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Robert Bryan Long

Abstract

Estimates of the ocean wave directional spectrum may be extracted from observations of surface vertical acceleration and slope made with a pitch/roll buoy. The analysis requires the specification of a parametrical model of the spectrum and a procedure by which the parameters are fixed. The statistical validity and variability of the result must then be examined. This is accomplished by formulating the hypothesis that the model spectrum is the true spectrum; the hypothesis is then rejected if the difference between observations and data computed from the model is improbably large. Otherwise, the model is accepted as statistically valid. Model variability may then be computed in terms of the variances of model parameters. One particular parametrical model and analysis scheme has received wide application in recent years; this paper examines the statistical validity and variability of results obtained with this “conventional” procedure. Explicit formulas for the data covariance matrix, which summarizes the statistics of the observations and forms the core of the statistical analysis, are presented as are formulas for the variances of derived spectral parameters.

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Linda Marie Lawson
and
Robert Bryan Long

Abstract

A sophisticated analysis technique is applied to a subset of pitch-roll buoy data collected by the research vessels Gilliss and Quadra during the GARP Tropical Atlantic Experiment (GATE) in September 1974. The procedure enables the examination of directional properties of the wave field at a level of detail not previously along 44°N latitude. BY comparing properties of the observed spectra with the predictions of a simple schematic model of the storm, we conclude that swell reaching the GATE area was emitted during the first half of the storm's lifetime; swell subsequently radiated from the storm was heavily attenuated, either by sheltering of the site by the Cape Verde Islands or because of radically lower emission levels from the storm itself.

This work illustrates the power, as well as the limitations of the pitch-roll buoy when used in conjunction with a fully effective analysis technique.

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Robert Bryan Long
and
Klaus Hasselmann

Abstract

The problem of extracting directional spectra from observed, multi-component wave data has two facets: 1) the observations provide information only on a finite number of integral properties of the wave field; hence the directional spectrum cannot be determined uniquely from the wave data alone; and 2) the observations contain statistical errors. These difficulties are dealt with by choosing an optimal directional spectrum model which simultaneously minimizes some integral property of the spectrum (its “nastiness”) and passes an appropriate test of statistical significance. Although developed here in the context of surface wave directional spectra, the technique (adopted from the Backus-Gilbert inverse method).is applicable to any problem requiring the fitting of a model to data which represent integral properties of the function being modeled.

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Eli Tziperman
,
William Carlisle Thacker
,
Robert Bryan Long
, and
Show-Ming Hwang

Abstract

This paper deals with the solution of inverse problems involving complex numerical models of the oceanic general circulation and large datasets. The goal of these inverse problems is to find values for model inputs consistent with a steady circulation and, at the same time, consistent with the available data. They are formulated as optimization problems, seeking values for the model's inputs that minimize a cost function measuring departures from steady state and from date. The two main objectives of this work are 1) to examine the feasibility of solving inverse problems involving a realistic numerical model of the oceanic general circulation and 2) to understand how the optimization uses various data to calculate the desired model parameters.

The model considered here is similar to the primitive equation model of Bryan and of Cox, the principal difference being that here the horizontal momentum balance is essentially geostrophic. The model's inputs calculated by the optimization consist of surface fluxes of heat, water, and momentum, as well as the eddy-mixing parameters. In addition, optimal estimates for the hydrography are obtained by requiring the hydrography to be consistent with both other types of data and the model's dynamics.

In the examples presented here, the data have been generated by the model from known inputs; in some cases, simulated noise has been added. The cost function is a sum of terms quadratic in the differences between the data and their model counterparts and terms quadratic in the temperature and salinity time rate of change as evaluated using the model equations. The different inverse problems considered differ in the choice of the model inputs calculated by the optimization and in the data used in the cost function. Optimal values of the model's inputs are computed using a conjugate-gradient minimization algorithm, with the gradient computed using the so-called adjoint method.

In examples without added noise, solutions for the model inputs were found efficiently and accurately. This was not the case when simulated data with randomly generated noise was used. Amplification of noise was especially felt in regions of deep-water formation due to the strong vertical mixing in these regions. Away from deep-water formation regions, the performance of the optimization with noisy data was still not satisfactory, possibly due to bad conditioning of the problem. The conditioning of the optimization and the difficulties due to the noise amplification are further discussed in Part II of this work using real oceanographic data for the North Atlantic Ocean.

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Eli Tziperman
,
William Carlisle Thacker
,
Robert Bryan Long
,
Show-Ming Hwang
, and
Stephen R. Rintoul

Abstract

A general circulation model and North Atlantic climatological data of temperature salinity, wind stress, evaporation minus precipitation, and air–sea heat fluxes are used to examine the possibility of solving inverse problems using a full-scale numerical GCM and real oceanographic data, combined through an optimization approach.

In this study several solutions for the model inputs and the structure of the cost function as a function of the model inputs are examined to demonstrate two of the main difficulties confronting such large-case nonlinear inverse problems (about 30 000 unknowns and a similar number of constraints for the problem examined here). The first is the possible existence of local minima of the cost function, which prevents convergence of the optimization to the global minimum representing the desired optimal solution for the model inputs. The second difficulty, which seems the dominant one for many of the problem examined in this part as well as in Part I, is the ill conditioning of the inverse problem. Simple model equations are used to analyze the conditioning of the optimization problem and to analyze the role of both dissipation and waves in the model dynamics in conditioning the problem. The analysis suggests what might be an improved formulation of the cost function resulting in better conditioning of the problem.

The relation between the optimization approach and the robust diagnostic method of Sarmiento and Bryan is explicitly demonstrated, and the solution obtained by combining the two methods is used to examine the performance of the GCM used here for the North Atlantic Ocean.

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Britton B. Stephens
,
Matthew C. Long
,
Ralph F. Keeling
,
Eric A. Kort
,
Colm Sweeney
,
Eric C. Apel
,
Elliot L. Atlas
,
Stuart Beaton
,
Jonathan D. Bent
,
Nicola J. Blake
,
James F. Bresch
,
Joanna Casey
,
Bruce C. Daube
,
Minghui Diao
,
Ernesto Diaz
,
Heidi Dierssen
,
Valeria Donets
,
Bo-Cai Gao
,
Michelle Gierach
,
Robert Green
,
Justin Haag
,
Matthew Hayman
,
Alan J. Hills
,
Martín S. Hoecker-Martínez
,
Shawn B. Honomichl
,
Rebecca S. Hornbrook
,
Jorgen B. Jensen
,
Rong-Rong Li
,
Ian McCubbin
,
Kathryn McKain
,
Eric J. Morgan
,
Scott Nolte
,
Jordan G. Powers
,
Bryan Rainwater
,
Kaylan Randolph
,
Mike Reeves
,
Sue M. Schauffler
,
Katherine Smith
,
Mackenzie Smith
,
Jeff Stith
,
Gregory Stossmeister
,
Darin W. Toohey
, and
Andrew S. Watt

Abstract

The Southern Ocean plays a critical role in the global climate system by mediating atmosphere–ocean partitioning of heat and carbon dioxide. However, Earth system models are demonstrably deficient in the Southern Ocean, leading to large uncertainties in future air–sea CO2 flux projections under climate warming and incomplete interpretations of natural variability on interannual to geologic time scales. Here, we describe a recent aircraft observational campaign, the O2/N2 Ratio and CO2 Airborne Southern Ocean (ORCAS) study, which collected measurements over the Southern Ocean during January and February 2016. The primary research objective of the ORCAS campaign was to improve observational constraints on the seasonal exchange of atmospheric carbon dioxide and oxygen with the Southern Ocean. The campaign also included measurements of anthropogenic and marine biogenic reactive gases; high-resolution, hyperspectral ocean color imaging of the ocean surface; and microphysical data relevant for understanding and modeling cloud processes. In each of these components of the ORCAS project, the campaign has significantly expanded the amount of observational data available for this remote region. Ongoing research based on these observations will contribute to advancing our understanding of this climatically important system across a range of topics including carbon cycling, atmospheric chemistry and transport, and cloud physics. This article presents an overview of the scientific and methodological aspects of the ORCAS project and highlights early findings.

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E. Povl Abrahamsen
,
Sandra Barreira
,
Cecilia M. Bitz
,
Amy Butler
,
Kyle R. Clem
,
Steve Colwell
,
Lawrence Coy
,
Jos de Laat
,
Marcel D. du Plessis
,
Ryan L. Fogt
,
Helen Amanda Fricker
,
John Fyfe
,
Alex S. Gardner
,
Sarah T. Gille
,
Tessa Gorte
,
L. Gregor
,
Will Hobbs
,
Bryan Johnson
,
Eric Keenan
,
Linda M. Keller
,
Natalya A. Kramarova
,
Matthew A. Lazzara
,
Jan T. M. Lenaerts
,
Jan L. Lieser
,
Hongxing Liu
,
Craig S. Long
,
Michelle Maclennan
,
Robert A. Massom
,
François Massonnet
,
Matthew R. Mazloff
,
David Mikolajczyk
,
A. Narayanan
,
Eric R. Nash
,
Paul A. Newman
,
Irina Petropavlovskikh
,
Michael Pitts
,
Bastien Y. Queste
,
Phillip Reid
,
F. Roquet
,
Michelle L. Santee
,
Susan Strahan
,
Sebastiann Swart
, and
Lei Wang
Free access
Sharon Stammerjohn
,
Ted A. Scambos
,
Susheel Adusumilli
,
Sandra Barreira
,
Germar H. Bernhard
,
Deniz Bozkurt
,
Seth M. Bushinsky
,
Kyle R. Clem
,
Steve Colwell
,
Lawrence Coy
,
Jos De Laat
,
Marcel D. du Plessis
,
Ryan L. Fogt
,
Annie Foppert
,
Helen Amanda Fricker
,
Alex S. Gardner
,
Sarah T. Gille
,
Tessa Gorte
,
Bryan Johnson
,
Eric Keenan
,
Daemon Kennett
,
Linda M. Keller
,
Natalya A. Kramarova
,
Kaisa Lakkala
,
Matthew A. Lazzara
,
Jan T. M. Lenaerts
,
Jan L. Lieser
,
Zhi Li
,
Hongxing Liu
,
Craig S. Long
,
Michael MacFerrin
,
Michelle L. Maclennan
,
Robert A. Massom
,
David Mikolajczyk
,
Lynn Montgomery
,
Thomas L. Mote
,
Eric R. Nash
,
Paul A. Newman
,
Irina Petropavlovskikh
,
Michael Pitts
,
Phillip Reid
,
Steven R. Rintoul
,
Michelle L. Santee
,
Elizabeth H. Shadwick
,
Alessandro Silvano
,
Scott Stierle
,
Susan Strahan
,
Adrienne J. Sutton
,
Sebastiaan Swart
,
Veronica Tamsitt
,
Bronte Tilbrook
,
Lei Wang
,
Nancy L. Williams
, and
Xiaojun Yuan
Free access