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228Thd,p (dpm m-3) - unpublished (available on BCO-DMO dataset page: http://lod.bco-dmo.org/id/dataset/3846, Charrette et al., 2014)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

Lerner_Th_P_model_parameters.csv