Algal Bloom Model Research Articles

Storm-induced coastward expansion of Margalefidinium polykrikoides bloom in Chesapeake Bay.

An unusual coastward expansion of the toxic dinoflagellate species Margalefidinium polykrikoides was observed in 2020 summer after a tropical storm passing Chesapeake Bay. Such coastward expansion was only recorded in 2007. A newly developed coupled Lagrangian particle tracking and harmful algal bloom model driven by environmental variables was used to investigate the underlying mechanisms and successfully reproduced the expansion patterns. Persistent pre-storm southerly winds favored the delivery of bloom source water originated inside the bay to the coast. Storm-induced strong upwelling of denser subsurface water interacted with the after-storm outflow plume (steered southward as the storm's impacts waned), forming a transport barrier to accumulate algae and delineate the coastwide bloom extent. Algal diel vertical migrations and transport barrier enable algae to stay in the nearshore regions. The storm-induced coastward expansion of M. polykrikoides might increase future bloom possibility in the coastal area.

Uncertainty quantification for ecological models with random parameters.

There is often considerable uncertainty in parameters in ecological models. This uncertainty can be incorporated into models by treating parameters as random variables with distributions, rather than fixed quantities. Recent advances in uncertainty quantification methods, such as polynomial chaos approaches, allow for the analysis of models with random parameters. We introduce these methods with a motivating case study of sea ice algal blooms in heterogeneous environments. We compare Monte Carlo methods with polynomial chaos techniques to help understand the dynamics of an algal bloom model with random parameters. Modelling key parameters in the algal bloom model as random variables changes the timing, intensity and overall productivity of the modelled bloom. The computational efficiency of polynomial chaos methods provides a promising avenue for the broader inclusion of parametric uncertainty in ecological models, leading to improved model predictions and synthesis between models and data.

Mathematical modeling of algal blooms due to swine CAFOs in Eastern North Carolina

<p style='text-indent:20px;'>Dramatic strides have been made in treating human waste to remove pathogens and excess nutrients before discharge into the environment, to the benefit of ground and surface water quality. Yet these advances have been undermined by the dramatic growth of Confined Animal Feeding Operations (CAFOs) which produce voluminous quantities of untreated waste. Industrial swine routinely produce waste streams similar to that of a municipality, yet these wastes are held in open-pit "lagoons" which are at risk of rupture or overflow. Eastern North Carolina is a coastal plain with productive estuaries which are imperiled by more than 2000 permitted swine facilities housing over 9 million hogs; the associated 3,500 permitted manure lagoons pose a risk to sensitive estuarine ecosystems, as breaches or overflows send large plumes of nutrient and pathogen-rich waste into surface waters. Understanding the relationship between nutrient pulses and surface water quality in coastal environments is essential to effective CAFO policy formation. In this work, we develop a system of ODEs to model algae growth in a coastal estuary due to a manure lagoon breach and investigate nutrient thresholds above which algal blooms are unresolvable.</p>

Algal bloom prediction influenced by the Water Transfer Project in the Middle-lower Hanjiang River

River algal blooms have become a complex and challenging environmental issue due to the impacts of human activities and inter-basin water transfer project. As the water source of the Middle Route Project (MRP) of South-to-North Water Diversion Project (SNWDP), the Hanjiang River (HR) has experienced frequent algal blooms and this caused potential risk to the drinking water safety of residents along the river. Here, an integrated river algal bloom model was developed to simulate river algal blooms and analyze the effects of MRP of SNWDP on algal bloom occurrence patterns in the middle-lower HR. The integrated river algal bloom model considered multiple physical-chemical-biological processes, which include the hydrological cycle of basin, the interactive mechanisms of river hydrodynamics and the improved algal dynamics process by adding a hydrology factor. The results show that the relative error between simulated and observed algae density at the Qin Duankou (QDK) and Zongguan (ZG) sections are 17.1% and 18.5% during the calibration period and are 18.3% and 19.7% during the validation period, indicating that the proposed integrated algal bloom model met the basic requirements for simulating river algal blooms. Additionally, our analysis indicates that the occurrence of algal bloom events in the middle-lower HR will increase by about two-fold under the water transfer scenario of 9.5 billion m3 year–1 and 2.5-fold under the scenario of 13 billion m3 year–1 at the QDK section. This study potentially provides scientific tool for local governments to carry out optimal scheduling of water conservancy projects for the protection of water ecological environment.

Prediction model of algal blooms using logistic regression and confusion matrix

Algal blooms data are collected and refined as experimental data for algal blooms prediction. Refined algal blooms dataset is analyzed by logistic regression analysis, and statistical tests and regularization are performed to find the marine environmental factors affecting algal blooms. The predicted value of algal bloom is obtained through logistic regression analysis using marine environment factors affecting algal blooms. The actual values and the predicted values of algal blooms dataset are applied to the confusion matrix. By improving the decision boundary of the existing logistic regression, and accuracy, sensitivity and precision for algal blooms prediction are improved. In this paper, the algal blooms prediction model is established by the ensemble method using logistic regression and confusion matrix. Algal blooms prediction is improved, and this is verified through big data analysis.

Stochastic modeling of algal bloom dynamics with delayed nutrient recycling.

Using the discrete Markov chain, in this paper we develop a stochastic model for algal bloom, in which white noise terms are introduced to describe the effects of environmental random fluctuations and time delay to account for the time needed in the conversion of detritus into nutrient. For the proposed model, we firstly discuss the well-posedness, namely the existence and uniqueness of the global positive solution. Then, it is followed by seeking the sufficient conditions for the stochastic stability of its washout equilibrium. Then by using Fourier transform method, the spectral densities of the nutrient and the algae population are estimated. Finally, we show that larger noise can make the algae population extinct exponentially with probability one. Our theoretical and numerical results suggest that the environmental random fluctuations may have more significant influences on the dynamics of the model than the delay. These findings are helpful for a better understanding of the formation mechanism of algal blooms.

Analysis and modeling of algal blooms in the Nakdong River, Korea

The purpose of this study is to improve the prediction accuracy of algal blooms in the Nakdong River, Korea, to support improved management practices. To improve algal bloom predictions, it is necessary to consider the microbiological characteristics of algal groups. Therefore, Korean governmental data, including water quality, flow rate, and meteorological data, over 12 years (2004–2015) were analyzed to characterize chlorophyll a (Chl-a) concentration dynamics in the Nakdong River, as the primary indicator of algae. The correlation between water temperature and Chl-a concentration differed by region at the study site. While a positive correlation (R = 0.63) was found in the relatively clean (i.e., mesotrophic) upstream area, a negative correlation (R = −0.51) was found in the more eutrophic downstream area. These results indicate that nutrients are a dominant factor of algal blooms in mesotrophic upstream areas, but other factors may have greater impacts in eutrophic downstream areas. Moreover, the dominance of different algal groups differed spatially and temporally at the study site. The three-dimensional hydrodynamics and water quality modeling-capable Environmental Fluid Dynamics Code model was applied to represent the hydrodynamics and kinetics of water quality variables, including Chl-a. Four statistics, the coefficient of determination (R2), Nash–Sutcliffe model efficiency (ME), percentage model bias (Pbias), and cost function (CF), were used to evaluate the model prediction accuracy against field observation data. Compared to the case in which only a single algal group was modeled, modeling multiple algal groups together improved the R2, ME, Pbias, and CF values from 0.25 to 0.50, 0.15 to 0.50, 30.43 to 4.98, and 0.56 to 0.48, respectively. The degree of improvement in the model prediction accuracy was greater for more eutrophic regions at the study site. These results show that there should be greater focus on studying multiple algal groups together when modeling algal bloom predictions to support the development of alternative management practices.

Development of a Coupled Spatiotemporal Algal Bloom Model for Coastal Areas: A Remote Sensing and Data Mining-Based Approach

We developed and successfully applied data-driven models that heavily rely on readily available remote sensing datasets to investigate probabilities of algal bloom occurrences in Kuwait Bay. An artificial neural network (ANN) model, a multivariate regression (MR) model, and a spatiotemporal hybrid model were constructed, optimized, and validated. Temporal and spatial submodels were coupled in a hybrid modeling framework to improve on the predictive powers of conventional ANN and MR generic models. Sixteen variables (sea surface temperature [SST], chlorophyll a OC3M, chlorophyll a Generalized Inherent Optical Property (GIOP), chlorophyll a Garver-Siegel-Maritorena (GSM), precipitation, CDOM, turbidity index, PAR, euphotic depth, Secchi depth, wind direction, wind speed, bathymetry, distance to nearest river outlet, distance to shore, and distance to aquaculture) were used as inputs for the spatial submodel; all of these, with the exception of bathymetry, distance to nearest river outlet, distance to shore, and distance to aquaculture were used for the temporal sub-model as well. Findings include: 1) the ANN model performance exceeded that of the MR model and 2) the hybrid models improved the model performance significantly; 3) the temporal variables most indicative of the timing of bloom propagation are sea surface temperature, Secchi disk depth, wind direction, chlorophyll a (OC3M), and wind speed; and 4) the spatial variables most indicative of algal bloom distribution are the ocean chlorophyll from OC3M, GSM, and the GIOP products; distance to shore; and SST. The adopted methodologies are reliable, cost-effective and could be used to forecast algal bloom occurrences in data-scarce regions.

Analysis of a stochastic model for algal bloom with nutrient recycling

In this paper, the dynamics of a stochastic model for algal bloom with nutrient recycling is investigated. The model incorporates a white noise term in the growth equation of algae population to describe the effects of random fluctuations in the environment, and a nutrient recycling term in the nutrient equation to account for the conversion of detritus into nutrient. The existence and uniqueness of the global positive solution of the model is first proved. Then we study the long-time behavior of the model. Conditions for the extinction and persistence in the mean of the algae population are established. By using the theory of integral Markov semigroups, we show that the model has an invariant and asymptotically stable density. Numerical simulations illustrate our theoretical results.

A high resolution hydrodynamic model system suitable for novel harmful algal bloom modelling in areas of complex coastline and topography

Fjordic coastlines provide sheltered locations for finfish and shellfish aquaculture, and are often subject to harmful algal blooms (HABs) some of which develop offshore and are then advected to impact nearshore aquaculture. Numerical models are a potentially important tool for providing early warning of such HAB events. However, the complex topography of fjordic shelf regions is a significant challenge to modelling. This is frequently compounded by complex bathymetry and local weather patterns. Existing structured grid models do not provide the resolution needed to represent these coastlines in their wider shelf context. In a number of locations advectively transported blooms of the ichthyotoxic dinoflagellate Karenia mikimotoi are of particular concern for the finfish industry. Here were present a novel hydrodynamic model of the coastal waters to the west of Scotland that is based on unstructured finite volume methodology, providing a sufficiently high resolution hydrodynamical structure to realistically simulate the transport of particles (such as K. mikimotoi cells) within nearshore waters where aquaculture sites are sited. Model–observation comparisons reveal close correspondence of tidal elevations for major semidiurnal and diurnal tidal constituents. The thermohaline structure of the model and its current fields are also in good agreement with a number of existing observational datasets. Simulations of the transport of Lagrangian drifting buoys, along with the incorporation of an individual-based biological model, based on a bloom of K. mikimotoi, demonstrate that unstructured grid models have considerable potential for HAB prediction in Scotland and in complex topographical regions elsewhere.

적조모형의 분류 및 성능평가 기법

적조모형의 분류 및 성능평가 기법

Spatial–temporal hydrodynamic and algal bloom modelling analysis of a reservoir tributary embayment

The tributary embayments of Three Gorges Reservoir have been frequented by algal blooms over the past decade. We develop a three-dimensional hydrodynamic and water quality model to study the spatial and temporal variation of hydrodynamics and algal bloom dynamics in a eutrophic tributary embayment, Xiangxi Bay. The study area exhibits distinct longitudinal gradients in hydrodynamics, and could be generally characterized into four longitudinal zones: riverine, intermediate, lacustrine, and mainstream influenced. Compared with the typical longitudinal zonation for a pure reservoir, there is an additional mainstream influenced zone (about 5–10 km long) near the mouth due to direct effects of its adjacent reservoir mainstream. The transport and transformation of key water quality constituents associated with algal blooms, such as chlorophyll, nitrogen, phosphorus, and silicon are simulated satisfactorily. We further investigate the algal bloom dynamics by combining the model results and in situ water quality observations. There is a strong spatial dependence of algal bloom events (occurrence and distribution) in Xiangxi Bay: (i) during 2003–2012, some 73.9% of algal bloom events were first observed in a 10 km long reach within the intermediate and lacustrine zones, and (ii) the spatial pattern of chlorophyll concentrations is closely related to the longitudinal variance of hydrodynamics. A conclusion from this paper is that the relatively calm environment of the intermediate and lacustrine zones provides favourable conditions for algal growth, suggesting the possibility of using longitudinal zonation for risk assessment of algal bloom initiation and levels in reservoir tributary embayments.

A mathematical model of algal blooms based on the characteristics of complex networks theory

To predict the outbreak time of algal blooms and its duration in an actual body of water, this paper developed a directed complex networks (CNs) model of algal blooms. This new model was based on the characteristics of CNs theory and the primary factors that influenced algal blooms. By calculating the shortest path and proposing a key degree node model, the role of each influencing factor during algal blooms was evaluated. Based on years of on-site monitoring data (collected from 1992 to 2000) concerning the Han River, a statistical characteristic function G that reflected the relationship between the statistical characteristics of dominant algae blooming and the degree of algal blooms pollution was proposed. The results indicate that the proposed function G is capable of effectively and semi-quantitatively characterizing the outbreak time and the duration of algal blooms. If the value of G in a body of water is less than 32.6, the body of water will outbreak an algal bloom. An increasingly smaller of G value indicates a greater degree of algal blooms pollution and longer bloom duration.

Modeling the depletion of dissolved oxygen in a lake due to algal bloom: Effect of time delay

We propose and analyze a non-linear mathematical model for algal bloom in a lake to account for the delay in conversion of detritus into nutrients. It is assumed that there is a continuous inflow of nutrients in the lake due to agricultural run off. The model involves four variables, namely nutrient concentration, algal population density, detritus density and dissolved oxygen concentration. The dynamics of the model is studied in terms of local stability analysis and Hopf-bifurcation analysis. It is found that the positive equilibrium of the model may switch from stability to instability to stability, and eventually instability sets in under certain conditions. The numerical simulation is performed to support the analytical results.

Random excitations in modelling of algal blooms in estuarine systems

Abstract This paper proposes and analyzes a non-linear model for the biological outbreaks that links the trophic structure of primary and secondary producers in the estuary. Some of the principles governing phytoplankton growth, biomass, and species composition in two-layered pelagic ecosystems are explored using an idealized, steady-state, mathematical model. Algal blooms often occur in estuary due to excessive flow of nutrients from domestic drainage, industrial and agricultural waste, and this causes the decrease in the concentration of dissolved oxygen in the estuary. We propose a description about interesting marine estuary systems which resembles to the behaviour of real media and construct a non-linear mathematical model with the main purpose of considering the severity and duration of algal blooms in the ecological arena. Although the environmental and physical factors that unleashed the bloom, but ensuing duration and severity of an outbreak are largely due to the subsequent biological interplay between organism. Hence, it threatens the survival of other species of the ecosystem indirectly, and also it is responsible for the degradation of water quality in the estuary because of less oxygen content. We give the results that are qualitatively resemble with those observed in the estuary and thereby offers an insight for the factors that sustain a bloom.

Genetic programming for analysis and real-time prediction of coastal algal blooms

Harmful algal blooms (HAB) have been widely reported and have become a serious environmental problem world wide due to its negative impacts to aquatic ecosystems, fisheries, and human health. A capability to predict the occurrence of algal blooms with an acceptable accuracy and lead-time would clearly be very beneficial to fisheries and environmental management. In this study, we present the first real-time modelling and prediction of algal blooms using a data driven evolutionary algorithm, Genetic Programming (GP). The daily prediction of the algal blooms is carried out at Kat O station in Hong Kong using 3 years of high frequency (two-hourly) chlorophyll fluorescence and related hydro-meteorological and water quality data. The results for the prediction of chlorophyll fluorescence, a measure of algal biomass, are within reasonable accuracy for a lead-time of up to 1 day. The results generally concur with those obtained with artificial neural network. As compared to traditional data-driven models, GP has the advantage of evolving an equation relating input and output variables. A detailed analysis of the results of the GP models shows that GP not only correctly identifies the key input variables in accordance with ecological reasoning, but also demonstrates the relationship between the auto-regressive nature of bloom dynamics and flushing time. This study shows GP to be a viable alternative for algal bloom modelling and prediction; the interpretation of the results is greatly facilitated by the analytical form of the evolved equations.

A robust fuzzy logic approach to modelling algae biomass

Modelling of algal bloom is an ambitious and difficult topic due to the complexity of aquatic ecosystem, insufficient knowledge of the detailed processes and mechanism involved and shortage of high quality data. Owing to the ability to deal with imprecise, uncertain data or ambiguous relationships among data, fuzzy logic (FL) has proved to be a useful and practical method in algal bloom modelling. However, common to any FL modelling approach, the definition of membership functions and inference rules remains difficult. Although, generating rules directly from measurements and observations (rather than consulting the expert) has recently been explored, the procedures turn out to be quite cumbersome. In this paper, a robust FL approach is explored to derive a model directly from measurements, using expert knowledge as a reference only. Its strength lies in the capability to combine partial knowledge on processes with partially available data from observations. The approach was successfully tested in a case for the North Sea to model chlorophyll a (Chl-a) concentration. It had also been introduced to the Dutch pilot study of the European Commission project Harmful Algal Bloom Expert System, which involves 13 institutes and universities from nine EU countries. The objectives of the paper are to illustrate how the robust fuzzy model is developed.

A robust fuzzy logic approach to modelling algae biomass / Une approche robuste de logique floue pour modéliser la biomasse d'algues

Modelling of algal bloom is an ambitious and difficult topic due to the complexity of aquatic ecosystem, insufficient knowledge of the detailed processes and mechanism involved and shortage of high quality data. Owing to the ability to deal with imprecise, uncertain data or ambiguous relationships among data, fuzzy logic (FL) has proved to be a useful and practical method in algal bloom modelling. However, common to any FL modelling approach, the definition of membership functions and inference rules remains difficult. Although, generating rules directly from measurements and observations (rather than consulting the expert) has recently been explored, the procedures turn out to be quite cumbersome. In this paper, a robust FL approach is explored to derive a model directly from measurements, using expert knowledge as a reference only. Its strength lies in the capability to combine partial knowledge on processes with partially available data from observations. The approach was successfully tested in a case ...

Comment on ‘Comparative application of artificial nueral networks and genetic algorithms for multivariate time-series modelling of algal blooms in freshwater lakes’

The prediction of the dynamics of algal blooms—the nonlinear oscillations in the concentration of algal species, with attendant implications on water quality, is a notoriously difficult problem in ecological sciences and environmental engineering. This problem is important because of the practical need to develop early warning systems for harmful algal blooms. There is an enormous literature on eutrophication modeling, in which the prediction of algal dynamics often plays a central role. In the past two decades, most of the major advances were made using deterministic water quality models that mimic the phytoplankton growth and nutrient cycles (e.g. Thomann and Mueller 1987; Di Toro 2001). When properly calibrated against extensive field data, these models can predict trends reasonably well and are often adequate for water quality management purposes (e.g. Lee and Lee 1995). On the other hand, the use of data-driven methods to model algal dynamics appeared only very recently. Recknagel et al. (2002) compare the performance of an artificial neural network model (ANNA) with the SALMO model with parameters estimated by a genetic algorithm and a linguistic model built by a genetic algorithm. The data used in the paper are from Lake Kasumigaura. The main conclusions from this paper are: (i) that multivariate modelling by machine learning techniques is superior to deterministic modelling techniques; (ii) artificial neural networks can be powerful short-term predictors of the timing of algal bloom events; and (iii) causal knowledge can be discovered from the evolutionary algorithms presented. Although the paper outlines an interesting approach to algal bloom modelling, we believe that certain essential details of the data analysis are missing. In the absence of the needed details, the conclusions of the paper are perhaps pre-mature and over-stated, and indeed can be misleading if the results are taken at face value. The following points are discussed in relation to a well-established body of knowledge of algal dynamics—derived from many field and modeling studies by many investigators.

Comparative application of artificial neural networks and genetic algorithms for multivariate time-series modelling of algal blooms in freshwater lakes

The paper compares potentials and achievements of artificial neural networks and genetic algorithms in terms of forecasting and understanding of algal blooms in Lake Kasumigaura (Japan). Despite the complex and nonlinear nature of ecological data, artificial neural networks allow seven-days-ahead predictions of timing and magnitudes of algal blooms with reasonable accuracy. Genetic algorithms possess the capability to evolve, refine and hybridize numerical and linguistic models. Examples presented in the paper show that models explicitly synthesized by genetic algorithms not only perform better in seven-days-ahead predictions of algal blooms than artificial neural network models, but provide more transparency for explanation as well.