The extended Kalman filter for forecast of algal bloom dynamics

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.

Synergistic controls of water column stability and groundwater phosphate on coastal algal blooms

Algal blooms have been identified as one major threat to coastal safety and marine ecosystem functioning, but the dominant mechanism regulating the formation of algal blooms remains controversial, ranging from physical control (via water column stability), the chemical control (via coastal nutrients) to joint control. Here we leveraged the unique data collected in the Hong Kong water over the annual cycle and past three decades, including direct observations of algal blooms and coastal nutrients and process model output of water column stability, and evaluated the differential competing hypotheses in regulating algal blooms. Our results demonstrate that the joint mechanism rather than the single mechanism effectively predicts all algal blooms. Meanwhile, we observed that the adequate nutrients (phosphate, PO43-) significantly originate from coastal groundwater. The production and fluctuation of PO43- in beach aquifers are primarily governed by groundwater temperature, leading to a sustained and sufficient supply of PO43- in a low groundwater temperature environment. Furthermore, along with submarine groundwater discharge (SGD), the ongoing release of PO43- in groundwater enters coastal waters and serves as sufficient nourishment for promoting algal blooms in coastal areas. These results highlight the importance of both physical and chemical mechanisms, as well as SGD, in regulating coastal algal blooms. These findings have practical implications for the prevention of coastal algal blooms and provide insights into mariculture, water security, and the sustainability of coastal ecosystems.

Combining physical-based model and machine learning to forecast chlorophyll-a concentration in freshwater lakes

Increasing algal blooms in freshwater lakes have become a serious challenge facing the world. Short-term forecast of chlorophyll-a concentration (Chla) is essential for providing early warnings and taking action to mitigate the risks of algal blooms in freshwater lakes. At present, a variety of data-driven models and physical-based models have been developed for Chla forecast, yet how to effectively combine multiple models for improving the forecast accuracy remains largely unknown. Here we developed an effective model by combining a physical-based model and machine learning algorithms (long short-term memory, LSTM; random forest, RF; support vector machine, SVM) to forecast the Chla in a freshwater lake, and a Bayesian model averaging (BMA) ensemble forecasting method was further proposed to improve the accuracy and reliability of the forecast results. We found that, with the increase of time steps of advance forecast from 1-day to 7-day, the forecast accuracy as measured by R2 of the machine learning algorithms is decreased from 0.95 to 0.68. The combination of physical-based modeling with LSTM had great capability in short-term forecast of Chla, owing to the fact that the physical-based model can provide high-frequency Chla data and LSTM is skilled at forecasting in the sequence. This is also evidenced by the weights in the BMA method. The proposed BMA short-term ensemble forecasting results had the robust performance when compared to each individual machine learning forecast model for the 7-day advance forecast, with the largest R2 (0.834) and the smallest RMSE (0.267 μg/L). In particular, the uncertainty of a single machine learning model can be effectively reduced by the BMA method.

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.

A Machine Learning Approach for Estimating the Trophic State of Urban Waters Based on Remote Sensing and Environmental Factors

To improve the accuracy of remotely sensed estimates of the trophic state index (TSI) of inland urban water bodies, key environmental factors (water temperature and wind field) were considered during the modelling process. Such environmental factors can be easily measured and display a strong correlation with TSI. Then, a backpropagation neural network (BP-NN) was applied to develop the TSI estimation model using remote sensing and environmental factors. The model was trained and validated using the TSI quantified by five water trophic indicators obtained for the period between 2018 and 2019, and then we selected the most appropriate combination of input variables according to the performance of the BP-NN. Our results demonstrate that the optimal performance can be obtained by combining the water temperature and single-band reflection values of Sentinel-2 satellite imagery as input variables (R2 = 0.922, RMSE = 3.256, MAPE = 2.494%, and classification accuracy rate = 86.364%). Finally, the spatial and temporal distribution of the aquatic trophic state over four months with different trophic levels was mapped in Gongqingcheng City using the TSI estimation model. In general, the predictive maps based on our proposed model show significant seasonal changes and spatial characteristics in the water trophic state, indicating the possibility of performing cost-effective, RS-based TSI estimation studies on complex urban water bodies elsewhere.

A real time data driven algal bloom risk forecast system for mariculture management

In eutrophic coastal waters, harmful algal blooms (HAB) often occur and present challenges to environmental and fisheries management. Despite decades of research on HAB early warning systems, the field validation of algal bloom forecast models have received scant attention. We propose a daily algal bloom risk forecast system based on: (i) a vertical stability theory verified against 191 past algal bloom events; and (ii) a data-driven artificial neural network (ANN) model that assimilates high frequency data to predict sea surface temperature (SST), vertical temperature and salinity differential with an accuracy of 0.35^oC, 0.51^oC, and 0.58 psu respectively. The model does not rely on past chlorophyll measurements and has been validated against extensive field data. Operational forecasts are illustrated for representative algal bloom events at a marine fish farm in Tolo Harbour, Hong Kong. The robust model can assist with traditional onsite monitoring as well as artificial-intelligence (AI) based methods.

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.

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.

Development and evaluation of a real-time forecasting framework for daily water quality forecasts for Lake Chaohu to Lead time of six days

The socioeconomic benefits associated with informative water quality forecasts for large lakes are becoming increasingly evident. However, it remains an enormous challenge to produce forecasts of water quality variables that are accurate enough to meet public demand. In this study, we developed and evaluated a new forecast framework for real-time forecasting of daily dissolved oxygen (DO), ammonium nitrogen (NH), total phosphorus (TP) and total nitrogen (TN) concentrations at lead times from one to six days for Lake Chaohu, the fifth largest freshwater lake in China. The forecast framework is based on a 3-D hydrodynamic ecological model referred to as EcoLake. We used hydrological, meteorological and water quality data from multiple sources to generate initial conditions and forcing functions. Solar radiation and inflows from tributaries which are not readily available were calculated using forecasted cloud cover and rainfall. Forecast skill was evaluated based on 122 forecasts produced on different days in 2017 and for each of the 12 sampling sites. Results indicate that the skill of the forecast framework varies considerably across water quality variables, sampling sites, and lead times. Generally, the forecast framework is more skillful than the persistence forecasts, which use the most recent observations as forecasts. The TN forecasts tend to be the most skillful with a mean RMSE skill score of 28.5% averaged across the six lead times. The DO forecasts tend to have the lowest skill with an average value of 10.9%. Model sensitivity experiments further revealed that errors in the raw air temperature and wind speed forecasts have a noticeable impact on the overall skill of DO and NH forecasts. The forecast framework proposed here could be a useful operational forecasting tool to enhance the effectiveness of the drinking water supply and public health protection based on the water quality management of Lake Chaohu.

Analysis of algal bloom risk with uncertainties in lakes by integrating self-organizing map and fuzzy information theory

Algal blooms are a serious problem in waters, which damage aquatic ecosystems and threaten drinking water safety. However, the outbreak mechanism of algal blooms is very complex with great uncertainty, especially for large water bodies where environmental conditions have obvious variation in both space and time. This study developed an innovative method which integrated a self-organizing map (SOM) and fuzzy information diffusion theory to comprehensively analyze algal bloom risks with uncertainties. The Lake Taihu was taken as study case and the long-term (2004-2010) on-site monitoring data were used. The results showed that algal blooms in Taihu Lake were classified into four categories and exhibited obvious spatial-temporal patterns. The lake was mainly characterized by moderate bloom but had high uncertainty, whereas severe blooms with low uncertainty were observed in the northwest part of the lake. The study gives insight on the spatial-temporal dynamics of algal blooms, and should help government and decision-makers outline policies and practices on bloom monitoring and prevention. The developed method provides a promising approach to estimate algal bloom risks under uncertainties.

Longitudinal hydrodynamic characteristics in reservoir tributary embayments and effects on algal blooms

Three Gorges Reservoir (TGR) is one of the largest man-made lakes in the world. Since the impoundment in 2003, however, algal blooms have been often observed in the tributary embayments. To control the algal blooms, a thorough understanding of the hydrodynamics (e.g., flow regime, velocity gradient, and velocity magnitude and direction) in the tributary embayments is particularly important. Using a calibrated three-dimensional hydrodynamic model, we carried out a hydrodynamic analysis of a typical tributary embayment (i.e., Xiangxi Bay) with emphasis on the longitudinal patterns. The results show distinct longitudinal gradients of hydrodynamics in the study area, which can be generally characterized as four zones: riverine, intermediate, lacustrine, and mainstream influenced zones. Compared with the typical longitudinal zonation for a pure reservoir, there is an additional mainstream influenced zone near the mouth due to the strong effects of TGR mainstream. The blooms are prone to occur in the intermediate and lacustrine zones; however, the hydrodynamic conditions of riverine and mainstream influence zones are not propitious for the formation of algal blooms. This finding helps to diagnose the sensitive areas for algal bloom occurrence.