ASU Scholarship Showcase

This paper studies the effect of targeted observations on state and parameter estimates determined with Kalman filter data assimilation (DA) techniques. We first provide an analytical result demonstrating that targeting observations within the Kalman filter for a linear model can significantly reduce state estimation error as opposed to fixed or randomly located observations. We next conduct observing system simulation experiments for a chaotic model of meteorological interest, where we demonstrate that the local ensemble transform Kalman filter (LETKF) with targeted observations based on largest ensemble variance is skillful in providing more accurate state estimates than the LETKF with randomly located observations. Additionally, we find that a hybrid ensemble Kalman filter parameter estimation method accurately updates model parameters within the targeted observation context to further improve state estimation.

The effects of urbanization on ozone levels have been widely investigated over cities primarily located in temperate and/or humid regions. In this study, nested WRF-Chem simulations with a finest grid resolution of 1 km are conducted to investigate ozone concentrations O₃ due to urbanization within cities in arid/semi-arid environments. First, a method based on a shape preserving Monotonic Cubic Interpolation (MCI) is developed and used to downscale anthropogenic emissions from the 4 km resolution 2005 National Emissions Inventory (NEI05) to the finest model resolution of 1 km. Using the rapidly expanding Phoenix metropolitan region as the area of focus, we demonstrate the proposed MCI method achieves ozone simulation results with appreciably improved correspondence to observations relative to the default interpolation method of the WRF-Chem system. Next, two additional sets of experiments are conducted, with the recommended MCI approach, to examine impacts of urbanization on ozone production: (1) the urban land cover is included (i.e., urbanization experiments) and, (2) the urban land cover is replaced with the region's native shrubland. Impacts due to the presence of the built environment on O₃ are highly heterogeneous across the metropolitan area. Increased near surface O₃ due to urbanization of 10–20 ppb is predominantly a nighttime phenomenon while simulated impacts during daytime are negligible. Urbanization narrows the daily O₃ range (by virtue of increasing nighttime minima), an impact largely due to the region's urban heat island. Our results demonstrate the importance of the MCI method for accurate representation of the diurnal profile of ozone, and highlight its utility for high-resolution air quality simulations for urban areas.

We present a new approach to computing event shape distributions or, more precisely, charge flow correlations in a generic conformal field theory (CFT). These infrared finite observables are familiar from collider physics studies and describe the angular distribution of global charges in outgoing radiation created from the vacuum by some source. The charge flow correlations can be expressed in terms of Wightman correlation functions in a certain limit. We explain how to compute these quantities starting from their Euclidean analogues by means of a nontrivial analytic continuation which, in the framework of CFT, can be performed elegantly in Mellin space. The relation between the charge flow correlations and Euclidean correlation functions can be reformulated directly in configuration space, bypassing the Mellin representation, as a certain Lorentzian double discontinuity of the correlation function integrated along the cuts. We illustrate the general formalism in N = 4 SYM, making use of the well-known results on the four-point correlation function of half-BPS scalar operators. We compute the double scalar flow correlation in N = 4 SYM, at weak and strong coupling and show that it agrees with known results obtained by different techniques. One of the remarkable features of the N = 4 theory is that the scalar and energy flow correlations are proportional to each other. Imposing natural physical conditions on the energy flow correlations (finiteness, positivity and regularity), we formulate additional constraints on the four-point correlation functions in N = 4SYM that should be valid at any coupling and away from the planar limit.

The Operator Product Expansion for null polygonal Wilson loop in planar maximally supersymmetric Yang–Mills theory runs systematically in terms of multi-particle pentagon transitions which encode the physics of excitations propagating on the color flux tube ending on the sides of the four-dimensional contour. Their dynamics was unraveled in the past several years and culminated in a complete description of pentagons as an exact function of the 't Hooft coupling. In this paper we provide a solution for the last building block in this program, the SU(4) matrix structure arising from internal symmetry indices of scalars and fermions. This is achieved by a recursive solution of the Mirror and Watson equations obeyed by the so-called singlet pentagons and fixing the form of the twisted component in their tensor decomposition. The non-singlet, or charged, pentagons are deduced from these by a limiting procedure.

We address the near-collinear expansion of NMHV six-particle scattering amplitudes at strong value of the 't Hooft coupling in planar maximally supersymmetric Yang–Mills theory. We complement recent studies of this observable within the context of the Pentagon Operator Product Expansion, via the dual superWilson loop description, by studying effects of multiple scalar exchanges that accompany (or not) massive flux-tube excitations. Due to the fact that holes have a very small, nonperturbatively generated mass m_h which is exponentially suppressed in the 't Hooft coupling, their exchanges must be resummed in the ultraviolet limit, T <<1/m_h. This procedure yields a contribution to the expectation value of the superloop which enters on equal footing with the classical area — a phenomenon which was earlier observed for MHV amplitudes. In all components, the near-massless scalar exchanges factorize from the ones of massive particles, at leading order in strong coupling.

Scattering amplitudes in maximally supersymmetric gauge theory receive a dual description in terms of the expectation value of the super Wilson loop stretched on a null polygonal contour. This makes the analysis amenable to nonperturbative techniques. Presently, we elaborate on a refined form of the operator product expansion in terms of pentagon transitions to compute twist-two contributions to NMHV amplitudes. To start with, we provide a novel derivation of scattering matrices starting from Baxter equations for flux-tube excitations propagating on magnon background. We propose bootstrap equations obeyed by pentagon form factors with nonsinglet quantum numbers with respect to the R-symmetry group and provide solutions to them to all orders in 't Hooft coupling. These are then successfully confronted against available perturbative calculations for NMHV amplitudes to four-loop order.

An interesting occurrence of a Rossby wave breaking event observed during the VORCORE experiment is presented and explained. Twenty-seven balloons were launched inside the Antarctic polar vortex. Almost all of these balloons evolved in the stratosphere around 500K within the vortex, except the one launched on 28 October 2005. In this case, the balloon was caught within a tongue of high potential vorticity (PV), and was ejected from the polar vortex. The evolution of this event is studied for the period between 19 and 25 November 2005. It is found that at the beginning of this period, the polar vortex experienced distortions due to the presence of Rossby waves. Then, these waves break and a tongue of high PV develops. On 25 November, the tongue became separated from the vortex and the balloon was ejected into the surf zone. Lagrangian simulations demonstrate that the air masses surrounding the balloon after its ejection were originating from the vortex edge. The wave breaking and the development of the tongue are confined within a region where a planetary Quasi-Stationary Wave 1 (QSW1) induces wind speeds with weaker values. The QSW1 causes asymmetry in the wind speed and the horizontal PV gradient along the edge of the polar vortex, resulting in a localized jet. Rossby waves with smaller scales propagating on top of this jet amplify as they enter the jet exit region and then break. The role of the QSW1 on the formation of the weak flow conditions that caused the non-linear wave breaking observed near the vortex edge is confirmed by three-dimensional numerical simulations using forcing with and without the contribution of the QSW1.

We address the near-collinear expansion of multiparticle NMHV amplitudes, namely, the heptagon and octagons in the dual language of null polygonal super Wilson loops. In particular, we verify multiparticle factorization of charged pentagon transitions in terms of pentagons for single flux-tube excitations within the framework of refined operator product expansion. We find a perfect agreement with available tree and one-loop data.

Scattering amplitudes in maximally supersymmetric gauge theory are dual to super-Wilson loops on null polygonal contours. The operator product expansion for the latter revealed that their dynamics is governed by the evolution of multiparticle GKP excitations. They were shown to emerge from the spectral problem of an underlying open spin chain. In this work we solve this model with the help of the Baxter Q-operator and Sklyanin's Separation of Variables methods. We provide an explicit construction for eigenfunctions and eigenvalues of GKP excitations. We demonstrate how the former define the so-called multiparticle hexagon transitions in super-Wilson loops and prove their factorized form at leading order of 't Hooft coupling for particle number-preserving transitions that were suggested earlier in a generic case.

We compute one-loop renormalization group equations for non-singlet twist-four operators in QCD. The calculation heavily relies on the light-cone gauge formalism in the momentum fraction space that essentially rephrases the analysis of all two-to-two and two-to-three transition kernels to purely algebraic manipulations both for non- and quasipartonic operators. This is the first brute force calculation of this sector available in the literature. Fourier transforming our findings to the coordinate space, we checked them against available results obtained within a conformal symmetry-based formalism that bypasses explicit diagrammatic calculations and confirmed agreement with the latter.