Academic Commons Search Results
http://academiccommons.columbia.edu/catalog.rss?f%5Bdepartment_facet%5D%5B%5D=Applied+Physics+and+Applied+Mathematics&q=&rows=500&sort=record_creation_date+desc
Academic Commons Search Resultsen-usIdentifying Hosts of Families of Viruses: A Machine Learning Approach
http://academiccommons.columbia.edu/catalog/ac:184169
Raj, Anil; Dewar, Michael; Palacios, Gustavo; Rabadan, Raul; Wiggins, Chris H.http://dx.doi.org/10.7916/D8RF5SXVFri, 06 Mar 2015 00:00:00 +0000Identifying emerging viral pathogens and characterizing their transmission is essential to developing effective public health measures in response to an epidemic. Phylogenetics, though currently the most popular tool used to characterize the likely host of a virus, can be ambiguous when studying species very distant to known species and when there is very little reliable sequence information available in the early stages of the outbreak of disease. Motivated by an existing framework for representing biological sequence information, we learn sparse, tree-structured models, built from decision rules based on subsequences, to predict viral hosts from protein sequence data using popular discriminative machine learning tools. Furthermore, the predictive motifs robustly selected by the learning algorithm are found to show strong host-specificity and occur in highly conserved regions of the viral proteome.Medicine, Virology, Public healthrr2579, chw2Applied Physics and Applied Mathematics, Biomedical InformaticsArticlesBifurcation of localized eigenstates of perturbed periodic Schrödinger operators
http://academiccommons.columbia.edu/catalog/ac:182973
Vukicevic, Ivahttp://dx.doi.org/10.7916/D88C9V2ZThu, 05 Feb 2015 00:00:00 +0000A spatially localized initial condition for an energy-conserving wave equation with periodic coefficients disperses (spatially spreads) and decays as time advances. This dispersion is associated with the continuous spectrum of the underlying differential operator and the absence of discrete eigenvalues. The introduction of spatially localized perturbations in a periodic medium leads to ``defect modes'', states in which the wave is spatially localized and periodic in time. These modes are associated with eigenvalues which bifurcate from the continuous spectrum induced by the perturbation. This thesis investigates specific families of perturbations of one-dimensional periodic Schrödinger operators and studies the resulting bifurcating eigenvalues from the unperturbed continuous spectrum. For Q(x) a real-valued periodic function, the Schrödinger operator H_Q = -∂_x^2 + Q(x) has a continuous spectrum equal to the union of closed intervals, called spectral bands, separated by open spectral gaps. We find that upon the introduction of a bounded, ``small'', and sufficiently decaying perturbation W(x), the spectrum of H_{Q+W} has discrete eigenvalues (with corresponding eigenstates which are exponentially decaying in |x|) which lie in the open spectral gaps of H_Q. Our analysis covers two large classes of perturbations W(x): 1. W(x) = λ V(x), 0<λ ≪ 1, and V(x) sufficiently rapidly decaying as x → ± ∞; 2. W(x) = q(x, x/ε), 0<ε ≪ 1, where x ⟼ q(x,y) is spatially localized, q(x,y+1) = q(x,y) for x ∈ ℝ, and y ⟼ q(x,y) has mean zero. In Case 1. W(x) corresponds to a small and localized absolute change in the medium's material properties. In Case 2. W(x) corresponds to a high-contrast microstructure. Q(x) + W(x) may be pointwise very large, but on average it is a small perturbation of Q(x).Applied mathematics, Mathematicsiv2143Applied Physics and Applied MathematicsDissertationsCloud Vertical Distribution across Warm and Cold Fronts in CloudSat–CALIPSO Data and a General Circulation Model
http://academiccommons.columbia.edu/catalog/ac:183326
Naud, Catherine M.; Del Genio, Anthony D.; Bauer, Mike; Kovari, Williamhttp://dx.doi.org/10.7916/D8BC3XC5Thu, 05 Feb 2015 00:00:00 +0000Cloud vertical distributions across extratropical warm and cold fronts are obtained using two consecutive winters of CloudSat–Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) observations and National Centers for Environmental Prediction reanalysis atmospheric state parameters over the Northern and Southern Hemisphere oceans (30°–70°N/S) between November 2006 and September 2008.These distributions generally resemble those from the original model introduced by the Bergen School in the 1920s, with the following exceptions: 1) substantial low cloudiness, which is present behind and ahead of the warm and cold fronts; 2) ubiquitous high cloudiness, some of it very thin, throughout the warm-frontal region; and 3) upright convective cloudiness near and behind some warm fronts. One winter of GISS general circulation model simulations of Northern and Southern Hemisphere warm and cold fronts at 2° x 2.5° x 32 levels resolution gives similar cloud distributions but with much lower cloud fraction, a shallower depth of cloudiness, and a shorter extent of tilted warm-frontal cloud cover on the cold air side of the surface frontal position. A close examination of the relationship between the cloudiness and relative humidity fields indicates that water vapor is not lifted enough in modeled midlatitude cyclones and this is related to weak vertical velocities in the model. The model also produces too little cloudiness for a given value of vertical velocity or relative humidity. For global climate models run at scales coarser than tens of kilometers, the authors suggest that the current underestimate of modeled cloud cover in the storm track regions, and in particular the 50°–60°S band of the Southern Oceans, could be reduced with the implementation of a slantwise convection parameterization.Climate change, Environmental studies, Applied mathematicscn2140, add1, mpb20, wk14Applied Physics and Applied Mathematics, Center for Climate Systems ResearchArticlesHelium-ion-induced radiation damage in LiNbO₃ thin-film electro-optic modulators
http://academiccommons.columbia.edu/catalog/ac:179745
Huang, Hsu-Cheng; Dadap Jr., Jerry I.; Malladi, Girish; Kymissis, Ioannis; Bakhru, Hassaram; Osgood Jr., Richard M.http://dx.doi.org/10.7916/D84Q7SPNWed, 19 Nov 2014 00:00:00 +0000Helium-ion-induced radiation damage in a LiNbO₃-thin-film (10 μm-thick) modulator is experimentally investigated. The results demonstrate a degradation of the device performance in the presence of He⁺ irradiation at doses of ≥ 1016 cm⁻². The experiments also show that the presence of the He⁺ stopping region, which determines the degree of overlap between the ion-damaged region and the guided optical mode, plays a major role in determining the degree of degradation in modulation performance. Our measurements showed that the higher overlap can lead to an additional ~5.5 dB propagation loss. The irradiation-induced change of crystal-film anisotropy(nₒ−nₑ )of ~36% was observed for the highest dose used in the experiments. The relevant device extinction ratio, VπL, and device insertion loss, as well the damage mechanisms of each of these parameters are also reported and discussed.Electrical engineering, Physicshh2362, jid5, ik2174, rmo1Applied Physics and Applied Mathematics, Electrical EngineeringArticlesRadiative convective equilibrium over a land surface
http://academiccommons.columbia.edu/catalog/ac:178573
Rochetin, Nicolas; Lintner, Benjamin R.; Findell, Kirsten L.; Sobel, Adam H.; Gentine, Pierrehttp://dx.doi.org/10.7916/D8CJ8C3WTue, 14 Oct 2014 00:00:00 +0000Radiative-convective equilibrium (RCE) describes an idealized state of the atmosphere in which the vertical temperature profile is determined by a balance between radiative and convective fluxes. While RCE has been applied extensively over oceans, its application over the land surface has been limited. The present study explores the properties of RCE over land using an atmospheric single column model (SCM) from the Laboratoire de Meteorologie Dynamique (LMD) General Circulation Model (LMDZ5B) coupled in temperature and moisture to a land surface model comprising a simplified bucket model with finite moisture capacity. Given the presence of a large-amplitude diurnal heat flux cycle, the resultant RCE exhibits multiple equilibria when conditions are neither strictly water- nor energy-limited. By varying top-of-the-atmosphere insolation (through changes in latitude), total system water content, and initial temperature conditions, the sensitivity of the land RCE states is assessed, with particular emphasis on the role of clouds. Based on this analysis, it appears that a necessary condition for the model to exhibit multiple equilibria is the presence of low-level clouds coupled to the diurnal cycle of radiation. In addition the simulated surface precipitation rate varies non-monotonically with latitude as a result of a tradeoff between in-cloud rain rate and subcloud rain re-evaporation, thus underscoring the importance of subcloud layer processes and unsaturated downdrafts. It is shown that clouds, especially at low levels, are key elements of the internal variability of the coupled land-atmosphere system through their feedback on radiation.Atmospheric sciences, Hydrologic sciences, Meteorologyahs129, pg2328Applied Physics and Applied Mathematics, Earth and Environmental Engineering, Earth and Environmental SciencesArticlesThe Effect of Electrode Coupling on Single Molecule Device Characteristics: An X-Ray Spectroscopy and Scanning Probe Microscopy Study
http://academiccommons.columbia.edu/catalog/ac:178216
Batra, Arunabhhttp://dx.doi.org/10.7916/D8MC8XMPTue, 07 Oct 2014 00:00:00 +0000This thesis studies electronic properties of molecular devices in the limiting cases of strong and weak electrode-molecule coupling. In these two limits, we use the complementary techniques of X-Ray spectroscopy and Scanning Tunneling Microscopy (STM) to understand the mechanisms for electrode-molecule bond formation, the energy level realignment due to metal-molecule bonds, the effect of coupling strength on single-molecule conductance in low-bias measurements, and the effect of coupling on transport under high-bias. We also introduce molecular designs with inherent asymmetries, and develop an analytical method to determine the effect of these features on high-bias conductance. This understanding of the role of electrode-molecule coupling in high-bias regimes enables us to develop a series of functional electronic devices whose properties can be predictably tuned through chemical design. First, we explore the weak electrode-molecule coupling regime by studing the interaction of two types of paracyclophane derivates that are coupled `through-space' to underlying gold substrates. The two paracyclophane derivatives differ in the strength of their intramolecular through-space coupling. X-Ray photoemission spectroscopy (XPS) and Near-Edge X-ray Absorbance Fine Structure (NEXAFS) spectroscopy allows us to determine the orientation of both molecules; Resonant Photoemission Spectroscopy (RPES) then allows us to measure charge transfer time from molecule to metal for both molecules. This study provides a quantititative measure of charge transfer time as a function of through-space coupling strength. Next we use this understanding in STM based single-molecule current-voltage measurements of a series of molecules that couple through-space to one electrode, and through-bond to the other. We find that in the high-bias regime, these molecules respond differently depending on the direction of the applied field. This asymmetric response to electric field direction results in diode-like behavior. We vary the length of these asymmetrically coupled molecules, and find that we can increase the rectifying characteristics of these molecules by increasing length. Next, we explore the strong-coupling regime with an X-Ray spectroscopy study of the formation of covalent gold-carbon bonds using benzyltrimethyltin molecules on gold surfaces in ultra high vacuum conditions. Through X-ray Photoemission Spectroscopy (XPS) and X-ray absorption measurements, we find that the molecule fragments at the Sn-Benzyl bond when exposed to gold and the resulting benzyl species only forms covalent Au-C bonds on less coordinated Au surfaces like Au(110). We also find spectroscopic evidence for a gap state localized on the Au-C bond that results from the covalent nature of the bond. Finally, we use Density Functional Theory based Nudged Elastic Band methods to find reaction pathways and energy barriers for this reaction. We use our knowledge of the electronic structure of these bonds to create single-molecule junctions containing Au-C bonds in STM-based break junction experiments. In analogy with our approach for the weakly coupled `through-space' systems, we study the high-bias current-voltage characteristics of molecules with one strong Au-C bond, and one weaker donor-acceptor bond. These experiments reveal that the `gap state' created due to the covalent nature of the Au-C bond remains essentially pinned to the Fermi level of its corresponding electrode, and that most of the electric potential drop in the junction occurs on the donor-acceptor bond; as a result, these molecules behave like rectifiers. We use this principle to create a series of three molecular rectifiers, and show that the unique properties of the Au-C bond allow us to easily tune the rectification ratio by modifying a single electronic parameter. We then explore the process of molecular self-assembly to create organic electronic structures on metal surfaces. Specifically, we study the formation of graphene nanoribbons using a brominated precursor deposited on Au(111) surface in ultra high vacuum. We find that the halogen atoms cleave from the precursors at surprisingly low temperatures of <100C, and find that the resulting radicals bind to Au, forming Au-C and Au-Br bonds. We show that the Br desorbs at relatively low temperatures of <250C, and that polymerization of the precursor molecules to form nanoribbons proceeds only after the debrominization of the surface. Finally, with Angle-Resolved Photoemission and Density Functional Theory calculations, we quantify the interaction strength of the resulting nanoribbons with the underlying gold substrate. Taken together, the results presented in this thesis offer a mechanistic understanding of the formation of electrode-molecule bonds, and also an insight into the high-bias behavior of molecular junctions as a function of electrode-molecule coupling. In addition, our work in developing tunable, functional electronic devices serves as a framework for future technological advances towards molecule-based computation.Nanoscience, Condensed matter physics, Molecular physicsab3279Applied Physics and Applied MathematicsDissertationsAdvancements for three-dimensional remote sensing of the atmosphere
http://academiccommons.columbia.edu/catalog/ac:178170
Martin, William George Kuleszhttp://dx.doi.org/10.7916/D8WM1BZCTue, 23 Sep 2014 00:00:00 +0000Climate modeling efforts depend on remote sensing observations of clouds and aerosols in the atmosphere. This dissertation presents a foundation for using three-dimensional (3D) remote sensing techniques to retrieve cloud and aerosol properties in complex cloud fields. The initial research was aimed at establishing a set of single-scattering properties that could be used in subsequent 3D remote sensing applications. A theoretical stability analysis was used to evaluate what information about the particulate scattering material could be determined from in situ radiance and polarization measurements, and particle size and refractive index were retrieved from synthetic measurements with noise levels comparable to those of existing laboratory instruments. Subsequent research focused on the techniques necessary to retrieve 3D atmosphere and surface properties from images taken by an airborne or space-borne instrument. With the goal of using 3D retrieval methods to extend monitoring capabilities to regions with broken cloud fields, we formulated an efficient procedure for using codes that solve the 3D vector radiative transfer equation (VRTE) to adjust atmosphere and surface properties to fit multi-angle/multi-pixel polarimetric measurements of the atmosphere. Taken together, these two bodies of work contribute to ongoing research which focuses on developing new methods for retrieving aerosols in complex 3D cloud fields, and may extend monitoring capabilities to these currently unresolved scenes.Applied mathematics, Atmospheric scienceswgm2111Applied Physics and Applied MathematicsDissertationsOptimal Signal Processing in Small Stochastic Biochemical Networks
http://academiccommons.columbia.edu/catalog/ac:177510
Ziv, Etay; Nemenman, Ilya; Wiggins, Chris H.http://dx.doi.org/10.7916/D8T72FZKSat, 20 Sep 2014 00:00:00 +0000We quantify the influence of the topology of a transcriptional regulatory network on its ability to process environmental signals. By posing the problem in terms of information theory, we do this without specifying the function performed by the network. Specifically, we study the maximum mutual information between the input (chemical) signal and the output (genetic) response attainable by the network in the context of an analytic model of particle number fluctuations. We perform this analysis for all biochemical circuits, including various feedback loops, that can be built out of 3 chemical species, each under the control of one regulator. We find that a generic network, constrained to low molecule numbers and reasonable response times, can transduce more information than a simple binary switch and, in fact, manages to achieve close to the optimal information transmission fidelity. These high-information solutions are robust to tenfold changes in most of the networks' biochemical parameters; moreover they are easier to achieve in networks containing cycles with an odd number of negative regulators (overall negative feedback) due to their decreased molecular noise (a result which we derive analytically). Finally, we demonstrate that a single circuit can support multiple high-information solutions. These findings suggest a potential resolution of the “cross-talk” phenomenon as well as the previously unexplained observation that transcription factors that undergo proteolysis are more likely to be auto-repressive.Biochemistrychw2Applied Physics and Applied Mathematics, Biological SciencesArticlesQuantification of Cell Edge Velocities and Traction Forces Reveals Distinct Motility Modules during Cell Spreading
http://academiccommons.columbia.edu/catalog/ac:177507
Dubin-Thaler, Benjamin J.; Hofman, Jake M.; Cai, Yunfei; Xenias, Harry; Spielman, Ingrid; Shneidman, Anna V.; David, Lawrence A.; Dobereiner, Hans-Gunther; Wiggins, Chris H.; Sheetz, Michael P.http://dx.doi.org/10.7916/D82N50SDSat, 20 Sep 2014 00:00:00 +0000Actin-based cell motility and force generation are central to immune response, tissue development, and cancer metastasis, and understanding actin cytoskeleton regulation is a major goal of cell biologists. Cell spreading is a commonly used model system for motility experiments – spreading fibroblasts exhibit stereotypic, spatially-isotropic edge dynamics during a reproducible sequence of functional phases: 1) During early spreading, cells form initial contacts with the surface. 2) The middle spreading phase exhibits rapidly increasing attachment area. 3) Late spreading is characterized by periodic contractions and stable adhesions formation. While differences in cytoskeletal regulation between phases are known, a global analysis of the spatial and temporal coordination of motility and force generation is missing. Implementing improved algorithms for analyzing edge dynamics over the entire cell periphery, we observed that a single domain of homogeneous cytoskeletal dynamics dominated each of the three phases of spreading. These domains exhibited a unique combination of biophysical and biochemical parameters – a motility module. Biophysical characterization of the motility modules revealed that the early phase was dominated by periodic, rapid membrane blebbing; the middle phase exhibited continuous protrusion with very low traction force generation; and the late phase was characterized by global periodic contractions and high force generation. Biochemically, each motility module exhibited a different distribution of the actin-related protein VASP, while inhibition of actin polymerization revealed different dependencies on barbed-end polymerization. In addition, our whole-cell analysis revealed that many cells exhibited heterogeneous combinations of motility modules in neighboring regions of the cell edge. Together, these observations support a model of motility in which regions of the cell edge exhibit one of a limited number of motility modules that, together, determine the overall motility function. Our data and algorithms are publicly available to encourage further exploration.Biophysics, Cellular biologychw2, ms2001Applied Physics and Applied Mathematics, Biological SciencesArticlesAllosteric collaboration between elongation factor G and the ribosomal L1 stalk directs tRNA movements during translation
http://academiccommons.columbia.edu/catalog/ac:177516
Fei, Jingyi; Bronson, Jonathan E.; Hofman, Jake M.; Stevens, Rathi L.; Wiggins, Chris H.; Gonzalez Jr., Ruben L.http://dx.doi.org/10.7916/D8959G2NSat, 20 Sep 2014 00:00:00 +0000Determining the mechanism by which tRNAs rapidly and precisely transit through the ribosomal A, P, and E sites during translation remains a major goal in the study of protein synthesis. Here, we report the real-time dynamics of the L1 stalk, a structural element of the large ribosomal subunit that is implicated in directing tRNA movements during translation. Within pretranslocation ribosomal complexes, the L1 stalk exists in a dynamic equilibrium between open and closed conformations. Binding of elongation factor G (EF-G) shifts this equilibrium toward the closed conformation through one of at least two distinct kinetic mechanisms, where the identity of the P-site tRNA dictates the kinetic route that is taken. Within posttranslocation complexes, L1 stalk dynamics are dependent on the presence and identity of the E-site tRNA. Collectively, our data demonstrate that EF-G and the L1 stalk allosterically collaborate to direct tRNA translocation from the P to the E sites, and suggest a model for the release of E-site tRNA.Biophysicschw2, rlg2118Applied Physics and Applied Mathematics, ChemistryArticlesStatistical method for revealing form-function relations in biological networks.
http://academiccommons.columbia.edu/catalog/ac:177513
Mugler, Andrew; Grinshpun, Boris; Franks, Riley; Wiggins, Chris H.http://dx.doi.org/10.7916/D8JQ0ZJ0Sat, 20 Sep 2014 00:00:00 +0000Over the past decade, a number of researchers in systems biology have sought to relate the function of biological systems to their network-level descriptions—lists of the most important players and the pairwise interactions between them. Both for large networks (in which statistical analysis is often framed in terms of the abundance of repeated small subgraphs) and for small networks which can be analyzed in greater detail (or even synthesized in vivo and subjected to experiment), revealing the relationship between the topology of small subgraphs and their biological function has been a central goal. We here seek to pose this revelation as a statistical task, illustrated using a particular setup which has been constructed experimentally and for which parameterized models of transcriptional regulation have been studied extensively. The question “how does function follow form” is here mathematized by identifying which topological attributes correlate with the diverse possible information-processing tasks which a transcriptional regulatory network can realize. The resulting method reveals one form-function relationship which had earlier been predicted based on analytic results, and reveals a second for which we can provide an analytic interpretation. Resulting source code is distributed via http://formfunction.sourceforge.net.Applied mathematicsbg2178, chw2Applied Physics and Applied Mathematics, Cellular, Molecular, Structural, and Genetic StudiesArticlesInferring network mechanisms: The Drosophila melanogaster protein interaction network
http://academiccommons.columbia.edu/catalog/ac:177528
Middendorf, Manuel; Ziv, Etay; Wiggins, Chris H.http://dx.doi.org/10.7916/D8862DZVSat, 20 Sep 2014 00:00:00 +0000Naturally occurring networks exhibit quantitative features revealing underlying growth mechanisms. Numerous network mechanisms have recently been proposed to reproduce specific properties such as degree distributions or clustering coefficients. We present a method for inferring the mechanism most accurately capturing a given network topology, exploiting discriminative tools from machine learning. The Drosophila melanogaster protein network is confidently and robustly (to noise and training data subsampling) classified as a duplication–mutation–complementation network over preferential attachment, small-world, and a duplication–mutation mechanism without complementation. Systematic classification, rather than statistical study of specific properties, provides a discriminative approach to understand the design of complex networks.Applied mathematicschw2Applied Physics and Applied MathematicsArticlesFast dynamics of supercoiled DNA revealed by single-molecule experiments.
http://academiccommons.columbia.edu/catalog/ac:177522
Crut, Aurelien; Koster, Daniel A.; Seidel, Ralf; Wiggins, Chris H.; Dekker, Nynke H.http://dx.doi.org/10.7916/D8S75DW3Sat, 20 Sep 2014 00:00:00 +0000The dynamics of supercoiled DNA play an important role in various cellular processes such as transcription and replication that involve DNA supercoiling. We present experiments that enhance our understanding of these dynamics by measuring the intrinsic response of single DNA molecules to sudden changes in tension or torsion. The observed dynamics can be accurately described by quasistatic models, independent of the degree of supercoiling initially present in the molecules. In particular, the dynamics are not affected by the continuous removal of the plectonemes. These results set an upper bound on the hydrodynamic drag opposing plectoneme removal, and thus provide a quantitative baseline for the dynamics of bare DNA.Biophysics, Biomechanicschw2Applied Physics and Applied MathematicsArticlesA stochastic spectral analysis of transcriptional regulatory cascades
http://academiccommons.columbia.edu/catalog/ac:177519
Walczak, Aleksandra M.; Mugler, Andrew; Wiggins, Chris H.http://dx.doi.org/10.7916/D81N7ZNNSat, 20 Sep 2014 00:00:00 +0000The past decade has seen great advances in our understanding of the role of noise in gene regulation and the physical limits to signaling in biological networks. Here, we introduce the spectral method for computation of the joint probability distribution over all species in a biological network. The spectral method exploits the natural eigenfunctions of the master equation of birth – death processes to solve for the joint distribution of modules within the network, which then inform each other and facilitate calculation of the entire joint distribution. We illustrate the method on a ubiquitous case in nature: linear regulatory cascades. The efficiency of the method makes possible numerical optimization of the input and regulatory parameters, revealing design properties of, e.g., the most informative cascades. We find, for threshold regulation, that a cascade of strong regulations converts a unimodal input to a bimodal output, that multimodal inputs are no more informative than bimodal inputs, and that a chain of up-regulations outperforms a chain of down-regulations. We anticipate that this numerical approach may be useful for modeling noise in a variety of small network topologies in biology.Applied mathematicschw2Applied Physics and Applied MathematicsArticlesMultiple events on single molecules: unbiased estimation in single-molecule biophysics.
http://academiccommons.columbia.edu/catalog/ac:177525
Koster, Daniel A.; Wiggins, Chris H.; Dekker, Nynke H.http://dx.doi.org/10.7916/D8HQ3XF2Sat, 20 Sep 2014 00:00:00 +0000Most analyses of single-molecule experiments consist of binning experimental outcomes into a histogram and finding the parameters that optimize the fit of this histogram to a given data model. Here we show that such an approach can introduce biases in the estimation of the parameters, thus great care must be taken in the estimation of model parameters from the experimental data. The bias can be particularly large when the observations themselves are not statistically independent and are subjected to global constraints, as, for example, when the iterated steps of a motor protein acting on a single molecule must not exceed the total molecule length. We have developed a maximum-likelihood analysis, respecting the experimental constraints, which allows for a robust and unbiased estimation of the parameters, even when the bias well exceeds 100%. We demonstrate the potential of the method for a number of single-molecule experiments, focusing on the removal of DNA supercoils by topoisomerase IB, and validate the method by numerical simulation of the experiment.Biophysics, Applied mathematicschw2Applied Physics and Applied MathematicsArticlesLearning ‘‘graph-mer’’ Motifs that Predict Gene Expression Trajectories in Development
http://academiccommons.columbia.edu/catalog/ac:177504
Li, Xuejing; Panea, Casandra; Wiggins, Chris; Reinke, Valerie; Leslie, Christinahttp://dx.doi.org/10.7916/D8B56H8XFri, 19 Sep 2014 00:00:00 +0000A key problem in understanding transcriptional regulatory networks is deciphering what cis regulatory logic is encoded in gene promoter sequences and how this sequence information maps to expression. A typical computational approach to this problem involves clustering genes by their expression profiles and then searching for overrepresented motifs in the promoter sequences of genes in a cluster. However, genes with similar expression profiles may be controlled by distinct regulatory programs. Moreover, if many gene expression profiles in a data set are highly correlated, as in the case of whole organism developmental time series, it may be difficult to resolve fine-grained clusters in the first place. We present a predictive framework for modeling the natural flow of information, from promoter sequence to expression, to learn cis regulatory motifs and characterize gene expression patterns in developmental time courses. We introduce a cluster-free algorithm based on a graph-regularized version of partial least squares (PLS) regression to learn sequence patterns—represented by graphs of k-mers, or “graph-mers”—that predict gene expression trajectories. Applying the approach to wildtype germline development in Caenorhabditis elegans, we found that the first and second latent PLS factors mapped to expression profiles for oocyte and sperm genes, respectively. We extracted both known and novel motifs from the graph-mers associated to these germline-specific patterns, including novel CG-rich motifs specific to oocyte genes. We found evidence supporting the functional relevance of these putative regulatory elements through analysis of positional bias, motif conservation and in situ gene expression. This study demonstrates that our regression model can learn biologically meaningful latent structure and identify potentially functional motifs from subtle developmental time course expression data.Applied mathematics, Geneticschw2Applied Physics and Applied MathematicsArticlesDynamic Patterns and Self-Knotting of a Driven Hanging Chain
http://academiccommons.columbia.edu/catalog/ac:177495
Belmonte, Andrew; Shelley, Michael J.; Eldakar, Shaden T.; Wiggins, Chris H.http://dx.doi.org/10.7916/D83N21XSFri, 19 Sep 2014 00:00:00 +0000When shaken vertically, a hanging chain displays a startling variety of distinct behaviors. We find experimentally that instabilities occur in tonguelike bands of parameter space, to swinging or rotating pendular motion, or to chaotic states. Mathematically, the dynamics are described by a nonlinear wave equation. A linear stability analysis predicts instabilities within the well-known resonance tongues; their boundaries agree very well with experiment. Full simulations of the 3D dynamics reproduce and elucidate many aspects of the experiment. The chain is also observed to tie knots in itself, some quite complex. This is beyond the reach of the current analysis and simulations.Biophysicschw2Applied Physics and Applied MathematicsArticlesViscous Nonlinear Dynamics of Twist and Writhe
http://academiccommons.columbia.edu/catalog/ac:177498
Goldstein, Raymond E.; Powers, Thomas R.; Wiggins, Chris H.http://dx.doi.org/10.7916/D8V40SRJFri, 19 Sep 2014 00:00:00 +0000Exploiting the “natural” frame of space curves, we formulate an intrinsic dynamics of a twisted elastic filament in a viscous fluid. Coupled nonlinear equations describing the temporal evolution of the filament's complex curvature and twist density capture the dynamic interplay of twist and writhe. These equations are used to illustrate a remarkable nonlinear phenomenon: geometric untwisting of open filaments, whereby twisting strains relax through a transient writhing instability without axial rotation. Experimentally observed writhing motions of fibers of the bacterium B. subtilis [N. H. Mendelson et al., J. Bacteriol. 177, 7060 (1995)] may be examples of this untwisting process.Biophysicschw2Applied Physics and Applied MathematicsArticlesFlexive and Propulsive Dynamics of Elastica at Low Reynolds Number
http://academiccommons.columbia.edu/catalog/ac:177501
Wiggins, Chris H.; Goldstein, Raymond E.http://dx.doi.org/10.7916/D8KP80P6Fri, 19 Sep 2014 00:00:00 +0000A stiff one-armed swimmer in glycerine goes nowhere. However, if its arm is elastic, the swimmer can go on its way. Quantifying this observation, we study a hyperdiffusion equation for the shape of the elastica in a viscous fluid, find solutions for impulsive or oscillatory forcing, and elucidate relevant aspects of propulsion. These results have application in a variety of physical and biological contexts, from dynamic experiments measuring biopolymer bending moduli to instabilities of twisted elastic filaments.Biophysics, Applied mathematicschw2Applied Physics and Applied MathematicsArticlesRelaxation Dynamics of Semiflexible Polymers
http://academiccommons.columbia.edu/catalog/ac:177492
Bohbot-Raviv, Y.; Zhao, W. Z.; Feingold, M.; Wiggins, Chris H.; Granek, R.http://dx.doi.org/10.7916/D8C53JD9Fri, 19 Sep 2014 00:00:00 +0000We study the relaxation dynamics of a semiflexible chain by introducing a time-dependent tension. The chain has one of its ends attached to a large bead, and the other end is fixed. We focus on the initial relaxation of the chain that is initially strongly stretched. Using a tension that is self-consistently determined, we obtain the evolution of the end-to-end distance with no free parameters. Our results are in good agreement with single molecule experiments on double stranded DNA.Biophysicschw2Applied Physics and Applied MathematicsArticlesNonmuscle Myosin IIA-Dependent Force Inhibits Cell Spreading and Drives F-Actin Flow
http://academiccommons.columbia.edu/catalog/ac:177409
Cai, Yunfei; Biais, Nicolas; Giannone, Gregory; Tanase, Monica; Jiang, Guoying; Hoffman, Jake M.; Wiggins, Chris H.; Silberzan, Pascal; Buguin, Alex; Ladoux, Benoit; Sheetz, Michael P.http://dx.doi.org/10.7916/D8028Q2BFri, 19 Sep 2014 00:00:00 +0000Nonmuscle myosin IIA (NMM-IIA) is involved in the formation of focal adhesions and neurite retraction. However, the role of NMM-IIA in these functions remains largely unknown. Using RNA interference as a tool to decrease NMM-IIA expression, we have found that NMM-IIA is the major myosin involved in traction force generation and retrograde F-actin flow in mouse embryonic fibroblast cells. Quantitative analyses revealed that ∼60% of traction force on fibronectin-coated surfaces is contributed by NMM-IIA and ∼30% by NMM-IIB. The retrograde F-actin flow decreased dramatically in NMM-IIA-depleted cells, but seemed unaffected by NMM-IIB deletion. In addition, we found that depletion of NMM-IIA caused cells to spread at a higher rate and to a greater area on fibronectin substrates during the early spreading period, whereas deletion of NMM-IIB appeared to have no effect on spreading. The distribution of NMM-IIA was concentrated on the dorsal surface and approached the ventral surface in the periphery, whereas NMM-IIB was primarily concentrated around the nucleus and to a lesser extent at the ventral surface in cell periphery. Our results suggest that NMM-IIA is involved in generating a coherent cytoplasmic contractile force from one side of the cell to the other through the cross-linking and the contraction of dorsal actin filaments.Biophysics, Cellular biologychw2, ms2001Applied Physics and Applied Mathematics, Biological SciencesArticlesTrapping and Wiggling: Elastohydrodynamics of Driven Microfilaments
http://academiccommons.columbia.edu/catalog/ac:177420
Wiggins, Chris H.; Riveline, D.; Ott, A.; Goldstein, Raymond E.http://dx.doi.org/10.7916/D8QJ7FTVFri, 19 Sep 2014 00:00:00 +0000We present an analysis of the planar motion of single semiflexible filaments subject to viscous drag or point forcing. These are the relevant forces in dynamic experiments designed to measure biopolymer bending moduli. By analogy with the “Stokes problems” in hydrodynamics (motion of a viscous fluid induced by that of a wall bounding the fluid), we consider the motion of a polymer, one end of which is moved in an impulsive or oscillatory way. Analytical solutions for the time-dependent shapes of such moving polymers are obtained within an analysis applicable to small-amplitude deformations. In the case of oscillatory driving, particular attention is paid to a characteristic length determined by the frequency of oscillation, the polymer persistence length, and the viscous drag coefficient. Experiments on actin filaments manipulated with optical traps confirm the scaling law predicted by the analysis and provide a new technique for measuring the elastic bending modulus. Exploiting this model, we also present a reanalysis of several published experiments on microtubules.Biophysicschw2Applied Physics and Applied MathematicsArticlesA classification-based framework for predicting and analyzing gene regulatory response
http://academiccommons.columbia.edu/catalog/ac:177435
Kundaje, Anshul; Middendorf, Manuel; Wiggins, Chris; Shah, Mihir; Freund, Yoav; Leslie, Christinahttp://dx.doi.org/10.7916/D82V2DNHFri, 19 Sep 2014 00:00:00 +0000We have recently introduced a predictive framework for studying gene transcriptional regulation in simpler organisms using a novel supervised learning algorithm called GeneClass. GeneClass is motivated by the hypothesis that in model organisms such as Saccharomyces cerevisiae, we can learn a decision rule for predicting whether a gene is up- or down-regulated in a particular microarray experiment based on the presence of binding site subsequences ("motifs") in the gene's regulatory region and the expression levels of regulators such as transcription factors in the experiment ("parents"). GeneClass formulates the learning task as a classification problem — predicting +1 and -1 labels corresponding to up- and down-regulation beyond the levels of biological and measurement noise in microarray measurements. Using the Adaboost algorithm, GeneClass learns a prediction function in the form of an alternating decision tree, a margin-based generalization of a decision tree. In the current work, we introduce a new, robust version of the GeneClass algorithm that increases stability and computational efficiency, yielding a more scalable and reliable predictive model. The improved stability of the prediction tree enables us to introduce a detailed post-processing framework for biological interpretation, including individual and group target gene analysis to reveal condition-specific regulation programs and to suggest signaling pathways. Robust GeneClass uses a novel stabilized variant of boosting that allows a set of correlated features, rather than single features, to be included at nodes of the tree; in this way, biologically important features that are correlated with the single best feature are retained rather than decorrelated and lost in the next round of boosting. Other computational developments include fast matrix computation of the loss function for all features, allowing scalability to large datasets, and the use of abstaining weak rules, which results in a more shallow and interpretable tree. We also show how to incorporate genome-wide protein-DNA binding data from ChIP chip experiments into the GeneClass algorithm, and we use an improved noise model for gene expression data. Using the improved scalability of Robust GeneClass, we present larger scale experiments on a yeast environmental stress dataset, training and testing on all genes and using a comprehensive set of potential regulators. We demonstrate the improved stability of the features in the learned prediction tree, and we show the utility of the post-processing framework by analyzing two groups of genes in yeast — the protein chaperones and a set of putative targets of the Nrg1 and Nrg2 transcription factors — and suggesting novel hypotheses about their transcriptional and post-transcriptional regulation. Detailed results and Robust GeneClass source code is available for download from http://www.cs.columbia.edu/compbio/robust-geneclassBioinformatics, Geneticschw2Applied Physics and Applied MathematicsArticlesGraphical models for inferring single molecule dynamics
http://academiccommons.columbia.edu/catalog/ac:177431
Bronson, Jonathan E. ; Hofman, Jake M.; Fei, Jingyi; Wiggins, Chris H.; Gonzalez, Ruben L.http://dx.doi.org/10.7916/D86M35BSFri, 19 Sep 2014 00:00:00 +0000The recent explosion of experimental techniques in single molecule biophysics has generated a variety of novel time series data requiring equally novel computational tools for analysis and inference. This article describes in general terms how graphical modeling may be used to learn from biophysical time series data using the variational Bayesian expectation maximization algorithm (VBEM). The discussion is illustrated by the example of single-molecule fluorescence resonance energy transfer (smFRET) versus time data, where the smFRET time series is modeled as a hidden Markov model (HMM) with Gaussian observables. A detailed description of smFRET is provided as well. The VBEM algorithm returns the model’s evidence and an approximating posterior parameter distribution given the data. The former provides a metric for model selection via maximum evidence (ME), and the latter a description of the model’s parameters learned from the data. ME/VBEM provide several advantages over the more commonly used approach of maximum likelihood (ML) optimized by the expectation maximization (EM) algorithm, the most important being a natural form of model selection and a well-posed (non-divergent) optimization problem. The results demonstrate the utility of graphical modeling for inference of dynamic processes in single molecule biophysics.Biophysics, Bioinformaticschw2, rlg2118Applied Physics and Applied Mathematics, ChemistryArticlesInformation-theoretic approach to network modularity
http://academiccommons.columbia.edu/catalog/ac:177474
Ziv, Etay; Middendorf, Manuel; Wiggins, Chris H.http://dx.doi.org/10.7916/D8X34VZVFri, 19 Sep 2014 00:00:00 +0000Exploiting recent developments in information theory, we propose, illustrate, and validate a principled information-theoretic algorithm for module discovery and the resulting measure of network modularity. This measure is an order parameter (a dimensionless number between 0 and 1). Comparison is made with other approaches to module discovery and to quantifying network modularity (using Monte Carlo generated Erdös-like modular networks). Finally, the network information bottleneck (NIB) algorithm is applied to a number of real world networks, including the “social” network of coauthors at the 2004 APS March Meeting.Applied mathematicschw2Applied Physics and Applied MathematicsArticlesMagma migration and magmatic solitary waves in 3-D
http://academiccommons.columbia.edu/catalog/ac:177438
Wiggins, Chris H.; Spiegelman, Marc W.http://dx.doi.org/10.7916/D8Z31X5JFri, 19 Sep 2014 00:00:00 +0000Numerical studies of fluid flow in the mantle suggest that magma migration is an inherently time-dependent process that produces magmatic solitary waves from obstructions in melt flux. Previous work has considered one and two dimensional problems. Here we present the results of three dimensional calculations that utilize a new, efficient multigrid scheme. We demonstrate that one and two dimensional solitary waves are unstable and break up into sets of 3-D solitary waves which are perfectly spherical when propagating through a uniform porosity medium. While these waves are not solitons, their non-linear interactions are qualitatively similar. The solitary waves are highly opportunistic and establish efficient pathways for migration by linking up with nearby waves. When the initial condition is a random distribution of porosity, the porosity structure can organize into elongate, time-dependent channels formed from chains of solitary waves. These results are natural consequences of the assumptions that the matrix is permeable and viscously deformable. We suggest that solitary waves are likely to exist in the mantle and may contribute to the episodicity of mantle magmatism.Physics, Geophysicschw2, msw6Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesSpectral solutions to stochastic models of gene expression with bursts and regulation
http://academiccommons.columbia.edu/catalog/ac:177467
Mugler, Andrew; Walczak, Aleksandra M.; Wiggins, Chris H.http://dx.doi.org/10.7916/D8F18X86Fri, 19 Sep 2014 00:00:00 +0000Signal-processing molecules inside cells are often present at low copy number, which necessitates probabilistic models to account for intrinsic noise. Probability distributions have traditionally been found using simulation-based approaches which then require estimating the distributions from many samples. Here we present in detail an alternative method for directly calculating a probability distribution by expanding in the natural eigenfunctions of the governing equation, which is linear. We apply the resulting spectral method to three general models of stochastic gene expression: a single gene with multiple expression states (often used as a model of bursting in the limit of two states), a gene regulatory cascade, and a combined model of bursting and regulation. In all cases we find either analytic results or numerical prescriptions that greatly outperform simulations in efficiency and accuracy. In the last case, we show that bimodal response in the limit of slow switching is not only possible but optimal in terms of information transmission.Applied mathematics, Bioinformaticschw2Applied Physics and Applied MathematicsArticlesDynamics of semiflexible polymers in a flow field
http://academiccommons.columbia.edu/catalog/ac:177471
Munk, Tobias; Hallatschek, Oskar; Wiggins, Chris H.; Frey, Erwinhttp://dx.doi.org/10.7916/D85M647VFri, 19 Sep 2014 00:00:00 +0000We present a method to investigate the dynamics of a single semiflexible polymer, subject to anisotropic friction in a viscous fluid. In contrast to previous approaches, we do not rely on a discrete bead-rod model, but introduce a suitable normal mode decomposition of a continuous space curve. By means of a perturbation expansion for stiff filaments, we derive a closed set of coupled Langevin equations in mode space for the nonlinear dynamics in two dimensions, taking into account exactly the local constraint of inextensibility. The stochastic differential equations obtained this way are solved numerically, with parameters adjusted to describe the motion of actin filaments. As an example, we show results for the tumbling motion in shear flow.Applied mathematics, Bioinformaticschw2Applied Physics and Applied MathematicsArticlesTime-dependent information transmission in a model regulatory circuit
http://academiccommons.columbia.edu/catalog/ac:177464
Mancini, F.; Wiggins, Chris H.; Marsili, M.; Walczak, Aleksandra. M.http://dx.doi.org/10.7916/D8PK0DNKFri, 19 Sep 2014 00:00:00 +0000Many biological regulatory systems respond with a physiological delay when processing signals. A simple model of regulation which respects these features shows how the ability of a delayed output to transmit information is limited: at short times by the time scale of the dynamic input, at long times by that of the dynamic output. We find that topologies of maximally informative networks correspond to commonly occurring biological circuits linked to stress response and that circuits functioning out of steady state may exploit absorbing states to transmit information optimally.Applied mathematics, Bioinformaticschw2Applied Physics and Applied MathematicsArticlesSystematic identification of statistically significant network measures
http://academiccommons.columbia.edu/catalog/ac:177477
Ziv, Etay; Koytcheff, Robin; Middendorf, Manuel; Wiggins, Chris H.http://dx.doi.org/10.7916/D8NK3CJNFri, 19 Sep 2014 00:00:00 +0000We present a graph embedding space (i.e., a set of measures on graphs) for performing statistical analyses of networks. Key improvements over existing approaches include discovery of “motif hubs” (multiple overlapping significant subgraphs), computational efficiency relative to subgraph census, and flexibility (the method is easily generalizable to weighted and signed graphs). The embedding space is based on scalars, functionals of the adjacency matrix representing the network. Scalars are global, involving all nodes; although they can be related to subgraph enumeration, there is not a one-to-one mapping between scalars and subgraphs. Improvements in network randomization and significance testing—we learn the distribution rather than assuming Gaussianity—are also presented. The resulting algorithm establishes a systematic approach to the identification of the most significant scalars and suggests machine-learning techniques for network classification.Applied mathematicschw2Applied Physics and Applied MathematicsArticlesBayesian Approach to Network Modularity
http://academiccommons.columbia.edu/catalog/ac:177486
Mugler, Andrew; Wiggins, Chris H.http://dx.doi.org/10.7916/D8W37TTGFri, 19 Sep 2014 00:00:00 +0000We present an efficient, principled, and interpretable technique for inferring module assignments and for identifying the optimal number of modules in a given network. We show how several existing methods for finding modules can be described as variant, special, or limiting cases of our work, and how the method overcomes the resolution limit problem, accurately recovering the true number of modules. Our approach is based on Bayesian methods for model selection which have been used with success for almost a century, implemented using a variational technique developed only in the past decade. We apply the technique to synthetic and real networks and outline how the method naturally allows selection among competing models.Biophysics, Applied mathematicschw2Applied Physics and Applied MathematicsArticlesInformation-Optimal Transcriptional Response to Oscillatory Driving
http://academiccommons.columbia.edu/catalog/ac:177483
Mugler, Andrew; Walczak, Aleksandra M.; Wiggins, Chris H.http://dx.doi.org/10.7916/D84M9321Fri, 19 Sep 2014 00:00:00 +0000Intracellular transmission of information via chemical and transcriptional networks is thwarted by a physical limitation: The finite copy number of the constituent chemical species introduces unavoidable intrinsic noise. Here we solve for the complete probabilistic description of the intrinsically noisy response to an oscillatory driving signal. We derive and numerically verify a number of simple scaling laws. Unlike in the case of measuring a static quantity, response to an oscillatory signal can exhibit a resonant frequency which maximizes information transmission. Furthermore, we show that the optimal regulatory design is dependent on biophysical constraints (i.e., the allowed copy number and response time). The resulting phase diagram illustrates under what conditions threshold regulation outperforms linear regulation.Biophysics, Applied mathematicschw2Applied Physics and Applied MathematicsArticlesLateral Membrane Waves Constitute a Universal Dynamic Pattern of Motile Cells
http://academiccommons.columbia.edu/catalog/ac:177489
Dobereiner, Hans-Gunther; Dubin-Thaler, Benjamin J.; Hofman, Jake M.; Xenias, Harry S.; Sims, Tasha N.; Giannone, Gregory; Dustin, Michael L.; Wiggins, Chris H.; Sheetz, Michael P.http://dx.doi.org/10.7916/D8MP51S4Fri, 19 Sep 2014 00:00:00 +0000We have monitored active movements of the cell circumference on specifically coated substrates for a variety of cells including mouse embryonic fibroblasts and T cells, as well as wing disk cells from fruit flies. Despite having different functions and being from multiple phyla, these cell types share a common spatiotemporal pattern in their normal membrane velocity; we show that protrusion and retraction events are organized in lateral waves along the cell membrane. These wave patterns indicate both spatial and temporal long-range periodic correlations of the actomyosin gel.Cellular biology, Biophysicschw2, ms2001Applied Physics and Applied Mathematics, Biological SciencesArticlesElastohydrodynamic study of actin filaments using fluorescence microscopy
http://academiccommons.columbia.edu/catalog/ac:177480
Riveline, D.; Wiggins, Chris H.; Golstein, Raymond E.; Ott, A.http://dx.doi.org/10.7916/D8D50KGSFri, 19 Sep 2014 00:00:00 +0000We probed the bending of actin subject to external forcing and viscous drag. Single actin filaments were moved perpendicular to their long axis in an oscillatory way by means of an optically tweezed latex bead attached to one end of the filaments. Shapes of these polymers were observed by epifluorescence microscopy. They were found to be in agreement with predictions of semiflexible polymer theory and slender-body hydrodynamics. A persistence length of 7.4±0.2 μm could be extracted.Biophysicschw2Applied Physics and Applied MathematicsArticlesARACNE: An Algorithm for the Reconstruction of Gene Regulatory Networks in a Mammalian Cellular Context
http://academiccommons.columbia.edu/catalog/ac:177427
Margolin, Adam A.; Nemenman, Ilya; Basso, Katia; Wiggins, Chris H.; Stolovitzky, Gustavo Alejandro; Favera, Riccardo Dalla; Califano, Andreahttp://dx.doi.org/10.7916/D8G15ZBPFri, 19 Sep 2014 00:00:00 +0000Elucidating gene regulatory networks is crucial for understanding normal cell physiology and complex pathologic phenotypes. Existing computational methods for the genome-wide "reverse engineering" of such networks have been successful only for lower eukaryotes with simple genomes. Here we present ARACNE, a novel algorithm, using microarray expression profiles, specifically designed to scale up to the complexity of regulatory networks in mammalian cells, yet general enough to address a wider range of network deconvolution problems. This method uses an information theoretic approach to eliminate the majority of indirect interactions inferred by co-expression methods. We prove that ARACNE reconstructs the network exactly (asymptotically) if the effect of loops in the network topology is negligible, and we show that the algorithm works well in practice, even in the presence of numerous loops and complex topologies. We assess ARACNE's ability to reconstruct transcriptional regulatory networks using both a realistic synthetic dataset and a microarray dataset from human B cells. On synthetic datasets ARACNE achieves very low error rates and outperforms established methods, such as Relevance Networks and Bayesian Networks. Application to the deconvolution of genetic networks in human B cells demonstrates ARACNE's ability to infer validated transcriptional targets of the cMYC proto-oncogene. We also study the effects of misestimation of mutual information on network reconstruction, and show that algorithms based on mutual information ranking are more resilient to estimation errors. ARACNE shows promise in identifying direct transcriptional interactions in mammalian cellular networks, a problem that has challenged existing reverse engineering algorithms. This approach should enhance our ability to use microarray data to elucidate functional mechanisms that underlie cellular processes and to identify molecular targets of pharmacological compounds in mammalian cellular networks.Bioinformatics, Cellular biologykb451, chw2, gs2331, ac2248Applied Physics and Applied Mathematics, Biomedical Informatics, Pathology and Cell BiologyArticlesUpdated coincident Ground and MODIS cloud Observations (2005-2011): Senator Beck and Swamp Angel study plots, Southwestern Colorado
http://academiccommons.columbia.edu/catalog/ac:177386
Naud, Catherine M.; Rangwala, Imtiazhttp://dx.doi.org/10.7916/D8W957QDThu, 18 Sep 2014 00:00:00 +0000Data Format: NETCDF These two files include only the coincident hourly observations from ground and satellite (MODIS) at the Senator Beck and Swamp Angel sites. The ground data are described and obtained from the Center for Snow and Avalanche Studies (http://www.snowstudies.org/). the MODIS (MOD06 and MYD06) cloud data were obtained from the GSFC LAADS website (http://ladsweb.nascom.nasa.gov/data/search.html). There are generally two observations per day. Day and night flag is also assigned to the data. The satellite observations included here are: (1) cloud fraction and (2) cloud optical depth (during overcast and daylight conditions only).Atmospheric sciences, Meteorology, Hydrologic sciencescn2140Applied Physics and Applied MathematicsDatasetsGraphical models for inferring single molecule dynamics
http://academiccommons.columbia.edu/catalog/ac:183652
Bronson, Jonathan; Hofman, Jake; Fei, Jingyi; Gonzalez Jr., Ruben L.; Wiggins, Chris H.http://dx.doi.org/10.7916/D8HT2MP4Mon, 08 Sep 2014 00:00:00 +0000The recent explosion of experimental techniques in single molecule biophysics has generated a variety of novel time series data requiring equally novel computational tools for analysis and inference. This article describes in general terms how graphical modeling may be used to learn from biophysical time series data using the variational Bayesian expectation maximization algorithm (VBEM). The discussion is illustrated by the example of single-molecule fluorescence resonance energy transfer (smFRET) versus time data, where the smFRET time series is modeled as a hidden Markov model (HMM) with Gaussian observables. A detailed description of smFRET is provided as well. The VBEM algorithm returns the model’s evidence and an approximating posterior parameter distribution given the data. The former provides a metric for model selection via maximum evidence (ME), and the latter a description of the model’s parameters learned from the data. ME/VBEM provide several advantages over the more commonly used approach of maximum likelihood (ML) optimized by the expectation maximization (EM) algorithm, the most important being a natural form of model selection and a well-posed (non-divergent) optimization problem. The results demonstrate the utility of graphical modeling for inference of dynamic processes in single molecule biophysics.Bioinformatics, Biophysicsrlg2118, chw2Applied Physics and Applied Mathematics, ChemistryArticlesProjected Changes in the Annual Cycle of Surface Temperature and Precipitation Due to Greenhouse Gas Increases
http://academiccommons.columbia.edu/catalog/ac:177091
Dwyer, Johnhttp://dx.doi.org/10.7916/D8CN7248Mon, 28 Jul 2014 00:00:00 +0000When forced with increasing greenhouse gases, global climate models project changes to the seasonality of several key climate variables. These include delays in the phase of surface temperature, precipitation, and vertical motion indicating maxima and minima occurring later in the year. The changes also include an increase in the amplitude (or annual range) of low-latitude surface temperature and tropical precipitation and a decrease in the amplitude of high-latitude surface temperature and vertical motion. The aim of this thesis is to detail these changes, understand the links between them and ultimately relate them to simple physical mechanisms. At high latitudes, all of the global climate models of the CMIP3 intercomparison suite project a phase delay and amplitude decrease in surface temperature. Evidence is provided that the changes are mainly driven by sea ice loss: as sea ice melts during the 21st century, the previously unexposed open ocean increases the effective heat capacity of the surface layer, slowing and damping the temperature response at the surface. In the tropics and subtropics, changes in phase and amplitude are smaller and less spatially uniform than near the poles, but they are still prevalent in the models. These regions experience a small phase delay, but an amplitude increase of the surface temperature cycle, a combination that is inconsistent with changes to the effective heat capacity of the system. Evidence suggests that changes in the tropics and subtropics are linked to changes in surface heat fluxes. The next chapter investigates the nature of the projected phase delay and amplitude increase of precipitation using AGCM experiments forced by SST perturbations representing idealizations of the changes in annual mean, amplitude, and phase as simulated by CMIP5 models. A uniform SST warming is sufficient to force both an amplification and a delay of the annual cycle of precipitation. The amplification is due to an increase in the annual mean vertical water vapor gradient, while the delay is linked to a phase delay in the annual cycle of the circulation. A budget analysis of this simulation reveals a large degree of similarity with the CMIP5 results. In the second experiment, only the seasonal characteristics of SST are changed. For an amplified annual cycle of SST there is an amplified annual cycle of precipitation, while for a delayed SST there is a delayed annual cycle of precipitation. Assuming that SST changes can entirely explain the seasonal precipitation changes, the AGCM simulations suggest that the annual mean warming explains most of the amplitude increase and much of the phase delay in the CMIP5 models. However, imperfect agreement between the changes in the SST-forced AGCM simulations and the CMIP5 coupled simulations suggests that coupled effects may play a significant role. Finally, the connections between changes in the seasonality of precipitation, temperature and circulation are studied in the tropics using models of varying complexity. These models include coupled model simulations with idealized forcing, a simple, semi-empirical model to describe the effect of land-ocean interactions, an aquaplanet model, and a dry, dynamical model. Each gives insights into the projected CMIP changes. Taken together they suggest that changes in the amplitude of vertical motions are consistent with a weakening of the annual mean circulation and can explain part of the changes in the amplitude of precipitation over both ocean and land, when combined with the thermodynamic effect described previously. By increasing the amplitude of the annual cycle of surface winds, the changes in circulation may also increase the amplitude of the surface temperature via the surface energy balance. The delay in the phase of circulation directly leads to a delay in the phase of precipitation, especially over ocean.Climate change, Atmospheric sciencesjgd2102Applied Physics and Applied Mathematics, Lamont-Doherty Earth ObservatoryDissertationsHow Rotation affects Instabilities and the Plasma Response to Magnetic Perturbations in a Tokamak Plasma
http://academiccommons.columbia.edu/catalog/ac:175361
DeBono, Bryanhttp://dx.doi.org/10.7916/D8J964HRMon, 07 Jul 2014 00:00:00 +0000This thesis presents the systematic study of the multimode external kink mode structure and dynamics in the High-Beta Tokamak Extended-Pulse experiment (HBT-EP) when the plasma rotation is externally controlled using a source of toroidal momentum input. The capabilities of the HBT-EP tokamak to study rotation physics was greatly extended during a 2009-2010 major upgrade, when a new adjustable conducting wall, a high-power modular control coil array system, and an extensive set of 216 poloidal and radial magnetic sensors were installed on the machine. HBT-EP was additionally equipped with a biased edge electrode which made it possible to adjust the plasma ion and plasma magnetohydrodynamics (MHD) mode rotation frequencies by imparting an electromagnetic torque on the plasma. The design of this biased edge electrode, and its capability to torque the plasma is described. The rotation frequency of the helical kink modes was directly inferred from analysis of the magnetics dataset. To directly measure the plasma ion acceleration as the plasma was torqued by the biased electrode, a novel high-throughput and fast-response spectroscopic rotation diagnostic was installed on HBT-EP. This spectroscopic rotation diagnostic was designed to measure the velocity of He ions, therefore when conducting experiments using the spectroscopic rotation diagnostic a gas mixture of 90%D and 10%He was used. With its current power supplies the bias probe is capable of accelerating the primary m/n=3/1 helical kink mode (which has a natural rotation frequency between +7-+9kHz) to somewhere between -50kHz-+25kHz depending on the probe bias. At a probe voltage of +175V the He impurity ions were seen to accelerate by 3km/sec. Biorthogonal decomposition (BD) analysis was applied to the large magnetics dataset and used to determine the multimode m/n spectrum of the helical kink modes present in HBT-EP. The dominant helicities present as revealed by the BD are the m/n=3/1 and m/n=6/2 modes, which represent about 85% and 8% of the total MHD activity respectively. This percentages remain consistent across the entire range of 3/1 mode rotation frequencies obtainable from the bias probe, (-50kHz-25kHz). The Hilbert transform technique was also applied to magnetic sensor data to determine the instantaneous amplitude and frequency of the total MHD activity. The total MHD amplitude was seen to decrease with increasing plasma rotation, a 35% reduction as the 3/1 mode was accelerated from +6-+24kHz. Active MHD spectroscopy experiments using a resonant magnetic perturbation (RMP) are able to excite a clear three-dimensional plasma response. Plasma rotation is theoretically expected to increase plasma stability to external resonant error elds, and in HBT-EP the plasma amplitude response to a m/n=3/1 RMP increases by a factor of 2.7 when the plasma rotation is decreased from +25kHz to +-2kHz. As the RMP amplitude increases, slower plasmas are seen to disrupt at a lower perturbation amplitude than unperturbed or rapidly rotating modes. The 6/2 helical kink mode also shows an amplitude and phase response to the 3/1 RMP, and like the 3/1 mode the amplitude response is largest when the plasma is slowly rotating. The ratio between the plasma 6/2 amplication and the 3/1 amplication to a 3/1 RMP is nearly constant, regardless of the plasma rotation or the RMP amplitude.Plasma physics, Physicsbad2115Applied Physics and Applied MathematicsDissertationsHigh-Speed Videography on HBT-EP
http://academiccommons.columbia.edu/catalog/ac:175984
Angelini, Sarahhttp://dx.doi.org/10.7916/D87942VVMon, 07 Jul 2014 00:00:00 +0000In this thesis, I present measurements from a high-speed video camera diagnostic on the High Beta Tokamak - Extended Pulse (HBT-EP). This work represents the first use of video data to analyze and understand the behavior of long wavelength kink perturbations in a wall-stabilized tokamak. A Phantom v7.3 camera was installed to capture the plasma's global behavior using visible light emissions and it operates at frame rates from 63 to 125 kfps. A USB2000 spectrometer was used to identify the dominant wavelength of light emitted in HBT-EP. At 656 nm, it is consistent with the D-alpha light expected from interactions between neutral deuterium and plasma electrons. The fast camera in combination with an Acktar vacuum black background produced images which were inverted using Abel techniques to determine the average radial emissivity profiles. These profiles were found to be hollow with a radial scale length of approximately 4 cm at the plasma edge. As a result, the behavior measured and analyzed using visible light videography is limited to the edge region. Using difference subtraction, biorthogonal decomposition and Fourier analysis, the structures of the observed edge fluctuations are computed. By comparing forward modelling results to measurements, the plasma is found to have an m/n = 3/1 helical shape that rotates in the electron drift direction with a lab-frame frequency between 5 and 10 kHz. The fast camera was also used to measure the plasma's response to applied helical magnetic perturbations which resonate with the equilibrium magnetic field at the plasma's edge. The static plasma response to non-rotating resonant magnetic perturbations (RMPs) is measured by comparing changes in the recorded image following a fast reversal, or phase flip, of the applied RMP. The programmed toroidal angle of the RMP is directly inferred from the resulting images of the plasma response. The plasma response and the intensityof the RMP are compared under different conditions. I found the resulting amplitude correlations to be consistent with previous measurements of the static response using an array of magnetic sensors. My work has shown that high-speed videography can be an extremely useful diagnostic for measuring edge perturbations in a tokamak. Future measurements, such as those using multiple cameras with different views, are expected to improve our understanding of plasma behavior and to detect edge fluctuations with higher temporal and spatial resolution. Supplementary Videos: Video 1 - This is an example of the video data from Shot 77324, an unforced plasma shot taken with the shells inserted. Video 2 - The strongest naturally-rotating mode has been extracted from a subset of the raw data shown in Video 1 using a biorthogonal decomposition. Long striations can be seen which are common in shots that have the shells inserted. Video 3 - In this video of the raw data from Shot 77537, the shells are retracted. The smooth non-reflective Acktar black background can be seen between the shells. Video 4 - The dominant BD mode from Shot 77537 shows pinwheel-like behavior. With the shells retracted, the plasma encounters fewer physical structures for neutral recycling and this affects the light emissions. Video 5 - This video shows the dominant BD modes from Shot 78029 during which a phase-flip RMP was used to influence the plasma. The mode seems to slow in its rotation as it resonates with the externally-applied field.Plasma physicsApplied Physics and Applied MathematicsDissertationsProbabilistic Approaches to Partial Differential Equations with Large Random Potentials
http://academiccommons.columbia.edu/catalog/ac:175891
Gu, Yuhttp://dx.doi.org/10.7916/D82R3PTDMon, 07 Jul 2014 00:00:00 +0000The thesis is devoted to an analysis of the heat equation with large random potentials in high dimensions. The size of the potential is chosen so that the large, highly oscillatory, random field is producing non-trivial effects in the asymptotic limit. We prove either homogenization, i.e., the random potential is replaced by some deterministic constant, or convergence to a stochastic partial differential equation, i.e., the random potential is replaced by some stochastic noise, depending on the correlation property. When the limit is deterministic, we provide estimates of the error between the heterogeneous and homogenized solutions when certain mixing assumption of the random potential is satisfied. We also prove a central limit type of result when the random potential is Gaussian or Poissonian. Lower dimensional and time-dependent cases are also treated. Most of the ingredients in the analysis are probabilistic, including a Feynman-Kac representation, a Brownian motion in random scenery, the Kipnis-Varadhan's method, and a quantitative martingale central limit theorem.Mathematicsyg2254Applied Physics and Applied MathematicsDissertationsDiscriminative topological features reveal biological network mechanisms
http://academiccommons.columbia.edu/catalog/ac:174771
Middendorf, Manuel; Ziv, Etay; Adams, Carter; Hom, Jennifer C.; Koytcheff, Robin; Levovitz, Chaya; Woods, Gregory; Chen, Linda; Wiggins, Chris H.http://dx.doi.org/10.7916/D8VD6WKKFri, 06 Jun 2014 00:00:00 +0000Background: Recent genomic and bioinformatic advances have motivated the development of numerous network models intending to describe graphs of biological, technological, and sociological origin. In most cases the success of a model has been evaluated by how well it reproduces a few key features of the real-world data, such as degree distributions, mean geodesic lengths, and clustering coefficients. Often pairs of models can reproduce these features with indistinguishable fidelity despite being generated by vastly different mechanisms. In such cases, these few target features are insufficient to distinguish which of the different models best describes real world networks of interest; moreover, it is not clear a priori that any of the presently-existing algorithms for network generation offers a predictive description of the networks inspiring them. Results: We present a method to assess systematically which of a set of proposed network generation algorithms gives the most accurate description of a given biological network. To derive discriminative classifiers, we construct a mapping from the set of all graphs to a high-dimensional (in principle infinite-dimensional) "word space". This map defines an input space for classification schemes which allow us to state unambiguously which models are most descriptive of a given network of interest. Our training sets include networks generated from 17 models either drawn from the literature or introduced in this work. We show that different duplication-mutation schemes best describe the E. coli genetic network, the S. cerevisiae protein interaction network, and the C. elegans neuronal network, out of a set of network models including a linear preferential attachment model and a small-world model. Conclusions: Our method is a first step towards systematizing network models and assessing their predictability, and we anticipate its usefulness for a number of communities.Bioinformaticsjch149, chw2Applied Physics and Applied Mathematics, Physics, MathematicsArticlesOn the Control of the Residual Circulation and Stratospheric Temperatures in the Arctic by Planetary Wave Coupling
http://academiccommons.columbia.edu/catalog/ac:172791
Shaw, Tiffany Ann; Perlwitz, Judithhttp://dx.doi.org/10.7916/D8TB14ZHFri, 28 Mar 2014 00:00:00 +0000It is well established that interannual variability of eddy (meridional) heat flux near the tropopause controls the variability of Arctic lower-stratospheric temperatures during spring via a modification of the strength of the residual circulation. While most studies focus on the role of anomalous heat flux values, here the impact of total (climatology plus anomaly) negative heat flux events on the Arctic stratosphere is investigated. Utilizing the Interim ECMWF Re-Analysis (ERA-Interim) dataset, it is found that total negative heat flux events coincide with a transient reversal of the residual circulation and cooling of the Arctic lower stratosphere. The negative events weaken the seasonally averaged adiabatic warming. The analysis provides a new interpretation of the winters of 1997 and 2011, which are known to have the lowest March Arctic lower-stratospheric temperatures in the satellite era. While most winters involve positive and negative heat flux extremes, the winters of 1997 and 2011 are unique in that they only involved extreme negative events. This behavior contributed to the weakest adiabatic downwelling in the satellite era and suggests a dynamical contribution to the extremely low temperatures during those winters that could not be accounted for by diabatic processes alone. While it is well established that dynamical processes contribute to the occurrence of stratospheric sudden warming events via extreme positive heat flux events, the results show that dynamical processes also contribute to cold winters with subsequent impact on Arctic ozone loss. The results highlight the importance of interpreting stratospheric temperatures in the Arctic in the context of the dynamical regime with which they are associated.Atmospheric sciences, Atmospheric chemistrytas2163Applied Physics and Applied Mathematics, Lamont-Doherty Earth ObservatoryArticlesMicro-Raman spectroscopic visualization of lattice vibrations and strain in He+- implanted single-crystal LiNbO3
http://academiccommons.columbia.edu/catalog/ac:172060
Huang, Hsu-Cheng; Dadap, Jerry I.; Herman, Irving P.; Bakhru, Hassaram; Osgood, Jr., Richard M.http://dx.doi.org/10.7916/D8BC3WKFThu, 27 Mar 2014 00:00:00 +0000Scanning micro-Raman spectroscopy has been utilized to image and investigate strain in He+-implanted congruent LiNbO3 samples. By using abruptly patterned implanted samples, we show that the spatial two-dimensional mapping of the Raman spectral peaks can be used to image the strain distribution and determine its absolute magnitude. We demonstrate that both short- and long-range length-scale in-plane and out-of-plane strain and stress states can be determined using the secular equations of phonon-deformation-potential theory. We also show that two-dimensional Raman imaging can be used to visualize the relaxation of strain in the crystal during low-temperature annealing.Electrical engineering, Physicshh2362, jid5, iph1, rmo1Applied Physics and Applied Mathematics, Electrical EngineeringArticlesThe Effect of Moist Convection on the Tropospheric Response to Tropical and Subtropical Zonally Asymmetric Torques
http://academiccommons.columbia.edu/catalog/ac:172076
Boos, William R. ; Shaw, Tiffany A. http://dx.doi.org/10.7916/D8765CCNFri, 07 Mar 2014 00:00:00 +0000Tropospheric winds can be altered by vertical transfers of momentum due to orographic gravity waves and convection. Previous work showed that, in dry models, such zonally asymmetric torques produce a pattern of tropical ascent that is well described by linear dynamics, together with meridional shifts of the midlatitude jet. Here a series of idealized models is used to understand the effects of moisture on the tropospheric response to tropical and subtropical zonally asymmetric, upper-tropospheric torques. The vertical motion response to a torque is shown to be amplified by the reduction in effective static stability that occurs in moist convecting atmospheres. This amplification occurs only in precipitating regions, and the magnitude of subsidence in nonprecipitating regions saturates when clear-sky radiative cooling balances induced adiabatic warming. For basic states in which precipitation is concentrated in an intertropical convergence zone (ITCZ), most of the vertical motion response is thus confined within the basic-state ITCZ, even when the torque is remote from the ITCZ. Tropical and subtropical torques perturb the extratropical baroclinic eddy field and the convectively coupled equatorial wave field. Resulting changes in momentum flux convergence by transient eddies induce secondary meridional overturning circulations that modify the zonal-mean response to a torque. The net effect allows tropical torques to merge a double ITCZ into a single equatorial ITCZ. The response of tropical transient eddies is highly sensitive to the representation of convection, so the zonal-mean response to a torque is similarly sensitive, even when the torque is located in the subtropics.Geophysics, Atmospheric sciencestas2163Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesToward an Understanding of Vertical Momentum Transports in Cloud-System-Resolving Model Simulations of Multiscale Tropical Convection
http://academiccommons.columbia.edu/catalog/ac:171435
Shaw, Tiffany A.; Lane, Todd P.http://dx.doi.org/10.7916/D80Z719SThu, 13 Feb 2014 00:00:00 +0000This study examines the characteristics of convective momentum transport (CMT) and gravity wave momentum transport (GWMT) in two-dimensional cloud-system-resolving model simulations, including the relationships between the two transports. A linear group velocity criterion is shown to objectively separate CMT and GWMT. The GWMT contribution is mostly consistent with upward-propagating gravity waves and is present in the troposphere and the stratosphere. The CMT contribution forms a large part of the residual (nonupward-propagating contribution) and dominates the fluxes in the troposphere. Additional analysis of the vertical sensible heat flux supports the physical interpretation of the two contributions, further isolating the effects of unstable convection from vertically propagating gravity waves. The role of transient and nonconservative (friction and diabatic heating) processes in generating momentum flux and their dependence on changes in convective organization was assessed using a pseudomomentum budget analysis. Nonconservative effects were found to dominate the transports; the GWMT contribution involved a diabatic source region in the troposphere and a dissipative sink region in the stratosphere. The CMT contribution was consistent with transport between the boundary layer and free troposphere via tilted convection. Transient buoyancy–vorticity correlations highlighted wave sources in the region of convective outflow and the boundary layer. These sources were akin to the previously described “mechanical oscillator” mechanism. Fluxes associated with this upper-level source were most sensitive to convective organization, highlighting the mechanism by which changes in organization are communicated to GWMT. The results elucidate important interactions between CMT and GWMT, adding further weight to suggestions that the two transports should be linked in parameterizations.Atmospheric sciences, Applied mathematicstas2163Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesMaterials Optimization and GHz Spin Dynamics of Metallic Ferromagnetic Thin Film Heterostructures
http://academiccommons.columbia.edu/catalog/ac:168924
Cheng, Chenghttp://dx.doi.org/10.7916/D81V5BZJWed, 22 Jan 2014 00:00:00 +0000Metallic ferromagnetic (FM) thin film heterostructures play an important role in emerging magnetoelectronic devices, which introduce the spin degree of freedom of electrons into conventional charge-based electronic devices. As the majority of magnetoelectronic devices operate in the GHz frequency range, it is critical to understand the high-frequency magnetization dynamics in these structures. In this thesis, we start with the static magnetic properties of FM thin films and their optimization via the field-sputtering process incorporating a specially designed in-situ electromagnet. We focus on the origins of anisotropy and hysteresis/coercivity in soft magnetic thin films, which are most relevant to magentic susceptibility and power dissipation in applications in the sub-GHz frequency regime, such as magnetic-core integrated inductors. Next we explore GHz magnetization dynamics in thin-film heterostructures, both in semi-infinite samples and confined geometries. All investigations are rooted in the Landau-Lifshitz-Gilbert (LLG) equation, the equation of motion for magnetization. The phenomenological Gilbert damping parameter in the LLG equation has been interpreted, since the 1970's, in terms of the electrical resistivity. We present the first interpretation of the size effect in Gilbert damping in single metallic FM films based on this electron theory of damping. The LLG equation is intrinsically nonlinear, which provides possibilities for rf signal processing. We analyze the frequency doubling effect at small-angle magnetization precession from the first-order expansion of the LLG equation, and demonstrate second harmonic generation from Ni81 Fe19 (Permalloy) thin film under ferromagnetic resonance (FMR), three orders of magnitude more efficient than in ferrites traditionally used in rf devices. Though the efficiency is less than in semiconductor devices, we provide field- and frequency-selectivity in the second harmonic generation. To address further the relationship between the rf excitation and the magnetization dynamics in systems with higher complexity, such as multilayered thin films consisting of nonmagnetic (NM) and FM layers, we employ the powerful time-resolved x-ray magnetic circular dichroism (TR-XMCD) spectroscopy. Soft x-rays have element-specific absorption, leading to layer-specific magnetization detection provided the FM layers have distinctive compositions. We discovered that in contrast to what has been routinely assumed, for layer thicknesses well below the skin depth of the EM wave, a significant phase difference exists between the rf magnetic fields Hrf in different FM layers separated by a Cu spacer layer. We propose an analysis based on the distribution of the EM waves in the film stack and substrate to interpret this striking observation. For confined geometries with lateral dimensions in the sub-micron regime, there has been a critical absence of experimental techniques which can image small-amplitude dynamics of these structures. We extend the TR-XMCD technique to scanning transmission x-ray microscopy (STXM), to observe directly the local magnetization dynamics in nanoscale FM thin-film elements, demonstrated at picosecond temporal, 40 nm spatial and less than 6° angular resolution. The experimental data are compared with our micromagnetic simulations based on the finite element analysis of the time-dependent LLG equation. We resolve standing spin wave modes in nanoscale Ni81 Fe19 thin film ellipses (1000 nm × 500 nm × 20 nm) with clear phase information to distinguish between degenerate eigenmodes with different symmetries for the first time. With the element-specific imaging capability of soft x-rays, spatial resolution up to 15 nm with improved optics, we see great potential for this technique to investigate functional devices with multiple FM layers, and provide insight into the studies of spin injection, manipulation and detection.Materials sciencecc3043Applied Physics and Applied Mathematics, Materials Science and EngineeringDissertationsNonlinear, Barotropic Response to a Localized Topographic Forcing: Formation of a “Tropical Surf Zone” and Its Effect on Interhemispheric Propagation
http://academiccommons.columbia.edu/catalog/ac:167160
Waugh, D. W.; Plumb, R. A.; Polvani, Lorenzo M.http://dx.doi.org/10.7916/D8057CV5Tue, 19 Nov 2013 00:00:00 +0000The nonlinear response of a barotropic, nondivergent, spherical flow representative of the upper troposphere (but without a tropical Hadley cell) to localized, extratropical topographic forcing is examined using high-resolution contour surgery calculations. The response is shown to vary greatly with forcing amplitude and can be significantly different from the linear response. At large amplitude, Rossby wave breaking occurs in the tropics irrespective of the direction of the equatorial winds, and leads to small-scale stirring and the formation of a “tropical surf zone,” which inhibits the meridional propagation of the disturbance.Atmospheric sciences, Meteorology, Aeronomylmp3Applied Physics and Applied MathematicsArticlesThe Roll-Up of Vorticity Strips on the Surface of a Sphere
http://academiccommons.columbia.edu/catalog/ac:167167
Dritschel, David G.; Polvani, Lorenzo M.http://dx.doi.org/10.7916/D8QN64NJTue, 19 Nov 2013 00:00:00 +0000We derive the conditions for the stability of strips or filaments of vorticity on the surface of a sphere. We find that the spherical results are surprisingly different from the planar ones, owing to the nature of the spherical geometry. Strips of vorticity on the surface of a sphere show a greater tendency to roll-up into vortices than do strips on a planar surface. The results are obtained by performing a linear stability analysis of the simplest, piecewise-constant vorticity configuration, namely a zonal band of uniform vorticity located in equilibrium between two latitudes. The presence of polar vortices is also considered, this having the effect of introducing adverse shear, a known stabilizing mechanism for planar flows. In several representative examples, the fully developed stages of the instabilities are illustrated by direct numerical simulation. The implication for planetary atmospheres is that barotropic flows on the sphere have a more pronounced tendency to produce small, long-lived vortices, especially in equatorial and mid-latitude regions, than was previously anticipated from the theoretical results for planar flows. Essentially, the curvature of the sphere's surface weakens the interaction between different parts of the flow, enabling these parts to behave in relative isolation.Atmospheric sciences, Applied mathematics, Aeronomylmp3Applied Physics and Applied MathematicsArticlesRossby Wave Breaking, Microbreaking, Filamentation, and Secondary Vortex Formation: The Dynamics of a Perturbed Vortex
http://academiccommons.columbia.edu/catalog/ac:167170
Polvani, Lorenzo M.; Plumb, R. Alanhttp://dx.doi.org/10.7916/D8KW5CXTTue, 19 Nov 2013 00:00:00 +0000The behavior of an isolated vortex perturbed by topographically forced Rossby waves is studied using the method of Contour Dynamics. For a single-contour vortex a distinct forcing threshold exists above which the wave breaks in a dynamically significant way, leading to a disruption of the vortex. This breaking is distinguished from the process of weak filamentary breaking described by Dritschel and classified here as microbreaking; the latter occurs in nondivergent flow even at very small forcing amplitudes but does not affect the vortex in a substantial manner. In cases with finite Rossby deformation radius (comparable with the vortex radius) neither breaking nor microbreaking occurs below the forcing threshold. In common with previous studies using high-resolution spectral models, the vortex is not diluted by intrusion of outside air, except during remerger with a secondary vortex shed previously from the main vortex during a breaking event. The kinematics of the breaking process and of the vortex interior and the morphology of material ejected from the vortex are described. When the Rossby radius is finite there is substantial mixing in the deep interior of the vortex, even when the vortex is only mildly disturbed. Implications for the stratospheric polar vortex are discussed.Atmospheric sciences, Aeronomy, Physicslmp3Applied Physics and Applied MathematicsArticlesTwo-Layer Geostrophic Vortex Dynamics. Part 1. Upper-Layer V-States and Merger
http://academiccommons.columbia.edu/catalog/ac:167179
Polvani, Lorenzo M.; Flierl, G. R.; Zabusky, N. J.http://dx.doi.org/10.7916/D86Q1V53Tue, 19 Nov 2013 00:00:00 +0000We generalize the methods of two-dimensional contour dynamics to study a two-layer rotating fluid that obeys the quasi-geostrophic equations. We consider here only the case of a constant-potential-vorticity lower layer. We derive equilibrium solutions for monopolar (rotating) and dipolar (translating) geostrophic vortices in the upper layer, and compare them with the Euler case. We show that the equivalent barotropic (infinite lower layer) case is a singular limit of the two-layer system. We also investigate the effect of a finite lower layer on the merger of two regions of equal-sign potential vorticity in the upper layer. We discuss our results in the light of the recent laboratory experiments of Griffiths and Hopfinger (1986). The process of filamentation is found to be greatly suppressed for equivalent barotropic dynamics on scales larger than the radius of deformation. We show that the variation of the critical initial distance for merger as a function of the radius of deformation and the ratio of the layers at rest is closely related to the existence of vortex-pair equilibria and their geometrical properties.Applied mathematics, Physics, Atmospheric scienceslmp3Applied Physics and Applied MathematicsArticlesThe Effect of Dissipation on Spatially Growing Nonlinear Baroclinic Waves
http://academiccommons.columbia.edu/catalog/ac:167185
Polvani, Lorenzo M.; Pedlosky, J.http://dx.doi.org/10.7916/D8Z60KZCTue, 19 Nov 2013 00:00:00 +0000The question of convective (i.e., spatial) instability of baroclinic waves on an f-plane is studied in the context of the two-layer model. The viscous and inviscid marginal curves for linear convective instability are obtained. The finite-amplitude problem shows that when dissipation is O(1) it acts to stabilize the waves that are of Eady type. For very small dissipation the weakly nonlinear analysis reveals that at low frequencies, contrary to what is known to occur in the temporal problem, in addition to the baroclinic component a barotropic correction to the “mean” flow is generated by the nonlinearities, and spatial equilibration occurs provided the ratio of shear to mean flow does not exceed some critical value. In the same limit, the slightly dissipative nonlinear dynamics reveals the presence of large spatial vacillations immediately downstream of the source, even if asymptotically (i.e., very far away from the source) the amplitudes are found to reach steady values. No case of period doubling or aperiodic behavior was found. The results obtained seem to be qualitatively independent of the form chosen to model the dissipation.Atmospheric sciences, Physics, Applied mathematicslmp3Applied Physics and Applied MathematicsArticlesWave–Wave Interaction of Unstable Baroclinic Waves
http://academiccommons.columbia.edu/catalog/ac:167188
Pedlosky, Joseph; Polvani, Lorenzo M.http://dx.doi.org/10.7916/D8TD9V7HTue, 19 Nov 2013 00:00:00 +0000Two slightly unstable baroclinic waves in the two-layer Phillips model are allowed to interact with each other as well as the mean flow. A theory for small dissipation rates is developed to examine the role of wave–wave interaction in the dynamics of vacillation and aperiodicity in unstable systems. It is shown that the form of the dissipation mechanism as well as the overall dissipation timescale determines the nature of the dynamics. In particular, dissipation proportional to potential vorticity is shown to expunge amplitude vacillation due to wave–mean flow interactions. Wave–wave interaction, however, can yield amplitude vacillation. As the dissipation is decreased, the solutions evolve from steady waves (although propagating) to periodic vacillation until finally at small dissipation rates, chaotic behavior is obtained. This occurs in a range of relative growth rates of the two waves which depends on the strength of the wave–wave and wave–mean flow interactions.Atmospheric sciences, Applied mathematics, Physicslmp3Applied Physics and Applied MathematicsArticlesTwo-Layer Geostrophic Vortex Dynamics. Part 2. Alignment and Two-Layer V-States
http://academiccommons.columbia.edu/catalog/ac:167173
Lorenzo M., Polvanihttp://dx.doi.org/10.7916/D8G44N6TTue, 19 Nov 2013 00:00:00 +0000The process of alignment, a new fundamental interaction between vortices in a stratified and rapidly rotating fluid, is defined and studied in detail in the context of the two-layer quasi-geostrophic model. Alignment occurs when two vortices in different density layers coalesce by reducing their horizontal separation. It is found that only vortices whose radii are comparable with or larger than the Rossby deformation radius can align. In the same way as the merger process (in a single two dimensional layer) is related to the reverse energy cascade of two-dimensional turbulence, geostrophic potential vorticity alignment is related the barotropic-to baroclinic energy cascade of geostrophic turbulence in two layers. It is also shown how alignment is intimately connected with the existence of two-layer doubly connected geostrophic potential vorticity equilibria (V-states), for which the analysis of the geometry of the stream function in the corotating frame is found to be a crucial diagnostic. The finite-area analogues of the hetons of Hogg and Stommel (1985) are also determined : they consist of a propagating pair of opposite-signed potential vorticity patches located in different layers.Atmospheric sciences, Physics, Applied mathematicslmp3Applied Physics and Applied MathematicsArticlesWave and Vortex Dynamics on the Surface of a Sphere
http://academiccommons.columbia.edu/catalog/ac:167163
Polvani, Lorenzo M.; Dritschel, David G.http://dx.doi.org/10.7916/D8VD6WCWTue, 19 Nov 2013 00:00:00 +0000Motivated by the observed potential vorticity structure of the stratospheric polar vortex, we study the dynamics of linear and nonlinear waves on a zonal vorticity interface in a two-dimensional barotropic flow on the surface of a sphere (interfacial Rossby waves). After reviewing the linear problem, we determine, with the help of an iterative scheme, the shapes of steadily propagating nonlinear waves; a stability analysis reveals that they are (nonlinearly) stable up to very large amplitude. We also consider multi-vortex equilibria on a sphere: we extend the results of Thompson (1883) and show that a (latitudinal) ring of point vortices is more unstable on the sphere than in the plane; notably, no more than three point vortices on the equator can be stable. We also determine the shapes of finite-area multi-vortex equilibria, and reveal additional modes of instability feeding off shape deformations which ultimately result in the complex merger of some or all of the vortices. We discuss two specific applications to geophysical flows: for conditions similar to those of the wintertime terrestrial stratosphere, we show that perturbations to a polar vortex with azimuthal wavenumber 3 are close to being stationary, and hence are likely to be resonant with the tropospheric wave forcing; this is often observed in high-resolution numerical simulations as well as in the ozone data. Secondly, we show that the linear dispersion relation for interfacial Rossby waves yields a good fit to the phase velocity of the waves observed on Saturn’s ‘ribbon’.Atmospheric sciences, Applied mathematics, Aeronomylmp3Applied Physics and Applied MathematicsArticlesFilamentation of Unstable Vortex Structures via Separatrix Crossing: A Quantitative Estimate of Onset Time
http://academiccommons.columbia.edu/catalog/ac:167182
Polvani, Lorenzo M.; Flierl, G. R.; Zabusky, N. J.http://dx.doi.org/10.7916/D82Z13FRTue, 19 Nov 2013 00:00:00 +0000The onset of filamentation for compact vortex structures in two-dimensional incompressible flows is elucidated. An estimate is presented for the filamentation time of an unstably perturbed Kirchhoff ellipse, obtained from a linear analysis of the geometry of the instantaneous corotating streamfunction.Applied mathematics, Physicslmp3Applied Physics and Applied MathematicsArticlesChaotic Lagrangian Trajectories around an Elliptical Vortex Patch Embedded in a Constant and Uniform Background Shear Flow
http://academiccommons.columbia.edu/catalog/ac:167176
Polvani, Lorenzo M.; Wisdom, J.http://dx.doi.org/10.7916/D8BG2KWDTue, 19 Nov 2013 00:00:00 +0000The Lagrangian flow around a Kida vortex [J. Phys. Soc. Jpn. 5 0, 3517 (1981)], an elliptical two‐dimensional vortex patch embedded in a uniform and constant background shear, is described by a nonintegrable two‐degree‐of‐freedom Hamiltonian. For small values of shear, there exist large chaotic zones surrounding the vortex, often much larger than the vortex itself and extremely close to its boundary. Motion within the vortex is integrable. Implications for two‐dimensional turbulence are discussed.Physics, Applied mathematicslmp3Applied Physics and Applied MathematicsArticlesProduction of Heavy Particles by Protons on Protons
http://academiccommons.columbia.edu/catalog/ac:167194
Afek, Y.; Margolis, B.; Polvani, Lorenzo M.http://dx.doi.org/10.7916/D8JW8BSFTue, 19 Nov 2013 00:00:00 +0000We calculate the production of heavy particles in the multi-GeV energy range using parton-model and statistical considerations. We discuss both central production and fragmentation. Our picture has implications for the question of the existence of a limiting temperature in hadron interactions.Physics, Applied mathematicslmp3Applied Physics and Applied MathematicsArticlesGeneralized Kirchhoff Vortices
http://academiccommons.columbia.edu/catalog/ac:167191
Polvani, Lorenzo M.; Flierl, G. R.http://dx.doi.org/10.7916/D8PN93H5Tue, 19 Nov 2013 00:00:00 +0000A family of exact solutions of the Euler equations is presented: they are generalizations of the Kirchhoff vortex to N confocal ellipses. Special attention is given to the case N=2, for which the stability is analyzed with a method similar to the one used by Love [Proc. London Math. Soc. 1, XXV 18 (1893)] for the Kirchhoff vortex. The results are compared with those for the corresponding circular problem.Applied mathematics, Physicslmp3Applied Physics and Applied MathematicsArticlesDelayed Southern Hemisphere Climate Change Induced by Stratospheric Ozone Recovery, as Projected by the CMIP5 Models
http://academiccommons.columbia.edu/catalog/ac:167200
Barnes, Elizabeth A.; Barnes, Nicholas W.; Polvani, Lorenzo M.http://dx.doi.org/10.7916/D8F769GRTue, 19 Nov 2013 00:00:00 +0000Stratospheric ozone is expected to recover by the end of this century due to the regulation of ozone depleting substances by the Montreal Protocol. Targeted modeling studies have suggested that the climate response to ozone recovery will greatly oppose the climate response to rising greenhouse-gas (GHG) emissions. However, the extent of this cancellation remains unclear since only a few such studies are available. Here, we analyze a much larger set of simulations performed for the Coupled Model Intercomparison Project, phase 5, all of which include ozone recovery. We show that the closing of the ozone hole will cause a delay in summer-time (DJF) Southern Hemisphere climate change, between now and 2045. Specifically, we find that the position of the jet stream, the width of the subtropical dry-zones, the seasonality of surface temperatures, and sea ice concentrations all exhibit significantly reduced summer-time trends over the first half of the 21st Century as a consequence of ozone recovery. After 2045, forcing from GHG emissions begins to dominate the climate response. Finally, comparing the relative influences of future GHG emissions and historic ozone depletion, we find that the simulated DJF tropospheric circulation changes between 1965-2005 (driven primarily by ozone depletion) are larger than the projected changes in any future scenario over the entire 21st Century.Atmospheric sciences, Aeronomy, Climate changeeab2207, lmp3Applied Physics and Applied Mathematics, Lamont-Doherty Earth ObservatoryArticlesThe Antarctic Atmospheric Energy Budget. Part II: The Effect of Ozone Depletion and its Projected Recovery
http://academiccommons.columbia.edu/catalog/ac:167203
Smith, Karen L.; Previdi, Michael; Polvani, Lorenzo M.http://dx.doi.org/10.7916/D89G5JR1Tue, 19 Nov 2013 00:00:00 +0000In this study we continue our investigation of the atmospheric energy budget of the Antarctic polar cap (the region poleward of 70°S) using integrations of the Whole Atmosphere Community Climate Model from the year 1960 to 2065. In agreement with observational data, we find that the climatological mean net top-of-atmosphere (TOA) radiative flux is primarily balanced by the horizontal energy flux convergence over the polar cap. On interannual timescales, changes in the net TOA radiative flux are also primarily balanced by changes in the energy flux convergence, with the variability in both terms significantly correlated with the Southern Annular Mode (SAM); positive and negative correlations, respectively. On multidecadal timescales, twentieth century stratospheric ozone depletion produces a negative trend in the net TOA radiative flux due to a decrease in the absorbed solar radiation within the atmosphere-surface column. The negative trend in the net TOA radiative flux is balanced by a positive trend in energy flux convergence, primarily in austral summer. This negative (positive) trend in the net TOA radiation (energy flux convergence) occurs despite a positive trend in the SAM, suggesting that the effects of the SAM on the energy budget are overwhelmed by the direct radiative effects of ozone depletion. In the twenty-first century, ozone recovery is expected to reverse the negative trend in the net TOA radiative flux, which would then, again, be balanced by a decrease in the energy flux convergence. Therefore, over the next several decades, ozone recovery will, in all likelihood, mask the effect of GHG warming on the Antarctic energy budget.Atmospheric sciences, Aeronomy, Climate changekls2177, mp2609, lmp3Ocean and Climate Physics, Applied Physics and Applied Mathematics, Lamont-Doherty Earth Observatory, Earth and Environmental SciencesArticlesThe Effect of a Hadley Circulation on the Propagation and Reflection of Planetary Waves in a Simple One-Layer Model
http://academiccommons.columbia.edu/catalog/ac:167050
Esler, J. Gavin; Polvani, Lorenzo M.; Plumb, R. Alanhttp://hdl.handle.net/10022/AC:P:22163Fri, 08 Nov 2013 00:00:00 +0000The effect of a simple representation of the Hadley circulation on the propagation and nonlinear reflection of planetary-scale Rossby waves in the winter hemisphere is investigated numerically in a single-layer shallow-water model. In the first instance, waves are forced by a zonal wavenumber three topography centered in the extratropics. In the linear limit the location of the low-latitude critical line at which the waves are absorbed is displaced poleward by the Hadley circulation. At finite forcing amplitude the critical layer regions where the waves break are found to be displaced poleward by a similar distance. The Hadley circulation is also found to inhibit the onset of nonlinear reflection by increasing the dissipation of wave activity in the critical layer. Second, for waves generated by an isolated mountain, the presence of the Hadley circulation further inhibits nonlinear reflection by generating a strong westerly flux of wave activity within the critical layer. This westerly flux is shown to be largely advective and is explained by the poleward displacement of the critical line into the region of westerly flow. A simple expression is derived for the minimum zonal wind strength allowing propagation in the case of a quasigeostrophic β-plane flow when the mean meridional wind ̅υ greater than 0.Geophysics, Atmospheric sciences, Physicslmp3Applied Physics and Applied MathematicsArticlesNonlinear Geostrophic Adjustment, Cyclone/Anticyclone Asymmetry, and Potential Vorticity Rearrangement
http://academiccommons.columbia.edu/catalog/ac:167047
Kuo, Allen C.; Polvani, Lorenzo M.http://hdl.handle.net/10022/AC:P:22162Fri, 08 Nov 2013 00:00:00 +0000Within the context of the rotating shallow water equations, it is shown how initially unbalanced states possessing certain symmetries dynamically evolve to lose those symmetries during nonlinear geostrophic adjustment. Using conservation law methods, it is demonstrated that the adjustment of equal and opposite (circular) mass imbalances results in a balanced end state where cyclones are stronger than anticyclones; the reverse holds true for momentum imbalances. In both cases, the degree of this asymmetry is shown to be directly proportional to the amount of initial imbalance (a measure of the nonlinearity occurring during time-dependent adjustment). On the other hand, the degree of asymmetry is maximal for imbalances of Rossby deformation scale. As for the potential vorticity, it is shown that its final profile can be noticeably different from its initial one; from an Eulerian perspective, this rearrangement is not confined to uniform shifts of potential vorticity fronts. Direct 2D numerical initial value problems confirm the asymmetry in the predicted final states and establish a relatively fast time scale for adjustment to complete. The robustness of these results is confirmed by studying, in addition, the adjustment of elliptical mass imbalances. The numerical integrations reveal that, during geostrophic adjustment, potential vorticity rearrangement occurs irreversibly on a fast wave time scale.Physics, Geophysics, Applied mathematicslmp3Applied Physics and Applied MathematicsArticlesTime Variability and Simmons–Wallace–Branstator Instability in a Simple Nonlinear One-Layer Model
http://academiccommons.columbia.edu/catalog/ac:167062
Polvani, Lorenzo M.; Esler, J. Gavin; Plumb, R. Alanhttp://hdl.handle.net/10022/AC:P:22167Fri, 08 Nov 2013 00:00:00 +0000Using a global, one-layer shallow water model, the response of a westerly flow to a localized mountain is investigated. A steady, linear response at small mountain heights successively gives way first to a steady flow in which nonlinearities are important and then to unsteady, but periodic, flow at larger mountain heights. At first the unsteady behavior consists of a low-frequency oscillation of the entire Northern Hemisphere zonal flow. As the mountain height is increased further, however, the oscillatory behavior becomes localized in the diffluent jet exit region downstream of the mountain. The oscillation then takes the form of a relatively rapid vortex shedding event, followed by a gradual readjustment of the split jet structure in the diffluent region. Although relatively simple, the model exhibits a surprisingly high sensitivity to slight parameter changes. A linear stability analysis of the time-averaged flow is able to capture the transition from steady to time-dependent behavior, but fails to capture the transition between the two distinct regimes of time-dependent response. Moreover, the most unstable modes of the time-averaged flow are found to be stationary and fail to capture the salient features of the EOFs of the full time-dependent flow. These results therefore suggest that, even in the simplest cases, such as the one studied here, a linear analysis of the time-averaged flow can be highly inadequate in describing the full nonlinear behavior.Atmospheric sciences, Geophysics, Applied mathematicslmp3Applied Physics and Applied MathematicsArticlesThe Contour-Advective Semi-Lagrangian Algorithm for the Shallow Water Equations
http://academiccommons.columbia.edu/catalog/ac:167065
Dritschel, David G.; Polvani, Lorenzo M.; Mohebalhojeh, Ali R.http://hdl.handle.net/10022/AC:P:22168Fri, 08 Nov 2013 00:00:00 +0000A new method for integrating shallow water equations, the contour-advective semi-Lagrangian (CASL) algorithm, is presented. This is the first implementation of a contour method to a system of equations for which exact potential vorticity invertibility does not exist. The new CASL method fuses the recent contour-advection technique with the traditional pseudospectral (PS) method. The potential vorticity field, which typically develops steep gradients and evolves into thin filaments, is discretized by level sets separated by contours that are advected in a fully Lagrangian way. The height and divergence fields, which are intrinsically broader in scale, are treated in an Eulerian way: they are discretized on an fixed grid and time stepped with a PS scheme. In fact, the CASL method is similar to the widely used semi-Lagrangian (SL) method in that material conservation of potential vorticity along particle trajectories is used to determine the potential vorticity at each time step from the previous one. The crucial difference is that, whereas in the CASL method the potential vorticity is merely advected, in the SL method the potential vorticity needs to be interpolated at each time step. This interpolation results in numerical diffusion in the SL method. By directly comparing the CASL, SL, and PS methods, it is demonstrated that the implicit diffusion associated with potential vorticity interpolation in the SL method and the explicit diffusion required for numerical stability in the PS method seriously degrade the solution accuracy compared with the CASL method. Moreover, it is shown that the CASL method is much more efficient than the SL and PS methods since, for a given solution accuracy, a much coarser grid can be used and hence much faster computations can be performed.Atmospheric sciences, Applied mathematics, Geophysicslmp3Applied Physics and Applied MathematicsArticlesThe Three-Dimensional Structure of Breaking Rossby Waves in the Polar Wintertime Stratosphere
http://academiccommons.columbia.edu/catalog/ac:167053
Polvani, Lorenzo M.; Saravanan, R.http://hdl.handle.net/10022/AC:P:22164Fri, 08 Nov 2013 00:00:00 +0000The three-dimensional nature of breaking Rossby waves in the polar wintertime stratosphere is studied using an idealized global primitive equation model. The model is initialized with a well-formed polar vortex, characterized by a latitudinal band of steep potential vorticity (PV) gradients. Planetary-scale Rossby waves are generated by varying the topography of the bottom boundary, corresponding to undulations of the tropopause. Such topographically forced Rossby waves then propagate up the edge of the vortex, and their amplification with height leads to irreversible wave breaking. These numerical experiments highlight several nonlinear aspects of stratospheric dynamics that are beyond the reach of both isentropic two-dimensional models and fully realistic GCM simulations. They also show that the polar vortex is contorted by the breaking Rossby waves in a surprisingly wide range of shapes. With zonal wavenumber-1 forcing, wave breaking usually initiates as a deep helical tongue of PV that is extruded from the polar vortex. This tongue is often observed to roll up into deep isolated columns, which, in turn, may be stretched and tilted by horizontal and vertical shears. The wave amplitude directly controls the depth of the wave breaking region and the amount of vortex erosion. At large forcing amplitudes, the wave breaking in the middle/lower portions of the vortex destroys the PV gradients essential for vertical propagation, thus shielding the top of the vortex from further wave breaking. The initial vertical structure of the polar vortex is shown to play an important role in determining the characteristics of the wave breaking. Perhaps surprisingly, initially steeper PV gradients allow for stronger vertical wave propagation and thus lead to stronger erosion. Vertical wind shear has the notable effect of tilting and stretching PV structures, and thus dramatically accelerating the downscale stirring. An initial decrease in vortex area with increasing height (i.e., a conical shape) leads to focusing of wave activity, which amplifies the wave breaking. This effect provides a geometric interpretation of the “preconditioning” that often precedes a stratospheric sudden warming event. The implications for stratospheric dynamics of these and other three-dimensional vortex properties are discussed.Atmospheric sciences, Aeronomy, Geophysicslmp3Applied Physics and Applied MathematicsArticlesWave-Vortex Interaction in Rotating Shallow Water. Part 1. One Space Dimension
http://academiccommons.columbia.edu/catalog/ac:167056
Kuo, Allen C.; Polvani, Lorenzo M.http://hdl.handle.net/10022/AC:P:22165Fri, 08 Nov 2013 00:00:00 +0000Using a physical space (i.e. non-modal) approach, we investigate interactions between fast inertio-gravity (IG) waves and slow balanced flows in a shallow rotating fluid. Specifically, we consider a train of IG waves impinging on a steady, exactly balanced vortex. For simplicity, the one-dimensional problem is studied first; the limitations of one-dimensionality are offset by the ability to define balance in an exact way. An asymptotic analysis of the problem in the small-amplitude limit is performed to demonstrate the existence of interactions. It is shown that these interactions are not confined to the modification of the wave field by the vortex but, more importantly, that the waves are able to alter in a non-trivial way the potential vorticity associated with that vortex. Interestingly, in this one-dimensional problem, once the waves have traversed the vortex region and have propagated away, the vortex exactly recovers its initial shape and thus bears no signature of the interaction. Furthermore, we prove this last result in the case of arbitrary vortex and wave amplitudes. Numerical integrations of the full one-dimensional shallow-water equations in strongly nonlinear regimes are also performed: they confirm that time-dependent interactions exist and increase with wave amplitude, while at the final state the vortex bears no sign of the interaction. In addition, they reveal that cyclonic vortices interact more strongly with the wave field than anticyclonic ones.Geophysics, Applied mathematics, Physicslmp3Applied Physics and Applied MathematicsArticlesOn the Mix-Down Times of Dynamically Active Potential Vorticity Filaments
http://academiccommons.columbia.edu/catalog/ac:167059
Esler, J. Gavin; Polvani, Lorenzo M.; Plumb, R. Alanhttp://hdl.handle.net/10022/AC:P:22166Fri, 08 Nov 2013 00:00:00 +0000A simple model is used to study the evolution of potential vorticity filaments, viewed in cross-section, subject to steady shear and deformation flows representative of the large-scale atmospheric circulation. It is found that the balanced,ageostrophic circulation induced by the anomalous potential vorticity can cause the evolution of a dynamically active filament to differ substantially from that of a dynamically passive filament in a similar background flow. It is suggested that estimates of the mix-down time of material contained in atmospheric filaments need to be corrected to allow for this effect.Atmospheric sciences, Geophysics, Applied mathematicslmp3Applied Physics and Applied MathematicsArticlesReply
http://academiccommons.columbia.edu/catalog/ac:167077
Polvani, Lorenzo M.; Waugh, D. W.; Plumb, R. Alanhttp://hdl.handle.net/10022/AC:P:22172Fri, 08 Nov 2013 00:00:00 +0000Reply to Juckes about the underlying dynamics of an edge in the subtropical statosphere that mirror the "sharp, poleward 'edge' to the stratospheric surf zones as a direct consequence of the termination at those edges of the breaking of quasi-stationary Rossby waves".Atmospheric sciences, Aeronomy, Geophysicslmp3Applied Physics and Applied MathematicsArticlesThe Emergence of Jets and Vortices in Freely Evolving, Shallow‐Water Turbulence on a Sphere
http://academiccommons.columbia.edu/catalog/ac:167074
Cho, James Y‐K.; Polvani, Lorenzo M.http://hdl.handle.net/10022/AC:P:22171Fri, 08 Nov 2013 00:00:00 +0000Results from a series of simulations of unforced turbulence evolving within a shallow layer of fluid on a rotating sphere are presented. Simulations show that the turbulent evolution in the spherical domain is strongly dependent on numerical and physical conditions. The independent effects of (1) (hyper)dissipation and initial spectrum, (2) rotation rate, and (3) Rossby deformation radius are carefully isolated and studied in detail. In the nondivergent and nonrotating case, an initially turbulent flow evolves into a vorticityquadrupole at long times, a direct consequence of angular momentumconservation. In the presence of sufficiently strong rotation, the nondivergent long‐time behavior yields a field dominated by polar vortices—as previously reported by Yoden and Yamada. In contrast, the case with a finite deformation radius (i.e., the full spherical shallow‐water system) spontaneously evolves toward a banded configuration, the number of bands increasing with the rotation rate. A direct application of this shallow‐water model to the Jovian atmosphere is discussed. Using standard values for the planetary radius and rotation, we show how the initially turbulent flow self‐organizes into a potential vorticity field containing zonal structures, where regions of steep potential vorticity gradients (jets) separate relatively homogenized bands. Moreover, Jovian parameter values in our simulations lead to a strong vorticity asymmetry, favoring anticyclonic vortices—in further agreement with observations.Geophysics, Atmospheric sciences, Applied mathematicslmp3Applied Physics and Applied MathematicsArticlesTime-Dependent Fully Nonlinear Geostrophic Adjustment
http://academiccommons.columbia.edu/catalog/ac:167071
Kuo, Allen C.; Polvani, Lorenzo M.http://hdl.handle.net/10022/AC:P:22170Fri, 08 Nov 2013 00:00:00 +0000Shock-capturing numerical methods are employed to integrate the fully nonlinear, rotating 1D shallow-water equations starting from steplike nongeostrophic initial conditions (a Rossby adjustment problem). Such numerical methods allow one to observe the formation of multiple bores during the transient adjustment process as well as their decay due to rotation. It is demonstrated that increasing the rotation and/or the nonlinearity increases the rate of decay. Additionally, the time required for adjustment to be completed and its dependence on nonlinearity is examined; this time is found to be highly measure dependent. Lastly, the final adjusted state of the system is observed through long time integrations. Although the bores that form provide a mechanism for dissipation, their decay results in a final state in very good agreement with the one computed by well-known (dissipationless) conservation methods.Physics, Geophysics, Applied mathematicslmp3Applied Physics and Applied MathematicsArticlesBarotropic Vortex Pairs on a Rotating Sphere
http://academiccommons.columbia.edu/catalog/ac:167068
DiBattista, Mark T.; Polvani, Lorenzo M.http://hdl.handle.net/10022/AC:P:22169Fri, 08 Nov 2013 00:00:00 +0000Using a barotropic model in spherical geometry, we construct new solutions for steadily travelling vortex pairs and study their stability properties. We consider pairs composed of both point and finite-area vortices, and we represent the rotating background with a set of zonal strips of uniform vorticity. After constructing the solution for a single point-vortex pair, we embed it in a rotating background, and determine the equilibrium configurations that travel at constant speed without changing shape. For equilibrium solutions, we find that the stability depends on the relative strength (which may be positive or negative) of the vortex pair to the rotating background: eastward-travelling pairs are always stable, while westward-travelling pairs are unstable when their speeds approach that of the linear Rossby–Haurwitz waves. This finding also applies (with minor differences) to the case when the vortices are of finite area; in that case we find that, in addition to the point-vortex-like instabilities, the rotating background excites some finite-area instabilities for vortex pairs that would otherwise be stable. As for practical applications to blocking events, for which the slow westward pairs are relevant, our results indicate that free barotropic solutions are highly unstable, and thus suggest that forcing mechanisms must play an important role in maintaining atmospheric blocking events.Atmospheric sciences, Geophysics, Applied mathematicslmp3Applied Physics and Applied MathematicsArticlesOn the Subtropical Edge of the Stratospheric Surf Zone
http://academiccommons.columbia.edu/catalog/ac:167080
Polvani, Lorenzo M.; Waugh, D. W.; Plumb, R. Alanhttp://hdl.handle.net/10022/AC:P:22173Fri, 08 Nov 2013 00:00:00 +0000The formation of a subtropical “transport barrier” in the wintertime stratosphere is investigated in the context of a high-resolution shallow-water model in which Rossby waves are topographically forced on a zonally symmetric basic state. Two sets of experiments are performed: in the first “adiabatic” set, no dissipation or forcing of the mean state is imposed; in the second set, the layer thickness is relaxed to an equilibrium state taken to be representative of middle stratospheric radiative equilibrium temperatures. It is found that in the adiabatic case only a very weak subtropical barrier forms for forcing amplitudes that generate realistically steep potential vorticity gradients at the edge of the polar vortex; the vigorous wave breaking in the surf zone generates secondary waves that spread and, in turn, break well into the summer hemisphere. In contrast, the inclusion of relaxation to a realistic thermal equilibrium leads to the formation of a subtropical region of steep PV gradients. The strong subtropical shear induced by die diabatic relaxation is shown to be an important factor for the formation of the subtropical edge of the surf zone. Furthermore, the authors demonstrate that a simple one-layer shallow-water model can capture the full process of the formation of a surf zone with both polar and tropical edges starting from conditions typical of the early fall–that is, with a flow in which the polar vortex is not initially present. Finally, the authors quantify the mixing of polar and subtropical air into the midlatitude surf zone with the help of the contour advection technique. Although the quantitative estimates depend sensitively on how the edges of the surf zone are defined, our results indicate that more tropical than polar air is entrained into the surf zone.Atmospheric sciences, Aeronomy, Geophysicslmp3Applied Physics and Applied MathematicsArticlesThe Coherent Structures of Shallowwater Turbulence: Deformationradius Effects, Cyclone/Anticyclone Asymmetry and Gravitywave Generation
http://academiccommons.columbia.edu/catalog/ac:167083
Polvani, Lorenzo M.; McWilliams, J. C.; Spall, M. A.; Ford, R.Fri, 08 Nov 2013 00:00:00 +0000Over a large range of Rossby and Froude numbers, we investigate the dynamics of initially balanced decaying turbulence in a shallow rotating fluid layer. As in the case of incompressible two‐dimensional decaying turbulence, coherent vortex structures spontaneously emerge from the initially random flow. However, owing to the presence of a free surface, a wealth of new phenomena appear in the shallow‐water system. The upscale energy cascade, common to strongly rotating flows, is arrested by the presence of a finite Rossby deformation radius. Moreover, in contrast to near‐geostrophic dynamics, a strong asymmetry is observed to develop as the Froude number is increased, leading to a clear dominance of anticyclonic vortices over cyclonic ones, even though no β effect is present in the system. Finally, we observe gravity waves to be generated around the vortex structures, and, in the strongest cases, they appear in the form of shocks. We briefly discuss the relevance of this study to the vortices observed in Jupiter’s atmosphere.Atmospheric sciences, Geophysics, Applied mathematicslmp3Applied Physics and Applied MathematicsArticlesClimatology of Intrusions into the Tropical Upper Troposphere
http://academiccommons.columbia.edu/catalog/ac:167044
Waugh, Darryn W.; Polvani, Lorenzo M.http://hdl.handle.net/10022/AC:P:22161Thu, 07 Nov 2013 00:00:00 +0000Regions of upper tropospheric equatorial westerly winds, observed over the Pacific and Atlantic Oceans during northern fall to spring, are important for extratropical-tropical interactions. This paper focuses on one feature of these “westerly ducts” that has received relatively little attention to date: the occurrence of Rossby wave breaking events that transport tongues of extratropical air deep into the tropics, mix tropical and subtropical air, and can affect deep convection. A climatology of these “intrusion” events formed from 20 years of meteorological analyses shows a strong dependence on the basic-state flow. Notably, intrusion events are found to occur almost exclusively within westerly ducts, with more events in the presence of stronger equatorial westerlies. It is also found that there is strong interannual variability in the frequency of Pacific events, with fewer events during the warm phases of ENSO (consistent with the changes in the basic flow). Since these intrusion events laterally mix trace constituents and have been linked to tropical convection, their spatial and temporal variability may cause related variability in the distribution of trace constituents and tropical convection.Atmospheric sciences, Aeronomy, Meteorologylmp3Applied Physics and Applied MathematicsArticlesA New Look at Stratospheric Sudden Warmings. Part I: Climatology and Modeling Benchmarks
http://academiccommons.columbia.edu/catalog/ac:166927
Charlton, Andrew J.; Polvani, Lorenzo M.http://hdl.handle.net/10022/AC:P:22113Mon, 04 Nov 2013 00:00:00 +0000Stratospheric sudden warmings are the clearest and strongest manifestation of dynamical coupling in the stratosphere–troposphere system. While many sudden warmings have been individually documented in the literature, this study aims at constructing a comprehensive climatology: all major midwinter warming events are identified and classified, in both the NCEP–NCAR and 40-yr ECMWF Re-Analysis (ERA-40) datasets. To accomplish this a new, objective identification algorithm is developed. This algorithm identifies sudden warmings based on the zonal mean zonal wind at 60°N and 10 hPa, and classifies them into events that do and do not split the stratospheric polar vortex. Major midwinter stratospheric sudden warmings are found to occur with a frequency of approximately six events per decade, and 46% of warming events lead to a splitting of the stratospheric polar vortex. The dynamics of vortex splitting events is contrasted to that of events where the vortex is merely displaced off the pole. In the stratosphere, the two types of events are found to be dynamically distinct: vortex splitting events occur after a clear preconditioning of the polar vortex, and their influence on middle-stratospheric temperatures lasts for up to 20 days longer than vortex displacement events. In contrast, the influence of sudden warmings on the tropospheric state is found to be largely insensitive to the event type. Finally, a table of dynamical benchmarks for major stratospheric sudden warming events is compiled. These benchmarks are used in a companion study to evaluate current numerical model simulations of the stratosphere.Atmospheric sciences, Aeronomy, Applied mathematicsac2343, lmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesThe Effect of Lower Stratospheric Shear on Baroclinic Instability
http://academiccommons.columbia.edu/catalog/ac:166918
Wittman, Matthew A. H.; Charlton, Andrew J.; Polvani, Lorenzo M.http://hdl.handle.net/10022/AC:P:22111Mon, 04 Nov 2013 00:00:00 +0000Using a hierarchy of models, and observations, the effect of vertical shear in the lower stratosphere on baroclinic instability in the tropospheric midlatitude jet is examined. It is found that increasing stratospheric shear increases the phase speed of growing baroclinic waves, increases the growth rate of modes with low synoptic wavenumbers, and decreases the growth rate of modes with higher wavenumbers. The meridional structure of the linear modes, and their acceleration of the zonal mean jet, changes with increasing stratospheric shear, but in a way that apparently contradicts the observed stratosphere–troposphere northern annular mode (NAM) connection. This contradiction is resolved at finite amplitude. In nonlinear life cycle experiments it is found that increasing stratospheric shear, without changing the jet structure in the troposphere, produces a transition from anticyclonic (LC1) to cyclonic (LC2) behavior at wavenumber 7. All life cycles with wavenumbers lower than 7 are LC1, and all with wavenumber greater than 7 are LC2. For the LC1 life cycles, the effect of increasing stratospheric shear is to increase the poleward displacement of the zonal mean jet by the eddies, which is consistent with the observed stratosphere–troposphere NAM connection. Finally, it is found that the connection between high stratospheric shear and high-tropospheric NAM is present by NCEP–NCAR reanalysis data.Atmospheric sciences, Aeronomy, Applied mathematicsmaw2006, ac2343, lmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesA New Look at Stratospheric Sudden Warmings. Part II: Evaluation of Numerical Model Simulations
http://academiccommons.columbia.edu/catalog/ac:166924
Charlton, Andrew J.; Polvani, Lorenzo M.; Perlwitz, Judith; Sassi, Fabrizio; Manzini, Elisa; Pawson, Steven; Shibata, Kiyotaka; Nielsen, J. Eric; Rind, Davidhttp://hdl.handle.net/10022/AC:P:22113Mon, 04 Nov 2013 00:00:00 +0000The simulation of major midwinter stratospheric sudden warmings (SSWs) in six stratosphere-resolving general circulation models (GCMs) is examined. The GCMs are compared to a new climatology of SSWs, based on the dynamical characteristics of the events. First, the number, type, and temporal distribution of SSW events are evaluated. Most of the models show a lower frequency of SSW events than the climatology, which has a mean frequency of 6.0 SSWs per decade. Statistical tests show that three of the six models produce significantly fewer SSWs than the climatology, between 1.0 and 2.6 SSWs per decade. Second, four process-based diagnostics are calculated for all of the SSW events in each model. It is found that SSWs in the GCMs compare favorably with dynamical benchmarks for SSW established in the first part of the study. These results indicate that GCMs are capable of quite accurately simulating the dynamics required to produce SSWs, but with lower frequency than the climatology. Further dynamical diagnostics hint that, in at least one case, this is due to a lack of meridional heat flux in the lower stratosphere. Even though the SSWs simulated by most GCMs are dynamically realistic when compared to the NCEP–NCAR reanalysis, the reasons for the relative paucity of SSWs in GCMs remains an important and open question.Atmospheric sciences, Aeronomy, Applied mathematicsac2343, lmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesInternal Variability of the Winter Stratosphere. Part II: Time-Dependent Forcing
http://academiccommons.columbia.edu/catalog/ac:166906
Scott, R. K.; Polvani, Lorenzo M.; Waugh, D. W.http://hdl.handle.net/10022/AC:P:22107Mon, 04 Nov 2013 00:00:00 +0000This paper considers the effect of time-dependent lower boundary wave forcing on the internal variability found to appear spontaneously in a stratosphere-only model when the forcing is perfectly steady. While the time-dependent forcing is found to modulate the internal variability, leading in some cases to frequency locking of the upper-stratospheric response to the forcing, the temporal and spatial structure of the variability remains similar to the case when the forcing is time independent. Experiments with a time-periodic modulation of the forcing amplitude indicate that the wave flux through the lower boundary is only partially related to the instantaneous forcing, but is more significantly influenced by the condition of the polar vortex itself. In cases of purely random wave forcing with zero time mean, the stratospheric response is similar to that obtained with steady forcing of magnitude equal to the root-mean-square of the time-varying forcing.Atmospheric sciences, Aeronomy, Applied mathematicslmp3Applied Physics and Applied MathematicsArticlesTesting the Annular Mode Autocorrelation Time Scale in Simple Atmospheric General Circulation Models
http://academiccommons.columbia.edu/catalog/ac:166909
Gerber, Edwin P.; Voronin, Sergey; Polvani, Lorenzo M.http://hdl.handle.net/10022/AC:P:22108Mon, 04 Nov 2013 00:00:00 +0000A new diagnostic for measuring the ability of atmospheric models to reproduce realistic low-frequency variability is introduced in the context of Held and Suarez’s 1994 proposal for comparing the dynamics of different general circulation models. A simple procedure to compute τ, the e-folding time scale of the annular mode autocorrelation function, is presented. This quantity concisely quantifies the strength of low-frequency variability in a model and is easy to compute in practice. The sensitivity of τ to model numerics is then studied for two dry primitive equation models driven with the Held–Suarez forcings: one pseudospectral and the other finite volume. For both models, τ is found to be unrealistically large when the horizontal resolutions are low, such as those that are often used in studies in which long integrations are needed to analyze model variability on low frequencies. More surprising is that it is found that, for the pseudospectral model, τ is particularly sensitive to vertical resolution, especially with a triangular truncation at wavenumber 42 (a very common resolution choice). At sufficiently high resolution, the annular mode autocorrelation time scale τ in both models appears to converge around values of 20–25 days, suggesting the existence of an intrinsic time scale at which the extratropical jet vacillates in the Held and Suarez system. The importance of τ for computing the correct response of a model to climate change is explicitly demonstrated by perturbing the pseudospectral model with simple torques. The amplitude of the model’s response to external forcing increases as τ increases, as suggested by the fluctuation–dissipation theorem.Atmospheric sciences, Meteorology, Applied mathematicsepg2108, sv2122, lmp3Applied Physics and Applied MathematicsArticlesTransport and Mixing of Chemical Air Masses in Idealized Baroclinic Life Cycles
http://academiccommons.columbia.edu/catalog/ac:166915
Polvani, Lorenzo M.; Esler, J. G.http://hdl.handle.net/10022/AC:P:22110Mon, 04 Nov 2013 00:00:00 +0000The transport, mixing, and three-dimensional evolution of chemically distinct air masses within growing baroclinic waves are studied in idealized, high-resolution, life cycle experiments using suitably initialized passive tracers, contrasting the two well-known life cycle paradigms, distinguished by predominantly anticyclonic (LC1) or cyclonic (LC2) flow at upper levels. Stratosphere-troposphere exchange differs significantly between the two life cycles. Specifically, transport from the stratosphere into the troposphere is significantly larger for LC2 (typically by 50%), due to the presence of large and deep cyclonic vortices that create a wider surf zone than for LC1. In contrast, the transport of tropospheric air into the stratosphere is nearly identical between the two life cycles. The mass of boundary layer air uplifted into the free troposphere is similar for both life cycles, but much more is directly injected into the stratosphere in the case of LC1 (fourfold, approximately). However, the total mixing of boundary layer with stratospheric air is larger for LC2, owing to the presence of the deep cyclonic vortices that entrain and mix both boundary layer air from the surface and stratospheric air from the upper levels. For LC1, boundary layer and stratospheric air are brought together by smaller cyclonic structures that develop on the poleward side of the jet in the lower part of the middleworld, resulting in correspondingly weaker mixing. As both the El Niño-Southern Oscillation and the North Atlantic Oscillation are correlated with the relative frequency of life cycle behaviors, corresponding changes in chemical transport and mixing are to be expected.Atmospheric sciences, Atmospheric chemistry, Aeronomylmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesOn the Wavelength of the Rossby Waves Radiated by Tropical Cyclones
http://academiccommons.columbia.edu/catalog/ac:166903
Krouse, Kyle D.; Sobel, Adam H.; Polvani, Lorenzo M.http://hdl.handle.net/10022/AC:P:22106Mon, 04 Nov 2013 00:00:00 +0000The authors present a theory for the zonal wavelength of tropical depression–type disturbances, which occur as a result of Rossby wave radiation from a preexisting tropical cyclone (TC). In some cases, such disturbances undergo tropical cyclogenesis, resulting in a pair of tropical cyclones; the theory then predicts the zonal separation distance of such tropical cyclone pairs. Numerical experiments are presented in which a thermally forced vortex, superimposed on an initial state of rest, is moved at different velocities in a shallow-water model on a sphere. Vortices moving westward generate coherent wave trains to the east or southeast (depending on the amplitude of the vortex), resembling those in observations. The zonal wavelengths of these wave trains in each case are well described by the linear stationary solution in the frame comoving with the vortex. Vortices moving eastward or remaining stationary do not generate such trains, also consistent with linear theory, which admits no stationary solutions in such cases. It is hypothesized that the wavelengths of observed disturbances are set by the properties of the relevant stationary solution. The environmental flow velocity that determines this wavelength is not the translation velocity of the tropical cyclone, but the difference between the steering flow of the radiated Rossby waves and that of the TC. The authors argue that either horizontal or vertical shear in the environment of the TC can generate differences between these steering flows of the necessary magnitude and sign to generate the observed wavelengths.Atmospheric sciences, Applied mathematics, Meteorologykdk8, ahs129, lmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesForced-Dissipative Shallow-Water Turbulence on the Sphere and the Atmospheric Circulation of the Giant Planets
http://academiccommons.columbia.edu/catalog/ac:166921
Scott, R. K.; Polvani, Lorenzo M.http://hdl.handle.net/10022/AC:P:22112Mon, 04 Nov 2013 00:00:00 +0000Although possibly the simplest model for the atmospheres of the giant planets, the turbulent forced-dissipative shallow-water system in spherical geometry has not, to date, been investigated; the present study aims to fill this gap. Unlike the freely decaying shallow-water system described by Cho and Polvani, equilibrium states in the forced-dissipative system are highly dependent on details of the forcing and the dissipation. For instance, it is found that for a given equilibrated energy level, the steadiness of zonal jets depends crucially on the balance between forcing and dissipation. With long (up to 100 000 days) high-resolution (T170) calculations, the dependence of the equilibrium states on Rossby number Ro and Rossby deformation radius LD is explored, for the case when the dissipation takes the form of hypodiffusion (acting predominantly at large scales) and the random forcing at small scales is δ correlated in time. When LD is large compared to the planetary radius, zonal jets are verified to scale closely with the Rhines scale over a wide range of Ro; furthermore, the jets at the equator are found to be both prograde and retrograde with approximately equal likelihood. As LD is decreased, the equatorial jets become increasingly and consistently retrograde, in agreement with the freely decaying turbulence results. Also, the regime recently discussed by Theiss, where zonal jets are confined to low latitudes, is illustrated to emerge robustly in the limit of small LD. Finally, specific calculations with parameter values typical of the giant planets are presented, confirming many of the earlier results obtained in the freely decaying case.Atmospheric sciences, Applied mathematics, Planetologylmp3Applied Physics and Applied MathematicsArticlesDynamical Formation of an Extra-Tropical Tropopause Inversion Layer in a Relatively Simple General Circulation Model
http://academiccommons.columbia.edu/catalog/ac:166912
Son, Seok-Woo; Polvani, Lorenzo M.http://hdl.handle.net/10022/AC:P:22109Mon, 04 Nov 2013 00:00:00 +0000The key factors contributing to the formation and maintenance of the recently discovered extra-tropical tropopause inversion layer are presently unclear. In this study, it is shown that such a layer can form as a consequence of the turbulent dynamics of synoptic-scale baroclinic eddies alone, in the absence of explicitly parameterized, small-scale, radiative-convective processes. A simple general circulation model, initialized from a state of rest, and driven with idealized forcings, is found to spontaneously develop an inversion layer above the tropopause under a wide variety of parameter choices and model resolutions. Furthermore, such a model is able to capture, qualitatively, both the latitudinal and (in part) the seasonal dependence of the observed tropopause inversion layer. However, the inability of our simple model to capture some detailed quantitative features strongly suggests that other physical processes, beyond balanced synoptic-scale dynamics, are likely to play an important role.Atmospheric sciences, Meteorology, Aeronomysws2112, lmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesThe Coupled Stratosphere–Troposphere Response to Impulsive Forcing from the Troposphere
http://academiccommons.columbia.edu/catalog/ac:166959
Reichler, Thomas; Kushner, Paul J.; Polvani, Lorenzo M.http://hdl.handle.net/10022/AC:P:22128Mon, 04 Nov 2013 00:00:00 +0000A simple atmospheric general circulation model (GCM) is used to investigate the transient response of the stratosphere–troposphere system to externally imposed pulses of lower-tropospheric planetary wave activity. The atmospheric GCM is a dry, hydrostatic, global primitive-equations model, whose circulation includes an active polar vortex and a tropospheric jet maintained by baroclinic eddies. Planetary wave activity pulses are generated by a perturbation of the solid lower boundary that grow and decay over a period of 10 days. The planetary wave pulses propagate upward and break in the stratosphere. Subsequently, a zonal-mean circulation anomaly propagates downward, often into the troposphere, at lags of 30–100 days. The evolution of the response is found to be dependent on the state of the stratosphere–troposphere system at the time the pulse is generated. In particular, on the basis of a large ensemble of these simulations, it is found that the length of time the signal takes to propagate downward from the stratosphere is controlled by initial anomalies in the zonal-mean circulation and in the zonal-mean wave drag. Criteria based on these anomaly patterns can be used, therefore, to predict the long-term surface response of the stratosphere–troposphere system to a planetary wave pulse up to 90 days after the pulse is generated. In an independent test, it is verified that the initial states that most strongly satisfy these criteria respond in the expected way to the lower-tropospheric wave activity pulse.Atmospheric sciences, Aeronomy, Applied mathematicslmp3Applied Physics and Applied MathematicsArticlesA Very Large, Spontaneous Stratospheric Sudden Warming in a Simple AGCM: A Prototype for the Southern Hemisphere Warming of 2002?
http://academiccommons.columbia.edu/catalog/ac:166956
Kushner, Paul J.; Polvani, Lorenzo M.http://hdl.handle.net/10022/AC:P:22127Mon, 04 Nov 2013 00:00:00 +0000An exceptionally strong stratospheric sudden warming (SSW) that spontaneously occurs in a very simple stratosphere–troposphere AGCM is discussed. The model is a dry, hydrostatic, primitive equation model without planetary stationary waves. Transient baroclinic wave–wave interaction in the troposphere thus provides the only source of upward-propagating wave activity into the stratosphere. The model’s SSW is grossly similar to the Southern Hemisphere major SSW of 2002: it occurs after weaker warmings “precondition” the polar vortex for breaking, it involves a split of the polar vortex, and it has a downward-propagating signature. These similarities suggest that the Southern Hemisphere SSW of 2002 might itself have been caused by transient baroclinic wave–wave interaction. The simple model used for this study also provides some insight into how often such extreme events might occur. The frequency distribution of SSWs in the model has exponential, as opposed to Gaussian, tails. This suggests that very large amplitude SSWs, though rare, might occur with higher frequency than might be naively expected.Atmospheric sciences, Aeronomy, Applied mathematicslmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesInternal Variability of the Winter Stratosphere. Part I: Time-Independent Forcing
http://academiccommons.columbia.edu/catalog/ac:166950
Scott, R. K.; Polvani, Lorenzo M.http://hdl.handle.net/10022/AC:P:22125Mon, 04 Nov 2013 00:00:00 +0000This paper examines the nature and robustness of internal stratospheric variability, namely the variability resulting from the internal dynamics of the stratosphere itself, as opposed to that forced by external sources such as the natural variability of the free troposphere. Internal stratospheric variability arises from the competing actions of radiative forcing, which under perpetual winter conditions strengthens the polar vortex, and planetary wave breaking, which weakens it. The results from a stratosphere-only model demonstrate that strong internal stratospheric variability, consisting of repeated sudden warming-type events, exists over a wide range of realistic radiative and wave forcing conditions, and is largely independent of other physical and numerical parameters. In particular, the coherent form of the variability persists as the number of degrees of freedom is increased, and is therefore not an artifact of severe model truncation. Various diagnostics, including three-dimensional representations of the potential vorticity, illustrate that the variability is determined by the vertical structure of the vortex and the extent to which upward wave propagation is favored or inhibited. In this paper, the variability arising from purely internal stratosphere dynamics is isolated by specifying thermal and wave forcings that are completely time independent. In a second paper, the authors investigate the relative importance of internal and external variability by considering time-dependent wave forcing as a simple representation of tropospheric variability.Atmospheric sciences, Aeronomy, Applied mathematicslmp3Applied Physics and Applied MathematicsArticlesStratosphere–Troposphere Coupling in a Relatively Simple AGCM: The Role of Eddies
http://academiccommons.columbia.edu/catalog/ac:166971
Kushner, Paul J.; Polvani, Lorenzo M.http://hdl.handle.net/10022/AC:P:22132Mon, 04 Nov 2013 00:00:00 +0000The extratropical circulation response to cooling of the polar-winter stratosphere in a simple AGCM is investigated. The AGCM is a dry hydrostatic primitive equation model with zonally symmetric boundary conditions and analytically specified physics. It is found that, as the polar-winter stratosphere is cooled, the tropospheric jet shifts poleward. This response projects almost entirely and positively (by convention) onto the AGCM's annular mode. At the same time, the vertical flux of wave activity from the troposphere to the stratosphere is reduced and the meridional flux of wave activity from high to low latitudes is increased. Thus, as the stratosphere is cooled, the stratospheric wave drag is reduced. In order to understand this response, the transient adjustment of the stratosphere–troposphere system is investigated using an ensemble of “switch on” stratospheric cooling runs of the AGCM. The response to the switch-on stratospheric cooling descends from the upper stratosphere into the troposphere on a time scale that matches simple downward-control theory estimates. The downward-control analysis is pursued with a zonally symmetric model that uses as input the thermal and eddy-driving terms from the eddying AGCM. With this model, the contributions to the response from the thermal and eddy-driving perturbations can be investigated separately, in the absence of eddy feedbacks. It is found that the stratospheric thermal perturbation, in the absence of such feedbacks, induces a response that is confined to the stratosphere. The stratospheric eddy-driving perturbation, on the other hand, induces a response that penetrates into the midtroposphere but does not account, in the zonally symmetric model, for the tropospheric jet shift. Furthermore, the tropospheric eddy-driving perturbation, in the zonally symmetric model, induces a strong upward response in the stratospheric winds. From these experiments and from additional experiments with the eddying AGCM, it is concluded that the stratospheric eddy-driving response induces a tropospheric response, but that the full circulation response results from a two-way coupling between the stratosphere and the troposphere.Atmospheric sciences, Aeronomy, Applied mathematicslmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesOn the Meridional Structure of Annular Modes
http://academiccommons.columbia.edu/catalog/ac:166962
Wittman, Matthew A. H.; Charlton, Andrew J.; Polvani, Lorenzo M.http://hdl.handle.net/10022/AC:P:22129Mon, 04 Nov 2013 00:00:00 +0000Using a simple stochastic model, the authors illustrate that the occurrence of a meridional dipole in the first empirical orthogonal function (EOF) of a time-dependent zonal jet is a simple consequence of the north–south excursion of the jet center, and this geometrical fact can be understood without appealing to fluid dynamical principles. From this it follows that one ought not, perhaps, be surprised at the fact that such dipoles, commonly referred to as the Arctic Oscillation (AO) or the Northern Annular Mode (NAM), have robustly been identified in many observational studies and appear to be ubiquitous in atmospheric models across a wide range of complexity.Atmospheric sciences, Aeronomy, Applied mathematicsmaw2006, ac2343, lmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesStratospheric Control of Upward Wave Flux near the Tropopause
http://academiccommons.columbia.edu/catalog/ac:166965
Scott, R. K.; Polvani, Lorenzo M.http://hdl.handle.net/10022/AC:P:22130Mon, 04 Nov 2013 00:00:00 +0000Using an idealized, global primitive equation model of the stratosphere-troposphere system in which all tropospheric variability is surpressed, we demonstrate the existence of internal modes of stratospheric variability. The variability in our model is similar to that observed in the winter stratosphere, consisting of sudden-warming like, wave-driven decelerations of the polar vortex followed by a more gradual re-establishment of the vortex by the radiative forcing. Using a common index of the strength of the stratospheric vortex, we find patterns of downward propagation resembling those found in recent observations. In addition, our model exhibits considerable variability in the upward flux of wave activity into the stratosphere; this variability strongly anti-correlates with the index of the mid-upper stratospheric vortex, again in agreement with recent observations.Atmospheric sciences, Applied mathematics, Aeronomylmp3Applied Physics and Applied MathematicsArticlesThe Antarctic Stratospheric Sudden Warming of 2002: A Self-Tuned Resonance?
http://academiccommons.columbia.edu/catalog/ac:166947
Esler, J. G.; Polvani, Lorenzo M.; Scott, R. K.http://hdl.handle.net/10022/AC:P:22124Mon, 04 Nov 2013 00:00:00 +0000The extraordinary Antarctic stratospheric warming event of 2002 was characterized by a remarkable vertical structure, with the vortex observed to divide at upper levels in the stratosphere but not at lower levels: such ‘partially’ split vortex events are relatively rare. A simple, yet fully three-dimensional, model is constructed to investigate the dynamics of this unique event. Planetary waves are excited on the model vortex edge by a lower boundary forcing characterized by two parameters: an amplitude hF and a frequency ωF, measured relative to a stationary frame. For realistic forcing amplitudes, a partial vortex split resembling that observed during the 2002 event is found only within a specific, narrow band of forcing frequencies. Exploiting the relative simplicity of our model, these frequencies are shown to be those causing a ‘self-tuning’ resonant excitation of the gravest linear mode, during which nonlinear feedback causes an initially off-resonant forcing to approach resonance.Atmospheric sciences, Aeronomy, Climate changelmp3Applied Physics and Applied MathematicsArticlesStratosphere–Troposphere Coupling in a Relatively Simple AGCM: Impact of the Seasonal Cycle
http://academiccommons.columbia.edu/catalog/ac:166953
Kushner, Paul J.; Polvani, Lorenzo M.http://hdl.handle.net/10022/AC:P:22126Mon, 04 Nov 2013 00:00:00 +0000The seasonal time dependence of the tropospheric circulation response to polar stratospheric cooling in a simple atmospheric general circulation model is investigated. When the model is run without a seasonal cycle, polar stratospheric cooling induces a positive annular-mode response in the troposphere that takes a remarkably long time—several hundred days—to fully equilibrate. One is thus led to ask whether the tropospheric response would survive in the presence of a seasonal cycle. When a seasonal cycle is introduced into the model stratosphere, the tropospheric response appears with a distinct time lag with respect to the stratospheric cooling, but, in the long-term mean, the pattern of the wind response is very similar to the one that results from stratospheric forcing in the absence of a seasonal cycle.Atmospheric sciences, Aeronomy, Applied mathematicslmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesStratospheric Influence on Baroclinic Lifecycles and its Connection to the Arctic Oscillation
http://academiccommons.columbia.edu/catalog/ac:166968
Wittman, Matthew A. H.; Polvani, Lorenzo M.; Charlton, Andrew J.; Scott, Richard K.http://hdl.handle.net/10022/AC:P:22131Mon, 04 Nov 2013 00:00:00 +0000Using an idealized primitive equation model, we investigate how stratospheric conditions alter the development of baroclinic instability in the troposphere. Starting from the lifecycle paradigm of Thorncroft et al., we consider the evolution of baroclinic lifecycles resulting from the addition of a stratospheric jet to the LC1 initial condition. We find that the addition of the stratospheric jet yields a net surface geopotential height anomaly that strongly resembles the Arctic Oscillation. With the additional modification of the tropospheric winds to resemble the high-AO climatology, the surface response is amplified by a factor 10 and, though dominated by the tropospheric changes, shows similar sensitivity to the stratospheric conditions.Atmospheric sciences, Applied mathematics, Aeronomymaw2006, lmp3, ac2343Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesEnhancement of Rossby Wave Breaking by Steep Potential Vorticity Gradients in the Winter Stratosphere
http://academiccommons.columbia.edu/catalog/ac:166977
Scott, R. K.; Dritschel, D. G.; Polvani, Lorenzo M.; Waugh, D. W.http://hdl.handle.net/10022/AC:P:22134Mon, 04 Nov 2013 00:00:00 +0000This work investigates the extent to which potential vorticity gradients affect the vertical propagation of planetary-scale Rossby waves on the edge of a stratospheric polar vortex and their eventual nonlinear saturation and breaking. Using two different numerical modeling approaches, it is shown that wave propagation and wave breaking are significantly reduced when the potential vorticity gradients at the vortex edge are anomalously weak. The efficiency of the first model, based on high-resolution contour dynamics, permits a full exploration of the parameter space of wave forcing amplitude and edge steepness. A more realistic primitive equation model in spherical geometry both confirms the contour dynamics results and highlights some direct implications for stratospheric modeling in more comprehensive models. The results suggest that stratospheric models using horizontal resolutions of spectral T42 or less may significantly underestimate the vertical propagation and breaking of planetary waves, and may consequently misrepresent such important stratospheric processes as the mean meridional circulation, sudden warmings, and the mixing of chemically distinct polar and midlatitude air.Atmospheric sciences, Aeronomy, Atmospheric chemistrylmp3Applied Physics and Applied MathematicsArticlesKelvin–Helmholtz Instability of Potential Vorticity Layers: A Route to Mixing
http://academiccommons.columbia.edu/catalog/ac:166980
Esler, J. G.; Polvani, Lorenzo M.http://hdl.handle.net/10022/AC:P:22135Mon, 04 Nov 2013 00:00:00 +0000The linear and nonlinear dynamics of layers of anomalously high potential vorticity (PV) are studied in detail. It is well known that PV layers are subject to slow, balanced, mixed barotropic–baroclinic instabilities. In this paper, it is shown that, in addition, PV layers are subject to a Kelvin–Helmholtz instability, operating on much smaller spatial and faster temporal scales. For simplicity, spatially infinite layers of uniform anomalous PV are considered. Such layers are characterized by two key parameters: the ratio Δq of their anomalous PV to the background PV, and the angle α between the layer and the direction of the ambient stratification gradient (in suitably scaled coordinates). It is found that Kelvin–Helmholtz appears, for certain values of α, whenever Δq greater than 8. Of notable interest is the case of an initially vertical PV layer embedded in a weak ambient shear flow: for sufficiently large Δq, once the PV layer is tilted past a critical angle, Kelvin–Helmholtz instability becomes possible. It is argued that the breakdown of PV layers due to a Kelvin–Helmholtz instability induced by ambient shear might be an important systematic mechanism leading to irreversible mixing during stratosphere–troposphere exchange events. This is discussed in the context of an example of Kelvin–Helmholtz instability observed near a tropopause fold.Atmospheric sciences, Aeronomy, Applied mathematicslmp3Applied Physics and Applied MathematicsArticlesNumerically Converged Solutions of the Global Primitive Equations for Testing the Dynamical Core of Atmospheric GCMs
http://academiccommons.columbia.edu/catalog/ac:166983
Polvani, Lorenzo M.; Scott, R. K.; Thomas, S. J.http://hdl.handle.net/10022/AC:P:22136Mon, 04 Nov 2013 00:00:00 +0000Solutions of the dry, adiabatic, primitive equations are computed, for the first time, to numerical convergence. These solutions consist of the short-time evolution of a slightly perturbed, baroclinically unstable, midlatitude jet, initially similar to the archetypal LC1 case of Thorncroft et al. The solutions are computed with two distinct numerical schemes to demonstrate that they are not dependent on the method used to obtain them. These solutions are used to propose a new test case for dynamical cores of atmospheric general circulation models. Instantaneous horizontal and vertical cross sections of vorticity and vertical velocity after 12 days, together with tables of key diagnostic quantities derived from the new solutions, are offered as reproducible benchmarks. Unlike the Held and Suarez benchmark, the partial differential equations and the initial conditions are here completely specified, and the new test case requires only 12 days of integration, involves no spatial or temporal averaging, and does not call for physical parameterizations to be added to the dynamical core itself.Atmospheric sciences, Meteorology, Applied mathematicslmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesAn Efficient Spectral Dynamical Core for Distributed Memory Computers
http://academiccommons.columbia.edu/catalog/ac:166989
Rivier, L.; Loft, R.; Polvani, Lorenzo M.http://hdl.handle.net/10022/AC:P:22138Mon, 04 Nov 2013 00:00:00 +0000The practical question of whether the classical spectral transform method, widely used in atmospheric modeling, can be efficiently implemented on inexpensive commodity clusters is addressed. Typically, such clusters have limited cache and memory sizes. To demonstrate that these limitations can be overcome, the authors have built a spherical general circulation model dynamical core, called BOB (“Built on Beowulf”), which can solve either the shallow water equations or the atmospheric primitive equations in pressure coordinates. That BOB is targeted for computing at high resolution on modestly sized and priced commodity clusters is reflected in four areas of its design. First, the associated Legendre polynomials (ALPs) are computed “on the fly” using a stable and accurate recursion relation. Second, an identity is employed that eliminates the storage of the derivatives of the ALPs. Both of these algorithmic choices reduce the memory footprint and memory bandwidth requirements of the spectral transform. Third, a cache-blocked and unrolled Legendre transform achieves a high performance level that resists deterioration as resolution is increased. Finally, the parallel implementation of BOB is transposition-based, employing load-balanced, one-dimensional decompositions in both latitude and wavenumber. A number of standard tests is used to compare BOB's performance to two well-known codes—the Parallel Spectral Transform Shallow Water Model (PSTSWM) and the dynamical core of NCAR's Community Climate Model CCM3. Compared to PSTSWM, BOB shows better timing results, particularly at the higher resolutions where cache effects become important. BOB also shows better performance in its comparison with CCM3's dynamical core. With 16 processors, at a triangular spectral truncation of T85, it is roughly five times faster when computing the solution to the standard Held–Suarez test case, which involves 18 levels in the vertical. BOB also shows a significantly smaller memory footprint in these comparison tests.Atmospheric sciences, Computer science, System sciencelmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesTropospheric Response to Stratospheric Perturbations in a Relatively Simple General Circulation Model
http://academiccommons.columbia.edu/catalog/ac:166992
Polvani, Lorenzo M.; Kushner, Paul J.http://hdl.handle.net/10022/AC:P:22139Mon, 04 Nov 2013 00:00:00 +0000The sensitivity of the tropospheric extratropical circulation to thermal perturbations of the polar stratosphere is examined in a dry primitive equation general circulation model with zonally symmetric forcing and boundary conditions. For sufficiently strong cooling of the polar winter stratosphere, the winter-hemisphere tropospheric jet shifts polewards and strengthens markedly at the surface; this is accompanied by a drop in surface pressure at high latitudes in the same hemisphere. In addition, this extratropical tropospheric response is found to be very similar to the model's leading pattern of internal variability. These results are tested for robustness at several horizontal and vertical resolutions, and the same tropospheric response is observed at all but the lowest resolution tested. The behavior of this relatively simple model is broadly consistent with recent observational and modeling studies of trends in extratropical atmospheric variability.Atmospheric sciences, Aeronomy, Meteorologylmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesThe Weak Temperature Gradient Approximation and Balanced Tropical Moisture Waves
http://academiccommons.columbia.edu/catalog/ac:166995
Sobel, Adam H.; Nilsson, Johan; Polvani, Lorenzo M.http://hdl.handle.net/10022/AC:P:22140Mon, 04 Nov 2013 00:00:00 +0000Horizontal temperature gradients are small in the tropical atmosphere, as a consequence of the smallness of the Coriolis parameter near the equator. This provides a strong constraint on both large-scale fluid dynamics and diabatic processes. This work is a step toward the construction of a balanced dynamical theory for the tropical circulation that is based on this constraint, and in which the diabatic processes are explicit and interactive. The authors first derive the basic fluid-dynamical scaling under the weak temperature gradient (WTG) approximation in a shallow water system with a fixed mass source representing an externally imposed heating. This derivation follows an earlier similar one by Held and Hoskins, but extends the analysis to the nonlinear case (though on an f plane), examines the resulting system in more detail, and presents a solution for an axisymmetric “top-hat” forcing. The system is truly balanced, having no gravity waves, but is different from other balance models in that the heating is included a priori in the scaling. The WTG scaling is then applied to a linear moist model in which the convective heating is controlled by a moisture variable that is advected by the flow. This moist model is derived from the Quasi-equilibrium Tropical Circulation Model (QTCM) equations of Neelin and Zeng but can be viewed as somewhat more general. A number of additional approximations are made in order to consider balanced dynamical modes, apparently not studied previously, which owe their existence to interactions of the moisture and flow fields. A particularly interesting mode arises on an f plane with a constant background moisture gradient. In the limit of low frequency and zero meridional wavenumber this mode has a dispersion relation mathematically identical to that of a barotropic Rossby wave, though the phase speed is eastward (for moisture decreasing poleward in the background state) and the propagation mechanism is quite different. This mode also has significant positive growth rate for low wavenumbers. The addition of the β effect complicates matters. For typical parameters, when β is included the direction of phase propagation is ambiguous, and the growth rate reduced, as the effects of the background gradients in moisture and planetary vorticity appear to cancel to a large degree. Possible relevance to intraseasonal variability and easterly wave dynamics is briefly discussed.Atmospheric sciences, Aeronomy, Meteorologyahs129, lmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesThe Hadley Circulation and the Weak Temperature Gradient Approximation
http://academiccommons.columbia.edu/catalog/ac:166986
Polvani, Lorenzo M.; Sobel, Adam H.http://hdl.handle.net/10022/AC:P:22137Mon, 04 Nov 2013 00:00:00 +0000The weak temperature gradient (WTG) approximation is applied to simple shallow-water models of the Hadley circulation. While it is difficult to formally justify the use of the WTG approximation for this problem, the derived WTG solutions are shown to agree well with numerical solutions of the full equations and to converge to the traditional angular momentum conserving (AMC) solutions in the inviscid limit. Heuristic arguments are given to explain this. The WTG method also provides semianalytical solutions in the case of nonvanishing viscosity, in contrast to the AMC solutions, which are strictly inviscid.Atmospheric sciences, Meteorology, Applied mathematicslmp3, ahs129Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticles