GiOcean is based on the Goddard Earth Observing System (GEOS) Subseasonal-to-Seasonal (GEOS-S2S) prediction system, developed by the Global Modeling and Assimilation Office (GMAO) . GEOS-S2S is a coupled Earth system modeling and data assimilation framework to produce forecasts on subseasonal to seasonal timescales. The core component of the GEOS-S2S system is the coupled Atmosphere-Ocean General Circulation Model (AOGCM). It includes atmosphere, land, aerosol, ocean, and sea ice components with spatial resolutions of approximately 50 km for the atmosphere and 25 km for the ocean. The atmosphere component of the GiOcean is the GEOS Atmospheric General Circulation Model (AGCM) . The ocean component of the GEOS AOGCM is the MOM5 (Modular Ocean Model version 5) ocean general circulation model , and the Community Ice CodE-4 sea ice model . Ocean data assimilation follows the Local Ensemble Transform Kalman Filter approach . The land surface model uses a catchment-based approach and statistically represents subgrid-scale variability in surface moisture . To produce GiOcean, GEOS-S2S is retrospectively integrated starting on January 1998 using a time step of 450 s and assimilating atmospheric and ocean observations every six hours for the atmospheric and aerosol components and five days for the ocean, as described below.

The GiOcean reanalysis employs weak or “one-way” coupling, meaning that the ocean and aerosol components use a full assimilation system, while the atmosphere is “replayed” to a preexisting atmospheric reanalysis. In this approach, the atmospheric analysis increments used for model correction are derived from the pre-existing atmosphere-only reanalysis but adjusted for differences in model physics. This approach stabilizes the reanalysis by avoiding a full meteorological assimilation system, though it limits feedback between the ocean and atmosphere. GEOS-IT, produced for NASA's instrument teams, serves as a stable meteorological dataset for GiOcean (https://gmao.gsfc.nasa.gov/GMAO_products/GEOS-5_FP-IT_details.php, last access: 6 November 2025). Similar to the Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2) , GEOS-IT is a multidecadal retrospective reanalysis integrating both aerosol and meteorological observations . However, it incorporates recent model enhancements that provide more accurate representations of moisture, temperature, and land surfaces as well as the latest satellite observations through updated analysis techniques. While the atmosphere component of GEOS-S2S is “replayed” using the GEOS-IT reanalysis , the aerosol and ocean data assimilation systems, however, remain fully active.

Of significance to this work is that GiOcean explicitly assimilates aerosol fields. Furthermore cloud microphysics is described using a two-moment scheme, where cloud formation is linked to the aerosol concentration. This allows GiOcean to explicitly capture the aerosol direct and indirect effects.

Transport of aerosols and gaseous tracers such as CO are simulated using the Goddard Chemistry Aerosol and Radiation model GOCART;. All components are coupled together using the Earth System Modeling Framework and the Modeling Analysis and Prediction Layer interface layer . GOCART is a mass-based aerosol transport model that explicitly calculates the transport and evolution of dust, black carbon, organic material, sea salt, and sulfate. To relate aerosol mass to number concentrations, prescribed size distributions were used to calculate mass-number conversion factors as detailed by . Dust and sea salt emissions are prognostic whereas sulfate and biomass burning data are prescribed . Volcanic SO₂ emissions are constrained by observations from the Ozone Monitoring Instrument (OMI) on-board NASA's EOS/Aura spacecraft .

Aerosol fields in GiOcean are assimilated using The Goddard Aerosol Assimilation System (GAAS) . Aerosol assimilation is carried out in two steps. First the aerosol optical depth (AOD), is assimilated using the observations of AOD from multiple sources described in Table 2 of , including the Multi-angle Imaging SpectroRadiometer (MISR), the Moderate Resolution Imaging Spectroradiometer (MODIS), the Aerosol Robotic Network (AERONET), etc. Then in a second step the analysis increment is distributed vertically and among the different aerosol species to update their mass mixing ratios. In GiOcean the overall assimilation cycle is controlled by the meteorology. The meteorological observing system (i.e., the collection of instruments, platforms, and networks that provide meteorological observations) is also much larger than the one used in GAAS . GAAS is used to assimilate aerosol fields in the MERRA-2 reanalysis, although the cloud microphysics scheme in MERRA-2 lacks a representation of the aerosol indirect effect.

In GiOcean a 2-moment cloud microphysics scheme is used to calculate the mixing ratio and number concentration of cloud droplets and ice crystals as prognostic variables for stratiform (i.e., stratocumulus, cirrus) and convective clouds . Cloud droplet activation follows the approach of . The stratiform cloud microphysics scheme follows (: MG08) with adjustments when incorporated into GiOcean . The droplet autoconversion parameterization is replaced by the formulation of . A parameterization of subgrid vertical velocity, which is important for particle activation, was developed and detailed in . MG08 is also modified to represent the impact of existing ice crystals on the development of cirrus clouds. Ice nucleation is estimated using a physically-based analytical approach that includes homogeneous and heterogeneous ice nucleation, and their competition. The description of heterogeneous ice droplet formation by immersion freezing and contact ice nucleation follows . Vertical velocity fluctuations are constrained by non-hydrostatic, high-resolution global simulations . This configuration has been shown to reproduce the global distribution of clouds, radiation, and precipitation in agreement with satellite retrievals and in situ observations .

This study focuses on the evaluation of ACI in warm clouds in GiOcean. We limit the scope to variables related to aerosol abundance, activation into cloud droplets, the state of cloud macrophysical properties, and precipitation rate. We focus on variables that can be compared relatively directly between GiOcean and spaceborne remote sensing, including aerosol optical depth (AOD), cloud droplet number concentration (Nd), liquid water path (LWP), and precipitation rate.

The aerosol metric we use is the AOD, which measures the column-integrated aerosol extinction (scattering and absorption of light) and is often related to the total amount of aerosols in the atmospheric column. Although AOD does not provide information for the vertical distribution of aerosols or the aerosol sizes and species in the column, AOD provides an estimate of column integrated aerosol loading nearly globally, with limitation at high latitudes due to snow contamination. This is in contrast to sparse in-situ observations of aerosols made by aircraft and surface sites, and can be compared relatively directly between models and observations.

The cloud microphysical property we evaluate in this study is Nd. Nd is key variable of state (or most important variable) in controlling ACI . Changes in Nd also alter cloud macrophysical properties .

The cloud macrophysical property we evaluate is liquid condensate mass. It provides a diagnostic of the liquid cloud adjustment to aerosol-induced changes in cloud microphysics . In practice, liquid condensate mass is usually observed as column-integrated liquid water from remote sensing observations, which is known as liquid water path (LWP).

Nd and LWP have been shown to be very important variables in understanding the physical processes related to ACI . While aerosol-driven changes in cloud microphysics and macrophysics are essential to ACI, they do not capture the full complexity of ACI processes. Precipitation drives coalescence-scavenging and depletes Nd . Precipitation also serves as a proxy for moisture convergence and contains information about the large-scale environment, which in turn affects LWP . To evaluate how these variables are represented in GiOcean, we compare AOD, Nd, LWP, and precipitation rate from the GiOcean reanalysis with satellite observations, as detailed in Sect. .

In this study, we calculate two key sensitivity metrics. The sensitivity metric follows previous studies examining ACI , as a way of evaluating the ACI presentation in GiOcean against satellite observations. The sensitivity of Nd to CCN represents the inferred efficacy of aerosol activation into cloud droplets and is expressed in Eq. (). 1SNd-AOD=dln⁡Nddln⁡AOD

Similarly, to quantify the extent of cloud macrophysical adjustments (e.g., changes in LWP) in response to microphysical perturbations, the sensitivity of LWP to Nd is calculated using Eq. (). 2SLWP-Nd=dln⁡LWPdln⁡Nd We apply a consistent binning approach to compute these inferred sensitivities in both the GiOcean reanalysis and satellite observations. Monthly Nd is binned into 15 logarithmically spaced bins, and mean values of relevant variables (e.g., LWP, Nd, AOD) are calculated within each bin. Relationships between AOD and Nd, and between LWP and Nd, are then plotted using these bin-averaged values (Sect. ). Logarithmic derivatives are then estimated using finite differences between the binned means. A weighted average of these derivatives is calculated, with weights corresponding to the number of data points in each bin. The binning approach smooths out random noise by enforcing 15 logarithmically spaced Nd bins, so that each derivative estimate is based on hundreds or thousands of observations and the resulting slopes (e.g., ln⁡LWP versus ln⁡Nd) are statistically robust and representative.

By comparing these metrics across GiOcean and satellite observations, we evaluate the representation of both aerosol activation and aerosol-cloud adjustment in the GiOcean reanalysis. The results are discussed in Sect. . We note that these inferred sensitivities (calculated from Eqs.  and ) do not imply causation and may be strongly affected by other factors than microphysical relations . Therefore, we refer to these sensitivities as inferred sensitivities.

Nd and LWP are two key variables that influence ACI . The sensitivity metrics introduced in Sect.  follow previous studies examining ACI . In this section, we introduce a source-sink budget framework to better understand the source of disagreement between GiOcean and satellite observations in terms of these quantities (whether the differences arise from aerosol effects on cloud properties or from variations in the large-scale environment). In this approach, we analyze the budget of Nd and LWP as a function of competing processes that supply or remove cloud-relevant quantities.

The steady-state Nd results from a balance between sources due to the activation of CCN into cloud droplets from free tropospheric sources, and sinks from removal by precipitation scavenging . In , a steady-state budget model was applied to airborne observations to explain spatial variations in Nd. Their study demonstrated that the offshore gradient of Nd near the coast of Peru was primarily driven by increasing precipitation sinks, rather than decreasing CCN sources. Here we characterize Nd in terms of precipitation rate and AOD, which is slightly different from , who used precipitation rates estimated from radar reflectivity and airborne in-situ CCN measurements. While these terms are imperfect analogs to CCN near cloud and coalescence-scavenging in cloud, they allow us to compare GiOcean to spaceborne observations of these quantities. The results are discussed in Sect. 

The simple source-sink framework of LWP provides a conceptual basis for interpreting how cloud liquid water (i.e., LWP) changes as the result of interacting processes: (1) adjustment of liquid cloud to changes in Nd (i.e., aerosol-cloud adjustment); (2) environmental influence on liquid cloud through the large-scale circulation and the pattern of sea surface temperature. We use Nd as a source term of LWP because Nd is a key determinant of LWP adjustment to aerosol-driven changes in microphysics , and we use precipitation rate as a sink for LWP. This approach follows previous work examining extratropical ACI in the context of the precipitation rate imposed by the large-scale moisture convergence . It is important to note that both precipitation rate and Nd serve as indirect indicators of the sink and source terms in the LWP budget. They do not directly determine increases or decreases in LWP, but instead reflect underlying processes that influence it (through large-scale moisture convergence and aerosol-cloud adjustment). This allows us to examine how cloud water responds to the interplay between aerosol-cloud adjustment (via Nd) and large-scale moisture convergence (via precipitation rate). The results are discussed in Sect. 

We apply the source and sink framework to examine the drivers of interannual variability in Nd and LWP. This differs from , who used the same framework to evaluate the drivers of spatial variation in Nd. To do so, we build random forest (RF) models of Nd and LWP using regionally averaged monthly data, with their source and sink variables as their predictors.

Sensitivity tests are conducted on the RF models for Nd and LWP. Specifically, we create three predictor scenarios: (1) the source variable is held constant at its multi-year mean, (2) the sink variable is held constant, and (3) both source and sink vary as in the original time series. Scenarios (1) and (2) are used to evaluate the contribution of each driver and to assess whether the framework can reproduce the interannual variability by setting either their sink or source a constant. We show that source-sink framework allows for the assessment of the sensitivity of key ACI variables (e.g., Nd and LWP) to their sinks and sources in GiOcean, in comparison to satellite-based observations (Sect. ).

In this work, observations of aerosol optical depth (AOD) for the period of 2003–2015 are taken from a passive imaging radiometer – the Moderate Resolution Imaging Spectroradiometer Collection 6 (MODIS C6), retrieved at 550 nm on the Aqua (01:30 p.m. local solar Equatorial crossing time) platform (https://ladsweb.modaps.eosdis.nasa.gov/search/order/1/MYD08_M3--61, last access: 6 November 2025). AOD is not a direct analog for the amount of aerosol that is relevant to the budget of cloud condensation nuclei available to liquid clouds because it includes all aerosol particles and does not directly characterize size distribution and chemical composition and is column-integrated. However, it does provide a dimensionless measure of the column-integrated extinction of solar radiation by aerosols, which is related to the total column loading of aerosols. AOD can be compared relatively directly between GiOcean reanalysis and observations from spaceborne remote sensing.

Observations of cloud droplet number concentration (Nd) are derived from cloud optical thickness (τc) and cloud effective radius (re) retrievals from MODIS C6 for the period of 2003–2015 based on adiabatic cloud assumptions . τc and re are simultaneously retrieved by a bispectral algorithm that relies on the cloud reflectance measured from both a non-absorbing visible wavelength and an absorbing shortwave infrared wavelength . MODIS Nd has been shown to be unbiased relative to in-situ measurements from aircraft and provides nearly global coverage of observations . However, there are several potential sources of uncertainty that affect the Nd calculated from this method including high sun-angle , cloud heterogeneity , and contamination by upper level cloud and aerosol .

GiOcean generates 3-hourly global, grid-averaged Nd fields across 27 vertical levels for stratiform and convective clouds. These model-derived fields are not directly comparable to MODIS as the retrievals rely on simplified assumptions such as adiabatic cloud structure, vertical homogeneity, and the presence of high cloud fraction, which are not inherent in GiOcean. To carry out a consistent comparison, we leverage the MODIS COSP (CFMIP Observation Simulator Package) satellite simulator implemented in the GEOS model . This tool emulates MODIS retrieved cloud fields like effective radius and cloud optical depth using model-generated fields, and allows us to apply the same methodology and assumptions described in but using the GiOcean COSP output. Consistently, we apply the same filtering criteria used in the MODIS Nd retrieval algorithm to compute GiOcean Nd. These include:

Only pixels with at least 80 % identified as liquid-phase clouds are used, as a high cloud fraction minimizes retrieval biases from broken clouds due to enhanced scattering at cloud edges .

In this study, we use observations of liquid water path (LWP) from the Multi-Sensor Advanced Climatology of Liquid Water Path (MAC-LWP) for the period 2003–2015 . MAC-LWP is an updated version of the University of Wisconsin (UWisc) cloud LWP (CLWP) climatology . Oceanic monthly-mean MAC-LWP at 1° spatial resolution is constructed from 7 sources of satellite microwave data sampling different parts of the diurnal cycle at 0.25° spatial resolution. One of the major updates to UWisc LWP is that the MAC-LWP bias was corrected by matchups to clear-sky scenes from MODIS. In this way, whenever MODIS observes a clear-sky scene but the microwave retrieval still reports a non-zero cloud LWP, MAC-LWP is set to zero. Because it is difficult to differentiate cloudwater from rainwater using passive microwave signal from cloudwater, uncertainty in MAC-LWP is usually larger in heavy-precipitating regions . MAC-LWP represents grid-box-averaged LWP, making it directly comparable to the native LWP output from GiOcean.

Observations of precipitation rate are taken from the Integrated Multi-satellitE Retrievals for Global Precipitation Mission (IMERG) . IMERG is a merged precipitation product that contains information from passive microwave precipitation estimates, microwave-calibrated infrared (IR) satellite estimates, gauge analyses, and other estimators via intercalibrating, merging, and interpolating the sources of precipitation estimates. IMERG provides precipitation data with global coverage spanning the entire Tropical Rainfall Measuring Mission (TRMM) and the Global Precipitation Measurement (GPM) mission record. In this study, we used IMERG version 07 (V07) final run daily data for the period of 2003–2015 for analysis .

Having characterized the spatial patterns of aerosols, cloud properties, and precipitation, we now examine their temporal variability. Our analysis focuses on the North American and East Asian outflow regions, as indicated by the rectangular boxes in Fig. , because these regions are major sources of anthropogenic aerosol emissions and are known to strongly influence downwind cloud properties . These two regions also show contrasting sensitivity of re to Nd (Fig. ). We examine the seasonal and decadal variability in each region.

Seasonal variability in AOD shows strong agreement between GiOcean and MODIS, with correlation coefficients (r) near 1 in both the East Asian and North American outflow regions (Fig. a, b). Peak AOD occurs during boreal spring in the East Asian outflow and during boreal summer in the North American outflow. This is expected as AOD is assimilated in GiOcean.

In the East Asian outflow, Nd from GiOcean exhibits a pronounced seasonal cycle with a peak during winter and a minimum in summer (Fig. c: pink). This pattern is likely driven by increased precipitation between June and September, peaking around August, possibly enhanced by the summer monsoon as indicated by the precipitation seasonal cycle (Fig. g: pink). Enhanced wet scavenging during this period reduces both aerosol concentrations and droplet number (Fig. a, c: pink). However, this effect may be confounded by increased biomass burning emissions during the same period . Interestingly, this strong seasonal signal in Nd is not evident in the MODIS retrieval over the East Asian outflow region (Fig. c: gray and orange), although notable discrepancies exist among different Nd datasets, with the data from showing a somewhat stronger seasonal cycle than the data from , though still weaker than in GiOcean.

In contrast, the North American outflow region displays a weaker seasonal cycle in Nd in GiOcean, with lower values during summer, and better consistency between GiOcean COSP Nd and the observational datasets, yet with significant differences in absolute value (Fig. d). The consistency in seasonal trends across datasets suggests that GiOcean and satellite observations capture similar seasonal signals. However, differences in absolute Nd values may partly reflect the spread across satellite retrieval algorithms, referred to as the retrieval bundle, which represents a form of systematic observational uncertainty .

Overall, we found larger discrepancies in the seasonal cycle of Nd over the East Asian outflow region (Fig. c) compared to the North American outflow, which may be due to active convection, which complicates the retrieval and modeling of Nd. Reanalysis products often exhibit greater biases in simulating Asian meteorology, and the assumptions underlying MODIS retrievals may break down under these meteorological conditions. As a result the disagreement in Nd seasonal cycle is higher over East Asian outflow than over the North American outflow.

The seasonal cycles of GiOcean and MAC-LWP both exhibit peak LWP in winter in the East Asian and North American outflow regions (Fig. e, f), but substantial differences in the overall seasonal patterns and magnitude remain. The GiOcean and MAC-LWP show a better agreement during winter in the East Asian outflow region, which might be due to the relatively accurate MAC-LWP estimates during winter over the study regions . However, correlation between MAC-LWP and GiOcean is weakly negative in East Asian outflow region (Fig. e). In the North American outflow region, the seasonal variability of LWP is mostly captured by GiOcean, with a correlation of r=0.76 compared to satellite observations (MAC-LWP) (Fig. f).

Seasonal variability in precipitation rate in GiOcean matches IMERG in both the East Asian and North American outflow regions, with differences statistically indistinguishable at the 95 % confidence level across all months (Fig. g, h). There is a high correlation of r=0.99 between GiOcean and IMERG in the East Asian outflow, where a strong seasonal cycle exists (Fig. g). In the North American outflow where the seasonal cycle is weaker the agreement is also good, with a correlation of r=0.83 (Fig. h). Although GiOcean slightly underestimates the amplitude of seasonal variation, it reproduces the broad features of the cycle, including a minimum in late spring and a gradual increase in precipitation from summer into fall. The high correlation between GiOcean and observed precipitation rates in the East Asia outflow (Fig. g) is consistent with the fact that GiOcean is constrained by SST fields from the GEOS-IT reanalysis. SST strongly influences moisture convergence through its impact on large-scale atmospheric circulation, and therefore plays a key role in shaping seasonal precipitation patterns .

The decadal trend in aerosol and cloud properties is a useful proxy for understanding the radiative forcing from ACI . The monthly time series of AOD, Nd, LWP and precipitation rate are shown in Fig. .

Both GiOcean and satellite observations show an overall downward trend in AOD, along with good agreement in the monthly anomaly time series across the two focus regions (Fig. a, b). This is consistent with trends in sulfur dioxide emissions in these regions driven by emissions control measures in the East Asian and North American outflow regions .

Generally MODIS and GiOcean broadly agree with the trend in Nd with a downward trend through the observational period in the North American outflow (Fig. d), suggesting that the observed decadal trend in Nd may be related to aerosol affecting cloud microphysical properties in that region. The downward trend in Nd in the North American outflow is also consistent with previous evaluation of trends in Nd . During the period with concurrent observational data over the East Asian outflow, MODIS Nd from and shows a downward trend while GiOcean COSP Nd is relatively flat (Fig. c). This may result from the disproportionate influence of convection over the region which tends to introduce uncertainty in both the retrieval and the reanalysis.

The monthly anomaly time series in LWP are consistent between MAC-LWP and GiOcean in the East Asian and North American outflows, with correlation coefficients close to 0.8 in both regions and no clear overall upward or downward trends during the study period (Fig. e, f). GiOcean has the microphysics scheme necessary to produce precipitation suppression and this may lead to the covariation of LWP and Nd from 2003 to 2015 in the East Asian outflow region, where increases in Nd are consistently accompanied by increases in LWP in GiOcean, and vice versa (Fig. c,e: pink, Fig. S1 in the Supplement). It must also be noticed that the response of LWP is not entirely driven by cloud microphysical processes in GiOcean. Large-scale moisture convergence, which is influenced by SST and large-scale atmospheric circulation , also plays a key role. The base model of GiOcean is constrained by SST and a moisture analysis increment is applied every six hours to correct the state of the model. The consistency in the monthly time series between observed LWP and GiOcean LWP suggests that GiOcean has the ability to represent both the moisture supply and the cloud response to Nd that are necessary to reproduce LWP interannual variability.

In keeping with the seasonal cycle, the monthly precipitation anomaly time series from GiOcean and IMERG are in good agreement and exhibit concurrent variation with LWP anomalies in GiOcean and observations across both regions during the study period. While consistent, there isn't a particularly strong overall trend in precipitation in either study region (Fig. g, h). Given the overall magnitude of the precipitation rate in these regions (Fig. h), this points to a fairly large interannual variability in the precipitation flux demand by the atmosphere that makes it difficult to disentangle the role of meteorology, data assimilation, aerosol, and precipitation-related scavenging in driving changes in cloud properties (i.e. Nd and LWP) . In the following section we attempt to evaluate the representation of ACI in GiOcean against satellite observations.

AOD is commonly used in satellite-based studies and model evaluations of how aerosols alter cloud microphysical properties, despite its known limitations as a proxy for cloud condensation nuclei (CCN) .

We found a positive inferred sensitivity of Nd to AOD in the East Asian outflow region in both the GiOcean reanalysis and satellite observations (Fig. : circles), indicating that increases in AOD are associated with increases in Nd. This is consistent with the aerosol indirect effect where increased aerosol enhances cloud droplet activation . The stronger inferred sensitivity in GiOcean (S=0.96: pink circles in Fig. a) compared to observations (S=0.64: gray circles) suggests that cloud droplet formation in the model responds more strongly to changes in AOD in GiOcean over East Asian outflow. However, this stronger slope does not imply that GiOcean has a stronger aerosol–cloud microphysical response at a given AOD. In fact, despite the higher inferred sensitivity, the absolute Nd in GiOcean is lower than in MODIS for the same AOD (Fig. a). This may suggest that GiOcean overestimates the relative response of Nd to aerosol changes, but underestimates the overall efficiency of aerosol activation into cloud droplets.

Similarly, we examined the inferred sensitivity of Nd to AOD in the North American outflow region (Fig. : triangles). The inferred sensitivity is slightly positive (S=0.22: pink triangles in Fig. ) in GiOcean, while near zero in observations (gray triangles in Fig. ). The low sensitivity of Nd to AOD over the North American outflow is primarily due to sampling. In GiOcean, COSP-derived Nd is sampled following the cloud-filtering criteria of to match the sampling of MODIS Nd. When cloud base Nd is used, or when COSP-derived Nd is recalculated without filtering, a strong positive sensitivity of Nd to AOD becomes apparent (Fig. S2). This indicates that the low sensitivity of Nd to AOD is inherent to the Nd sampling strategy over the North American outflow, rather than a result of GiOcean being unable to represent aerosol–cloud microphysical responses. We also note that the analysis of the inferred sensitivity of Nd to AOD does not account for the role of meteorological factors in driving the sensitivity terms. Precipitation scavenges aerosol and cloud droplets, potentially dampening the signal of changes in cloud properties induced by aerosol perturbation. We will discuss the role of precipitation in the Sect. .

In addition to changes in cloud microphysics, changes in Nd can also change macrophysical cloud properties. The inferred sensitivity of LWP to Nd is characterized using Eq. (). In observation, there is a very low inferred sensitivity of LWP to Nd in both regions (S = 0.02–0.06) (Fig. b: gray shapes). Instead, GiOcean shows stronger response in LWP with Nd than observed in both regions (Fig. b: pink). In East Aisan outflow, GiOcean shows monotonic increase in LWP with Nd (Fig. b: pink circles). In the North American outflow region LWP first increases with Nd in the low Nd regime and and then decrease with Nd in the high Nd regime (Fig. : pink triangles). This is consistent with the theoretical evidence of competing precipitation suppression and entrainment effects on liquid cloud adjustment . However, interpreting the relationship between Nd and LWP is complicated by coalescence-scavenging from precipitation . Precipitation is a strong sink of Nd in marine low clouds , and depletes aerosol at cloud base . The amount of liquid water in clouds (i.e., LWP) also depends on how much rain the clouds produce, which is strongly controlled by environmental factors such as large-scale atmospheric circulation and sea surface temperature patterns.

To illustrate the importance of precipitation in the context of aerosol affecting cloud microphysical properties (Eq. ) and liquid cloud adjustment induced by changes in Nd (Eq. ), we interpret the budget of Nd and LWP using a sink-source perspective in Sect. .

To visualize the response of Nd to AOD or precipitation rate we formulated the source-sink budget of Nd as two-dimensional lookup tables using monthly datasets at each grid point over the study regions. The lookup table is constructed by dividing monthly AOD and precipitation rate into 50 × 50 two-dimensional bins and bin averages are calculated within each bin. This allows us to examine how Nd responds across varying combinations of AOD and precipitation. We note that because the lookup tables are constructed using monthly data across all grid points, the Nd–AOD–precipitation relationships reflect a combination of spatial and temporal variability. Due to the large range and log-normal distributions of precipitation rate and AOD we use logarithmic bins. The dependence of Nd on AOD and precipitation rate for each outflow region and for GiOcean and observations is visualized in the lookup tables in Fig. .

By analyzing the marginal distribution of Nd across AOD while holding precipitation rate fixed, we assess how aerosol alters cloud properties. Conversely, examining Nd across precipitation rate while holding AOD fixed provides insight into how precipitation controlled by large-scale environment modulates Nd through wet scavenging.

Overall, the ranges of precipitation rate and AOD in GiOcean match those from satellite observations in the outflow regions of both East Asia and North America, as well as over the broader Northern Hemisphere (Fig. ). In East Asia, the range of precipitation rate and AOD spans nearly two orders of magnitude in both GiOcean and observations (Fig. a, d), whereas in North America, it covers only one.

In the North American outflow, the pattern of Nd as a function of AOD and precipitation rate is not clear for either GiOcean or observations (Fig. b, e). This might be because the sampling of Nd following , which can obscure the sensitivity of Nd to AOD and precipitation in this region. In contrast, a clearer relationship emerges in the outflow region of East Asia and over the Northern Hemisphere ocean (first and third columns of Fig. ).

In the East Asian outflow region (first column of Fig. ), GiOcean Nd increases with AOD at fixed precipitation rates (Fig. a), indicating a microphysical response of Nd to aerosol loading at fixed coalescence-scavenging. Similarly, when AOD is held approximately constant within its range, Nd decreases with increasing precipitation (high Nd is associated with low precipitation rate). This pattern suggests that the Nd budget in GiOcean reflects a combination of a source driven by effective CCN and a sink associated with wet scavenging (via precipitation), which is modulated by environmental conditions. We use the same methodology to analyze the Nd pattern in satellite observations (Fig. c). Similar to GiOcean, satellite data shows an increase in Nd with increasing AOD at fixed precipitation rates, indicating a consistent aerosol–cloud microphysical relationship. However, unlike GiOcean, we find a much weaker covariance between precipitation rate and Nd when AOD is held constant, particularly at low AOD concentrations. This might suggest that, in the observational data, the precipitation sink of Nd via wet scavenging is either less pronounced or obscured by retrieval uncertainties or other confounding factors such as satellite sampling biases, differences in vertical overlap between precipitation and aerosol layers, or cloud regime heterogeneity . The more pronounced link between Nd and precipitation rate in GiOcean might also indicate that the precipitation dependence of Nd may be amplified by the representation of coalescence scavenging in GiOcean.

Extending the compositing analysis using lookup tables to the NH ocean (third column of Fig. ), the relationship between Nd and precipitation rate becomes weaker. This weakened link is consistent in both GiOcean and satellite data (Fig. c, f).

Overall, the dependence of Nd on AOD and precipitation rate inferred from the compositing in Fig.  is consistent with prior expectations based on . Increasing AOD corresponds to an increase in CCN-relevant aerosol and an increasing in Nd. This behavior is consistently captured in both GiOcean and satellite observations across regional and broader Northern Hemisphere analyses (Fig. a, d, c, f). Increasing precipitation removes cloud droplets through coalescence scavenging, leading to a decrease in Nd with increasing precipitation rate. This pattern is more clearly represented in GiOcean over heavily polluted regions such as East Asian outflow (Fig. a), but is less pronounced in satellite observations over the same area (Fig. d). The weak link between precipitation and Nd is also seen in both GiOcean and satellite data over the broader NH ocean (Fig. c, f). Taken together, this suggests that precipitation scavenging of Nd may be overestimated in heavily polluted regions in GiOcean.

The interpretation of the LWP lookup tables follows the same logic as that of the compositing analysis using Nd lookup tables discussed earlier in Sect. . We assess how liquid clouds adjust to changes in Nd by analyzing variations in LWP across Nd bins while holding precipitation rate constant. Conversely, we evaluate how large-scale moisture convergence influences liquid cloud amount (i.e., LWP) by examining LWP across precipitation bins while holding Nd constant (Fig. ). Furthermore, by comparing the relative sensitivity of LWP to changes in Nd and precipitation, we can assess how liquid cloud adjustment responds to aerosol and environmental controls in both GiOcean (Fig. a, b) and satellite observations (Fig. c, d).

The dependence of LWP on Nd and precipitation rate is consistent with a priori expectations. In all study regions, and in both observations and GiOcean, LWP increases with precipitation rate when Nd is held constant (Fig. ), consistent with the interpretation that greater large-scale moisture convergence leads to increased cloud water content, assuming precipitation efficiency remains approximately unchanged (via fixed Nd). This suggests that higher precipitation rates reflect not only enhanced removal of cloud water, but also stronger moisture supply to the cloud layer.

The patterns of inferred liquid cloud adjustment shows varying degree of agreement between GiOcean and satellite observations over different study regimes (Fig. ). In the North American outflow region, both GiOcean (Fig. b) and satellite observations (Fig. e) indicate a weak liquid cloud adjustment to Nd (weak variation in LWP with Nd at fixed precipitation rate). This consistency suggests that GiOcean realistically captures the weak liquid cloud adjustment in this region.

In the East Asian outflow, GiOcean reanalysis shows that LWP increases with higher Nd when precipitation rate is held constant (Fig. a). This pattern is consistent with the suppression of precipitation: at higher Nd, more LWP is needed to maintain the same precipitation rate due to reduced collision–coalescence efficiency. However, the liquid cloud adjustment through precipitation suppression is less pronounced in satellite observations over the East Asian outflow region (Fig. d). This may reflect limitations in satellite retrievals, such as uncertainties in Nd under multilayer cloud conditions or partial cloud cover , and uncertainty in LWP under heavy-precipitating regions . Additionally, satellite observations represent instantaneous snapshots, which may not fully capture the temporal evolution of cloud water accumulation in response to aerosol loading. This may also indicate that the effects of precipitation suppression may be overestimated in GiOcean compared with what occurs in reality in the East Asian outflow region.

The NH ocean pattern is similar with that in the outflow of East Asia in GiOcean: LWP increases with Nd at fixed precipitation rate, indicating suppressed precipitation and accumulation of liquid water. This positive Nd–LWP relationship is especially pronounced at high precipitation rates (Fig. c). In contrast, satellite observations show a negative Nd–LWP relationship when precipitation rate is fixed, particularly at low precipitation rates. This negative Nd–LWP correlation is found across satellite retrieval methods . This suggests that the contrast with GiOcean likely reflects model biases in representing cloud microphysics, rather than retrieval artifacts alone.

Figure  shows the decadal predictions of Nd from RF models trained for GiOcean and satellite observations under the full-predictor (gray lines), fixed-sink (green lines), and fixed-source (pink lines) scenarios, as well as the comparison to the original datasets (black dashed lines). The performance of these sensitivity experiments is evaluated based on how well they reproduce the original temporal patterns of Nd by calculating the correlation (r) between the time series from sensitivity experiments with that of the original datasets as indicated by the r values in the legend. The RF model trained on the full-predictor experiments (Fig. a, b: gray line) successfully reproduces the decadal trends in Nd and LWP from the original datasets (Fig. a, b: black dashed line) with r-values close to 1. This agreement provides confidence in using the RF model for sensitivity tests that isolate the influence of individual source and sink terms. We examine each region of interest one by one.

In the East Asian outflow region, Nd prediction from fixed-sink (precipitation) and fixed-source (AOD) experiments in GiOcean reproduces the decadal variability of Nd with r values of 0.55 and 0.74 (Fig. a). This indicates that Nd interannual variability is driven by both aerosol affecting cloud microphysics (source) and wet scavenging via precipitation (sink) in this region in GiOcean. The dependence of temporal variability in Nd is consistent with the lookup table analysis in Fig. a which shows the spatial and temporal variability in Nd is driven by both sinks and sources. The fixed-source (AOD) experiment has a greater capacity of recreating Nd decadal trend than fixed-sink (precipitation) case with r values of 0.74 and 0.55, implying the majority of Nd temporal variability is driven by variation in the sink term by removal of Nd through precipitation-scavenging in GiOcean (Fig. a). In the satellite observations, the sink also appears to play a greater role in influencing the Nd decadal variability. However, the overall sensitivity to both source and sink is weaker than in GiOcean, as reflected by the lower correlation values in Fig. b compared to a.

In the North American outflow region, GiOcean and satellite observations show contrasting roles of source and sink in driving the Nd decadal variability. In GiOcean, precipitation (the sink) plays a greater role than aerosols (represented by AOD), whereas in satellite observations, AOD is more influential (Fig. c, d).

Extending the sensitivity analysis to NH ocean, we find a similar result to that in the East Asian outflow region: setting source a constant while letting precipitation rate varies with time largely reproduces the decadal trend in Nd, implying precipitation (sink) plays a greater role than aerosols (source) in driving Nd interannual variability, and this pattern is consistent between GiOcean and satellite observations (Fig. e, f).

The decadal prediction of LWP from GiOcean and satellite observations based on the full-predictor, fixed-sink, and fixed-source cases using RF models is shown in Fig. . We evaluate the interannual variability of LWP in both GiOcean and satellite observations by comparing the fixed-source and fixed-sink predictions to their respective original LWP monthly time series. In GiOcean, the correlation between the original LWP time series and the fixed-source experiment (Fig. : pink lines) is higher than that of the fixed-sink experiment (Fig. : green lines), indicating that LWP temporal variability can be largely reproduced without accounting for changes in source (Nd). This highlights the dominant role of precipitation in controlling LWP variability. This precipitation-driven pattern in LWP temporal variability is consistently found in both GiOcean and satellite datasets across all three regions (Fig. ), which reflects the importance of large-scale environment on temporal variations in liquid cloud amount. A similar precipitation-driven signal also emerges from the joint analysis of spatial and temporal variability in LWP and is consistent between GiOcean and observations (Fig. ).

An interesting feature in Fig. e is that the RF model sensitivity test, which holds regionally averaged precipitation constant, shows an anticorrelation between Nd and LWP. This contrasts with the lookup table result, which shows a positive Nd–LWP relationship at fixed precipitation rate at each grid points (Fig. a). The difference likely reflects the effect of spatial averaging in the RF analysis, which may smooth out subregional variations and obscure the co-variability captured at the grid scale (∼ 100 km) in the lookup table.