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This project integrates N15 values into Linear Inverse Models for ecosystem modeling. Below are the actual scripts, available in multiple formats. A major goal of this project is to facilitate the use of this tool within the oceanographic community. We welcome any questions or concerns, especially regarding how to get started with Linear Inverse Modeling.

  1. N15 Setup File: Reads in the spreadsheets and prepares the matricies and vectors used in the LIM. Also loads results from the Forward model for use in the LIM.
  2. Model Initialization Script: Gets the run-time enviroment ready and handles all the bunr-in stages as well as the actual model runs. Saves all results at the end.
  3. A Modified MCMC Sampling Algorithm: Is called by the Model Initialization Script, not meant to be edited from one model to the next. Adapted from Van den Meersche's xsample script.
  4. With these additional functions: Includes the function that updates the N15-related equations during the random walk. Also an ideal file for accessory functions.
  5. A full working demo is also included with both model input and output files.

Multiple Formats

In general, the user accessible scripts are available as with jupyter notebook files or as straight R code.

About Notebook Files

Since not everyone is familiar with the Jupyter Notebook platform, let us say a few words about it. Jupyter, formally iPython Notebook, is an interactive scripting environment for use in data analysis, script development and, importanly, for sharing scripts and workflows with others. While designed with Python in mind, the platform is nearly language agnostic with ready backends (i.e. kernels) for numerous languages: R, MatLab, C, Java, Clojure, Lisp, Fortran, etc. Do yourself a favor and check it out, it is certainly worth the time to learn about this valuable, open source resource.

Abstract & Citation

ABSTRACT Oceanographic field programs often use δ15N biogeochemical measurements and in-situ rate measurements to investigate nitrogen cycling and planktonic ecosystem structure. However, integrative modeling approaches capable of synthesizing these distinct measurement types are lacking. We develop a novel approach for incorporating δ15N isotopic data into existing Markov Chain Monte Carlo (MCMC) random walk methods for solving linear inverse ecosystem models. We test the ability of this approach to recover food web indices (nitrate uptake, nitrogen fixation, zooplankton trophic level, and secondary production) derived from forward models simulating the planktonic ecosystems of the California Current and Amazon River Plume. We show that the MCMC with δ15N approach typically does a better job of recovering ecosystem structure than the standard MCMC or L2 minimum norm (L2MN) approaches, and also outperforms an L2MN with δ15N approach. Furthermore, we find that the MCMC with δ15N approach is robust to the removal of input equations and hence is well suited to typical pelagic ecosystem studies for which the system is usually vastly under-constrained. Our approach is easily extendable for use with δ13C isotopic measurements or variable carbon:nitrogen stoichiometry.


Stukel M.R., Decima M., Kelly T.B. A new approach for incorporating 15N isotopic data into linear inverse ecosystem models with Markov Chain Monte Carlo sampling.


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