Content in the Context of 4D-Var Data Assimilation. II: Application to Global Ozone Assimilation

Data assimilation obtains improved estimates of the state of a physical system by combining imperfect model results with sparse and noisy observations of reality. Not all observations used in data assimilation are equally valuable. The ability to characterize the usefulness of different data points is important for analyzing the effectiveness of the assimilation system, for data pruning, and for the design of future sensor systems. In the companion paper [Sandu et al.(2011)] we derived an ensemble-based computational procedure to estimate the information content of various observations in the context of 4D-Var. Here we apply this methodology to quantify two information metrics (the signal and degrees of freedom for signal) for satellite observations used in a global chemical data assimilation problem with the GEOS-Chem chemical transport model. The assimilation of a subset of data points characterized by the highest information content, gives analyses that are comparable in quality with the one obtained using the entire data set

A Practical Method to Estimate Information Content in the Context of 4D-Var Data Assimilation. I: Methodology

Data assimilation obtains improved estimates of the state of a physical system by combining imperfect model results with sparse and noisy observations of reality. Not all observations used in data assimilation are equally valuable. The ability to characterize the usefulness of different data points is important for analyzing the effectiveness of the assimilation system, for data pruning, and for the design of future sensor systems. This paper focuses on the four dimensional variational (4D-Var) data assimilation framework. Metrics from information theory are used to quantify the contribution of observations to decreasing the uncertainty with which the system state is known. We establish an interesting relationship between different information-theoretic metrics and the variational cost function/gradient under Gaussian linear assumptions. Based on this insight we derive an ensemble-based computational procedure to estimate the information content of various observations in the context of 4D-Var. The approach is illustrated on linear and nonlinear test problems. In the companion paper [Singh et al.(2011)] the methodology is applied to a global chemical data assimilation problem

A Practical Method to Estimate Information Content in the Context of 4D-Var Data Assimilation. II: Application to Global Ozone Assimilation

Data assimilation obtains improved estimates of the state of a physical system by combining imperfect model results with sparse and noisy observations of reality. Not all observations used in data assimilation are equally valuable. The ability to characterize the usefulness of different data points is important for analyzing the effectiveness of the assimilation system, for data pruning, and for the design of future sensor systems. In the companion paper (Sandu et al., 2012) we derive an ensemble-based computational procedure to estimate the information content of various observations in the context of 4D-Var. Here we apply this methodology to quantify the signal and degrees of freedom for signal information metrics of satellite observations used in a global chemical data assimilation problem with the GEOS-Chem chemical transport model. The assimilation of a subset of data points characterized by the highest information content yields an analysis comparable in quality with the one obtained using the entire data set

Geostationary Coastal and Air Pollution Events (GEO-CAPE) Sensitivity Analysis Experiment

Geostationary Coastal and Air pollution Events (GEO-CAPE) is a NASA decadal survey mission to be designed to provide surface reflectance at high spectral, spatial, and temporal resolutions from a geostationary orbit necessary for studying regional-scale air quality issues and their impact on global atmospheric composition processes. GEO-CAPE's Atmospheric Science Questions explore the influence of both gases and particles on air quality, atmospheric composition, and climate. The objective of the GEO-CAPE Observing System Simulation Experiment (OSSE) is to analyze the sensitivity of ozone to the global and regional NOx emissions and improve the science impact of GEO-CAPE with respect to the global air quality. The GEO-CAPE OSSE team at Jet propulsion Laboratory has developed a comprehensive OSSE framework that can perform adjoint-sensitivity analysis for a wide range of observation scenarios and measurement qualities. This report discusses the OSSE framework and presents the sensitivity analysis results obtained from the GEO-CAPE OSSE framework for seven observation scenarios and three instrument systems

Dynamic stereo microscopy for studying particle sedimentation

We demonstrate a new method for measuring the sedimentation of a single colloidal bead by using a combination of optical tweezers and a stereo microscope based on a spatial light modulator. We use optical tweezers to raise a micron-sized silica bead to a fixed height and then release it to observe its 3D motion while it sediments under gravity. This experimental procedure provides two independent measurements of bead diameter and a measure of Faxén’s correction, where the motion changes due to presence of the boundary

Position clamping in a holographic counterpropagating optical trap

Optical traps consisting of two counterpropagating, divergent beams of light allow relatively high forces to be exerted along the optical axis by turning off one beam, however the axial stiffness of the trap is generally low due to the lower numerical apertures typically used. Using a high speed spatial light modulator and CMOS camera, we demonstrate 3D servocontrol of a trapped particle, increasing the stiffness from 0.004 to 1.5μNm<sup>−1</sup>. This is achieved in the “macro-tweezers” geometry [Thalhammer, J. Opt. 13, 044024 (2011); Pitzek, Opt. Express 17, 19414 (2009)], which has a much larger field of view and working distance than single-beam tweezers due to its lower numerical aperture requirements. Using a 10×, 0.2NA objective, active feedback produces a trap with similar effective stiffness to a conventional single-beam gradient trap, of order 1μNm<sup>−1</sup> in 3D. Our control loop has a round-trip latency of 10ms, leading to a resonance at 20Hz. This is sufficient bandwidth to reduce the position fluctuations of a 10μm bead due to Brownian motion by two orders of magnitude. This approach can be trivially extended to multiple particles, and we show three simultaneously position-clamped beads

On the vanishing viscosity limit in a disk

We say that the solution u to the Navier-Stokes equations converges to a solution v to the Euler equations in the vanishing viscosity limit if u converges to v in the energy norm uniformly over a finite time interval. Working specifically in the unit disk, we show that a necessary and sufficient condition for the vanishing viscosity limit to hold is the vanishing with the viscosity of the time-space average of the energy of u in a boundary layer of width proportional to the viscosity due to modes (eigenfunctions of the Stokes operator) whose frequencies in the radial or the tangential direction lie between L and M. Here, L must be of order less than 1/(viscosity) and M must be of order greater than 1/(viscosity)