Academic Commons Search Results
https://academiccommons.columbia.edu/catalog?action=index&controller=catalog&f%5Bsubject_facet%5D%5B%5D=Mathematics&format=rss&fq%5B%5D=has_model_ssim%3A%22info%3Afedora%2Fldpd%3AContentAggregator%22&q=&rows=500&sort=record_creation_date+desc
Academic Commons Search Resultsen-usTransient Dynamics in Neural Networks
https://academiccommons.columbia.edu/catalog/ac:r7sqv9s4q2
Schaffer, Evan Shuman10.7916/D8S198BQTue, 05 Dec 2017 18:24:09 +0000The motivation for this thesis is to devise a simple model of transient dynamics in neural networks. Neural circuits are capable of performing many computations without reaching an equilibrium, but instead through transient changes in activity. Thus, having a good model for transient activity is important. In particular, this thesis focuses on a firing-rate description of neural activity. Firing rates offer a convenient simplification of neural activity, and have been shown experimentally to convey information about stimuli and behavior.
This work begins by review the philosophy of modeling firing rates, as well as the problems that go with it. It examines traditional approaches to modeling firing rates, and in particular how common assumptions lead to a model that fails to capture transient dynamics.
Chapter 2 applies a traditional model of firing rates in order to gain insight into properties of cortical circuitry. In collaboration with the lab of David Ferster at Northwestern University, we found that surround suppression in cat primary visual cortex is mediated by a withdrawal of excitation in the cortical circuit. In theoretical work, we find that this behavior can only arise if excitatory recurrence alone is strong enough to destabilize visual responses but feedback inhibition maintains stability.
Chapter 3 reviews concepts and literature related to the dynamics of large networks of spiking neurons. Population density approaches are common for describing the dynamics of networks of spiking neurons. These approaches allow for a rigorous approach to relate the dynamics of individual neurons to the population firing rate.
Chapter 4 explores a method for accurately approximating the firing-rate dynamics of a population of spiking neurons. We describe the population by the probability density of membrane potentials, so the dynamics are governed by a Fokker-Planck equation. Using a spiking model with periodic boundary conditions, we write the Fokker-Planck dynamics in a Fourier basis. We find that the lowest Fourier modes dominate the dynamics.
Chapter 5 presents a novel rate model that successfully captures synchronous dynamics. As in the previous chapter, we invoke an approximation to the dynamics of a population of spiking neurons in order to develop a firing-rate model. Our approach derives from an eigenfunction expansion of a Fokker-Planck equation, which is a common approach to solving such problems. We find that a very simple approximation turns out to be surprisingly accurate. This approximation allows us to write a closed-form expression for the firing rate that resembles the equations for a damped harmonic oscillator.
Finally, chapter 6 uses the formalism derived in the previous chapter to analyze activity in a large randomly-connected network of neurons. Comparing this large spiking network to a network of two coupled rate units, we find that the firing rate network gives a good approximation to the time-varying activity of a spiking network across a wide range of parameters. Perhaps most surprisingly, we also find that the rate network can approximate the phase diagram of the spiking network, predicting the bifurcation line between synchronous and asynchronous states.Neurosciences, Mathematics, Biophysics, Neural networks (Neurobiology), Transients (Dynamics), Neural circuitryNeurobiology and BehaviorThesesExpansion of a filtration with a stochastic process: a high frequency trading perspective
https://academiccommons.columbia.edu/catalog/ac:tb2rbnzs9t
Neufcourt, Léo10.7916/D8571QKPFri, 13 Oct 2017 22:18:55 +0000A theory of expansion of filtrations has been developed since the 1970s to model dynamic probabilistic problems with asymmetric information. It has found a special echo in mathematical finance around the concept of insider trading, which has appeared in return very convenient for expressing the abstract properties of augmentations of filtrations. Research has historically focused on two particular classes of expansions, initial and progressive expansions, corresponding to additional information generated respectively by a random variable and a random time. Although they can reproduce some stylized facts in the insider trading paradigm, those two types of expansions are too restrictive to model quantitatively dynamic phenomenons of contemporary interest such as the topical high-frequency trading. In order to model such a continuous flow of information Kchia and Protter (2015) introduce augmentations of filtrations where the additional information is generated by a stochastic process.
This thesis complements the pioneering work of Kchia and Protter (2015) with an analysis of the information drift appearing in the transformation of semimartingales, which leads to a quantitative valuation of the additional information. In the preliminary chapters we introduce the general framework of expansions of filtrations and present the information drift as a key proxy to the value of information by characterizing its existence as a no-arbitrage condition and expressing problems the value increase of optimization problems associated with additional information as one of its integrals. The theoretical core of this thesis is formed by two series of convergence theorems for semimartingales and their information drifts under a new topology on filtrations, from which we derive the transformation of semimartingales when the filtration is augmented with a stochastic process as well as a computational method to estimate the information drift. We finally study several dynamical examples of anticipative expansions of a Brownian filtration with stochastic processes, where the information drift does or does not exist, and set the foundations for an ongoing application to estimating the advantage of high-frequency traders on the general market.Statistics, Mathematics, Financeln2294StatisticsThesesInteger programming techniques for Polynomial Optimization
https://academiccommons.columbia.edu/catalog/ac:p8cz8w9gm0
Munoz, Gonzalo10.7916/D82F812GFri, 13 Oct 2017 22:18:27 +0000Modern problems arising in many domains are driving a need for more capable, state-of-the-art optimization tools. A sharp focus on performance and accuracy has appeared, for example, in science and engineering applications. In particular, we have seen a growth in studies related to Polynomial Optimization: a field with beautiful and deep theory, offering flexibility for modeling and high impact in diverse areas.
The understanding of structural aspects of the feasible sets in Polynomial Optimization, mainly studied in Real Algebraic Geometry, has a long tradition in Mathematics and it has recently acquired increased computational maturity, opening the gate for new Optimization methodologies to be developed. The celebrated hierarchies due to Lasserre, for example, emerged as good algorithmic templates. They allow the representation of semi-algebraic sets, possibly non-convex, through convex sets in lifted spaces, thus enabling the use of long-studied Convex Optimization methods. Nonetheless, there are some computational drawbacks for these approaches: they often rely on possibly large semidefinite programs, and due to scalability and numerical issues associated with SDPs, alternatives and complements are arising.
In this dissertation, we will explore theoretical and practical Integer-Programming-based techniques for Polynomial Optimization problems. We first present a Linear Programming relaxation for the AC-OPF problem in Power Systems, a non-convex quadratic problem, and show how such relaxation can be used to develop a tractable MIP-based algorithm for the AC Transmission Switching problem. From a more theoretical perspective, and motivated by the AC-OPF problem, we study how sparsity can be exploited as a tool for analysis of the fundamental complexity of a Polynomial Optimization problem, by showing LP formulations that can efficiently approximate sparse polynomial problems. Finally, we show a computationally practical approach for constructing strong LP approximations on-the-fly, using cutting plane approaches. We will show two different frameworks that can generate cutting planes, which are based on classical methods used in Mixed-Integer Programming.
Our methods mainly rely on the maturity of current MIP technology; we believe these contributions are important for the development of manageable approaches to general Polynomial Optimization problems.Operations research, Mathematics, Polynomials, Integer programming, Mathematical optimizationgm2543Industrial Engineering and Operations ResearchThesesA unified view of high-dimensional bridge regression
https://academiccommons.columbia.edu/catalog/ac:3xsj3tx96j
Weng, Haolei10.7916/D82V2THPTue, 15 Aug 2017 22:36:12 +0000In many application areas ranging from bioinformatics to imaging, we are interested in recovering a sparse coefficient in the high-dimensional linear model, when the sample size n is comparable to or less than the dimension p. One of the most popular classes of estimators is the Lq-regularized least squares (LQLS), a.k.a. bridge regression. There have been extensive studies towards understanding the performance of the best subset selection (q=0), LASSO (q=1) and ridge (q=2), three widely known estimators from the LQLS family. This thesis aims at giving a unified view of LQLS for all the non-negative values of q. In contrast to most existing works which obtain order-wise error bounds with loose constants, we derive asymptotically exact error formulas characterized through a series of fixed point equations. A delicate analysis of the fixed point equations enables us to gain fruitful insights into the statistical properties of LQLS across the entire spectrum of Lq-regularization. Our work not only validates the scope of folklore understanding of Lq-minimization, but also provides new insights into high-dimensional statistics as a whole. We will elaborate on our theoretical findings mainly from parameter estimation point of view. At the end of the thesis, we briefly mention bridge regression for variable selection and prediction.
We start by considering the parameter estimation problem and evaluate the performance of LQLS by characterizing the asymptotic mean square error (AMSE). The expression we derive for AMSE does not have explicit forms and hence is not useful in comparing LQLS for different values of q, or providing information in evaluating the effect of relative sample size n/p or the sparsity level of the coefficient. To simplify the expression, we first perform the phase transition (PT) analysis, a widely accepted analysis diagram, of LQLS. Our results reveal some of the limitations and misleading features of the PT framework. To overcome these limitations, we propose the small-error analysis of LQLS. Our new analysis framework not only sheds light on the results of the phase transition analysis, but also describes when phase transition analysis is reliable, and presents a more accurate comparison among different Lq-regularizations.
We then extend our low noise sensitivity analysis to linear models without sparsity structure. Our analysis, as a generalization of phase transition analysis, reveals a clear picture of bridge regression for estimating generic coefficients. Moreover, by a simple transformation we connect our low-noise sensitivity framework to the classical asymptotic regime in which n/p goes to infinity, and give some insightful implications beyond what classical asymptotic analysis of bridge regression can offer.
Furthermore, following the same idea of the new analysis framework, we are able to obtain an explicit characterization of AMSE in the form of second-order expansions under the large noise regime. The expansions provide us some intriguing messages. For example, ridge will outperform LASSO in terms of estimating sparse coefficients when the measurement noise is large.
Finally, we present a short analysis of LQLS, for the purpose of variable selection and prediction. We propose a two-stage variable selection technique based on the LQLS estimators, and describe its superiority and close connection to parameter estimation. For prediction, we illustrate the intricate relation between the tuning parameter selection for optimal in-sample prediction and optimal parameter estimation.Statistics, Regression analysis, Mathematicshw2375StatisticsThesesEssays on Aggregation in Deliberation and Inquiry
https://academiccommons.columbia.edu/catalog/ac:1vhhmgqnkw
Stewart, Rush T.10.7916/D8J67VC0Fri, 04 Aug 2017 16:15:51 +0000Mathematical aggregation frameworks are general and precise settings in which to study ways of forming a consensus or group point of view from a set of potentially diverse points of view. Yet the standard frameworks have significant limitations. A number of results show that certain sets of desirable aggregation properties cannot be simultaneously satisfied. Drawing on work in the theory of imprecise probabilities, I propose philosophically-motivated generalizations of the standard aggregation frameworks (for probability, preference, full belief) that I prove can satisfy the desired properties. I then look at some applications and consequences of these proposals in decision theory, epistemology, and the social sciences.Philosophy, Science--Philosophy, Mathematics, Group decision makingrts2121PhilosophyThesesOptimal Dynamic Strategies for Index Tracking and Algorithmic Trading
https://academiccommons.columbia.edu/catalog/ac:xwdbrv15h9
Ward, Brian Michael10.7916/D82F80R1Fri, 21 Jul 2017 19:11:27 +0000In this thesis we study dynamic strategies for index tracking and algorithmic trading. Tracking problems have become ever more important in Financial Engineering as investors seek to precisely control their portfolio risks and exposures over different time horizons. This thesis analyzes various tracking problems and elucidates the tracking errors and strategies one can employ to minimize those errors and maximize profit.
In Chapters 2 and 3, we study the empirical tracking properties of exchange traded funds (ETFs), leveraged ETFs (LETFs), and futures products related to spot gold and the Chicago Board Option Exchange (CBOE) Volatility Index (VIX), respectively. These two markets provide interesting and differing examples for understanding index tracking. We find that static strategies work well in the nonleveraged case for gold, but fail to track well in the corresponding leveraged case. For VIX, tracking via neither ETFs, nor futures portfolios succeeds, even in the nonleveraged case. This motivates the need for dynamic strategies, some of which we construct in these two chapters and further expand on in Chapter 4. There, we analyze a framework for index tracking and risk exposure control through financial derivatives. We derive a tracking condition that restricts our exposure choices and also define a slippage process that characterizes the deviations from the index over longer horizons. The framework is applied to a number of models, for example, Black-Scholes model and Heston model for equity index tracking, as well as the Square Root (SQR) model and the Concatenated Square Root (CSQR) model for VIX tracking. By specifying how each of these models fall into our framework, we are able to understand the tracking errors in each of these models.
Finally, Chapter 5 analyzes a tracking problem of a different kind that arises in algorithmic trading: schedule following for optimal execution. We formulate and solve a stochastic control problem to obtain the optimal trading rates using both market and limit orders. There is a quadratic terminal penalty to ensure complete liquidation as well as a trade speed limiter and trader director to provide better control on the trading rates. The latter two penalties allow the trader to tailor the magnitude and sign (respectively) of the optimal trading rates. We demonstrate the applicability of the model to following a benchmark schedule. In addition, we identify conditions on the model parameters to ensure optimality of the controls and finiteness of the associated value functions. Throughout the chapter, numerical simulations are provided to demonstrate the properties of the optimal trading rates.Operations research, Mathematics, Finance, Financial engineeringbmw2150Industrial Engineering and Operations ResearchThesesWave dynamics in locally periodic structures by multiscale analysis
https://academiccommons.columbia.edu/catalog/ac:stqjq2bvsf
Watson, Alexander Bruce10.7916/D89W0SSMFri, 21 Jul 2017 19:11:16 +0000We study the propagation of waves in spatially non-homogeneous media focusing on Schrodinger’s equation of quantum mechanics and Maxwell’s equations of electromagnetism. We assume that medium variation occurs over two distinct length scales: a short ‘fast’ scale with respect to which the variation is periodic, and a long ‘slow’ scale over which the variation is smooth. Let epsilon denote the ratio of these scales. We focus primarily on the time evolution of asymptotic solutions (as epsilon tends to zero) known as semiclassical wavepackets. Such solutions generalize exact time-dependent Gaussian solutions and ideas of Heller and Hagedorn to periodic media. Our results are as follows:
1) To leading order in epsilon and up to the ‘Ehrenfest’ time-scale t ~ log 1/epsilon, the center of mass and average (quasi-)momentum of the semiclassical wavepacket satisfy the equations of motion of the classical Hamiltonian given by the wavepacket’s Bloch band energy. Our first result is to derive all corrections to these dynamics proportional to epsilon. These corrections consist of terms proportional to the Bloch band’s Berry curvature and terms which describe coupling to the evolution of the wavepacket envelope. These results rely on the assumption that the wavepacket’s Bloch band energy is non-degenerate.
2) We then consider the case where, in one spatial dimension, a semiclassical wavepacket is incident on a Bloch band crossing, a point in phase space where the wavepacket’s Bloch band energy is degenerate. By a rigorous matched asymptotic analysis, we show that at the time the wavepacket meets the crossing point a second wavepacket, associated with the other Bloch band involved in the crossing, is excited. Our result can be seen as a rigorous justification of the Landau-Zener formula in this setting.
3) Our final result generalizes the recent work of Fefferman, Lee-Thorp, and Weinstein on one-dimensional ‘edge’ states. We characterize the bound states of a Schrodinger operator with a periodic potential perturbed by multiple well-separated domain wall ‘edge’ modulations, by proving a theorem on the near zero eigenstates of an emergent Dirac operator.Mathematics, Wave mechanics, Condensed matter, Quantum theoryaw2645Applied Physics and Applied MathematicsThesesLong Time Propagation of Stochasticity by Dynamical Polynomial Chaos Expansions
https://academiccommons.columbia.edu/catalog/ac:r4xgxd256c
Ozen, Hasan Cagan10.7916/D8WH32C5Tue, 11 Jul 2017 16:09:43 +0000Stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) play an important role in many areas of engineering and applied sciences such as atmospheric sciences, mechanical and aerospace engineering, geosciences, and finance. Equilibrium statistics and long-time solutions of these equations are pertinent to many applications. Typically, these models contain several uncertain parameters which need to be propagated in order to facilitate uncertainty quantification and prediction. Correspondingly, in this thesis, we propose a generalization of the Polynomial Chaos (PC) framework for long-time solutions of SDEs and SPDEs driven by Brownian motion forcing.
Polynomial chaos expansions (PCEs) allow us to propagate uncertainties in the coefficients of these equations to the statistics of their solutions. Their main advantages are: (i) they replace stochastic equations by systems of deterministic equations; and (ii) they provide fast convergence. Their main challenge is that the computational cost becomes prohibitive when the dimension of the parameters modeling the stochasticity is even moderately large. In particular, for equations with Brownian motion forcing, the long-time simulation by PC-based methods is notoriously difficult as the dimension of stochastic variables increases with time.
With the goal in mind to deliver computationally efficient numerical algorithms for stochastic equations in the long time, our main strategy is to leverage the intrinsic sparsity in the dynamics by identifying the influential random parameters and construct spectral approximations to the solutions in terms of those relevant variables. Once this strategy is employed dynamically in time, using online constructions, approximations can retain their sparsity and accuracy; even for long times. To this end, exploiting Markov property of Brownian motion, we present a restart procedure that allows PCEs to expand the solutions at future times in terms of orthogonal polynomials of the measure describing the solution at a given time and the future Brownian motion. In case of SPDEs, the Karhunen-Loeve expansion (KLE) is applied at each restart to select the influential variables and keep the dimensionality minimal. Using frequent restarts and low degree polynomials, the algorithms are able to capture long-time solutions accurately. We will also introduce, using the same principles, a similar algorithm based on a stochastic collocation method for the solutions of SDEs.
We apply the methods to the numerical simulation of linear and nonlinear SDEs, and stochastic Burgers and Navier-Stokes equations with white noise forcing. Our methods also allow us to incorporate time-independent random coefficients such as a random viscosity. We propose several numerical simulations, and show that the algorithms compare favorably with standard Monte Carlo methods in terms of accuracy and computational times. To demonstrate the efficiency of the algorithms for long-time simulations, we compute invariant measures of the solutions when they exist.Mathematics, Stochastic differential equations, Algorithmshco2104Applied Physics and Applied MathematicsThesesUser association for energy harvesting relay stations in cellular networks
https://academiccommons.columbia.edu/catalog/ac:196929
Wang, Zhe; Wang, Xiaodong; Aldiab, Motasem; Jaber, Tareq10.7916/D89886X6Fri, 30 Jun 2017 00:46:00 +0000We consider a cellular wireless network enhanced by relay stations that are powered by renewable energy sources. Such a network consists of the macro base stations (BS), relay stations (RSs), and many mobile stations (MSs). In addition to the traditional data/voice transmission between the BS and the MSs, a higher service tier may be provided by using the energy harvesting RSs for some MSs. We propose a network scenario utilizing the energy harvesting relay stations to improve the service quality without taking the additional licensed frequency band and transmission power, and design a user association algorithm for the energy harvesting RSs in such a network. The goal is to assign each MS an RS for relaying its signal to minimize the probability of the relay service outage, i.e, the probability that an MS’s relay service request is rejected. First, we propose a network scenario and develop a mathematical model to estimate the rejection probability for a given user association. We then propose a low-complexity local search algorithm, which balances the computational complexity and the performance, to obtain a locally optimal user association. Simulation results are provided to demonstrate the superior performance of the proposed techniques over the traditional methods.Wireless communication systems, Energy harvesting, Mobile radio stations, Radio relay systems, Electrical engineering, Mathematicszw2168, xw2008Electrical EngineeringArticlesReconstruction of novel transcription factor regulons through inference of their binding sites
https://academiccommons.columbia.edu/catalog/ac:196938
Elmas, Abdulkadir; Wang, Xiaodong; Samoilov, Michael S.10.7916/D8K07469Fri, 30 Jun 2017 00:44:01 +0000Background
In most sequenced organisms the number of known regulatory genes (e.g., transcription factors (TFs)) vastly exceeds the number of experimentally-verified regulons that could be associated with them. At present, identification of TF regulons is mostly done through comparative genomics approaches. Such methods could miss organism-specific regulatory interactions and often require expensive and time-consuming experimental techniques to generate the underlying data.
Results
In this work, we present an efficient algorithm that aims to identify a given transcription factor’s regulon through inference of its unknown binding sites, based on the discovery of its binding motif. The proposed approach relies on computational methods that utilize gene expression data sets and knockout fitness data sets which are available or may be straightforwardly obtained for many organisms. We computationally constructed the profiles of putative regulons for the TFs LexA, PurR and Fur in E. coli K12 and identified their binding motifs. Comparisons with an experimentally-verified database showed high recovery rates of the known regulon members, and indicated good predictions for the newly found genes with high biological significance. The proposed approach is also applicable to novel organisms for predicting unknown regulons of the transcriptional regulators. Results for the hypothetical protein D d e0289 in D. alaskensis include the discovery of a Fis-type TF binding motif.
Conclusions
The proposed motif-based regulon inference approach can discover the organism-specific regulatory interactions on a single genome, which may be missed by current comparative genomics techniques due to their limitations.Comparative genomics, Bioinformatics, Genomics--Data processing, Computational biology, Transcription factors, Electrical engineering, Genetics, Molecular biology, Mathematicsae2321, xw2008Electrical EngineeringArticlesWave-induced light field fluctuations in measured irradiance depth profiles: A wavelet analysis
https://academiccommons.columbia.edu/catalog/ac:194415
Wei, Jianwei; Lewis, Marlon R.; Dommelen, Ronnie Van; Zappa, Christopher J.; Twardowski, Michael S.10.7916/D8862G95Fri, 30 Jun 2017 00:42:59 +0000Rapid variations in the intensities of light are commonly observed in profiles of downwelling plane irradiance in the ocean. These fluctuations are often treated as noise and filtered out. Here an effort is made to extract the pertinent statistics to quantify the light field fluctuations from vertical profiles of irradiance measured under clear skies. The irradiance data are collected in oceanic and coastal waters using a traditional free-fall downwelling plane irradiance sensor. The irradiance profiles are transformed into time-frequency domain with a wavelet technique. Two signatures including the dominant frequency (<3.5 Hz) and the coefficient of variation of irradiance fluctuations along the water column are identified from the variance spectrum. Both the dominant frequency and the amplitude decrease as the inverse square root of depth, consistent with simple models of wave focusing and data from other studies. Mechanisms contributing to the observed variations and the observational uncertainties are discussed.Wavelets (Mathematics), Analysis of variance, Spectral irradiance, Oceanography, Mathematicscjz9Lamont-Doherty Earth ObservatoryArticlesOptical measurements of small deeply penetrating bubble populations generated by breaking waves in the Southern Ocean
https://academiccommons.columbia.edu/catalog/ac:194418
Randolph, Kaylan; Dierssen, Heidi M.; Twardowski, Michael; Cifuentes-Lorenzen, Alejandro; Zappa, Christopher J.10.7916/D80P0ZVQFri, 30 Jun 2017 00:42:27 +0000Bubble size distributions ranging from 0.5 to 125 μm radius were measured optically during high winds of 13 m s−1 and large-scale wave breaking as part of the Southern Ocean Gas Exchange Experiment. Very small bubbles with radii less than 60 µm were measured at 6–9 m depth using optical measurements of the near-forward volume scattering function and critical scattering angle for bubbles (∼80°). The bubble size distributions generally followed a power law distribution with mean slope values ranging from 3.6 to 4.6. The steeper slopes measured here were consistent with what would be expected near the base of the bubble plume. Bubbles, likely stabilized with organic coatings, were present for time periods on the order of 10–100 s at depths of 6–9 m. Here, relatively young seas, with an inverse wave age of approximately 0.88 and shorter characteristic wave scales, produced lower bubble concentrations, shallower bubble penetration depths, and steep bubble size distribution slopes. Conversely, older seas, with an inverse wave age of 0.70 and longer characteristic wave scales, produced relatively higher bubble concentrations penetrating to 15 m depth, larger bubble sizes, and shallower bubble size distribution slopes. When extrapolated to 4 m depth using a previously published bubble size distribution, our estimates suggest that the deeply penetrating small bubbles measured in the Southern Ocean supplied ∼36% of the total void fraction and likely contributed to the transfer and supersaturation of low-solubility gases.Ocean-atmosphere interaction, Optical measurements, Bubbles, Oceanography, Mathematics, Hydrologycjz9Lamont-Doherty Earth ObservatoryArticlesA parameter model of gas exchange for the seasonal sea ice zone
https://academiccommons.columbia.edu/catalog/ac:194400
Loose, B.; McGillis, Wade R.; Perovich, D.; Zappa, Christopher J.; Schlosser, Peter10.7916/D81N810BFri, 30 Jun 2017 00:42:13 +0000Carbon budgets for the polar oceans require better constraint on air–sea gas exchange in the sea ice zone (SIZ). Here, we utilize advances in the theory of turbulence, mixing and air–sea flux in the ice–ocean boundary layer (IOBL) to formulate a simple model for gas exchange when the surface ocean is partially covered by sea ice. The gas transfer velocity (k) is related to shear-driven and convection-driven turbulence in the aqueous mass boundary layer, and to the mean-squared wave slope at the air–sea interface. We use the model to estimate k along the drift track of ice-tethered profilers (ITPs) in the Arctic. Individual estimates of daily-averaged k from ITP drifts ranged between 1.1 and 22 m d−1, and the fraction of open water (f) ranged from 0 to 0.83. Converted to area-weighted effective transfer velocities (keff), the minimum value of keff was 10−55 m d−1 near f = 0 with values exceeding keff = 5 m d−1 at f = 0.4. The model indicates that effects from shear and convection in the sea ice zone contribute an additional 40% to the magnitude of keff, beyond what would be predicted from an estimate of keff based solely upon a wind speed parameterization. Although the ultimate scaling relationship for gas exchange in the sea ice zone will require validation in laboratory and field studies, the basic parameter model described here demonstrates that it is feasible to formulate estimates of k based upon properties of the IOBL using data sources that presently exist.Ocean-atmosphere interaction, Atmospheric turbulence--Mathematical models, Sea ice, Oceanography, Mathematics, Meteorologywrm2102, cjz9, ps10Lamont-Doherty Earth Observatory, Earth and Environmental Engineering, Earth and Environmental SciencesArticlesA Note on the Phillips Spectral Framework for Ocean Whitecaps
https://academiccommons.columbia.edu/catalog/ac:194403
Banner, Michael L.; Zappa, Christopher J.; Gemmrich, Johannes R.10.7916/D8S46RTPFri, 30 Jun 2017 00:42:03 +0000There has been a recent upsurge in interest in quantifying kinematic, dynamic, and energetic properties of wave breaking in the open ocean, especially in severe sea states. The underpinning observational and modeling framework is provided by the seminal paper of O. M. Phillips. In this note, a fundamental issue contributing to the scatter in results between investigators is highlighted. This issue relates to the choice of the independent variable used in the expression for the spectral density of the mean breaking crest length per unit area. This note investigates the consequences of the different choices of independent variable presently used by various investigators for validating Phillips model predictions for the spectral density of the breaking crest length per unit area and the associated spectral breaking strength coefficient. These spectral measures have a central role in inferring the associated turbulent kinetic energy dissipation rate and the momentum flux to the upper ocean from breaking wave observations.Turbulence, Oceanography--Remote sensing, Ocean circulation, Wind waves--Mathematical models, Oceanography, Mathematics, Meteorologymlb2121, cjz9Lamont-Doherty Earth ObservatoryArticlesAnalyzing the footprints of near-surface aqueous turbulence: An image processing-based approach
https://academiccommons.columbia.edu/catalog/ac:194439
Schnieders, J.; Garbe, C. S.; Peirson, W. L.; Smith, G. B.; Zappa, Christopher J.10.7916/D8P84BRHFri, 30 Jun 2017 00:41:52 +0000In this contribution, a detailed investigation of surface thermal patterns on the water surface is presented, with wind speeds ranging from 1 to 7 m s − 1 and various surface conditions. Distinct structures can be observed on the surface—small-scale short-lived structures termed fish scales and larger-scale cold streaks that are consistent with the footprints of Langmuir circulations. The structure of the surface heat pattern depends strongly on wind-induced stress. Consistent behavior regarding the spacing of cold streaks can be observed in a range of laboratory facilities when expressed as a function of water-sided friction velocity, u * . This behavior systematically decreased until a point of saturation at u * = 0.7 cm/s. We present a new image processing-based approach to the analysis of the spacing of cold streaks based on a machine learning approach to classify the thermal footprints of near-surface turbulence. Comparison is made with studies of Langmuir circulation and the following key points are found. Results suggest a saturation in the tangential stress, anticipating that similar behavior will be observed in the open ocean. A relation to Langmuir numbers shows that thermal footprints in infrared images are consistent with Langmuir circulations and depend strongly on wind wave conditions.Turbulence--Mathematical models, Image processing--Data processing, Ocean circulation--Data processing, Surface waves (Oceanography), Oceanography, Mathematics, Hydrologycjz9Lamont-Doherty Earth ObservatoryArticlesWave breaking in developing and mature seas
https://academiccommons.columbia.edu/catalog/ac:194433
Gemmrich, Johannes; Zappa, Christopher J.; Banner, Michael L.; Morison, Russel P.10.7916/D8668D1DFri, 30 Jun 2017 00:41:31 +0000In response to the growing need for robust validation data for Phillips (1985) breaking wave spectral framework, we contribute new field results observed from R/P FLIP for the breaking crest length distributions, Λ, during two different wind-wave conditions, and breaking strength during one wind-wave condition. The first experiment in Santa Barbara Channel had developing seas and the second experiment in the central Pacific Ocean south of Hawaii had mature seas. These are among the first experiments to use dissipation rate measurements probing up into the breaking crest together with simultaneous measurements of breaking crest length distributions. We directly measured the effective breaking strength parameter to be inline image in mature seas with wave age, inline image, of 40–47. We also found that the velocity scale of the breaking dissipation rate peak decreases with increasing wave age. Further, the breaking crest length spectrum falls off slower than the inline image behavior predicted by Phillips (1985). The integrated dissipation rate was consistently higher for mature seas compared to developing seas due to higher energy and momentum fluxes from the wind.Surface waves (Oceanography), Wind waves--Mathematical models, Ocean-atmosphere interaction, Oceanography, Mathematics, Hydrologycjz9, mlb2121Lamont-Doherty Earth ObservatoryArticlesIntroduction to special section on Recent Advances in the Study of Optical Variability in the Near-Surface and Upper Ocean
https://academiccommons.columbia.edu/catalog/ac:194448
Dickey, T.; Banner, M. L.; Bhandari, P.; Boyd, T.; Carvalho, L.; Chang, G.; Chao, Y.; Czerski, H.; Darecki, M.; Dong, C.; Farmer, D.; Freeman, S.; Gemmrich, J.; Gernez, P.; Hall-Patch, N.; Holt, B.; Jiang, S.; Jones, C.; Kattawar, G.; LeBel, D.; Lenain, L.; Lewis, M.; Liu, Y.; Logan, L.; Manov, D.; Melville, W. K.; Moline, M. A.; Morison, R.; Nencioli, F.; Pegau, W. S.; Reineman, B.; Robbins, I.; Röttgers, R.; Schultz, H.; Shen, L.; Shinki, M.; Slivkoff, M.; Sokólski, M.; Spada, F.; Statom, N.; Stramski, D.; Sutherland, P.; Twardowski, M.; Vagle, S.; Van Dommelen, R.; Voss, K.; Washburn, L.; Wei, J.; Wijesekera, H.; Wurl, O.; Yang, D.; Yildiz, S.; You, Y.; Yue, D. K. P.; Zaneveld, R.; Zappa, Christopher J.10.7916/D8WS8T4SFri, 30 Jun 2017 00:41:04 +0000Optical variability occurs in the near-surface and upper ocean on very short time and space scales (e.g., milliseconds and millimeters and less) as well as greater scales. This variability is caused by solar, meteorological, and other physical forcing as well as biological and chemical processes that affect optical properties and their distributions, which in turn control the propagation of light across the air-sea interface and within the upper ocean. Recent developments in several technologies and modeling capabilities have enabled the investigation of a variety of fundamental and applied problems related to upper ocean physics, chemistry, and light propagation and utilization in the dynamic near-surface ocean. The purpose here is to provide background for and an introduction to a collection of papers devoted to new technologies and observational results as well as model simulations, which are facilitating new insights into optical variability and light propagation in the ocean as they are affected by changing atmospheric and oceanic conditions.Analysis of variance, Optical measurements, Surface waves (Oceanography), Oceanography, Mathematics, Hydrologycjz9Lamont-Doherty Earth ObservatoryArticlesStatistics of surface divergence and their relation to air-water gas transfer velocity
https://academiccommons.columbia.edu/catalog/ac:194442
Asher, William E.; Liang, Hanzhuang; Zappa, Christopher J.; Loewen, Mark R.; Mukto, Moniz A.; Litchendorf, Trina M.; Jessup, Andrew T.10.7916/D8571BVQFri, 30 Jun 2017 00:40:37 +0000Air-sea gas fluxes are generally defined in terms of the air/water concentration difference of the gas and the gas transfer velocity,kL. Because it is difficult to measure kLin the ocean, it is often parameterized using more easily measured physical properties. Surface divergence theory suggests that infrared (IR) images of the water surface, which contain information concerning the movement of water very near the air-water interface, might be used to estimatekL. Therefore, a series of experiments testing whether IR imagery could provide a convenient means for estimating the surface divergence applicable to air-sea exchange were conducted in a synthetic jet array tank embedded in a wind tunnel. Gas transfer velocities were measured as a function of wind stress and mechanically generated turbulence; laser-induced fluorescence was used to measure the concentration of carbon dioxide in the top 300 μm of the water surface; IR imagery was used to measure the spatial and temporal distribution of the aqueous skin temperature; and particle image velocimetry was used to measure turbulence at a depth of 1 cm below the air-water interface. It is shown that an estimate of the surface divergence for both wind-shear driven turbulence and mechanically generated turbulence can be derived from the surface skin temperature. The estimates derived from the IR images are compared to velocity field divergences measured by the PIV and to independent estimates of the divergence made using the laser-induced fluorescence data. Divergence is shown to scale withkLvalues measured using gaseous tracers as predicted by conceptual models for both wind-driven and mechanically generated turbulence.Ocean-atmosphere interaction, Divergence theorem, Gas flow--Mathematical models, Surface waves (Oceanography), Oceanography, Mathematics, Statisticscjz9Lamont-Doherty Earth ObservatoryArticlesSea surface pCO2 and O2 in the Southern Ocean during the austral fall, 2008
https://academiccommons.columbia.edu/catalog/ac:194451
Moore, T. S.; DeGrandpre, M. D.; Sabine, C. L.; Hamme, R. C.; Zappa, Christopher J.; McGillis, Wade R.; Feely, R. A.; Drennan, W. M.10.7916/D8CR5T6JFri, 30 Jun 2017 00:40:35 +0000The physical and biological processes controlling surface mixed layer pCO2 and O2 were evaluated using in situ sensors mounted on a Lagrangian drifter deployed in the Atlantic sector of the Southern Ocean (∼50°S, ∼37°W) during the austral fall of 2008. The drifter was deployed three times during different phases of the study. The surface ocean pCO2 was always less than atmospheric pCO2 (−50.4 to −76.1 μatm), and the ocean was a net sink for CO2 with fluxes averaging between 16.2 and 17.8 mmol C m−2 d−1. Vertical entrainment was the dominant process controlling mixed layer CO2, with fluxes that were 1.8 to 2.2 times greater than the gas exchange fluxes during the first two drifter deployments, and was 1.7 times greater during the third deployment. In contrast, during the first two deployments the surface mixed layer was always a source of O2 to the atmosphere, and air-sea gas exchange was the dominant process occurring, with fluxes that were 2.0 to 4.1 times greater than the vertical entrainment flux. During the third deployment O2 was near saturation the entire deployment and was a small source of O2 to the atmosphere. Net community production (NCP) was low during this study, with mean fluxes of 3.2 to 6.4 mmol C m−2 d−1 during the first deployment and nondetectable (within uncertainty) in the third. During the second deployment the NCP was not separable from lateral advection. Overall, this study indicates that in the early fall the area is a significant sink for atmospheric CO2.Atmospheric carbon dioxide--Measurement, Chemical oceanography--Data processing, Oceanography, Mathematics, Hydrologycjz9, wrm2102Lamont-Doherty Earth ObservatoryArticlesPolarized light field under dynamic ocean surfaces: Numerical modeling compared with measurements
https://academiccommons.columbia.edu/catalog/ac:194463
You, Yu; Kattawar, George W.; Voss, Kenneth J.; Bhandari, Purushottam; Wei, Jianwei; Lewis, Marlon; Zappa, Christopher J.; Schultz, Howard10.7916/D8TT4QS8Fri, 30 Jun 2017 00:40:17 +0000As part of the Radiance in a Dynamic Ocean (RaDyO) program, we have developed a numerical model for efficiently simulating the polarized light field under highly dynamic ocean surfaces. Combining the advantages of the three-dimensional Monte Carlo and matrix operator methods, this hybrid model has proven to be computationally effective for simulations involving a dynamic air-sea interface. Given water optical properties and ocean surface wave slopes obtained from RaDyO field measurements, model-simulated radiance and polarization fields under a dynamic surface are found to be qualitatively comparable to their counterparts from field measurements and should be quantitatively comparable if the light field measurement and the wave slope/water optical property measurements are appropriately collocated and synchronized. This model serves as a bridge to connect field measurements of water optical properties, wave slopes and polarized light fields. It can also be used as a powerful yet convenient tool to predict the temporal underwater polarized radiance in a real-world situation. When appropriate surface measurements are available, model simulation is shown to reveal more dynamic features in the underwater light field than direct measurements.Polarization (Light)--Measurement, Ocean surface topography, Underwater light--Measurement, Brightness temperature, Oceanography, Mathematicscjz9Lamont-Doherty Earth ObservatoryArticlesDirect covariance measurement of CO2 gas transfer velocity during the 2008 Southern Ocean Gas Exchange Experiment: Wind speed dependency
https://academiccommons.columbia.edu/catalog/ac:194466
Edson, J. B.; Fairall, C. W.; Bariteau, L.; Zappa, Christopher J.; Cifuentes-Lorenzen, A.; McGillis, Wade R.; Pezoa, S.; Hare, J. E.; Helmig, D.10.7916/D8K937CCFri, 30 Jun 2017 00:40:08 +0000Direct measurements of air-sea heat, momentum, and mass (including CO2, DMS, and water vapor) fluxes using the direct covariance method were made over the open ocean from the NOAA R/V Ronald H. Brown during the Southern Ocean Gas Exchange (SO GasEx) program. Observations of fluxes and the physical processes associated with driving air-sea exchange are key components of SO GasEx. This paper focuses on the exchange of CO2 and the wind speed dependency of the transfer velocity, k, used to model the CO2 flux between the atmosphere and ocean. A quadratic dependence of k on wind speed based on dual tracer experiments is most frequently encountered in the literature. However, in recent years, bubble-mediated enhancement of k, which exhibits a cubic relationship with wind speed, has emerged as a key issue for flux parameterization in high-wind regions. Therefore, a major question addressed in SO GasEx is whether the transfer velocities obey a quadratic or cubic relationship with wind speed. After significant correction to the flux estimates (primarily due to moisture contamination), the direct covariance CO2 fluxes confirm a significant enhancement of the transfer velocity at high winds compared with previous quadratic formulations. Regression analysis suggests that a cubic relationship provides a more accurate parameterization over a wind speed range of 0 to 18 m s−1. The Southern Ocean results are in good agreement with the 1998 GasEx experiment in the North Atlantic and a recent separate field program in the North Sea.Ocean-atmosphere interaction--Measurement, Atmospheric carbon dioxide--Measurement, Winds--Speeds, Analysis of covariance, Oceanography, Mathematics, Atmospheric chemistrycjz9, wrm2102Lamont-Doherty Earth ObservatoryArticlesVariations in Ocean Surface Temperature due to Near-Surface Flow: Straining the Cool Skin Layer
https://academiccommons.columbia.edu/catalog/ac:194406
Wells, Andrew J.; Cenedese, Claudia; Farrar, J. Thomas; Zappa, Christopher J.10.7916/D8HQ3ZRHFri, 30 Jun 2017 00:39:24 +0000The aqueous thermal boundary layer near to the ocean surface, or skin layer, has thickness O(1 mm) and plays an important role in controlling the exchange of heat between the atmosphere and the ocean. Theoretical arguments and experimental measurements are used to investigate the dynamics of the skin layer under the influence of an upwelling flow, which is imposed in addition to free convection below a cooled water surface. Previous theories of straining flow in the skin layer are considered and a simple extension of a surface straining model is posed to describe the combination of turbulence and an upwelling flow. An additional theory is also proposed, conceptually based on the buoyancy-driven instability of a laminar straining flow cooled from above. In all three theories considered two distinct regimes are observed for different values of the Péclet number, which characterizes the ratio of advection to diffusion within the skin layer. For large Péclet numbers, the upwelling flow dominates and increases the free surface temperature, or skin temperature, to follow the scaling expected for a laminar straining flow. For small Péclet numbers, it is shown that any flow that is steady or varies over long time scales produces only a small change in skin temperature by direct straining of the skin layer. Experimental measurements demonstrate that a strong upwelling flow increases the skin temperature and suggest that the mean change in skin temperature with Péclet number is consistent with the theoretical trends for large Péclet number flow. However, all of the models considered consistently underpredict the measured skin temperature, both with and without an upwelling flow, possibly a result of surfactant effects not included in the models.Thermal boundary layer, Heat budget (Geophysics), Ocean temperature--Research, Oceanography, Mathematics, Hydrologycjz9Lamont-Doherty Earth ObservatoryArticlesSeamless Precipitation Prediction Skill in the Tropics and Extratropics from a Global Model
https://academiccommons.columbia.edu/catalog/ac:189235
Zhu, Hongyan; Wheeler, Matthew C.; Sobel, Adam H.; Hudson, Debra10.7916/D8JM2931Thu, 29 Jun 2017 17:08:46 +0000The skill with which a coupled ocean–atmosphere model is able to predict precipitation over a range of time scales (days to months) is analyzed. For a fair comparison across the seamless range of scales, the verification is performed using data averaged over time windows equal in length to the lead time. At a lead time of 1 day, skill is greatest in the extratropics around 40°–60° latitude and lowest around 20°, and has a secondary local maximum close to the equator. The extratropical skill at this short range is highest in the winter hemisphere, presumably due to the higher predictability of winter baroclinic systems. The local equatorial maximum comes mostly from the Pacific Ocean, and thus appears to be mostly from El Niño–Southern Oscillation (ENSO). As both the lead time and averaging window are simultaneously increased, the extratropical skill drops rapidly with lead time, while the equatorial maximum remains approximately constant, causing the equatorial skill to exceed the extratropical at leads of greater than 4 days in austral summer and 1 week in boreal summer. At leads longer than 2 weeks, the extratropical skill flattens out or increases, but remains below the equatorial values. Comparisons with persistence confirm that the model beats persistence for most leads and latitudes, including for the equatorial Pacific where persistence is high. The results are consistent with the view that extratropical predictability is mostly derived from synoptic-scale atmospheric dynamics, while tropical predictability is primarily derived from the response of moist convection to slowly varying forcing such as from ENSO.Precipitation forecasting, Mathematics, Meteorology, Atmosphereahs129Applied Physics and Applied Mathematics, Earth and Environmental Sciences, Lamont-Doherty Earth ObservatoryArticlesThe Downward Influence of Stratospheric Sudden Warmings
https://academiccommons.columbia.edu/catalog/ac:190045
Hitchcock, Peter; Simpson, Isla R.10.7916/D8PV6JWDThu, 29 Jun 2017 17:07:44 +0000The coupling between the stratosphere and the troposphere following two major stratospheric sudden warmings is studied in the Canadian Middle Atmosphere Model using a nudging technique by which the zonal-mean evolution of the reference sudden warmings are artificially induced in an ~100-member ensemble spun off from a control simulation. Both reference warmings are taken from a freely running integration of the model. One event is a displacement, the other is a split, and both are followed by extended recoveries in the lower stratosphere. The methodology permits a statistically robust study of their influence on the troposphere below.
The nudged ensembles exhibit a tropospheric annular mode response closely analogous to that seen in observations, confirming the downward influence of sudden warmings on the troposphere in a comprehensive model. This tropospheric response coincides more closely with the lower-stratospheric annular mode anomalies than with the midstratospheric wind reversal. In addition to the expected synoptic-scale eddy feedback, the planetary-scale eddies also reinforce the tropospheric wind changes, apparently responding directly to the stratospheric anomalies.
Furthermore, despite the zonal symmetry of the stratospheric perturbation, a highly zonally asymmetric near-surface response is produced, corresponding to a strongly negative phase of the North Atlantic Oscillation with a much weaker response over the Pacific basin that matches composites of sudden warmings from the Interim ECMWF Re-Analysis (ERA-Interim). Phase 5 of the Coupled Model Intercomparison Project models exhibit a similar response, though in most models the response’s magnitude is underrepresented.Meteorology, Atmosphere, Atmosphere, Upper, Mathematicsirs2113Lamont-Doherty Earth ObservatoryArticlesMoisture Modes and the Eastward Propagation of the MJO
https://academiccommons.columbia.edu/catalog/ac:189151
Sobel, Adam H.; Maloney, Eric D.10.7916/D8H70F82Thu, 29 Jun 2017 17:06:54 +0000The authors discuss modifications to a simple linear model of intraseasonal moisture modes. Wind–evaporation feedbacks were shown in an earlier study to induce westward propagation in an eastward mean low-level flow in this model. Here additional processes, which provide effective sources of moist static energy to the disturbances and which also depend on the low-level wind, are considered. Several processes can act as positive sources in perturbation easterlies: zonal advection (if the mean zonal moisture gradient is eastward), modulation of synoptic eddy drying by the MJO-scale wind perturbations, and frictional convergence. If the sum of these is stronger than the wind–evaporation feedback—as observations suggest may be the case, though with considerable uncertainty—the model produces unstable modes that propagate weakly eastward relative to the mean flow. With a small amount of horizontal diffusion or other scale-selective damping, the growth rate is greatest at the largest horizontal scales and decreases monotonically with wavenumber.Atmosphere, Mathematics, Meteorologyahs129Applied Physics and Applied Mathematics, Earth and Environmental Sciences, Lamont-Doherty Earth ObservatoryArticlesToward an Understanding of Vertical Momentum Transports in Cloud-System-Resolving Model Simulations of Multiscale Tropical Convection
https://academiccommons.columbia.edu/catalog/ac:189334
Shaw, Tiffany Ann; Lane, Todd P.10.7916/D8WD4016Thu, 29 Jun 2017 17:06:49 +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.Atmosphere, Mathematics, Atmosphere, Uppertas2163Earth and Environmental Sciences, Applied Physics and Applied MathematicsArticlesSimple scaling of catastrophic landslide dynamics
https://academiccommons.columbia.edu/catalog/ac:189139
Ekstrom, Goran; Stark, Colin P.10.7916/D8TQ610DThu, 29 Jun 2017 17:06:18 +0000Catastrophic landslides involve the acceleration and deceleration of millions of tons of rock and debris in response to the forces of gravity and dissipation. Their unpredictability and frequent location in remote areas have made observations of their dynamics rare. Through real-time detection and inverse modeling of teleseismic data, we show that landslide dynamics are primarily determined by the length scale of the source mass. When combined with geometric constraints from satellite imagery, the seismically determined landslide force histories yield estimates of landslide duration, momenta, potential energy loss, mass, and runout trajectory. Measurements of these dynamical properties for 29 teleseismogenic landslides are consistent with a simple acceleration model in which height drop and rupture depth scale with the length of the failing slope.Geology, Petrology, Mathematicsge21, cps13Lamont-Doherty Earth ObservatoryArticlesMoist Static Energy Budget of the MJO during DYNAMO
https://academiccommons.columbia.edu/catalog/ac:191146
Sobel, Adam H.; Wang, Shuguang; Kim, Daehyun10.7916/D8JS9PTCThu, 29 Jun 2017 16:37:20 +0000The authors analyze the column-integrated moist static energy budget over the region of the tropical Indian Ocean covered by the sounding array during the Cooperative Indian Ocean Experiment on Intraseasonal Variability in the Year 2011 (CINDY2011)/Dynamics of the Madden–Julian Oscillation (DYNAMO) field experiment in late 2011. The analysis is performed using data from the sounding array complemented by additional observational datasets for surface turbulent fluxes and atmospheric radiative heating. The entire analysis is repeated using the ECMWF Interim Re-Analysis (ERA-Interim). The roles of surface turbulent fluxes, radiative heating, and advection are quantified for the two MJO events that occurred in October and November using the sounding data; a third event in December is also studied in the ERA-Interim data.
These results are consistent with the view that the MJO’s moist static energy anomalies grow and are sustained to a significant extent by the radiative feedbacks associated with MJO water vapor and cloud anomalies and that propagation of the MJO is associated with advection of moist static energy. Both horizontal and vertical advection appear to play significant roles in the events studied here. Horizontal advection strongly moistens the atmosphere during the buildup to the active phase of the October event when the low-level winds switch from westerly to easterly. Horizontal advection strongly dries the atmosphere in the wake of the active phases of the November and December events as the westerlies associated with off-equatorial cyclonic gyres bring subtropical dry air into the convective region from the west and north. Vertical advection provides relative moistening ahead of the active phase and drying behind it, associated with an increase of the normalized gross moist stability.Atmospheric circulation, Madden-Julian oscillation, Atmosphere, Climatic changes, Mathematicsahs129, sw2526, dk2558Applied Physics and Applied MathematicsArticlesCloud Vertical Distribution across Warm and Cold Fronts in CloudSat–CALIPSO Data and a General Circulation Model
https://academiccommons.columbia.edu/catalog/ac:183326
Naud, Catherine M.; Del Genio, Anthony D.; Bauer, Mike; Kovari, William10.7916/D8BC3XC5Thu, 29 Jun 2017 03:39:46 +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.Climatic changes, Ecology, Mathematicscn2140, add1, mpb20, wk14Applied Physics and Applied Mathematics, Center for Climate Systems ResearchArticlesClustering on the Main Diagonal in Mobility Matrices
https://academiccommons.columbia.edu/catalog/ac:178652
Singer, Burton; Spilerman, Seymour10.7916/D8X63KJTThu, 29 Jun 2017 02:47:33 +0000In this paper we compare Markov, semi-Markov, and heterogeneity formulations. We demonstrate that the familiar phenomenon of clustering on the main diagonal is an inherent consequence of the structure of certain model types. Further, underprediction of the main diagonal elements should be associated with other kinds of stochastic models, beyond Markovian, that are also applicable to social processesSociology, Mathematicsss50SociologyArticlesDynamics of semiflexible polymers in a flow field
https://academiccommons.columbia.edu/catalog/ac:177471
Munk, Tobias; Hallatschek, Oskar; Wiggins, Chris H.; Frey, Erwin10.7916/D85M647VWed, 28 Jun 2017 21:10:36 +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.Mathematics, Bioinformaticschw2Applied Physics and Applied MathematicsArticlesGene regulatory network inference by point-based Gaussian approximation filters incorporating the prior information
https://academiccommons.columbia.edu/catalog/ac:194860
Jia, Bin; Wang, Xiaodong10.7916/D8833QGNWed, 28 Jun 2017 21:06:36 +0000The extended Kalman filter (EKF) has been applied to inferring gene regulatory networks. However, it is well known that the EKF becomes less accurate when the system exhibits high nonlinearity. In addition, certain prior information about the gene regulatory network exists in practice, and no systematic approach has been developed to incorporate such prior information into the Kalman-type filter for inferring the structure of the gene regulatory network. In this paper, an inference framework based on point-based Gaussian approximation filters that can exploit the prior information is developed to solve the gene regulatory network inference problem. Different point-based Gaussian approximation filters, including the unscented Kalman filter (UKF), the third-degree cubature Kalman filter (CKF3), and the fifth-degree cubature Kalman filter (CKF5) are employed. Several types of network prior information, including the existing network structure information, sparsity assumption, and the range constraint of parameters, are considered, and the corresponding filters incorporating the prior information are developed. Experiments on a synthetic network of eight genes and the yeast protein synthesis network of five genes are carried out to demonstrate the performance of the proposed framework. The results show that the proposed methods provide more accurate inference results than existing methods, such as the EKF and the traditional UKF.Gaussian distribution, Iterative methods (Mathematics), Kalman filtering, Gene regulatory networks, Bioinformatics, Biometry, Mathematicsxw2008Electrical EngineeringArticlesTime-dependent information transmission in a model regulatory circuit
https://academiccommons.columbia.edu/catalog/ac:177464
Mancini, F.; Wiggins, Chris H.; Marsili, M.; Walczak, Aleksandra. M.10.7916/D8PK0DNKWed, 28 Jun 2017 21:05:09 +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.Mathematics, Bioinformaticschw2ArticlesStatistical method for revealing form-function relations in biological networks.
https://academiccommons.columbia.edu/catalog/ac:177513
Mugler, Andrew; Grinshpun, Boris; Franks, Riley; Wiggins, Chris H.10.7916/D8JQ0ZJ0Wed, 28 Jun 2017 21:03:18 +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.Mathematicsbg2178, chw2Applied Physics and Applied MathematicsArticlesLearning ‘‘graph-mer’’ Motifs that Predict Gene Expression Trajectories in Development
https://academiccommons.columbia.edu/catalog/ac:177504
Li, Xuejing; Panea, Casandra; Wiggins, Chris H.; Reinke, Valerie; Leslie, Christina10.7916/D8B56H8XWed, 28 Jun 2017 21:02:35 +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.Mathematics, Geneticsxl2118, chw2Applied Physics and Applied MathematicsArticlesInformation-Optimal Transcriptional Response to Oscillatory Driving
https://academiccommons.columbia.edu/catalog/ac:177483
Mugler, Andrew; Walczak, Aleksandra M.; Wiggins, Chris H.10.7916/D84M9321Wed, 28 Jun 2017 21:02:35 +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, Mathematicschw2Applied Physics and Applied MathematicsArticlesA stochastic spectral analysis of transcriptional regulatory cascades
https://academiccommons.columbia.edu/catalog/ac:177519
Walczak, Aleksandra M.; Mugler, Andrew; Wiggins, Chris H.10.7916/D81N7ZNNWed, 28 Jun 2017 21:02:17 +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.Mathematicschw2Applied Physics and Applied MathematicsArticlesSpectral solutions to stochastic models of gene expression with bursts and regulation
https://academiccommons.columbia.edu/catalog/ac:177467
Mugler, Andrew; Walczak, Aleksandra M.; Wiggins, Chris H.10.7916/D8F18X86Wed, 28 Jun 2017 21:02:16 +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.Mathematics, Bioinformaticschw2Applied Physics and Applied MathematicsArticlesBayesian Approach to Network Modularity
https://academiccommons.columbia.edu/catalog/ac:177486
Mugler, Andrew; Wiggins, Chris H.10.7916/D8W37TTGWed, 28 Jun 2017 21:01:49 +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, Mathematicschw2Applied Physics and Applied MathematicsArticlesMultiple events on single molecules: unbiased estimation in single-molecule biophysics.
https://academiccommons.columbia.edu/catalog/ac:177525
Koster, Daniel A.; Wiggins, Chris H.; Dekker, Nynke H.10.7916/D8HQ3XF2Wed, 28 Jun 2017 21:00:37 +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, Mathematicschw2Applied Physics and Applied MathematicsArticlesInferring network mechanisms: The Drosophila melanogaster protein interaction network
https://academiccommons.columbia.edu/catalog/ac:177528
Middendorf, Manuel; Ziv, Etay; Wiggins, Chris H.10.7916/D8862DZVWed, 28 Jun 2017 20:59:00 +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.Mathematicschw2Applied Physics and Applied MathematicsArticlesInformation-theoretic approach to network modularity
https://academiccommons.columbia.edu/catalog/ac:177474
Ziv, Etay; Middendorf, Manuel; Wiggins, Chris H.10.7916/D8X34VZVWed, 28 Jun 2017 20:59:00 +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.Mathematicschw2Applied Physics and Applied MathematicsArticlesSystematic identification of statistically significant network measures
https://academiccommons.columbia.edu/catalog/ac:177477
Ziv, Etay; Koytcheff, Robin; Middendorf, Manuel; Wiggins, Chris H.10.7916/D8NK3CJNWed, 28 Jun 2017 20:59:00 +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.Mathematicschw2Applied Physics and Applied MathematicsArticlesA General Class of Heuristics for Minimum Weight Perfect Matching and Fast Special Cases with Doubly and Triply Logarithmic Errors
https://academiccommons.columbia.edu/catalog/ac:177681
Imielinska, Celina Z.; Kalantari, B.10.7916/D8SJ1J5XWed, 28 Jun 2017 20:57:06 +0000We give a class of heuristic algorithms for minimum weight perfect matching on a complete edgeweighted graph K(V) satisfying the triangle inequality, where V is a set of an even number, n, of vertices.This class is a generalization of the Onethird heuristics, the hypergreedy heuristic, and it possibly employs any given exact or approximate perfect matching algorithm as an auxiliary heuristic to an appropriate subgraph of K(V).Computer science, Mathematicsci42Biomedical InformaticsArticlesA Generalized Hypergreedy Algorithm for Weighted Perfect Matching
https://academiccommons.columbia.edu/catalog/ac:177678
Imielinska, Celina Z.; Kalantari, Bahman10.7916/D8222SB3Wed, 28 Jun 2017 20:57:06 +0000We give a generalization of the hypergreedy algorithm for minimum weight perfect matching on a complete edge weighted graph whose weights satisfy the triangle inequality.Computer science, Mathematicsci42Biomedical InformaticsArticlesFlexive and Propulsive Dynamics of Elastica at Low Reynolds Number
https://academiccommons.columbia.edu/catalog/ac:177501
Wiggins, Chris H.; Goldstein, Raymond E.10.7916/D8KP80P6Wed, 28 Jun 2017 20:57:06 +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, Mathematicschw2Applied Physics and Applied MathematicsArticlesThermodynamic Properties of Poly(trans 1,4-butadiene) Crystals. Relationship to Molecular Structure
https://academiccommons.columbia.edu/catalog/ac:172751
Stellman, Jeanne M.; Woodward, Arthur E.; Stellman, Steven D.10.7916/D87S7KV1Wed, 28 Jun 2017 20:29:22 +0000Heat capacity measurements of melt crystallized poly( trans-1,4-butadiene) (PTBD) were carried out in the 50-130" region and the entropy change from 73" to the melting point, 139", was calculated. A value of the entropy change obtained using the rotational isomeric state approximation is found to underestimate the experimental entropy change. Theoretical energy calculations were carried out using empirical potential energy functions for a single PTBD chain, a unit cell and a lattice of cells. Minimization of the lattice energy with respect to two of the monoclinic cell constants for the low-temperature crystal form gave results in good agreement with X-ray diffraction data. The energy of transition from the low-temperature form was calculated and a theoretical heat capacity curve was obtained.Polymers, Mathematics, Chemistryjms13, sds91Epidemiology, Health Policy and ManagementArticlesArrival-angle anomalies across the USArray Transportable Array
https://academiccommons.columbia.edu/catalog/ac:172088
Foster, Anna; Ekström, Göran; Hjorleifsdottir, Vala10.7916/D8CJ8BJ9Wed, 28 Jun 2017 20:28:47 +0000We construct composite maps of surface-wave arrival-angle anomalies using clustered earthquakes and an array method for measuring wave-front geometry. This results in observations of arrival angles covering the entire footprint of the USArray Transportable Array during 2006–2010. Bands of arrival-angle deviations in the propagation direction indicate the presence of heterogeneous velocity structure both inside and outside of the array. We compare the observed patterns to arrival angles predicted using two global tomographic models, the mantle model S362ANI and the surface-wave-dispersion model GDM52. We use both ray-theory-based prediction methods and measurements on synthetic data calculated using a spectral-element method. Both models and all prediction methods produce similar mean arrival angles and long-wavelength patterns of anomalies which are similar to the observations. Predicted short-wavelength features generally do not agree with the observations. The spectral-element method produces some complexity that is not obtained using the ray-theory-based methods; this predicted complexity is similar in character to the observed patterns, but does not match them.Geophysics, Mathematicsaef2127, ge21Earth and Environmental SciencesArticlesToward an Understanding of Vertical Momentum Transports in Cloud-System-Resolving Model Simulations of Multiscale Tropical Convection
https://academiccommons.columbia.edu/catalog/ac:171435
Shaw, Tiffany A.; Lane, Todd P.10.7916/D80Z719SWed, 28 Jun 2017 20:28:16 +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.Atmosphere, Mathematicstas2163Earth and Environmental Sciences, Applied Physics and Applied MathematicsArticlesLie-group interpolation and variational recovery for internal variables
https://academiccommons.columbia.edu/catalog/ac:171906
Mota, Alejandro; Sun, WaiChing; Ostien, Jakob T.; Long, Kevin N.; Foulk, James W.10.7916/D8H70CW9Wed, 28 Jun 2017 20:28:08 +0000We propose a variational procedure for the recovery of internal variables, in effect extending them from integration points to the entire domain. The objective is to perform the recovery with minimum error and at the same time guarantee that the internal variables remain in their admissible spaces. The minimization of the error is achieved by a three-field finite element formulation. The fields in the formulation are the deformation mapping, the target or mapped internal variables and a Lagrange multiplier that enforces the equality between the source and target internal variables. This formulation leads to an L2 projection that minimizes the distance between the source and target internal variables as measured in the L2 norm of the internal variable space. To ensure that the target internal variables remain in their original space, their interpolation is performed by recourse to Lie groups, which allows for direct polynomial interpolation of the corresponding Lie algebras by means of the logarithmic map. Once the Lie algebras are interpolated, the mapped variables are recovered by the exponential map, thus guaranteeing that they remain in the appropriate space.Mathematicsws2414Civil Engineering and Engineering MechanicsArticlesSurface wave phase velocities of the Western United States from a two-station method
https://academiccommons.columbia.edu/catalog/ac:172091
Foster, Anna; Ekström, Göran; Nettles, Meredith K.10.7916/D87W6979Wed, 28 Jun 2017 20:27:43 +0000We calculate two-station phase measurements using single-station measurements made on USArray Transportable Array data for surface waves at periods from 25 to 100 s. The phase measurements are inverted for baseline Love and Rayleigh wave phase velocity maps on a 0.5° × 0.5° grid. We make estimates of the arrival angle for each event at each station using a mini array method similar to beamforming, and apply this information to correct the geometry of the two-station measurements. These corrected measurements are inverted for an additional set of phase velocity maps. Arrival angles range from 0° to ±15°, and the associated corrections result in local changes of up to 4 per cent in the final phase velocity maps. We select our preferred models on the basis of the internal consistency of the measurements, finding that the arrival-angle corrections improve the two-station phase measurements, but that Love wave arrival-angle estimates may be contaminated by overtone interference. Our preferred models compare favourably with recent studies of the phase velocity of the Western United States. The corrected Rayleigh wave models achieve greater variance reduction than the baseline Rayleigh wave models, and the baseline Love wave models, which are more difficult to obtain, are robust and could be used in conjunction with the Rayleigh wave models to constrain radially anisotropic earth structure.Geophysics, Mathematicsaef2127, ge21, mn2237Earth and Environmental SciencesArticlesBayesian Hierarchical Rule Modeling for Predicting Medical Conditions
https://academiccommons.columbia.edu/catalog/ac:173882
McCormick, Tyler H.; Rudin, Cynthia; Madigan, David B.10.7916/D8V69GP1Wed, 28 Jun 2017 20:26:51 +0000We propose a statistical modeling technique, called the Hierarchical Association Rule Model (HARM), that predicts a patient’s possible future medical conditions given the patient’s current and past history of reported conditions. The core of our technique is a Bayesian hierarchical model for selecting predictive association rules (such as “condition 1 and condition 2 → condition 3”) from a large set of candidate rules. Because this method “borrows strength” using the conditions of many similar patients, it is able to provide predictions specialized to any given patient, even when little information about the patient’s history of conditions is available.Mathematics, Statistics, Medicinethm2105, dm2418StatisticsArticlesA Hierarchical Model for Association Rule Mining of Sequential Events: An Approach to Automated Medical Symptom Prediction
https://academiccommons.columbia.edu/catalog/ac:173838
McCormick, Tyler H.; Rudin, Cynthia; Madigan, David B.10.7916/D89C6VJDWed, 28 Jun 2017 20:25:55 +0000In many healthcare settings, patients visit healthcare professionals periodically and report multiple medical conditions, or symptoms, at each encounter. We propose a statistical modeling technique, called the Hierarchical Association Rule Model (HARM), that predicts a patient’s possible future symptoms given the patient’s current and past history of reported symptoms. The core of our technique is a Bayesian hierarchical model for selecting predictive association rules (such as “symptom 1 and symptom 2 → symptom 3 ”) from a large set of candidate rules. Because this method “borrows strength” using the symptoms of many similar patients, it is able to provide predictions specialized to any given patient, even when little information about the patient’s history of symptoms is available.Mathematics, Statistics, Medicinethm2105, dm2418StatisticsArticlesLocation Estimation in Wireless Networks: A Bayesian Approach
https://academiccommons.columbia.edu/catalog/ac:173820
Madigan, David B.; Ju, Wen-Hua; Krishnan, P.; Krishnakumar, A. S.; Zorych, Ivan10.7916/D82V2D74Wed, 28 Jun 2017 20:23:52 +0000We present a Bayesian hierarchical model for indoor location estimation in wireless networks. We demonstrate that out model achieves accuracy that is similar to other published models and algorithms. By harnessing prior knowledge, our model drastically reduces the requirement for training data as compared with existing approaches.Mathematics, Statisticsdm2418StatisticsArticlesA One-Pass Sequential Monte Carlo Method for Bayesian Analysis of Massive Datasets
https://academiccommons.columbia.edu/catalog/ac:173899
Balakrishnan, Suhrid; Madigan, David B.10.7916/D8B56GTPWed, 28 Jun 2017 20:23:50 +0000For Bayesian analysis of massive data, Markov chain Monte Carlo (MCMC) techniques often prove infeasible due to computational resource constraints. Standard MCMC methods generally require a complete scan of the dataset for each iteration. Ridgeway and Madigan (2002) and Chopin (2002b) recently presented importance sampling algorithms that combined simulations from a posterior distribution conditioned on a small portion of the dataset with a reweighting of those simulations to condition on the remainder of the dataset. While these algorithms drastically reduce the number of data accesses as compared to traditional MCMC, they still require substantially more than a single pass over the dataset. In this paper, we present "1PFS," an efficient, one-pass algorithm. The algorithm employs a simple modification of the Ridgeway and Madigan (2002) particle filtering algorithm that replaces the MCMC based "rejuvenation" step with a more efficient "shrinkage" kernel smoothing based step. To show proof-of-concept and to enable a direct comparison, we demonstrate 1PFS on the same examples presented in Ridgeway and Madigan (2002), namely a mixture model for Markov chains and Bayesian logistic regression. Our results indicate the proposed scheme delivers accurate parameter estimates while employing only a single pass through the data.Mathematics, Statisticsdm2418StatisticsArticles[Least Angle Regression]: Discussion
https://academiccommons.columbia.edu/catalog/ac:173841
Madigan, David B.; Ridgeway, Greg10.7916/D81V5C29Wed, 28 Jun 2017 20:23:33 +0000Algorithms for simultaneous shrinkage and selection in regression and classification provide attractive solutions to knotty old statistical challenges. Nevertheless, as far as we can tell, Tibshirani's Lasso algorithm has had little impact on statistical practice. Two particular reasons for this may be the relative inefficiency of the original Lasso algorithm and the relative complexity of more recent Lasso algorithms [e.g., Osborne, Presnell and Turlach (2000)]. Efron, Hastie, Johnstone and Tibshirani have provided an efficient, simple algorithm for the Lasso as well as algorithms for stagewise regression and the new least angle regression. As such this paper is an important contribution to statistical computing.Mathematics, Statisticsdm2418StatisticsArticlesCorrection: Separation and completeness properties for AMP chain graph Markov models
https://academiccommons.columbia.edu/catalog/ac:173887
Madigan, David B.; Levitz, Michael; Perlman, Michael D.10.7916/D8QF8R05Wed, 28 Jun 2017 20:23:16 +0000Correction of table 2 on page 1757 of 'Separation and completeness properties for AMP chain graph Markov models', Annals of Statistics, volume 29 (2001).Mathematics, Statisticsdm2418StatisticsArticlesSeparation and Completeness Properties for Amp Chain Graph Markov Models
https://academiccommons.columbia.edu/catalog/ac:173847
Levitz, Michael; Perlman, Michael D.; Madigan, David B.10.7916/D8X34VJGWed, 28 Jun 2017 20:23:00 +0000Pearl’s well-known d-separation criterion for an acyclic directed graph (ADG) is a pathwise separation criterion that can be used to efficiently identify all valid conditional independence relations in the Markov model determined by the graph. This paper introduces p-separation, a pathwise separation criterion that efficiently identifies all valid conditional independences under the Andersson–Madigan–Perlman (AMP) alternative Markov property for chain graphs (= adicyclic graphs), which include both ADGs and undirected graphs as special cases. The equivalence of p-separation to the augmentation criterion occurring in the AMP global Markov property is established, and p-separation is applied to prove completeness of the global Markov property for AMP chain graph models. Strong completeness of the AMP Markov property is established, that is, the existence of Markov perfect distributions that satisfy those and only those conditional independences implied by the AMP property(equivalently, by p-separation). A linear-time algorithm for determining p-separation is presented.Mathematics, Statisticsdm2418StatisticsArticlesA Characterization of Markov Equivalence Classes for Acyclic Digraphs
https://academiccommons.columbia.edu/catalog/ac:173896
Andersson, Steen A.; Madigan, David B.; Perlman, Michael D.10.7916/D8FX77J3Wed, 28 Jun 2017 20:22:39 +0000Undirected graphs and acyclic digraphs (ADG's), as well as their mutual extension to chain graphs, are widely used to describe dependencies among variables in multiviarate distributions. In particular, the likelihood functions of ADG models admit convenient recursive factorizations that often allow explicit maximum likelihood estimates and that are well suited to building Bayesian networks for expert systems. Whereas the undirected graph associated with a dependence model is uniquely determined, there may be many ADG's that determine the same dependence (i.e., Markov) model. Thus, the family of all ADG's with a given set of vertices is naturally partitioned into Markov-equivalence classes, each class being associated with a unique statistical model. Statistical procedures, such as model selection of model averaging, that fail to take into account these equivalence classes may incur substantial computational or other inefficiences. Here it is show that each Markov-equivalence class is uniquely determined by a single chain graph, the essential graph, that is itself simultaneously Markov equivalent to all ADG's in the equivalence class. Essential graphs are characterized, a polynomial-time algorithm for their construction is given, and their applications to model selection and other statistical questions are described.Mathematics, Statisticsdm2418StatisticsArticlesA Note on Equivalence Classes of Directed Acyclic Independence Graphs
https://academiccommons.columbia.edu/catalog/ac:173826
Madigan, David B.10.7916/D8TB150CWed, 28 Jun 2017 20:22:29 +0000Directed acyclic independence graphs (DAIGs) play an important role in recent developments in probabilistic expert systems and influence diagrams (Chyu [1]). The purpose of this note is to show that DAIGs can usefully be grouped into equivalence classes where the members of a single class share identical Markov properties. These equivalence classes can be identified via a simple graphical criterion. This result is particularly relevant to model selection procedures for DAIGs (see, e.g., Cooper and Herskovits [2] and Madigan and Raftery [4]) because it reduces the problem of searching among possible orientations of a given graph to that of searching among the equivalence classes.Mathematics, Statisticsdm2418StatisticsArticles[Bayesian Analysis in Expert Systems]: Comment: What's Next?
https://academiccommons.columbia.edu/catalog/ac:173856
Madigan, David B.10.7916/D8W37TFJWed, 28 Jun 2017 20:22:27 +0000"These papers represent two of the many different graphical modeling camps that have emerged from a flurry of activity in the past decade. The paper by Cox and Wermuth falls within the statistical graphical modeling camp and provides a useful generalization of that body of work. There is, of course, a price to be paid for this generality, namely that the interpretation of the graphs is more complex...The paper by Spiegelhalter, Dawid, Lauritzen and Cowell falls within the probabilistic expert system camp. This is a tour de force by researchers responsible for much of the astonishing progress in this area. Ten years ago, probabilistic models were shunned by the artificial intelligence community. That they are now widely accepted and used is due in large measure to the insights and efforts of these authors, along with other pioneers such as Judea Pearl and Peter Cheeseman..." -- page 261Mathematics, Statisticsdm2418StatisticsArticlesComputer Graphics in the Solution of the Chain Deformation Problem
https://academiccommons.columbia.edu/catalog/ac:172760
Stellman, Steven D.10.7916/D8QR4V6PWed, 28 Jun 2017 18:16:28 +0000Go and Scheraga have given a general solution for determining the possible conformations of a section of a flexible polymeric chain between two fixed bonds (if the bonds coincide, the problem is equivalent to ring closure). Often, the fixed bonds are related by symmetry, such as that imposed by helicity or folding of antiparallel chains. A technique is shown for obtaining solutions using interactive computer graphics, whereby a plausible chain conformation or fold is approximated manually and completed by mathematical minimization. The procedure allows rapid, repetitive exploration of multiple solutions, and has many options for changing constraints. As an example, the backbone conformation of GpC, a dinucleoside phosphate, is used as a starting model, and gives upon minimization a set of backbone angles in the range of 11-fold helical RNA.Polymers, Mathematicssds91EpidemiologyArticlesConformation of Guanosine Cytidine 3',5'-Monophosphate (GpC)
https://academiccommons.columbia.edu/catalog/ac:172748
Stellman, Steven D.; Hingerty, B.; Broyde, S. B.; Subramanian, E.; Sato, T.; Langridge, R.10.7916/D8CJ8BKRWed, 28 Jun 2017 18:16:18 +0000A brief communication of preliminary results of solution of dinucleoside phosphate GpC.Mathematics, Polymerssds91EpidemiologyArticlesA Spherical Chicken
https://academiccommons.columbia.edu/catalog/ac:172754
Stellman, Steven D.10.7916/D80863C7Wed, 28 Jun 2017 18:16:17 +0000Letter to the editor, published in Science (magazine).Biochemistry, Mathematicssds91EpidemiologyArticlesEfficient Computation of Polymer Conformation Energy
https://academiccommons.columbia.edu/catalog/ac:171438
Stellman, Steven D.; Froimowitz, Mark; Gans, Paul J.10.7916/D8W95757Wed, 28 Jun 2017 18:16:17 +0000Calculation of intramolecular energy of a polymer due to interactions of non-bonded atoms can be speeded up using simple geometric inequalities. This "zippering" method reduces time dependence of computation from n^2 to n^1.25, where n is the chain length. This technique is especially useful in applications of the pivot algorithm.Epidemiology, Mathematicssds91EpidemiologyArticlesEfficient Computer Simulation of Polymer Conformation. I. Geometric Properties of the Hard-Sphere Model
https://academiccommons.columbia.edu/catalog/ac:172736
Stellman, Steven D.; Gans, Paul J.10.7916/D8N58JF4Wed, 28 Jun 2017 18:16:17 +0000A system of efficient computer programs has been developed for simulating the conformations of macromolecules. The conformation of an individual polymer is defined as a point in conformation space, whose mutually orthogonal axes represent the successive dihedral angles of the backbone chain. The statistical-mechanical average of any property is obtained as the usual configuration integral over this space. A Monte Carlo method for estimating averages is used because of the impossibility of direct numerical integration. Monte Carlo corresponds to the execution of a Markoffian random walk of a representative point through the conformation space. Unlike many previous Monte Carlo studies of polymers, which sample conformation space indiscriminately, importance sampling increases efficiency because selection of new polymers is biased to reflect their Boltzmann probabilities in the canonical ensemble, leading to reduction of sampling variance and hence to greater accuracy! in given computing time. The simulation is illustrated in detail. Overall running time is proportional to n^(5/4), where n is the chain length. Results are presented for a hard-sphere linear polymer of n atoms, with free dihedral rotation, with n = 20-298. The fraction of polymers accepted in the importance sampling scheme, fA, is fit to a Fisher-Sykes attrition relation, giving an effective attrition constant of zero. fA is itself an upper bound to the partition function, Q, relative to the unrestricted walk. The mean-squared end-to-end distance and radius of gyration exhibit the expected exponential dependence, but with exponent for the radius of gyration significantly greater than that of the end-to-end distance. The 90% confidence limits calculated for both exponents did not include either 6/5 or 4/3, the lattice and zero-order perturbation values, respectively. A self-correcting scheme for generating coordinates free of roundoff error is given in an Appendix.Mathematics, Polymerssds91EpidemiologyArticlesComputer Simulation of Polymer Conformation. II. Distribution Function for Polymers with Excluded Volume
https://academiccommons.columbia.edu/catalog/ac:172739
Stellman, Steven D.; Gans, Paul J.10.7916/D8SQ8XGWWed, 28 Jun 2017 18:16:17 +0000Numerical distributions of end-to-end distances were generated by a Monte Carlo method for hard-sphere off-lattice polymers of length N = 20, 40, 60, 80, 98, and 298 atoms. Comparison by xz tests against five recently proposed theoretical distribution functions showed that for N = 80 and N = 98, the data could be described, with 95% confidence, by the equation f(r) = exp[ -(ar2 + br + c)], where a and b are fitted parameters and c is a normalization constant. For N = 298, limitations of sample size lead to lower confidence limits (about 80%), but good fit. The above equation, and not its gaussian counterpart exp( -cr^2), is probably the limiting distribution function. The function accurately predicts the 1st through 12th observed moments at all chain lengths.Polymers, Mathematicssds91EpidemiologyArticlesIntraseasonal and Interannual Variability in North American Storm Tracks and Its Relationship to Equatorial Pacific Variability
https://academiccommons.columbia.edu/catalog/ac:174585
Grise, Kevin Michael; Son, Seok-Woo; Gyakum, John R.10.7916/D89021RVWed, 28 Jun 2017 17:15:45 +0000Extratropical cyclones play a principal role in wintertime precipitation and severe weather over North America. On average, the greatest number of cyclones track 1) from the lee of the Rocky Mountains eastward across the Great Lakes and 2) over the Gulf Stream along the eastern coastline of North America. However, the cyclone tracks are highly variable within individual winters and between winter seasons. In this study, the authors apply a Lagrangian tracking algorithm to examine variability in extratropical cyclone tracks over North America during winter. A series of methodological criteria is used to isolate cyclone development and decay regions and to account for the elevated topography over western North America. The results confirm the signatures of four climate phenomena in the intraseasonal and interannual variability in North American cyclone tracks: the North Atlantic Oscillation (NAO), the El Niño–Southern Oscillation (ENSO), the Pacific–North American pattern (PNA), and the Madden–Julian oscillation (MJO). Similar signatures are found using Eulerian bandpass-filtered eddy variances. Variability in the number of extratropical cyclones at most locations in North America is linked to fluctuations in Rossby wave trains extending from the central tropical Pacific Ocean. Only over the far northeastern United States and northeastern Canada is cyclone variability strongly linked to the NAO. The results suggest that Pacific sector variability (ENSO, PNA, and MJO) is a key contributor to intraseasonal and interannual variability in the frequency of extratropical cyclones at most locations across North America.Atmosphere, Meteorology, Mathematicskmg2164, sws2112Lamont-Doherty Earth ObservatoryArticlesUnderstanding Hadley Cell Expansion versus Contraction: Insights from Simplified Models and Implications for Recent Observations
https://academiccommons.columbia.edu/catalog/ac:168459
Tandon, Neil F.; Gerber, Edwin P.; Sobel, Adam H.; Polvani, Lorenzo M.10.7916/D8086GG4Wed, 28 Jun 2017 17:14:03 +0000This study seeks a deeper understanding of the causes of Hadley Cell (HC) expansion, as projected under global warming, and HC contraction, as observed under El Niño. Using an idealized general circulation model, the authors show that a thermal forcing applied to a narrow region around the equator produces “El Niño–like” HC contraction, while a forcing with wider meridional extent produces “global warming–like” HC expansion. These circulation responses are sensitive primarily to the thermal forcing’s meridional structure and are less sensitive to its vertical structure. If the thermal forcing is confined to the midlatitudes, the amount of HC expansion is more than three times that of a forcing of comparable amplitude that is spread over the tropics. This finding may be relevant to recently observed trends of rapid tropical widening.
The shift of the HC edge is explained using a very simple model in which the transformed Eulerian mean (TEM) circulation acts to diffuse heat meridionally. In this context, the HC edge is defined as the downward maximum of residual vertical velocity in the upper troposphere ϖmax *; this corresponds well with the conventional Eulerian definition of the HC edge. In response to a positive thermal forcing, there is anomalous diabatic cooling, and hence anomalous TEM descent, on the poleward flank of the thermal forcing. This causes the HC edge (ϖmax *) to shift toward the descending anomaly, so that a narrow forcing causes HC contraction and a wide forcing causes HC expansion.Atmosphere, Mathematics, Climatic changesnft2104, epg2108, ahs129, lmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesThe Antarctic Atmospheric Energy Budget. Part I: Climatology and Intraseasonal-to-Interannual Variability
https://academiccommons.columbia.edu/catalog/ac:172197
Previdi, Michael; Smith, Karen L.; Polvani, Lorenzo M.10.7916/D86W9N78Wed, 28 Jun 2017 17:12:43 +0000The authors present a new, observationally based estimate of the atmospheric energy budget for the Antarctic polar cap (the region poleward of 70°S). This energy budget is constructed using state-of-the-art reanalysis products from ECMWF [the ECMWF Interim Re-Analysis (ERA-Interim)] and Clouds and the Earth's Radiant Energy System (CERES) top-of-atmosphere (TOA) radiative fluxes for the period 2001–10. The climatological mean Antarctic energy budget is characterized by an approximate balance between the TOA net outgoing radiation and the horizontal convergence of atmospheric energy transport, with the net surface energy flux and atmospheric energy storage generally being small in comparison. Variability in the energy budget on intraseasonal-to-interannual time scales bears a strong signature of the southern annular mode (SAM), with El Niño–Southern Oscillation (ENSO) having a smaller impact. The energy budget framework is shown to be a useful alternative to the SAM for interpreting surface climate variability in the Antarctic region.Atmosphere, Meteorology, Mathematicsmp2609, kls2177, lmp3Lamont-Doherty Earth Observatory, Ocean and Climate Physics, Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesUncertainty in Climate Change Projections of the Hadley Circulation: The Role of Internal Variability
https://academiccommons.columbia.edu/catalog/ac:172651
Kang, Sarah M.; Deser, Clara; Polvani, Lorenzo M.10.7916/D8XK8RPCWed, 28 Jun 2017 17:11:24 +0000The uncertainty arising from internal climate variability in climate change projections of the Hadley circulation (HC) is presently unknown. In this paper it is quantified by analyzing a 40-member ensemble of integrations of the Community Climate System Model, version 3 (CCSM3), under the Special Report on Emissions Scenarios (SRES) A1B scenario over the period 2000–60. An additional set of 100-yr-long time-slice integrations with the atmospheric component of the same model [Community Atmosphere Model, version 3.0 (CAM3)] is also analyzed.
Focusing on simple metrics of the HC—its strength, width, and height—three key results emerge from the analysis of the CCSM3 ensemble. First, the projected weakening of the HC is almost entirely confined to the Northern Hemisphere, and is stronger in winter than in summer. Second, the projected widening of the HC occurs only in the winter season but in both hemispheres. Third, the projected rise of the tropical tropopause occurs in both hemispheres and in all seasons and is, by far, the most robust of the three metrics.
This paper shows further that uncertainty in future trends of the HC width is largely controlled by extratropical variability, while those of HC strength and height are associated primarily with tropical dynamics. Comparison of the CCSM3 and CAM3 integrations reveals that ocean–atmosphere coupling is the dominant source of uncertainty in future trends of HC strength and height and of the tropical mean meridional circulation in general. Finally, uncertainty in future trends of the hydrological cycle is largely captured by the uncertainty in future trends of the mean meridional circulation.Atmosphere, Meteorology, Mathematicssmk2182, lmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesScaling in Surface Hydrology: Progress and Challenges
https://academiccommons.columbia.edu/catalog/ac:165839
Gentine, Pierre; Troy, Tara J.; Lintner, Benjamin R.; Findell, Kirsten L.10.7916/D84M9FP7Wed, 28 Jun 2017 17:05:17 +0000This paper presents a review of the challenges in spatial and temporal scales in surface hydrology. Fundamental issues and gaps in our understanding of hydrologic scaling are highlighted and shown to limit predictive skill, with heterogeneities, nonlinearities, and non-local transport processes among the most significant difficulties faced in scaling. The discrepancy between the physical process scale and the measurement scale has played a major role in restricting the development of theories, for example, relating observational scales to scales of climate and weather models. Progress in our knowledge of scaling in hydrology requires systematic determination of critical scales and scale invariance of physical processes. In addition, viewing the surface hydrologic system as composed of interacting dynamical subsystems should facilitate the definition of scales observed in nature. Such an approach would inform the development of careful, resolution-dependent, physical law formulation based on mathematical techniques and physical laws.Hydrology, Mathematicspg2328Earth and Environmental Engineering, Lamont-Doherty Earth ObservatoryArticlesEquatorial Superrotation on Tidally Locked Exoplanets
https://academiccommons.columbia.edu/catalog/ac:166848
Showman, Adam P.; Polvani, Lorenzo M.10.7916/D8Z328TKWed, 28 Jun 2017 17:04:03 +0000The increasing richness of exoplanet observations has motivated a variety of three-dimensional (3D) atmospheric circulation models of these planets. Under strongly irradiated conditions, models of tidally locked, short-period planets (both hot Jupiters and terrestrial planets) tend to exhibit a circulation dominated by a fast eastward, or "superrotating," jet stream at the equator. When the radiative and advection timescales are comparable, this phenomenon can cause the hottest regions to be displaced eastward from the substellar point by tens of degrees longitude. Such an offset has been subsequently observed on HD 189733b, supporting the possibility of equatorial jets on short-period exoplanets. Despite its relevance, however, the dynamical mechanisms responsible for generating the equatorial superrotation in such models have not been identified. Here, we show that the equatorial jet results from the interaction of the mean flow with standing Rossby waves induced by the day-night thermal forcing. The strong longitudinal variations in radiative heating—namely intense dayside heating and nightside cooling—trigger the formation of standing, planetary-scale equatorial Rossby and Kelvin waves. The Rossby waves develop phase tilts that pump eastward momentum from high latitudes to the equator, thereby inducing equatorial superrotation. We present an analytic theory demonstrating this mechanism and explore its properties in a hierarchy of one-layer (shallow-water) calculations and fully 3D models. The wave-mean-flow interaction produces an equatorial jet whose latitudinal width is comparable to that of the Rossby waves, namely the equatorial Rossby deformation radius modified by radiative and frictional effects. For conditions typical of synchronously rotating hot Jupiters, this length is comparable to a planetary radius, explaining the broad scale of the equatorial jet obtained in most hot-Jupiter models. Our theory illuminates the dependence of the equatorial jet speed on forcing amplitude, strength of friction, and other parameters, as well as the conditions under which jets can form at all.Atmosphere, Mathematicslmp3Applied Physics and Applied Mathematics, Lamont-Doherty Earth ObservatoryArticlesEl Niño, La Niña, and Stratospheric Sudden Warmings: A Reevaluation in Light of the Observational Record
https://academiccommons.columbia.edu/catalog/ac:166842
Butler, Amy H.; Polvani, Lorenzo M.10.7916/D8QJ7TFGWed, 28 Jun 2017 17:03:40 +0000Recent studies have suggested that El Niño-Southern Oscillation (ENSO) may have a considerable impact on Northern Hemisphere wintertime stratospheric conditions. Notably, during El Niño the stratosphere is warmer than during ENSO-neutral winters, and the polar vortex is weaker. Opposite-signed anomalies have been reported during La Niña, but are considerably smaller in amplitude than during El Niño. This has led to the perception that El Niño is able to substantially affect stratospheric conditions, but La Niña is of secondary importance. Here we revisit this issue, but focus on the extreme events that couple the troposphere to the stratosphere: major, mid-winter stratospheric sudden warmings (SSWs). We examine 53 years of reanalysis data and find, as expected, that SSWs are nearly twice as frequent during ENSO winters as during non-ENSO winters. Surprisingly, however, we also find that SSWs occur with equal probability during El Niño and La Niña winters. These findings corroborate the impact of ENSO on stratospheric variability, and highlight that both phases of ENSO are important in enhancing stratosphere-troposphere dynamical coupling via an increased frequency of SSWs.Atmosphere, Meteorology, Mathematicslmp3Applied Physics and Applied Mathematics, Earth and Environmental Sciences, Lamont-Doherty Earth ObservatoryArticlesThe Effect of Topography on Storm-Track Intensity in a Relatively Simple General Circulation Model
https://academiccommons.columbia.edu/catalog/ac:166878
Son, Seok-Woo; Polvani, Lorenzo M.; Ting, Mingfang10.7916/D8W66WX9Wed, 28 Jun 2017 17:02:26 +0000The effect of topography on storm-track intensity is examined with a set of primitive equation model integrations. This effect is found to be crucially dependent on the latitudinal structure of the background flow impinging on the topography. If the background flow consists of a weak double jet, higher topography leads to an intensification of the storm track downstream of the topography, consistent with enhanced baroclinicity in that region. However, if the background flow consists of a strong single jet, topography weakens the storm track, despite the fact that the baroclinicity downstream of the topography is again enhanced.
The different topographic impact results from the different wave packets in the two background flows. For a weak double-jet state, wave packets tend to radiate equatorward and storm-track eddies grow primarily at the expense of local baroclinicity. In contrast, for a strong single-jet state, wave packets persistently propagate in the zonal direction and storm tracks are affected not only by local baroclinicity but also by far-upstream disturbances via downstream development. It is the reduction of the latter by the topography that leads to weaker storm tracks in a strong single-jet state. The implications of these findings for Northern Hemisphere storm tracks are also discussed.Atmosphere, Meteorology, Mathematicssws2112, lmp3, mt2204Applied Physics and Applied Mathematics, Lamont-Doherty Earth Observatory, Ocean and Climate Physics, Earth and Environmental SciencesArticlesTesting the Annular Mode Autocorrelation Time Scale in Simple Atmospheric General Circulation Models
https://academiccommons.columbia.edu/catalog/ac:166909
Gerber, Edwin P.; Voronin, Sergey; Polvani, Lorenzo M.10.7916/D85Q567BWed, 28 Jun 2017 17:02:01 +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.Atmosphere, Meteorology, Mathematicsepg2108, sv2122, lmp3Applied Physics and Applied MathematicsArticlesAnnular Mode Time Scales in the Intergovernmental Panel on Climate Change Fourth Assessment Report Models
https://academiccommons.columbia.edu/catalog/ac:166896
Gerber, Edwin P.; Polvani, Lorenzo M.; Ancukiewicz, Damian10.7916/D89G5XZ8Wed, 28 Jun 2017 17:02:00 +0000The ability of climate models in the Intergovernmental Panel on Climate Change Fourth Assessment Report to capture the temporal structure of the annular modes is evaluated. The vertical structure and annual cycle of the variability is quantified by the e-folding time scale of the annular mode autocorrelation function. Models vaguely capture the qualitative features of the Northern and Southern Annular Modes: Northern Hemisphere time scales are shorter than those of the Southern Hemisphere and peak in boreal winter, while Southern Hemisphere time scales peak in austral spring and summer. Models, however, systematically overestimate the time scales, particularly in the Southern Hemisphere summer, where the multimodel ensemble average is twice that of reanalyses. Fluctuation-dissipation theory suggests that long time scales in models could be associated with increased sensitivity to anthropogenic forcing. Comparison of model pairs with similar forcings but different annular mode time scales provides a hint of a fluctuation-dissipation relationship.Atmosphere, Mathematics, Climatic changesepg2108, lmp3, da2260Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesInternal Variability of the Winter Stratosphere. Part II: Time-Dependent Forcing
https://academiccommons.columbia.edu/catalog/ac:166906
Scott, R. K.; Polvani, Lorenzo M.; Waugh, D. W.10.7916/D8X63Z23Wed, 28 Jun 2017 17:01:59 +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.Atmosphere, Atmosphere, Upper, Mathematicslmp3Applied Physics and Applied MathematicsArticlesOn the Wavelength of the Rossby Waves Radiated by Tropical Cyclones
https://academiccommons.columbia.edu/catalog/ac:166903
Krouse, Kyle D.; Sobel, Adam H.; Polvani, Lorenzo M.10.7916/D81Z4FJ2Wed, 28 Jun 2017 17:01:59 +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.Atmosphere, Mathematics, Meteorologykdk8, ahs129, lmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesEquatorial Superrotation in Shallow Atmospheres
https://academiccommons.columbia.edu/catalog/ac:166899
Scott, R. K.; Polvani, Lorenzo M.10.7916/D8SF3699Wed, 28 Jun 2017 17:01:59 +0000Simple, shallow-water models have been successful in reproducing two key observables in the atmospheres of the giant planets: the formation of robust, and fully turbulent, latitudinal jets and the decrease of the zonal wind amplitude with latitude. However, they have to date consistently failed in reproducing the strong prograde (superrotating) equatorial winds that are often observed on such planets. In this paper we show that shallow water models not only can give rise to superrotating winds, but can do so very robustly, provided that the physical process of large-scale energy dissipation by radiative relaxation is taken into account. When energy is removed by linear friction, equatorial superrotation does not develop; when energy is removed by radiative relaxation, superrotation develops at apparently any deformation radius.Atmosphere, Meteorology, Mathematicslmp3Applied Physics and Applied MathematicsArticlesThe Effect of Lower Stratospheric Shear on Baroclinic Instability
https://academiccommons.columbia.edu/catalog/ac:166918
Wittman, Matthew A. H.; Charlton, Andrew J.; Polvani, Lorenzo M.10.7916/D8JW8R1JWed, 28 Jun 2017 17:01:48 +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.Atmosphere, Atmosphere, Upper, Mathematicsmaw2006, ac2343, lmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesA New Look at Stratospheric Sudden Warmings. Part II: Evaluation of Numerical Model Simulations
https://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, David10.7916/D86Q27CQWed, 28 Jun 2017 17:01:39 +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.Atmosphere, Atmosphere, Upper, Mathematicsac2343, lmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesA New Look at Stratospheric Sudden Warmings. Part I: Climatology and
Modeling Benchmarks
https://academiccommons.columbia.edu/catalog/ac:166927
Charlton, Andrew J.; Polvani, Lorenzo M.10.7916/D82Z1GN0Wed, 28 Jun 2017 17:01:37 +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.Atmosphere, Atmosphere, Upper, Mathematicsac2343, lmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesForced-Dissipative Shallow-Water Turbulence on the Sphere and the Atmospheric Circulation of the Giant Planets
https://academiccommons.columbia.edu/catalog/ac:166921
Scott, R. K.; Polvani, Lorenzo M.10.7916/D8Z6105DWed, 28 Jun 2017 17:01:37 +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.Atmosphere, Mathematicslmp3Applied Physics and Applied MathematicsArticlesInternal Variability of the Winter Stratosphere. Part I: Time-Independent Forcing
https://academiccommons.columbia.edu/catalog/ac:166950
Scott, R. K.; Polvani, Lorenzo M.10.7916/D8BG303FWed, 28 Jun 2017 17:01:37 +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.Atmosphere, Atmosphere, Upper, Mathematicslmp3Applied Physics and Applied MathematicsArticlesStratosphere–Troposphere Coupling in a Relatively Simple AGCM: Impact of the Seasonal Cycle
https://academiccommons.columbia.edu/catalog/ac:166953
Kushner, Paul J.; Polvani, Lorenzo M.10.7916/D8G451FWWed, 28 Jun 2017 17:01:37 +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.Atmosphere, Atmosphere, Upper, Mathematicslmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesStratospheric Influence on Baroclinic Lifecycles and its Connection to the Arctic Oscillation
https://academiccommons.columbia.edu/catalog/ac:166968
Wittman, Matthew A. H.; Polvani, Lorenzo M.; Charlton, Andrew J.; Scott, Richard K.10.7916/D87P98J0Wed, 28 Jun 2017 17:01:14 +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.Atmosphere, Mathematics, Atmosphere, Uppermaw2006, lmp3, ac2343Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesOn the Meridional Structure of Annular Modes
https://academiccommons.columbia.edu/catalog/ac:166962
Wittman, Matthew A. H.; Charlton, Andrew J.; Polvani, Lorenzo M.10.7916/D8QN6HW7Wed, 28 Jun 2017 17:01:13 +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.Atmosphere, Atmosphere, Upper, Mathematicsmaw2006, ac2343, lmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesThe Coupled Stratosphere–Troposphere Response to Impulsive Forcing from the Troposphere
https://academiccommons.columbia.edu/catalog/ac:166959
Reichler, Thomas; Kushner, Paul J.; Polvani, Lorenzo M.10.7916/D8VD78KHWed, 28 Jun 2017 17:01:13 +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.Atmosphere, Atmosphere, Upper, Mathematicslmp3Applied Physics and Applied MathematicsArticlesA Very Large, Spontaneous Stratospheric Sudden Warming in a Simple AGCM: A Prototype for the Southern Hemisphere Warming of 2002?
https://academiccommons.columbia.edu/catalog/ac:166956
Kushner, Paul J.; Polvani, Lorenzo M.10.7916/D8057S2TWed, 28 Jun 2017 17:01:12 +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.Atmosphere, Atmosphere, Upper, Mathematicslmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesKelvin–Helmholtz Instability of Potential Vorticity Layers: A Route to Mixing
https://academiccommons.columbia.edu/catalog/ac:166980
Esler, J. G.; Polvani, Lorenzo M.10.7916/D84X5JX6Wed, 28 Jun 2017 17:00:52 +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.Atmosphere, Atmosphere, Upper, Mathematicslmp3Applied Physics and Applied MathematicsArticlesNumerically Converged Solutions of the Global Primitive Equations for Testing the Dynamical Core of Atmospheric GCMs
https://academiccommons.columbia.edu/catalog/ac:166983
Polvani, Lorenzo M.; Scott, R. K.; Thomas, S. J.10.7916/D8RN3K0KWed, 28 Jun 2017 17:00:52 +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.Atmosphere, Meteorology, Mathematicslmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesStratospheric Control of Upward Wave Flux near the Tropopause
https://academiccommons.columbia.edu/catalog/ac:166965
Scott, R. K.; Polvani, Lorenzo M.10.7916/D8MW2T99Wed, 28 Jun 2017 17:00:52 +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.Atmosphere, Mathematics, Atmosphere, Upperlmp3Applied Physics and Applied MathematicsArticlesStratosphere–Troposphere Coupling in a Relatively Simple AGCM: The Role of Eddies
https://academiccommons.columbia.edu/catalog/ac:166971
Kushner, Paul J.; Polvani, Lorenzo M.10.7916/D8154T66Wed, 28 Jun 2017 17:00:44 +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.Atmosphere, Atmosphere, Upper, Mathematicslmp3Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesOptimal Monetary and Fiscal Policy: A Linear-Quadratic Approach
https://academiccommons.columbia.edu/catalog/ac:167750
Benigno, Pierpaolo; Woodford, Michael10.7916/D8H70CRHWed, 28 Jun 2017 17:00:27 +0000We propose an integrated treatment of the problems of optimal monetary and fiscal policy, for an economy in which prices are sticky (so that the supply-side effects of tax changes are more complex than in standard fiscal analyses) and the only available sources of government revenue are distorting taxes (so that the fiscal consequences of monetary policy must be considered alongside the usual stabilization objectives). Our linear-quadratic approach allows us to nest both conventional analyses of optimal monetary stabilization policy and analyses of optimal tax-smoothing as special cases of our more general framework. We show how a linear-quadratic policy problem can be derived which yields a correct linear approximation to the optimal policy rules from the point of view of the maximization of expected discounted utility in a dynamic stochastic general-equilibrium model. Finally, in addition to characterizing the optimal dynamic responses to shocks under an optimal policy, we derive policy rules through which the monetary and fiscal authorities may implement the optimal equilibrium. These take the form of optimal targeting rules, specifying an appropriate target criterion for each authority.Economics, Mathematicsmw2230EconomicsConference postersThe Hadley Circulation and the Weak Temperature Gradient Approximation
https://academiccommons.columbia.edu/catalog/ac:166986
Polvani, Lorenzo M.; Sobel, Adam H.10.7916/D8251VBKWed, 28 Jun 2017 17:00:27 +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.Atmosphere, Meteorology, Mathematicslmp3, ahs129Applied Physics and Applied Mathematics, Earth and Environmental SciencesArticlesNonlinear Geostrophic Adjustment, Cyclone/Anticyclone Asymmetry, and Potential Vorticity Rearrangement
https://academiccommons.columbia.edu/catalog/ac:167047
Kuo, Allen C.; Polvani, Lorenzo M.10.7916/D8VM4PD5Wed, 28 Jun 2017 16:59:34 +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, Mathematicslmp3Applied Physics and Applied MathematicsArticlesTime Variability and Simmons–Wallace–Branstator Instability in a Simple Nonlinear One-Layer Model
https://academiccommons.columbia.edu/catalog/ac:167062
Polvani, Lorenzo M.; Esler, J. Gavin; Plumb, R. Alan10.7916/D8H99GBGWed, 28 Jun 2017 16:59:34 +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.Atmosphere, Geophysics, Mathematicslmp3Applied Physics and Applied MathematicsArticlesBarotropic Vortex Pairs on a Rotating Sphere
https://academiccommons.columbia.edu/catalog/ac:167068
DiBattista, Mark T.; Polvani, Lorenzo M.10.7916/D88S512NWed, 28 Jun 2017 16:59:10 +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.Atmosphere, Geophysics, Mathematicslmp3Applied Physics and Applied MathematicsArticlesOn the Mix-Down Times of Dynamically Active Potential Vorticity Filaments
https://academiccommons.columbia.edu/catalog/ac:167059
Esler, J. Gavin; Polvani, Lorenzo M.; Plumb, R. Alan10.7916/D8RV0ZTTWed, 28 Jun 2017 16:59:10 +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.Atmosphere, Geophysics, Mathematicslmp3Applied Physics and Applied MathematicsArticles