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Accurate atmospheric 3D wind observations are a high priority in the science community. To address this requirement and to support researchers' needs to acquire and analyze wind data from multiple sources, the System for Analysis of Wind Collocations (SAWC) was jointly developed by NOAA/NESDIS/STAR, UMD/ESSIC/CISESS, and UW-Madison/CIMSS. SAWC encompasses a multi-year archive of global 3D winds observed by Aeolus, sondes, aircraft, stratospheric superpressure balloons, and satellite-derived atmospheric motion vectors, archived and uniformly formatted in netCDF for public consumption; identified pairings between select datasets collocated in space and time; and a downloadable software application developed for users to interactively collocate and statistically compare wind observations based on their research needs. The utility of SAWC is demonstrated by conducting a one-year (September 2019-August 2020) evaluation of Aeolus level-2B (L2B) winds (Baseline 11 L2B processor version). Observations from four archived conventional wind datasets are collocated with Aeolus. Recommended quality controls are applied. Wind comparisons are assessed using the SAWC collocation application. Comparison statistics are stratified by season, geographic region, and Aeolus observing mode. The results highlight the value of SAWC's capabilities, from product validation through intercomparison studies to the evaluation of data usage in applications and advances in the global Earth observing architecture, Comment: 20 pages, 13 figures, 6 tables

We develop a framework to study the role of variability in transport across a streamline of a reference flow. Two complementary schemes are presented: a graphical approach for individual cases, and an analytical approach for general properties. The spatially nonlinear interaction of dynamic variability and the reference flow results in flux variability. The characteristic time-scale of the dynamic variability and the length-scale of the flux variability in a unit of flight-time govern the spatio-temporal interaction that leads to transport. The non-dimensional ratio of the two characteristic scales is shown to be a a critical parameter. The pseudo-lobe sequence along the reference streamline describes spatial coherency and temporal evolution of transport. For finite-time transport from an initial time up to the present, the characteristic length-scale of the flux variability regulates the width of the pseudo-lobes. The phase speed of pseudo-lobe propagation averages the reference flow and the flux variability. In contrast, for definite transport over a fixed time interval and spatial segment, the characteristic time-scale of the dynamic variability regulates the width of the pseudo-lobes. Generation of the pseudo-lobe sequence appears to be synchronous with the dynamic variability, although it propagates with the reference flow. In either case, the critical characteristic ratio is found to be one, corresponding to a resonance of the flux variability with the reference flow. Using a kinematic model, we demonstrate the framework for two types of transport in a blocked flow of the mid-latitude atmosphere: across the meandering jet axis and between the jet and recirculating cell., Comment: 49 pages, 13 figures

We present a framework for the analysis of transport processes resulting from the mean-eddy interaction in a flow. The framework is based on the {\bf T}ransport {\bf I}nduced by the {\bf M}ean-{\bf E}ddy {\bf I}nteraction (TIME) method presented in a companion paper \cite{ide_wiggins_pd06a}. The TIME method estimates the (Lagrangian) transport across stationary (Eulerian) boundaries defined by chosen streamlines of the mean flow. Our framework proceeds after first carrying out a sequence of preparatory steps that link the flow dynamics to the transport processes. This includes the construction of the so-called "instantaneous flux" as the Hovm\"{o}ller diagram. Transport processes are studied by linking the signals of the instantaneous flux field to the dynamical variability of the flow. This linkage also reveals how the variability of the flow contributes to the transport. The spatio-temporal analysis of the flux diagram can be used to assess the efficiency of the variability in transport processes. We apply the method to the double-gyre ocean circulation model in the situation where the Rossby-wave mode dominates the dynamic variability. The spatio-temporal analysis shows that the inter-gyre transport is controlled by the circulating eddy vortices in the fast eastward jet region, whereas the basin-scale Rossby waves have very little impact., Comment: 32 pages, 7 figures

In this paper we develop a method for the estimation of {\bf T}ransport {\bf I}nduced by the {\bf M}ean-{\bf E}ddy interaction (TIME) in two-dimensional unsteady flows. The method is built on the dynamical systems approach and can be viewed as a hybrid combination of Lagrangian and Eulerian methods. The (Eulerian) boundaries across which we consider (Lagrangian) transport are kinematically defined by appropriately chosen streamlines of the mean flow. By evaluating the impact of the mean-eddy interaction on transport, the TIME method can be used as a diagnostic tool for transport processes that occur during a specified time interval along a specified boundary segment. We introduce two types of TIME functions: one that quantifies the accumulation of flow properties and another that measures the displacement of the transport geometry. The spatial geometry of transport is described by the so-called pseudo-lobes, and temporal evolution of transport by their dynamics. In the case where the TIME functions are evaluated along a separatrix, the pseudo-lobes have a relationship to the lobes of Lagrangian transport theory. In fact, one of the TIME functions is identical to the Melnikov function that is used to measure the distance, at leading order in a small parameter, between the two invariant manifolds that define the Lagrangian lobes. We contrast the similarities and differences between the TIME and Lagrangian lobe dynamics in detail. An application of the TIME method is carried out for inter-gyre transport in the wind-driven oceanic circulation model and a comparison with the Lagrangian transport theory is made., Comment: 48 pages, 9 figures

Two recent works have adapted the Kalman-Bucy filter into an ensemble setting. In the first formulation, BR10, the full ensemble is updated in the analysis step as the solution of single set of ODEs in pseudo-BGR09, the ensemble of perturbations is updated by the solution of an ordinary differential equation (ODE) in pseudo-time, while the mean is updated as in the standard KF. In the second formulation, BR10, the full ensemble is updated in the analysis step as the solution of single set of ODEs in pseudo-time. Neither requires matrix inversions except for the frequently diagonal observation error covariance. We analyze the behavior of the ODEs involved in these formulations. We demonstrate that they stiffen for large magnitudes of the ratio of background to observational error covariance, and that using the integration scheme proposed in both BGR09 and BR10 can lead to failure. An integration scheme that is both stable and is not computationally expensive is proposed. We develop transform-based alternatives for these Bucy-type approaches so that the integrations are computed in ensemble space where the variables are weights (of dimension equal to the ensemble size) rather than model variables. Finally, the performance of our ensemble transform Kalman-Bucy implementations is evaluated using three models: the 3-variable Lorenz 1963 model, the 40-variable Lorenz 1996 model, and a medium complexity atmospheric general circulation model (AGCM) known as SPEEDY. The results from all three models are encouraging and warrant further exploration of these assimilation techniques.

Validation is often defined as the process of determining the degree to which a model is an accurate representation of the real world from the perspective of its intended uses. Validation is crucial as industries and governments depend increasingly on predictions by computer models to justify their decisions. In this article, we survey the model validation literature and propose to formulate validation as an iterative construction process that mimics the process occurring implicitly in the minds of scientists. We thus offer a formal representation of the progressive build-up of trust in the model, and thereby replace incapacitating claims on the impossibility of validating a given model by an adaptive process of constructive approximation. This approach is better adapted to the fuzzy, coarse-grained nature of validation. Our procedure factors in the degree of redundancy versus novelty of the experiments used for validation as well as the degree to which the model predicts the observations. We illustrate the new methodology first with the maturation of Quantum Mechanics as the arguably best established physics theory and then with several concrete examples drawn from some of our primary scientific interests: a cellular automaton model for earthquakes, an anomalous diffusion model for solar radiation transport in the cloudy atmosphere, and a computational fluid dynamics code for the Richtmyer-Meshkov instability. This article is an augmented version of Sornette et al. [2007] that appeared in Proceedings of the National Academy of Sciences in 2007 (doi: 10.1073/pnas.0611677104), with an electronic supplement at URL http://www.pnas.org/cgi/content/full/0611677104/DC1. Sornette et al. [2007] is also available in preprint form at physics/0511219., Comment: 50 pages, 5 figures, be published in the Lecture Notes in Computational Science and Engineering, Vol. TBD), Proceedings of in Computational Methods in Transport, Granlibakken 2006, F. Graziani and D. Swesty (Eds.), Springer-Verlag, New York (NY), 2007

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