Parameter uncertainty drives important incongruities between simulated chlorophyll-a and phytoplankton functional group dynamics in a mechanistic management model

Highlights

• 42 PFG growth equation parameters were evaluated with Global Sensitivity Analysis.

• Outputs were most sensitive to chlorophyll-to-carbon and phosphorus uptake factors.

• Parameterization targeting chlorophyll-a may not capture underlying PFG dynamics.

Abstract

Mechanistic phytoplankton functional group (PFG) models are used to develop water quality targets designed to mitigate cyanobacteria blooms, but it remains unclear whether PFG models adequately simulate cyanobacteria dynamics as most are evaluated against observations of chlorophyll-a instead of PFG biomass. To address this challenge, we analyzed an application of CE-QUAL-ICM, a 3D mechanistic PFG model used by water managers and modelers. Global Sensitivity Analysis was employed to assess the sensitivity of modeled chlorophyll-a, cyanobacteria biomass, and eukaryotic phytoplankton biomass to 42 uncertain input factors in CE-QUAL-ICM's PFG growth and loss functions. Results revealed that parameterization of CE-QUAL-ICM captured bloom variation but underpredicted bloom peaks, and simulated chlorophyll-a with greater skill than PFG biomass. Additionally, when run across realistic ranges of PFG parameter values, model outputs were highly sensitive to chlorophyll-to-carbon ratios and phosphorus uptake parameters, indicating that these factors should be the focus of targeted parameterization efforts.

Introduction

Research organizations and government agencies conduct long-term water quality sampling to monitor threats posed by phytoplankton blooms, which are intensifying in magnitude, frequency, and duration, in many cases because of the impacts of human activities such as cultural eutrophication and climate change (Carey et al., 2012; Glibert et al., 2005; O'Neil et al., 2012; Paerl et al., 2011). Chlorophyll-a is classically measured as a proxy of phytoplankton biomass within these monitoring programs and used as a response variable in models designed to explain and predict blooms and their secondary effects (e.g., changes in dissolved oxygen). However, chlorophyll-a is an aggregate measure, and its dynamics may not fully reflect shifts in biomass of key functional groups (e.g., Ní Longphuirt et al., 2019). Additionally, changes in phytoplankton community composition and eco-physiological responses to changing environmental conditions can alter the relationship between chlorophyll-a and biomass (Jakobsen and Markager, 2016).

To capture phytoplankton community dynamics underlying changes in chlorophyll-a, scientists and engineers have developed models that simulate phytoplankton functional groups (PFGs), which are groups of phytoplankton with shared characteristics, such as morphological and eco-physiological traits (Kruk et al., 2002; C. S. Reynolds et al., 2002). In theory, these models quantify phytoplankton growth kinetics and temporal variations in the ecological processes underpinning phytoplankton community structure, thereby representing pelagic productivity dynamics more realistically as compared to models that solely simulate chlorophyll-a. In practice, PFG models can be difficult to parameterize and validate because the processes they simulate are contextualized by significant ecological and biological complexity (Arhonditsis and Brett, 2004; Rigosi et al., 2010; Robson, 2014; Shimoda and Arhonditsis, 2016). Consequently, PFG parameterization often occurs subjectively or through calibration (Frede Thingstad et al., 2010). These complexities result in PFG model algorithms and their parameters being largely uncertain. Many PFG model parameters, such as rates associated with growth kinetics, are not extensively measured or documented in existing literature (Anderson, 2005; Franks, 2009; Shimoda and Arhonditsis, 2016).

Although uncertainties propagate through direct and interactive effects to model outputs, it remains difficult to assess the degree to which parameter uncertainties impact PFG model simulation skill, in part because there are relatively few published PFG modeling studies that include quantified performance metrics. A recent review of PFG modeling analyses by Shimoda and Arhonditsis (2016) revealed that only around 30% of published studies applying PFG models within freshwater systems reported PFG goodness-of-fit measures. The lack of information on PFG performance may partly result from limitations in the availability of detailed and long-term observational PFG data (Shimoda and Arhonditsis, 2016). Among the PFG modeling studies that have presented observations to support simulated outputs, the performances are often poor. For example, Shimoda and Arhonditsis (2016) discovered that published PFG modeling studies in which cyanobacteria was included as a state variable (n = 68) simulatedcyanobacteria dynamics with a median model efficiency of 0.06 (calculated as $1-\sum {(O-P)}^2/\sum {(O-\bar{O})}^2$, where $O$ = observations, $P$ = predictions, and $\bar{O}$ = the mean of observations), a level of performance not ideal for supporting management and policymaking (Ritter and Muñoz-Carpena, 2013). Increasing demands on water managers to mitigate the effects of harmful algal blooms, such as those composed of toxic cyanobacteria, will be met by a growing need for PFG models that can support managers’ decision-making. Thus, it is important that efforts be made to improve PFG model structure and performance by taking a critical look at the processes and parameters contributing uncertainty to simulated PFG dynamics.

One approach that allows for systematic assessment of PFG model structure and performance is Global Sensitivity Analysis (GSA). As with any type of sensitivity analysis, GSA is used to quantify the degree to which model outputs are sensitive to changes in input factors (e.g., parameter values, boundary conditions, algorithm structures, etc.) (Saltelli et al., 2008). GSA contrasts with other sensitivity analysis approaches due to its capacity to assess nonlinear and interactive effects in high-dimensional models (Saltelli et al., 2004, 2008). Results produced from applications of GSA reveal the relative importance of model input factors. Model input factors that are found to dictate model performance should be addressed in order to ensure they are being assigned the most accurate values. Conversely, factors identified as unimportant could potentially be removed from the model, thereby helping to reduce model complexity and uncertainty (Jakeman et al., 2006; Muñoz-Carpena et al., 2007; Saltelli et al., 2004, 2008). In addition, GSA can help identify processes involving important factors that could be targeted for model improvement. Thus, by methodically informing ways to improve upon the algorithmic structures of PFG models, GSA can markedly increase their utility.

The overall goal of this study was to address the need for further quantitative scrutiny of state-of-the-art PFG models. Our primary objective was to quantify the global sensitivity of PFG model outputs to parameters related to phytoplankton growth and loss processes. To meet this objective, we applied GSA to the Corps of Engineers Integrated Compartment Water Quality Model (CE-QUAL-ICM), a highly-specified and state-of-the-art 3D mechanistic water quality and PFG model that couples with the Environmental Fluid Dynamics Code (EFDC), a 3D mechanistic hydrodynamic model. CE-QUAL-ICM is supported by the United States Environmental Protection Agency and used to inform the development of water quality targets for regulatory purposes (Cerco and Cole, 1995). Specifically, the GSA was used to assess CE-QUAL-ICM's sensitivity to a large number of input factors when simulating chlorophyll-a, cyanobacteria biomass, and eukaryotic phytoplankton biomass over an 8-year period in a flow-through lake located in Florida, USA. The availability of detailed and long-term phytoplankton monitoring data allowed for model goodness-of-fit to be quantified for all outputs and for application of GSA. Parameters were varied across realistic value ranges supported by a survey of the literature, thus making the findings regarding model sensitivity of broad interest. To our knowledge, this is the first application of GSA to a highly complex PFG model.