## 1 Introduction

[2] Quantification of uncertainty is an important part of numerical modeling. Knowledge of model uncertainty allows for an assessment of the reliability and precision of the model and therefore its general usefulness as a tool for prediction and analysis [*Karniadakis and Glimm*, 2006]. Model uncertainty is the model error due to incomplete knowledge of the simulated system, e.g., unknown boundary or initial conditions due to errors in the model formulation and equations or due to lack of (computational) resources to simulate the degree of complexity of the system, e.g., a low model resolution. Inherently connected to the concept of model uncertainty is that of model sensitivity which characterizes the response of model output to changes in its input. A model is said to be sensitive to a particular input if a slight change in the input triggers a large change in the output. Sensitivity thus contributes to uncertainty in outputs. Typically, many model inputs are not well known, which, combined with model sensitivity, can lead to large uncertainty in model outputs.

[3] In this study, we performed a combined sensitivity and uncertainty analysis for a three-dimensional (three spatial dimensions in addition to the time dimension) physical-biological model set on the Texas-Louisiana shelf. The model includes a nitrogen-based biological module coupled with dissolved oxygen dynamics and is described in *Fennel et al*. [2011, 2013]. In *Fennel* *et al*. [2013], it is shown that the model reproduces observed hypoxic extent well for certain configurations. The goal of this study is to assess the sensitivity of these predicted hypoxia estimates to model inputs of two categories: (i) biological inputs, including one biological parameter (the maximum growth rate of phytoplankton), biological boundary and initial conditions, and river nutrient concentration and (ii) physical inputs, including two parameters controlling subgrid scale horizontal mixing, wind forcing, which can have a significant impact on the extent of hypoxia [*Forrest* *et al*. 2011; *Feng* *et al*. 2012], and the amount of freshwater discharge.

[4] Previous studies of model uncertainty and sensitivity have focused on physical ocean models [*Lermusiaux*, 2006; *Kim* *et al*. 2010; *Thacker* *et al*. 2012]. Sensitivity analyses are also commonly found in the field of ecosystem modelling [*Clancy* *et al*. 2010; *Makler-Pick* *et al*. 2011; *Gibson and Spitz*, 2011; *Melbourne-Thomas* *et al*. 2011] but not typically for coupled three-dimensional biological-physical models. Only a few studies have investigated uncertainty propagation in physical-biological ocean models, e.g., *Béal* *et al*. [2010] assessed the effect of mixing errors on biological properties in a physical-biological model, and *Cossarini* *et al*. [2009] simulate the error dynamics of a model of the Lagoon of Venice ecosystem using a data assimilative approach.

[5] Unless uncertainty is directly integrated into the model [see, e.g., *Lermusiaux*, 2006], an uncertainty or sensitivity analysis entails many model simulations and is thus computationally demanding, in particular for three-dimensional models. Typically, uncertainty analyses represent input uncertainty via random samples using Monte Carlo techniques [*Clancy et al*., 2010; *Kim et al*., 2010; *Melbourne-Thomas et al*., 2011], a computationally inefficient approach that is not practical for three-dimensional models. Emulator-based approaches, such as the polynomial chaos expansion [introduced by *Wiener*, 1938] which we use here, offer a computationally more efficient alternative for propagating uncertainty in model inputs to their outputs [*Xiu and Karniadakis*, 2003; *Shen* *et al*. 2010; *Thacker* *et al*. 2012]. These techniques sample the input probability distribution in a nonrandom fashion and interpolate model output in between samples.

[6] Our results highlight the relative importance of the biological and physical model inputs on hypoxia predictions. The inputs cause distinct temporal and spatial distributions in model uncertainty, where high uncertainties are typically found on the inner shelf region in summer. We show that model predictions of oxygen concentration, hypoxia, and surface chlorophyll are sensitive to uncertainty in various model inputs, especially the physical inputs which perturb the model's stochastic flow field. Uncertainties in the inputs show strong local effects, such as the oxygen concentration in a specific grid cell, as well as larger scale features, such as the size of the predicted hypoxic area.