Incremental four-dimensional variational data assimilation of positive-definite oceanic variables using a logarithm transformation

Hajoon Song, Christopher A. Edwards, Andrew M. Moore, Jerome Fiechter

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

A data assimilation method for positive-definite variables is investigated and applied to a 1-Dimensional (1D) advection-diffusion model and a 3-variable nutrient-phytoplankton-zooplankton (NPZ) model. Conventional data assimilation methods that assume Gaussian distributed errors are problematic for most biogeochemical models because they do not constrain posterior estimates for concentration-based variables to be positive-definite. We apply the approach outlined by Fletcher (2010) that formulates the 4-dimensional variational (4DVAR) assimilation problem assuming lognormally distributed errors. This approach is sensible because many biogeochemical variables are better represented by lognormal than by Gaussian statistics, and it ensures positive-definite state variables. We introduce the incremental formulation of lognormal 4DVAR (L4DVAR) and consider two solutions - incremental mode (imode) and incremental median (imedian) which approximate the mode and the median of different posterior probability density functions. In a simple 0D test case, the two solutions performed similarly with small observation and background uncertainty, but the imedian solution resulted in smaller geometric bias and root-mean-squared error as uncertainty increased. Both solutions of incremental L4DVAR using a 1D linear advection-diffusion model and a nonlinear NPZ model reduce misfit between the model and observations significantly in various assimilation settings and yield a positive-definite adjusted state. We report also on the success of the incremental L4DVAR approach when model error is introduced.

Original languageEnglish
Pages (from-to)1-17
Number of pages17
JournalOcean Modelling
Volume54-55
DOIs
Publication statusPublished - 2012 Sep 1

Fingerprint

data assimilation
Phytoplankton
Advection
Nutrients
zooplankton
advection
phytoplankton
nutrient
probability density function
Probability density function
Statistics

All Science Journal Classification (ASJC) codes

  • Oceanography
  • Computer Science (miscellaneous)
  • Geotechnical Engineering and Engineering Geology
  • Atmospheric Science

Cite this

@article{4af2b73433bd4f47bbca94f098cc7466,
title = "Incremental four-dimensional variational data assimilation of positive-definite oceanic variables using a logarithm transformation",
abstract = "A data assimilation method for positive-definite variables is investigated and applied to a 1-Dimensional (1D) advection-diffusion model and a 3-variable nutrient-phytoplankton-zooplankton (NPZ) model. Conventional data assimilation methods that assume Gaussian distributed errors are problematic for most biogeochemical models because they do not constrain posterior estimates for concentration-based variables to be positive-definite. We apply the approach outlined by Fletcher (2010) that formulates the 4-dimensional variational (4DVAR) assimilation problem assuming lognormally distributed errors. This approach is sensible because many biogeochemical variables are better represented by lognormal than by Gaussian statistics, and it ensures positive-definite state variables. We introduce the incremental formulation of lognormal 4DVAR (L4DVAR) and consider two solutions - incremental mode (imode) and incremental median (imedian) which approximate the mode and the median of different posterior probability density functions. In a simple 0D test case, the two solutions performed similarly with small observation and background uncertainty, but the imedian solution resulted in smaller geometric bias and root-mean-squared error as uncertainty increased. Both solutions of incremental L4DVAR using a 1D linear advection-diffusion model and a nonlinear NPZ model reduce misfit between the model and observations significantly in various assimilation settings and yield a positive-definite adjusted state. We report also on the success of the incremental L4DVAR approach when model error is introduced.",
author = "Hajoon Song and Edwards, {Christopher A.} and Moore, {Andrew M.} and Jerome Fiechter",
year = "2012",
month = "9",
day = "1",
doi = "10.1016/j.ocemod.2012.06.001",
language = "English",
volume = "54-55",
pages = "1--17",
journal = "Ocean Modelling",
issn = "1463-5003",
publisher = "Elsevier BV",

}

Incremental four-dimensional variational data assimilation of positive-definite oceanic variables using a logarithm transformation. / Song, Hajoon; Edwards, Christopher A.; Moore, Andrew M.; Fiechter, Jerome.

In: Ocean Modelling, Vol. 54-55, 01.09.2012, p. 1-17.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Incremental four-dimensional variational data assimilation of positive-definite oceanic variables using a logarithm transformation

AU - Song, Hajoon

AU - Edwards, Christopher A.

AU - Moore, Andrew M.

AU - Fiechter, Jerome

PY - 2012/9/1

Y1 - 2012/9/1

N2 - A data assimilation method for positive-definite variables is investigated and applied to a 1-Dimensional (1D) advection-diffusion model and a 3-variable nutrient-phytoplankton-zooplankton (NPZ) model. Conventional data assimilation methods that assume Gaussian distributed errors are problematic for most biogeochemical models because they do not constrain posterior estimates for concentration-based variables to be positive-definite. We apply the approach outlined by Fletcher (2010) that formulates the 4-dimensional variational (4DVAR) assimilation problem assuming lognormally distributed errors. This approach is sensible because many biogeochemical variables are better represented by lognormal than by Gaussian statistics, and it ensures positive-definite state variables. We introduce the incremental formulation of lognormal 4DVAR (L4DVAR) and consider two solutions - incremental mode (imode) and incremental median (imedian) which approximate the mode and the median of different posterior probability density functions. In a simple 0D test case, the two solutions performed similarly with small observation and background uncertainty, but the imedian solution resulted in smaller geometric bias and root-mean-squared error as uncertainty increased. Both solutions of incremental L4DVAR using a 1D linear advection-diffusion model and a nonlinear NPZ model reduce misfit between the model and observations significantly in various assimilation settings and yield a positive-definite adjusted state. We report also on the success of the incremental L4DVAR approach when model error is introduced.

AB - A data assimilation method for positive-definite variables is investigated and applied to a 1-Dimensional (1D) advection-diffusion model and a 3-variable nutrient-phytoplankton-zooplankton (NPZ) model. Conventional data assimilation methods that assume Gaussian distributed errors are problematic for most biogeochemical models because they do not constrain posterior estimates for concentration-based variables to be positive-definite. We apply the approach outlined by Fletcher (2010) that formulates the 4-dimensional variational (4DVAR) assimilation problem assuming lognormally distributed errors. This approach is sensible because many biogeochemical variables are better represented by lognormal than by Gaussian statistics, and it ensures positive-definite state variables. We introduce the incremental formulation of lognormal 4DVAR (L4DVAR) and consider two solutions - incremental mode (imode) and incremental median (imedian) which approximate the mode and the median of different posterior probability density functions. In a simple 0D test case, the two solutions performed similarly with small observation and background uncertainty, but the imedian solution resulted in smaller geometric bias and root-mean-squared error as uncertainty increased. Both solutions of incremental L4DVAR using a 1D linear advection-diffusion model and a nonlinear NPZ model reduce misfit between the model and observations significantly in various assimilation settings and yield a positive-definite adjusted state. We report also on the success of the incremental L4DVAR approach when model error is introduced.

UR - http://www.scopus.com/inward/record.url?scp=84865364995&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84865364995&partnerID=8YFLogxK

U2 - 10.1016/j.ocemod.2012.06.001

DO - 10.1016/j.ocemod.2012.06.001

M3 - Article

AN - SCOPUS:84865364995

VL - 54-55

SP - 1

EP - 17

JO - Ocean Modelling

JF - Ocean Modelling

SN - 1463-5003

ER -