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Sjoerd Groeskamp
,
Jan D. Zika
,
Bernadette M. Sloyan
,
Trevor J. McDougall
, and
Peter C. McIntosh

along with tracer observations to obtain a steady-state estimate of D . Munk’s study demonstrated that observed estimates of tracers can be used to obtain estimates of ocean circulation and mixing. To obtain estimates of the structure and magnitude of the ocean circulation from observations, Stommel and Schott (1977) and Wunsch (1978) introduced inverse methods into the field of oceanography. Ever since, many inverse studies have provided observationally based estimates of circulation ( Schott

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Hayley V. Dosser
and
Mary-Louise Timmermans

quantify the processes driving changes in water mass properties using empirical orthogonal function (EOF) analysis and an inverse method based on the tracer conservation equations adapted for the deep Canada Basin. Water masses in the Canada Basin are largely defined based on the origin of the inflow. Between roughly 200- and 2000-m depth, water of Atlantic origin enters the basin in a boundary current and a series of intrusive features. The Atlantic Water is divided into two branches: Fram Strait

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Neill Mackay
,
Chris Wilson
,
N. Penny Holliday
, and
Jan D. Zika

. Surface forcing tends to increase the spread of water masses in T – S space; mixing tends to bring them together. The term γ n indicates a neutral density surface. Figure adapted from Groeskamp et al. (2014a) . The regional thermohaline inverse method (RTHIM) was developed to investigate water mass transformation north of the OSNAP section, and to diagnose the relative roles of the transforming processes for each water mass. Using inputs of surface fluxes of heat and freshwater, Conservative

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William J. Koshak
and
Richard J. Solakiewicz

demonstrates that one can apply the APM method to arbitrary population densities that have nothing to do with lightning; that is, the APM is a general inversion technique that can be applied to any inverse problem having a similar problem statement to the lightning problem studied here. In this particular test, the population densities are defined by phase-shifted absolute value sine functions that have been appropriately normalized. We have also mixed various exponential distributions with absolute value

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Shifeng Hao
,
Xiaopeng Cui
, and
Jianping Huang

different and larger compared with the two others due to the affection of polar problem, but the maximum error is only 3.8 for both forward and backward simulations. The error norms and other information of backward simulations are given in Fig. 9 , which are identity to those with 0.25° resolution given in Fig. 5 . Based on the above results, we think the backward model based on SCEIM method can solve the inverse problems of cosine bell tests. Fig . 8. The errors (shaded) and numerical solutions

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William J. Koshak
,
Douglas M. Mach
, and
Phillip M. Bitzer

, network geometry, network extent, and to some degree sensor altitude). In addition, two close LMA networks could potentially be merged into a single larger network. With all of these possible adjustments, the findings in this work provide both insight and recommendations. The writing is organized as follows. Section 2 gives an overview of the basic inverse problem and provides the standard retrieval method employed for inferring the four unknown parameters (3D location and time of occurrence) of a

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Grégory Turbelin
,
Sarvesh Singh
,
Jean Pierre Issartel
,
Xavier Busch
, and
Pramod Kumar

paper is organized as follows. Section 2 presents the method and its theoretical background in the general framework of nonparametric STE inverse problems. In section 3 , we present the new algorithm, and its complexity is analyzed. To illustrate the efficiency of the algorithm, some numerical experiments are reported in section 4 . Note that, throughout the manuscript, vectors and matrices are denoted by boldface symbols and scalars by italic symbols. The superscript “T” denotes the

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Eugenia Kalnay
,
Seon Ki Park
,
Zhao-Xia Pu
, and
Jidong Gao

tangent linear or the full nonlinear model, each of which has advantages for different applications. The quasi-inverse linear (QIL) method has been tested successfully at NCEP in several different applications, for example, forecast error sensitivity analysis and data assimilation ( Pu et al. 1997a ), and adaptive observations ( Pu et al. 1998 ). Wang et al. (1997) adopted the quasi-inverse approach for their adjoint Newton algorithm (ANA), and applied it to a simplified 4D-Var problem, using

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Ryan J. Longman
,
Abby G. Frazier
,
Andrew J. Newman
,
Thomas W. Giambelluca
,
David Schanzenbach
,
Aurora Kagawa-Viviani
,
Heidi Needham
,
Jeffrey R Arnold
, and
Martyn P. Clark

( Di Piazza et al. 2011 ), splines (e.g., Hofstra et al. 2008 ), Thiessen polygons (e.g., Wagner et al. 2012 ), inverse distance weighting (IDW; e.g., Camera et al. 2014 ), angular distance weighting (e.g., Hofstra et al. 2008 ), nearest neighbor (e.g., Shen et al. 2001 ), artificial neural networks (e.g., Di Piazza et al. 2011 ), or various types of kriging (e.g., Brinckmann et al. 2016 ; Di Piazza et al. 2011 ; Frazier et al. 2016 ). The most appropriate interpolation method for gridded

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Hyun Sup Soh
,
Sung Yong Kim
,
P. Michael Kosro
, and
Alexander L. Kurapov

mapping error may generate unrealistic and spurious oceanographic features ( Chelton and Schlax 2003 ; Schlax and Chelton 2003 ). Kim et al. (2008) reported the mathematical relevance and performance of the two inverse methods (LSF and OI) in extracting a vector current map from the HFR-derived radial velocity maps. Additionally, Yoo et al. (2017) focused on the covariance estimates of the orthogonal vector currents directly from the HFR-derived radial velocities without any redundant steps

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