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Numerical Modeling of Dissolved Oxygen Dynamics Using a Finite-Difference Solution to the Streeter-Phelps Equation: Applications to a Small Stream and an Engineered River System

Abstract

Dissolved Oxygen (DO) is an important indicator of stream health, and modeling dissolved oxygen (DO) dynamics can provide insight into the processes governing oxygen availability in urban waterways. The Streeter-Phelps model (SPM) provides a foundational framework for representing DO dynamics, but its simplified formulation may not fully represent heterogeneous urban river systems. This study evaluates a finite-difference implementation of the SPM using field measurements from the UCLA Botanical Garden stream and characterizes preliminary hydraulic and water quality conditions in the Los Angeles River to inform future model application. Sensitivity analysis of the Botanical Garden model revealed that DO predictions were most sensitive to reaeration, highlighting the importance of hydraulic conditions in governing modeled DO dynamics. The final model reproduced observed DO values with an RMSE of 0.3364, however, achieving this fit required a high initial BOD value of 50 mg/L, which is not representative of the study system. The baseline model, using an initial BOD of 2.26 mg/L, did not reproduce the observed variability in the field data. Increasing the initial BOD improved the modeled DO profile, but could not fully account for the observed DO dynamics without reaching physically unrealistic concentrations. These findings suggest that additional oxygen sink terms, such as sediment oxygen demand and photosynthesis and respiration, are needed to better represent the distributed oxygen demand within the stream. Preliminary measurements from the LA River highlight the need for spatially resolved monitoring and site-specific model parameterization in future applications. Future modeling of the LA River should also consider more rigorous BOD measurements and additional oxygen sink terms. Overall, the findings demonstrate both the utility and limitations of applying a simplified mechanistic framework to evaluate DO dynamics in heterogeneous urban stream systems.