scholarly journals Characterization of ocean biogeochemical processes: a generalized total least-squares estimator of the Redfield ratios

2015 ◽  
Vol 6 (2) ◽  
pp. 2383-2416
Author(s):  
V. Guglielmi ◽  
C. Goyet ◽  
F. Touratier
Keyword(s):  
Least Squares ◽  
Geographical Location ◽  
Total Least Squares ◽  
Least Squares Estimator ◽  
Global Ocean ◽  
Biogeochemical Processes ◽  
Physical Processes ◽  
Hydrological Characteristics ◽  
Redfield Ratios

Abstract. The chemical composition of the global ocean is governed by biological, chemical and physical processes. These processes interact with each other so that the concentrations of carbon dioxide, oxygen, nitrate and phosphate vary in constant proportions, referred to as the Redfield ratios. We build here the Generalized Total Least-Squares estimator of these ratios. The interest of our approach is twofold: it respects the hydrological characteristics of the studied areas, and it can be applied identically in any area where enough data are available. The tests performed on the Atlantic Ocean highlight a variability of the Redfield ratios, both with geographical location and with depth. This variability emphasizes the importance of local and accurate estimates of Redfield ratios.

scholarly journals Two Explicit Characterizations of the General Nonnegative-Definite Covariance Matrix Structure for Equality of BLUEs, WLSEs, and LSEs

2020 ◽  
Vol 9 (6) ◽  
pp. 108
Author(s):  
Phil D. Young ◽  
Joshua D. Patrick ◽  
Dean M. Young
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Sufficient Conditions ◽  
Covariance Structure ◽  
Least Squares Estimator ◽  
Weighted Least Squares Estimator ◽  
Best Linear Unbiased ◽  
Necessary And Sufficient ◽  
Nonnegative Definite

We provide a new, concise derivation of necessary and sufficient conditions for the explicit characterization of the general nonnegative-definite covariance structure V of a general Gauss-Markov model with E(y) and Var(y) such that the best linear unbiased estimator, the weighted least squares estimator, and the least squares estimator of Xβ are identical. In addition, we derive a representation of the general nonnegative-definite covariance structure V defined above in terms of its Moore-Penrose pseudo-inverse.

Bootstrapped Total Least Squares estimator using (circular) overlap for Errors-In-Variables identification

2009 ◽  
Vol 42 (10) ◽  
pp. 1568-1573
Author(s):  
Gerd Vandersteen ◽  
Kurt Barbé ◽  
Rik Pintelon ◽  
Johan Schoukens
Keyword(s):  
Least Squares ◽  
Total Least Squares ◽  
Least Squares Estimator ◽  
Errors In Variables

scholarly journals The effects of biogeochemical processes on oceanic conductivity/salinity/density relationships and the characterization of real seawater

2010 ◽  
Vol 7 (2) ◽  
pp. 773-836 ◽  
Author(s):  
R. Pawlowicz ◽  
D. G. Wright ◽  
F. J. Millero
Keyword(s):  
North Atlantic ◽  
Laboratory Experiments ◽  
Added Mass ◽  
Global Ocean ◽  
Biogeochemical Processes ◽  
The North ◽  
Relative Composition ◽  
Mathematical Investigation ◽  
Density Relationship

Abstract. As seawater circulates through the global ocean, its relative composition undergoes small variations. This results in changes to the conductivity/salinity/density relationship, which is currently well-defined only for Standard Seawater obtained from a particular area in the North Atlantic. These changes are investigated here by analysis of laboratory experiments in which salts are added to seawater, by analysis of oceanic observations of density and composition anomalies, and by mathematical investigation using a model relating composition, conductivity, and density of arbitrary seawaters. Mathematical analysis shows that understanding and describing the effect of changes in relative composition on operational estimates of salinity using the Practical Salinity Scale 1978 and on density using an equation of state for Standard Seawater require the use of a number of different salinity variables and a family of haline contraction coefficients. These salinity variables include an absolute salinity SAsoln, a density salinity SAdens, the reference salinity SR, and an added-mass salinity SAadd. In addition, a new salinity variable S∗ is defined, which represents the preformed salinity of a Standard Seawater component to which biogeochemical processes add material. In spite of this complexity, observed correlations between different ocean biogeochemical processes allow the creation of simple formulas that can be used to convert between the different salinity and density measures, allowing for the operational reduction of routine oceanographic observations.

Generalized total least squares to characterize biogeochemical processes of the ocean

2016 ◽  
Vol 67 (1) ◽  
pp. 37-49 ◽  
Author(s):  
Véronique Guglielmi ◽  
Catherine Goyet ◽  
Franck Touratier ◽  
Marie El Jai
Keyword(s):  
Least Squares ◽  
Total Least Squares ◽  
Biogeochemical Processes
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