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Applications of Mathematics to Climate Modeling : = Analysis and Development of Ocean Parameterizations and Multivariate Localization Functions.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Applications of Mathematics to Climate Modeling :/
Reminder of title:	Analysis and Development of Ocean Parameterizations and Multivariate Localization Functions.
Author:	Stanley, Z. C.
Description:	1 online resource (129 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 83-03, Section: B.
Contained By:	Dissertations Abstracts International83-03B.
Subject:	Applied mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28648776click for full text (PQDT)
ISBN:	9798538153879

Applications of Mathematics to Climate Modeling : = Analysis and Development of Ocean Parameterizations and Multivariate Localization Functions.
Stanley, Z. C.

Applications of Mathematics to Climate Modeling :Analysis and Development of Ocean Parameterizations and Multivariate Localization Functions. - 1 online resource (129 pages)

Source: Dissertations Abstracts International, Volume: 83-03, Section: B.

Thesis (Ph.D.)--University of Colorado at Boulder, 2021.

Includes bibliographical references

This thesis discusses three different ways in which mathematics and statistics have led to improved understandings of our climate models. The first two chapters focus on different aspects of how ocean eddies are parameterized in ocean models, with particular attention to the use of high resolution ocean model output to inform coarser ocean models. The third chapter presents a method for dealing with the multiple length scales in coupled data assimilation. The Gent-McWilliams parameterization is commonly used in global ocean models to model the advective component of tracer transport effected by unresolved mesoscale eddies. In chapter 2 the vertical structure of the transfer coefficient in this parameterization is studied using data from a $0.1.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798538153879Subjects--Topical Terms:

2122814
Applied mathematics.
Subjects--Index Terms:

Coupled data assimilationIndex Terms--Genre/Form:

542853
Electronic books.

Applications of Mathematics to Climate Modeling : = Analysis and Development of Ocean Parameterizations and Multivariate Localization Functions.
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100 1 $a Stanley, Z. C. $3 3699925
245 1 0 $a Applications of Mathematics to Climate Modeling : $b Analysis and Development of Ocean Parameterizations and Multivariate Localization Functions.
264 0 $c 2021
300 $a 1 online resource (129 pages)
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500 $a Source: Dissertations Abstracts International, Volume: 83-03, Section: B.
500 $a Advisor: Grooms, Ian; Kleiber, William.
502 $a Thesis (Ph.D.)--University of Colorado at Boulder, 2021.
504 $a Includes bibliographical references
520 $a This thesis discusses three different ways in which mathematics and statistics have led to improved understandings of our climate models. The first two chapters focus on different aspects of how ocean eddies are parameterized in ocean models, with particular attention to the use of high resolution ocean model output to inform coarser ocean models. The third chapter presents a method for dealing with the multiple length scales in coupled data assimilation. The Gent-McWilliams parameterization is commonly used in global ocean models to model the advective component of tracer transport effected by unresolved mesoscale eddies. In chapter 2 the vertical structure of the transfer coefficient in this parameterization is studied using data from a $0.1.
520 $a \\circ$ resolution global ocean-ice simulation.The vertical structure is found to be well approximated by a baroclinic mode structure with no flow at the bottom, though horizontal anisotropy is crucial for obtaining a good fit. This vertical structure is motivated by reference to the vertical structure of mesoscale eddy velocity and density anomalies, which are also diagnosed from the data.Unresolved temperature and salinity fluctuations interact with a nonlinear seawater equation of state to produce significant errors in the ocean model evaluation of the large scale density field. In chapter 3 it is shown that the impact of temperature fluctuations dominates the impact of salinity fluctuations and that the error in density is, to leading order, proportional to the product of a subgrid scale temperature variance and a second derivative of the equation of state. Two parameterizations are proposed to correct the large scale density field: one deterministic and one stochastic. Free parameters in both parameterizations are fit using fine-resolution model data. Both parameterizations are computationally efficient as they require only one additional evaluation of a nonlinear equation at each grid cell. A companion paper will discuss the climate impacts of the parameterizations proposed here. Localization is widely used in data assimilation schemes to mitigate the impact of sampling errors on ensemble-derived background error covariance matrices. Strongly coupled data assimilation allows observations in one component of a coupled model to directly impact another component through inclusion of cross-domain terms in the background error covariance matrix. When different components have disparate dominant spatial scales, localization between model domains must properly account for the multiple length scales at play. In chapter 4 we develop two new multivariate localization functions, one of which is a multivariate extension of the fifth-order piecewise rational Gaspari-Cohn localization function; the within-component localization functions are standard Gaspari-Cohn with different localization radii while the cross-localization function is newly constructed. The functions produce positive semidefinite localization matrices, which are suitable for use in both Kalman Filters and variational data assimilation schemes. We compare the performance of our two new multivariate localization functions to two other multivariate localization functions and to the univariate and weakly coupled analogs of all four functions in a simple experiment with the bivariate Lorenz '96 system. In our experiments the multivariate Gaspari-Cohn function leads to better performance than any of the other multivariate localization functions.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2023
538 $a Mode of access: World Wide Web
650 4 $a Applied mathematics. $3 2122814
650 4 $a Statistics. $3 517247
650 4 $a Physical oceanography. $3 3168433
650 4 $a Velocity. $3 3560495
650 4 $a Ocean circulation. $3 544145
650 4 $a Localization. $3 3560711
650 4 $a Atmosphere. $3 542821
650 4 $a General circulation models. $3 3694484
650 4 $a Data assimilation. $3 3682570
653 $a Coupled data assimilation
653 $a Multivariate localization functions
653 $a Ocean eddy parameterizations
653 $a Stochastic parameterizations
653 $a Subgrid scale temperature variance
653 $a Vertical structure of ocean eddies
655 7 $a Electronic books. $2 lcsh $3 542853
690 $a 0364
690 $a 0463
690 $a 0415
710 2 $a ProQuest Information and Learning Co. $3 783688
710 2 $a University of Colorado at Boulder. $b Applied Mathematics. $3 1030307
773 0 $t Dissertations Abstracts International $g 83-03B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28648776 $z click for full text (PQDT)