{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/33727"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/33727","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Large-Scale Simulations Using First and Second Order Adjoints with Applications in Data Assimilation","abstract":"In large-scale air quality simulations we are interested in the influence factors which cause changes of pollutants, and optimization methods which improve forecasts. The solutions to these problems can be achieved by incorporating adjoint models, which are efficient in computing the derivatives of a functional with respect to a large number of model parameters. In this research we employ first order adjoints in air quality simulations. Moreover, we explore theoretically the computation of second order adjoints for chemical transport models, and illustrate their feasibility in several aspects. We apply first order adjoints to sensitivity analysis and data assimilation. Through sensitivity analysis, we can discover the area that has the largest influence on changes of ozone concentrations at a receptor. For data assimilation with optimization methods which use first order adjoints, we assess their performance under different scenarios. The results indicate that the L-BFGS method is the most efficient. Compared with first order adjoints, second order adjoints have not been used to date in air quality simulation. To explore their utility, we show the construction of second order adjoints for chemical transport models and demonstrate several applications including sensitivity analysis, optimization, uncertainty quantification, and Hessian singular vectors. Since second order adjoints provide second order information in the form of Hessian-vector product instead of the entire Hessian matrix, it is possible to implement applications for large-scale models which require second order derivatives. Finally, we conclude that second order adjoints for chemical transport models are computationally feasible and effective.","abstract_html":"In large-scale air quality simulations we are interested in the influence factors which cause changes of pollutants, and optimization methods which improve forecasts. The solutions to these problems can be achieved by incorporating adjoint models, which are efficient in computing the derivatives of a functional with respect to a large number of model parameters. In this research we employ first order adjoints in air quality simulations. Moreover, we explore theoretically the computation of second order adjoints for chemical transport models, and illustrate their feasibility in several aspects. We apply first order adjoints to sensitivity analysis and data assimilation. Through sensitivity analysis, we can discover the area that has the largest influence on changes of ozone concentrations at a receptor. For data assimilation with optimization methods which use first order adjoints, we assess their performance under different scenarios. The results indicate that the L-BFGS method is the most efficient. Compared with first order adjoints, second order adjoints have not been used to date in air quality simulation. To explore their utility, we show the construction of second order adjoints for chemical transport models and demonstrate several applications including sensitivity analysis, optimization, uncertainty quantification, and Hessian singular vectors. Since second order adjoints provide second order information in the form of Hessian-vector product instead of the entire Hessian matrix, it is possible to implement applications for large-scale models which require second order derivatives. Finally, we conclude that second order adjoints for chemical transport models are computationally feasible and effective.","abstract_has_math":false,"creators":["Zhang, Lin"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Computer Science","degree_department":"Computer Science","school":null,"contributors":[],"advisors":[],"committee_chairs":["Sandu, Adrian"],"committee_members":["Ribbens, Calvin J.","Borggaard, Jeffrey T.","Cao, Yang"],"year":2007,"date_issued":"2007-06-09","date_published":"2007-06-09","updated_at":"2026-07-22T22:19:21Z","subjects":["Sensitivity Analysis","Second Order Adjoints","4D-Var Data Assimilation","Optimization"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-06242007-154228"],"render_values":[{"text":"etd-06242007-154228","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/33727","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Sandu, Adrian"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Ribbens, Calvin J.","Borggaard, Jeffrey T.","Cao, Yang"]},{"key":"dc:contributor.department","label":"Department","values":["Computer Science"]},{"key":"dc:creator","label":"Author","values":["Zhang, Lin"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T20:40:28Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T20:40:28Z","2007-07-23"]},{"key":"dc:date.issued","label":"Date","values":["2007-06-09"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Sensitivity Analysis","Second Order Adjoints","4D-Var Data Assimilation","Optimization"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-06242007-154228"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/33727"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In large-scale air quality simulations we are interested in the influence factors which cause changes of pollutants, and optimization methods which improve forecasts. The solutions to these problems can be achieved by incorporating adjoint models, which are efficient in computing the derivatives of a functional with respect to a large number of model parameters. In this research we employ first order adjoints in air quality simulations. Moreover, we explore theoretically the computation of second order adjoints for chemical transport models, and illustrate their feasibility in several aspects. We apply first order adjoints to sensitivity analysis and data assimilation. Through sensitivity analysis, we can discover the area that has the largest influence on changes of ozone concentrations at a receptor. For data assimilation with optimization methods which use first order adjoints, we assess their performance under different scenarios. The results indicate that the L-BFGS method is the most efficient. Compared with first order adjoints, second order adjoints have not been used to date in air quality simulation. To explore their utility, we show the construction of second order adjoints for chemical transport models and demonstrate several applications including sensitivity analysis, optimization, uncertainty quantification, and Hessian singular vectors. Since second order adjoints provide second order information in the form of Hessian-vector product instead of the entire Hessian matrix, it is possible to implement applications for large-scale models which require second order derivatives. Finally, we conclude that second order adjoints for chemical transport models are computationally feasible and effective."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:title","label":"Title","values":["Large-Scale Simulations Using First and Second Order Adjoints with Applications in Data Assimilation"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Sandu, Adrian"],"dc:contributor.committeemember":["Ribbens, Calvin J.","Borggaard, Jeffrey T.","Cao, Yang"],"dc:contributor.department":["Computer Science"],"dc:creator":["Zhang, Lin"],"dc:date.accessioned":["2014-03-14T20:40:28Z"],"dc:date.available":["2014-03-14T20:40:28Z","2007-07-23"],"dc:date.issued":["2007-06-09"],"dc:description.abstract":["In large-scale air quality simulations we are interested in the influence factors which cause changes of pollutants, and optimization methods which improve forecasts. The solutions to these problems can be achieved by incorporating adjoint models, which are efficient in computing the derivatives of a functional with respect to a large number of model parameters. In this research we employ first order adjoints in air quality simulations. Moreover, we explore theoretically the computation of second order adjoints for chemical transport models, and illustrate their feasibility in several aspects. We apply first order adjoints to sensitivity analysis and data assimilation. Through sensitivity analysis, we can discover the area that has the largest influence on changes of ozone concentrations at a receptor. For data assimilation with optimization methods which use first order adjoints, we assess their performance under different scenarios. The results indicate that the L-BFGS method is the most efficient. Compared with first order adjoints, second order adjoints have not been used to date in air quality simulation. To explore their utility, we show the construction of second order adjoints for chemical transport models and demonstrate several applications including sensitivity analysis, optimization, uncertainty quantification, and Hessian singular vectors. Since second order adjoints provide second order information in the form of Hessian-vector product instead of the entire Hessian matrix, it is possible to implement applications for large-scale models which require second order derivatives. 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