
We feel that this combination of radiometers in constraining adjustments is particularly advantageous because there is no shared information between the microwave retrieval of LWP, and the shortwave and near-infrared retrieval of Nd. This is in contrast to the common practice of utilizing MODIS retrievals of cloud droplet effective radius and optical depth to calculate both the in-cloud LWP and Nd, making it conceptually difficult to cleanly infer changes in LWP due to changes in 10 Nd.
The meteorological state of the atmosphere is characterized using reanalysis from MERRA2 (Molod et al., 2015) and microwave observations of water vapor path (WVP) from MAC-LWP. The period during which all of these observations are available stretches from 2003 to 2015. A list of variables and data sources is given in Table 1.  (Sindelarova et al., 2014), and natural emissions over ocean follow the POET inventory (Granier et al., 2005). These simulations are conducted to calculate the response of cloud to anthropogenic aerosol. Additional sensitivity 25 studies were carried out starting nudging at level 27 (approximately 5 km) and without nudging. In the latter case simulations of the PI and PD were run for ten years and three months starting in September 2003. The results of this analysis are shown in the supplementary materials and do not differ substantially from the results in the main text.

Simulations
In GA7.1 aerosol number concentration has the potential to affect cloud microphysics in three places: First, the conversion of cloud water to rain, where enhanced Nd suppresses the conversion of cloud water to rain water. This is 30 parameterized using the scheme in Khairoutdinov and Kogan (2000), bias corrected as described in (Boutle et al., 2014). The conversion rate of cloud to rain is parameterized as [1] Deleted: Table 1 Deleted: and a half 35 Deleted: 1.7

Deleted: aerosols
Deleted: (Granier, 2005) Deleted: and are nudged to temperature and wind above 1.7 km.

7
where / $%&'( is the cloud liquid water mixing ratio. Second, the gravitational settling of cloud droplets, where enhanced Nd suppresses the settling of cloud droplets out of the cloud. The flux of water settling out of a cloud layer is given as Third, enhanced cloud albedo from changes in Nd in the radiative transfer code (Twomey, 1977).
However, clouds may affect aerosol concentrations via wet scavenging. UKCA allows scavenging to be configured 5 in two ways: the default configuration, or using the scavenging coefficients in the ECHAM5-HAM model (Stier et al., 2005).
To evaluate some of the uncertainty related to scavenging we perform simulations with both sets of coefficients. A list of model simulations conducted is given in Table 2.

Analyzing covariance in the system
Our goal in this paper is to characterize how Nd drives LWP. However, to reveal robust correlations between Nd and LWP, 10 meteorological variability must be accounted for. To achieve this we follow previous empirical analysis of cloud controlling factors and utilize multiple linear regression to characterize the dependence of various cloud properties as predictands on the predictors described above . As with all empirical analyses of observations, correlation between predictors and the predictand does not necessarily mean that they are causally linked. The meteorological predictors selected here have had mechanisms hypothesized to link them to cloud variability. Another issue with this, and similar analyses of the 15 response of cloud to cloud-controlling factors is that thermodynamic and dynamical predictors within the Earth's atmosphere are correlated (McCoy et al., 2017;Norris, 2015, 2013). As the variance shared by predictors grows, the uncertainty in the coefficients calculated by multiple linear regression increases. While this is an issue, it is inescapable in trying to disentangle the effects of different cloud controlling factors on cloud properties. Examples of meteorological variables that are correlated, but have opposing effects on cloud cover include subsidence and stability; and stability and SST 20 (Myers and Norris, 2013;Qu et al., 2015;Wall et al., 2017).
To reduce predictor covariance we bin our 1°x1° daily-mean data from model output and observations into the space of SST and WVP. All output over oceans is considered in the analysis. We choose these predictors to bin our data by before performing regression analysis because they represent two of the most basic meteorological state variables, they covary strongly, and because LWP varies significantly as a function of WVP and SST in both observations and simulations 25 ( Fig. 2). Nine bins are used to span WVP (0-40 kg/m2) and ten for SST (275-305 K). We propose that a multiple linear regression model of the form @A# = C DD-EE5 + C 0 ! <<G + C = HIJ + C 2 AK# + C < JJL + C M JNO + C 3 [3] be trained in each bin of SST and WVP. All the predictors within the regression model are environmental drivers that are external to the clouds being influenced. However, robust remote-sensing observations of CCN are lacking and ln(Nd) is used 30 in its place. As discussed above, Nd is predominantly a function of CCN availability. Thus, the multiple linear regression model Deleted: as @A# = C 7 ln (5 ( ) + C 0 ! <<G + C = HIJ + C 2 AK# + C < JJL + C M JNO + C 3 [4] is trained in each bin of WVP and SST. Bins that contain fewer than 3000 data points are excluded. Units of LWP are in g m -2 , Nd is in cm -3 , subsidence is in Pa s -1 , EIS is in K, WVP is in kg m -2 , SST is in K, and SHF is in Wm -2 . A 99% confidence interval is used to determine if a coefficient is significant (different than zero). The initiation of precipitation in boundary layer cloud can substantially impact LWP within a given cloud with a timescale longer than the daily sampling time scale 5 utilized here (Berner et al., 2013). However, the spatial scale of our analysis (1°x1°) samples clouds at many stages of their lifecycle. This means we do not need to consider rain as a predictor of LWP, and may think of it as scaling with cloud LWP.
Training the regression model in Eq. 4 produces a measure of the covariance between predictors and predictand. In particular, it produces a measure of the covariability between ln(Nd) and LWP (a1). However, this covariance does not show causality. Nd may enhance LWP by, for instance, suppressing rain (Albrecht, 1989), and it is this relationship where 10 causality runs from Nd to LWP that is of interest in understanding adjustments. However, the observed covariability between Nd and LWP is also the product of causality running from LWP to Nd due to precipitation removing aerosol and reducing Nd . The overall covariance between Nd and LWP is the product of these two causal pathways as well as correlation induced by environmental factors driving both clouds and aerosol, and by geographic and seasonal distribution of sources of aerosol relative to cloud. Fig. 3 shows a schematic of these causal flows. 15 How do we constrain adjustments based on examination of modeled and observed Nd and LWP if we can't disentangle causality? The solution we propose is to use a simplified version of the model to characterize the sensitivity of Nd to precipitation and other factors and use this sensitivity to interpret the full model. To conceptualize why this process can estimate the sensitivity of LWP to Nd we can write an equation describing small changes in LWP in the space of small changes in Nd. First, we consider Nd acting on cloud microphysics (5 ( TUVWX ) and Nd when precipitation scavenging is the 20 only causal factor linking cloudiness and Nd (5 ( 9D+Y ) as separate entities. In the latter case air mass history and sinks unrelated to precipitation can affect Nd, in addition to the effect of precipitation scavenging, but precipitation scavenging is the only causal link between cloud and aerosol (see Fig. 3). We consider changes in LWP relative to 5 ( TUVWX , and 5 ( 9D+Y . That is to say we consider @A# = Z[(ln (5 ( TUVWX ), ln (5 ( 9D+Y )), where the logs are added for consistency with Eq. 4 and all other terms in equation 1 are held fixed and the first term is expanded. 25 Conceptually, LWP is increased with increasing 5 ( TUVWX (Fig. 4b) and 5 ( 9D+Y is reduced by increasing rain-rates, which increase with LWP (Fig. 4c). In the topographic space describing LWP in terms of 5 ( TUVWX and 5 ( 9D+Y , reduced 5 ( 9D+Y corresponds to increased precipitation rates, and in turn, LWP. That is to say where R is rain rate, so the reciprocal of the product of these terms gives 30 Thus, a small change in LWP in terms of changes in these two variables alone is We assume that scavenging is unaffected by changes in 5 ( TUVWX affecting rain rates, so there are no higher-order terms, although this may not be the case in reality , and this feedback is found to substantially enhance the strength of adjustments in some models (Jing and Suzuki, 2018). A visualization of Eq. 7 is shown in Fig. 4a. The best fit of LWP to Nd gives the sum of the partial derivatives of the two terms 5 We will use this correction for variability induced by factors besides adjustments throughout the paper to infer the effects of Nd on cloud properties in model configurations and the observations. We note that this methodology is subject to several limitations. First, as noted above, it assumes that feedbacks between adjustments and scavenging are small. This assumption will break down as adjustments become stronger. However, the response in cloud to transient changes in aerosol does not appear to permit very strong adjustments (Malavelle et al., 2017;Toll et al., 2019;Toll et al., 2017). Second, it is assumed here that the relationship between LWP and ln(Nd) is linear. Empirically this assumption appears to hold in the models and observations (as shown in the following section) and inclusion of higher-order polynomials of ln(Nd) in Eq. 3 did not alter 5 our results.
To reiterate, non-causal factors also lead to correlation between Nd and LWP because air mass history is important for both clouds and aerosol (Mauger and Norris, 2007). In the discussion of the conceptual model presented above we focused on the impact of changes in Nd on LWP, and vice-versa. Spurious correlation due to air mass history will affect both terms on the right-hand side of Eq. 11 when they are calculated using regression. Thus, the correction for scavenging-10 induced variability in Eq. 11 also corrects for variability induced by air mass history simultaneously affecting Nd and LWP.

Variance in LWP as a function of Nd
As described in the methods section, data from observations and the control simulation in the UM between 30°N and 60°N over oceans and 2000 km from cyclone centers at daily-mean resolution is binned by WVP and SST and the regression 15 model shown in Eq. 4 is trained in each bin. If we plot the quantity @A# − C 0 ! <GG − C = HIJ − C 2 AK# − C < JJL − C M JNO − C 3 [12] as a function of Nd we can see that the coefficient relating LWP to Nd is greater than zero at 99% confidence, once variability associated with meteorological predictors is removed (Fig. 5). The residual variance in LWP covaries with Nd similarly between the observations and UM simulations where observations exist. However, one key difference is the span of Nd 20 values in the observations and simulations. Observed Nd almost never falls below 30 cm -3 (the dashed line in Fig. 5), while the Nd calculated by the model occasionally falls below this value (~10% of modeled ln(Nd)). This is not surprising because the model suffers from no retrieval limitations and can always measure an Nd, even when cloud is extremely tenuous.
Ultimately the goal of this study is to utilize the slope of LWP with respect to Nd to infer adjustment strength. However, using the slope from the observations and the models will produce quite different values due to the strong increase in LWP 25 with Nd below 30 cm -3 . In order to compare observations and models fairly we exclude data for Nd<30 cm -3 .
For Nd>30 cm -3 residual LWP decreases with increasing Nd in both observations and models. This agrees with the notion that precipitation variability drives Nd , and agrees with previous analysis (Gryspeerdt et al., 2019). Clearly, this does not mean that the model reduces cloudiness in response to aerosol. The cloud microphysics within the UM GA7.1 must increase LWP in response to a change in Nd, and analysis of the model response to changes from pre-30 industrial (PI) to present day (PD) aerosol have confirmed a negative forcing from adjustments (Mulcahy et al., 2018). As discussed in the methods, the difference in slopes between the scavenging-only and control simulation is a proxy for the response in cloud microphysics to Nd. Before analyzing this difference, we will briefly discuss the covariance between LWP and meteorological predictors in the observations and the control simulations.

Covariances between LWP and meteorology
Before returning to discussing aerosol-cloud adjustments, we discuss the covariances between observed LWP and the other predictors in Eq. 4. This is shown in Fig. 6. The explained variance (R 2 ) by the regression model exceeds 40% except at low 5 WVP and SST. The variance explained across all bins of SST and WVP is 46% of daily-mean 1x1° variability. That is to say, nearly half the day-to-day variability in LWP across the midlatitudes away from cyclones can be explained as a simple linear combination of five variables.

Several of the predictors have uniform effects on LWP: LWP decreases with subsidence (consistent with Myers and
Norris (2013)); increases with WVP; decreases with increasing SST (consistent with Qu et al. (2015), and references 10 therein); and increases with sensible heat flux (consistent with Miyamoto et al. (2018)). We note that at very low SST it appears that LWP may increase with SST. It is possible that this feature is related to ice to liquid transitions (McCoy et al., 2015b;McCoy et al., 2016;Tsushima et al., 2006;Senior and Mitchell, 1993;Tan et al., 2016), but this region only accounts for a small fraction of the overall data volume. The only meteorological predictor that correlates positively and negatively with LWP across the SST-WVP phase space is EIS. At higher WVP and lower SST EIS and LWP are negatively correlated, 15 while at low WVP and high SST they are positively correlated. The latter effect is consistent with increasing EIS increasing cloud fraction (Wood and Bretherton, 2006). One possibility is that because clouds are closer to 100% in areal coverage at higher WVP and lower SST, increasing stability suppresses thickening of cloud in this regime, while the clouds cannot expand horizontally.
Examination of the control simulation shows very similar covariances between meteorological predictors and LWP 20 (Fig. 7). Notable differences are the stronger positive covariance between SST and LWP at low SST, and uniform negative covariance between EIS and LWP across the SST-WVP phase space. However, the relationship between LWP and meteorology is strikingly similar between observations and the UM. The explained variance by predictors tends to be higher in the UM GA7.1 (64%), but it is hard to say how much of this difference in explained variance is due to simplification of the real atmosphere and cloud physics by the model, and how much is due to observational error. 25 In this framework we also characterize the covariance between ln(Nd) and LWP. The correlation between ln(Nd) and LWP is primarily negative in the observations, with positive correlations only occurring at high WVP and low SST. The correlation between LWP and ln(Nd) in the model is almost uniformly negative (in the data set restricted to Nd>30 cm-3).
Standardization of the predictor strength estimates the effect of a standard deviation change in each predictor in standard deviations of LWP. In both the observations and models the impact of a standard deviation in meteorological predictors 30 dwarfs the effect of a standard deviation in ln(Nd), with contributions from subsidence and SHF dominating variability. That is to say, the relative contributions of variability in Nd are quite small in comparison to variability that is simply due to the weather.

Inferring the effect of Nd on LWP
As we have seen, the correlation between LWP and Nd is mostly negative. The slope relating ln(Nd) to LWP in the context of Eq. 4 is reproduced in Fig. 8ab. However, if we manually set the Nd seen by autoconversion, radiation, and settling to 75 cm -3 in the UM GA7.1 (the approximate mean value in the study region) the negative covariance strengthens substantially 5 (Fig. 8c). This model version is termed 'scavenging-only' because scavenging is the only causal link between cloud and aerosol (Fig. 3). As discussed in the methods section, the effect of changes in Nd on LWP may be approximated by the difference between Fig. 8b and Fig. 8c. This is shown in Fig. 8e. This agrees with our expectation based on our knowledge of how the UM GA7.1 treats liquid cloud processes. We know that the effect of increasing Nd on autoconversion and settling is to inhibit the conversion of cloud to rain and reduce cloud droplet fall speed. 10 To evaluate the accuracy of this method in inferring the sensitivity of LWP to Nd we conduct simulations where causality is forced to flow from the Nd to LWP. This is done by setting the Nd seen by the autoconversion, settling, and radiation to constant values. Two simulations are conducted for each mechanism with Nd set to 100 cm -3 , and 300 cm -3 . The Nd seen by the other mechanisms is held constant at 30 cm -3 . A further three simulations are conducted where Nd seen by all three mechanisms is set to 30 cm -3 , 100 cm -3 , and 300 cm -3 (Table 2). This yields a set of simulations describing the effects 15 on LWP of an increase in Nd in the autoconversion, settling, or radiation, as well as via all three mechanisms simultaneously.
Analysis of the effects of increased Nd seen by the radiation code showed negligible changes in LWP and are not shown here. Fig. 7, the fit in Eq. 4 is trained in each bin of WVP and SST across each set of three simulations. The Nd seen by the model parameterization is used in the multiple linear regression (Eq. 4). As expected, given the functional form of 20 these parameterizations (Eq. 1 and Eq. 2) the effect of increasing Nd in either autoconversion or settling results in an increase in LWP, as does the case where Nd in the settling, autoconversion, and radiation are all varied together. The effect of a perturbation in the Nd seen by autoconversion, radiation, and settling on LWP is nearly identical to the slope inferred by subtracting the slope in the scavenging-only run from the control run following Eq. 11 (Fig. 8f). This comparison between the true model sensitivity of LWP to changes in Nd supports the validity of the multiple linear regression-based inference 25 approach pursued here.

As in
Autoconversion and settling are likely to interact with each other in a non-linear manner. As one is suppressed as a sink of cloud liquid, the other will grow (for example, if the conversion of cloud to rain is rendered inefficient then the gravitational settling of cloud droplets will become more efficient as the liquid content grows). Analysis of cross talk between these terms is not the focus of this article, but sensitivity of LWP to changes in each mechanism is shown in Fig. 8f. 30 The effect of perturbing settling Nd on LWP is larger than the effect of perturbing the autoconversion Nd, singling it out as an important lever in controlling adjustment strength for future study. This result is consistent with the large process rate for settling relative to autoconversion found in weakly precipitating low cloud regimes in CAM5 (Gettelman et al., 2013). It is Formatted: Font: Italic Formatted: Font: Italic, Subscript 13 also possible that interactions between settling and Nd may decrease the sensitivity of warm rain to autoconversion representation that is diagnosed in other models Jing et al., 2019). Overall, the results of this study are insensitive to whether settling or autoconversion have a stronger effect on aerosol-cloud adjustments because we assume that feedbacks between scavenging and adjustments are small.
Given that the scavenging-only simulation can be used to infer the adjustment strength in the UM, we also attempt 5 to use the scavenging-only simulation to infer the strength of adjustments in the real world (Fig. 8d). This assumes that the statistical relationship between LWP and rain rates in the UM GA7.1, and the scavenging of CCN-relevant aerosol by precipitation in the UM GA7.1 are realistic.
Based on the covariance between Nd and LWP in the scavenging-only simulations in the UM GA7.1 and observations we offer an estimate of adjustment strength. The adjustment strength inferred from observations is stronger than 10 the UM for low SST and high WVP. Unlike the UM, weak negative covariance between LWP and Nd exists for high SST and low WVP. This may indicate that the scavenging of aerosol by the UM is too efficient, or some other confounder of the relationship between LWP and Nd is poorly represented in the model, or it may point to thinning of cloud via enhanced entrainment (Ackerman et al., 2004), which is not represented in the UM. Overall, the effect of increasing Nd in the UM is to increase LWP. 15 We have discussed how to infer adjustment strength from the total covariance between Nd and LWP, which mixes covariance induced by causality flowing from cloud to aerosol and aerosol to cloud. In the next section we show how this inferred adjustment strength from the simple regression model is able to predict LWP adjustments in response to anthropogenic aerosols within the full GCM simulation.

Reproducing simulated adjustments between the pre-industrial and present day
We have produced an estimate of the sensitivity of LWP to changes in Nd in the UM GA7.1 model (Fig. 8e). Does this simple regression model hold skill in reproducing the actual change in LWP within the model between the present day (PD) and pre-industrial (PI) aerosol emissions? Simulations are carried out setting aerosol emission to pre-industrial values. This is done for simulations using the GA7.1 scavenging parameterization. A second set of simulations is conducted where 25 the ECHAM-HAM5 scavenging coefficients are used to estimate the sensitivity to the representation of scavenging. PI, PD, and scavenging-only simulations are conducted for each scavenging configuration.
The change in LWP between the PI and PD (∆LWPPD-PI) simulated by the UM is 2.9 g/m 2 averaged across the 30-60°N region. Using the UM-simulated change in Nd (∆NdPD-PI) and the slope relating ln(Nd) to LWP diagnosed from presentday variability (Fig. 8) we calculate ∆LWPPD-PI. If the covariance between ln(Nd) and LWP observed in the control run (Fig.  30 8b) of the model and ∆ NdPD-PI are used to predict ∆LWPPD-PI, the negative correlation introduced by precipitation scavenging leads to a negative ∆LWPPD-PI (Fig. 9a, in disagreement with the UM-simulated ∆LWPPD-PI). If the covariance in the scavenging-only simulation (causality flows from clouds to precipitation to aerosol to Nd) is used (Fig. 8c), the regression model-predicted decrease in LWP between PI and PD aerosol levels doubles. However, if we difference the sensitivity in the control and scavenging-only simulation to yield the sensitivity of LWP to changes in Nd (Fig. 8e), the ∆LWPPD-PI predicted by the regression model and the UM-simulated ∆NdPD-PI agrees well with the UM-simulated ∆LWPPD-PI (Fig. 9).
This result supports the utility of the inferred sensitivity of LWP to Nd in examining adjustments due to PD aerosol.
What does the covariance between LWP and ln(Nd) in the real world tell us about the model? Use of the 5 observational estimate of adjustment strength (Fig. 8d) calculates a ∆LWPPD-PI that is two thirds of the ∆LWPPD-PI inferred from the control run and ∆NdPD-PI (Fig. 9). This is because, while the inferred sensitivity of LWP to Nd from observations is quite strong in some regions, it is weakly negative in the most commonly-occurring WVP-SST regimes (Fig. 8d). That is to say, if the efficacy of precipitation in removing CCN-relevant aerosol in the real-atmosphere is near to the efficacy in UM, the relationship between LWP and rain rates in the real atmosphere is near to the relationship in the UM, and the 10 covariability between Nd and LWP induced by other confounders of the Nd-LWP relationship are realistic, then the adjustments (∆LWPPD-PI) simulated by the UM are not unreasonable, albeit a little large. This result is consistent with constraints provided by simulation of the Holuhraun eruption (Malavelle et al., 2017), which showed that the anomaly predicted by HadGEM3 was within the observed range. However, the observationally-inferred sensitivity of LWP to changes in Nd is stronger in low SST, and high WVP regimes than it is in the UM GA7.1, but much weaker, or even slightly 15 negative in low WVP and high SST regimes. This results in a strong latitudinal gradient in ∆LWPPD-PI between 30°N and 60°N inferred from observations (Fig. 9b).
The predicted ∆LWPPD-PI based on the control and scavenging-only simulations (Fig. 8e) underestimates the UMsimulated ∆LWPPD-PI by around 10%. This may result from disregarding feedbacks between precipitation suppression and Nd (Jing and Suzuki, 2018), may simply be due to shortcomings in the simple linear model relating ln(Nd) to LWP, or may relate 20 to meteorological differences between the PI and PD simulations not accounted for by meteorological predictors or compositing. However, the fractional reduction in inferred ∆LWPPD-PI when observations are used to constrain the sensitivity of LWP to Nd suggests that ∆LWPPD-PI should be around 60-70% of the value predicted by the UM GA7.1 averaged across the NH. ∆LWPPD-PI inferred from observations is extremely dependent on latitude with almost no change in LWP over lower latitudes and warmer SSTs. We hasten to note that the change in Nd between the PI and PD is uncertain and 25 its prediction by UM GA7.1 may be biased, making the absolute values of the constrained ∆LWPPD-PI less relevant than the fractional overestimation in UM-simulated ∆LWPPD-PI. This analysis is repeated using simulations that are only nudged above level 27 of the model (Fig. S1), and not nudged at all (Fig. S2) with minimal differences from the results presented in the main text.
We have focused on changes in LWP in this work because it is a variable that we have good observations of, it can 30 be compared between models and observations in a straight-forward way, and it clearly links to adjustments. However, this variable is not the key variable in discussing radiative forcing and climate sensitivity. How does the radiative forcing from adjustments scale with LWP? Determining the precise effects of adjustments on shortwave cloud radiative effect is difficult,

Deleted: 25-35
Deleted: or 35 Deleted: may not be perfectly reflect the real change in Nd but if we assume that the perturbations in LWP induced by adjustments are similar to the perturbations that are driven by meteorology we can offer a simple estimate to inform our understanding of the modeled forcing from adjustments.
Examination of the relationship between LWP and albedo within the UM GA7.1 shows a rapid climb in albedo for low LWP, followed by saturation at higher values, as expected from saturation of cloud fraction and optical depth (Fig. 10).
This curve can be fit by a second-degree polynomial, meaning that the sensitivity of albedo to changes in LWP is a function 5 of the LWP. That is to say, regions where LWP is already high are going to have a smaller increase in albedo for a unit change in LWP. The change in LWP between PI and PD is much smaller than the range of the variation of LWP in the climate mean-state, so we use the average of monthly-mean LWP between PI and PD to calculate the sensitivity of albedo to changes in LWP for the NH midlatitudes. This sensitivity (hs/h@A#) is multiplied by the change in LWP to yield change in albedo. This change in albedo is scaled by downwelling shortwave to give the change in reflected shortwave. 10 The change in reflected shortwave predicted from LWP changes in the UM GA7.1 is 1.9-2.0 Wm -2 , depending on the scavenging parametrization used. The change in shortwave inferred from the regression model of LWP trained in the control run and corrected by the scavenging-only run is 1.5 Wm -2 . If the observed sensitivity of LWP to Nd is used to constrain ∆LWP, the predicted change in reflected shortwave is approximately 1.0 Wm -2 . Thus, we estimate that GA7.1 overpredicts the change in reflected shortwave due to adjustments in response to a given change in Nd by around 50%. This 15 estimate is subject to the caveat that changes in LWP due to adjustments may not affect albedo in the same way as suggested by examining the total variability. For example, adjustments might only increase the liquid content of the very thickest clouds and have a relatively slight impact on albedo. However, it is unclear how to provide a more complex calculation than presented here.

Discussion 20
As the possible range for the radiative forcing from the first indirect effect has narrowed aerosol-cloud adjustments have become an increasingly central source of uncertainty in aerosol-cloud radiative forcing (Bellouin et al., 2019). Here we focus on the northern midlatitudes, where the majority of anthropogenic aerosol is emitted (Myhre et al., 2013). Previous work has examined aerosol-cloud adjustments in midlatitude cyclones, showing that cyclone liquid water path (LWP) increases with cloud droplet number concentration (Nd) (McCoy et al., 2018c). This work focuses on the remainder of cases 25 in the midlatitudes when there is no cyclone center within 2000 km (roughly 42% of the time between 30°N-60°N, see Fig.   1).
Untangling the effect of cloud microphysics on cloud macrophysics from the total variability in cloud macrophysics is challenging. In the observational record we can only characterize the covariance between predictors and predictands. In interrogating the observed covariances between cloud properties and different meteorological predictors we find many of the 30 relationships that have been described in the literature documenting cloud controlling factors .
Once meteorological variability is accounted for, statistically significant relationships between cloud microphysics (Nd) and Deleted: ¶ Deleted: Fig. 1 cloud macrophysics (LWP) appear. In keeping with previous studies (Gryspeerdt et al., 2019), LWP and Nd are found to be negatively correlated. However, this is clearly not consistent with the UM GA7.1 GCM's actual response in LWP to changes in aerosol emissions between PI and PD. This negative correlation is due to a combination of Nd being driven by scavenging, as shown in Wood et al. (2012), and spurious correlation between Nd and LWP driven by external variables affecting both terms (Mauger and Norris, 2007) overwhelming any positive covariance driven by aerosol cloud adjustments. 5 While we cannot disentangle the covariance due to adjustments and covariance due to scavenging and other confounders in the observational record, we can create simulations in which causality is forced to flow from clouds to Nd (scavenging-only). Using this measure of non-adjustment-induced variability in Nd, we can infer the effect of changing Nd on LWP. This inferred sensitivity of LWP to Nd agrees well with simulations where Nd is manually varied in the cloud microphysics (Fig. 8f). The inferred sensitivity of LWP to Nd, combined with the UM-predicted change in Nd reproduces the 10 UM-predicted change in LWP between the PI and PD (∆LWPPD-PI, Fig. 9). These two tests support this method's relevance to understanding aerosol-cloud adjustments. Extension of this study to the subtropics, and tropics is reserved for a future analysis. While extrapolating the present results to the tropics is difficult, it seems reasonable to suppose that the pattern of adjustments in the subtropics is relatively similar to the inter-cyclone regime analyzed here and to expect a negative forcing in this region due to adjustments, although this 30 may be weaker than the midlatitude adjustments due to decreasing LWP for increasing Nd over higher SSTs and lower WVP over some of the subtropics (Fig. 8d). One important limitation of this study is that it assumes weak feedbacks between adjustments and scavenging. If some regimes have very strong feedback between precipitation and adjustments then our analysis will infer adjustments that are too weak. Our result is in contradiction with previous empirical constraint studies that have postulated that changes in Nd greatly enhance LWP (Rosenfeld et al., 2019), have little effect (Malavelle et al., 2017;Toll et al., 2017), or reduce LWP (Sato et al., 2018;Gryspeerdt et al., 2019). We suggest that this diversity within the literature is because a range of constraints may be arrived at depending on the degree to which precipitation scavenging and meteorological driving of aerosol and cloud occludes aerosol-cloud adjustments and what steps are taken in the analysis to account for scavenging-5 induced and meteorologically-induced covariability. Based on the analysis presented here we believe that positive, zero, or extremely strongly negative radiative forcings due to aerosol-cloud adjustments in the midlatitudes are not supported by the observations.

Author contributions
All authors contributed ideas and helped edit the paper. DTM and PRF planned the paper. Data analysis and writing were undertaken by DTM. Present day and pre-industrial simulation suites were set up by HG. Simulations were run by DTM.
Idealized simulations were set up by DTM. Development of simulations was conducted by HG, PRF, DPG, and DTM. 25 MODIS data was created by DPG. MAC-LWP data was created by GSE.

Competing interests
The authors declare that they have no conflict of interest.

1989.
Andersen, H., Cermak, J., Fuchs, J., Knutti, R., and Lohmann, U.: Understanding the drivers of marine liquid-water cloud occurrence and properties with global observations using neural networks, Atmos. Chem. Phys., 17, 9535-9546, 10.5194/acp-17-9535-2017. Ayers, G. P., and Gras, J. L.: Seasonal relationship between cloud condensation nuclei and aerosol methanesulphonate in marine air, Nature, 353, 834-835, 1991.    where t uz{|}u is set to a constant value is shown with a blue line and where t uz{|}u is increased independently is shown with a red line. In a causal sense this implies t uz{|}u driving LWP (shown in b) and t uvwxy being driven by LWP (shown in c), where t uvwxy is negatively correlated with LWP because ut uvwxy u~< ⁄ and uÄÅÇ u~> ⁄ , where R is rain rate. The observed variability of LWP in terms of Nd is shown in (d) for the cases t uz{|}u = t u and t uvwxy = w|ÉÑÖxÉÖ (red); t uvwxy = t u and t uz{|}u = w|ÉÑÖxÉÖ (blue); and t uz{|}u = t uvwxy = t u (the real world, dashed line).