Global Parameterization Research Articles

A Global Ocean Opal Ballasting–Silicate Relationship

AbstractOpal and calcium carbonate are thought to regulate the biological pump's transfer of organic carbon to the deep ocean. A global sediment trap database exhibits large regional variations in the organic carbon flux associated with opal flux. These variations are well‐explained by upper ocean silicate concentrations, with high opal ‘ballasting’ in the silicate‐deplete tropical Atlantic Ocean, and low ballasting in the silicate‐rich Southern Ocean. A plausible, testable hypothesis is that opal ballasting varies because diatoms grow thicker frustules where silicate concentrations are higher, carrying less organic carbon per unit opal. The observed pattern does not fully emerge in an advanced ocean biogeochemical model when diatom silicification is represented using a single global parameterization as a function of silicate and iron. Our results suggest a need for improving understanding of currently modeled processes and/or considering additional parameterizations to capture the links between elemental cycles and future biological pump changes.

Reduced order modeling of hybrid soft-rigid robots using global, local, and state-dependent strain parameterization

Reduced order modeling of hybrid soft-rigid robots using global, local, and state-dependent strain parameterization

Parametrically guided design of beta barrels and transmembrane nanopores using deep learning.

Francis Crick's global parameterization of coiled coil geometry has been widely useful for guiding design of new protein structures and functions. However, design guided by similar global parameterization of beta barrel structures has been less successful, likely due to the deviations required from ideal beta barrel geometry to maintain extensive inter-strand hydrogen bonding without introducing considerable backbone strain. Instead, beta barrels and other protein folds have been designed guided by 2D structural blueprints; while this approach has successfully generated new fluorescent proteins, transmembrane nanopores, and other structures, it requires considerable expert knowledge and provides only indirect control over the global barrel shape. Here we show that the simplicity and control over shape and structure provided by global parametric representations can be generalized beyond coiled coils by taking advantage of the rich sequence-structure relationships implicit in RoseTTAFold based inpainting and diffusion design methods. Starting from parametrically generated idealized barrel backbones, both RFjoint inpainting and RFdiffusion readily incorporate the backbone irregularities necessary for proper folding with minimal deviation from the idealized barrel geometries. We show that for beta barrels across a broad range of global beta sheet parameterizations, these methods achieve high in silico and experimental success rates, with atomic accuracy confirmed by an X-ray crystal structure of a novel beta barrel topology, and de novo designed 12, 14, and 16 stranded transmembrane nanopores with conductances ranging from 200 to 500 pS. By combining the simplicity and control of parametric generation with the high success rates of deep learning based protein design methods, our approach makes the design of proteins where global shape confers function, such as beta barrel nanopores, more precisely specifiable and accessible.

Quadratic surface preserving parameterization of unorganized point data

Finding parameterizations of spatial point data is a fundamental step for surface reconstruction in Computer Aided Geometric Design. Especially the case of unstructured point clouds is challenging and not widely studied. In this work, we show how to parameterize a point cloud by using barycentric coordinates in the parameter domain, with the aim of reproducing the parameterizations provided by quadratic triangular Bézier surfaces. To this end, we train an artificial neural network that predicts suitable barycentric parameters for a fixed number of data points. In a subsequent step we improve the parameterization using non-linear optimization methods. We then use a number of local parameterizations to obtain a global parameterization using a new overdetermined barycentric parameterization approach. We study the behavior of our method numerically in the zero-residual case (i.e., data sampled from quadratic polynomial surfaces) and in the non-zero residual case and observe an improvement of the accuracy in comparison to standard methods. We also compare different approaches for non-linear surface fitting such as tangent distance minimization, squared distance minimization and the Levenberg Marquardt algorithm.

Global patterns and edaphic-climatic controls of soil carbon decomposition kinetics predicted from incubation experiments

Knowledge about global patterns of the decomposition kinetics of distinct soil organic matter (SOM) pools is crucial to robust estimates of land-atmosphere carbon fluxes under climate change. However, the current Earth system models often adopt globally-consistent reference SOM decomposition rates (kref), ignoring effects from edaphic-climate heterogeneity. Here, we compile a comprehensive set of edaphic-climatic and SOM decomposition data from published incubation experiments and employ machine-learning techniques to develop models capable of predicting the expected sizes and kref of multiple SOM pools (fast, slow, and passive). We show that soil texture dominates the turnover of the fast pools, whereas pH predominantly regulates passive SOM decomposition. This suggests that pH-sensitive bacterial decomposers might have larger effects on stable SOM decomposition than previously believed. Using these predictive models, we provide a 1-km resolution global-scale dataset of the sizes and kref of these SOM pools, which may improve global biogeochemical model parameterization and predictions.

Enhanced conformational exploration of protein loops using a global parameterization of the backbone geometry.

Flexible loops are paramount to protein functions, with action modes ranging from localized dynamics contributing to the free energy of the system, to large amplitude conformational changes accounting for the repositioning whole secondary structure elements or protein domains. However, generating diverse and low energy loops remains a difficult problem. This work introduces a novel paradigm to sample loop conformations, in the spirit of the hit-and-run (HAR) Markov chain Monte Carlo technique. The algorithm uses a decomposition of the loop into tripeptides, and a novel characterization of necessary conditions for Tripeptide Loop Closure to admit solutions. Denoting m the number of tripeptides, the algorithm works in an angular space of dimension 12 m. In this space, the hyper-surfaces associated with the aforementioned necessary conditions are used to run a HAR-like sampling technique. On classical loop cases up to 15 amino acids, our parameter free method compares favorably to previous work, generating more diverse conformational ensembles. We also report experiments on a 30 amino acids long loop, a size not processed in any previous work.

Evaluation and uncertainty assessment of weather data and model calibration on daily streamflow simulation in a large-scale regulated and snow-dominated river basin

The choice of proper input data and suitable calibration schemes is challenging in the hydrological modeling of higher-latitude watersheds with their unique hydro-climatic conditions. Based on the Soil and Water Assessment Tool (SWAT) and Sequential Uncertainty Fitting Program (SUFI2) of the SWATCUP tool, our study revisits various climate data and calibration schemes, and develops a more automatic calibration framework to thoroughly assess model performance in simulating Snow Water Equivalent (SWE) and resulting streamflow in a cold region watershed, the Peace River Basin (PRB) in western Canada. We evaluated the effects of (1) the observed and two widely used gridded climate data sources; (2) unrealistic snow parameter combinations arising from SUFI2-SWATCUP parameter sampling; and (3) ‘calibration schemes’ including the choice of (i) objective function, (ii) number of simulations in each calibration iterations, (iii) regional versus global parameterization and calibration schemes, and (iv) single-variable (streamflow) versus multi-variable calibration (streamflow and SWE). Model results showed that the gridded ERA5 data was the best climate input for driving the SWAT model in PRB. A modified SUFI2-SWATCUP method to automatically remove unrealistic snow parameter combinations outperformed the standard SUFI2-SWATCUP, and it significantly reduced the total number of simulations. Compared with single-variable calibration using streamflow, an automatic multi-variable calibration using streamflow and SWE was shown to effectively limit the uncertainty of snow-related parameters and provide better prediction of snow-affected spring streamflow. The framework developed in our study can help reduce uncertainties in the hydrological modeling of large-scale, regulated, and snow-dominated watersheds in higher latitudes and can help the development of reliable strategies for water resources planning and management.

Parallelizable Global Quasi-Conformal Parameterization of Multiply Connected Surfaces via Partial Welding

Conformal and quasi-conformal mappings have widespread applications in imaging science, computer vision and computer graphics, such as surface registration, segmentation, remeshing, and texture map compression. While various conformal and quasi-conformal parameterization methods for simply connected surfaces have been proposed, efficient parameterization methods for multiply connected surfaces are less explored. In this paper, we propose a novel parallelizable algorithm for computing the global conformal and quasi-conformal parameterization of multiply connected surfaces onto a 2D circular domain using variants of the partial welding algorithm and the Koebe's iteration. The main idea is to partition a multiply connected surface into several subdomains and compute the free-boundary conformal or quasi-conformal parameterizations of them respectively, and then apply a variant of the partial welding algorithm to reconstruct the global mapping. We apply the Koebe's iteration together with the geodesic algorithm to the boundary points and welding paths before and after the global welding to transform all the boundaries to circles conformally. After getting all the updated boundary conditions, we obtain the global parameterization of the multiply connected surface by solving the Laplace equation for each subdomain. Using this divide-and-conquer approach, the parameterization of surfaces with very high resolution can be efficiently computed. Experimental results are presented to demonstrate the effectiveness of our proposed algorithms.

A WAVEWATCH III® model approach to investigating ocean wave source terms for West Africa: Non-linear wave-wave interaction source terms

• Investigation of ocean wave model parameterization schemes for West Africa. • Selection of appropriate non-linear source terms for ocean wave projections. • DIA term best estimates wave heights for sub-sections of West Africa. • Application of no non-linear term best estimates wave heights for the entire region. Ocean wave forecasting for West Africa has mostly relied on global parameterization schemes and data outputs. Investigating non-linear ocean wave-wave interaction source terms ( S nl ) for the region, that forms part of the wave model parameterization schemes, is a contribution of this study towards developing a regional wave modelling scheme for West Africa. The study evaluates five non-linear source term configurations with the WAVEWATCH III® (WW3) numerical ocean wave model version 5.16; (i) No source term applied - NL0, (ii) Discrete Interaction Approximation (DIA) – NL1, (iii) Exact Interaction Approximation – NL2, (iv) Generalized Multiple DIA – NL3, and (v) Two-Scale Approximation – NL4, in order to determine best performing S nl for projecting significant wave heights and directions for the region. The wave simulations were run on three separate grids comprising a low resolution West Africa grid (latitudes 10 o S – 30 o N; longitudes 35 o W – 15 o E), high resolution south-eastern (latitudes 2 o S – 8 o N; longitudes 10 o W – 10 o E) and north-western (latitudes 10 o N – 25 o N; longitudes 30 o W – 10 o W) sub-grids. Simulations for the entire West Africa grid produced higher accuracies for the wave parameters compared to the higher resolution sub-grids. NL0 best estimates significant wave height whereas NL3 best estimates wave directions for the West Africa grid. For combined stations of the south-eastern sub-grid, while NL1 best estimates wave heights, NL3 best estimates the wave directions with possible alternation with NL1 due to insignificant differences. Similarly, for the north-western sub-grid, while NL1 best estimates significant wave heights, NL0 best estimates wave directions with similar ability to alternate with NL2 in projecting wave directions. Generally, insignificant differences exist between the source terms in projecting wave directions, especially for the north-western sub-region, implying that any of the source terms may be used in projecting wave directions without significantly compromising on accuracy. Thus, NL1 which best estimates significant wave heights for both south-eastern and north-western sub-regions can also be used in estimating the wave directions. Similarly, NL0 would be appropriate for the entire West Africa region.

Aircraft Observations of Turbulence in Cloudy and Cloud‐Free Boundary Layers Over the Western North Atlantic Ocean From ACTIVATE and Implications for the Earth System Model Evaluation and Development

AbstractThis study examines boundary layer turbulence derived from high temporal resolution meteorological measurements from 40 research flights over the western North Atlantic Ocean during the 2020 deployments of ACTIVATE. Frequency distributions of various turbulent quantities reveal stronger turbulence during the winter deployment than in summer and for cloud‐topped than in cloud‐free boundary layers during the summer deployment. Maximum turbulence kinetic energy (TKE) is most often within cloud from observations in winter and summer, whereas it is mostly below cloud in both seasons by a global model turbulence parameterization. Bivariate frequency distributions are consistent with the bivariate Gaussian probability distribution functions assumed for the closure of higher‐order turbulence/shallow convection parameterizations used by some global models. Turbulence simulated by the Community Atmosphere Model version 6 and the Energy Exascale Earth System Model Atmosphere Model version 2 using such parameterizations is not as strong as observed, with more TKE going into vertical wind perturbations rather than into zonal wind perturbations as observed, suggesting that the treatment of turbulence in Earth system models still needs to be further improved.

Retrieving ice-nucleating particle concentration and ice multiplication factors using active remote sensing validated by in situ observations

Abstract. Understanding the evolution of the ice phase within mixed-phase clouds (MPCs) is necessary to reduce uncertainties related to the cloud radiative feedback in climate projections and precipitation initiation. Both primary ice formation via ice-nucleating particles (INPs) and secondary ice production (SIP) within MPCs are unconstrained, not least because of the lack of atmospheric observations. In the past decades, advanced remote sensing methods have emerged which provide high-resolution data of aerosol and cloud properties and could be key in understanding microphysical processes on a global scale. In this study, we retrieved INP concentrations and ice multiplication factors (IMFs) in wintertime orographic clouds using active remote sensing and in situ observations obtained during the RACLETS campaign in the Swiss Alps. INP concentrations in air masses dominated by Saharan dust and continental aerosol were retrieved from a polarization Raman lidar and validated with aerosol and INP in situ observations on a mountaintop. A calibration factor of 0.0204 for the global INP parameterization by DeMott et al. (2010) is derived by comparing in situ aerosol and INP measurements, improving the INP concentration retrieval for continental aerosols. Based on combined lidar and radar measurements, the ice crystal number concentration and ice water content were retrieved and validated with balloon-borne in situ observations, which agreed with the balloon-borne in situ observations within an order of magnitude. For seven cloud cases the ice multiplication factors (IMFs), defined as the quotient of the ice crystal number concentration to the INP concentration, were calculated. The median IMF was around 80, and SIP was active (defined as IMFs > 1) nearly 85 % of the time. SIP was found to be active at all observed temperatures (−30 to −5 ∘C), with the highest IMFs between −20 and −5 ∘C. The introduced methodology could be extended to larger datasets to better understand the impact of SIP not only over the Alps but also at other locations and for other cloud types.

An Isogeometric Bézier Finite Element Method for Vibration Optimization of Functionally Graded Plate with Local Refinement

An effective free vibration optimization procedure in combination with the isogeometric approach (IGA), particle swarm optimization (PSO) and an integrated global and local parameterization is presented. The natural frequency of functionally graded (FG) plates is calculated by the IGA based on the Bézier extraction of non-uniform rational B-splines (NURBS) with the cubic NURBS basis function. The material composition is assumed to vary only in the thickness direction, and the volumetric fraction is described by the NURBS basis function in light of the superior properties of NURBS curves. The volume fractions of the control points are then optimized by the PSO. In most of the previous work, the control points for the volume fraction are usually equally spaced, which is incapable of identifying the optimal location of the graded zones in most cases. To overcome this bottleneck, a novel local refinement strategy is proposed. The reliability and effectiveness of the proposed approach are demonstrated through several numerical examples. It is interesting to observe that the optimal results are sandwich or laminate plates, and few parameters are involved in the integrated global and local parameterization.

Topology Optimization on Complex Surfaces Based on the Moving Morphable Component Method and Computational Conformal Mapping

Abstract In the present article, an integrated paradigm for topology optimization on complex surfaces with arbitrary genus is proposed. The approach is constructed based on the two-dimensional (2D) Moving Morphable Component (MMC) framework, where a set of structural components are used as the basic units of optimization, and computational conformal mapping (CCM) technique, with which a complex surface represented by an unstructured triangular mesh can be mapped into a set of regular 2D parameter domains numerically. A multipatch stitching scheme is also developed to achieve an MMC-friendly global parameterization through a number of local parameterizations. Numerical examples including a saddle-shaped shell, a torus-shape shell, and a tee-branch pipe are solved to demonstrate the validity and efficiency of the proposed approach. It is found that compared with traditional approaches for topology optimization on 2D surfaces, optimized designs with clear load transmission paths can be obtained with much fewer numbers of design variables and degrees-of-freedom for finite element analysis (FEA) via the proposed approach.

A parameterization of long-continuing-current (LCC) lightning in the lightning submodel LNOX (version 3.0) of the Modular Earth Submodel System (MESSy, version 2.54)

Abstract. Lightning flashes can produce a discharge in which a continuing electrical current flows for more than 40 ms. Such flashes are proposed to be the main precursors of lightning-ignited wildfires and also to trigger sprite discharges in the mesosphere. However, lightning parameterizations implemented in global atmospheric models do not include information about the continuing electrical current of flashes. The continuing current of lightning flashes cannot be detected by conventional lightning location systems. Instead, these so-called long-continuing-current (LCC) flashes are commonly observed by extremely low-frequency (ELF) sensors and by optical instruments located in space. Reports of LCC lightning flashes tend to occur in winter and oceanic thunderstorms, which suggests a connection between weak convection and the occurrence of this type of discharge. In this study, we develop a parameterization of LCC lightning flashes based on a climatology derived from optical lightning measurements reported by the Lightning Imaging Sensor (LIS) on board the International Space Station (ISS) between March 2017 and March 2020. We use meteorological data from reanalyses to develop a global parameterization that uses vertical velocity at the 450 hPa pressure level as a proxy for the ratio of LCC to total lightning in thunderstorms. We implement this parameterization into the LNOX submodel of the Modular Earth Submodel System (MESSy) for usage within the European Center HAMburg general circulation model (ECHAM)/MESSy Atmospheric Chemistry (EMAC) model and compare the observed and simulated climatologies of LCC lightning flashes using six different lightning parameterizations. We find that the best agreement between the simulated and observed spatial distribution is obtained when using a novel combined lightning parameterization based on the cloud-top height over land and on the convective precipitation over ocean.

Frequency Response Data-Driven LPV Controller Synthesis for MIMO Systems

The linear parameter-varying framework enables systematic control design approaches to meet increasing performance requirements and complexity of systems. The aim of this paper is to develop local frequency response data-based analysis and synthesis conditions for multiple-input multiple-output linear parameter-varying systems to facilitate fast tuning. Key advantages are local stability and performance guarantees and a global controller parameterization. The effectiveness of the proposed methods are evaluated based on a simulation example.

Investigation of a non-linear complementary relationship model for monthly evapotranspiration estimation at global flux sites

AbstractProper parameterization of the parameter (αe) that governs the wet environment evaporation is critical for the regional estimation of evapotranspiration (ET) using the generalized complementary relationship (GCR) model. Here, we proposed a global parameterization for the GCR model. We found that the GCR model is sensitive to the parameter αe, which varies spatially with the climate aridity index (AI, the ratio between the apparent potential ET and the precipitation) across 60 sites that span a large variety in climate types worldwide. We found that αe and the AI are generally more strongly correlated in drier climates (AI > 2) where water supply instead of energy supply is the limiting factor for actual ET. The strong correlation between αe and AI can be partly explained by 1) the usage of the air temperature measurements in the non-potential conditions instead of potential conditions, and 2) the insensitivity of the actual ET to the apparent potential ET in the drier climate. Temporally, the parameter αe exhibits seasonal courses at monthly scales and decreases with increasing of vapor pressure deficit (VPD) in a hysteresis loop. Incorporation of the seasonal course and hysteresis significantly improved the model performances at most of the sites. The global parameterization we established can help the GCR model to be a more useful tool for regional and global ET estimations.

Practical Computation of the Cut Locus on Discrete Surfaces

AbstractWe present a novel method to compute the cut locus of a distance function encoded on a polygonal mesh. Our method exploits theoretical findings about the cut locus and – with a combination of analytic, geometric and topological tools – it is able to compute a topologically correct and geometrically accurate approximation of it. Our result can be either restricted to the mesh edges, or aligned with the real cut locus. Both outputs may be useful for practical applications. We also provide a convenient tool to optionally prune the weak branches of the cut locus, simplifying its structure. Our approach supersedes prior art, in that it is easier to use and also orders of magnitude faster. In fact, it depends on just one parameter, and it flawlessly operates on meshes with high genus and very high element count at interactive rates. We experiment with different datasets and methods for geodesic distance estimation. We also present applications to local and global surface parameterization.

Non-Rigid Image Registration based on Parameterized Surfaces: Application to 3D Cardiac Motion Image Analysis

This paper describes the Fast Radial Basis Function (RBF) method for cardiac motion tracking in 3D CT using non-rigid medical image registration based on parameterized (regular) surfaces. The technique is a point-based registration evaluation algorithm which does register 3D MR or CT images in real time. We first extract the surface of the whole heart 3D CT and its contrast enhanced part (left ventricle (LV) blood cavity) of each dataset with a semiautomatic contouring and a fully-automatic triangulation method followed by a global surface parameterization and optimization algorithm. In second step, a set of registration experiments are run to calculate the deformation field at various phases of cardiac motion or cycle from CT images, which results into significant deformation during each phase of a cycle. The surface points of the whole heart and LV are used to register the source systole image to various diastole target images taken at different phases during a heart beat. Our registration accuracy improves with the increase in number of salient feature points (i.e. optimized parameterized surfaces) and it has no effect on the speed of the algorithm (i.e. still less than a second). The results show that the target registration error is less than 3[Formula: see text]mm (2.53) and the performance of the Fast RBF algorithm is less than a second using a whole heart CT dataset of a single patient taken over the course of the entire cardiac cycle. At the end, the results for recovery (or analysis) of bigger deformation in heart CT images using the Fast RBF algorithm is compared to the state-of-the-art Free Form Deformation (FFD) registration technique. It is proved that the Fast RBF method is performing better in speed and slightly less accurate than the FFD (when measured in terms of NMI) due to iterative nature of the latter.

Buckling analysis of cracked orthotropic 3D plates and shells via an isogeometric-reproducing kernel particle method

This paper aims to develop a three-dimensional isogeometric-reproducing kernel particle method (IGA-RKPM) coupling approach to study the buckling behavior of cracked isotropic and orthotropic plate and shell structures. The IGA and RKPM-based meshfree methods are coupled successfully through a reproducing condition in the physical domain that guarantees the higher-order polynomial continuity of basis functions and overcomes the barrier of global parameterization in the physical domain. The resulting coupling approach not only preserves the geometry exactness and offers a higher-order approximation based on IGA basis functions but also allows local refinement flexibility. Linear eigenvalue buckling analyses for cracked orthotropic plate and shell structures have been carried out within the framework of the proposed coupling approach. The effects of several parameters such as the crack length ratio, thickness-to-length ratio, and orthotropy angle on the critical buckling stress of the structures have been investigated in detail under different boundary and loading conditions. The efficacy and robustness of the proposed coupling approach have been demonstrated by comparing the present results with those available in literature.

3D B-Rep meshing for real-time data-based geometric parametric analysis

This paper presents an effective framework to automatically construct 3D quadrilateral meshes of complicated geometry and arbitrary topology adapted for parametric studies. The input is a triangulation of the solid 3D model’s boundary provided from B-Rep CAD models or scanned geometry. The triangulated mesh is decomposed into a set of cuboids in two steps: pants decomposition and cuboid decomposition. This workflow includes an integration of a geometry-feature-aware pants-to-cuboids decomposition algorithm. This set of cuboids perfectly replicates the input surface topology. Using aligned global parameterization, patches are re-positioned on the surface in a way to achieve low overall distortion, and alignment to principal curvature directions and sharp features. Based on the cuboid decomposition and global parameterization, a 3D quadrilateral mesh is extracted. For different parametric instances with the same topology but different geometries, the MEG-IsoQuad method allows to have the same representation: isotopological meshes holding the same connectivity where each point on a mesh has an analogous one into all other meshes. Faithful 3D numerical charts of parametric geometries are then built using standard data-based techniques. Geometries are then evaluated in real-time. The efficiency and the robustness of the proposed approach are illustrated through a few parametric examples.