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            <gmx:Anchor xlink:href="http://lod.bco-dmo.org/id/dataset/721940.rdf" xlink:actuate="onRequest">Estimation of the parameters of a simple model of thorium and particle cycling in the ocean water column, based on a fit to radionuclide and particle data from the US GEOTRACES North Atlantic Section (GA03)</gmx:Anchor>
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                <gmx:Anchor xlink:href="http://lod.bco-dmo.org/id/person/721936.rdf" xlink:actuate="onRequest">Olivier Marchal</gmx:Anchor>
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                <gmx:Anchor xlink:href="https://ror.org/03zbnzt98" xlink:title="ROR ID" xlink:actuate="onRequest">Woods Hole Oceanographic Institution</gmx:Anchor>
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                <gmx:Anchor xlink:href="https://ror.org/03s65by71" xlink:title="ROR ID" xlink:actuate="onRequest">University of California-Santa Cruz</gmx:Anchor>
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            <gco:CharacterString>Cite this dataset as: Marchal, O., Lam, P. J., Lerner, P. (2018) Estimation of the parameters of a simple model of thorium and particle cycling in the ocean water column, based on a fit to radionuclide and particle data from the US GEOTRACES North Atlantic Section (GA03). Biological and Chemical Oceanography Data Management Office (BCO-DMO). Version Date 2018-02-26 [if applicable, indicate subset used]. http://lod.bco-dmo.org/id/dataset/721940 [access date]</gco:CharacterString>
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      <gmd:abstract>
        <gco:CharacterString>Thorium and Particle Cycling Inverse Model and parameter estimates Dataset Description: &amp;lt;p&amp;gt;This dataset contains model code and output from a thorium and particle cycling model.&amp;amp;nbsp;&amp;lt;/p&amp;gt;

&amp;lt;p&amp;gt;The model code and documentation are available for download as a .zip file:&amp;amp;nbsp;&amp;lt;a href=&amp;quot;http://datadocs.bco-dmo.org/docs/GEOTRACES_Particle_Dynamics/data_docs/Lerner_Th_P_inverseModel.zip&amp;quot; target=&amp;quot;_blank&amp;quot;&amp;gt;Lerner_Th_P_InverseModel.zip (2.6 MB)&amp;lt;/a&amp;gt;&amp;lt;/p&amp;gt;

&amp;lt;p&amp;gt;Model output data are available by clicking the &amp;quot;Get Data&amp;quot; button above.&amp;amp;nbsp; These data are parameter estimates from fitting the model to radionuclide and particle data from the US GEOTRACES North Atlantic Section,&amp;amp;nbsp;not samples collected in the field.&amp;amp;nbsp;&amp;lt;/p&amp;gt;

&amp;lt;p&amp;gt;Both the model and inverse method are described in detail in the model manual “&amp;lt;a href=&amp;quot;http://datadocs.bco-dmo.org/docs/GEOTRACES_Particle_Dynamics/data_docs/Lerner_Th_P_inversion_manual.pdf&amp;quot; target=&amp;quot;_blank&amp;quot;&amp;gt;Manual of Matlab Code: Nonlinear Inversion of Thorium and Particle Data&amp;lt;/a&amp;gt;,” as well as in Lerner et al., 2017.&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;This document describes how to use the routine submitted here to fit a 1-d thorium and particle cycling model to radionuclide and particle data&amp;lt;/p&amp;gt;

&amp;lt;p&amp;gt;These data and model were&amp;amp;nbsp;published in:&amp;lt;/p&amp;gt;

&amp;lt;p&amp;gt;Lerner, P., Marchal, O., Lam, P. J., Buesseler, K., and Charette, M. (2017). Kinetics of thorium and particle cycling along the US GEOTRACES North Atlantic Transect. Deep Sea Research Part I: Oceanographic Research Papers, 125, 106-128, Fig. 12, Supplementary Figs. S1-S3. doi: &amp;lt;a href=&amp;quot;https://doi.org/10.1016/j.dsr.2017.05.003&amp;quot; target=&amp;quot;_blank&amp;quot;&amp;gt;10.1016/j.dsr.2017.05.003&amp;lt;/a&amp;gt;&amp;lt;/p&amp;gt; Methods and Sampling: &amp;lt;p&amp;gt;&amp;lt;strong&amp;gt;Location: &amp;lt;/strong&amp;gt;The model is fit to&amp;amp;nbsp;&amp;lt;sup&amp;gt;228,230,234&amp;lt;/sup&amp;gt;Th,&amp;amp;nbsp;&amp;lt;sup&amp;gt;234,238&amp;lt;/sup&amp;gt;U,&amp;amp;nbsp;&amp;lt;sup&amp;gt;228&amp;lt;/sup&amp;gt;Ra, and particle concentration data collected from a section from Bermuda to a station just off the coast of Mauritania. The section crosses the Mid-Atlantic Ridge and the southeastern portion of the North Atlantic Subtropical gyre. The locations and depth ranges of data used to estimate model parameters are listed below (Table 1 of Lerner et al., 2017).&amp;lt;/p&amp;gt;

&amp;lt;div&amp;gt;&amp;lt;img alt=&amp;quot;locations&amp;quot; src=&amp;quot;http://datadocs.bco-dmo.org/docs/GEOTRACES_Particle_Dynamics/data_docs/Lerner_et_al_Table1.png&amp;quot; /&amp;gt;&amp;lt;/div&amp;gt;

&amp;lt;div&amp;gt;
&amp;lt;p&amp;gt;&amp;lt;strong&amp;gt;Data: &amp;lt;/strong&amp;gt;The thorium and particle cycling model is fit to radionuclide and particle data from the US GEOTRACES North Atlantic Section (GA03). The following lists these data, along with their associated references, in which analytical methods associated with these data are published. The subscript “p” denotes particulate data and “d” denotes “dissolved” data, where particulate and dissolved material are separated by filters with a pore size of 0.8 µm. &amp;amp;nbsp;These data have all been submitted to BCO-DMO, and all except&amp;amp;nbsp;&amp;lt;sup&amp;gt;228&amp;lt;/sup&amp;gt;Th are published. These data are also available as part of the GEOTRACES Intermediate Data Product (Mawji et al., 2014).&amp;amp;nbsp;&amp;lt;/p&amp;gt;

&amp;lt;div&amp;gt;&amp;lt;sup&amp;gt;234,238&amp;lt;/sup&amp;gt;U (obtained from salinity) - Owens et al., 2011 (available in datasets of project:&amp;amp;nbsp;&amp;lt;a href=&amp;quot;https://www.bco-dmo.org/project/2066&amp;quot; target=&amp;quot;_blank&amp;quot;&amp;gt;https://www.bco-dmo.org/project/2066&amp;lt;/a&amp;gt;)&amp;lt;/div&amp;gt;

&amp;lt;div&amp;gt;&amp;lt;sup&amp;gt;234&amp;lt;/sup&amp;gt;Th&amp;lt;sub&amp;gt;d,p&amp;lt;/sub&amp;gt;&amp;amp;nbsp;(dpm&amp;amp;nbsp;m-3) - Owens et al., 2015&amp;amp;nbsp;(available in datasets of project:&amp;amp;nbsp;&amp;lt;a href=&amp;quot;https://www.bco-dmo.org/project/2066&amp;quot; target=&amp;quot;_blank&amp;quot;&amp;gt;https://www.bco-dmo.org/project/2066&amp;lt;/a&amp;gt;)&amp;lt;/div&amp;gt;

&amp;lt;div&amp;gt;&amp;lt;sup&amp;gt;230&amp;lt;/sup&amp;gt;Th&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;&amp;amp;nbsp;(dpm&amp;amp;nbsp;m-3)&amp;amp;nbsp; - Hayes et al., 2015a (available in dataset&amp;amp;nbsp;&amp;lt;a href=&amp;quot;https://www.bco-dmo.org/dataset/3847&amp;quot; target=&amp;quot;_blank&amp;quot;&amp;gt;https://www.bco-dmo.org/dataset/3847&amp;lt;/a&amp;gt;)&amp;lt;/div&amp;gt;

&amp;lt;div&amp;gt;&amp;lt;sup&amp;gt;230&amp;lt;/sup&amp;gt;Th&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt;&amp;amp;nbsp;(dpm&amp;amp;nbsp;m-3)&amp;amp;nbsp; - Hayes et al., 2015b (available in dataset&amp;amp;nbsp;&amp;lt;a href=&amp;quot;https://www.bco-dmo.org/dataset/3847&amp;quot; target=&amp;quot;_blank&amp;quot;&amp;gt;https://www.bco-dmo.org/dataset/3847&amp;lt;/a&amp;gt;)&amp;lt;/div&amp;gt;

&amp;lt;div&amp;gt;&amp;lt;sup&amp;gt;228&amp;lt;/sup&amp;gt;Ra (dpm&amp;amp;nbsp;m-3)&amp;amp;nbsp; - Charrette et al., 2015 (available in dataset&amp;amp;nbsp;&amp;lt;a href=&amp;quot;https://www.bco-dmo.org/dataset/3847&amp;quot; target=&amp;quot;_blank&amp;quot;&amp;gt;https://www.bco-dmo.org/dataset/3847&amp;lt;/a&amp;gt;)&amp;lt;/div&amp;gt;

&amp;lt;div&amp;gt;&amp;lt;sup&amp;gt;228&amp;lt;/sup&amp;gt;Th&amp;lt;sub&amp;gt;d,p&amp;lt;/sub&amp;gt;&amp;amp;nbsp;(dpm&amp;amp;nbsp;m-3) - unpublished (available on BCO-DMO dataset page: &amp;lt;a href=&amp;quot;http://lod.bco-dmo.org/id/dataset/3846&amp;quot; target=&amp;quot;_blank&amp;quot;&amp;gt;http://lod.bco-dmo.org/id/dataset/3846&amp;lt;/a&amp;gt;, Charrette et al., 2014)&amp;amp;nbsp;&amp;lt;/div&amp;gt;

&amp;lt;div&amp;gt;Particle concentration (mg m-3) - Lam et al., 2015 (available in dataset&amp;amp;nbsp;&amp;lt;a href=&amp;quot;https://www.bco-dmo.org/dataset/3871&amp;quot; target=&amp;quot;_blank&amp;quot;&amp;gt;https://www.bco-dmo.org/dataset/3871&amp;lt;/a&amp;gt;)&amp;lt;/div&amp;gt;

&amp;lt;div&amp;gt;&amp;amp;nbsp;&amp;lt;/div&amp;gt;

&amp;lt;div&amp;gt;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp; The depths at which the radiochemical and particle data are available do not generally coincide. Hence, at each station, an objective interpolation procedure was used to interpolate the data onto an irregular grid (the grid varies with each station and the range of the grid is the same as the “depth range” ). This procedure is described in detail in section 2.4 of Lerner et al., 2016.&amp;lt;/div&amp;gt;

&amp;lt;p&amp;gt;&amp;lt;strong&amp;gt;Inverse Method:&amp;amp;nbsp;&amp;lt;/strong&amp;gt;The algorithm used to fit the model (eqs. 1-3 available in the&amp;lt;a href=&amp;quot;http://datadocs.bco-dmo.org/docs/GEOTRACES_Particle_Dynamics/data_docs/Lerner_Th_P_inversion_manual.pdf&amp;quot; target=&amp;quot;_blank&amp;quot;&amp;gt; model manual&amp;lt;/a&amp;gt;) to the radionuclide and particle data is a nonlinear programming technique as implemented in Matlab’s FMINCON (Matlab R2016b), a constrained optimization routine used to solve nonlinear problems. This algorithm takes as its argument a vector&amp;amp;nbsp;&amp;lt;strong&amp;gt;&amp;lt;em&amp;gt;x&amp;lt;/em&amp;gt;&amp;lt;/strong&amp;gt;&amp;lt;sub&amp;gt;0&amp;amp;nbsp;&amp;lt;/sub&amp;gt;&amp;amp;nbsp;containing radionuclide activities, particle concentration, and prior estimates of the rate parameters (parameters listed in “Parameter&amp;amp;nbsp;names…” section, all at different depths of the model grid, as well as an error covariance matrix,&amp;amp;nbsp;&amp;lt;strong&amp;gt;C&amp;lt;sub&amp;gt;0&amp;lt;/sub&amp;gt;&amp;lt;/strong&amp;gt;, whose diagonal elements are the variances in&amp;amp;nbsp;&amp;lt;strong&amp;gt;&amp;lt;em&amp;gt;x&amp;lt;/em&amp;gt;&amp;lt;/strong&amp;gt;&amp;lt;sub&amp;gt;0&amp;lt;/sub&amp;gt;&amp;amp;nbsp;and whose off-diagonal elements are the error covariances in&amp;amp;nbsp;&amp;lt;strong&amp;gt;&amp;lt;em&amp;gt;x&amp;lt;/em&amp;gt;&amp;lt;/strong&amp;gt;&amp;lt;sub&amp;gt;0&amp;lt;/sub&amp;gt;. FMINCON seeks a vector&amp;amp;nbsp;&amp;lt;strong&amp;gt;&amp;lt;em&amp;gt;x&amp;amp;nbsp;&amp;lt;/em&amp;gt;&amp;lt;/strong&amp;gt;which both perfectly satisfies the model (that is, the&amp;amp;nbsp;rhs&amp;amp;nbsp;of equations (1-3) equal 0 when a solution is found), and fits radionuclide and particle concentration data, as well as prior estimates of rate parameters, in a least squares sense, with due consideration for the errors in the data and in the estimates (see equation Further details on the procedure used by FMINCON are reported in Byrd et al. (2000) and Waltz et al. (2005).&amp;lt;/p&amp;gt;
&amp;lt;/div&amp;gt;

&amp;lt;p&amp;gt;For more detail see the model manual “&amp;lt;a href=&amp;quot;http://datadocs.bco-dmo.org/docs/GEOTRACES_Particle_Dynamics/data_docs/Lerner_Th_P_inversion_manual.pdf&amp;quot; target=&amp;quot;_blank&amp;quot;&amp;gt;Manual of Matlab Code: Nonlinear Inversion of Thorium and Particle Data&amp;lt;/a&amp;gt;.&amp;quot;&amp;lt;/p&amp;gt;</gco:CharacterString>
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                <gco:CharacterString>&amp;lt;p&amp;gt;&amp;lt;strong&amp;gt;Location: &amp;lt;/strong&amp;gt;The model is fit to&amp;amp;nbsp;&amp;lt;sup&amp;gt;228,230,234&amp;lt;/sup&amp;gt;Th,&amp;amp;nbsp;&amp;lt;sup&amp;gt;234,238&amp;lt;/sup&amp;gt;U,&amp;amp;nbsp;&amp;lt;sup&amp;gt;228&amp;lt;/sup&amp;gt;Ra, and particle concentration data collected from a section from Bermuda to a station just off the coast of Mauritania. The section crosses the Mid-Atlantic Ridge and the southeastern portion of the North Atlantic Subtropical gyre. The locations and depth ranges of data used to estimate model parameters are listed below (Table 1 of Lerner et al., 2017).&amp;lt;/p&amp;gt;

&amp;lt;div&amp;gt;&amp;lt;img alt=&amp;quot;locations&amp;quot; src=&amp;quot;http://datadocs.bco-dmo.org/docs/GEOTRACES_Particle_Dynamics/data_docs/Lerner_et_al_Table1.png&amp;quot; /&amp;gt;&amp;lt;/div&amp;gt;

&amp;lt;div&amp;gt;
&amp;lt;p&amp;gt;&amp;lt;strong&amp;gt;Data: &amp;lt;/strong&amp;gt;The thorium and particle cycling model is fit to radionuclide and particle data from the US GEOTRACES North Atlantic Section (GA03). The following lists these data, along with their associated references, in which analytical methods associated with these data are published. The subscript “p” denotes particulate data and “d” denotes “dissolved” data, where particulate and dissolved material are separated by filters with a pore size of 0.8 µm. &amp;amp;nbsp;These data have all been submitted to BCO-DMO, and all except&amp;amp;nbsp;&amp;lt;sup&amp;gt;228&amp;lt;/sup&amp;gt;Th are published. These data are also available as part of the GEOTRACES Intermediate Data Product (Mawji et al., 2014).&amp;amp;nbsp;&amp;lt;/p&amp;gt;

&amp;lt;div&amp;gt;&amp;lt;sup&amp;gt;234,238&amp;lt;/sup&amp;gt;U (obtained from salinity) - Owens et al., 2011 (available in datasets of project:&amp;amp;nbsp;&amp;lt;a href=&amp;quot;https://www.bco-dmo.org/project/2066&amp;quot; target=&amp;quot;_blank&amp;quot;&amp;gt;https://www.bco-dmo.org/project/2066&amp;lt;/a&amp;gt;)&amp;lt;/div&amp;gt;

&amp;lt;div&amp;gt;&amp;lt;sup&amp;gt;234&amp;lt;/sup&amp;gt;Th&amp;lt;sub&amp;gt;d,p&amp;lt;/sub&amp;gt;&amp;amp;nbsp;(dpm&amp;amp;nbsp;m-3) - Owens et al., 2015&amp;amp;nbsp;(available in datasets of project:&amp;amp;nbsp;&amp;lt;a href=&amp;quot;https://www.bco-dmo.org/project/2066&amp;quot; target=&amp;quot;_blank&amp;quot;&amp;gt;https://www.bco-dmo.org/project/2066&amp;lt;/a&amp;gt;)&amp;lt;/div&amp;gt;

&amp;lt;div&amp;gt;&amp;lt;sup&amp;gt;230&amp;lt;/sup&amp;gt;Th&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;&amp;amp;nbsp;(dpm&amp;amp;nbsp;m-3)&amp;amp;nbsp; - Hayes et al., 2015a (available in dataset&amp;amp;nbsp;&amp;lt;a href=&amp;quot;https://www.bco-dmo.org/dataset/3847&amp;quot; target=&amp;quot;_blank&amp;quot;&amp;gt;https://www.bco-dmo.org/dataset/3847&amp;lt;/a&amp;gt;)&amp;lt;/div&amp;gt;

&amp;lt;div&amp;gt;&amp;lt;sup&amp;gt;230&amp;lt;/sup&amp;gt;Th&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt;&amp;amp;nbsp;(dpm&amp;amp;nbsp;m-3)&amp;amp;nbsp; - Hayes et al., 2015b (available in dataset&amp;amp;nbsp;&amp;lt;a href=&amp;quot;https://www.bco-dmo.org/dataset/3847&amp;quot; target=&amp;quot;_blank&amp;quot;&amp;gt;https://www.bco-dmo.org/dataset/3847&amp;lt;/a&amp;gt;)&amp;lt;/div&amp;gt;

&amp;lt;div&amp;gt;&amp;lt;sup&amp;gt;228&amp;lt;/sup&amp;gt;Ra (dpm&amp;amp;nbsp;m-3)&amp;amp;nbsp; - Charrette et al., 2015 (available in dataset&amp;amp;nbsp;&amp;lt;a href=&amp;quot;https://www.bco-dmo.org/dataset/3847&amp;quot; target=&amp;quot;_blank&amp;quot;&amp;gt;https://www.bco-dmo.org/dataset/3847&amp;lt;/a&amp;gt;)&amp;lt;/div&amp;gt;

&amp;lt;div&amp;gt;&amp;lt;sup&amp;gt;228&amp;lt;/sup&amp;gt;Th&amp;lt;sub&amp;gt;d,p&amp;lt;/sub&amp;gt;&amp;amp;nbsp;(dpm&amp;amp;nbsp;m-3) - unpublished (available on BCO-DMO dataset page: &amp;lt;a href=&amp;quot;http://lod.bco-dmo.org/id/dataset/3846&amp;quot; target=&amp;quot;_blank&amp;quot;&amp;gt;http://lod.bco-dmo.org/id/dataset/3846&amp;lt;/a&amp;gt;, Charrette et al., 2014)&amp;amp;nbsp;&amp;lt;/div&amp;gt;

&amp;lt;div&amp;gt;Particle concentration (mg m-3) - Lam et al., 2015 (available in dataset&amp;amp;nbsp;&amp;lt;a href=&amp;quot;https://www.bco-dmo.org/dataset/3871&amp;quot; target=&amp;quot;_blank&amp;quot;&amp;gt;https://www.bco-dmo.org/dataset/3871&amp;lt;/a&amp;gt;)&amp;lt;/div&amp;gt;

&amp;lt;div&amp;gt;&amp;amp;nbsp;&amp;lt;/div&amp;gt;

&amp;lt;div&amp;gt;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp; The depths at which the radiochemical and particle data are available do not generally coincide. Hence, at each station, an objective interpolation procedure was used to interpolate the data onto an irregular grid (the grid varies with each station and the range of the grid is the same as the “depth range” ). This procedure is described in detail in section 2.4 of Lerner et al., 2016.&amp;lt;/div&amp;gt;

&amp;lt;p&amp;gt;&amp;lt;strong&amp;gt;Inverse Method:&amp;amp;nbsp;&amp;lt;/strong&amp;gt;The algorithm used to fit the model (eqs. 1-3 available in the&amp;lt;a href=&amp;quot;http://datadocs.bco-dmo.org/docs/GEOTRACES_Particle_Dynamics/data_docs/Lerner_Th_P_inversion_manual.pdf&amp;quot; target=&amp;quot;_blank&amp;quot;&amp;gt; model manual&amp;lt;/a&amp;gt;) to the radionuclide and particle data is a nonlinear programming technique as implemented in Matlab’s FMINCON (Matlab R2016b), a constrained optimization routine used to solve nonlinear problems. This algorithm takes as its argument a vector&amp;amp;nbsp;&amp;lt;strong&amp;gt;&amp;lt;em&amp;gt;x&amp;lt;/em&amp;gt;&amp;lt;/strong&amp;gt;&amp;lt;sub&amp;gt;0&amp;amp;nbsp;&amp;lt;/sub&amp;gt;&amp;amp;nbsp;containing radionuclide activities, particle concentration, and prior estimates of the rate parameters (parameters listed in “Parameter&amp;amp;nbsp;names…” section, all at different depths of the model grid, as well as an error covariance matrix,&amp;amp;nbsp;&amp;lt;strong&amp;gt;C&amp;lt;sub&amp;gt;0&amp;lt;/sub&amp;gt;&amp;lt;/strong&amp;gt;, whose diagonal elements are the variances in&amp;amp;nbsp;&amp;lt;strong&amp;gt;&amp;lt;em&amp;gt;x&amp;lt;/em&amp;gt;&amp;lt;/strong&amp;gt;&amp;lt;sub&amp;gt;0&amp;lt;/sub&amp;gt;&amp;amp;nbsp;and whose off-diagonal elements are the error covariances in&amp;amp;nbsp;&amp;lt;strong&amp;gt;&amp;lt;em&amp;gt;x&amp;lt;/em&amp;gt;&amp;lt;/strong&amp;gt;&amp;lt;sub&amp;gt;0&amp;lt;/sub&amp;gt;. FMINCON seeks a vector&amp;amp;nbsp;&amp;lt;strong&amp;gt;&amp;lt;em&amp;gt;x&amp;amp;nbsp;&amp;lt;/em&amp;gt;&amp;lt;/strong&amp;gt;which both perfectly satisfies the model (that is, the&amp;amp;nbsp;rhs&amp;amp;nbsp;of equations (1-3) equal 0 when a solution is found), and fits radionuclide and particle concentration data, as well as prior estimates of rate parameters, in a least squares sense, with due consideration for the errors in the data and in the estimates (see equation Further details on the procedure used by FMINCON are reported in Byrd et al. (2000) and Waltz et al. (2005).&amp;lt;/p&amp;gt;
&amp;lt;/div&amp;gt;

&amp;lt;p&amp;gt;For more detail see the model manual “&amp;lt;a href=&amp;quot;http://datadocs.bco-dmo.org/docs/GEOTRACES_Particle_Dynamics/data_docs/Lerner_Th_P_inversion_manual.pdf&amp;quot; target=&amp;quot;_blank&amp;quot;&amp;gt;Manual of Matlab Code: Nonlinear Inversion of Thorium and Particle Data&amp;lt;/a&amp;gt;.&amp;quot;&amp;lt;/p&amp;gt;</gco:CharacterString>
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