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A Data-Constrained Framework for Marine Biogeochemistry Modeling with Applications to the Paranaguá Estuarine Complex

Leticia Becher

Abstract

Marine biogeochemical models are widely used to study nutrient dynamics, water quality, and climate-related processes in coastal and estuarine systems. However, developing models that reliably represent specific environments remains computationally demanding, which makes their application to complex systems such as river plumes and estuarine environments challenging. In addition, these models contain several parameters that must be calibrated for the region of interest, a process that is often performed empirically using limited observational data. This thesis advances the development and calibration of marine biogeochemical models in the Brazilian context through three main contributions. First, we develop a conceptual model describing nutrient-phytoplankton dynamics in the Paranagua Estuarine Complex (PEC) in southern Brazil. The model is intentionally simple and computationally inexpensive, allowing simulations to be performed on standard personal computers. Second, we propose a systematic calibration framework based on tracer datasets and derivative-free optimization techniques. Finally, we demonstrate the practical application of this approach by calibrating the PEC model using in situ observations. Results show that, despite its simplicity, the model can reproduce observed nutrient dynamics when properly calibrated. The proposed framework is general and can be extended to multi-parameter calibration, seasonal parameter variation, and the coupling of biogeochemical models with higher-fidelity hydrodynamic models.

A Data-Constrained Framework for Marine Biogeochemistry Modeling with Applications to the Paranaguá Estuarine Complex

Abstract

Marine biogeochemical models are widely used to study nutrient dynamics, water quality, and climate-related processes in coastal and estuarine systems. However, developing models that reliably represent specific environments remains computationally demanding, which makes their application to complex systems such as river plumes and estuarine environments challenging. In addition, these models contain several parameters that must be calibrated for the region of interest, a process that is often performed empirically using limited observational data. This thesis advances the development and calibration of marine biogeochemical models in the Brazilian context through three main contributions. First, we develop a conceptual model describing nutrient-phytoplankton dynamics in the Paranagua Estuarine Complex (PEC) in southern Brazil. The model is intentionally simple and computationally inexpensive, allowing simulations to be performed on standard personal computers. Second, we propose a systematic calibration framework based on tracer datasets and derivative-free optimization techniques. Finally, we demonstrate the practical application of this approach by calibrating the PEC model using in situ observations. Results show that, despite its simplicity, the model can reproduce observed nutrient dynamics when properly calibrated. The proposed framework is general and can be extended to multi-parameter calibration, seasonal parameter variation, and the coupling of biogeochemical models with higher-fidelity hydrodynamic models.
Paper Structure (77 sections, 2 theorems, 140 equations, 74 figures, 1 table, 1 algorithm)

This paper contains 77 sections, 2 theorems, 140 equations, 74 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Modeling marine biogeochemical cycles
  3. Tracers and parameters
  4. Source Minus Sink equations
  5. Increasing model complexity: how to couple a biochemical conceptual model to a geophysical box model
  6. Developing a model in practice
  7. A conceptual model for the Paranaguá Estuarine Complex
  8. The PEC environment and data availability
  9. Model development
  10. A conceptual biochemical model for the NP dynamics
  11. A conceptual box-model representing geophysical interactions
  12. Boxes dimensions
  13. Volumetric flow and salinity
  14. A conceptual biogeochemical model for PEC
  15. Results and discussion
  16. ...and 62 more sections

Key Result

Proposition 4.2

Problem (prob001) is equivalent to the linear system of equations: where the matrix $W \in \mathbb{R}^{(p+1) \times (n+1)}$ is defined as

Figures (74)

  • Figure 1: Diagram representing a conceptual biochemical NP-model within an aquatic environment.
  • Figure 2: Evolution of nitrate (upper plot) and phytoplankton (lower plot) concentrations over time for Example \ref{['exonebox02']}.
  • Figure 3: Illustrative representation of the advection and diffusion processes.
  • Figure 4: Model domain: Paranaguá Estuarine Complex.
  • Figure 5: Boxplot of the main phytoplankton groups observed in the PEC waters.
  • ...and 69 more figures

Theorems & Definitions (9)

  • Example 2.1: Conceptual model for nitrate-phytoplankton dynamics
  • Example 2.2
  • Example 2.3
  • Example 2.4
  • Definition 4.1: Local and global minimizers
  • Proposition 4.2
  • Proposition 4.3
  • Example 5.1
  • Example 5.2: A constant equilibrium