Fast Ensemble Smoothing

Smoothing is essential to many oceanographic, meteorological and hydrological applications. The interval smoothing problem updates all desired states within a time interval using all available observations. The fixed-lag smoothing problem updates only a fixed number of states prior to the observation at current time. The fixed-lag smoothing problem is, in general, thought to be computationally faster than a fixed-interval smoother, and can be an appropriate approximation for long interval-smoothing problems. In this paper, we use an ensemble-based approach to fixed-interval and fixed-lag smoothing, and synthesize two algorithms. The first algorithm produces a linear time solution to the interval smoothing problem with a fixed factor, and the second one produces a fixed-lag solution that is independent of the lag length. Identical-twin experiments conducted with the Lorenz-95 model show that for lag lengths approximately equal to the error doubling time, or for long intervals the proposed methods can provide significant computational savings. These results suggest that ensemble methods yield both fixed-interval and fixed-lag smoothing solutions that cost little additional effort over filtering and model propagation, in the sense that in practical ensemble application the additional increment is a small fraction of either filtering or model propagation costs. We also show that fixed-interval smoothing can perform as fast as fixed-lag smoothing and may be advantageous when memory is not an issue

Morphing Ensemble Kalman Filters

A new type of ensemble filter is proposed, which combines an ensemble Kalman filter (EnKF) with the ideas of morphing and registration from image processing. This results in filters suitable for nonlinear problems whose solutions exhibit moving coherent features, such as thin interfaces in wildfire modeling. The ensemble members are represented as the composition of one common state with a spatial transformation, called registration mapping, plus a residual. A fully automatic registration method is used that requires only gridded data, so the features in the model state do not need to be identified by the user. The morphing EnKF operates on a transformed state consisting of the registration mapping and the residual. Essentially, the morphing EnKF uses intermediate states obtained by morphing instead of linear combinations of the states.Comment: 17 pages, 7 figures. Added DDDAS references to the introductio

The nature of the pandemic:Exploring the negative impacts of the COVID-19 pandemic upon recreation visitor behaviors and experiences in parks and protected areas

The COVID-19 pandemic dramatically affected parks and protected areas and overall recreation visitation across the United States. While outdoor recreation has been demonstrated to be beneficial, especially during a pandemic, the resulting increase in recreation visitation raises concerns regarding the broader influence of social, situational, ecological, and behavioral factors upon overall visitor experiences. This study investigated the extent to which recreation visitors’ behaviors and experiences have been impacted by the COVID-19 pandemic within the White Mountain National Forest (WMNF). A modified drop-off pick-up survey method was employed to collect population-level data from WMNF visitors from June to August of 2020 (n=317), at the height of the pandemic. Results from this mixed-method study suggest social factors (e.g., crowding and conflict), situational factors (e.g., access and closures), ecological factors (e.g., vegetation damage), behavioral factors (e.g., substitution), and sociodemographic factors (e.g., gender and income) significantly influenced overall visitor decision-making and experience quality within the WMNF. For example, more than one-third of visitors indicated the pandemic had either a major or severe impact upon their WMNF recreation experience. A more nuanced investigation of qualitative data determined that the majority of pandemic-related recreation impacts revolved around the themes of social impacts, general negative recreation impacts, situational and ecological impacts, and behavioral adaptation impacts. Moreover, historically marginalized populations (e.g., low-income households and females) within the sample reported significantly higher recreation experience impacts during the pandemic. This study demonstrates the influence of the pandemic upon outdoor recreation visitor experiences and behaviors and considers outdoor recreation as a central component within the broader social-ecological systems framework. This study demonstrates the influence of the pandemic upon outdoor recreation visitor experiences and behaviors and considers resource users a central component within the broader social-ecological systems conceptual framework. MANAGEMENT IMPLICATIONS: This study found that during the peak of the COVID-19 pandemic, social, situational, ecological, behavioral, and sociodemographic factors significantly influenced overall visitor decision-making andexperience quality: · Social and general recreation impacts were most common, with approximately 56% of the sample reporting these issues. · Results suggest significant crowding and conflict impacts stemmed from interactions between in-state and out-of-state visitors, largely based upon perceived violations of pandemic protocols. · Moreover, historically marginalized populations stated unique recreation impacts during the pandemic. For instance, visitors from low-income households reported significantly less substitution options as opposed to high-income visitors. · Female visitors perceived significantly more pandemic-related conflict than male visitors. Study findings suggest visitor crowding and conflict should be prioritized by resource managers, especially amongst historically marginalized populations. Resource managers should consider adopting a broader social-ecological systems approach to parks and protected areas management, particularly during a global pandemic

Variational data assimilation for the initial-value dynamo problem

The secular variation of the geomagnetic field as observed at the Earth's surface results from the complex magnetohydrodynamics taking place in the fluid core of the Earth. One way to analyze this system is to use the data in concert with an underlying dynamical model of the system through the technique of variational data assimilation, in much the same way as is employed in meteorology and oceanography. The aim is to discover an optimal initial condition that leads to a trajectory of the system in agreement with observations. Taking the Earth's core to be an electrically conducting fluid sphere in which convection takes place, we develop the continuous adjoint forms of the magnetohydrodynamic equations that govern the dynamical system together with the corresponding numerical algorithms appropriate for a fully spectral method. These adjoint equations enable a computationally fast iterative improvement of the initial condition that determines the system evolution. The initial condition depends on the three dimensional form of quantities such as the magnetic field in the entire sphere. For the magnetic field, conservation of the divergence-free condition for the adjoint magnetic field requires the introduction of an adjoint pressure term satisfying a zero boundary condition. We thus find that solving the forward and adjoint dynamo system requires different numerical algorithms. In this paper, an efficient algorithm for numerically solving this problem is developed and tested for two illustrative problems in a whole sphere: one is a kinematic problem with prescribed velocity field, and the second is associated with the Hall-effect dynamo, exhibiting considerable nonlinearity. The algorithm exhibits reliable numerical accuracy and stability. Using both the analytical and the numerical techniques of this paper, the adjoint dynamo system can be solved directly with the same order of computational complexity as that required to solve the forward problem. These numerical techniques form a foundation for ultimate application to observations of the geomagnetic field over the time scale of centuries

A wildland fire model with data assimilation

A wildfire model is formulated based on balance equations for energy and fuel, where the fuel loss due to combustion corresponds to the fuel reaction rate. The resulting coupled partial differential equations have coefficients that can be approximated from prior measurements of wildfires. An ensemble Kalman filter technique with regularization is then used to assimilate temperatures measured at selected points into running wildfire simulations. The assimilation technique is able to modify the simulations to track the measurements correctly even if the simulations were started with an erroneous ignition location that is quite far away from the correct one.Comment: 35 pages, 12 figures; minor revision January 2008. Original version available from http://www-math.cudenver.edu/ccm/report

A comparison of variational and Markov chain Monte Carlo methods for inference in partially observed stochastic dynamic systems

In recent work we have developed a novel variational inference method for partially observed systems governed by stochastic differential equations. In this paper we provide a comparison of the Variational Gaussian Process Smoother with an exact solution computed using a Hybrid Monte Carlo approach to path sampling, applied to a stochastic double well potential model. It is demonstrated that the variational smoother provides us a very accurate estimate of mean path while conditional variance is slightly underestimated. We conclude with some remarks as to the advantages and disadvantages of the variational smoother. © 2008 Springer Science + Business Media LLC

Pattern Recognition in a Bimodal Aquifer Using the Normal-Score Ensemble Kalman Filter

The ensemble Kalman filter (EnKF) is now widely used in diverse disciplines to estimate model parameters and update model states by integrating observed data. The EnKF is known to perform optimally only for multi-Gaussian distributed states and parameters. A new approach, the normal-score EnKF (NS-EnKF), has been recently proposed to handle complex aquifers with non-Gaussian distributed parameters. In this work, we aim at investigating the capacity of the NS-EnKF to identify patterns in the spatial distribution of the model parameters (hydraulic conductivities) by assimilating dynamic observations in the absence of direct measurements of the parameters themselves. In some situations, hydraulic conductivity measurements (hard data) may not be available, which requires the estimation of conductivities from indirect observations, such as piezometric heads. We show how the NS-EnKF is capable of retrieving the bimodal nature of a synthetic aquifer solely from piezometric head data. 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DADA: data assimilation for the detection and attribution of weather and climate-related events

A new nudging method for data assimilation, delay‐coordinate nudging, is presented. Delay‐coordinate nudging makes explicit use of present and past observations in the formulation of the forcing driving the model evolution at each time step. Numerical experiments with a low‐order chaotic system show that the new method systematically outperforms standard nudging in different model and observational scenarios, also when using an unoptimized formulation of the delay‐nudging coefficients. A connection between the optimal delay and the dominant Lyapunov exponent of the dynamics is found based on heuristic arguments and is confirmed by the numerical results, providing a guideline for the practical implementation of the algorithm. Delay‐coordinate nudging preserves the easiness of implementation, the intuitive functioning and the reduced computational cost of the standard nudging, making it a potential alternative especially in the field of seasonal‐to‐decadal predictions with large Earth system models that limit the use of more sophisticated data assimilation procedures

Decarbonisation and its discontents: a critical energy justice perspective on four low-carbon transitions

Low carbon transitions are often assumed as normative goods, because they supposedly reduce carbon emissions, yet without vigilance there is evidence that they can in fact create new injustices and vulnerabilities, while also failing to address pre-existing structural drivers of injustice in energy markets and the wider socio-economy. With this in mind, we examine four European low-carbon transitions from an unusual normative perspective: that of energy justice. Because a multitude of studies looks at the co-benefits renewable energy, low-carbon mobility, or climate change mitigation, we instead ask in this paper: what are the types of injustices associated with low-carbon transitions? Relatedly, in what ways do low-carbon transitions worsen social risks or vulnerabilities? Lastly, what policies might be deployed to make these transitions more just? We answer these questions by first elaborating an “energy justice” framework consisting of four distinct dimensions—distributive justice (costs and benefits), procedural justice (due process), cosmopolitan justice (global externalities), and recognition justice (vulnerable groups). We then examine four European low-carbon transitions—nuclear power in France, smart meters in Great Britain, electric vehicles in Norway, and solar energy in Germany—through this critical justice lens. In doing so, we draw from original data collected from 64 semi-structured interviews with expert partisans as well as five public focus groups and the monitoring of twelve internet forums. We document 120 distinct energy injustices across these four transitions, including 19 commonly recurring injustices. We aim to show how when low-carbon transitions unfold, deeper injustices related to equity, distribution, and fairness invariably arise