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Deep learning can accurately represent sub-grid-scale convective processes in climate models, learning from high resolution simulations. However, deep learning methods usually lack interpretability due to large internal dimensionality, resulting in reduced trustworthiness in these methods. Here, we use Variational Encoder Decoder structures (VED), a non-linear dimensionality reduction technique, to learn and understand convective processes in an aquaplanet superparameterized climate model simulation, where deep convective processes are simulated explicitly. We show that similar to previous deep learning studies based on feed-forward neural nets, the VED is capable of learning and accurately reproducing convective processes. In contrast to past work, we show this can be achieved by compressing the original information into only five latent nodes. As a result, the VED can be used to understand convective processes and delineate modes of convection through the exploration of its latent dimensions. A close investigation of the latent space enables the identification of different convective regimes: (a) stable conditions are clearly distinguished from deep convection with low outgoing longwave radiation and strong precipitation; (b) high optically thin cirrus-like clouds are separated from low optically thick cumulus clouds; and (c) shallow convective processes are associated with large-scale moisture content and surface diabatic heating. Our results demonstrate that VEDs can accurately represent convective processes in climate models, while enabling interpretability and better understanding of sub-grid-scale physical processes, paving the way to increasingly interpretable machine learning parameterizations with promising generative properties.

The representation of nonlinear subgrid processes, especially clouds, has been a major source of uncertainty in climate models for decades. Cloud-resolving models better represent many of these processes and can now be run globally but only for short-term simulations of at most a few years because of computational limitations. Here we demonstrate that deep learning can be used to capture many advantages of cloud-resolving modeling at a fraction of the computational cost. We train a deep neural network to represent all atmospheric subgrid processes in a climate model by learning from a multiscale model in which convection is treated explicitly. The trained neural network then replaces the traditional subgrid parameterizations in a global general circulation model in which it freely interacts with the resolved dynamics and the surface-flux scheme. The prognostic multiyear simulations are stable and closely reproduce not only the mean climate of the cloud-resolving simulation but also key aspects of variability, including precipitation extremes and the equatorial wave spectrum. Furthermore, the neural network approximately conserves energy despite not being explicitly instructed to. Finally, we show that the neural network parameterization generalizes to new surface forcing patterns but struggles to cope with temperatures far outside its training manifold. Our results show the feasibility of using deep learning for climate model parameterization. In a broader context, we anticipate that data-driven Earth system model development could play a key role in reducing climate prediction uncertainty in the coming decade.

Machine learning (ML)‐based parameterizations have been developed for Earth System Models (ESMs) with the goal to better represent subgrid‐scale processes or to accelerate computations. ML‐based parameterizations within hybrid ESMs have successfully learned subgrid‐scale processes from short high‐resolution simulations. However, most studies used a particular ML method to parameterize the subgrid tendencies or fluxes originating from the compound effect of various small‐scale processes (e.g., radiation, convection, gravity waves) in mostly idealized settings or from superparameterizations. Here, we use a filtering technique to explicitly separate convection from these processes in simulations with the Icosahedral Non‐hydrostatic modeling framework (ICON) in a realistic setting and benchmark various ML algorithms against each other offline. We discover that an unablated U‐Net, while showing the best offline performance, learns reverse causal relations between convective precipitation and subgrid fluxes. While we were able to connect the learned relations of the U‐Net to physical processes this was not possible for the non‐deep learning‐based Gradient Boosted Trees. The ML algorithms are then coupled online to the host ICON model. Our best online performing model, an ablated U‐Net excluding precipitating tracer species, indicates higher agreement for simulated precipitation extremes and mean with the high‐resolution simulation compared to the traditional scheme. However, a smoothing bias is introduced both in water vapor path and mean precipitation. Online, the ablated U‐Net significantly improves stability compared to the non‐ablated U‐Net and runs stable for the full simulation period of 180 days. Our results hint to the potential to significantly reduce systematic errors with hybrid ESMs. Plain Language Summary: Due to their computational costs, it is currently not feasible to run more accurate high‐resolution climate models on a global domain on climate (century) time‐scales. However, high‐accuracy climate simulations are needed for more robust and detailed projections of our future climate. Here, we develop and evaluate various machine learning‐based convection parameterizations learned on reconstructed and coarse‐grained high‐resolution subgrid fluxes to solve this problem, and benchmark their performance. The data set is chosen from simulations of the Icosahedral Non‐hydrostatic modeling framework (ICON) in a realistic setting of the tropical Atlantic and at storm‐resolving resolutions. We focus only on convective subgrid fluxes that are isolated from other components. We improve the best ML algorithms further by excluding variables that cause unphysical correlations. Finally, we explain the learned relations of the best data‐driven schemes based on physical process understanding, test their performance when coupled to the ICON model, and achieve stable coupled simulations for 180 days as well as improved precipitation predictions. Key Points: We train/benchmark machine learning models on convective fluxes derived from realistic coarse‐grained data of storm‐resolving simulationsShapley values reveal that the best offline model, a U‐Net, learns non‐causal links to precipitation and shows poor online performanceA model, without non‐causal precipitation connections, runs more stable coupled to ICON and indicates better precipitation predictions [ABSTRACT FROM AUTHOR]

Climate models are essential to understand and project climate change, yet long‐standing biases and uncertainties in their projections remain. This is largely associated with the representation of subgrid‐scale processes, particularly clouds and convection. Deep learning can learn these subgrid‐scale processes from computationally expensive storm‐resolving models while retaining many features at a fraction of computational cost. Yet, climate simulations with embedded neural network parameterizations are still challenging and highly depend on the deep learning solution. This is likely associated with spurious non‐physical correlations learned by the neural networks due to the complexity of the physical dynamical system. Here, we show that the combination of causality with deep learning helps removing spurious correlations and optimizing the neural network algorithm. To resolve this, we apply a causal discovery method to unveil causal drivers in the set of input predictors of atmospheric subgrid‐scale processes of a superparameterized climate model in which deep convection is explicitly resolved. The resulting causally‐informed neural networks are coupled to the climate model, hence, replacing the superparameterization and radiation scheme. We show that the climate simulations with causally‐informed neural network parameterizations retain many convection‐related properties and accurately generate the climate of the original high‐resolution climate model, while retaining similar generalization capabilities to unseen climates compared to the non‐causal approach. The combination of causal discovery and deep learning is a new and promising approach that leads to stable and more trustworthy climate simulations and paves the way toward more physically‐based causal deep learning approaches also in other scientific disciplines. Plain Language Summary: Climate models have biases compared to observations that have been present for a long time because certain processes, like convection, are only approximated using simplified methods. Neural networks can better represent these processes, but often learn incorrect connections leading to unreliable results and climate model crashes. To solve this, we used a new method that informs neural networks with causal drivers, therefore, respecting the underlying physical processes. By doing so, we developed more reliable and trustworthy neural networks, allowing us to accurately represent the climate of the original high‐resolution simulation on which these neural networks were trained. Key Points: Causal discovery unveils causal drivers of subgrid‐scale processes across climatesThe causally‐informed hybrid model runs stably and generates a climate close to the original high‐resolution simulationSpurious correlations are evident in the non‐causal parameterization, leading to underestimate feature importance of physical drivers [ABSTRACT FROM AUTHOR]

A basic understanding of the mechanisms controlling the characteristics of thermally induced mesoscale circulations rests primarily on observations and model studies of dry convection, whereas the influence of moist convection on these characteristics is not well understood. Large-eddy simulations are used to investigate the effect of moist convection on an idealized mesoscale circulation. Sensitivity studies show that moist convection has a significant influence on the characteristics of the mesoscale circulation. We identify three distinct convective phases that influence the mesoscale circulation within the diurnal cycle: firstly, dry convective onset, with a weak circulation and a breeze front that propagates slowly from the cold region into the warmer fluid as a result of the surface discontinuity; secondly, a deep convective phase, where the circulation intensifies and the breeze front propagates faster; and finally a precipitating phase, where strong cold pools develop at the breeze front and accelerate the propagation speed further. Classical density-current theory fails to represent the second phase and is extended using the cloud-base mass flux to account for the observed effects of moist non-precipitating convection on the propagation speed. We demonstrate the applicability of this theory to the results from large-eddy simulations, identify the subtle role of cold pools on density-current propagation and highlight implications for numerical weather prediction. [ABSTRACT FROM AUTHOR]

The role of surface heat fluxes underneath cold pools is investigated using cloud‐resolving simulations with either interactive or horizontally homogenous surface heat fluxes over an ocean and a simplified land surface. Over the ocean, there are limited changes in the distribution of the cold pool temperature, humidity, and gust front velocity, yet interactive heat fluxes induce more cold pools, which are smaller, and convection is then less organized. Correspondingly, the updraft mass flux and lateral entrainment are modified. Over the land surface, the heat fluxes underneath cold pools drastically impact the cold pool characteristics with more numerous and smaller pools, which are warmer and more humid and accompanied by smaller gust front velocities. The interactive fluxes also modify the updraft mass flux and reduce convective organization. These results emphasize the importance of interactive surface fluxes instead of prescribed flux boundary conditions, as well as the formulation of surface heat fluxes, when studying convection.

The probabilistic bulk convection model (PBCM) developed in a companion paper is here extended to shallow nonprecipitating convection. The PBCM unifies the clear-sky and shallow convection boundary layer regimes by obtaining mixed-layer growth, cloud fraction, and convective inhibition from a single parameterization based on physical principles. The evolution of the shallow convection PBCM is based on the statistical distribution of the surface thermodynamic state of convective plumes. The entrainment velocity of the mixed layer is related to the mass flux of the updrafts overshooting the dry inversion capping the mixed layer. The updrafts overcoming the convective inhibition generate active cloud-base mass flux, which is the boundary condition for the shallow cumulus scheme. The subcloud-layer entrainment velocity is directly coupled to the cloud-base mass flux through the distribution of vertical velocity and fractional cover of the updrafts. Comparisons of the PBCM against large-eddy simulations from the Barbados Oceanographic and Meteorological Experiment (BOMEX) and from the Southern Great Plains Atmospheric Radiation Measurement Program (ARM) facility demonstrate good agreement in terms of thermodynamic structure, cloud-base mass flux, and cloud top. The equilibrium between the cloud-base mass flux and rate of growth of the mixed layer determines the equilibrium convective inhibition and cloud cover. This process is an important new insight on the coupling between the mixed-layer and cumulus dynamics. Given its relative simplicity and transparency, the PBCM represents a powerful tool for developing process-based understanding and intuition about the physical processes involved in boundary layer-convection interactions, as well as a test bed for diagnosing and validating shallow convection parameterizations. [ABSTRACT FROM AUTHOR]

A new bulk model of the convective boundary layer, the probabilistic bulk convection model (PBCM), is presented. Unlike prior bulk approaches that have modeled the mixed-layer-top buoyancy flux as a constant fraction of the surface buoyancy flux, PBCM implements a new mixed-layer-top entrainment closure based on the mass flux of updrafts overshooting the inversion. This mass flux is related to the variability of the surface state (potential temperature θ and specific humidity q) of an ensemble of updraft plumes. The authors evaluate the model against observed clear-sky weak and strong inversion cases and show that PBCM performs well. The height, state, and timing of the boundary layer growth are accurately reproduced. Sensitivity studies are performed highlighting the role of the main parameters (surface variances, lateral entrainment). The model is weakly sensitive to the exact specification of the variability at the surface and is most sensitive to the lateral entrainment of environmental air into the rising plumes. Apart from allowing time-dependent top-of-the-boundary-layer entrainment rates expressed in terms of surface properties, which can be observed in situ, PBCM naturally takes into account the transition to the shallow convection regime, as described in a companion paper. Thus, PBCM represents an important step toward a unified framework bridging parameterizations of mixed-layer entrainment velocity in both clear-sky and moist convective boundary layers. [ABSTRACT FROM AUTHOR]