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Chiral amines are key building blocks in producing active pharmaceutical ingredients and can be synthesized via the amine transaminase pathway under mild conditions with eco‐friendly solvents. For model‐based design and control, mathematical models can be utilized. This requires reliable parameterization of the model. In this study, a model for the production of (S)‐(3 methoxyphenyl)‐ethylamine is presented. Parameter identifiability is analyzed using the method of profile likelihoods. The parameter identifiability is then tested in two different batch operation scenarios by using moving horizon estimation, which can be applied for on‐line model adaption and control purposes. In a batch process, identifiability decreases over time. A repetitive batch strategy improves parameter identifiability. [ABSTRACT FROM AUTHOR]

A fundamental characteristic of extreme precipitation events (EPEs) is their horizontal scale. This horizontal scale can influence the intensity of an EPE through its effect on the timescale of an EPE as well as its effect on the strength of convective feedbacks. Thus, to have confidence in future projections of extreme precipitation, the horizontal scales of EPEs in global climate models (GCMs) should be evaluated. Analyzing daily output from 27 models participating in the Coupled Model Intercomparison Project phase 6 (CMIP6), including 13 models participating in the High Resolution Model Intercomparison Project (HighResMIP), we computed the horizontal scales of EPEs and extreme ascent for annual maximum EPEs during 1981–2000. We found that the horizontal scales of both EPEs and the associated ascending motion are resolution‐dependent: for a factor of seven increase in horizontal resolution, the horizontal scale decreases by a factor of approximately two to five, with higher sensitivity in the tropics than in the midlatitudes. Further analysis in the southern hemisphere midlatitudes reveals that this resolution dependence results from precipitation during the simulated EPEs that is almost entirely resolved rather than parameterized. However, the EPEs are not simply grid box storms, and analysis of the horizontal scales of geopotential anomalies suggests that the planetary‐scale dynamics in GCMs is not resolution‐dependent. Thus, the dominance of resolved precipitation during EPEs is more likely due to convection on the model grid or formation of strong, poorly resolved fronts, and additional work is needed to explore these possibilities and find a remedy for this resolution dependence. Plain Language Summary: Extreme precipitation is of great human interest because of the potentially severe flooding that it can cause. We are reliant on global climate models (GCMs) to project future changes in extreme precipitation, so there is a need to assess the realism of extreme precipitation in GCMs. One fundamental characteristic of an extreme precipitation event (EPE) is its horizontal size or "scale." In this study, we analyze a large archive of output from simulations using state‐of‐the‐art GCMs and compute the horizontal scale of EPEs during 1981–2000. We found that the horizontal scale depends on the spacing between grid points in the model. These grid points are like pixels in a digital photo, and the smaller the distance between grid points, the higher the model resolution. The fact that the EPE horizontal scale in GCMs is resolution‐dependent is concerning because the horizontal scale should be dictated by realistic physical processes rather than artificial aspects of the model configuration. While we have provided some initial insights into the reasons for this resolution dependence, additional work is needed to develop more complete explanations and improve models. Key Points: The simulated horizontal scale of the annual maximum of daily precipitation anomalies is sensitive to a model's horizontal resolutionThis extreme precipitation horizontal scale is determined almost entirely by resolved, not parameterized, precipitationThe simulated horizontal scale of geopotential disturbances during these extreme precipitation events is not resolution dependent [ABSTRACT FROM AUTHOR]

Rate coefficients, k(T), for the gas‐phase OH radical reaction with decamethyltetrasiloxane ((CH3)3SiO[Si(CH3)2O]2Si(CH3)3, L4, k1), dodecamethylpentasiloxane ((CH3)3SiO[Si(CH3)2O]3Si(CH3)3, L5, k2), and decamethylcyclopentasiloxane ([–Si(CH3)2O–]5, D5, k3), and dodecamethylcyclohexasiloxane ([–Si(CH3)2O–]6, D6, k4) were measured using a pulsed laser photolysis—laser induced fluorescence absolute method over the temperature range 270–370 K. The obtained room temperature rate coefficients, with quoted 2σ absolute uncertainties, and fitted temperature dependence are (cm−3 molecule−1 s−1): k1295K=2.50±0.18×10−12,k1270−370K=1.707×10−13T/2984.45exp807/Tk2295K=3.12±0.32×10−12,k2295−370K=2.65±0.02×10−11exp−630±60/Tk3295K=2.02±0.12×10−12,k3270−370K=8.97×10−13T/2982.90exp248/Tk4297K=2.89±0.16×10−12,k4297−370K=3.13±0.05×10−11exp−717±119/T$$\begin{equation*} \hspace*{45pt} \def\eqcellsep{&}\begin{array}{rcl} {k}_1\left( {295\;{\mathrm{K}}} \right) &=& \left( {2.50 \pm 0.18} \right) \times {{10}}^{ - 12},\quad {k}_1\left( {270-370\;{\mathrm{K}}} \right)\\ & =& 1.707 \times {{10}}^{ - 13}{{\left( {{\mathrm{T}}/298} \right)}}^{4.45}\exp \left( {807/{\mathrm{T}}} \right)\\ {k}_2\left( {295\;{\mathrm{K}}} \right) &=& \left( {3.12 \pm 0.32} \right) \times {{10}}^{ - 12},\quad {k}_2\left( {295-370\;{\mathrm{K}}} \right)\\ &=& \left( {2.65 \pm 0.02} \right) \times {{10}}^{ - 11}\exp \left( { - \left( {630 \pm 60} \right)/{\mathrm{T}}} \right)\\ {k}_3\left( {295\;{\mathrm{K}}} \right) &=& \left( {2.02 \pm 0.12} \right) \times {{10}}^{ - 12},\quad {k}_3\left( {270-370\;{\mathrm{K}}} \right)\\ & =& 8.97 \times {{10}}^{ - 13}{{\left( {T/298} \right)}}^{2.90}\exp \left( {248/{\mathrm{T}}} \right)\\ {k}_4\left( {297\;{\mathrm{K}}} \right) &=& \left( {2.89 \pm 0.16} \right) \times {{10}}^{ - 12},\quad {k}_4\left( {297-370\;{\mathrm{K}}} \right)\\ & =& \left( {3.13 \pm 0.05} \right) \times {{10}}^{ - 11}\exp \left( { - \left( {717 \pm 119} \right)/{\mathrm{T}}} \right) \end{array} \end{equation*}$$The 2σ absolute rate coefficient uncertainty, for all compounds included in this study, is conservatively estimated to be ∼10% over the entire temperature range. The cyclic permethylsiloxanes were found to be less reactive than the analogous linear compound, while both linear and cyclic compounds show increasing reactivity with increasing number of CH3‐ groups. A structure activity relationship (SAR) parameterization for the permethylsiloxanes is presented. The estimated atmospheric lifetimes due to OH reaction for L4, L5, D5, and D6 are 5.2, 4.4, 6.8, and 5.2 days, respectively. [ABSTRACT FROM AUTHOR]

Atmospheric turbulence over the Arctic sea‐ice surface has been understudied due to the lack of observational data. In this study, we focus on the turbulence kinetic energy (TKE) over sea ice and distinguish its two different vertical structures, the "Surface" type and the "Elevated" type, using observations during the Multidisciplinary drifting Observatory for the Study of Arctic Climate expedition (MOSAiC). The "Surface" type has the maximum TKE near the surface (at 2 m), while the "Elevated" type has the maximum TKE at a higher level (6 m). The TKE budget analysis indicates that the "Elevated" type is caused by the increased shear production of TKE at 6 m. In addition, spectral analysis reveals that the contribution to TKE by horizontal large eddies is enhanced in the "Elevated" type. Finally, how the vertical structure of TKE affects the parameterization of turbulent momentum flux is discussed. Plain Language Summary: In recent years, the Arctic near‐surface temperature has increased at a rate that is 3–4 times faster than the global average, which has significant impacts on the global climate. Explaining this phenomenon and predicting future scenarios are urgently needed. Turbulent motions within the Arctic atmospheric boundary layer over the sea‐ice surface play an important role in determining near‐surface temperature variations, but these turbulent motions and their impacts are not thoroughly understood. To enhance our understanding of the turbulent characteristics of the Arctic boundary layer, the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) was conducted in the central Arctic and collected a wealth of data. Based on the MOSAiC observational data, we investigate the vertical structures of turbulence kinetic energy (TKE) in the surface layer and two different vertical structures of TKE are distinguished. We then compare the production of TKE between these two vertical structures. In addition, we evaluate the performance of parameterization schemes for momentum flux under different vertical TKE structures. Key Points: The vertical structures of turbulence kinetic energy (TKE) over the Arctic sea‐ice surface are investigated using MOSAiC dataBudget analysis and spectral analysis are used to analyze TKE vertical structures near the Arctic sea‐ice surfaceThe TKE vertical structures affect the performance of commonly used turbulence parameterizations [ABSTRACT FROM AUTHOR]

Arctic clouds play a key role in Arctic climate variability and change; however, contemporary climate models struggle to simulate cloud properties accurately. Model‐simulated cloud properties are determined by the physical parameterizations and their interactions within the model configuration. Quantifying effects of individual parameterization changes on model‐simulated clouds informs efforts to improve models and provides insights on climate system behavior. This study quantities the influence of parameterization scheme changes on Arctic low cloud properties within the Hadley Center Global Environmental Model 3 atmospheric model using a suite of experiments where individual parameterization packages are changed between the two configurations. The results indicate, surprisingly, that single parameterization changes explain most of the cloud property changes, whereas multiple parameterizations, including non‐cloud schemes, contribute to cloud radiative effect differences. Non‐cloud parameterizations are those not used to compute time step cloud properties. We employ a three‐term decomposition to quantify contributions from (a) regime independent, (b) regime dependent, and (c) the regime frequency of occurrence changes. Decomposition results indicate that cloud property changes vary by meteorological regime, each term contributes differently to each cloud property change, and non‐cloud parameterization changes make substantial contributions to the LW and SW cloud radiative effects by affecting clear‐sky fluxes. The analysis provides insights on the role of non‐cloud parameterizations for setting cloud radiative effects, a pathway for cloud‐atmosphere circulation interactions, raises questions on the importance of infrequently occurring regimes to climate simulations, and on useful observational approaches for improving models. Plain Language Summary: Arctic clouds play a key role in Arctic climate variability and change; however, state‐of‐the‐art climate models struggle to accurately simulate clouds. Errors in model‐simulated clouds have known and unknown influences on the simulated climate and climate change projections. Model cloud properties are determined by the physical parameterizations and their interactions within the model. Thus, to improve model‐simulated clouds, we need to understand the effects of parameterization changes. We use a series of Hadley Center Global Environmental Model 3 atmospheric model simulations where individual parameterizations are changed one‐at‐a‐time. This approach allows us to isolate the influence of individual cloud parameterizations on model‐simulated cloud properties to inform model development and the observations needed to improve models. The results show that individual parameterizations are most important for specific cloud variables and that multiple parameterizations are important to determining the model‐simulated influence of clouds on the energy budget. We also find that changes in model‐simulated cloud properties respond differently under different weather conditions. The analysis provides insights on the role of non‐cloud parameterizations, defined as those that are not used to directly compute cloud properties, for setting cloud radiative effects, the ways that clouds and the atmosphere interact, raises questions on the importance of infrequently occurring weather conditions to climate simulations, and on useful observational approaches for improving models. Key Points: Individual parameterization changes explain cloud property changes while multiple parameterizations explain cloud radiative effect changesThe large‐scale cloud scheme accounts for most of the changes in Arctic meteorological regime frequencyNon‐cloud parameterizations must be considered to understand the full influence of parameterization changes on cloud radiative effects [ABSTRACT FROM AUTHOR]

The Luzon Undercurrent (LUC) is one of the most significant western boundary undercurrents in the northern western Pacific Ocean (WPO), essential for subsurface water transport and connecting subtropical–equatorial circulations. Over the last three decades, abundant observational progress has been made in revealing the basic features of the LUC. However, the dynamics and thus successful modeling of the LUC remain unresolved. In this work, we conducted a high‐resolution (3 km, 60 levels) numerical investigation of the WPO circulation using the China sea multi‐scale ocean modeling system. We paid particular attention to the vertical mixing, aiming to reasonably resolve the LUC by modifying the vertical mixing parameterization. Based on physics reasoning and experiments of physically based modeling, we designed an adaptive mixing scheme (AMS), which used a Munk‐like function in the thermocline for enhanced vertical mixing in the areas of small Richardson numbers. Using the AMS, we reproduced the two‐layer WPO circulations well and captured the inshore component of the LUC consistent with observations. Furthermore, we studied the dynamics of the LUC by analyzing the momentum balance and found that the LUC is primarily maintained by baroclinic pressure gradient force due to strong thermocline tilting near the western boundary. Enhanced vertical mixing in this highly sheared region crucially provides sufficient geostrophic support to sustain the LUC. Also, nonlinearity and submesoscale motions contribute positively to the LUC. This work advances physical understanding of the current‐undercurrent system and improves numerical capability in capturing the LUC and WPO circulations. Plain Language Summary: In the northern western Pacific Ocean (WPO), there exists complex undercurrents below the upper layer (depth ∼500–1,500 m), which flow in the opposite direction from the strong circulation in the upper ocean (depth <∼500 m). The undercurrents are significant for subsurface transport and connecting subtropical‐equatorial circulations; together with the upper circulation, they form the WPO circulation system. The undercurrents are less understood and their underlying physics remains unclear. In this study, we investigate the Luzon Undercurrent (LUC), which flows southward beneath the northward Kuroshio to the east coast off Luzon Island. Abundant observational works have unveiled the characteristics of the LUC, but little attention was paid to its dynamics. So far, the LUC is poorly resolved in prevailing global/regional ocean models. In this work, we developed an adaptive mixing scheme based on physics reasoning and modeling experiments, such that the LUC physics can be resolved and well reproduced in our regional model. Furthermore, we revealed the dynamics of the LUC and summarized key factors to its formation and maintenance. This work advances our physical understanding toward the undercurrents and improves numerical capability in simulating the LUC and WPO circulations. Key Points: Baroclinic pressure gradient force due to strong isopycnal tilting in the thermocline is crucial to the formation and maintenance of the Luzon Undercurrent (LUC)The strong isopycnal tilting is induced by locally enhanced vertical mixing. Nonlinearity and submesoscales also benefit the LUC formationA Munk‐like adaptive mixing scheme is designed to capture the LUC, providing significant improvement over previous results [ABSTRACT FROM AUTHOR]

This article focuses on the fault detection filtering problem for Itô stochastic Takagi–Sugeno (T‐S) fuzzy systems. In terms of line integral Lyapunov function, a sufficient condition of exponential stability in mean square and extended dissipativity for the systems under consideration is established which has less conservatism than the one based on quadratic Lyapunov function. The obtained sufficient condition is nonlinear, which makes the synthesis of fault detection filter being difficult and challenging. By choosing general matrix variables and constructing the appropriate orthogonal complement matrices, the nonlinear sufficient condition can be converted into linear one ingeniously via utilizing Finsler's lemma twice. Thus, the fault detection filter can be developed by virtue of parameterization. It should be pointed out that our filter determined by the parameterization approach includes the one obtained by the equivalent transformation method as a special case. Finally, we demonstrate the feasibility and superiority of our proposed approach through three numerical examples. [ABSTRACT FROM AUTHOR]

Satellite synthetic aperture radar (SAR) provides ocean surface wind fields at 10 m above sea level. The objective is to investigate the capability of SAR satellite StriX observations for mapping offshore wind farm wakes. The focus is on the conditions under which an apparent wind speed‐up is generated, measured in 48% of the 67 images available. The results compare well to Sentinel‐1 observations, showing a 34% wind speed‐up rate during several years based on 1171 images. Three wind speed‐up cases have been studied in detail using the mesoscale Weather, Research, and Forecasting (WRF) model with two wind farm parameterizations. At 10 m above sea level, the SAR‐based observations and WRF model compare for most cases, though only when turbulent kinetic energy (TKE) is included in the wind farm parameterization. The TKE mixes higher momentum downward in a stable atmosphere, causing surface wind speed‐up near the surface. [ABSTRACT FROM AUTHOR]

Accurately inferring realistic subsurface structures poses a considerable challenge due to the impact of morphology on flow and transport behaviors. Traditional subsurface characterization relies on two primary types of data: hard data, derived from direct subsurface measurements, and soft data, encompassing remotely sensed geophysical information and its interpretation. Existing deep‐learning‐based methodologies predominantly focus on the transition from multiple observations to subsurface structures. However, implicit non‐linear correlations among diverse data sources often remain underutilized, leading to potential bias and errors. In this study, we introduce a multiple‐condition fusion network (MCF‐Net) to characterize subsurface structures based on both hard and soft data. To harness the full potential of multiple‐source subsurface observations, two distinct neural networks extract implicit features from hard and soft data. The integration of these features is achieved through multiple‐condition fusion blocks, designed to capture representative characteristics. These blocks are also adept at reconstructing heterogeneous structures and facilitating hydrological parameterization. MCF‐Net exhibits accuracy in estimating subsurface structures across various types of subsurface observations. Experimental results underscore the utility and superiority of MCF‐Net in applications of hydrogeological modeling. Key Points: A novel approach for describing complex subsurface structures using sparse observations (hard data) and auxiliary variables (soft data)The proposed deep learning network is able to establish the implicit relationship among multiple observationsThe proposed approach can be easily extended and widely used for reservoir characterization, hydrogeophysical modeling, and other fields [ABSTRACT FROM AUTHOR]

Representing and preserving complex (non‐Gaussian) spatial patterns in aquifer flow properties during model calibration are challenging. Conventional parameterization methods that rely on linear/Gaussian assumptions are not suitable for representation of property maps with more complex spatial patterns. Deep learning techniques, such as Variational Autoencoders (VAE) and Generative Adversarial Networks (GAN), have recently been proposed to address this difficulty by learning complex spatial patterns from prior training images and synthesizing similar realizations using low‐dimensional latent variables with Gaussian distributions. The resulting Gaussian latent variables lend themselves to calibration with the ensemble Kalman filter‐based updating schemes that are suitable for parameters with Gaussian distribution. Despite their superior performance in generating complex spatial patterns, these generative models may not provide desirable properties that are needed for parameterization of model calibration problems, including robustness, smoothness in the latent domain, and reconstruction fidelity. This paper introduces the second generation of style‐based Generative Adversarial Networks (StyleGAN) for parameterization of complex subsurface flow properties and compares its model calibration properties and performance with those of the convolutional VAE and GAN architectures. Numerical experiments involving model calibration with the Ensemble Smoother with Multiple Data Assimilation (ES‐MDA) in single‐phase and two‐phase fluid flow examples are used to assess the capabilities and limitations of these methods. The results show that parameterization with StyleGANs provides superior performance in terms of reconstruction fidelity and flexibility, underscoring its potential for improving the representation and reconstruction of complex spatial patterns in subsurface flow model calibration problems. Plain Language Summary: Understanding and predicting the complex nature of fluid flow behavior in subsurface environments is important for developing the underlying resources. The quality of predictive models depends on the accuracy of the input parameters that control the fluid flow response. These parameters are typically heterogeneous and highly uncertain. We present a new way of representing and inferring the complex heterogeneity in subsurface flow properties by combining an advanced deep learning architecture with ensemble data assimilation techniques. These methods help with creating more representative models of the Earth's subsurface to better predict their flow response behavior. Unlike the traditional methods that can struggle with producing representative models, the proposed deep learning model (called StyleGAN) offers an improved approach for reconstruction of complex subsurface flow properties from flow response data. In this paper, we introduce this parameterization approach and evaluate it using groundwater pumping tests and two‐phase fluid flow experiments. We also compare the performance of this approach with those from recently introduced deep learning‐based parameterization methods. Our results show that StyleGAN offers a superior model calibration performance with improved reconstruction quality and robustness. Key Points: Style‐based Generative Adversarial Network models improve the parameterization and calibration of complex subsurface flow modelsEnsemble Smoother with Multiple Data Assimilation is used to demonstrate the superior performance of StyleGAN compared to GAN and VAEStyleGAN architecture improves latent domain regularity, leading to enhanced parameterization and improved calibration results [ABSTRACT FROM AUTHOR]

Entrainment rates at varying horizontal grid spacing were diagnosed and analyzed based on Large Eddy Model (LES) and Cloud Resolving Model (CRM) simulations of shallow and deep convection. Results show the estimated entrainment rates increase with increasing resolution, and the growth rate is roughly power‐law related to resolution. However, all commonly used parameterizations except for the buoyancy sorting scheme fail to reproduce the monotonic increase of entrainment with resolution, but rather a slight decrease instead. For these schemes, it is suggested the power‐law fitting formula derived from LES/CRM simulations can be used as a scaling function for high‐resolution entrainment correction. Preliminary tests show that the application of entrainment scaling largely reduces the parcel buoyancy and thus the convective available potential energy, favoring the reduction of parameterized convection at high resolution. Plain Language Summary: As model resolution continues to increase with increasing computational power, cumulus convection becomes partially resolved by the model grid, which requires parameterized convection to be reduced with increasing resolution. The purpose of this study is to investigate the scale dependence of entrainment rate, which is an important component in convection parameterization, by using multiple cloud resolving model simulations of shallow and deep convections. It was found that the estimated entrainment rates increase with increasing resolution, but most current entrainment schemes are unable to reproduce the monotonic increase in entrainment rate with increasing resolution. As a result, a scaling factor between entrainment and resolution was derived and suggested for use in correcting parameterized entrainment rates at high resolution. Key Points: The estimated LES/CRM entrainment rates increase with increasing resolution, and the growth rate is roughly power‐law related to resolutionThe majority of entrainment schemes fail to reproduce the monotonic increase in entrainment rate with increasing resolutionEntrainment scaling helps reduce the parcel buoyancy and thus the convective available potential energy toward higher resolutions [ABSTRACT FROM AUTHOR]

B‐spline curve interpolation is a fundamental algorithm in computer‐aided geometric design. Determining suitable parameters based on data points distribution has always been an important issue for high‐quality interpolation curves generation. Various parameterization methods have been proposed. However, there is no universally satisfactory method that is applicable to data points with diverse distributions. In this work, a hybrid parametrization method is proposed to overcome the problem. For a given set of data points, a classifier via supervised learning identifies an optimal local parameterization method based on the local geometric distribution of four adjacent data points, and the optimal local parameters are computed using the selected optimal local parameterization method for the four adjacent data points. Then a merging method is employed to calculate global parameters which align closely with the local parameters. Experiments demonstrate that the proposed hybrid parameterization method well adapts the different distributions of data points statistically. The proposed method has a flexible and scalable framework, which can includes current and potential new parameterization methods as its components. [ABSTRACT FROM AUTHOR]

Ocean mesoscale eddies are often poorly represented in climate models, and therefore, their effects on the large scale circulation must be parameterized. Traditional parameterizations, which represent the bulk effect of the unresolved eddies, can be improved with new subgrid models learned directly from data. Zanna and Bolton (2020), https://doi.org/10.1029/2020gl088376 (ZB20) applied an equation‐discovery algorithm to reveal an interpretable expression parameterizing the subgrid momentum fluxes by mesoscale eddies through the components of the velocity‐gradient tensor. In this work, we implement the ZB20 parameterization into the primitive‐equation GFDL MOM6 ocean model and test it in two idealized configurations with significantly different dynamical regimes and topography. The original parameterization was found to generate excessive numerical noise near the grid scale. We propose two filtering approaches to avoid the numerical issues and additionally enhance the strength of large‐scale energy backscatter. The filtered ZB20 parameterizations led to improved climatological mean state and energy distributions, compared to the current state‐of‐the‐art energy backscatter parameterizations. The filtered ZB20 parameterizations are scale‐aware and, consequently, can be used with a single value of the non‐dimensional scaling coefficient for a range of resolutions. The successful application of the filtered ZB20 parameterizations to parameterize mesoscale eddies in two idealized configurations offers a promising opportunity to reduce long‐standing biases in global ocean simulations in future studies. Plain Language Summary: This research focuses on improving the accuracy of ocean models by addressing the challenges of representing the mesoscale eddies on coarse grids. These eddies play a crucial role in the Earth's climate system, but traditional climate models struggle to capture their effects. Here, we implemented a new data‐driven parameterization simulating the physics of the mesoscale eddies into the state‐of‐the‐art ocean model. The parameterization is interpretable and captures key physical processes related to the mesoscale eddies known as energy backscatter. We tested this parameterization in two idealized ocean scenarios and found that it significantly improves the biases in the representation of the mean state and energetics. We propose new filtering schemes which improve the physical and numerical properties of the parameterization. Accurate representation of the mesoscale eddies by the present scheme has the potential to resolve long‐standing biases present in global ocean models and thus allow for more reliable climate simulations. Key Points: A data‐driven mesoscale eddy parameterization is implemented and evaluated in different configurations of the GFDL MOM6 ocean modelWe introduce filtering schemes to reduce the generation of grid‐scale noise and enhance the large‐scale backscatterThe subgrid parameterization improves the representation of the energy distributions and the climatological mean state [ABSTRACT FROM AUTHOR]

This study presents the development of a so‐called Turbulent Kinetic Energy (TKE)‐l, or TKE‐l, parameterization of the diffusion coefficients for the representation of turbulent diffusion in neutral and stable conditions in large‐scale atmospheric models. The parameterization has been carefully designed to be completely tunable in the sense that all adjustable parameters have been clearly identified and the number of parameters has been minimized as much as possible to help the calibration and to thoroughly assess the parametric sensitivity. We choose a mixing length formulation that depends on both static stability and wind shear to cover the different regimes of stable boundary layers. We follow a heuristic approach for expressing the stability functions and turbulent Prandlt number in order to guarantee the versatility of the scheme and its applicability for planetary atmospheres composed of an ideal and perfect gas such as that of Earth and Mars. Particular attention has been paid to the numerical stability and convergence of the TKE equation at large time steps, an essential prerequisite for capturing stable boundary layers in General Circulation Models (GCMs). Tests, parametric sensitivity assessments and preliminary tuning are performed on single‐column idealized simulations of the weakly stable boundary layer. The robustness and versatility of the scheme are assessed through its implementation in the Laboratoire de Météorologie Dynamique Zoom GCM and the Mars Planetary Climate Model and by running simulations of the Antarctic and Martian nocturnal boundary layers. Plain Language Summary: In planetary atmospheres, turbulent motions actively contribute to the mixing of quantities such as heat, momentum, and chemical species. Such motions are not resolved in coarse‐grid atmospheric models and have to be parameterized. The parameterization of turbulent mixing should ideally be based on physical laws and sufficiently sophisticated to realistically represent the full spectrum of motions over the full range of stability encountered in the atmospheres. However, it also necessarily contains a number of closure parameters not always well identified and whose values are determined empirically—thereby questioning the universality of the parameterization and its potential application over the full globe or even to other planets—or adjusted to guarantee the numerical stability of the model. This study presents the design of a turbulent mixing parameterization that can be fully calibrated and applied in planetary atmospheres such as that of Mars. We then calibrate the parameterization on an idealized simulation set‐up and test its robustness and performance by running simulations of the Antarctic and Martian atmospheres. Key Points: A simple TKE‐l turbulent diffusion scheme is developed in a semi‐heuristic way for applications in models of the Earth and Mars atmospheresAll adjustable parameters are clearly identified and the number of parameters is minimized to thoroughly assess the parametric sensitivityOnce tuned on GEWEX Atmospheric Boundary Layer Study 1 1D simulations, the scheme is able to capture the Antarctic and Martian stable boundary layers in 3D simulations [ABSTRACT FROM AUTHOR]

Purpose: The J‐difference edited γ‐aminobutyric acid (GABA) signal is contaminated by other co‐edited signals—the largest of which originates from co‐edited macromolecules (MMs)—and is consequently often reported as "GABA+." MM signals are broader and less well‐characterized than the metabolites, and are commonly approximated using a Gaussian model parameterization. Experimentally measured MM signals are a consensus‐recommended alternative to parameterized modeling; however, they are relatively under‐studied in the context of edited MRS. Methods: To address this limitation in the literature, we have acquired GABA‐edited MEGA‐PRESS data with pre‐inversion to null metabolite signals in 13 healthy controls. An experimental MM basis function was derived from the mean across subjects. We further derived a new parameterization of the MM signals from the experimental data, using multiple Gaussians to accurately represent their observed asymmetry. The previous single‐Gaussian parameterization, mean experimental MM spectrum and new multi‐Gaussian parameterization were compared in a three‐way analysis of a public MEGA‐PRESS dataset of 61 healthy participants. Results: Both the experimental MMs and the multi‐Gaussian parameterization exhibited reduced fit residuals compared to the single‐Gaussian approach (p = 0.034 and p = 0.031, respectively), suggesting they better represent the underlying data than the single‐Gaussian parameterization. Furthermore, both experimentally derived models estimated larger MM fractional contribution to the GABA+ signal for the experimental MMs (58%) and multi‐Gaussian parameterization (58%), compared to the single‐Gaussian approach (50%). Conclusions: Our results indicate that single‐Gaussian parameterization of edited MM signals is insufficient and that both experimentally derived GABA+ spectra and their parameterized replicas improve the modeling of GABA+ spectra. [ABSTRACT FROM AUTHOR]

Shape optimization approaches to inverse design offer low‐dimensional, physically‐guided parameterizations of structures by representing them as combinations of primitives. However, on fixed grids, computing the gradient of a user objective via the adjoint variables method requires a product of forward/adjoint field solutions and the Jacobian of the simulation material distribution with respect to the structural shape parameters. Shape parameters often perturb global parts of the simulation grid resulting in many non‐zero Jacobian entries. These are often computed by finite‐difference (FD) in practice, and hence can be non‐trivial. In this work, the gradient calculation is accelerated by invoking automatic differentiation (AD) in instantiations of structural material distributions, enabled by the development of extensible differentiable feature‐mappings from parameters to primitives and differentiable effective logic operations (denoted AutoDiffGeo or ADG). ADG can also be used to accelerate FD‐based shape optimization by efficient boundary selection. AD‐enhanced shape optimization is demonstrated using three integrated photonic examples: a blazed grating coupler, a waveguide transition taper, and a polarization‐splitting grating coupler. The accelerations of the gradient calculation by AD relative to FD with boundary selection exceed 10×$\times$, resulting in total optimization wall time accelerations of 1.4×$1.4\times$–3.8×$3.8\times$ on the same hardware with no compromise to device figure‐of‐merit. [ABSTRACT FROM AUTHOR]

Image processing often requires filtering, which can be effectively performed by using B‐spline surface approximation. This article presents a fast method of approximating data in rectangular (image) form using such surfaces. The method considers dynamic changes of data by representing rows and columns in chordal parameterized form. To improve performance, after parametrization, lines are uniformly resampled using linear interpolation. It allows using the same basis functions with uniform parameterization for approximation of all processed lines. After approximation, reconstruction of original parameterization is required, but its computational complexity is also linear. [ABSTRACT FROM AUTHOR]

The study on the characteristic and the parameterization of cloud droplet effective radius (re) is important for the optimization of warm cloud microphysical schemes in numerical models. Based on numerical simulations combined with the four aircraft observations of stratiform warm clouds in Jiangxi, China, this work investigated their microphysical properties, focusing on the evolutionary pattern and the parameterization of re, as well as the correlation between re and the number concentration (Nc) of cloud droplet and liquid water path (LWP). It is found that there is a negative correlation between re and Nc, and the rate of the decrease could be increased by 2–4 times with a strengthening of collision‐coalescence process. What's more, the direct introduction of collision‐coalescence is conducted based on the existing re parameterization schemes, and the results show that it can perform well in most of collision‐coalescence intensities. It is also found that LWP is positively correlated with re when re is less than 12 μm, after which the relationship changes to a negative correlation due to the impact of rainfall intensity. Plain Language Summary: The bin microphysical scheme can reproduce the microphysical structures of warm cloud, combined with aircraft observations to investigate the microphysics within warm clouds. This work analyzes the evolution characteristics and the parameterization of effective radius in warm clouds based on bin microphysics simulations. Thereafter, the impact of these cloud microphysical quantities to liquid water path (LWP) are also researched. The results show that the rate of effective radius decrease with number concentration can be intensified by collision‐coalescence intensity, and an effective radius parameterization scheme related to collision‐coalescence is proposed based on the existing parameterization schemes. The variation pattern of LWP with effective radius is linked to the critical radius for rainfall intensity. Above all, the effective radius variation pattern depends largely on collision‐coalescence intensity and can affect LWP a lot. These findings are important for understanding warm cloud microphysical parameterization and improving climate assessment. Key Points: The relation between the effective radius and cloud droplet number concentration greatly influenced by collision‐coalescence intensityAn effective radius parameterization scheme which is directly related to collision‐coalescence is considered based on the existing schemesLiquid water path has different relationship with number and effective radius of cloud droplets, also affected by the rainfall intensity [ABSTRACT FROM AUTHOR]

The paper develops a systematic procedure for formulating finite elements on manifolds. The theoretical developments give rise to a modular computational framework for composing coordinate transformations and manifold parameterizations. The procedure is demonstrated with the Cosserat rod model furnishing a novel finite element formulation that rectifies the lack of objectivity of existing finite elements without violating the director constraints or compromising the symmetry of the tangent stiffness at equilibrium. The framework is element‐independent, allowing its implementation as a wrapper to existing element libraries without modification of the element state determination procedures. [ABSTRACT FROM AUTHOR]

This study utilizes Deep Neural Networks (DNN) to improve the K‐Profile Parameterization (KPP) for the vertical mixing effects in the ocean's surface boundary layer turbulence. The deep neural networks were trained using 11‐year turbulence‐resolving solutions, obtained by running a large eddy simulation model for Ocean Station Papa, to predict the turbulence velocity scale coefficient and unresolved shear coefficient in the KPP. The DNN‐augmented KPP schemes (KPP_DNN) have been implemented in the General Ocean Turbulence Model (GOTM). The KPP_DNN is stable for long‐term integration and more efficient than existing variants of KPP schemes with wave effects. Three different KPP_DNN schemes, each differing in their input and output variables, have been developed and trained. The performance of models utilizing the KPP_DNN schemes is compared to those employing traditional deterministic first‐order and second‐moment closure turbulent mixing parameterizations. Solution comparisons indicate that the simulated mixed layer becomes cooler and deeper when wave effects are included in parameterizations, aligning closer with observations. In the KPP framework, the velocity scale of unresolved shear, which is used to calculate ocean surface boundary layer depth, has a greater impact on the simulated mixed layer than the magnitude of diffusivity does. In the KPP_DNN, unresolved shear depends not only on wave forcing, but also on the mixed layer depth and buoyancy forcing. Plain Language Summary: The uppermost tens of meters of the ocean, known as the ocean surface boundary layer, are rich in intricate and chaotic fine‐scale (cm to 100s m) ocean currents referred to as turbulence. These currents, spanning from centimeters to hundreds of meters, play pivotal roles in shaping the oceanic environment and influencing Earth's climate dynamics. Despite their significance, simulating these fine‐scale ocean currents remains beyond the capabilities of current and foreseeable supercomputing resources. Consequently, simplified formulas derived from fundamental principles are commonly employed to approximate these currents in ocean and climate models. However, these approximations still cannot cover all types of choppy currents and uncertainties in these approximations represent a substantial source of bias in contemporary ocean and climate modeling endeavors. In this study, we enhance one of the prevalent physics‐based approximations of fine‐scale turbulent currents using machine learning techniques. Our tests show that integrating machine learning in physics‐based approximation is stable and efficient and is suitable for use in ocean and climate models. Key Points: New versions of K‐Profile Parameterization (KPP), augmented by deep neural networks (DNNs) (KPP_DNN), were developedThe KPP_DNN schemes were trained using Large Eddy Simulations and implemented in the General Ocean Turbulence ModelThe KPP_DNN schemes are stable for long‐term integration and as efficient as the physics‐based KPP schemes [ABSTRACT FROM AUTHOR]

The demand for immersive technology and realistic virtual environments has created a need for automated solutions to generate characters with morphological variations. However, existing approaches either rely on manual labour or oversimplify the problem by limiting it to static meshes or deformation transfers without shape morphing. In this paper, we propose a new cross‐parameterization approach that semi‐automates the generation of morphologically diverse characters with synthesized articulations and animations. The main contribution of this work is that our approach parameterizes deforming characters into a novel hierarchical multi‐sphere domain, while considering the attributes of mesh topology, deformation and animation. With such a multi‐sphere domain, our approach minimizes parametric distortion rates, enhances the bijectivity of parameterization and aligns deforming feature correspondences. The alignment process we propose allows users to focus only on major joint pairs, which is much simpler and more intuitive than the existing alignment solutions that involve a manual process of identifying feature points on mesh surfaces. Compared to recent works, our approach achieves high‐quality results in the applications of 3D morphing, texture transfer, character synthesis and deformation transfer. [ABSTRACT FROM AUTHOR]

A detailed analysis is made of horizontal‐component geomagnetic‐disturbance data acquired at the Colaba observatory in India recording the Carrington magnetic storm of September 1859. Prior to attaining its maximum absolute value, disturbance at Colaba increased with an e‐folding timescale of 0.46 hr (28 min). Following its maximum, absolute disturbance at Colaba decreased as a trend having an e‐folding timescale of 0.31 hr (19 min). Both of these timescales are much shorter than those characterizing the drift period of ring‐current ions. Furthermore, over one 28‐min interval when absolute disturbance was increasing, the data indicate an absolute rate of change of ≥2,436 nT/hr. If this is representative of disturbance generated by a symmetric magnetospheric ring current, then, assuming a standard and widely used parameterization, an interplanetary electric field of ≥451 mV/m is indicated. An idealized and extreme solar‐wind dynamic pressure could, conceivably, reduce this bound on the interplanetary electric field to ≥202 mV/m. If the parameterization for electric‐field extrapolation is accurate, but the field strengths obtained are deemed implausible, then it can be concluded that the Colaba disturbance data were significantly affected by partial‐ring, field‐aligned, or ionospheric currents. The same conclusion is supported by the shortness of the e‐folding timescales characterizing the Colaba data. Several prominent studies of the Carrington event need to be reconsidered. Key Points: Before (after) maximum, the absolute value of disturbance at Colaba increased (decreased) with an exponential timescale of 0.46 hr (0.31 hr)If Colaba disturbance was due to a symmetric ring current, standard extrapolations require an interplanetary electric field of >451 mV/mResults suggest significant contributions to Colaba disturbance by partial‐ring, dayside field‐aligned, or dayside ionospheric currents [ABSTRACT FROM AUTHOR]

Sea ice formation over open water exerts critical control on polar atmosphere‐ocean‐ice interactions, but is only crudely represented in sea ice models. In this study, a collection depth parameterization of new ice for flux polynya models is modified by including the sea ice concentration and ice growth rate as additional factors. We evaluated it in a climate model BCC‐CSM2‐MR and found that it improves simulation of Antarctic sea ice concentration and thickness in most of Indian and Atlantic sectors. Disagreement between the observed Antarctic sea ice expansion during 1981–2014 and the modeled decline still exists but is mitigated when the modified scheme is implemented. Further analysis indicates that these improvements are associated with the overcoming of premature closure of open water, which enhances the response of ocean to surface wind intensification during 1981–2014, and consequently slowdowns the sea surface temperature increase and the resulting Antarctic sea ice reduction. Plain Language Summary: Open water ice formation critically modulates sea ice variations and the associated polar atmosphere‐ocean interaction, but is not well represented in sea ice models. In this study, a modified collection depth parameterization of new ice based on an existing scheme is presented after including sea ice concentration and ice growth rate as additional factors. We evaluated this modified scheme in BCC‐CSM2‐MR and found that it can improve the simulation of mean Antarctic sea ice thickness and concentration in winter as well as Antarctic sea ice expansion from 1981 to 2014. Further analysis implies that these improvements can be attributed to the overcoming of the premature closure of open water areas in model simulations. Key Points: A modified collection thickness parameterization of new ice suitable for large‐scale climate simulations is presentedIt improves the simulation of Antarctic sea ice thickness and concentration, as well as Antarctic sea ice expansion during 1981–2014The improved simulations can be attributed to the overcoming of the premature closure of open water areas where new ice forms [ABSTRACT FROM AUTHOR]

A parameterization of a triangle mesh is a realization in the plane so that all triangles have positive signed area. Triangle mesh parameterizations are commonly computed by minimizing a distortion energy, measuring the distortions of the triangles as they are mapped into the parameter domain. It is assumed that the triangulation is fixed and the triangles are mapped affinely. We consider a more general setup and additionally optimize among the intrinsic triangulations of the piecewise linear input geometry. This means the distortion energy is computed for the same geometry, yet the space of possible parameterizations is enlarged. For minimizing the distortion energy, we suggest alternating between varying the parameter locations of the vertices and intrinsic flipping. We show that this process improves the mapping for different distortion energies at moderate additional cost. We also find intrinsic triangulations that are better starting points for the optimization of positions, offering a compromise between the full optimization approach and exploiting the additional freedom of intrinsic triangulations. [ABSTRACT FROM AUTHOR]

Summary: Grid‐forming (GFM) inverters offer stable frequency support for microgrid systems, even in the absence of synchronous generators. However, the GFM inverters have low inertia and vulnerability to system uncertainties and external disturbances. The conventional dual‐loop proportional integral (PI) control strategy, while widely used for its simplicity and robustness, suffers from poor dynamic performance. Motivated by this, this paper presents an observer‐based residual‐driven dynamic compensation (RDDC) strategy based on the coprime factorization technic and the Youla parameterization theory to achieve the primary control of the GFM inverter. The observer‐based RDDC strategy comprises four components: a PI controller for tracking control, a linear quadratic regulator (LQR) controller for dynamic adjustment, a residual generator based on the Kalman filter for state estimation and residual generation, and a residual compensation controller designed using model matching theory and solved through linear matrix inequality (LMI) methods for disturbance suppression. Simulation and experiment results consistently demonstrate that the observer‐based RDDC strategy ensures system robustness, enhances the dynamic and steady‐state performance of the GFM inverter system, and strengthens the ability of the GFM inverter to suppress disturbances. [ABSTRACT FROM AUTHOR]

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]

Machine learning (ML) is used to build a bulk microphysical parameterization including ice processes. Simulations of the Lagrangian super‐particle model McSnow are used as training data. The ML performs a coarse‐graining of the particle‐resolved microphysics to multi‐category two‐moment bulk equations. Besides mass and number, prognostic particle properties (P3) like melt water, rime mass, and rime volume are predicted by the ML‐based bulk model. The ML‐based scheme is tested with simulations of increasing complexity. As a box model, the ML‐based bulk scheme can reproduce the simulations of McSnow quite accurately. In 3d idealized squall line simulations, the ML‐based P3‐like scheme provides a more realistic extended stratiform region when compared to the standard two‐moment bulk scheme in ICON. In a realistic case study, the ML‐based scheme runs stably, but can not significantly improve the results. This shows that ML can be used to coarse‐grain super‐particle simulations to a bulk scheme of arbitrary complexity. Plain Language Summary: Numerical weather prediction and climate models need a description of unresolved cloud microphysical processes. Such microphysical parameterizations are usually formulated as systems of equations for bulk variables that describe the time evolution of clouds and precipitation. In this study, we use machine learning (ML) techniques to build such a parameterization. As input or training data simulations of a very detailed cloud model are used. This detailed model provides information not only on the mass and number of cloud particles but also other properties like the degree of melting or the mass of liquid drops frozen on the ice particles called rime mass. The ML approach can successfully construct the necessary statistical relations that are needed for microphysical parameterization. This parameterization is then tested in simulations of increasing complexity. The new ML‐based scheme provides physically reasonable solutions and improves the simulation of a line of thunderstorms. Key Points: Machine learning (ML) is successfully applied to build a complex bulk ice microphysics scheme by coarse‐graining output of a Lagrangian particle microphysics modelThe ML‐based P3‐like microphysics scheme improves the representation of the stratiform region of an idealized squall line compared to a classic two‐moment schemeThe ML‐based P3‐like microphysics scheme runs stable and provides meaningful results in three‐dimensional real‐case simulations [ABSTRACT FROM AUTHOR]

Eddy viscosity is employed throughout the majority of numerical fluid dynamical models, and has been the subject of a vigorous body of research spanning a variety of disciplines. It has long been recognized that the proper description of eddy viscosity uses tensor mathematics, but in practice it is almost always employed as a scalar due to uncertainty about how to constrain the extra degrees of freedom and physical properties of its tensorial form. This manuscript borrows techniques from outside the realm of geophysical fluid dynamics to consider the eddy viscosity tensor using its eigenvalues and eigenvectors, establishing a new framework by which tensorial eddy viscosity can be tested. This is made possible by a careful analysis of an operation called tensor unrolling, which casts the eigenvalue problem for a fourth‐order tensor into a more familiar matrix‐vector form, whereby it becomes far easier to understand and manipulate. New constraints are established for the eddy viscosity coefficients that are guaranteed to result in energy dissipation, backscatter, or a combination of both. Finally, a testing protocol is developed by which tensorial eddy viscosity can be systematically evaluated across a wide range of fluid regimes. Plain Language Summary: Numerical fluid flow solvers need to dissipate energy in order to remain numerically stable, and this is most often achieved by adding a mechanism to the governing equations called eddy viscosity. Generally the implementation of eddy viscosity boils down to specifying a scalar coefficient that governs the rate of energy dissipation. However, the true mathematical form of eddy viscosity is that of a higher‐order geometric object called a tensor, and the potential advantages of using this form remain unexplored. This paper uses a generalized version of familiar linear algebra operations (eigenvalues, trace, and determinant) to establish new constraints on the eddy viscosity coefficients that promise to open up this parameterization to renewed scrutiny. Key Points: Eddy viscosity is usually employed as a scalar coefficient, but its true form is that of a tensorEigenanalysis can reveal new constraints on the coefficients of the eddy viscosity tensorTensor unrolling can help expose the power of the eigenanalysis, but only if done in a particular way [ABSTRACT FROM AUTHOR]

In this paper, the vector extension operation is proposed to replace the de Boor‐Cox formula for a fast algorithm to B‐spline basis functions. This B‐spline basis function based on vector extending operation is implemented in the class and shape transformation (CST) parameterization method in place of the traditional Bézier polynomials to enhance the local ability of control and accuracy to represent an airfoil shape. To calculate the k‐degree B‐spline function's nonzero values, the algorithm can improve the computing efficiency by 2k+1 times. [ABSTRACT FROM AUTHOR]

This paper deals with finite‐horizon minimum‐variance and covariance steering problems subject to constraints. The goal of the minimum variance problem is to steer the state mean of an uncertain system to a prescribed vector while minimizing the trace of its terminal state covariance whereas the goal in the covariance steering problem is to steer the covariance matrix of the terminal state to a prescribed positive definite matrix. The paper proposes a solution approach that relies on a stochastic version of the affine disturbance feedback control parametrization. In this control policy parametrization, the control input at each stage is expressed as an affine function of the history of disturbances that have acted upon the system. It is shown that this particular parametrization reduces the stochastic optimal control problems considered in this paper into tractable convex programs or difference of convex functions programs with essentially the same decision variables. In addition, the paper proposes a variation of this control parametrization that relies on truncated histories of past disturbances, which allows for sub‐optimal controllers to be designed that strike a balance between performance and computational cost. The suboptimality of the truncated policies is formally analyzed and closed form expressions are provided for the performance loss due to the use of the truncation scheme. Finally, the paper concludes with a comparative analysis of the truncated versions of the proposed policy parametrization and other standard policy parametrizations through numerical simulations. [ABSTRACT FROM AUTHOR]

Entrainment and detrainment rates (ε and δ) constitute the most critical free parameters in mass flux schemes commonly employed for cumulus parameterizations. Recently, Zhu et al. (2021) introduced a new approach that utilizes aircraft observations to simultaneously estimate ε and δ for cumulus clouds, overcoming the limitation of other observation‐based approaches that solely yield ε without offering insights into δ. This study aims to comprehensively evaluate the reliability of this new approach. First, evaluation using an Explicit Mixing Parcel Model demonstrates the capability of the new approach to back‐calculate predetermined ε and δ based on the physical properties before and after the entrainment mixing. Second, evaluation using large‐eddy simulations illustrates that the new approach yields consistent ε and δ profiles compared to the traditional approach. Sensitivity tests indicate a weak sensitivity of the estimated δ with the new approach to the entrained air source. A decrease in the proportion of cloudy air in the assumed detrained air leads to a reduction in the estimated δ, while ε remains unaffected. Finally, the most appropriate assumptions for entrained and detrained air are discussed. Estimating ε for cumulus parameterizations involves acquiring ambient air more than 500 m away from the cloud edge as entrained air. Due to implicit mean field approximations in the traditional approach, determining the optimal assumption for detrained air properties proves challenging. This study confirms the reliability of the new approach in estimating ε and δ, providing confidence in its application to extensive observational data and advancement in parameterization. Plain Language Summary: Cumulus clouds play a crucial role in weather and climate models and accurately estimating parameters like entrainment and detrainment rates is essential for their representation. Recent research by Zhu et al. (2021) offers a new approach to simultaneously estimate both entrainment and detrainment rates using aircraft observations. This study thoroughly evaluates the reliability of this approach. Based on two advanced high‐resolution models, the new approach proves effective in calculating entrainment and detrainment rates. Sensitivity tests on the source of entrained air and the assumption for detrained air are conducted. To accurately estimate entrainment rates used for cumulus parameterizations, it is advisable to obtain entrained air more than 500 m from the cloud edge. This study faces challenges in determining optimal detrained air properties as the traditional approach of deriving the properties of detrained air—that it is equal to its mean value within the cloud—is flawed. Overall, this study affirms the reliability of the new approach in estimating entrainment and detrainment rates, boosting confidence in its application to extensive observational data and the improvement of cumulus parameterizations. Key Points: A new approach for simultaneously estimating entrainment and detrainment rates in observations is comprehensively evaluatedResults from two high‐resolution models affirm the reliability of the new approachThe optimal source of entrained air for estimating entrainment rates required in cumulus parameterizations is identified [ABSTRACT FROM AUTHOR]

Mesoscale eddies modulate the stratification, mixing, tracer transport, and dissipation pathways of oceanic flows over a wide range of spatiotemporal scales. The parameterization of buoyancy and momentum fluxes associated with mesoscale eddies thus presents an evolving challenge for ocean modelers, particularly as modern climate models approach eddy‐permitting resolutions. Here we present a parameterization targeting such resolutions through the use of a subgrid mesoscale eddy kinetic energy budget (MEKE) framework. Our study presents two novel insights: (a) both the potential and kinetic energy effects of eddies may be parameterized via a kinetic energy backscatter, with no Gent‐McWilliams along‐isopycnal transport; (b) a dominant factor in ensuring a physically‐accurate backscatter is the vertical structure of the parameterized momentum fluxes. We present simulations of 1/2° and 1/4° resolution idealized models with backscatter applied to the equivalent barotropic mode. Remarkably, the global kinetic and potential energies, isopycnal structure, and vertical energy partitioning show significantly improved agreement with a 1/32° reference solution. Our work provides guidance on how to parameterize mesoscale eddy effects in the challenging eddy‐permitting regime. Plain Language Summary: Ocean eddies evolving on horizontal lengthscales of order 10–100 km are not sufficiently resolved in modern global ocean models that have horizontal resolutions of about 25–100 km. The under‐representation of such eddies leads to inaccuracies in the modeled ocean state, including weakened current systems, incorrect stratification, and erroneous distributions of physical and biological ocean tracers. Here we develop a novel approach to mimicking the unresolved eddy effects by artificially energizing the flow in a way that is consistent with eddy dynamics, specifically their vertical structure. We find that our approach is able to correct for a variety of unresolved eddy effects when employed in a coarse‐resolution ocean model and compared against a high‐resolution reference case. Our work provides new insights on how to account for unresolved eddies in the next generation of climate models. Key Points: We propose a parameterization for mesoscale eddies targeting ocean models at eddy‐permitting resolutionsWe find that both the potential and kinetic energy effects of eddies on the flow may be parameterized via a kinetic energy backscatterThe novel approach of our backscatter scheme is its use of vertical structure, that is, backscattering onto the equivalent barotropic mode [ABSTRACT FROM AUTHOR]

There is growing interest in discovering interpretable, closed‐form equations for subgrid‐scale (SGS) closures/parameterizations of complex processes in Earth systems. Here, we apply a common equation‐discovery technique with expansive libraries to learn closures from filtered direct numerical simulations of 2D turbulence and Rayleigh‐Bénard convection (RBC). Across common filters (e.g., Gaussian, box), we robustly discover closures of the same form for momentum and heat fluxes. These closures depend on nonlinear combinations of gradients of filtered variables, with constants that are independent of the fluid/flow properties and only depend on filter type/size. We show that these closures are the nonlinear gradient model (NGM), which is derivable analytically using Taylor‐series. Indeed, we suggest that with common (physics‐free) equation‐discovery algorithms, for many common systems/physics, discovered closures are consistent with the leading term of the Taylor‐series (except when cutoff filters are used). Like previous studies, we find that large‐eddy simulations with NGM closures are unstable, despite significant similarities between the true and NGM‐predicted fluxes (correlations >0.95). We identify two shortcomings as reasons for these instabilities: in 2D, NGM produces zero kinetic energy transfer between resolved and subgrid scales, lacking both diffusion and backscattering. In RBC, potential energy backscattering is poorly predicted. Moreover, we show that SGS fluxes diagnosed from data, presumed the "truth" for discovery, depend on filtering procedures and are not unique. Accordingly, to learn accurate, stable closures in future work, we propose several ideas around using physics‐informed libraries, loss functions, and metrics. These findings are relevant to closure modeling of any multi‐scale system. Plain Language Summary: Even in state‐of‐the‐art climate models, the effects of many important small‐scale processes cannot be directly simulated due to limited computing power. Thus, these effects are represented using functions called parameterizations. However, many of the current physics‐based parameterizations have major shortcomings, leading to biases and uncertainties in the models' predictions. Recently, there has been substantial interest in learning such parameterizations directly from short but very high‐resolution simulations. Most studies have focused on using deep neural networks, which while leading to successful parameterizations in some cases, are hard to interpret and explain. A few more recent studies have focused on another class of machine‐learning methods that discover equations. This approach has resulted in fully interpretable but unsuccessful parameterizations that produce unphysical results. Here, using widely used test cases, we (a) explain the reasons for these unphysical results, (b) connect the discovered equations to well‐known mathematically derived parameterizations, and (c) present ideas for learning successful parameterizations using equation‐discovery methods. Our main finding is that the common loss functions that match patterns representing effects of small‐scale processes are not enough, as important physical phenomena are not properly learned. Based on this, we have proposed a number of physics‐aware metrics and loss functions for future work. Key Points: Subgrid‐scale momentum/heat flux closures discovered using common algorithms are the analytically derivable nonlinear gradient model (NGM)In 2D turbulence/convection, NGM leads to unstable online simulations due to its inability to fully capture key inter‐scale energy transfersWe suggest that physics‐informed loss functions, libraries, metrics, and sparsity selections are needed to discover accurate/stable closures [ABSTRACT FROM AUTHOR]

Subgrid‐scale processes, such as atmospheric gravity waves (GWs), play a pivotal role in shaping the Earth's climate but cannot be explicitly resolved in climate models due to limitations on resolution. Instead, subgrid‐scale parameterizations are used to capture their effects. Recently, machine learning (ML) has emerged as a promising approach to learn parameterizations. In this study, we explore uncertainties associated with a ML parameterization for atmospheric GWs. Focusing on the uncertainties in the training process (parametric uncertainty), we use an ensemble of neural networks to emulate an existing GW parameterization. We estimate both offline uncertainties in raw NN output and online uncertainties in climate model output, after the neural networks are coupled. We find that online parametric uncertainty contributes a significant source of uncertainty in climate model output that must be considered when introducing NN parameterizations. This uncertainty quantification provides valuable insights into the reliability and robustness of ML‐based GW parameterizations, thus advancing our understanding of their potential applications in climate modeling. Plain Language Summary: Climate models are unable to resolve processes that vary on length and time scales smaller than the model resolution and timestep. For example, atmospheric gravity waves (GWs), which are waves created when winds encounter disturbances to the flow, such as mountains, convection and fronts, can have wavelengths smaller than the spacing between grid cells. Climate models use "parameterizations" to capture the effect of these processes. Machine learning based parameterizations are becoming popular because they can learn relationships purely from data. However, we do not have a good understanding of the uncertainties introduced through machine learning parameterizations. This study estimates uncertainties associated with training a neural network (NN) GW parameterization. We explore uncertainties in the NN output, as well as the uncertainties in the climate model output, when the NN is used for the GW parameterization. Key Points: Using ensembles of neural networks, we learn parametric uncertainties associated with an emulator of a gravity wave parameterizationWhen coupled to the climate model, the ensemble of neural networks reveals increased climate variabilityParametric uncertainty dominates the Quasi‐Biennial Oscillation statistics, although polar vortex properties remain robust to parameters [ABSTRACT FROM AUTHOR]

Neural networks (NNs) are increasingly used for data‐driven subgrid‐scale parameterizations in weather and climate models. While NNs are powerful tools for learning complex non‐linear relationships from data, there are several challenges in using them for parameterizations. Three of these challenges are (a) data imbalance related to learning rare, often large‐amplitude, samples; (b) uncertainty quantification (UQ) of the predictions to provide an accuracy indicator; and (c) generalization to other climates, for example, those with different radiative forcings. Here, we examine the performance of methods for addressing these challenges using NN‐based emulators of the Whole Atmosphere Community Climate Model (WACCM) physics‐based gravity wave (GW) parameterizations as a test case. WACCM has complex, state‐of‐the‐art parameterizations for orography‐, convection‐, and front‐driven GWs. Convection‐ and orography‐driven GWs have significant data imbalance due to the absence of convection or orography in most grid points. We address data imbalance using resampling and/or weighted loss functions, enabling the successful emulation of parameterizations for all three sources. We demonstrate that three UQ methods (Bayesian NNs, variational auto‐encoders, and dropouts) provide ensemble spreads that correspond to accuracy during testing, offering criteria for identifying when an NN gives inaccurate predictions. Finally, we show that the accuracy of these NNs decreases for a warmer climate (4 × CO2). However, their performance is significantly improved by applying transfer learning, for example, re‐training only one layer using ∼1% new data from the warmer climate. The findings of this study offer insights for developing reliable and generalizable data‐driven parameterizations for various processes, including (but not limited to) GWs. Plain Language Summary: Scientists increasingly use machine learning methods, especially neural networks (NNs), to improve weather and climate models. However, it can be challenging for an NN to learn rare, large‐amplitude events because they are infrequent in training data. In addition, NNs need to express their confidence (certainty) about a prediction and work effectively across different climates, for example, warmer climates due to increased CO2. Traditional NNs often struggle with these challenges. Here, we share insights from emulating known physics (gravity waves) with NNs in a state‐of‐the‐art climate model. We propose specific strategies for effectively learning rare events, quantifying the uncertainty of NN predictions, and making reliable predictions across various climates. For instance, one strategy to address the learning of rare events involves inflating the impact of infrequent events in the training data. We also demonstrate that several methods could be useful in determining the uncertainty of the predictions. Furthermore, we show that NNs trained on simulations of the historical period do not perform as well in warmer climates. We then improve NN performance by employing transfer learning using limited new data from warmer climates. This study provides lessons for developing robust and generalizable approaches for using NNs to improve models in the future. Key Points: Whole Atmosphere Community Climate Model's orographic, convective, and frontal gravity wave parameterizations are emulated using neural nets to inform future modeling effortsData imbalance is addressed via resampling and weighted loss; uncertainty quantification via Bayesian, dropout, and variational methodsPerformance of the neural nets in a warmer climate is improved via transfer learning with ∼1% new data [ABSTRACT FROM AUTHOR]

We train random and boosted forests, two machine learning architectures based on regression trees, to emulate a physics‐based parameterization of atmospheric gravity wave momentum transport. We compare the forests to a neural network benchmark, evaluating both offline errors and online performance when coupled to an atmospheric model under the present day climate and in 800 and 1,200 ppm CO2 global warming scenarios. Offline, the boosted forest exhibits similar skill to the neural network, while the random forest scores significantly lower. Both forest models couple stably to the atmospheric model, and control climate integrations with the boosted forest exhibit lower biases than those with the neural network. Integrations with all three data‐driven emulators successfully capture the Quasi‐Biennial Oscillation (QBO) and sudden stratospheric warmings, key modes of stratospheric variability, with the boosted forest more accurate than the random forest in replicating their statistics across our range of carbon dioxide perturbations. The boosted forest and neural network capture the sign of the QBO period response to increased CO2, though both struggle with the magnitude of this response under the more extreme 1,200 ppm scenario. To investigate the connection between performance in the control climate and the ability to generalize, we use techniques from interpretable machine learning to understand how the data‐driven methods use physical information. We leverage this understanding to develop a retraining procedure that improves the coupled performance of the boosted forest in the control climate and under the 800 ppm CO2 scenario. Plain Language Summary: Parameterizations are reduced‐complexity models that estimate the effects of physical processes smaller than what can be resolved by the grid of a weather or climate model. While necessary for realistic simulations, they are a source of uncertainty in climate projections. Recently, machine learning has been used to augment or replace conventional parameterizations of atmospheric gravity waves, a type of motion by which disturbances near the Earth's surface can affect the wind higher up. We compare several machine learning approaches to the gravity wave parameterization problem. In particular, we test neural networks against random and boosted forests, which are built around flowchart‐like models called regression trees. We find that boosted forests, though not widely used for climate model parameterization, are especially successful, scoring as well as or better than neural networks on various performance metrics. We then provide proof‐of‐concept of a novel method to retrain the boosted forest so that it uses its input data more in line with the physics of the system, and show that this technique improves the forest's behavior when used together with an atmospheric model. Key Points: Two kinds of regression forest emulate a gravity wave parameterization offline and online, with boosted forests outperforming random forestsRelative to a neural network benchmark, the boosted forest exhibits similar online skill and ability to generalize to new climatesFeature importance analysis informs a retraining procedure to improve online behavior of data‐driven parameterizations [ABSTRACT FROM AUTHOR]

This paper introduces a novel multi‐variate volatility model that can accommodate appropriately defined network structures based on low‐frequency and high‐frequency data. The model offers substantial reductions in the number of unknown parameters and computational complexity. The model formulation, along with iterative multi‐step‐ahead forecasting and targeting parameterization are discussed. Quasi‐likelihood functions for parameter estimation are proposed and their asymptotic properties are established. A series of simulation studies are carried out to assess the performance of parameter estimation in finite samples. Furthermore, a real data analysis demonstrates that the proposed model outperforms the existing volatility models in prediction of future variances of daily return and realized measures. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we investigate the global adaptive stabilization problem via partial‐state feedback for a class of uncertain chained‐form nonholonomic systems with the dynamic uncertainty and nonlinear parameterization. The notions of Sontag's input‐to‐state stability (ISS) and ISS‐Lyapunov function, together with the changing supply rates technique are used to overcome the dynamic uncertainty. The nonlinear parameterization is well treated with the aid of the parameter separation technique. The discontinuous input‐to‐state scaling technique is employed in this procedure to derive the global stabilization controllers. Additionally, we develop a switching adaptive control strategy in order to get around the smooth stabilization burden associated with nonholonomic systems. The simulation results illustrate the efficacy of the presented algorithm. [ABSTRACT FROM AUTHOR]

This paper considers structural controllability of multi‐agent systems (MASs) with switching topologies, in which each interaction topology is modeled by a weighted digraph. Under the adopted relative protocol, the MASs with directed switching topologies are modeled by a switched system with parameter interdependence. The technique of linear parameterization, the graph theory, and so forth are applied to tackle the structural controllability of the switched system. A graph‐theoretic interpretation for structural controllability of the system is proposed. Examples with single leader and multiple leaders are presented to illustrate our work. [ABSTRACT FROM AUTHOR]

Forest fires darken snow albedo and degrade forest structure, ultimately reducing peak snow–water storage, and advancing snowmelt timing for up to 15 years following fire. To date, no volumetric estimates of watershed‐scale postfire effects on snow–water storage and snowmelt timing have been quantified over decades of postfire recovery. Using postfire parameterizations in a spatially‐distributed snow mass and energy balance model, SnowModel, we estimated postfire recovery of forest fire effects on snow–water equivalent (SWE) and snowmelt timing over decades following fire. Using this model, we quantified volumetric recovery of forest fire effects on snow hydrology across a chronosequence of eight sub‐alpine forests burned between 2000 and 2019 in the Triple Divide of western Wyoming. We found that immediately following fire, forest fire effects reduced snow–water storage by 6.8% (SD = 11.2%) and advanced the snow disappearance date by 31 days (SD = 9 days). Across the 15‐year recovery following fire, forest fire effects reduced snow–water storage by 4.5% (SD = 11.4%). Postfire effects on snow hydrology generally recovered over time, but still persisted beyond 15‐years following fire due to the observed postfire shift from forest to open meadow. Estimates of postfire reductions on peak SWE summed over the entire 15‐year postfire recovery period were 18 times greater than the immediate losses in the first winter following fire alone. These lasting effects of forest fires on snow hydrology decades following fire highlight the importance of postfire parameterizations for more accurate watershed‐scale volumetric estimates of forest fire effects on snow–water resources. [ABSTRACT FROM AUTHOR]

A one‐dimensional (1D) multifluid population balance model approach is presented as a compromise between computational effort and accuracy. The approach is used to test process scenarios, perform sensitivity analysis, and provide a reliable reactor scale‐up and optimization tool. The article focuses on a mini‐plant batch bubble column, where the scale‐up behavior in terms of bubble column height, gas flux, and composition of the liquid phase is investigated. Although simplifications were made, the model requires calibration to experimental data using different calibration methods. An optimal calibration procedure is found that minimizes experimental effort while maximizing scalability. The model was tested on various liquid‐phase compositions, and it was found to reproduce experimental data accurately. However, the model cannot reproduce flow regime changes and does not perform well across substance systems. The study shows that the applied 1D multifluid population balance approach is a valuable and reliable tool in multiphase reactor scale‐up and optimization. [ABSTRACT FROM AUTHOR]

Freezing temperature parameterization significantly impacts the heat balance at sea‐ice bottom and, consequently, the simulated sea‐ice thickness. Here, the single‐column model ICEPACK was used to investigate the impact of the freezing temperature parameterization on the simulated sea‐ice thermodynamic growth during the MOSAiC expedition from October 2019 to September 2020. It is shown that large model errors exist with the standard parameterization and that different formulations for calculating the freezing temperature impact the simulated sea‐ice thickness significantly. Considering the winter mixed layer temperature, a modified parameterization of the freezing point temperature based on Mushy scheme was developed. The mean absolute error (ratio) of simulating sea‐ice thickness for all buoys reduces from 7.4 cm (4.9%) with the "Millero" scheme, which performs the best among the existing schemes in the ICEPACK model, to 4.2 cm (2.9%) with the new developed scheme. Plain Language Summary: The heat transferred from the ocean to the sea‐ice influences the growth and melting of the sea‐ice. Freezing temperature is an essential parameter for calculating the heat transfer. Nevertheless, few studies have attempted to evaluate the impact of different freezing temperature parameterizations on the simulated sea‐ice thermodynamic growth. This study uses observed atmosphere and ocean data to force a single‐column model. Using different methods to calculate the freezing temperature significantly impacts the simulated sea‐ice thickness. After a series of testing and comparisons, we have developed a modified parameterization of freezing temperature that significantly reduces the simulation deviation from the observations. Key Points: Different parameterizations of the freezing temperature significantly influence the simulated sea‐ice thicknessA modified‐Mushy parameterization method is developed for the freezing temperature, significantly improving ice thickness simulation [ABSTRACT FROM AUTHOR]

This study explores the impact of coupling cumulus and planetary boundary layer (PBL) parameterizations on diurnal precipitation forecasting during the plum rainy season in Jiangsu Province, China, using a double grid‐nesting approach. Results show that coherent coupling of cumulus (only in the 15 km grid outer domain [O]) and PBL parameterizations leads to improved forecasting of diurnal variations in the morning, afternoon, and the evening. Increasing the frequency of the Kain‐Fritsch (KF) cumulus scheme in [O] enhances subgrid precipitation while reducing grid‐scale precipitation, resulting in a more accurate representation of daytime convective activities and a reduction in over‐forecasting of evening valley and early‐morning precipitation. Additionally, coupling a suitable PBL scheme mitigates the overpredicted afternoon peak by facilitating turbulent mixing to penetrate higher altitudes with a thicker layer, thereby reducing instability energy accumulation. A higher KF frequency in [O] retains less low tropospheric moisture, reducing moisture convergence into the 1 km grid inner domain [I] and decreasing overpredicted daytime precipitation in [I]. Various PBL schemes produce distinct vertical distributions of turbulent moisture and heat transport, impacting convection and precipitation in [I] resolved by cloud microphysics processes. The coherent coupling of these parameterizations maintains a balanced supply of convective energy and water vapor, significantly improving diurnal precipitation forecasts in [I]. Isolating these parameterizations between nested grids may undermine this improvement. Plain Language Summary: Accurate diurnal precipitation forecasting remains a challenge. This study aims to effectively couple cumulus and planetary boundary layer (PBL) parameterizations to enhance diurnal precipitation forecasts using a double grid‐nesting approach. We showed that coherent coupling of cumulus and PBL parameterizations improves forecasting of diurnal variations during the plum rainy season in Jiangsu Province, China. Increasing the frequency of the KF cumulus scheme more accurately represents daytime convective activities and reduces over‐forecasting of evening valley and early‐morning precipitation. Coupling an appropriate PBL scheme that extends turbulent mixing into deeper layers mitigates the accumulation of instability energy, thereby reducing overpredicting of the afternoon peak. A higher KF frequency in the 15 km grid outer domain [O] retains less low tropospheric moisture, reducing moisture convergence into the 1 km grid inner domain [I] and decreasing overpredicted daytime precipitation in [I]. Diverse PBL schemes result in varying vertical distributions of turbulent moisture and heat transport, affecting explicit convection and precipitation in [I]. Therefore, the cohesive integration of cumulus and PBL parameterizations across nested grids significantly enhances diurnal precipitation forecasts. Key Points: Coherent coupling between cumulus and planetary boundary layer (PBL) parameterizations improves the nested rainfall diurnal cycle forecastIncreasing cumulus parameterization frequency reduces the nested morning and outer‐domain evening valley rainfall overforecastAdjusting PBL parameterization weakens the rainfall afternoon peak and daytime total amount overprediction [ABSTRACT FROM AUTHOR]

Identifying how aerosol particles interact with atmospheric water is critical to understand climate and precipitation. Ice‐nucleating particles (INP) trigger the formation of atmospheric ice crystals at higher temperatures than pure water. They are difficult to characterize because of their scarce occurrence, and variability, in the atmosphere, especially at temperatures above −20°C. It has been demonstrated that at these temperatures, biological aerosol particles can contribute significantly to INP number concentration. This study incorporates a series of offline, size‐segregated measurements of INPs collected at the Puy de Dôme station (PUY, 1,465 m a.s.l.) over a 6 month period from October to May, covering the transitions from autumn, winter, to spring. These measurements show a general trend of decreasing particle number concentrations during the winter months and higher concentration during autumn and spring. INP concentrations measured in the range of −5 and −18°C, had concentrations of 0.001 INP/Lair at the warmest temperatures, and between 0.01 and 0.1 INP/Lair at the coldest temperatures. The majority of INP measured at temperatures warmer than −15°C were heat labile, suggesting a biological or organic origin. The INP variability was compared with collocated aerosol physical and chemical properties, allowing us to associate highest INP concentrations with local and marine origins. Following these comparisons, we use aerosol total number concentration to develop a new parameterization. In addition, this parameterization is specifically optimized for warmer temperature INP measurements, and demonstrated a good performance when tested on independent data sets. Plain Language Summary: Understanding how tiny particles in the air (aerosol particles) interact with water in the atmosphere is crucial for studying climate and precipitation. Ice Nuclei Particles (INP) play a role in forming ice crystals in the atmosphere, especially at higher temperatures. This is important because it's been found that biological aerosol particles can significantly contribute to INP at temperatures above −20°C. The study conducted offline measurements of INPs over 6 months at the Puy de Dôme station, covering the transition from autumn to spring. Results showed a general trend of fewer particles during winter and more during autumn and spring. The INP concentrations were highest at temperatures between −5 and −18°C, with warmer temperatures having 0.001 INP per liter of air and colder temperatures having 0.01 to 0.1 INP per liter of air. Most INPs at temperatures above −15°C were heat‐sensitive, indicating a biological or organic origin. This study linked high INP concentrations to local and marine sources by comparing them with aerosol properties. A new parameterization based on total aerosol number concentration, specifically optimized for warmer temperatures, performed well when tested on independent data sets. Key Points: Size‐segregated airborne ice‐nucleating particles (INP) concentrations were measured at an altitude station in Central France over 6 monthsSeasonal variations are observed with a minimum in winter. The majority of INPs is biological and activated above −18°CWe developed a parameterization for predicting INP concentrations at warm temperatures based on total aerosol concentrations [ABSTRACT FROM AUTHOR]

The non‐local model of mixing based on internal wave breaking, IDEMIX, is implemented as an enhancement of a turbulent kinetic energy closure model in three non‐eddy resolving general circulation ocean models that differ in the discretization and choice of computational grids. In IDEMIX internal wave energy is generated by an energy flux resulting from near‐inertial waves induced by wind forcing at the surface, and at the bottom, by an energy flux that parameterizes the transfer of energy between baroclinic and barotropic tides. In all model simulations with IDEMIX, the mixing work is increased compared to the reference solutions without IDEMIX, reaching values in better agreement with finestructure observations. Furthermore, the horizontal structure of the mixing work is more realistic as a consequence of the heterogeneous forcing functions. All models with IDEMIX simulate deeper thermocline depths related to stronger shallow overturning cells in the Indo‐Pacific. In the North Atlantic, deeper mixed layers in simulations with IDEMIX are associated with an increased Atlantic overturning circulation and an increase of northward heat transports toward more realistic values. The response of the deep Indo‐Pacific overturning circulation and the weak bottom cell of the Atlantic to the inclusion of IDEMIX is incoherent between the models, suggesting that additional unidentified processes and numerical mixing may confound the analysis. Applying different tidal forcing functions leads to simulation differences that are small compared to differences between the different models or between simulations with IDEMIX and without IDEMIX. Plain Language Summary: Waves in the ocean interior play a fundamental role for ocean dynamics since they can carry energy over long distances and, once they break, lead to turbulent mixing. This turbulent mixing can cause dense water masses to rise from the deep ocean with a direct impact on large‐scale currents. The wave dynamics occur on spatial scales that cannot be resolved in global ocean or climate models. To account for these processes, we apply the new parameterization IDEMIX that describes internal wave generation, propagation, and mixing. Using three different ocean models with and without IDEMIX ensures that we can identify model‐specific effects of the parameterization and discriminate them from those independent of the model. We find that the simulated mixing patterns agree better with observations once IDEMIX is applied. Large‐scale currents and the vertical temperature distribution are substantially affected by the internal wave parameterization. Whether this leads to an improved agreement with observed currents and water mass properties depends on the specific model and on numerical effects. In most cases, simulations with IDEMIX are not very sensitive to details of how the internal wave model is driven by tidal energy input. Key Points: the IDEMIX closure for a consistent representation of internal wave‐induced mixing is evaluated in three state‐of‐the‐art ocean modelsonly in simulations with IDEMIX can the models reproduce the magnitude and spatial variability of the observed mixing workmost changes with IDEMIX can be attributed to stronger mixing, but some effects are confounded by other processes and numerical mixing [ABSTRACT FROM AUTHOR]

A single column model with parameterized large‐scale (LS) dynamics is used to better understand the response of steady‐state tropical precipitation to relative sea surface temperature under various representations of radiation, convection, and circulation. The large‐scale dynamics are parametrized via the weak temperature gradient (WTG), damped gravity wave (DGW), and spectral weak temperature gradient (Spectral WTG) method in NCAR's Single Column Atmosphere Model (SCAM6). Radiative cooling is either specified or interactive, and the convective parameterization is run using two different values of a parameter that controls the degree of convective inhibition. Results are interpreted in the context of the Global Atmospheric System Studies ‐Weak Temperature Gradient (GASS‐WTG) Intercomparison project. Using the same parameter settings and simulation configuration as in the GASS‐WTG Intercomparison project, SCAM6 under the WTG and DGW methods produces erratic results, suggestive of numerical instability. However, when key parameters are changed to weaken the large‐scale circulation's damping of tropospheric temperature variations, SCAM6 performs comparably to single column models in the GASS‐WTG Intercomparison project. The Spectral WTG method is less sensitive to changes in convection and radiation than are the other two methods, performing qualitatively similarly across all configurations considered. Under all three methods, circulation strength, represented in 1D by grid‐scale vertical velocity, is decreased when barriers to convection are reduced. This effect is most extreme under specified radiative cooling, and is shown to come from increased static stability in the column's reference radiative‐convective equilibrium profile. This argument can be extended to interactive radiation cases as well, though perhaps less conclusively. Plain Language Summary: Single column models, as the name suggests, only model the vertical dimension of the atmosphere. They are simpler than full‐scale 3D global circulation models, but nonetheless play an important role in model development and in better understanding physical phenomena. We use NCAR's Single Column Atmosphere Model (SCAM6) to better understand tropical rainfall. In a single column model, the atmospheric wind coming from other locations (the large‐scale circulation) must be either specified or approximated using a parameterization. We implement three different parameterizations of the large‐scale circulation into SCAM6 and assess how SCAM6 responds to various changes while using these parameterizations. The Global Atmospheric System Studies‐Weak Temperature Gradient (GASS‐WTG) Intercomparison project assessed the performance of various other single column models using two parameterizations of the large‐scale circulation. We fold SCAM6 into this Intercomparison, and we find that SCAM6 performs substantially differently to its peers under the settings used in the GASS‐WTG Intercomparison project, but more comparably to its peers when key circulation parameters are relaxed. Another notable finding is that, across all three parameterizations of large‐scale dynamics, circulation strength decreases when we reduce SCAM6's barrier to convection. Key Points: We use three different methods to parameterize the large‐scale (LS) dynamics in NCAR's single column atmospheric model (SCAM6)As in the Global Atmospheric System Studies Intercomparison, we test SCAM6's response to various boundary conditions and model parametersUnder all three methods, circulation strength is decreased when barriers to convection are reduced [ABSTRACT FROM AUTHOR]

This paper presents a Youla‐Kucera based interpolation between a set of Linear Parameter‐Varying (LPV) controllers, each one being a gain‐scheduled of Linear Time‐Invariant (LTI) controllers designed separately for different operating points. The gain‐scheduling is achieved based on Youla‐Kucera (YK) parameterization. A generalized LPV‐YK control structure is designed to interpolate between various LPV controllers. The closed‐loop system is proved to guarantee the quadratic stability for any continuous/discontinuous interpolating signals in terms of a set of Linear Matrix Inequalities (LMIs). The proposed method can help multi‐variable and multi‐objective systems to achieve high performances at different operating conditions and different critical situations regardless of the interpolation rate. A numerical example is simulated to show the importance of the proposed method to achieve different objectives for lateral control of autonomous vehicles. In addition, the approach has been tested on a real Renault ZOE vehicle to validate its real performance, and compare it with a standard polytopic LPV controller. [ABSTRACT FROM AUTHOR]

Identifiability constraints are necessary for parameter estimation when fitting models with nonlinear covariate associations. The choice of constraint affects standard errors of the estimated curve. Centring constraints are often applied by default because they are thought to yield lowest standard errors out of any constraint, but this claim has not been investigated. We show that whether centring constraints are optimal depends on the response distribution and parameterization, and that for natural exponential family responses under the canonical parametrization, centring constraints are optimal only for Gaussian response. [ABSTRACT FROM AUTHOR]

A recent study comparing ozone column depths and methane lifetimes at varied atmospheric O2 (pO2) levels calculated in the Kasting‐group 1‐D photochemical model and the Whole Atmosphere Community Climate Model version 6 (WACCM6) 3‐D model (Ji, Kasting, et al., 2023; https://doi.org/10.1098/rsos.230056) has exposed weaknesses in both models in parameterizing photolysis in the O2 Schumann‐Runge bands, 175–205 nm. WACCM6 does a good job for Earth's present atmosphere but neglects scattering, which becomes important at low pO2. The 1‐D model includes scattering but is based on an out‐of‐date band model, and it neglects the temperature dependence of photolysis at low pO2. We have revised and improved the 1‐D photochemical model by replacing the old O2 photolysis algorithm with a new correlated‐k parameterization, which improves accuracy for all O2 levels and all temperature profiles. The WACCM6 parameterization was also included in the 1‐D model for comparative purposes. The correlated‐k and WACCM6 photolysis algorithms agree well for both the present atmosphere and for an atmosphere containing 10−3 times the present O2 level, but only if multiple scattering is included at low pO2. The correlated‐k parameterization will be made available to photochemical modeling groups who might choose to adopt it. Plain Language Summary: In today's atmosphere, the absorption of incoming ultraviolet radiation by O2 plays a decisive role in creating O atoms that can react to form ozone (O3), as well as shielding other gases from photolysis. However, this absorption is difficult to parameterize in atmospheric models due to its complex structure at wavelengths of 175–205 nm, which we call the Schumann‐Runge bands. Good models for SR absorption in today's atmosphere already exist, but not all of them may be suitable for use in low‐O2 atmospheres in which multiple scattering is important. Here, we develop a new parameterization for SR absorption by employing a "correlated‐k" approach that has been widely used in climate models at both visible and infrared wavelengths. This approach accounts for the strong temperature dependence of the absorption and agrees well with existing models of O2 absorption in the present atmosphere. It should also be useful in simulations of low‐O2 atmospheres on early Earth, for which scattering must be included, as well as for atmospheres of putative Earth‐like exoplanets that astronomers hope to identify over the next several decades. Key Points: To parameterize O2 absorption, we generated a correlated‐k table based on detailed line‐by‐line calculations at 150, 200, 250, and 300 KThe new parameterization matches laboratory measurements and is well suited to include scattering at lower O2 levelsEarly earth photochemical models based on the old exponential sum fits should consider the new correlated‐k to achieve more accurate results [ABSTRACT FROM AUTHOR]

The charge structure in thunderstorms may be strongly affected by different secondary ice production (SIP) processes, but has not been well understood. In this study, the impacts of three SIP mechanisms on microphysics and electrification in a squall line are investigated using model simulation, including the rime‐splintering, ice‐ice collisional breakup, and shattering of freezing drops. The parameterization of the three SIP mechanisms, a noninductive and an inductive charging parameterization are implemented in the spectral bin microphysics. The results show that with SIP processes included, the modeled radar reflectivity is more consistent with observation. It is found that both the mass and concentrations of graupel/hail are enhanced by SIP processes, while the diameter decreases. The mixing ratio of ice/snow decreases due to the rime‐splintering, and increases in mixing ratio are due to the shattering of freezing drops. Particle charging is significantly affected by SIP, leading to a dipole structure of the total charge density, which includes a lower negative and an upper positive charge region. With both the noninductive and inductive charging considered, the charge carried by graupel/hail changes from negative to a bipolar structure, and the charge sign carried by ice/snow is inverted due to the SIP. The modeled lightning activity is enhanced by implementing all three SIP processes, while if only considering the rime‐splintering process, the flash rate would be suppressed. The insights obtained from this study highlight the importance of considering different mechanisms of SIP in modeling the charge structure and lightning activity in thunderstorms. Plain Language Summary: Electrification in thunderstorms is strongly related to microphysics, especially the ice‐phase processes. However, the ice microphysics in deep convective clouds is very complicated, and the impacts of different ice‐phase processes on cloud electrification are not well understood. One of the unresolved questions is how the charge structure in thunderstorms can be affected by various secondary ice production (SIP) mechanisms. Until now, only a small number of studies have investigated this issue, and most of them focused on a single SIP (rime‐splintering process). However, recent studies have shown that other SIP mechanisms, especially the shattering of freezing drops and ice‐ice collisional breakup, can greatly enhance ice generation in convective clouds. Therefore, the various mechanisms of SIP may potentially have strong impacts on the charge structure in thunderstorms. In this study, the parameterizations of three different mechanisms of SIP, as well as the noninductive and inductive charge parametrization are implemented in a spectral bin microphysics model scheme in WRF (Weather Research and Forecasting model). A squall line is modeled to investigate the impacts of the three mechanisms of SIP on charge structure and flash rate. The results highlight the importance of considering various mechanisms of SIP in modeling cloud electrification and lightning. Key Points: The impacts of three secondary ice production (SIP) mechanisms on the electrification of a squall line is investigated using a modelThe SIP processes have strong impacts on the cloud microphysics, resulting in significant modification of charge structureThe flash rate is suppressed by rime‐splintering, while enhanced by ice‐ice collisional breakup and shattering of freezing drops [ABSTRACT FROM AUTHOR]