Uncertainty Quantification of Density and Stratification Estimates with Implications for Predicting Ocean Dynamics

A. Manderson, M. D. Rayson, E. Cripps, M. Girolami, J. P. Gosling, M. Hodkiewicz, G. N. Ivey, N. L. Jones

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Abstract

We present a statistical method for reconstructing continuous background density profiles that embeds incomplete measurements and a physically intuitive density stratification model within a Bayesian hierarchal framework. A double hyperbolic tangent function is used as a parametric density stratification model that captures various pycnocline structures in the upper ocean and offers insight into several density profile characteristics (e.g., pycnocline depth). The posterior distribution is used to quantify uncertainty and is estimated using recent advances in Markov chain Monte Carlo sampling. Temporally evolving posterior distributions of density profile characteristics, isopycnal heights, and nonlinear ocean process models for internal gravity waves are presented as examples of how uncertainty propagates through models dependent on the density stratification. The results show 0.95 posterior interval widths that ranged from 2.5% to 4% of the expected values for the linear internal wave phase speed and 15%-40% for the nonlinear internal wave steepening parameter. The data, collected over a year from a through-the-column mooring, and code, implemented in the software package Stan, accompany the article.

Original languageEnglish
Pages (from-to)1313-1330
Number of pages18
JournalJournal of Atmospheric and Oceanic Technology
Volume36
Issue number7
DOIs
Publication statusPublished - Jul 2019

Cite this

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title = "Uncertainty Quantification of Density and Stratification Estimates with Implications for Predicting Ocean Dynamics",
abstract = "We present a statistical method for reconstructing continuous background density profiles that embeds incomplete measurements and a physically intuitive density stratification model within a Bayesian hierarchal framework. A double hyperbolic tangent function is used as a parametric density stratification model that captures various pycnocline structures in the upper ocean and offers insight into several density profile characteristics (e.g., pycnocline depth). The posterior distribution is used to quantify uncertainty and is estimated using recent advances in Markov chain Monte Carlo sampling. Temporally evolving posterior distributions of density profile characteristics, isopycnal heights, and nonlinear ocean process models for internal gravity waves are presented as examples of how uncertainty propagates through models dependent on the density stratification. The results show 0.95 posterior interval widths that ranged from 2.5{\%} to 4{\%} of the expected values for the linear internal wave phase speed and 15{\%}-40{\%} for the nonlinear internal wave steepening parameter. The data, collected over a year from a through-the-column mooring, and code, implemented in the software package Stan, accompany the article.",
keywords = "Thermocline, In situ oceanic observations, Bayesian methods, Model errors, Model output statistics, MODEL, ENERGY, EVOLUTION, PROFILES, WAVES",
author = "A. Manderson and Rayson, {M. D.} and E. Cripps and M. Girolami and Gosling, {J. P.} and M. Hodkiewicz and Ivey, {G. N.} and Jones, {N. L.}",
year = "2019",
month = "7",
doi = "10.1175/JTECH-D-18-0200.1",
language = "English",
volume = "36",
pages = "1313--1330",
journal = "Journal of Atmospheric and Oceanic Technology",
issn = "0739-0572",
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TY - JOUR

T1 - Uncertainty Quantification of Density and Stratification Estimates with Implications for Predicting Ocean Dynamics

AU - Manderson, A.

AU - Rayson, M. D.

AU - Cripps, E.

AU - Girolami, M.

AU - Gosling, J. P.

AU - Hodkiewicz, M.

AU - Ivey, G. N.

AU - Jones, N. L.

PY - 2019/7

Y1 - 2019/7

N2 - We present a statistical method for reconstructing continuous background density profiles that embeds incomplete measurements and a physically intuitive density stratification model within a Bayesian hierarchal framework. A double hyperbolic tangent function is used as a parametric density stratification model that captures various pycnocline structures in the upper ocean and offers insight into several density profile characteristics (e.g., pycnocline depth). The posterior distribution is used to quantify uncertainty and is estimated using recent advances in Markov chain Monte Carlo sampling. Temporally evolving posterior distributions of density profile characteristics, isopycnal heights, and nonlinear ocean process models for internal gravity waves are presented as examples of how uncertainty propagates through models dependent on the density stratification. The results show 0.95 posterior interval widths that ranged from 2.5% to 4% of the expected values for the linear internal wave phase speed and 15%-40% for the nonlinear internal wave steepening parameter. The data, collected over a year from a through-the-column mooring, and code, implemented in the software package Stan, accompany the article.

AB - We present a statistical method for reconstructing continuous background density profiles that embeds incomplete measurements and a physically intuitive density stratification model within a Bayesian hierarchal framework. A double hyperbolic tangent function is used as a parametric density stratification model that captures various pycnocline structures in the upper ocean and offers insight into several density profile characteristics (e.g., pycnocline depth). The posterior distribution is used to quantify uncertainty and is estimated using recent advances in Markov chain Monte Carlo sampling. Temporally evolving posterior distributions of density profile characteristics, isopycnal heights, and nonlinear ocean process models for internal gravity waves are presented as examples of how uncertainty propagates through models dependent on the density stratification. The results show 0.95 posterior interval widths that ranged from 2.5% to 4% of the expected values for the linear internal wave phase speed and 15%-40% for the nonlinear internal wave steepening parameter. The data, collected over a year from a through-the-column mooring, and code, implemented in the software package Stan, accompany the article.

KW - Thermocline

KW - In situ oceanic observations

KW - Bayesian methods

KW - Model errors

KW - Model output statistics

KW - MODEL

KW - ENERGY

KW - EVOLUTION

KW - PROFILES

KW - WAVES

U2 - 10.1175/JTECH-D-18-0200.1

DO - 10.1175/JTECH-D-18-0200.1

M3 - Article

VL - 36

SP - 1313

EP - 1330

JO - Journal of Atmospheric and Oceanic Technology

JF - Journal of Atmospheric and Oceanic Technology

SN - 0739-0572

IS - 7

ER -