Upstream Large-Scale Control of Subtropical Low-Cloud Climatology

Hamish Lewis aDepartment of Physics, University of Auckland, Auckland, New Zealand

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Gilles Bellon aDepartment of Physics, University of Auckland, Auckland, New Zealand
bCentre National de Recherches Météorologiques, Université de Toulouse, Météo France, CNRS, Toulouse, France

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Tra Dinh aDepartment of Physics, University of Auckland, Auckland, New Zealand

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Abstract

This study investigates the impact of the adjustment times of the atmospheric boundary layer (ABL) on the control of low-cloud coverage (LCC) climatology by large-scale atmospheric conditions in the subtropics. Using monthly data, we calculate back-trajectories and use machine learning statistical models with feature selection capabilities to determine the influence of local and upstream large-scale conditions on LCC for four physical cloud regimes: the stratocumulus (Sc) deck, the along-flow transition into the Sc deck (“Inflow”), the Sc-to-cumulus transition, and trade-cumulus clouds. All four regimes have unique local and upstream relationships with the large-scale meteorological variables within our parameter space, with upstream controls of LCC being the dominant processes in Sc deck and Sc-to-cumulus transition regimes. The time scales associated with these upstream controls across all regimes are consistent with known adjustment time scales of the ABL, determined in both modeling and observational studies. We find that low-level thermodynamic stratification (estimated inversion strength) is not the most important large-scale variable for LCC prediction in transition and trade-cumulus regimes despite its ubiquitous use as a proxy for LCC throughout the subtropics. Including upstream control provides significant improvements to the skill of statistical models predicting monthly LCC, increasing explained variance on the order of 15% in the Inflow, Sc deck, and transition regimes, but provides no improvement in the trade-cumulus regime.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Hamish Lewis, hamish.lewis@auckland.ac.nz

Abstract

This study investigates the impact of the adjustment times of the atmospheric boundary layer (ABL) on the control of low-cloud coverage (LCC) climatology by large-scale atmospheric conditions in the subtropics. Using monthly data, we calculate back-trajectories and use machine learning statistical models with feature selection capabilities to determine the influence of local and upstream large-scale conditions on LCC for four physical cloud regimes: the stratocumulus (Sc) deck, the along-flow transition into the Sc deck (“Inflow”), the Sc-to-cumulus transition, and trade-cumulus clouds. All four regimes have unique local and upstream relationships with the large-scale meteorological variables within our parameter space, with upstream controls of LCC being the dominant processes in Sc deck and Sc-to-cumulus transition regimes. The time scales associated with these upstream controls across all regimes are consistent with known adjustment time scales of the ABL, determined in both modeling and observational studies. We find that low-level thermodynamic stratification (estimated inversion strength) is not the most important large-scale variable for LCC prediction in transition and trade-cumulus regimes despite its ubiquitous use as a proxy for LCC throughout the subtropics. Including upstream control provides significant improvements to the skill of statistical models predicting monthly LCC, increasing explained variance on the order of 15% in the Inflow, Sc deck, and transition regimes, but provides no improvement in the trade-cumulus regime.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Hamish Lewis, hamish.lewis@auckland.ac.nz

1. Introduction

The large areas of marine stratocumulus (Sc) located in the eastern subtropical basins of Earth’s oceans (Fig. 1a) cool the climate significantly. Characterized by turbulent motions on scales significantly smaller than the typical resolution in general circulation models (GCMs), low-clouds must be parameterized using large-scale thermodynamic and dynamic variables in these models. These parameterizations struggle to simulate the spatial low-cloud cover (LCC) correctly in Sc regions, generally producing too few clouds, which are excessively bright to compensate (Nam et al. 2012; Klein et al. 2013; Cesana and Waliser 2016; Konsta et al. 2022). GCM estimates of low-cloud response to warming generally predict a positive radiative feedback in the subtropics associated with reduced LCC, with the strength of this feedback varying greatly across models within the Coupled Model Intercomparison Project (CMIP) ensembles (Bony and Dufresne 2005; Vial et al. 2013; Myers and Norris 2016; Zelinka et al. 2020; Myers et al. 2021). Consequently, improving our understanding of cloud controls will provide new ways to evaluate GCM parameterizations and to improve them.

Fig. 1.
Fig. 1.

(a) The global distribution of clouds and regions of interest in this study. (b)–(f) The four physical cloud regimes: Inflow “In,” Sc deck “Sc,” Transition “Trans,” and Trade-Cu “Trade” in (b) the Californian region, (c) the Canarian region, (d) the Australian region, (e) the Peruvian region, and (f) the Namibian region. In (e), the Trade-Cu regime centered at 3.5°S, 136.5°W is not shown. The colors indicate the climatologically averaged LCC obtained from MODIS monthly mean data, and the vectors indicate the climatological mean wind from ERA5 monthly mean data at the 925 hPa level.

Citation: Journal of Climate 36, 10; 10.1175/JCLI-D-22-0676.1

Low clouds are strongly coupled to the turbulent processes in the atmospheric boundary layer (ABL). Large-scale meteorological conditions influence these processes, and can consequently control a large part of the LCC variability. Past studies have identified the main large-scale variables impacting the LCC: Lower-tropospheric stratification, sea surface temperature (SST), free-tropospheric subsidence and humidity, and ABL wind speed (Klein et al. 2017). Sc clouds generally occupy the upper few hundred meters of the ABL, being favored in statically stable lower-tropospheric conditions (Klein and Hartmann 1993). Their increased vertical extent is inhibited by an abrupt temperature inversion only tens of meters thick, which strongly limits the mixing of dry free-tropospheric air into the ABL. The magnitude of this temperature inversion can be quantified using the estimated inversion strength (EIS), which is a strong predictor of LCC (Wood and Bretherton 2006). In Sc-topped ABLs, negatively buoyant air parcels produced at the cloud top through radiative cooling sink to the surface, driving the turbulent overturning circulation, which homogenizes the ABL and mixes the cloud layer with the subcloud layer (Lilly 1968; Nicholls 1984; Bellon and Geoffroy 2016a). Mixing is also enhanced by the turbulent surface heat fluxes, which warm and moisten the subcloud layer, creating positively buoyant parcels, which then ascend. The SST strongly influences these surface heat fluxes, and SST is consequently a good predictor of LCC as well (Oreopoulos and Davies 1993), even independently of its contribution via the EIS (Myers and Norris 2016). As Sc are advected equatorward, increased turbulent surface heat fluxes from increasing SST provides additional buoyancy, which enhances turbulent mixing, deepening the ABL, creating cumulus (Cu) updrafts under the Sc and thickening the clouds, resulting in increased LCC on short time scales (Moeng et al. 1992). Eventually the ABL becomes too deep for the negatively buoyant cloud-top parcels to reach the surface and the cloud layer becomes decoupled from the underlying moist surface layer (Bretherton and Wyant 1997). The Sc clouds that are separated from their surface moisture source eventually break up, and the underlying Cu clouds remain; this Sc-to-Cu transition reduces the LCC. Enhanced free-tropospheric subsidence (taken at 700 hPa; ω700), suppresses the growth of the boundary layer, and has been shown to be favorable for the formation of shallow and well-mixed boundary layers (Zhang et al. 2009). Free-tropospheric relative humidity (taken at 700 hPa; RH700), can strongly impact the moisture content of the boundary layer when free-tropospheric air is entrained at the cloud top, potentially thinning the clouds, and once entrained can cause further entrainment through buoyancy feedback processes (van der Dussen et al. 2015). The magnitude of the ABL wind contributes to the turbulent kinetic energy budget of the ABL by invigorating surface turbulent buoyancy fluxes, and shear production, which enhances the LCC (Brueck et al. 2015). Here we use the wind taken at 925 hPa (UV925) level as it is a good representation of the homogeneous wind in the ABL, and is highly correlated to the near surface wind, which directly affects surface turbulent fluxes. The ABL wind is also known to deepen the ABL in trade-Cu regions, due to a transient response off the mass flux through increased surface latent heating (Nuijens and Stevens 2012). The deepening brings warm dry air to the surface, which increases latent heating, and reduces sensible heating, reducing the surface buoyancy flux, and damping the increase in the cloud base mass flux. Consequently, trade Cu are deeper, but not more numerous or energetic at stronger wind speeds. Off the coast of California, low-level winds are associated with large spatial cloud clearings of Sc, which cause strong gradients of LCC (Dadashazar et al. 2020). Similarly, atmospheric gravity waves are suggested to control cloud clearings off the coast of Namibia (Yuter et al. 2018). Non-meteorological factors that affect LCC but are not explored in this manuscript include aerosols: low clouds, which form along ABL trajectories with relatively high concentrations of anthropogenic aerosols, experience a delay in the breakup of Sc, and lead to higher cloud fractions in stable atmospheric conditions (Goren et al. 2019; Christensen et al. 2020). The presence of aerosols above the inversion can produce a more broken cloud field; however, following contact with the cloud layer and nighttime recovery they can delay the Sc-to-Cu transition (Yamaguchi et al. 2015).

Analysis of large-scale meteorological variables in GCM parameterizations and studies of the climate response of LCC to warming are limited so far to the local relationship between these variables and LCC (Zhai et al. 2015; Myers and Norris 2016; Brient and Schneider 2016; McCoy et al. 2017; Myers et al. 2021). On the other hand, it is now well known that the adjustment times of the ABL are significant, up to a couple of days. Large-eddy simulation studies performed by Bretherton et al. (2010a) and Bellon and Stevens (2013) identify time scales of 6–12 h for the adjustment of LCC with the thermodynamic conditions within the ABL (temperature and humidity), and a few days for ABL depth. Observational studies performed by Pincus et al. (1997) and Eastman and Wood (2016) find that LCC is best correlated with lower-tropospheric temperature stratification (LTS) 16 h prior and suggest that SST plays a continuous role in determining LCC, with increasing SST deepening the ABL and permitting increased LCC on short time scales (hours), but eventually leading to decoupling and transition to trade Cu on longer time scales (days). Mauger and Norris (2010) find similar results for thermodynamic variables, but in addition that LCC is negatively correlated with synoptic-scale divergence (which, by continuity, is related to ω700) 0–12 h prior, and positively correlated with free-tropospheric humidity and 0–36 h prior. Eastman and Wood (2018) observationally evaluate the competing effects of ABL stability and above-inversion humidity along Lagrangian trajectories. They find that upstream effects of stability (EIS) are only evident when taking humidity into account, and confirm that high stability is associated with increased LCC and smaller ABL depths. They also find that the ABL depth is more sensitive to the “radiative humidity” (the humidity that sits above the entrained humidity, which exerts longwave effects on the cloud top), while the cloud amount is more sensitive to the entrained humidity. Eastman et al. (2021) perform a Lagrangian analysis of clouds in observations and two climate models with the models showing stronger ABL deepening across the Sc-to-Cu transition than the observations. They also find inconsistent responses of LCC to wind speed, SST, and subsidence between the models and observations, highlighting deficiencies in the simulation of ABL processes controlling LCC, especially in their relationship to the surrounding meteorology.

We will call these relationships between LCC and these upstream large-scale meteorological variables “upstream control.” It is unknown how systematic the upstream control of subtropical LCC is across marine domains. Previous observational studies generally focus on clouds in the Sc deck, and transition regimes only. These studies also generally use a high temporal resolution (hours), leaving it unresolved whether upstream controls are prevalent on climatological time scales, when the control of these variables has been shown to be time scale dependent (de Szoeke et al. 2016). The relative importance of the local effects of large-scale meteorological variables compared to their upstream control has not been assessed. Clarifying these issues is the goal of this manuscript. We use data from back-trajectories and machine learning models with feature selection capabilities to investigate the robustness and significance of the upstream and local control of the LCC by large-scale meteorological variables across four subtropical marine cloud regimes: the “Inflow” region upstream of the Sc deck, the Sc deck, Sc-to-Cu transition, and trade-Cu regime.

This paper is organized as follows: in section 2a we introduce the observational and reanalysis datasets used in our analysis. In section 2b we discuss the selection of locations to sample four different physical regimes to investigate. In section 2c we discuss our methodology for back-trajectories, which sample large-scale meteorological variables upstream of each cloud regime. In section 2d we present our feature selection methods, their training, and interpretation. In section 3a we document the spatial correlation between LCC and large-scale meteorological variables. In section 3b we present and interpret the results of our feature selection models. In section 3c we show how the inclusion of upstream effects improves the statistical representation of LCC variability. In section 3d we use a test case of the 2013–15 marine heatwave in the northeast Pacific to determine the ability of our statistical models to extrapolate under climate change.

2. Data and methods

a. Data

In this study we use monthly mean fields to show that the delayed relationships between LCC and large-scale meteorological variables manifest themselves as upstream control in temporal averages, as well as showing the validity of these relationships on time scales relevant to climate. Here we provide an overview of the datasets for LCC and the large-scale meteorological variables.

1) MODIS

Moderate Resolution Imaging Spectroradiometer (MODIS) instruments ride on board both Aqua and Terra satellites (Platnick et al. 2003). We use monthly low-cloud fraction estimates for daytime scenes from the MCD06COSP product, which uses retrievals from both Aqua and Terra. This product is highly useful for future comparisons to climate models as it is used for the observation simulator in CFMIP studies. Low clouds are defined as those with cloud-top pressure greater than 680 hPa. We use the high-cloud fraction from the MCD06COSP product in the selection process of the cloud regimes used in this study. High clouds are defined as those with cloud top pressure less than 440 hPa. Here we use 17 full years of data, from 2003 to 2019.

2) ERA5

We use the European Centre for Medium-Range Weather Forecasts (ECMWF) fifth generation atmospheric reanalysis (ERA5; Hersbach et al. 2020), for our large-scale meteorological variables EIS, SST, RH700, ω700, and UV925. We obtain monthly fields for the years overlapping with the MODIS dataset. We calculate the EIS as described by Wood and Bretherton (2006), using surface temperature and humidity variables at 1000 hPa, and Romps (2017) expression for the lifting condensation level. We chose to use satellite estimates of LCC rather than ERA5 LCC as dependent variable in our analysis because cloud fraction is simulated by the reanalysis GCM. Even if observations are assimilated, the reanalysis LCC could present a modeling bias and a model-dependent relationship to large-scale meteorological variables.

b. Regime selection

To assess the impact of upstream control on low clouds in different meteorological conditions, we analyze four physical regimes of interest; these are upstream of the main Sc region (“Inflow”), where LCC is maximal (“Sc-deck”), where the transition to trade Cu occurs (“Transition”), and where trade Cu occur (“Trade-Cu”). Satellite images representative of each of these physical regimes can be seen in Fig. 2.

Fig. 2.
Fig. 2.

Representative satellite images from MODIS (Terra) of the four cloud regimes examined in this study. Each domain shown is approximately 5° × 5°. These images were obtained through https://worldview.earthdata.nasa.gov/.

Citation: Journal of Climate 36, 10; 10.1175/JCLI-D-22-0676.1

For each of these regimes we identify a 10° × 10° box (see Figs. 1b–f), which serves as the site where LCC is sampled and the initialized location of the semi-Lagrangian back-trajectories are started. Here, semi-Lagrangian refers to the fact that the back-trajectories are computed using the climatological wind fields rather than instantaneous winds. The physical regimes are identified in each of the eastern subtropical ocean basins, which we denote by the name of the land to their east: California, Peru, Namibia, Canary (Islands), and Australia. We first identify the box with the highest climatological-mean LCC as representative of the Sc-deck regime. From the center of this region a semi-Lagrangian back-trajectory is calculated using the climatological-mean wind at 925 hPa. The box along this back-trajectory with the highest positive rate of change of LCC (LCC/t) is selected as representative of the transition into the Sc deck, that we call “Inflow” regime (This regime has not been investigated thoroughly in the past, with most work focusing on the Sc-to-trade-Cu evolution). This regime is generally very closely situated to the coast, so the gradient of LCC sampled may be a product of both low-cloud formation, and dissipation due to coastal processes. The Sc-deck (and thus Inflow) regime is shifted northward in the Canarian region, as back-trajectories initialized from the area of maximal climatological LCC frequently advect over the Sahara, shrinking the pool of available data (see Fig. 1c). It is not possible to define an Inflow regime for the Australian region, because the Sc-deck regime sits northward of a midlatitude LCC maximum (see Fig. 1d) and there is no clear location with a large rate of change of LCC. Consequently, analysis performed on the Inflow regime does not include Australian data. The Transition regime is represented by the box with the highest spatial rate of decrease of LCC (LCC/t) along boundary layer winds exiting the Sc-deck regime, with the condition that MODIS climatological high-cloud coverage within the box is below 0.4, to avoid sampling an area where deep convection occurs frequently. Finally the Trade-Cu regime is chosen as the box with minimal LCC with the same condition that climatological high-cloud coverage within the box is below 0.4.

c. Probability density function trajectories

To sample each target cloud regimes climatological history, we construct a probability density function (PDF) from an ensemble of 10 000 parcels initialized in the box of interest, which are then advected backward. The normally distributed initialized parcels are simultaneously released into the linearly interpolated, stationary monthly mean ABL winds, where we solve the two-dimensional equations of motion using a 3-h time step. These trajectories are performed on an isobaric surface at the 925 hPa level, using a similar routine to Bretherton et al. (2010b). We acknowledge that air mass origins have been shown to control LCC in the South Atlantic (Fuchs et al. 2017), but work within the assumption in this calculation that the ABL is well mixed and the air mass can be represented by the wind at a single level. The use of a PDF created from a distribution of parcels, as opposed to a single trajectory originating from the center of the box, minimizes the effect of local errors in the estimated wind field and accounts for some of the variability in the wind field, which is not captured by one monthly mean at the center of the box. Additionally, as the parcels are advected further, there is a greater amount of uncertainty of the parcels true position due to the effects of the unresolved wind. To account for this increasing uncertainty, the area in which each parcel within the ensemble distributes its probability grows exponentially from a 2D Gaussian in the ERA5 grid with radius 0.25°, at the beginning of the trajectory, to a radius of about 2.25° at the end of trajectory (this is visualized in Fig. B1 in appendix B).These PDFs sample a time series of the large-scale meteorological variable monthly fields. While a 3-h time increment is necessary for a decent integration of the back-trajectory, a 6-h time step is more appropriate to sample the large-scale meteorological variables since these are strongly auto-correlated and using a 3-h sampling does not improve the performance of our feature selection models.

d. Feature selection methods

The machine learning models used for feature selection in this study are L1-Regularization (LASSO regression) and random-forest regression. These algorithms were implemented using scikit-learn (Pedregosa et al. 2011).

LASSO regression (Tibshirani 1996) is a machine learning algorithm, which aims to minimize and eliminate the least significant predictors while performing a least squares regression. It minimizes the sum of squared residuals of the regression fit and of the absolute values of the regression coefficients multiplied by a regularization constant λ:
argmin[i=1N(yij=1Mβjxij)2+λj=1M|βj|],
with y = (yi)1≤iN the predictand or target variable (the monthly mean LCC over 204 months, in the 5 subtropical regions, N = 5 × 204 = 1020 for each regime), xj = (xij)1≤iN the predictors, also called features, being the 5 monthly mean meteorological variables, each at 17 lead times between 0 and 96 h in 6-h increments, M = 5 × 17 = 85. The algorithm minimizes this function by reducing the magnitude, and potentially eliminating, the regression coefficients βj for features that do not significantly improve the fit of the model. This means LASSO will select only the most relevant features to LCC prediction, allowing us to simultaneously assess local and upstream effects of the large-scale meteorological conditions. The data are standardized so that the magnitude of each LASSO regression coefficient reflects the relative importance of the corresponding feature. The data from each regime is split into 75% training data and 25% testing data to ensure that statistical models for each regime are not over-trained. The evaluation of the models performance presented in section 3c is performed on the testing data, which is unseen in the training of the models (an out of sample test). The regularization constant λ ∈ [0.001, …, 0.1] (length [0.001, …, 0.1] = 50) is chosen through fivefold cross validation, this involves splitting the training dataset into five subportions (“folds,” with 15% of the total data) and then training the model with a given λ on four folds and evaluating it on the fifth. By permuting which fold is left out of training and evaluated on, we can calculate the average R2 (explained variance by the model compared to the variance in the dependent variable) across these five permutations. The λ with the best average R2 is then used for training the model on the entirety of the training data and evaluated on the testing portion (the remaining 25%) of the dataset.

Random forest regression (Breiman 2001) is a machine learning algorithm that trains an ensemble (forest) of independent decision trees on subsets of the training dataset. It then aggregates the output of all the trees within the forest as the model output. The decision trees can capture nonlinear dependencies of the predictand on the predictors. The hyper-parameters of the random forest are chosen using a random grid-search, which selects a random set of parameters from an input parameter space, which determine: The number of trees in the forest, the number of levels in each tree, the number of features considered at every decision, the minimum number of samples required to make a decision, the minimum samples required for each terminal node, and whether to bootstrap. The best set of hyper-parameters is determined using fivefold cross validation, similarly to the method used for the LASSO regression. Here the training dataset is split into five folds, the model is then trained on four folds and evaluated on the fifth. By permuting the fold which is left out of training and evaluated on, we calculate the average R2 across these five permutations. The random set of parameters with the best average R2 is then used for training the model on the entirety of the training data and evaluated on the testing portion of the dataset. The performances of the LASSO and random-forest models presented in section 3c are the performances on the testing data.

The importance of each feature for the random-forest results is evaluated using the game-theory-based approach SHapley Additive Explanations (SHAP) proposed by Lundberg and Lee (2017). SHAP use an additive feature attribution method to interpret machine learning models a posteriori. SHAP values encapsulate the contribution of the different features of the statistical model to the predictand value produced by the random-forest algorithm for each set of predictor values, similarly to coefficients of a linear regression multiplied by their respective predictor variable. These values are calculated by evaluating the models on the testing data. The absolute magnitude of these values is used to indicate their importance to LCC prediction. The sign of their covariance with LCC is determined through comparing the upper-quartile of SHAP values of a feature to the lower-quartile. The consistency of this covariance is calculated over 50 train test splits. This turns covariance from a binary to continuous variable, which demonstrates the uncertainty in the sign of the covariance (this is denoted by the color bar in Figs. 47). More details on SHAP can be found in appendix A, for complete treatment of feature attribution see Lundberg and Lee (2017). An alternative method to assess the importance of features, the permutation feature importance gave similar results (see appendix A).

These two models were chosen as they are both highly interpretable while using distinct methodologies. Their agreement provides robustness to our result. LASSO provides a simple, discrete distribution of feature importance, for features chosen by the algorithm, while SHAP applied to random-forest regression provides a continuous measure of feature importance across all features. Second these models allow us to assess the performance of linear versus nonlinear approaches to this commonly used variable space (Klein et al. 2017). Many approaches to assess the climate response of LCC to warming are based on linear methods, thus assessing whether nonlinear methods are superior is useful. Ordinary least squares (OLS) and ridge regression were both tested for use in this study. However, without more aggressive regularization the strongly covarying predictors create statistical artifacts in the results.

Data from each regime type across the globe (Inflow, Sc-deck, Transition, and Trade-Cu regimes) is combined to train the feature selection models on a larger dataset from boundary layers in similar states. The datasets used are stratified to have an equal amount of data from each region in both training and testing stages. To account for the variations in feature importance and skill of the statistical models based on the variations in training and testing data, we perform 50 train-test splits of the data as this is where we find convergence of mean model skill (explained variance). We present the mean of these models feature importance, and the mean skill over these multiple splits. [In Figs. 48 (and Fig. A1), we present the 2σ standard error (2 times the standard error), which is used for a comparison of sampled means by Eastman and Wood (2018) and Eastman et al. (2021).] This allows the comparison of the mean feature importance between regimes in this study, and with future results.

3. Results

a. Correlation analysis

To demonstrate how the adjustment times of the ABL affect monthly mean LCC, LCC anomalies in a target area are spatially correlated with an extended domain of EIS, and SST anomaly pixels. Figure 3 shows the correlation of LCC in the target area indicated by a green box with an extended domain of EIS and SST for the Californian Sc-deck regime. The region of maximum correlation between local EIS and LCC in the target area is located upstream in the climatological mean wind. For SST, an extended region of anticorrelation between target-area LCC and SST is located upstream of the target area in the climatological wind. Both reveal the upstream control resulting from the long ABL adjustment time scales, with a longer time scale of adjustment of LCC to SST perturbations than that of LCC to EIS perturbations, which is consistent with the longer adjustment time of SST deepening the ABL. These results suggest that the upstream large-scale control of the LCC is significant on climate time scales and that a better documentation and quantification of this control is worthy of further study.

Fig. 3.
Fig. 3.

Correlation of LCC anomalies within the Californian Sc-deck regime (indicated by the green box) to surrounding anomalies of EIS and SST. Arrows indicate the 925 hPa climatological wind field from ERA5. White areas indicate insignificant correlation coefficients. Note the color map for the EIS has range 0 to 0.75, and −0.75 to 0 for the SST.

Citation: Journal of Climate 36, 10; 10.1175/JCLI-D-22-0676.1

b. Feature selection of upstream effects

Random forest models and LASSO regression statistical models trained for each physical regime (Inflow, Sc-deck, Transition, and Trade-Cu) are used to assess the statistical significance of the influence of upstream and local large-scale meteorological variables on LCC. This section discusses the importance of upstream control when compared to local effects, the changes in feature importance and thus the driving physical mechanisms of LCC sensitivity between regimes, and the robustness of our results between random-forest and LASSO regressions. Note that random-forest and LASSO regressions are different statistical techniques and there cannot be a one-to-one comparison of their outputs. LASSO eliminates some coefficients providing a discrete distribution, while SHAP applied to the random-forest models provides a continuous measure of feature importance across all features. Overall, analysis using both methods provides a measure of robustness to our results.

Figure 4 shows the average SHAP values and average LASSO regression coefficients of our predictors as a function of advection time, or lead time, along the back-trajectory, for the Inflow regime, over the four regions where we consider Inflow. The most significant feature in terms of both SHAP values and LASSO coefficients is the local positive EIS feature, which is over twice as large as any feature importance from another variable. This is followed by multiple highly significant EIS SHAP values from 6 to 24 h. This indicates that a strong temperature inversion is associated with low-cloud formation within this regime. SST SHAP values 0–42 h prior have a relatively uniform magnitude and negative covariance indicating a continuous role of SST in dissipating low clouds in this regime through increased buoyancy flux and ABL mixing with the free troposphere. The local LASSO coefficient has a similar magnitude and sign to its corresponding SHAP value. However, there is a positive LASSO coefficient 24 h prior, which is contrary to its corresponding SHAP value, suggesting a limited robustness of the results in this case. Free-tropospheric relative humidity and subsidence have smaller SHAP values locally and upstream relative to the EIS and SST, apart from a small humidity upstream effect. This could be due to the statistical information covarying with that of the EIS, but more likely variables providing information about large-scale transport appear less important than variables measuring the stability of the lower troposphere and constraining turbulent mixing in the ABL. The boundary layer wind has its most significant SHAP value and LASSO coefficient 36 h prior to the Inflow regime with positive covariance. The sensitivity of the LCC to low-level wind is attributed to the moistening and shoaling of the ABL (Bretherton et al. 2013). Our results show that this adjustment is slow, consistent with the adjustment time scale of ABL depth (Bretherton et al. 2010a; Bellon and Stevens 2013). We note that the local SHAP value has a weak covariance, and the local LASSO coefficient is negative indicating that some signal of the cloud clearings initiated by low-level winds (Dadashazar et al. 2020) may be captured in the monthly mean.

Fig. 4.
Fig. 4.

Average absolute SHAP values for random-forest models (dots) and average LASSO regression coefficients (bars) as a function of advection time (in 6-hourly temporal resolution) for the Inflow regime. Red corresponds to a consistently positive covariance of the SHAP values with LCC and positive LASSO coefficients, and blue corresponds to a consistently negative covariance of the SHAP values with LCC and negative LASSO coefficients. Lighter colors of SHAP coefficients indicate inconsistent covariances over multiple splits of the data; this is indicated by the color bar. The shaded area around the average SHAP values indicates the 2σ standard error of the mean, while the error bars indicate the same for the average LASSO coefficients. Orange diamonds at the top of the panels indicate an inconsistent sign between the SHAP covariance and LASSO coefficient.

Citation: Journal of Climate 36, 10; 10.1175/JCLI-D-22-0676.1

Figure 5 shows the average SHAP values, and average LASSO coefficients of our predictors as a function of climatological history, for the Sc-deck regime, over all five regions. The most significant SHAP value is the positive EIS value occurring 24 h prior, with a corresponding LASSO coefficient 18 h prior. Here the upstream control by inversion strength is over twice as important as the local control. This is consistent with results from past studies based on Lagrangian trajectories (Pincus et al. 1997; Mauger and Norris 2010; Eastman and Wood 2016). This upstream control by EIS could be due to a combination of the fast (6–28 h) adjustment of the ABL humidity and temperature and the slower adjustment of ABL depth. This could also be due to the dependence of Sc formation on local EIS in the Inflow box. The clouds formed in the Inflow box are advected into the Sc-deck box by the trade winds. The conditions within the Sc-deck box are favorable to Sc so advected clouds can persist there. As a result, the local control in the Inflow regime can become an upstream control for the Sc-deck regime. The SST SHAP values show a distinct negative peak between 30 and 48 h prior, with a corresponding negative LASSO coefficient 30 h prior. This suggests a role of the slowly adjusting ABL depth and it could correspond to ABL slow deepening resulting from warmer SST contrasting with the faster moistening (Schubert et al. 1979; Bretherton et al. 2010a). Similarly to the EIS in this regime the upstream control of SST has over double the SHAP magnitude of its local value. The free-tropospheric humidity has a positive local SHAP value and corresponding positive LASSO coefficients consistent with the physical reasoning that moist free-tropospheric air dries the boundary layer less when entrained, having a smaller impact on reducing LCC, with a fast thermodynamic adjustment time. The boundary layer wind exerts a small upstream control with a maximal positive SHAP value 18 h prior and LASSO coefficient 12 h prior, due to similar mechanisms to the Inflow regime (Bretherton et al. 2013).

Fig. 5.
Fig. 5.

As in Fig. 4, but for the Sc-deck regime.

Citation: Journal of Climate 36, 10; 10.1175/JCLI-D-22-0676.1

Figure 6 shows the average SHAP values for the random-forest models, and average LASSO regression coefficients of our predictors as a function of climatological history, for the Transition regime, over all five regions. The most significant SHAP value is the negative SST values occurring 42 h prior, with a corresponding LASSO coefficient 30 h prior. This again highlights the role of SST in the ABL moistening via evaporation, deepening and decoupling that lead to the Sc-to-Cu transition (Bretherton and Wyant 1997; Sandu and Stevens 2011). We see that the importance of the SST far outweighs that of the EIS in this regime, but the time leads are similar (36 h for SHAP values and LASSO coefficients). This highlights a competition between the effect of stratification preventing deepening and the effect of surface fluxes, with a dominant effect of the latter. The free-tropospheric humidity has a maximal positive SHAP value occurring 24 h prior, with a corresponding LASSO coefficient 30 h prior. We see that the free-tropospheric humidity has a similar importance to that of the EIS in this regime, which indicates the importance of moisture transport into the ABL for the Sc-to-Cu transition, as a complement to moistening by evaporation. In this regime, both free-tropospheric subsidence and ABL wind have small SHAP values and LASSO coefficients compared to other the other predictors in this regime. All time leads are long in this regime compared to others, which is consistent with the fact that the Sc-to-Cu transition is essentially a transient regime resulting from the destabilization of the Sc-topped ABL by increased SSTs (Sandu and Stevens 2011; Bellon and Geoffroy 2016b); when and where this occurs along the trade wind flow depends on large-scale conditions and the timing of this destabilization also introduces upstream control. This transition involves a large adjustment of the ABL depth, which is the slowest-adjusting characteristic of the ABL (Bretherton et al. 2010a; Bellon and Stevens 2013). It is striking that the SST and free-tropospheric humidity upstream controls are much more significant in this regime than in the Inflow and Sc-deck regimes in which the EIS upstream control predominates. It confirms the role of the ABL moisture budget in the Sc-to-Cu transition (Bretherton and Wyant 1997). In addition to its influence of the subsidence drying of the ABL, the free-tropospheric humidity also influences evaporative cooling in the inversion layer, which is the main shallow-convective mechanism for ABL growth (Stevens 2007; Bellon and Stevens 2012).

Fig. 6.
Fig. 6.

As in Fig. 4, but for the Transition regime.

Citation: Journal of Climate 36, 10; 10.1175/JCLI-D-22-0676.1

Figure 7 shows the average SHAP values for the random-forest models, and average LASSO regression coefficients of our predictors as a function of climatological history, for the Trade-Cu regime over all five regions. Here the local importance’s and LASSO coefficients of free-tropospheric humidity, subsidence, and ABL wind all have relatively high significance, alongside an SST SHAP values between 30 and 96 h. The ABL wind is the dominant variable in this regime, it exerts control on the height of the ABL in trade-Cu regions, causing trade-Cu clouds to deepen, increasing LCC (Nuijens and Stevens 2012). The local features indicate the importance of the local ABL moisture budget in producing Cu clouds through shallow convection: An increased free-tropospheric humidity or a decreased subsidence moisten the ABL and increase the LCC. The upstream control of the SST is negative, suggesting that either LCC responds to past stability in an integrative way, or that the SST varies on large spatial scales in this regime, which makes the SST signal upstream somewhat independent of time lead, making it difficult for the machine learning models to select a well-defined time lead interval. The EIS in this regime is essentially irrelevant and indicates that outside of regimes involving Sc clouds, the predicting power of EIS is greatly reduced.

The robustness of the results between our feature selection models gives us confidence in our results. Both LASSO and random-forest consistently identified the most important features for each variable in each regime, being upstream or local control, with a maximum of 12 h of difference. This gives us confidence that our result is statistical-model agnostic, and we are indeed finding upstream controls as extremely important features in LCC prediction.

Fig. 7.
Fig. 7.

As in Fig. 4, but for the Trade-Cu regime.

Citation: Journal of Climate 36, 10; 10.1175/JCLI-D-22-0676.1

The SHAP values for the four physical cloud regimes are compared in Fig. 8. This figure shows that each regime in our analysis has a unique combination of physical mechanisms controlling LCC. Both Inflow and Trade-Cu regimes are dominated by differing local features. The Inflow regime is strongly controlled by the EIS, highlighting the dominant control of stability, while the Trade cumulus regime, is controlled by free-tropospheric humidity, subsidence, and boundary layer wind, suggesting a dominant control of the moisture budget. The Sc-deck and Transition regimes are dominated by upstream control of EIS, SST and free-tropospheric relative humidity. This presents a challenge for the representation of clouds within GCMs, as a single prescriptive low-cloud parameterization based on local parameters does not explicitly incorporate upstream control. Climate models might capture some upstream control through their prognostic variables (temperature, humidity) but these rarely include cloud type or ABL depth.

Fig. 8.
Fig. 8.

Average absolute SHAP values importance’s for random-forest models in 6-hourly resolution, 4 days into all regimes respective climatological history. The shaded area around the average SHAP values indicates the 2σ standard error of the mean.

Citation: Journal of Climate 36, 10; 10.1175/JCLI-D-22-0676.1

c. Improved low-cloud modeling with upstream effects

To demonstrate the impact of upstream control on local cloud prediction, we evaluate the performance of our random-forest and LASSO models versus a control statistical model using only local large-scale meteorological variables.

Including upstream controls in our feature-selection statistical models provides significant improvements in the accuracy of these models in most cloud regimes. Figure 9 shows the explained variance of our random-forest models and LASSO models, alongside the corresponding control model of OLS regression using only local predictors. Upstream controls incorporated into the random-forest models improve the explained variance by an average of 16.2% in Inflow regime, 12.7% for the Sc-deck regime, 14.7% for the Transition regime, and 0% for the Trade-Cu regime, while these controls incorporated into the LASSO models improve explained variance by 10.5% for the Inflow regime, 7.7% for the Sc-deck regime, 11.6% for the Transition regime, and 2.1% for the Trade-Cu regime. As there is insufficient data, these models cannot be evaluated on the individual geographic regions within regimes in a statistically significant way. Overall, we see that upstream controls incorporated into statistical models can significantly outperform local control models in most cases, with the exception of the Trade-Cu regime, which is dominated by multiple significant local features (see Fig. 7). We do not present a control LASSO model using only local variables, as this would perform worse than the OLS model using the same variables, because LASSO regression includes a loss function based on the amplitude of the coefficients. A control random-forest model using only local variables performs approximately 5% better than the OLS model in the Inflow, Sc-deck, and Transition regimes, and 5% worse than the OLS model in the Trade-Cu regime.

Fig. 9.
Fig. 9.

Explained variance (R2) by OLS, LASSO, and random-forest statistical models. The control OLS model uses only local predictors, while LASSO and random forest incorporate upstream predictors. The error bars indicate the range of R2 over the 50 train test splits.

Citation: Journal of Climate 36, 10; 10.1175/JCLI-D-22-0676.1

Overall we find that the random-forest model outperforms the LASSO model. As LASSO is a linear model, and random forest is nonlinear, this difference can be explained if significant nonlinearity arising through the interaction of variables within the physical system is present, which is highly likely. We suggest future studies using these predictors to examine LCC take this into consideration. We believe that this is part of the reason that the most significant improvements in explained variance occur in the Inflow regime from the random-forest models despite the feature importance of upstream controls being relatively small compared to the local effects in this regime. The improvements in accuracy of our statistical models gives us confidence that the large upstream control features that we identified actually correspond to physical mechanisms occurring in our regimes’ climatological history.

d. Marine heatwave test case

We further test the robustness of our approach to works subject to climate change. To do so, we can identify a period when a regional climate experiences a multiyear climate event, train our models on a period excluding this multiyear event and test them on the period of the multiyear event to evaluate their robustness.

Following the example of Myers et al. (2021), we use the test case of the 2013–15 marine heatwave in the northeast Pacific to determine the ability of our statistical models to extrapolate to significantly increased SSTs, analogous to those that accompany climate change. This northeast Pacific region where this heatwave occurred coincides with our Californian Sc-deck, and Transition regimes, thus we use models trained on data from these regions in this test case.

We train both random forest and LASSO models on the first 10 years of data we have used in this analysis (2003–12) for Californian Sc-deck, and Transition regimes, respectively, then evaluate the models performance during the marine heatwave (2013–15), and on the remainder of the data unseen in the testing portion (2016–19). The regularization constant of the LASSO model, and hyper-parameters of the random forest model are chosen through the cross-validation process as described in section 2d, performed on the training data for this test case (2003–12).

Table 1 shows the models performance during the marine heatwave and on the remainder of the unseen testing data, for Californian Sc deck, and Transition regimes. The correlation between observed and predicted LCC is high, being higher during the marine heatwave than during the remainder of the data period. This gives us confidence that similar methodologies may be extrapolated in a changing climate.

Table 1.

Correlations between MODIS-observed LCC and statistical model predictions for the periods of the northeast Pacific marine heatwave (2013–15) and the remainder of the testing data (2016–19).

Table 1.

We also see that the LASSO model performs better than the random forest model, a reversal of the result seen in section 3c, where the random forest was superior. This highlights a deficiency of random forests as well as other machine learning methodologies, which do not extrapolate as well as linear models. If random forest has not seen data under certain conditions, in this case higher than usual SSTs, then it cannot form paths in its decision trees, which describe LCCs response to these changes. This demonstrates the relevance of linear models despite the general superiority of the random forest model in this work.

4. Conclusions

In this work we use data from monthly fields, sampled using semi-Lagrangian back-trajectories, within machine learning feature selection models to assess the upstream control of large-scale meteorological variables on subtropical marine LCC. The large-scale meteorological variables considered are the EIS, SST, free-tropospheric relative humidity, free-tropospheric subsidence, and the magnitude of the ABL wind. Four physical cloud regimes are considered: Inflow (upstream from the Sc deck), Sc-deck, Transition, and Trade-Cu regimes.

We find unique local and upstream relationships between LCC and the large-scale meteorological variables within our parameter space in each cloud regime. This highlights the need to consider these regimes independently from each other, as the controlling physical mechanisms differ from one regime to the next.

In the Inflow regime, fast formation of LCC due to local thermodynamic stratification is the dominant process. In the Sc-deck regime, upstream thermodynamic stratification is the dominant process, and a slower adjustment to SST is a secondary process. In the Transition regime, slow adjustment to the SST with a wide range of time scales is the dominant process, with secondary adjustments to the thermal stratification and free-tropospheric moisture on time scales of about one day. In the Trade-Cu regime, local control of LCC by the boundary layer wind, free-tropospheric humidity, and subsidence point to a strong role of the local moisture budget, while upstream control of SST points to an influence of the slow adjustment of ABL depth. Thermal stratification as described by EIS does not appear to have a strong influence.

In the random-forest models, incorporating upstream controls improves the explained variance on average by 16.2% in the Inflow regime, 12.7% in the Sc-deck regime, 14.7% in the Transition regime, and 0% in the Trade-Cu regime. In the LASSO model the incorporating upstream controls improves explained variance by 10.5% in the Inflow regime, 7.7% in the Sc-deck regime, 11.6% in the Transition regime, and 2.1% for the Trade-Cu regime.

A test case using the 2013–15 marine heatwave in the northeast Pacific showed the robustness of our statistical models to extrapolate in a changing climate.

Our results clearly show that the known adjustment times of the ABL (Pincus et al. 1997) translate into an upstream control at the climate (monthly) time scale.

We suggest that distinguishing cloud regimes and including upstream controls in observational constraints of low-cloud feedbacks to climate change (e.g., Myers et al. 2021) might improve the accuracy of the projected climate sensitivity.

These results also raise the issue of representing these upstream control in climate models. Many of the characteristics of the ABL (e.g., ABL depth, cloud type) are not prognostic variables in GCMs and their history is lost when air masses are advected from one grid box to another by the wind. Because the adjustment of some of these ABL characteristics is slower than the typical advection time from one grid box to the next, it is unclear whether these upstream control are simulated. This issue will be investigated in future work.

Acknowledgments.

Supported by the Marsden Fund Council from Government funding, managed by Royal Society Te Aparangi, Grant 9152 3718724. Gilles Bellon thanks Aurélien Ribes, and Hamish Lewis thanks David Noone for useful discussions. The authors would also like to acknowledge the three anonymous reviewers who provided valuable comments.

Data availability statement.

MODIS data were obtained through NASA EarthData: https://earthdata.nasa.gov/. ERA5 data were obtained through Climate Data Store: https://cds.climate.copernicus.eu/.

APPENDIX A

Feature Importance Methodologies

a. Shapley additive explanations

Following Lundberg and Lee (2017), for a statistical model that we wish to explain f(x) [in our case a random-forest regression for LCC: LCC(x)] with features (xj)1≤jM, a simplified, linear explanatory function g(x′) can be constructed, with simplified binary features (xj)1jM with xj{0,1}, linked to the original by a given mapping function x = hx(x′). This explanatory function is based on a linear combination of binary variables:
f(x)=g(x)=ϕ0+j=1Mϕjxj,
with M is the number of simplified input features xj, ϕ0 a constant offset vector in the absence of influence from any feature on f, and ϕi are the SHAP values, representing the contribution from each feature xj, and xj are the binary simplified input features (1 if the influence of the feature xj is included, 0 otherwise).

b. Permutation feature importance

Another measure of feature importance, permutation feature importance (also called accuracy feature importance, Breiman 2001) can be used to interpret the random-forest models trained in this work. Let us consider a statistical model f(x) produced by a random forest to approximate the predictand y. We wish to explain f with dataset X containing M features xj of N samples each, we first calculate the reference explained variance by f, s = s[y, f(X)]. Then for K repetitions, the data of a feature xj in X is shuffled to corrupt that feature, generating the corrupt dataset Xkj. The explained variance is evaluated on this corrupt dataset skj = s[y, f(Xkj)], giving the permutation importance of that feature Ij the following form:
Ij=s1Kk=1Kskj.
We use K = 5 repetitions and evaluate the average permutation importance I of each feature over 50 train test splits of the data. We show our results in Fig. A1: there is a strong similarity between the average permutation feature importance and the average absolute SHAP values. This proves the robustness of the results presented with SHAP values in the section 3b.
Fig. A1.
Fig. A1.

Average permutation importance from random-forest models in 6-hourly resolution, 4 days into all regimes’ respective climatological history. The shaded area around the average permutation feature importance indicates the 2σ standard error of the mean.

Citation: Journal of Climate 36, 10; 10.1175/JCLI-D-22-0676.1

APPENDIX B

Growth of Parcel PDF Area

Figure B1 shows an example of the exponential growth of the area in which parcels distribute their probability throughout a trajectory, for 10 parcels initialized within the Californian Sc-deck region.

Fig. B1.
Fig. B1.

Time series of probability density functions, demonstrating the enlargement of the area in which parcels distribute their probability for 10 parcels initialized within the Californian Sc-deck region, at lag times 24, 48, 72, and 96 h. The vectors indicate the monthly mean wind from ERA5 for December 2019 at the 925 hPa level.

Citation: Journal of Climate 36, 10; 10.1175/JCLI-D-22-0676.1

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    • Export Citation
  • Sandu, I., and B. Stevens, 2011: On the factors modulating the stratocumulus to cumulus transitions. J. Atmos. Sci., 68, 18651881, https://doi.org/10.1175/2011JAS3614.1.

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    • Export Citation
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    • Export Citation
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  • van der Dussen, J. J., S. R. de Roode, S. D. Gesso, and A. P. Siebesma, 2015: An LES model study of the influence of the free tropospheric thermodynamic conditions on the stratocumulus response to a climate perturbation. J. Adv. Model. Earth Syst., 7, 670691, https://doi.org/10.1002/2014MS000380.

    • Search Google Scholar
    • Export Citation
  • Vial, J., J.-L. Dufresne, and S. Bony, 2013: On the interpretation of inter-model spread in CMIP5 climate sensitivity estimates. Climate Dyn., 41, 33393362, https://doi.org/10.1007/s00382-013-1725-9.

    • Search Google Scholar
    • Export Citation
  • Wood, R., and C. S. Bretherton, 2006: On the relationship between stratiform low cloud cover and lower-tropospheric stability. J. Climate, 19, 64256432, https://doi.org/10.1175/JCLI3988.1.

    • Search Google Scholar
    • Export Citation
  • Yamaguchi, T., G. Feingold, J. Kazil, and A. McComiskey, 2015: Stratocumulus to cumulus transition in the presence of elevated smoke layers. Geophys. Res. Lett., 42, 10 47810 485, https://doi.org/10.1002/2015GL066544.

    • Search Google Scholar
    • Export Citation
  • Yuter, S. E., J. D. Hader, M. A. Miller, and D. B. Mechem, 2018: Abrupt cloud clearing of marine stratocumulus in the subtropical Southeast Atlantic. Science, 361, 697701, https://doi.org/10.1126/science.aar5836.

    • Search Google Scholar
    • Export Citation
  • Zelinka, M. D., T. A. Myers, D. T. McCoy, S. Po-Chedley, P. M. Caldwell, P. Ceppi, S. A. Klein, and K. E. Taylor, 2020: Causes of higher climate sensitivity in CMIP6 models. Geophys. Res. Lett., 47, e2019GL085782, https://doi.org/10.1029/2019GL085782.

    • Search Google Scholar
    • Export Citation
  • Zhai, C., J. H. Jiang, and H. Su, 2015: Long-term cloud change imprinted in seasonal cloud variation: More evidence of high climate sensitivity. Geophys. Res. Lett., 42, 87298737, https://doi.org/10.1002/2015GL065911.

    • Search Google Scholar
    • Export Citation
  • Zhang, Y., B. Stevens, B. Medeiros, and M. Ghil, 2009: Low-cloud fraction, lower-tropospheric stability, and large-scale divergence. J. Climate, 22, 48274844, https://doi.org/10.1175/2009JCLI2891.1.

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  • Fig. 1.

    (a) The global distribution of clouds and regions of interest in this study. (b)–(f) The four physical cloud regimes: Inflow “In,” Sc deck “Sc,” Transition “Trans,” and Trade-Cu “Trade” in (b) the Californian region, (c) the Canarian region, (d) the Australian region, (e) the Peruvian region, and (f) the Namibian region. In (e), the Trade-Cu regime centered at 3.5°S, 136.5°W is not shown. The colors indicate the climatologically averaged LCC obtained from MODIS monthly mean data, and the vectors indicate the climatological mean wind from ERA5 monthly mean data at the 925 hPa level.

  • Fig. 2.

    Representative satellite images from MODIS (Terra) of the four cloud regimes examined in this study. Each domain shown is approximately 5° × 5°. These images were obtained through https://worldview.earthdata.nasa.gov/.

  • Fig. 3.

    Correlation of LCC anomalies within the Californian Sc-deck regime (indicated by the green box) to surrounding anomalies of EIS and SST. Arrows indicate the 925 hPa climatological wind field from ERA5. White areas indicate insignificant correlation coefficients. Note the color map for the EIS has range 0 to 0.75, and −0.75 to 0 for the SST.

  • Fig. 4.

    Average absolute SHAP values for random-forest models (dots) and average LASSO regression coefficients (bars) as a function of advection time (in 6-hourly temporal resolution) for the Inflow regime. Red corresponds to a consistently positive covariance of the SHAP values with LCC and positive LASSO coefficients, and blue corresponds to a consistently negative covariance of the SHAP values with LCC and negative LASSO coefficients. Lighter colors of SHAP coefficients indicate inconsistent covariances over multiple splits of the data; this is indicated by the color bar. The shaded area around the average SHAP values indicates the 2σ standard error of the mean, while the error bars indicate the same for the average LASSO coefficients. Orange diamonds at the top of the panels indicate an inconsistent sign between the SHAP covariance and LASSO coefficient.

  • Fig. 5.

    As in Fig. 4, but for the Sc-deck regime.

  • Fig. 6.

    As in Fig. 4, but for the Transition regime.

  • Fig. 7.

    As in Fig. 4, but for the Trade-Cu regime.

  • Fig. 8.

    Average absolute SHAP values importance’s for random-forest models in 6-hourly resolution, 4 days into all regimes respective climatological history. The shaded area around the average SHAP values indicates the 2σ standard error of the mean.

  • Fig. 9.

    Explained variance (R2) by OLS, LASSO, and random-forest statistical models. The control OLS model uses only local predictors, while LASSO and random forest incorporate upstream predictors. The error bars indicate the range of R2 over the 50 train test splits.

  • Fig. A1.

    Average permutation importance from random-forest models in 6-hourly resolution, 4 days into all regimes’ respective climatological history. The shaded area around the average permutation feature importance indicates the 2σ standard error of the mean.

  • Fig. B1.

    Time series of probability density functions, demonstrating the enlargement of the area in which parcels distribute their probability for 10 parcels initialized within the Californian Sc-deck region, at lag times 24, 48, 72, and 96 h. The vectors indicate the monthly mean wind from ERA5 for December 2019 at the 925 hPa level.

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