# Reception and Poster Session

Tuesday, March 12, 2013 - 4:30pm - 6:30pm

Lind 400

**Estimating Ocean Circulation : A Likelihood-free MCMC Approach via a Bernoulli Factory**

Radu Herbei (The Ohio State University)

We describe a novel Markov chain Monte Carlo approach that does not require a likelihood evaluation. Rather, we use unbiased estimates of the likelihood and a Bernoulli factory to decide whether proposed states are accepted or not. We illustrate this approach using a oceanographic data inversion example. The variates required to estimate the likelihood function are obtained via a Feynman-Kac representation. This lifts the restriction of selecting a regular grid for the physical model and eliminates the need for data pre-processing. We implement our approach using the parallel GPU computing environment.**Toward Stochastic Parameterization: Dynamical Analysis of Localized Random Forcing**

Pavel Berloff (Imperial College London)**Adaptive Ensemble Kalman Filtering of Nonlinear Systems**

Tyrus Berry (George Mason University)

A common assumption of Kalman filtering methods for nonlinear dynamics is that the covariance structures of the system noise and observation noise are readily available. If these covariances are not known, or are changing, filter performance will be compromised. Early in the development of Kalman filters, Mehra enabled adaptivity by showing how to estimate these needed covariances, but only in the case of linear dynamics with full observation. We propose an adaptive filter based on the unscented version of the ensemble Kalman filter (EnKF) which estimates the covariances in real time even for nonlinear dynamics and observations. We test the adaptive filter on a 40-dimensional Lorenz96 model and show the dramatic improvements in state estimation that are possible. We also discuss the extent to which such an adaptive filter can compensate for model error.**Phase Transitions in Permafrost and Carbon-Climate Feedback**

Ivan Sudakov (The University of Utah)

In this research, we consider a mathematical model of permafrost lake growth and then using this model we propose a simple phenomenological equation that allows us to evaluate the impact of the Siberian permafrost on climate. Mathematically, permafrost thawing can be described by the classical Stefan approach. We can use a modified approach based on the phase transition theory. This takes into account that thawing layer has a small but non-zero width. The transition from the frozen state to the thawing state is a microscopic process, while lakes are great macroscopic objects. Thus we can assume that locally a lake boundary is a sphere of a large radius of curvature. Moreover, the growth is a slow process. Under such assumptions, thawing front velocity can be investigated. Indeed, there are possible asymptotic approaches based on so-called mean curvature motion. As a result, we obtain a deterministic equation that serves as an extremely simplified model of lake growth. We can, therefore, propose here a simple method to compute methane emission into the atmosphere using natural assumption that the horizontal dimensions of the lakes are much larger than the lake depth. We note that the permafrost lake model that we developed for the methane emission positive feedback loop problem is a conceptual climate model.**Power Law Behavior of Atmospheric Variability**

Philip Sura (Florida State University)

(Joint work with Robert West)

Extreme climate events may be defined as atmospheric or oceanic phenomena that occupy the tails of a data set’s probability density function (PDF), where the magnitude of the event is large, but the probability of occurrence is rare. Though these types of events are statistically sparse, it is necessary to understand the distribution of events in the tails, as quantifying the likelihood of climate extremes is an important step in predicting overall climate variability. It has been known for some time that the PDFs of atmospheric phenomena are decidedly non-Gaussian, though the shape of PDF has not been specified explicitly. More recently, it has been shown from observations that many atmospheric variables follow a power law distribution in the tails. This is in agreement with stochastic theory, which asserts that power law distributions should exist in the tails. However, a statistically rigorous study of the resulting power law distributions has not yet been performed. To show the relationship systematically, we examine the PDF tails of dynamically significant atmospheric variables (such as geopotential height and relative vorticity) for evidence of power law behavior. This is achieved by using statistical algorithms that test PDFs for the bounds and magnitude of power law distributions and estimating the statistical significance of the power law tails. Local and spatial examples of power law distributions in the atmosphere are presented using time series of atmospheric data.**Slope of Vorticity Lines Derived from Numerical Models as a Tornado Predictor**

Douglas Dokken (University of St. Thomas)

We investigate the consequences of power laws and self similarity in mesocyclones and tornados as presented in (Cai 2005; Wurman and Gill 2001; Wurman and Alexander 2005). We give a model for tornado genesis and maintainence using the 3-dimensional vortex gas theory of (Chorin 1994). High energy vortices with negative temperature in the sense of (Onsager 1949) play an important role in the model. We speculate that the high temperature vortices formation is related to the helicity they inherit as they form or tilt into the vertical. We also exploit the notion of self-similarity to justify power laws for weak and strong tornados given in (Cai 2005; Wurman and Gill 2001; Wurman and Alexander 2005). Doing a nested grid simulation using ARPS we find results consistent with scaling in the studies above.

Joint work with Pavel Belik, Kurt Scholz and Misha Shvartsman**Derivation of Realizable Dynamic Sub-Grid Scale Stress Models Based on Stochastic Models**

Ehsan Kazemi (University of Wyoming)

Stochastic analysis was already shown to represent a powerful tool for the derivation of realizable linear and nonlinear SGS stress models, and for the development of unified turbulence models that can be used continuously as LES and RANS, or FDF and PDF methods. Here, it was shown that stochastic analysis is also very helpful for the development of realizable linear and nonlinear dynamic SGS stress models. We verified the derived model for simulation of turbulent Ekman layer.**Stochastic and Deterministic Models for Tropical Convection**

Boualem Khouider (University of Victoria)

Organized convection in the tropics hinders long term weather and climate predictions on the global scale and in midlatitudes in particular.

Improvement in the representation of organized convection and cloud processes in coarse-resolution climate models is one of the major challenges in contemporary climate modelling.

The multicloud model of Khouider and Majda (2006, 2008) is based on the self-similar structure of tropical convective systems as the building block.

It carries the three main cloud types that characterize organized tropical convection. As such it is very successful in capturing the physical and dynamical features of synoptic scale convectively coupled waves and the associated planetary scale intra-seasonal oscillation known as the Madden-Jullian oscillation. In order to represent the sub-grid variability due to unresolved interactions between those clouds and the environment, a stochastic multi-cloud model is proposed by Khouider, Biello, and Majda (2010). This model is further refined and compared against its deterministic counterpart by Frenkel, Majda, and Khouider (2012,2013). This poster summarizes the new results from this assessment and comparison.**Parametric Estimation of Wind Speed Models Via the Infinitesimal Generator**

William Thompson (University of British Columbia)

Estimation of continuous-time stochastic dynamics is a common task for researchers in many fields. In many cases, the goal is to obtain estimates of parameters in assumed dynamical models for the data. This poster will present such a method developed by D. Crommelin and E. Vanden-Eijnden that minimizes a spectral distance between a model and a time series. We apply it to simulated data from the Ornstein-Uhlenbeck process and discuss ways of improving the estimates of the associated parameters. Finally, the method is applied to ERA-40 reanalysis vector wind data and a sea surface wind model to obtain global parameter field estimates.**Ensemble Data Assimilation Using Reduced Stochastic Models**

Lewis Mitchell (University of Vermont)

We study a deterministic chaotic slow-fast system which exhibits noise-induced tipping between metastable regimes. We investigate whether stochastic forecast models can be beneficial in ensemble data assimilation, in particular in the realistic setting when observations are only available for slow variables. The main result is that under certain conditions stochastic forecast models with model error can improve the analysis skill when used in place of the perfect full deterministic model. The stochastic climate model is far superior at detecting transitions between regimes. Stochastic climate models are capable of producing superior skill in an ensemble setting due to finite ensemble size effects; ensembles obtained from the perfect deterministic forecast model lack sufficient spread even for moderate ensemble sizes. This is corroborated with numerical simulations.**The Skewness-Kurtosis Relationship Within a Stochastic Model for Sea**

Surface Temperature Variability With Seasonal Cycle.

Dong Sun (Florida State University)

It is known that observed sea surface temperature (SST) variability

satisfies a certain skewness-kurtosis constraint which is a

characterization of the strong non-Gaussian behavior. We present a

stochastic model for SST variability with seasonally varying mixed

layer depth and forcing. The model incorporates both additive and

multiplicative noise. The strongly non-Gaussian skewness-kurtosis

relationship found in daily SST data is recovered through

stochastic and asymptotic analysis, and simple computation. This

generalizes an earlier result of P. Sura et. al. where the seasonal

impact was neglected.**Stochastic Modeling for the Trojan Y-Chromosome Eradication Strategy of an Invasive Species**

Xueying Wang (Texas A & M University)

The Trojan Y-Chromosome (TYC) strategy, an autocidal genetic biocontrol method, has been proposed to eliminate invasive alien species. In this work, we develop a stochastic model to study the viability of the TYC eradication and control strategy of an invasive species. The dynamics of this stochastic model is governed by a Markov jump process. We rigorously prove that there is a positive probability that the extinction of wild-type females takes place within a finite time. Moreover, in the case where sex-reversed trojan females are introduced at a constant size, we formulate a stochastic differential equation (SDE) model, as an approximation to the proposed Markov jump process model. Using the SDE model, we investigate the probability distribution and expectation of the eradication time of wild-type females by solving Kolmogorov equations associated with these statistics. The results illustrate how the probability distribution and expectation of the eradication time are shaped by the initial conditions and the model parameters. In particular, the results indicate that (1) the extinction of wild-type females is expected solely with the presence of supermales; (2) elevating the constant size of the sex-reversed trojan females being introduced into the population will lead to an decrease in the expected extinction time, as opposed to an increase in the probability for the extinction to take place within a given investigation time.**Capturing Intermittent and Low-frequency Variability in High-dimensional Data Through Nonlinear Laplacian Spectral Analysis**

Dimitris Giannakis (Courant Institute of Mathematical Sciences)Andrew Majda (New York University)

Nonlinear Laplacian spectral analysis (NLSA) is a method for spatiotemporal analysis of high-dimensional data, which represents spatial and temporal patterns through singular value decomposition of a family of maps acting on scalar functions on the nonlinear data manifold. Through the use of orthogonal basis functions (determined by means of graph Laplace-Beltrami eigenfunction algorithms) and time-lagged embedding, NLSA captures intermittency, rare events, and other nonlinear dynamical features which are not accessible through classical linear approaches such as singular spectrum analysis. We present applications of NLSA to detection of decadal and intermittent modes of variability in the North Pacific sector of comprehensive climate models.