Subgrid Parameterization Research Articles

Urbisphere-Berlin Campaign: Investigating Multiscale Urban Impacts on the Atmospheric Boundary Layer

Abstract For next-generation weather and climate numerical models to resolve cities, both higher spatial resolution and subgrid parameterizations of urban canopy–atmosphere processes are required. The key is to better understand intraurban variability and urban–rural differences in atmospheric boundary layer (ABL) dynamics. This includes upwind–downwind effects due to cities’ influences on the atmosphere beyond their boundaries. To address these aspects, a network of >25 ground-based remote sensing sites was designed for the Berlin region (Germany), considering city form, function, and typical weather conditions. This allows investigation of how different urban densities and human activities impact ABL dynamics. As part of the interdisciplinary European Research Council Grant urbisphere, the network was operated from autumn 2021 to autumn 2022. Here, we provide an overview of the scientific aims, campaign setup, and results from 2 days, highlighting multiscale urban impacts on the atmosphere in combination with high-resolution numerical modeling at 100-m grid spacing. During a spring day, the analyses show systematic upwind-city-downwind effects in ABL heights, largely driven by urban–rural differences in surface heat fluxes. During a heatwave day, ABL height is remarkably deep, yet spatial differences in ABL heights are less pronounced due to regionally dry soil conditions, resulting in similar observed surface heat fluxes. Our modeling results provide further insights into ABL characteristics not resolved by the observation network, highlighting synergies between both approaches. Our data and findings will support modeling to help deliver services to a wider community from citizens to those managing health, energy, transport, land use, and other city infrastructure and operations.

Effect of particle Froude number on sub-grid effective drag, filtered and residual stresses in fluidized gas-particle flows

Sub-grid effective drag, filtered and residual stresses in the meso-scale of gas-particle fluidized flows are intrinsically affected by underlying micro-scale conditions as well as non-local effects related to macro-scale conditions. In this work we applied microscopic two-fluid modeling to experiment with particle Froude number in order to evaluate the impact of this micro-scale condition over the concerning meso-scale derived sub-grid parameters. We performed highly resolved simulations in periodic domains for particle Froude numbers from 12.21 to 799.22, for a wide range of macro-scale conditions. Results were filtered and classified by ranges of meso-scale markers for the various particle Froude numbers. The particle Froude number was found to considerably affect the structural refinement of the heterogeneous flow fields thereby directly impacting effective drag, filtered and residual stresses. All of those parameters showed systematic behaviors in relation to particle Froude number, thereby providing sound data for new sub-grid modeling propositions.

A High-Precision Sub-Grid Parameterization Scheme for Clear-Sky Direct Solar Radiation in Complex Terrain—Part II: Considering Atmospheric Transparency Differences in Sub-Grid; Pre-Research for Application

Existing sub-grid parameterization schemes for clear-sky direct solar radiation (SPS-CSDSR) assume that the sub-grid cells have the same atmospheric transparency. This study shows that in undulating terrain, significant errors can occur when the sub-grid is in turbid weather or partly above the cloud top. A correction factor was proposed. It can effectively eliminate errors under a cloudless sky and can reduce some errors when part of the sub-grid is above the cloud or fog top. For atmospheric models with high horizontal resolution, example test verification shows that the cast shadowless coverage method can lead to large errors. It should no longer be used based on current computing power. These improvements and the high-precision fast terrain occlusion algorithm in Part I will allow SPS-CSDSR to achieve unprecedented high accuracy. Based on the proposed daily interpolation method, the high-precision SPS-CSDSR is also feasible for regional climate simulation. The analysis pointed out that the sub-grid terrain radiative effect (STRE) is distributed over inclined surfaces with larger areas and at different heights. Existing methods of coupling STRE on one flat surface have certain physical drawbacks. This paper suggests introducing parameterization of STRE at different altitudes and improving the coupling of land–air.

A High-Precision Sub-Grid Parameterization Scheme for Clear-Sky Direct Solar Radiation in Complex Terrain—Part I: A High-Precision Fast Terrain Occlusion Algorithm

In atmospheric modeling, sub-grid parameterization is an important method for studying the topographic effects of solar radiation using high-resolution Digital Elevation Model (DEM) data. For reducing the amount of computation, some approximate methods that can lead to errors are used in existing sub-grid parameterization schemes for clear-sky direct solar radiation (SPS-CSDSR). The lack of a high-precision fast terrain occlusion algorithm (HPFTOA) remains one of the biggest constraints in this field. This study proposed an HPFTOA. It mainly uses two kinds of acceleration algorithms. One method is to use a dynamic, lossless, and fast occlusion search radius. Another way is to use the rectangular grid for calculations within the accuracy of DEM data to avoid coordinate projection conversions. The test results indicate that the HPFTOA can carry out large-scale computation based on DEM data with a resolution of 90 m. Because it rarely uses approximation algorithms and considers the curvature of the Earth, SPS-CSDSR can achieve unprecedented precision. The HPFTOA can also be used in the fields of mountain solar energy assessment, remote sensing, and telemetry, including terrain-obscuring the probe. As computer performance improves and algorithms and execution code are optimized, the application prospects will be very broad.

Formation of low-mass protostars and their circumstellar disks

Understanding circumstellar disks is of prime importance in astrophysics; however, their birth process remains poorly constrained due to observational and numerical challenges. Recent numerical works have shown that the small-scale physics, often wrapped into a sub-grid model, play a crucial role in disk formation and evolution. This calls for a combined approach in which both the protostar and circumstellar disk are studied in concert. We aim to elucidate the small-scale physics and constrain sub-grid parameters commonly chosen in the literature by resolving the star-disk interaction. We carried out a set of very high resolution 3D radiative-hydrodynamics simulations that self-consistently describe the collapse of a turbulent, dense molecular cloud core to stellar densities. We studied the birth of the protostar, the circumstellar disk, and its early evolution ($<6\ yr $ after protostellar formation). Following the second gravitational collapse, the nascent protostar quickly reaches breakup velocity and sheds its surface material, thus forming a hot ($ K $), dense, and highly flared circumstellar disk. The protostar is embedded within the disk such that material can flow without crossing any shock fronts. The circumstellar disk mass quickly exceeds that of the protostar, and its kinematics are dominated by self-gravity. Accretion onto the disk is highly anisotropic, and accretion onto the protostar mainly occurs through material that slides on the disk surface. The polar mass flux is negligible in comparison. The radiative behavior also displays a strong anisotropy, as the polar accretion shock was shown to be supercritical, whereas its equatorial counterpart is subcritical. We also find a remarkable convergence of our results with respect to initial conditions. These results reveal the structure and kinematics in the smallest spatial scales relevant to protostellar and circumstellar disk evolution. They can be used to describe accretion onto regions commonly described by sub-grid models in simulations studying larger-scale physics.

Accurate assessment of land–atmosphere coupling in climate models requires high-frequency data output

Abstract. Land–atmosphere (L–A) interactions are important for understanding convective processes, climate feedbacks, the development and perpetuation of droughts, heatwaves, pluvials, and other land-centered climate anomalies. Local L–A coupling (LoCo) metrics capture relevant L–A processes, highlighting the impact of soil and vegetation states on surface flux partitioning and the impact of surface fluxes on boundary layer (BL) growth and development and the entrainment of air above the BL. A primary goal of the Climate Process Team in the Coupling Land and Atmospheric Subgrid Parameterizations (CLASP) project is parameterizing and characterizing the impact of subgrid heterogeneity in global and regional Earth system models (ESMs) to improve the connection between land and atmospheric states and processes. A critical step in achieving that aim is the incorporation of L–A metrics, especially LoCo metrics, into climate model diagnostic process streams. However, because land–atmosphere interactions span timescales of minutes (e.g., turbulent fluxes), hours (e.g., BL growth and decay), days (e.g., soil moisture memory), and seasons (e.g., variability in behavioral regimes between soil moisture and latent heat flux), with multiple processes of interest happening in different geographic regions at different times of year, there is not a single metric that captures all the modes, means, and methods of interaction between the land and the atmosphere. And while monthly means of most of the LoCo-relevant variables are routinely saved from ESM simulations, data storage constraints typically preclude routine archival of the hourly data that would enable the calculation of all LoCo metrics. Here, we outline a reasonable data request that would allow for adequate characterization of sub-daily coupling processes between the land and the atmosphere, preserving enough sub-daily output to describe, analyze, and better understand L–A coupling in modern climate models. A secondary request involves embedding calculations within the models to determine mean properties in and above the BL to further improve characterization of model behavior. Higher-frequency model output will (i) allow for more direct comparison with observational field campaigns on process-relevant timescales, (ii) enable demonstration of inter-model spread in L–A coupling processes, and (iii) aid in targeted identification of sources of deficiencies and opportunities for improvement of the models.

A Study of Intermittent Turbulence in Stable Arctic Boundary Layers

Polar boundary layers are difficult to model due to the existence of intermittent turbulence within stable layers. Here we present a case study evaluation of coherent structures in a stable boundary layer observed during a series of flights with an uncrewed aircraft system (DataHawk2) on 19 October 2016 at Oliktok Point, Alaska as part of the ERASMUS (Evaluation of Routine Atmospheric Sounding Measurements using Unmanned Systems) field campaign. During a sequence of five flights over a nine-hour period, 57 profiles of atmospheric properties (0–400 m a.g.l) were collected. Turbulence was identified using derived Richardson Number, temperature structure function parameter, and turbulence kinetic energy dissipation. Throughout all flights on this strongly stable day, intermittent turbulence was observed. These turbulent layers showed well-mixed potential temperature profiles embedded within otherwise stable potential temperature profiles; often resulting in a characteristic staircase pattern. Turbulent layers ranged from 1 to 30 m deep, with most individual layers being 1–2 m deep. Vertical propagation velocities of layers in the lower atmosphere were on the order of a few cm s−1, typical of non-convective environments. In different regions of the profile, turbulence was driven by a different balance of buoyancy and shear forces, with turbulence in the near surface environment driven by strong shear forces overcoming strong resistance to buoyancy, while turbulence in elevated layers characterized by weaker shear forces overcoming weaker resistance to buoyancy. We discuss the potential of such datasets for improving subgrid parameterizations of small-scale turbulence embedded within stable boundary layers.

Modeling and evaluating the effects of irrigation on land–atmosphere interaction in southwestern Europe with the regional climate model REMO2020–iMOVE using a newly developed parameterization

Abstract. Irrigation is a crucial land use practice to adapt agriculture to unsuitable climate and soil conditions. Aiming to improve the growth of plants, irrigation modifies the soil condition, which causes atmospheric effects and feedbacks through land–atmosphere interaction. These effects can be quantified with numerical climate models, as has been done in various studies. It could be shown that irrigation effects, such as air temperature reduction and humidity increase, are well understood and should not be neglected on local and regional scales. However, there is a lack of studies including the role of vegetation in the altered land–atmosphere interaction. With the increasing resolution of numerical climate models, these detailed processes have a chance to be better resolved and studied. This study aims to analyze the effects of irrigation on land–atmosphere interaction, including the effects and feedbacks of vegetation. We developed a new parameterization for irrigation, implemented it into the REgional climate MOdel (REMO2020), and coupled it with the interactive MOsaic-based VEgetation module (iMOVE). Following this new approach of a separate irrigated fraction, the parameterization is suitable as a subgrid parameterization for high-resolution studies and resolves irrigation effects on land, atmosphere, and vegetation. Further, the parameterization is designed with three different water application schemes in order to analyze different parameterization approaches and their influence on the representation of irrigation effects. We apply the irrigation parameterization for southwestern Europe including the Mediterranean region at a 0.11∘ horizontal resolution for hot extremes. The simulation results are evaluated in terms of the consistency of physical processes. We found direct effects of irrigation, like a changed surface energy balance with increased latent and decreased sensible heat fluxes, and a surface temperature reduction of more than −4 K as a mean during the growing season. Further, vegetation reacts to irrigation with direct effects, such as reduced water stress, but also with feedbacks, such as a delayed growing season caused by the reduction of the near-surface temperature. Furthermore, the results were compared to observational data, showing a significant bias reduction in the 2 m mean temperature when using the irrigation parameterization.

FLAMINGO: calibrating large cosmological hydrodynamical simulations with machine learning.

To fully take advantage of the data provided by large-scale structure surveys, we need to quantify the potential impact of baryonic effects, such as feedback from active galactic nuclei (AGN) and star formation, on cosmological observables. In simulations, feedback processes originate on scales that remain unresolved. Therefore, they need to be sourced via subgrid models that contain free parameters. We use machine learning to calibrate the AGN and stellar feedback models for the FLAMINGO (Fullhydro Large-scale structure simulations with All-sky Mapping for the Interpretation of Next Generation Observations) cosmological hydrodynamical simulations. Using Gaussian process emulators trained on Latin hypercubes of 32 smaller volume simulations, we model how the galaxy stellar mass function (SMF) and cluster gas fractions change as a function of the subgrid parameters. The emulators are then fit to observational data, allowing for the inclusion of potential observational biases. We apply our method to the three different FLAMINGO resolutions, spanning a factor of 64 in particle mass, recovering the observed relations within the respective resolved mass ranges. We also use the emulators, which link changes in subgrid parameters to changes in observables, to find models that skirt or exceed the observationally allowed range for cluster gas fractions and the SMF. Our method enables us to define model variations in terms of the data that they are calibrated to rather than the values of specific subgrid parameters. This approach is useful, because subgrid parameters are typically not directly linked to particular observables, and predictions for a specific observable are influenced by multiple subgrid parameters.

Generative Data‐Driven Approaches for Stochastic Subgrid Parameterizations in an Idealized Ocean Model

AbstractSubgrid parameterizations of mesoscale eddies continue to be in demand for climate simulations. These subgrid parameterizations can be powerfully designed using physics and/or data‐driven methods, with uncertainty quantification. For example, Guillaumin and Zanna (2021, https://doi.org/10.1029/2021ms002534) proposed a Machine Learning (ML) model that predicts subgrid forcing and its local uncertainty. The major assumption and potential drawback of this model is the statistical independence of stochastic residuals between grid points. Here, we aim to improve the simulation of stochastic forcing with generative models of ML, such as Generative adversarial network (GAN) and Variational autoencoder (VAE). Generative models learn the distribution of subgrid forcing conditioned on the resolved flow directly from data and they can produce new samples from this distribution. Generative models can potentially capture not only the spatial correlation but any statistically significant property of subgrid forcing. We test the proposed stochastic parameterizations offline and online in an idealized ocean model. We show that generative models are able to predict subgrid forcing and its uncertainty with spatially correlated stochastic forcing. Online simulations for a range of resolutions demonstrated that generative models are superior to the baseline ML model at the coarsest resolution.

Machine Learning for Nonorographic Gravity Waves in a Climate Model

Abstract There is growing use of machine learning algorithms to replicate subgrid parameterization schemes in global climate models. Parameterizations rely on approximations; thus, there is potential for machine learning to aid improvements. In this study, a neural network is used to mimic the behavior of the nonorographic gravity wave scheme used in the Met Office climate model, important for stratospheric climate and variability. The neural network is found to require only two of the six inputs used by the parameterization scheme, suggesting the potential for greater efficiency in this scheme. Use of a one-dimensional mechanistic model is advocated, allowing neural network hyperparameters to be chosen based on emergent features of the coupled system with minimal computational cost, and providing a testbed prior to coupling to a climate model. A climate model simulation, using the neural network in place of the existing parameterization scheme, is found to accurately generate a quasi-biennial oscillation of the tropical stratospheric winds, and correctly simulate the nonorographic gravity wave variability associated with El Niño–Southern Oscillation and stratospheric polar vortex variability. These internal sources of variability are essential for providing seasonal forecast skill, and the gravity wave forcing associated with them is reproduced without explicit training for these patterns. Significance Statement Climate simulations are required for providing advice to government, industry, and society regarding the expected climate on time scales of months to decades. Machine learning has the potential to improve the representation of some sources of variability in climate models that are too small to be directly simulated by the model. This study demonstrates that a neural network can simulate the variability due to atmospheric gravity waves that is associated with El Niño–Southern Oscillation and with the tropical and polar regions of the stratosphere. These details are important for a model to produce more accurate predictions of regional climate.

Two Decades of Temperature and Specific Humidity Variance Scaling With the Atmospheric Infrared Sounder

AbstractA two‐decade climatology of height‐resolved horizontal variance scaling exponents (𝛼) for temperature (T) and specific humidity (q) is described using Aqua Atmospheric Infrared Sounder (AIRS) sounding profiles. The AIRS Team Version 6 (V6), Version 7 (V7), and Community Long‐term Infrared Microwave Combined Atmospheric Product System (CLIMCAPS) retrieval algorithms are compared to European Centre for Medium‐Range Weather Forecasts Reanalysis v5 (ERA5) and Modern‐Era Retrospective analysis for Research and Applications, Version 2 (MERRA‐2) reanalyses. Large‐scale T exponents derived between 600 and 1,200 km (𝛼L) show close agreement between V6, V7, and CLIMCAPS algorithms. However, small‐scale q exponents derived between 150 and 400 km (𝛼S) are in poor agreement, including an unrealistically steep 𝛼S in the planetary boundary layer (PBL) in the V7 and CLIMCAPS algorithms that is caused by a combination of algorithm damping and overconstraint by the first guess fields. ERA5 and MERRA‐2 reanalyses have large values of 𝛼L and 𝛼S for both T and q that indicate reduced small‐scale variability in the reanalysis fields. Differences in 𝛼S between free‐running MERRA‐2 AMIP and MERRA‐2 are negligible, implying that suppressed small‐scale variability in reanalyses is imposed by the background model and not caused by the data assimilation process. AIRS has positively skewed T distributions in the tropical‐free troposphere that is consistent with positively buoyant air parcels in convection, and negative skewness in the PBL that is related to the existence of cold pools, behavior that is mostly absent in ERA5 and MERRA‐2. AIRS provides a global view of scale‐dependent variance and skewness that is useful for subgrid parameterization development and validation of weather and climate prediction models.

Spurious heating of stellar motions by dark matter particles in cosmological simulations of galaxy formation

ABSTRACT We use two cosmological simulations to study the impact of spurious heating of stellar motions within simulated galaxies by dark matter (DM) particles. The simulations share the same numerical and subgrid parameters, but one used a factor of 7 more DM particles. Many galaxy properties are unaffected by spurious heating, including their masses, star formation histories, and the spatial distribution of their gaseous baryons. The distribution and kinematics of stellar and DM particles, however, are affected. Below a resolution-dependent virial mass, $M_{200}^{\rm spur}$, galaxies have higher characteristic velocities, larger sizes, and more angular momentum in the simulation with lower DM mass resolution; haloes have higher central densities and lower velocity dispersions. Above $M_{200}^{\rm spur}$, galaxies and haloes have similar properties in both runs. The differences arise due to spurious heating, which transfers energy from DM to stellar particles, causing galaxies to heat up and haloes to cool down. The value of $M_{200}^{\rm spur}$ can be derived from an empirical disc heating model, and coincides with the mass below which the predicted spurious velocity dispersion exceeds the measured velocity dispersion of simulated galaxies. We predict that galaxies in the $100^3\, {\rm Mpc}^3$eagle run and IllustrisTNG-100 are robust to spurious collisional effects at their half-mass radii provided $M_{200}^{\rm spur}\approx 10^{11.7}\, {\rm M_\odot }$; for the $25^3\, {\rm Mpc}^3$eagle run and IllustrisTNG-50, we predict $M_{200}^{\rm spur}\approx 10^{11}\, {\rm M_\odot }$. Suppressing spurious heating at smaller/larger radii, or for older/younger stellar populations, requires haloes to be resolved with more/fewer DM particles.

Operational snow-hydrological modeling for Switzerland

The seasonal evolution of snow cover has significant impacts on the hydrological cycle and microclimate in mountainous regions. However, snow processes also play a crucial role in triggering alpine mass movements and flooding, posing risks to people and infrastructure. To mitigate these risks, many countries use operational forecast systems for snow distribution and melt. This paper presents the Swiss Operational Snow-hydrological (OSHD) model system, developed to provide daily analysis and forecasts on snow cover dynamics throughout Switzerland. The OSHD system is a sophisticated snow hydrological model designed specifically for the high-alpine terrain of the Swiss Alps. It leverages exceptional station data and high-resolution meteorological forcing data, as well as various reanalysis products to combine snow modeling with advanced data assimilation and meteorological downscaling methods. The system offers models of varying complexity, each tailored to specific modeling strategies and applications. For snowmelt runoff forecasting, monitoring snow water resources, and research-grade purposes, the OSHD system employs physics-based modeling chains. For snow climatological assessments, a conceptual model chain is available. We are pleased to present two comprehensive datasets from the conceptual and physics-based models that cover the entirety of Switzerland. The first dataset comprises a snow water equivalent climatology spanning 1998–2022, with a spatial resolution of 1 km. The second dataset includes snow distribution and snow melt data spanning 2016–2022 at a high spatial resolution of 250 m. To meet the needs of a multi-purpose snow hydrological model framework, the OSHD system employs various strategies for process representation and sub-grid parameterizations at the snow-canopy-atmosphere interface, particularly in complex terrain. Recent and ongoing model developments are aimed at accounting for complex forest snow processes, representing slope and ridge-scale precipitation and snow redistribution processes, as well as improving probabilistic snow forecasts and data assimilation procedures based on remote sensing products.

Multi-epoch machine learning 2: identifying physical drivers of galaxy properties in simulations

ABSTRACT Using a novel machine learning method, we investigate the buildup of galaxy properties in different simulations, and in various environments within a single simulation. The aim of this work is to show the power of this approach at identifying the physical drivers of galaxy properties within simulations. We compare how the stellar mass is dependent on the value of other galaxy and halo properties at different points in time by examining the feature importance values of a machine learning model. By training the model on IllustrisTNG, we show that stars are produced at earlier times in higher density regions of the universe than they are in low density regions. We also apply the technique to the Illustris, EAGLE, and CAMELS simulations. We find that stellar mass is built up in a similar way in EAGLE and IllustrisTNG, but significantly differently in the original Illustris, suggesting that subgrid model physics is more important than the choice of hydrodynamics method. These differences are driven by the efficiency of supernova feedback. Applying principal component analysis to the CAMELS simulations allows us to identify a component associated with the importance of a halo’s gravitational potential and another component representing the time at which galaxies form. We discover that the speed of galactic winds is a more critical subgrid parameter than the total energy per unit star formation. Finally, we find that the Simba black hole feedback model has a larger effect on galaxy formation than the IllustrisTNG black hole feedback model.

Aerosol–cloud–radiation interaction during Saharan dust episodes: the dusty cirrus puzzle

Abstract. Dusty cirrus clouds are extended optically thick cirrocumulus decks that occur during strong mineral dust events. So far they have mostly been documented over Europe associated with dust-infused baroclinic storms. Since today's global numerical weather prediction models neither predict mineral dust distributions nor consider the interaction of dust with cloud microphysics, they cannot simulate this phenomenon. We postulate that the dusty cirrus forms through a mixing instability of moist clean air with drier dusty air. A corresponding sub-grid parameterization is suggested and tested in the ICOsahedral Nonhydrostatic model with Aerosol and Reactive Trace gases (ICON-ART). Only with the help of this parameterization is ICON-ART able to simulate the formation of the dusty cirrus, which leads to substantial improvements in cloud cover and radiative fluxes compared to simulations without this parameterization. A statistical evaluation over six Saharan dust events with and without observed dusty cirrus shows robust improvements in cloud and radiation scores. The ability to simulate dusty cirrus formation removes the linear dependency on mineral dust aerosol optical depth from the bias of the radiative fluxes. For the six Saharan dust episodes investigated in this study, the formation of dusty cirrus clouds is the dominant aerosol–cloud–radiation effect of mineral dust over Europe.

Subgrid Parameterization of Eddy, Meanfield and Topographic Interactions in Simulations of an Idealized Antarctic Circumpolar Current

AbstractThe ocean circulation dynamics can be represented as a high‐dimensional multi‐scale nonlinear system with inhomogenous meanfields and topography. Numerical simulations of the ocean dynamics resolve the large scales of motion on a computational grid, with the unresolved subgrid interactions parameterized. These simulations are highly dependent upon the grid resolution, unless the subgrid terms are appropriately parameterized. There are five fundamental classes of subgrid interactions: eddy‐eddy; eddy‐topographic; eddy‐meanfield; meanfield‐meanfield; and meanfield‐topographic. Scale dependent parameterizations representing each of these interaction classes are presented here in oceanic flows for the first time. Subgrid parameterizations are calculated and validated in baroclinic quasi‐geostrophic simulations of idealized Antarctic Circumpolar Current flows with representative mean currents and ocean floor topography. The parameterization coefficients are derived from the coarse grained statistics of high resolution reference simulations in spectral space. Stochastic and deterministic parameterizations are developed for the eddy‐eddy interactions, and deterministic forms for the remaining classes. The kinetic energy spectra and meanfield resulting from large eddy simulations (LES) adopting these coefficients accurately replicate those of the reference simulation. The eddy‐eddy interactions are dominant, but all classes need to be parameterized for best results. For LES where baroclinic instability is explicitly resolved the stochastic variants out‐perform the deterministic ones across all scales. When baroclinic instability is not explicitly resolved, the stochastic variants out‐perform the deterministic cases at the large scales, but introduce some distortions at the smallest resolved scales. This study provides an assessment of the relevant strengths of the subgrid interaction classes in an idealized yet representative ocean.

Benchmarking of Machine Learning Ocean Subgrid Parameterizations in an Idealized Model

AbstractRecently, a growing number of studies have used machine learning (ML) models to parameterize computationally intensive subgrid‐scale processes in ocean models. Such studies typically train ML models with filtered and coarse‐grained high‐resolution data and evaluate their predictive performance offline, before implementing them in a coarse resolution model and assessing their online performance. In this work, we systematically benchmark the online performance of such models, their generalization to domains not encountered during training, and their sensitivity to data set design choices. We apply this proposed framework to compare a large number of physical and neural network (NN)‐based parameterizations. We find that the choice of filtering and coarse‐graining operator is particularly critical and this choice should be guided by the application. We also show that all of our physics‐constrained NNs are stable and perform well when implemented online, but generalize poorly to new regimes. To improve generalization and also interpretability, we propose a novel equation‐discovery approach combining linear regression and genetic programming with spatial derivatives. We find this approach performs on par with neural networks on the training domain but generalizes better beyond it. We release code and data to reproduce our results and provide the research community with easy‐to‐use resources to develop and evaluate additional parameterizations.

Linking Large-Scale Double-ITCZ Bias to Local-Scale Drizzling Bias in Climate Models

Abstract Tropical precipitation in climate models presents significant biases in both the large-scale pattern (i.e., double intertropical convergence zone bias) and local-scale characteristics (i.e., drizzling bias with too frequent drizzle/convection and reduced occurrences of no and heavy precipitation). By untangling the coupled system and analyzing the biases in precipitation, cloud, and radiation, this study shows that local-scale drizzling bias in atmospheric models can lead to large-scale double-ITCZ bias in coupled models by inducing convective-regime-dependent biases in precipitation and cloud radiative effects (CRE). The double-ITCZ bias consists of a hemispherically asymmetric component that arises from the asymmetric SST bias and a nearly symmetric component that exists in atmospheric models without the SST bias. By increasing light rain but reducing heavy rain, local-scale drizzling bias induces positive (negative) precipitation bias in the moderate (strong) convective regime, leading to the nearly symmetric wet bias in atmospheric models. By affecting the cloud profile, local-scale drizzling bias induces positive (negative) CRE bias in the stratocumulus (convective) regime in atmospheric models. Because the stratocumulus (convective) region is climatologically more pronounced in the southern (northern) tropics, the CRE bias is deemed to be hemispherically asymmetric and drives warm and wet (cold and dry) biases in the southern (northern) tropics when coupled to ocean. Our results suggest that correcting local-scale drizzling bias is critical for fixing large-scale double-ITCZ bias. The drizzling and double-ITCZ biases are not alleviated in models with mesoscale (0.25°–0.5°) or even storm-resolving (∼3 km) resolution, implying that either large-eddy simulation or fundamental improvement in small-scale subgrid parameterizations is needed.

A Method for Choosing the Spatial and Temporal Approximations for the LES Approach

Analysis and optimization of the hybrid upwind-central numerical methods for modern versions of large eddy simulations (LESs) are presented herein. Optimization was performed based on examination of the characteristics of the spatial and temporal finite-volume approximations of the convective terms of filtered Navier–Stokes equations. A method for selecting level of subgrid viscosity that corresponds to the chosen numerical scheme and makes it possible to obtain an extended inertial interval of the energy spectrum is proposed. A series of LESs of homogeneous isotropic turbulence decay were carried out, and the optimal values of the subgrid model constants included in the hybrid shear stress transport delay detached eddy simulation (SST-DDES) method were determined. A procedure for generating a consistent initial field of subgrid parameters for these simulations is described. The three-stage explicit Runge–Kutta method was demonstrated to be sufficient for stable time integration, while the popular explicit midpoint method was not. The slope of the energy spectrum was shown to be almost independent of the central-difference scheme order and of the mesh spacing when the correct numerical method was applied. Numerical viscosity was found to become much greater than subgrid viscosity when the upwind scheme contributed about 10% or more to the convective flux approximation.