State and parameter update of a hydrodynamic-phytoplankton model using ensemble Kalman filter

Improved data assimilation for algal bloom dynamics simulation in the Three Gorges Reservoir using particle filter

Algal blooms have been increasingly prevalent in recent years, especially in lakes and reservoirs; their accurate prediction is essential for preserving water quality. In this study, the observed chlorophyll a (chl-a) levels were assimilated into the Environmental Fluid Dynamics Code (EFDC) of algal bloom dynamics by using a particle filter (PF), and the state variables of water quality and model parameters were simultaneously updated to achieve enhanced algal bloom predictive performance. The developed data assimilation system for algal blooms was applied to Xiangxi Bay (XXB) in the Three Gorges Reservoir (TGR). The results show that the ensemble mean accuracy and reliability of the confidence intervals of the predicted state variables, including chl-a and indirectly updated phosphate (PO4), ammonium (NH4), and nitrate (NO3) levels, were considerably improved after PF assimilation. Thus, PF assimilation is an effective tool for the dynamic correction of parameters to represent their inherent variations. Increased assimilation frequency can effectively suppress the accumulation of model errors; therefore, the use of high-frequency water quality data for assimilation is recommended to ensure more accurate and reliable algal bloom prediction.

Uncertainty in projections of future lake thermal dynamics is differentially driven by lake and global climate models

Freshwater ecosystems provide vital services, yet are facing increasing risks from global change. In particular, lake thermal dynamics have been altered around the world as a result of climate change, necessitating a predictive understanding of how climate will continue to alter lakes in the future as well as the associated uncertainty in these predictions. Numerous sources of uncertainty affect projections of future lake conditions but few are quantified, limiting the use of lake modeling projections as management tools. To quantify and evaluate the effects of two potentially important sources of uncertainty, lake model selection uncertainty and climate model selection uncertainty, we developed ensemble projections of lake thermal dynamics for a dimictic lake in New Hampshire, USA (Lake Sunapee). Our ensemble projections used four different climate models as inputs to five vertical one-dimensional (1-D) hydrodynamic lake models under three different climate change scenarios to simulate thermal metrics from 2006 to 2099. We found that almost all the lake thermal metrics modeled (surface water temperature, bottom water temperature, Schmidt stability, stratification duration, and ice cover, but not thermocline depth) are projected to change over the next century. Importantly, we found that the dominant source of uncertainty varied among the thermal metrics, as thermal metrics associated with the surface waters (surface water temperature, total ice duration) were driven primarily by climate model selection uncertainty, while metrics associated with deeper depths (bottom water temperature, stratification duration) were dominated by lake model selection uncertainty. Consequently, our results indicate that researchers generating projections of lake bottom water metrics should prioritize including multiple lake models for best capturing projection uncertainty, while those focusing on lake surface metrics should prioritize including multiple climate models. Overall, our ensemble modeling study reveals important information on how climate change will affect lake thermal properties, and also provides some of the first analyses on how climate model selection uncertainty and lake model selection uncertainty interact to affect projections of future lake dynamics.

Near-term phytoplankton forecasts reveal the effects of model time step and forecast horizon on predictability

As climate and land use increase the variability of many ecosystems, forecasts of ecological variables are needed to inform management and use of ecosystem services. In particular, forecasts of phytoplankton would be especially useful for drinking water management, as phytoplankton populations are exhibiting greater fluctuations due to human activities. While phytoplankton forecasts are increasing in number, many questions remain regarding the optimal model time step (the temporal frequency of the forecast model output), time horizon (the length of time into the future a prediction is made) for maximizing forecast performance, as well as what factors contribute to uncertainty in forecasts and their scalability among sites. To answer these questions, we developed near-term, iterative forecasts of phytoplankton 1-14 days into the future using forecast models with three different time steps (daily, weekly, fortnightly), that included a full uncertainty partitioning analysis at two drinking water reservoirs. We found that forecast accuracy varies with model time step and forecast horizon, and that forecast models can outperform null estimates under most conditions. Weekly and fortnightly forecasts consistently outperformed daily forecasts at 7-day and 14-day horizons, a trend that increased up to the 14-day forecast horizon. Importantly, our work suggests that forecast accuracy can be increased by matching the forecast model time step to the forecast horizon for which predictions are needed. We found that model process uncertainty was the primary source of uncertainty in our phytoplankton forecasts over the forecast period, but parameter uncertainty increased during phytoplankton blooms and when scaling the forecast model to a new site. Overall, our scalability analysis shows promising results that simple models can be transferred to produce forecasts at additional sites. Altogether, our study advances our understanding of how forecast model time step and forecast horizon influence the forecastability of phytoplankton dynamics in aquatic systems and adds to the growing body of work regarding the predictability of ecological systems broadly.

Using near-term forecasts and uncertainty partitioning to inform prediction of oligotrophic lake cyanobacterial density

Near-term ecological forecasts provide resource managers advance notice of changes in ecosystem services, such as fisheries stocks, timber yields, or water quality. Importantly, ecological forecasts can identify where there is uncertainty in the forecasting system, which is necessary to improve forecast skill and guide interpretation of forecast results. Uncertainty partitioning identifies the relative contributions to total forecast variance introduced by different sources, including specification of the model structure, errors in driver data, and estimation of current states (initial conditions). Uncertainty partitioning could be particularly useful in improving forecasts of highly variable cyanobacterial densities, which are difficult to predict and present a persistent challenge for lake managers. As cyanobacteria can produce toxic and unsightly surface scums, advance warning when cyanobacterial densities are increasing could help managers mitigate water quality issues. Here, we fit 13 Bayesian state-space models to evaluate different hypotheses about cyanobacterial densities in a low nutrient lake that experiences sporadic surface scums of the toxin-producing cyanobacterium, Gloeotrichia echinulata. We used data from several summers of weekly cyanobacteria samples to identify dominant sources of uncertainty for near-term (1- to 4-week) forecasts of G. echinulata densities. Water temperature was an important predictor of cyanobacterial densities during model fitting and at the 4-week forecast horizon. However, no physical covariates improved model performance over a simple model including the previous week's densities in 1-week-ahead forecasts. Even the best fit models exhibited large variance in forecasted cyanobacterial densities and did not capture rare peak occurrences, indicating that significant explanatory variables when fitting models to historical data are not always effective for forecasting. Uncertainty partitioning revealed that model process specification and initial conditions dominated forecast uncertainty. These findings indicate that long-term studies of different cyanobacterial life stages and movement in the water column as well as measurements of drivers relevant to different life stages could improve model process representation of cyanobacteria abundance. In addition, improved observation protocols could better define initial conditions and reduce spatial misalignment of environmental data and cyanobacteria observations. Our results emphasize the importance of ecological forecasting principles and uncertainty partitioning to refine and understand predictive capacity across ecosystems.

Data assimilation in surface water quality modeling: A review

Data assimilation (DA) techniques are powerful means of dynamic natural system modeling that allow for the use of data as soon as it appears to improve model predictions and reduce prediction uncertainty by correcting state variables, model parameters, and boundary and initial conditions. The objectives of this review are to explore existing approaches and advances in DA applications for surface water quality modeling and to identify future research prospects. We first reviewed the DA methods used in water quality modeling as reported in literature. We then addressed observations and suggestions regarding various factors of DA performance, such as the mismatch between both lateral and vertical spatial detail of measurements and modeling, subgrid heterogeneity, presence of temporally stable spatial patterns in water quality parameters and related biases, evaluation of uncertainty in data and modeling results, mismatch between scales and schedules of data from multiple sources, selection of parameters to be updated along with state variables, update frequency and forecast skill. The review concludes with the outlook section that outlines current challenges and opportunities related to growing role of novel data sources, scale mismatch between model discretization and observation, structural uncertainty of models and conversion of measured to simulated vales, experimentation with DA prior to applications, using DA performance or model selection, the role of sensitivity analysis, and the expanding use of DA in water quality management.

Variable update strategy to improve water quality forecast accuracy in multivariate data assimilation using the ensemble Kalman filter

Data assimilation in complex water quality modeling is inevitably multivariate because several water quality variables interact and correlate. In ensemble Kalman filter applications, determining which variables to include and the structure of the relationships among these variables is important to achieve accurate forecast results. In this study, various analysis methods with different combinations of variables and interaction structures were evaluated under two different simulation conditions: synthetic and real. In the former, a synthetic experimental setting was formulated to ensure that issues, including incorrect model error assumption problem, spurious correlation between variables, and observational data inconsistency, would not distort the analysis results. The latter did not have such considerations. Therefore, this process could demonstrate the undistorted effects of the different analysis methods on the assimilated outputs and how these effects might diminish in real applications. Under synthetic conditions, updating a single active variable was found to improve the accuracy of the other active variables, and updating multiple active variables in a multivariate manner mutually enhanced the accuracy of the variables if proper ensemble covariance and observation data consistency were ensured. The results of the real case indicated a weakened mutual enhancement effect, and the methods in which variable localization were applied yielded the best analysis results. However, the multivariate analysis methods produced more accurate forecasting results, indicating that these methods could be superior. Therefore, it is suggested that multivariate analysis methods be considered first for water quality modeling, and the application of variable localization should be considered if significant spurious correlations and data inconsistency are present.

Oxygen data assimilation for estimating micro-organism communities' parameters in river systems

The coupling of high frequency data of water quality with physically based models of river systems is of great interest for the management of urban socio-ecosystems. One approach to exploit high frequency data is data assimilation which has received an increasing attention in the field of hydrology, but not for water quality modeling so far. We present here a first implementation of a particle filtering algorithm into a community-centered hydro-biogeochemical model to assimilate high frequency dissolved oxygen data and to estimate metabolism parameters in the Seine River system. The procedure is designed based on the results of a former sensitivity analysis of the model (Wang et al., 2018) that allows for the identification of the twelve most sensible parameters all over the year. Those parameters are both physical and related to micro-organisms (reaeration coefficient, photosynthetic parameters, growth rates, respiration rates and optimal temperature). The performances of the approach are assessed on a synthetic case study that mimics 66 km of the Seine River. Virtual dissolved oxygen data are generated using time varying parameters. This paper aims at retrieving the predefined parameters by assimilating those data. The simulated dissolved oxygen concentrations match the reference concentrations. The identification of the parameters depends on the hydrological and trophic contexts and more surprisingly on the thermal state of the river. The physical, bacterial and phytoplanktonic parameters can be retrieved properly, leading to the differentiation of two successive algal blooms by comparing the estimated posterior distribution of the optimal temperature for phytoplankton growth. Finally, photosynthetic parameters' distributions following circadian cycles during algal blooms are discussed.

Modelling eutrophication in lake ecosystems: A review

Eutrophication is one of the main causes of the degradation of lake ecosystems. Its intensification during the last decades has led the stakeholders to seek for water management and restoration solutions, including those based on modelling approaches. This paper presents a review of lake eutrophication modelling, on the basis of a scientific appraisal performed by researchers for the French ministries of Environment and Agriculture. After a brief introduction presenting the scientific context, a bibliography analysis is presented. Then the main results obtained with process-based models are summarized. A synthesis of the scientist recommendations in order to improve the lake eutrophication modelling is finally given before the conclusion.

Adaptive forecasting of phytoplankton communities

The global proliferation of harmful algal blooms poses an increasing threat to water resources, recreation and ecosystems. Predicting the occurrence of these blooms is therefore needed to assist water managers in making management decisions to mitigate their impact. Evaluation of the potential for forecasting of algal blooms using the phytoplankton community model PROTECH was undertaken in pseudo-real-time. This was achieved within a data assimilation scheme using the Ensemble Kalman Filter to allow uncertainties and model nonlinearities to be propagated to forecast outputs. Tests were made on two mesotrophic lakes in the English Lake District, which differ in depth and nutrient regime. Some forecasting success was shown for chlorophyll a, but not all forecasts were able to perform better than a persistence forecast. There was a general reduction in forecast skill with increasing forecasting period but forecasts for up to four or five days showed noticeably greater promise than those for longer periods. Associated forecasts of phytoplankton community structure were broadly consistent with observations but their translation to cyanobacteria forecasts was challenging owing to the interchangeability of simulated functional species.