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Shingtung Yau - One of the best experts on this subject based on the ideXlab platform.
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brain surface conformal parameterization using riemann surface structure
IEEE Transactions on Medical Imaging, 2007Co-Authors: Yalin Wang, Tony F Chan, Paul M Thompson, Lok Ming Lui, Kiralee M Hayashi, Arthur W Toga, Shingtung YauAbstract:In medical imaging, parameterized 3-D surface models are useful for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal processing. Here we introduce a parameterization method based on Riemann surface structure, which uses a special curvilinear net structure (conformal net) to partition the surface into a set of patches that can each be conformally mapped to a parallelogram. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable (their solutions tend to be smooth functions and the boundary conditions of the Dirichlet problem can be enforced). Conformal parameterization also helps transform partial differential equations (PDEs) that may be defined on 3-D brain surface manifolds to modified PDEs on a two-dimensional parameter domain. Since the Jacobian matrix of a conformal parameterization is diagonal, the modified PDE on the parameter domain is readily solved. To illustrate our techniques, we computed parameterizations for several types of anatomical surfaces in 3-D magnetic resonance imaging scans of the brain, including the cerebral cortex, hippocampi, and lateral ventricles. For surfaces that are topologically homeomorphic to each other and have similar geometrical structures, we show that the parameterization results are consistent and the subdivided surfaces can be matched to each other. Finally, we present an automatic sulcal landmark location algorithm by solving PDEs on cortical surfaces. The landmark detection results are used as constraints for building conformal maps between surfaces that also match explicitly defined landmarks.
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brain surface conformal parameterization with the ricci flow
International Symposium on Biomedical Imaging, 2007Co-Authors: Yalin Wang, Tony F Chan, Paul M Thompson, Shingtung YauAbstract:In medical imaging, parameterized 3D surface models are of great interest for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal processing. By solving the Yamabe equation with the Ricci flow method, we can conformally parameterize a brain surface via a mapping to a multi-hole disk. The resulting parameterizations do not have any singularities and are intrinsic and stable. To illustrate the technique, we computed parameterizations of cortical surfaces in MRI scans of the brain. We also show the parameterization results are consistent with constraints imposed on the mappings of selected landmark curves, and the resulting surfaces can be matched to each other using constrained harmonic maps. Unlike previous planar conformal parameterization methods, our algorithm does not introduce any singularity points
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brain surface conformal parameterization with algebraic functions
Lecture Notes in Computer Science, 2006Co-Authors: Yalin Wang, Tony F Chan, Paul M Thompson, Shingtung YauAbstract:In medical imaging, parameterized 3D surface models are of great interest for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal processing. Here we introduce a parameterization method based on algebraic functions. By solving the Yamabe equation with the Ricci flow method, we can conformally map a brain surface to a multi-hole disk. The resulting parameterizations do not have any singularities and are intrinsic and stable. To illustrate the technique, we computed parameterizations of several types of anatomical surfaces in MRI scans of the brain, including the hippocampi and the cerebral cortices with various landmark curves labeled. For the cerebral cortical surfaces, we show the parameterization results are consistent with selected landmark curves and can be matched to each other using constrained harmonic maps. Unlike previous planar conformal parameterization methods, our algorithm does not introduce any singularity points. It also offers a method to explicitly match landmark curves between anatomical surfaces such as the cortex, and to compute conformal invariants for statistical comparisons of anatomy.
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optimal global conformal surface parameterization
IEEE Visualization, 2004Co-Authors: Miao Jin, Yalin Wang, Shingtung YauAbstract:All orientable metric surfaces are Riemann surfaces and admit global conformal parameterizations. Riemann surface structure is a fundamental structure and governs many natural physical phenomena, such as heat diffusion and electro-magnetic fields on the surface. A good parameterization is crucial for simulation and visualization. This paper provides an explicit method for finding optimal global conformal parameterizations of arbitrary surfaces. It relies on certain holomorphic differential forms and conformal mappings from differential geometry and Riemann surface theories. Algorithms are developed to modify topology, locate zero points, and determine cohomology types of differential forms. The implementation is based on a finite dimensional optimization method. The optimal parameterization is intrinsic to the geometry, preserves angular structure, and can play an important role in various applications including texture mapping, remeshing, morphing and simulation. The method is demonstrated by visualizing the Riemann surface structure of real surfaces represented as triangle meshes.
Yalin Wang - One of the best experts on this subject based on the ideXlab platform.
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brain surface conformal parameterization using riemann surface structure
IEEE Transactions on Medical Imaging, 2007Co-Authors: Yalin Wang, Tony F Chan, Paul M Thompson, Lok Ming Lui, Kiralee M Hayashi, Arthur W Toga, Shingtung YauAbstract:In medical imaging, parameterized 3-D surface models are useful for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal processing. Here we introduce a parameterization method based on Riemann surface structure, which uses a special curvilinear net structure (conformal net) to partition the surface into a set of patches that can each be conformally mapped to a parallelogram. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable (their solutions tend to be smooth functions and the boundary conditions of the Dirichlet problem can be enforced). Conformal parameterization also helps transform partial differential equations (PDEs) that may be defined on 3-D brain surface manifolds to modified PDEs on a two-dimensional parameter domain. Since the Jacobian matrix of a conformal parameterization is diagonal, the modified PDE on the parameter domain is readily solved. To illustrate our techniques, we computed parameterizations for several types of anatomical surfaces in 3-D magnetic resonance imaging scans of the brain, including the cerebral cortex, hippocampi, and lateral ventricles. For surfaces that are topologically homeomorphic to each other and have similar geometrical structures, we show that the parameterization results are consistent and the subdivided surfaces can be matched to each other. Finally, we present an automatic sulcal landmark location algorithm by solving PDEs on cortical surfaces. The landmark detection results are used as constraints for building conformal maps between surfaces that also match explicitly defined landmarks.
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brain surface conformal parameterization with the ricci flow
International Symposium on Biomedical Imaging, 2007Co-Authors: Yalin Wang, Tony F Chan, Paul M Thompson, Shingtung YauAbstract:In medical imaging, parameterized 3D surface models are of great interest for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal processing. By solving the Yamabe equation with the Ricci flow method, we can conformally parameterize a brain surface via a mapping to a multi-hole disk. The resulting parameterizations do not have any singularities and are intrinsic and stable. To illustrate the technique, we computed parameterizations of cortical surfaces in MRI scans of the brain. We also show the parameterization results are consistent with constraints imposed on the mappings of selected landmark curves, and the resulting surfaces can be matched to each other using constrained harmonic maps. Unlike previous planar conformal parameterization methods, our algorithm does not introduce any singularity points
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brain surface conformal parameterization with algebraic functions
Lecture Notes in Computer Science, 2006Co-Authors: Yalin Wang, Tony F Chan, Paul M Thompson, Shingtung YauAbstract:In medical imaging, parameterized 3D surface models are of great interest for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal processing. Here we introduce a parameterization method based on algebraic functions. By solving the Yamabe equation with the Ricci flow method, we can conformally map a brain surface to a multi-hole disk. The resulting parameterizations do not have any singularities and are intrinsic and stable. To illustrate the technique, we computed parameterizations of several types of anatomical surfaces in MRI scans of the brain, including the hippocampi and the cerebral cortices with various landmark curves labeled. For the cerebral cortical surfaces, we show the parameterization results are consistent with selected landmark curves and can be matched to each other using constrained harmonic maps. Unlike previous planar conformal parameterization methods, our algorithm does not introduce any singularity points. It also offers a method to explicitly match landmark curves between anatomical surfaces such as the cortex, and to compute conformal invariants for statistical comparisons of anatomy.
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optimal global conformal surface parameterization
IEEE Visualization, 2004Co-Authors: Miao Jin, Yalin Wang, Shingtung YauAbstract:All orientable metric surfaces are Riemann surfaces and admit global conformal parameterizations. Riemann surface structure is a fundamental structure and governs many natural physical phenomena, such as heat diffusion and electro-magnetic fields on the surface. A good parameterization is crucial for simulation and visualization. This paper provides an explicit method for finding optimal global conformal parameterizations of arbitrary surfaces. It relies on certain holomorphic differential forms and conformal mappings from differential geometry and Riemann surface theories. Algorithms are developed to modify topology, locate zero points, and determine cohomology types of differential forms. The implementation is based on a finite dimensional optimization method. The optimal parameterization is intrinsic to the geometry, preserves angular structure, and can play an important role in various applications including texture mapping, remeshing, morphing and simulation. The method is demonstrated by visualizing the Riemann surface structure of real surfaces represented as triangle meshes.
Hyeyeong Chun - One of the best experts on this subject based on the ideXlab platform.
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a lagrangian spectral parameterization of gravity wave drag induced by cumulus convection
Journal of the Atmospheric Sciences, 2008Co-Authors: In Sun Song, Hyeyeong ChunAbstract:Abstract A Lagrangian spectral parameterization of gravity wave drag (GWD) induced by cumulus convection (GWDC) is developed based on ray theory and several assumptions and implemented into the NCAR Whole Atmosphere Community Climate Model. The Lagrangian parameterization calculates explicitly gravity wave (GW) propagation that has been treated too simply in existing column-based parameterizations. For comparison with column-based parameterization, a hydrostatic and Boussinesq version of the Lagrangian parameterization is used in the present study. One-day convective GW-packet trajectories demonstrate that the Lagrangian parameterization calculates reasonably the GW-packet propagation, and GW packets propagate upward along curved paths determined by Doppler shifting and the variation of stability. The GW trajectories show that the horizontal extent of GW propagation can be as large as 20° as GWs approach critical levels. Comparison with column-based parameterization through one-month simulations indicates...
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a computationally efficient nonstationary convective gravity wave drag parameterization for global atmospheric prediction systems
Geophysical Research Letters, 2005Co-Authors: Youngjoon Kim, Hyeyeong ChunAbstract:[1] We extend the Chun-Baik parameterization of convectively forced stationary gravity-wave drag by adding a set of discrete nonzero phase speeds to incorporate the effects of nonstationary gravity waves. The extended scheme is computationally very efficient in comparison with full spectral parameterizations and eliminates the need to specify the wave source information at the interface level. We validate the extended parameterization against an explicit simulation of convection over a tropical ocean. The distribution of the cloud-top momentum flux for a typical range of phase speeds is roughly similar to those from more refined studies. It is shown that nonstationary waves should be included to reproduce the vertical variation of explicitly simulated momentum flux.
Paul A Ogorman - One of the best experts on this subject based on the ideXlab platform.
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stable machine learning parameterization of subgrid processes for climate modeling at a range of resolutions
Nature Communications, 2020Co-Authors: Janni Yuval, Paul A OgormanAbstract:Global climate models represent small-scale processes such as convection using subgrid models known as parameterizations, and these parameterizations contribute substantially to uncertainty in climate projections. Machine learning of new parameterizations from high-resolution model output is a promising approach, but such parameterizations have been prone to issues of instability and climate drift, and their performance for different grid spacings has not yet been investigated. Here we use a random forest to learn a parameterization from coarse-grained output of a three-dimensional high-resolution idealized atmospheric model. The parameterization leads to stable simulations at coarse resolution that replicate the climate of the high-resolution simulation. Retraining for different coarse-graining factors shows the parameterization performs best at smaller horizontal grid spacings. Our results yield insights into parameterization performance across length scales, and they also demonstrate the potential for learning parameterizations from global high-resolution simulations that are now emerging. Machine learning has been used to represent small-scale processes, such as clouds, in atmospheric models but this can lead to instability in simulations of climate. Here, the authors demonstrate a use of machine learning in an atmospheric model that leads to stable simulations of climate at a range of grid spacings.
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stable machine learning parameterization of subgrid processes for climate modeling at a range of resolutions
arXiv: Atmospheric and Oceanic Physics, 2020Co-Authors: Janni Yuval, Paul A OgormanAbstract:Global climate models represent small-scale processes such as clouds and convection using quasi-empirical models known as parameterizations, and these parameterizations are a leading cause of uncertainty in climate projections. A promising alternative approach is to use machine learning to build new parameterizations directly from high-resolution model output. However, parameterizations learned from three-dimensional model output have not yet been successfully used for simulations of climate. Here we use a random forest to learn a parameterization of subgrid processes from output of a three-dimensional high-resolution atmospheric model. Integrating this parameterization into the atmospheric model leads to stable simulations at coarse resolution that replicate the climate of the high-resolution simulation. The parameterization obeys physical constraints and captures important statistics such as precipitation extremes. The ability to learn from a fully three-dimensional simulation presents an opportunity for learning parameterizations from the wide range of global high-resolution simulations that are now emerging.
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using machine learning to parameterize moist convection potential for modeling of climate climate change and extreme events
Journal of Advances in Modeling Earth Systems, 2018Co-Authors: Paul A Ogorman, J G DwyerAbstract:The parameterization of moist convection contributes to uncertainty in climate modeling and numerical weather prediction. Machine learning (ML) can be used to learn new parameterizations directly from high-resolution model output, but it remains poorly understood how such parameterizations behave when fully coupled in a general circulation model (GCM) and whether they are useful for simulations of climate change or extreme events. Here, we focus on these issues using idealized tests in which an ML-based parameterization is trained on output from a conventional parameterization and its performance is assessed in simulations with a GCM. We use an ensemble of decision trees (random forest) as the ML algorithm, and this has the advantage that it automatically ensures conservation of energy and non-negativity of surface precipitation. The GCM with the ML convective parameterization runs stably and accurately captures important climate statistics including precipitation extremes without the need for special training on extremes. Climate change between a control climate and a warm climate is not captured if the ML parameterization is only trained on the control climate, but it is captured if the training includes samples from both climates. Remarkably, climate change is also captured when training only on the warm climate, and this is because the extratropics of the warm climate provides training samples for the tropics of the control climate. In addition to being potentially useful for the simulation of climate, we show that ML parameterizations can be interrogated to provide diagnostics of the interaction between convection and the large-scale environment.
Baylor Foxkemper - One of the best experts on this subject based on the ideXlab platform.
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evaluation of scale aware subgrid mesoscale eddy models in a global eddy rich model
Ocean Modelling, 2017Co-Authors: Brodie Pearson, Baylor Foxkemper, Scott Bachman, Frank O BryanAbstract:Abstract Two parameterizations for horizontal mixing of momentum and tracers by subgrid mesoscale eddies are implemented in a high-resolution global ocean model. These parameterizations follow on the techniques of large eddy simulation (LES). The theory underlying one parameterization (2D Leith due to Leith, 1996) is that of enstrophy cascades in two-dimensional turbulence, while the other (QG Leith) is designed for potential enstrophy cascades in quasi-geostrophic turbulence. Simulations using each of these parameterizations are compared with a control simulation using standard biharmonic horizontal mixing.Simulations using the 2D Leith and QG Leith parameterizations are more realistic than those using biharmonic mixing. In particular, the 2D Leith and QG Leith simulations have more energy in resolved mesoscale eddies, have a spectral slope more consistent with turbulence theory (an inertial enstrophy or potential enstrophy cascade), have bottom drag and vertical viscosity as the primary sinks of energy instead of lateral friction, and have isoneutral parameterized mesoscale tracer transport. The parameterization choice also affects mass transports, but the impact varies regionally in magnitude and sign.
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parameterization of mixed layer eddies iii implementation and impact in global ocean climate simulations
Ocean Modelling, 2011Co-Authors: Raffaele Ferrari, Baylor Foxkemper, Robert Hallberg, Gokhan Danabasoglu, Stephen M Griffies, Marika M Holland, Mathew E Maltrud, Synte Peacock, Bonita L SamuelsAbstract:Abstract A parameterization for the restratification by finite-amplitude, submesoscale, mixed layer eddies, formulated as an overturning streamfunction, has been recently proposed to approximate eddy fluxes of density and other tracers. Here, the technicalities of implementing the parameterization in the coarse-resolution ocean component of global climate models are made explicit, and the primary impacts on model solutions of implementing the parameterization are discussed. Three global ocean general circulation models including this parameterization are contrasted with control simulations lacking the parameterization. The MLE parameterization behaves as expected and fairly consistently in models differing in discretization, boundary layer mixing, resolution, and other parameterizations. The primary impact of the parameterization is a shoaling of the mixed layer, with the largest effect in polar winter regions. Secondary impacts include strengthening the Atlantic meridional overturning while reducing its variability, reducing CFC and tracer ventilation, modest changes to sea surface temperature and air–sea fluxes, and an apparent reduction of sea ice basal melting.
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parameterization of mixed layer eddies part i theory and diagnosis
Journal of Physical Oceanography, 2008Co-Authors: Baylor Foxkemper, Raffaele Ferrari, Robert HallbergAbstract:Ageostrophic baroclinic instabilities develop within the surface mixed layer of the ocean at horizontal fronts and efficiently restratify the upper ocean. In this paper a parameterization for the restratification driven by finite-amplitude baroclinic instabilities of the mixed layer is proposed in terms of an overturning streamfunction that tilts isopycnals from the vertical to the horizontal. The streamfunction is proportional to the product of the horizontal density gradient, the mixed layer depth squared, and the inertial period. Hence restratification proceeds faster at strong fronts in deep mixed layers with a weak latitude dependence. In this paper the parameterization is theoretically motivated, confirmed to perform well for a wide range of mixed layer depths, rotation rates, and vertical and horizontal stratifications. It is shown to be superior to alternative extant parameterizations of baroclinic instability for the problem of mixed layer restratification. Two companion papers discuss the numerical implementation and the climate impacts of this parameterization.
