Table of Contents

• Dataset Description
  • Methods & Sampling
  • Data Processing Description
• Data Files
• Related Publications
• Parameters
• Deployments
• Project Information
• Funding

This dataset contains model code and output from a thorium and particle cycling model. 

The model code and documentation are available for download as a .zip file: Lerner_Th_P_InverseModel.zip (2.6 MB)

Model output data are available by clicking the "Get Data" button above.  These data are parameter estimates from fitting the model to radionuclide and particle data from the US GEOTRACES North Atlantic Section, not samples collected in the field. 

Both the model and inverse method are described in detail in the model manual “Manual of Matlab Code: Nonlinear Inversion of Thorium and Particle Data,” as well as in Lerner et al., 2017.   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

These data and model were published in:

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: 10.1016/j.dsr.2017.05.003

Location: The model is fit to 228,230,234Th, 234,238U, 228Ra, 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).

Data: 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.  These data have all been submitted to BCO-DMO, and all except 228Th are published. These data are also available as part of the GEOTRACES Intermediate Data Product (Mawji et al., 2014). 

234,238U (obtained from salinity) - Owens et al., 2011 (available in datasets of project: https://www.bco-dmo.org/project/2066)

234Thd,p (dpm m-3) - Owens et al., 2015 (available in datasets of project: https://www.bco-dmo.org/project/2066)

230Thd (dpm m-3)  - Hayes et al., 2015a (available in dataset https://www.bco-dmo.org/dataset/3847)

230Thp (dpm m-3)  - Hayes et al., 2015b (available in dataset https://www.bco-dmo.org/dataset/3847)

228Ra (dpm m-3)  - Charrette et al., 2015 (available in dataset https://www.bco-dmo.org/dataset/3847)

228Thd,p (dpm m-3) - unpublished (available on BCO-DMO dataset page: http://lod.bco-dmo.org/id/dataset/3846, Charrette et al., 2014) 

Particle concentration (mg m-3) - Lam et al., 2015 (available in dataset https://www.bco-dmo.org/dataset/3871)

           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.

Inverse Method: The algorithm used to fit the model (eqs. 1-3 available in the model manual) 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 x0  containing radionuclide activities, particle concentration, and prior estimates of the rate parameters (parameters listed in “Parameter names…” section, all at different depths of the model grid, as well as an error covariance matrix, C0, whose diagonal elements are the variances in x0 and whose off-diagonal elements are the error covariances in x0. FMINCON seeks a vector x which both perfectly satisfies the model (that is, the rhs 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).

For more detail see the model manual “Manual of Matlab Code: Nonlinear Inversion of Thorium and Particle Data."

Problem report: Beyond issue with gaps in previously reported radionuclide and particle measurements, there are no known issues with rate parameters and routine provided. 

NSF abstract:

Processes affecting ocean particles have important consequences for the marine biogeochemical cycles of trace elements; however, our present understanding of these processes is incomplete, as shown by the very large uncertainties (spanning orders of magnitude) of current estimates of particle cycling rates in the ocean. The extensive trace element dataset being generated as part of the GEOTRACES program provides an opportunity to enhance our knowledge of particle processes in a variety of oceanic environments. A scientist from Woods Hole Oceanographic Institution plans to determine the adequacy of different inverse methods to constrain particle processes such as solid-solution exchange and particle processes in the water column from measurements of thorium isotope activity, particle composition, and particle concentration in different size fractions. To attain this goal, the researcher would first assess the adequacy of different inverse methods to infer, from such an eclectic dataset, rate constants of sorption reactions (adsorption and desorption) and particle dynamics (aggregation, disaggregation, sinking, and remineralization). The second step would involve applying the selected method to estimate these constants and their uncertainties at the "superstations" of the GEOTRACES North Atlantic Zonal Section. Once the model is in place, the scientist would test the hypotheses that the rate constants varied (1) vertically within the mesopelagic layer and the deeper layers at these stations and (2) horizontally across the diverse environments sampled along the section.

Broader Impacts: The software to be developed would be archived with the Biological and Chemical Oceanography Data Management Office with instructions so other scientist can use it. One graduate student would be trained on the use of inverse methods in data analyses.