466 research outputs found
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
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. 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
Inverse Problems and Data Assimilation
These notes are designed with the aim of providing a clear and concise
introduction to the subjects of Inverse Problems and Data Assimilation, and
their inter-relations, together with citations to some relevant literature in
this area. The first half of the notes is dedicated to studying the Bayesian
framework for inverse problems. Techniques such as importance sampling and
Markov Chain Monte Carlo (MCMC) methods are introduced; these methods have the
desirable property that in the limit of an infinite number of samples they
reproduce the full posterior distribution. Since it is often computationally
intensive to implement these methods, especially in high dimensional problems,
approximate techniques such as approximating the posterior by a Dirac or a
Gaussian distribution are discussed. The second half of the notes cover data
assimilation. This refers to a particular class of inverse problems in which
the unknown parameter is the initial condition of a dynamical system, and in
the stochastic dynamics case the subsequent states of the system, and the data
comprises partial and noisy observations of that (possibly stochastic)
dynamical system. We will also demonstrate that methods developed in data
assimilation may be employed to study generic inverse problems, by introducing
an artificial time to generate a sequence of probability measures interpolating
from the prior to the posterior
Data Assimilation and Inverse Problems
These notes are designed with the aim of providing a clear and concise introduction to the subjects of Inverse Problems and Data Assimilation, and their inter-relations, together with citations to some relevant literature in this area. The first half of the notes is dedicated to studying the Bayesian framework for inverse problems. Techniques such as importance sampling and Markov Chain Monte Carlo (MCMC) methods are introduced; these methods have the desirable property that in the limit of an infinite number of samples they reproduce the full posterior distribution. Since it is often computationally intensive to implement these methods, especially in high dimensional problems, approximate techniques such as approximating the posterior by a Dirac or a Gaussian distribution are discussed. The second half of the notes cover data assimilation. This refers to a particular class of inverse problems in which the unknown parameter is the initial condition of a dynamical system, and in the stochastic dynamics case the subsequent states of the system, and the data comprises partial and noisy observations of that (possibly stochastic) dynamical system. We will also demonstrate that methods developed in data assimilation may be employed to study generic inverse problems, by introducing an artificial time to generate a sequence of probability measures interpolating from the prior to the posterior
Advancing Urban Flood Resilience With Smart Water Infrastructure
Advances in wireless communications and low-power electronics are enabling a new generation of smart water systems that will employ real-time sensing and control to solve our most pressing water challenges. In a future characterized by these systems, networks of sensors will detect and communicate flood events at the neighborhood scale to improve disaster response. Meanwhile, wirelessly-controlled valves and pumps will coordinate reservoir releases to halt combined sewer overflows and restore water quality in urban streams. While these technologies promise to transform the field of water resources engineering, considerable knowledge gaps remain with regards to how smart water systems should be designed and operated. This dissertation presents foundational work towards building the smart water systems of the future, with a particular focus on applications to urban flooding. First, I introduce a first-of-its-kind embedded platform for real-time sensing and control of stormwater systems that will enable emergency managers to detect and respond to urban flood events in real-time. Next, I introduce new methods for hydrologic data assimilation that will enable real-time geolocation of floods and water quality hazards. Finally, I present theoretical contributions to the problem of controller placement in hydraulic networks that will help guide the design of future decentralized flood control systems. Taken together, these contributions pave the way for adaptive stormwater infrastructure that will mitigate the impacts of urban flooding through real-time response.PHDCivil EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163144/1/mdbartos_1.pd
Machine Learning for Stochastic Parameterization: Generative Adversarial Networks in the Lorenz '96 Model
Stochastic parameterizations account for uncertainty in the representation of
unresolved sub-grid processes by sampling from the distribution of possible
sub-grid forcings. Some existing stochastic parameterizations utilize
data-driven approaches to characterize uncertainty, but these approaches
require significant structural assumptions that can limit their scalability.
Machine learning models, including neural networks, are able to represent a
wide range of distributions and build optimized mappings between a large number
of inputs and sub-grid forcings. Recent research on machine learning
parameterizations has focused only on deterministic parameterizations. In this
study, we develop a stochastic parameterization using the generative
adversarial network (GAN) machine learning framework. The GAN stochastic
parameterization is trained and evaluated on output from the Lorenz '96 model,
which is a common baseline model for evaluating both parameterization and data
assimilation techniques. We evaluate different ways of characterizing the input
noise for the model and perform model runs with the GAN parameterization at
weather and climate timescales. Some of the GAN configurations perform better
than a baseline bespoke parameterization at both timescales, and the networks
closely reproduce the spatio-temporal correlations and regimes of the Lorenz
'96 system. We also find that in general those models which produce skillful
forecasts are also associated with the best climate simulations.Comment: Submitted to Journal of Advances in Modeling Earth Systems (JAMES
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