Revision of TR-09-25: A Hybrid Variational/Ensemble Filter Approach to Data Assimilation

Two families of methods are widely used in data assimilation: the four dimensional variational (4D-Var) approach, and the ensemble Kalman filter (EnKF) approach. The two families have been developed largely through parallel research efforts. Each method has its advantages and disadvantages. It is of interest to develop hybrid data assimilation algorithms that can combine the relative strengths of the two approaches. This paper proposes a subspace approach to investigate the theoretical equivalence between the suboptimal 4D-Var method (where only a small number of optimization iterations are performed) and the practical EnKF method (where only a small number of ensemble members are used) in a linear Gaussian setting. The analysis motivates a new hybrid algorithm: the optimization directions obtained from a short window 4D-Var run are used to construct the EnKF initial ensemble. The proposed hybrid method is computationally less expensive than a full 4D-Var, as only short assimilation windows are considered. The hybrid method has the potential to perform better than the regular EnKF due to its look-ahead property. Numerical results show that the proposed hybrid ensemble filter method performs better than the regular EnKF method for both linear and nonlinear test problems

Efficient Uncertainty Quantification with the Polynomial Chaos Method for Stiff Systems

The polynomial chaos method has been widely adopted as a computationally feasible approach for uncertainty quantification. Most studies to date have focused on non-stiff systems. When stiff systems are considered, implicit numerical integration requires the solution of a nonlinear system of equations at every time step. Using the Galerkin approach, the size of the system state increases from $n$ to $S \times n$, where $S$ is the number of the polynomial chaos basis functions. Solving such systems with full linear algebra causes the computational cost to increase from $O(n^3)$ to $O(S^3n^3)$. The $S^3$-fold increase can make the computational cost prohibitive. This paper explores computationally efficient uncertainty quantification techniques for stiff systems using the Galerkin, collocation and collocation least-squares formulations of polynomial chaos. In the Galerkin approach, we propose a modification in the implicit time stepping process using an approximation of the Jacobian matrix to reduce the computational cost. The numerical results show a run time reduction with a small impact on accuracy. In the stochastic collocation formulation, we propose a least-squares approach based on collocation at a low-discrepancy set of points. Numerical experiments illustrate that the collocation least-squares approach for uncertainty quantification has similar accuracy with the Galerkin approach, is more efficient, and does not require any modifications of the original code

Uncertainty Quantification and Apportionment in Air Quality Models using the Polynomial Chaos Method

Simulations of large-scale physical systems are often affected by the uncertainties in data, in model parameters, and by incomplete knowledge of the underlying physics. The traditional deterministic simulations do not account for such uncertainties. It is of interest to extend simulation results with ``error bars'' that quantify the degree of uncertainty. This added information provides a confidence level for the simulation result. For example, the air quality forecast with an associated uncertainty information is very useful for making policy decisions regarding environmental protection. Techniques such as Monte Carlo (MC) and response surface are popular for uncertainty quantification, but accurate results require a large number of runs. This incurs a high computational cost, which maybe prohibitive for large-scale models. The polynomial chaos (PC) method was proposed as a practical and efficient approach for uncertainty quantification, and has been successfully applied in many engineering fields. Polynomial chaos uses a spectral representation of uncertainty. It has the ability to handle both linear and nonlinear problems with either Gaussian or non-Gaussian uncertainties. This work extends the functionality of the polynomial chaos method to Source Uncertainty Apportionment (SUA), i.e., we use the polynomial chaos approach to attribute the uncertainty in model results to different sources of uncertainty. The uncertainty quantification and source apportionment are implemented in the Sulfur Transport Eulerian Model (STEM-III). It allows us to assess the combined effects of different sources of uncertainty to the ozone forecast. It also enables to quantify the contribution of each source to the total uncertainty in the predicted ozone levels

Authorization-enhanced security framework for OGSA support.

Security plays an important role for a large distributed system in an open community. Without enough knowledge about the user, it is hard to make access decision to the local resources. Current Public Key Infrastructure (PKI) uses a trusted third party, called Certificate Authority (CA), to check the identity of the users. The assumption of PKI is that every entity trusts CA absolutely and equally. This is also a weakness of PKI. The security problem in a Single-Sign-On (SSO) environment is more difficult to manage. Most of the current SSO security approach relies heavily on the pre-established trust relationship. This prevents wider adoption of SSO and greatly affects the local autonomy of the security policy making. Such SSO approaches have been employed recently in the Security Assertion Mark-up Language (SAML). Based on the Dempster-Shafer theory and derived subjective logic, we propose an authorization-enhanced framework for large-distributed systems using a Single-Sign-On security approach. We extended the SAML assertion set to include opinions of the assertion issuer about the user. Based on the assertion issuer\u27s opinion about the user and the trust relationship between the asserting party and accepting party, new assertion is generated at each local site. The probability expectation about the user\u27s trustworthiness is computed. This value provides a reference for the system to make the access control decision. Two sub-frameworks will be discussed. The first is a Peer-to-Peer model involving two parties and a technique of discounting opinions. The second is a multi-party model. In the latter case, opinions about the user from many asserting parties are considered and computed using a consensus operator to combine opinions. A numerical study is performed to compare these two models. We also compare this approach with other work related with trust management. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2003 .C48. Source: Masters Abstracts International, Volume: 42-03, page: 0959. Adviser: Robert Kent. Thesis (M.Sc.)--University of Windsor (Canada), 2003

A Hybrid Approach to Estimating Error Covariances in Variational Data Assimilation

Data Assimilation (DA) involves the combination of observational data with the underlying dynamical principles governing the system under observation. In this work we combine the advantages of the two prominent advanced data assimilation systems, the 4D-Var and the ensemble methods. The proposed method consists of identifying the subspace spanned by the major 4D-Var error reduction directions. These directions are then removed from the background covariance through a Galerkin-type projection. This generates an updated error covariance information at both end points of an assimilation window. The error covariance information is updated between assimilation windows to capture the ``error of the day''. Numerical results using our new hybrid approach on a nonlinear model demonstrate how the background covariance matrix leads to an error covariance update that improves the 4D-Var DA results

Dosimetric comparison of intensity modulated radiotherapy and three-dimensional conformal radiotherapy in patients with gynecologic malignancies: a systematic review and meta-analysis

BACKGROUND: To quantitatively evaluate the safety and related-toxicities of intensity modulated radiotherapy (IMRT) dose–volume histograms (DVHs), as compared to the conventional three-dimensional conformal radiotherapy (3D-CRT), in gynecologic malignancy patients by systematic review of the related publications and meta-analysis. METHODS: Relevant articles were retrieved from the PubMed, Embase, and Cochrane Library databases up to August 2011. Two independent reviewers assessed the included studies and extracted data. Pooled average percent irradiated volumes of adjacent non-cancerous tissues were calculated and compared between IMRT and 3D-CRT for a range of common radiation doses (5-45Gy). RESULTS: In total, 13 articles comprised of 222 IMRT-treated and 233 3D-CRT-treated patients were included. For rectum receiving doses ≥30 Gy, the IMRT pooled average irradiated volumes were less than those from 3D-CRT by 26.40% (30 Gy, p = 0.004), 27.00% (35 Gy, p = 0.040), 37.30% (40 Gy, p = 0.006), and 39.50% (45 Gy, p = 0.002). Reduction in irradiated small bowel was also observed for IMRT-delivered 40 Gy and 45 Gy (by 17.80% (p = 0.043) and 17.30% (p = 0.012), respectively), as compared with 3D-CRT. However, there were no significant differences in the IMRT and 3D-CRT pooled average percent volumes of irradiated small bowel or rectum from lower doses, or in the bladder or bone marrow from any of the doses. IMRT-treated patients did not experience more severe acute or chronic toxicities than 3D-CRT-treated patients. CONCLUSIONS: IMRT-delivered high radiation dose produced significantly less average percent volumes of irradiated rectum and small bowel than 3D-CRT, but did not differentially affect the average percent volumes in the bladder and bone marrow