Projected climate change impact on cyanobacterial bloom phenology in temperate rivers based on temperature dependency.

Climate warming is linked to earlier onset and extended duration of cyanobacterial blooms in temperate rivers. This causes an unpredictable extent of harm to the functioning of the ecosystem and public health. We used Microcystis spp. cell density data monitored for seven years (2016-2022) in ten sites across four temperate rivers of the Republic of Korea to define the phenology of cyanobacterial blooms and elucidate the climatic effect on their pattern. The day of year marking the onset, peak, and end of Microcystis growth were estimated using a Weibull function, and linear mixed-effect models were employed to analyze their relationships with environmental variables. These models identified river-specific temperatures at the beginning and end dates of cyanobacterial blooms. Furthermore, the most realistic models were employed to project future Microcystis bloom phenology, considering downscaled and quantile-mapped regional air temperatures from a general circulation model. Daily minimum and daily maximum air temperatures (mintemp and maxtemp) primarily drove the timing of the beginning and end of the bloom, respectively. The models successfully captured the spatiotemporal variations of the beginning and end dates, with mintemp and maxtemp predicted to be 24℃ (R2 = 0.68) and 16℃ (R2 = 0.35), respectively. The beginning and end dates were projected to advance considerably in the future under the Representative Concentration Pathway 2.6, 4.5, and 8.5. The simulations suggested that the largest uncertainty lies in the timing of when the bloom ends, whereas the timing of when blooming begins has less variation. Our study highlights the dependency of cyanobacterial bloom phenology on temperatures and earlier and prolonged bloom development.

Deep learning-based efficient drone-borne sensing of cyanobacterial blooms using a clique-based feature extraction approach.

Recent advances in remote sensing techniques provide a new horizon for monitoring the spatiotemporal variations of harmful algal blooms (HABs) using hyperspectral data in inland water. In this study, a hierarchical concatenated variational autoencoder (HCVAE) is proposed as an efficient and accurate deep learning (DL) based bio-optical model. To demonstrate its usefulness in retrieving algal pigments, the HCVAE is applied to bloom-prone regions in Daecheong Lake, South Korea. By abstracting the similarity between highly related features using layer-wise clique-based latent-feature extraction, HCVAE reduces the computational loads in deriving outputs while preventing performance degradation. Graph-based clique-detection uses information theory-based criteria to group the related reflectance spectra. Consequently, six latent features were extracted from 79 spectral bands to consist of a multilevel hierarchy of HCVAE that can simultaneously estimate concentrations of chlorophyll-a (Chl-a) and phycocyanin (PC). Despite the parsimonious model architecture, the Chl-a and PC concentrations estimated by HCVAE closely agree with the measured concentrations, with test R2 values of 0.76 and 0.82, respectively. In addition, spatial distribution maps of algal pigments obtained from HCVAE using drone-borne reflectance successfully capture the blooming spots. Based on its multilevel hierarchical architecture, HCVAE can provide the importance of latent features along with their individual wavelengths using Shapley additive explanations. The most important latent features covered the spectral regions associated with both Chl-a and PC. The lightweight neural network DNNsel, which uses only the spectral bands of highest importance in latent-feature extraction, performed comparably to HCVAE. The study results demonstrate the utility of the multilevel hierarchical architecture as a comprehensive assessment model for near-real-time drone-borne sensing of HABs. Moreover, HCVAE is applicable to a wide range of environmental big data, as it can handle numerous sets of features.

Hybrid model for daily streamflow and phosphorus load prediction.

Environmental factors, such as climate change and land use changes, affect water quality drastically. To consider these, various predictive models, both process-based and data-driven, have been used. However, each model has distinct limitations. In this study, a hybrid model combining the soil and water assessment tool and the reverse time attention mechanism (SWAT-RETAIN) was proposed for predicting daily streamflow and total phosphorus (TP) load of a watershed. SWAT-RETAIN was applied to Hwangryong River, South Korea. The hybrid model uses the SWAT output as input data for the RETAIN. Spatial, meteorological, and hydrological data were collected to develop the SWAT to generate high temporal resolution data. RETAIN facilitated effective simultaneous prediction. The SWAT-RETAIN exhibited high accuracy in predicting streamflow (Nash-Sutcliffe efficiency (NSE): 0.45, root mean square error (RMSE): 27.74, percent bias (PBIAS): 22.63 for test sets), and TP load (NSE: 0.50, RMSE: 423.93, PBIAS: 22.09 for test sets). This result was evident in the performance evaluation using flow duration and load duration curves. The SWAT-RETAIN provides enhanced temporal resolution and performance, enabling the simultaneous prediction of multiple variables. It can be applied to predict various water quality variables in larger watersheds.

Assessing the impacts of dam/weir operation on streamflow predictions using LSTM across South Korea.

Recently, weather data have been applied to one of deep learning techniques known as "long short-term memory (LSTM)" to predict streamflow in rainfall-runoff relationships. However, this approach may not be suitable for regions with artificial water management structures such as dams and weirs. Therefore, this study aims to evaluate the prediction accuracy of LSTM for streamflow depending on the availability of dam/weir operational data across South Korea. Four scenarios were prepared for 25 streamflow stations. Scenarios #1 and #2 used weather data and weather and dam/weir operational data, respectively, with the same LSTM model conditions for all stations. Scenarios #3 and #4 used weather data and weather and dam/weir operational data, respectively, with the different LSTM models for individual stations. The Nash-Sutcliffe efficiency (NSE) and the root mean squared error (RMSE) were adopted to assess the LSTM's performance. The results indicated that the mean values of NSE and RMSE were 0.277 and 292.6 (Scenario #1), 0.482 and 214.3 (Scenario #2), 0.410 and 260.7 (Scenario #3), and 0.592 and 181.1 (Scenario #4), respectively. Overall, the model performance was improved by the addition of dam/weir operational data, with an increase in NSE values of 0.182-0.206 and a decrease in RMSE values of 78.2-79.6. Surprisingly, the degree of performance improvement varied according to the operational characteristics of the dam/weir, and the performance tended to increase when the dam/weir with high frequency and great amount of water discharge was included. Our findings showed that the overall LSTM prediction of streamflow was improved by the inclusion of dam/weir operational data. When using dam/weir operational data to predict streamflow using LSTM, understanding of their operational characteristics is important to obtain reliable streamflow predictions.

Machine learning-guided prediction of potential engineering targets for microbial production of lycopene.

The process of designing streamlined workflows for developing microbial strains using classical methods from vast amounts of biological big data has reached its limits. With the continuous increase in the amount of biological big data, data-driven machine learning approaches are being used to overcome the limits of classical approaches for strain development. Here, machine learning-guided engineering of Deinococcus radiodurans R1 for high-yield production of lycopene was demonstrated. The multilayer perceptron models were first trained using the mRNA expression levels of the key genes along with lycopene titers and yields obtained from 17 strains. Then, the potential overexpression targets from 2,047 possible combinations were predicted by the multilayer perceptron combined with a genetic algorithm. Through the machine learning-aided fine-tuning of the predicted genes, the final-engineered LY04 strain resulted in an 8-fold increase in the lycopene production, up to 1.25 g/L from glycerol, and a 6-fold increase in the lycopene yield.

Simultaneous feature engineering and interpretation: Forecasting harmful algal blooms using a deep learning approach.

Routine monitoring for harmful algal blooms (HABs) is generally undertaken at low temporal frequency (e.g., weekly to monthly) that is unsuitable for capturing highly dynamic variations in cyanobacteria abundance. Therefore, we developed a model incorporating reverse time attention with a decay mechanism (RETAIN-D) to forecast HABs with simultaneous improvements in temporal resolution, forecasting performance, and interpretability. The usefulness of RETAIN-D in forecasting HABs was illustrated by its application to two sites located in the lower sections of the Nakdong and Yeongsan rivers, South Korea, where HABs pose a critical water quality issue. Three variations of recurrent neural network models, i.e., long short-term memory (LSTM), gated recurrent unit (GRU), and reverse time attention (RETAIN), were adopted for comparisons of performance with RETAIN-D. Input features encompassing meteorological, hydrological, environmental, and biological factors were used to forecast cyanobacteria abundance (total cyanobacteria cell counts and cell counts of dominant cyanobacteria taxa). Incorporation of a decay mechanism into the deep learning structure in RETAIN-D allowed forecasts of HABs on a high temporal resolution (daily) without manual feature engineering, increasing the usefulness of resulting forecasts for water quality and resources management. RETAIN-D yielded a high degree of accuracy (RMSE = 0.29-1.67, R2 = 0.76-0.98, MAE = 0.18-1.14, SMAPE = 9.77-87.94% for test sets; on natural log scales) across model outputs and sites, successfully capturing high variability and irregularities in the time series. RETAIN-D showed higher accuracy than RETAIN (except for comparable accuracy in forecasting Microcystis abundance at the Nakdong River site) and outperformed LSTM and GRU across all model outputs and sites. Ambient temperature had high importance in forecasting cyanobacteria abundance across all model outputs and sites, whereas the relative importance of other input features varied by the output and site. Increases in contributions with increasing irradiance, decreasing flow rates, and increasing residence time were more pronounced in summer than other seasons. Differences in the contributions of input features among different time steps (1 to 7 days prior to forecasting) were larger in the Yeongsan River site. RETAIN-D is applicable to a wide range of forecasting models that can benefit from improved temporal resolution, performance, and interpretability.

Learning hierarchical Bayesian networks to assess the interaction effects of controlling factors on spatiotemporal patterns of fecal pollution in streams.

The dynamics of fecal indicator bacteria, such as fecal coliforms (FC) in streams, are influenced by the interactions of a myriad of factors. To predict complex spatiotemporal patterns of FC in streams and assess the relative importance of numerous controlling factors, the adoption of a hierarchical Bayesian network (HBN) was proposed in this study. By introducing latent variables correlated to the observed variables into a Bayesian network, the HBN can represent causal relationships among a large set of variables with a multilevel hierarchy. The study area encompasses 215 sites across the watersheds of the four major rivers in South Korea. The monitoring data collected during the 2012-2019 period included 32 input variables pertaining to meteorology, geography, soil characteristics, land cover, urbanization index, livestock density, and point sources. As model endpoints, the exceedance probability of the FC standard concentration as well as two pollution characteristics (i.e., pollution degree and type), derived from FC load duration curves were used. The probability of exceeding an FC threshold value (200 CFU/100 mL) showed spatiotemporal variations, whereas pollution degree and type showed spatial variations that represent long-term severity and relative dominance of nonpoint and point source fecal pollution, respectively. The conceptual model was validated using structural equation modeling to develop the HBN. The results demonstrate that the HBN effectively simplified the model structure, while showing strong model performance (AUC = 0.81, accuracy = 0.74). The results of the sensitivity analysis indicate that land cover is the most important factor in predicting the probability of exceedance and pollution degree, whereas the urbanization index explains most of the variability in pollution type. Furthermore, the results of the scenario analysis suggest that the HBN provides an interpretable framework in which the interaction of controlling factors has causal relationships at different levels that can be identified and visualized.

An interpretable machine learning method for supporting ecosystem management: Application to species distribution models of freshwater macroinvertebrates.

Species distribution models (SDMs), in which species occurrences are related to a suite of environmental variables, have been used as a decision-making tool in ecosystem management. Complex machine learning (ML) algorithms that lack interpretability may hinder the use of SDMs for ecological explanations, possibly limiting the role of SDMs as a decision-support tool. To meet the growing demand of explainable MLs, several interpretable ML methods have recently been proposed. Among these methods, SHaply Additive exPlanation (SHAP) has drawn attention for its robust theoretical justification and analytical gains. In this study, the utility of SHAP was demonstrated by the application of SDMs of four benthic macroinvertebrate species. In addition to species responses, the dataset contained 22 environmental variables monitored at 436 sites across five major rivers of South Korea. A range of ML algorithms was employed for model development. Each ML model was trained and optimized using 10-fold cross-validation. Model evaluation based on the test dataset indicated strong model performance, with an accuracy of ≥0.7 in all evaluation metrics for all MLs and species. However, only the random forest algorithm showed a behavior consistent with the known ecology of the investigated species. SHAP presents an integrated framework in which local interpretations that incorporate local interaction effects are combined to represent the global model structure. Consequently, this framework offered a novel opportunity to assess the importance of variables in predicting species occurrence, not only across sites, but also for individual sites. Furthermore, removing interaction effects from variable importance values (SHAP values) clearly revealed non-linear species responses to variations in environmental variables, indicating the existence of ecological thresholds. This study provides guidelines for the use of a new interpretable method supporting ecosystem management.

The implications of Simpson's paradox for cross-scale inference among lakes.

Using cross-sectional data for making ecological inference started as a practical means of pooling data to enable meaningful empirical model development. For example, limnologists routinely use sample averages from numerous individual lakes to examine patterns across lakes. The basic assumption behind the use of cross-lake data is often that responses within and across lakes are identical. As data from multiple study units across a wide spatiotemporal scale are increasingly accessible for researchers, an assessment of this assumption is now feasible. In this study, we demonstrate that this assumption is usually unjustified, due largely to a statistical phenomenon known as the Simpson's paradox. Through comparisons of a commonly used empirical model of the effect of nutrients on algal growth developed using several data sets, we discuss the cognitive importance of distinguishing factors affecting lake eutrophication operating at different spatial and temporal scales. Our study proposes the use of the Bayesian hierarchical modeling approach to properly structure the data analysis when data from multiple lakes are employed.

Evaluating physico-chemical influences on cyanobacterial blooms using hyperspectral images in inland water, Korea.

Understanding harmful algal blooms is imperative to protect aquatic ecosystems and human health. This study describes the spatial and temporal distributions of cyanobacterial blooms to identify the relations between blooms and environmental factors in the Baekje Reservoir. Two-year cyanobacterial cell data at one fixed station and four remotely sensed distributions of phycocyanin (PC) concentrations based on hyperspectral images (HSIs) were used to describe the relation between the spatial and temporal variations in the blooms and the affecting factors. An artificial neural network model and a three-dimensional hydrodynamic model were implemented to estimate the PC concentrations using remotely sensed HSIs and simulate the hydrodynamics, respectively. The statistical test results showed that the variations in the cyanobacterial biomass depended significantly on variations in the water temperature (slope = 0.13, p-value < 0.01), total nitrogen (slope = -0.487, p-value < 0.01), and total phosphorus (slope = 20.7, p-value < 0.05), whereas the variation in the biomass was moderately dependent on the variation in the outflow (slope = -0.0097, p-value = 0.065). Water temperature was the main factor affecting variations in the PC concentrations for the three months from August to October and was significantly different for the three months (p-value < 0.01). Hydrodynamic parameters also had a partial effect on the variations in the PC concentrations in those three months. Overall, this study helps to describe spatial and temporal variations in cyanobacterial blooms and identify the factors affecting the variation in the blooms. This study may play an important role as a basis for developing strategies to reduce bloom frequency and severity.

The relative importance of water temperature and residence time in predicting cyanobacteria abundance in regulated rivers.

Despite a growing awareness of the problems associated with cyanobacterial blooms in rivers, and particularly in regulated rivers, the drivers of bloom formation and abundance in rivers are not well understood. We developed a Bayesian hierarchical model to assess the relative importance of predictors of summer cyanobacteria abundance, and to test whether the relative importance of each predictor varies by site, using monitoring data from 16 sites in the four major rivers of South Korea. The results suggested that temperature and residence time, but not nutrient levels, are important predictors of summer cyanobacteria abundance in rivers. Although the two predictors were of similar significance across the sites, the residence time was marginally better in accounting for the variation in cyanobacteria abundance. The model with spatial hierarchy demonstrated that temperature played a consistently significant role at all sites, and showed no effect from site-specific factors. In contrast, the importance of residence time varied significantly from site to site. This variation was shown to depend on the trophic state, indicated by the chlorophyll-a and total phosphorus levels. Our results also suggested that the magnitude of weir inflow is a key factor determining the cyanobacteria abundance under baseline conditions.

Modeling spatiotemporal bacterial variability with meteorological and watershed land-use characteristics.

Bacteria are a primary contaminant in natural surface water. The instream concentration of fecal coliform, a potential indicator of pathogens, is influenced by meteorological conditions and land-use characteristics. However, the relationships between these conditions and fecal coliforms are not fully understood. Furthermore, the sources of large variability in fecal coliform counts, e.g., temporal or spatial sources, remain unexplained, especially at large scales. This study proposes the use of Bayesian overdispersed Poisson models, whereby the combined effects of temperature, rainfall, and land-use characteristics on fecal coliform concentration are quantified with predictive uncertainty, and the sources of variability in fecal coliform concentration are assessed. The models were developed using 8-year weekly observations of fecal coliforms obtained from the Wachusett Reservoir watershed in Massachusetts, USA. The results highlight the importance of interactions among meteorological and land-use characteristics in controlling the instream fecal coliform concentration; the increase in fecal coliform concentration with temperature increase was more drastic when rainfall occurred. Also, the responses of fecal coliforms to temperature increases were more pronounced in forest-dominated than in urban-dominated areas. In contrast, the fecal coliform concentration increased more rapidly with rainfall increases in urban-dominated than in forest-dominated areas. The models also demonstrate that among the sources of variability, the monthly component made the most significant contribution to the variability in fecal coliform concentrations. Our results suggest that seasonally dependent processes, including surface runoff, are critical factors that regulate fecal coliform concentration in streams.

Bayesian modeling approach for characterizing groundwater arsenic contamination in the Mekong River basin.

In the Mekong River basin, groundwater from tube-wells is a major drinking water source. However, arsenic (As) contamination in groundwater resources has become a critical issue in the watershed. In this study, As species such as total As (AsTOT), As(III), and As(V), were monitored across the watershed to investigate their characteristics and inter-relationships with water quality parameters, including pH and redox potential (Eh). The data illustrated a dramatic change in the relationship between AsTOT and Eh over a specific Eh range, suggesting the importance of Eh in predicting AsTOT. Thus, a Bayesian change-point model was developed to predict AsTOT concentrations based on Eh and pH, to determine changes in the AsTOT-Eh relationship. The model captured the Eh change-point (∼-100±15mV), which was compatible with the data. Importantly, the inclusion of this change-point in the model resulted in improved model fit and prediction accuracy; AsTOT concentrations were strongly negatively related to Eh values higher than the change-point. The process underlying this relationship was subsequently posited to be the reductive dissolution of mineral oxides and As release. Overall, AsTOT showed a weak positive relationship with Eh at a lower range, similar to those commonly observed in the Mekong River basin delta. It is expected that these results would serve as a guide for establishing public health strategies in the Mekong River Basin.

Implications of Stein's Paradox for Environmental Standard Compliance Assessment.

The implications of Stein's paradox stirred considerable debate in statistical circles when the concept was first introduced in the 1950s. The paradox arises when we are interested in estimating the means of several variables simultaneously. In this situation, the best estimator for an individual mean, the sample average, is no longer the best. Rather, a shrinkage estimator, which shrinks individual sample averages toward the overall average is shown to have improved overall accuracy. Although controversial at the time, the concept of shrinking toward overall average is now widely accepted as a good practice for improving statistical stability and reducing error, not only in simple estimation problems, but also in complicated modeling problems. However, the utility of Stein's insights are not widely recognized in the environmental management community, where mean pollutant concentrations of multiple waters are routinely estimated for management decision-making. In this essay, we introduce Stein's paradox and its modern generalization, the Bayesian hierarchical model, in the context of environmental standard compliance assessment. Using simulated data and nutrient monitoring data from wadeable streams around the Great Lakes, we show that a Bayesian hierarchical model can improve overall estimation accuracy, thereby improving our confidence in the assessment results, especially for standard compliance assessment of waters with small sample sizes.

Long-term and seasonal trend decomposition of Maumee River nutrient inputs to western Lake Erie.

Cyanobacterial blooms in western Lake Erie have recently garnered widespread attention. Current evidence indicates that a major source of the nutrients that fuel these blooms is the Maumee River. We applied a seasonal trend decomposition technique to examine long-term and seasonal changes in Maumee River discharge and nutrient concentrations and loads. Our results indicate similar long-term increases in both regional precipitation and Maumee River discharge (1975-2013), although changes in the seasonal cycles are less pronounced. Total and dissolved phosphorus concentrations declined from the 1970s into the 1990s; since then, total phosphorus concentrations have been relatively stable, while dissolved phosphorus concentrations have increased. However, both total and dissolved phosphorus loads have increased since the 1990s because of the Maumee River discharge increases. Total nitrogen and nitrate concentrations and loads exhibited patterns that were almost the reverse of those of phosphorus, with increases into the 1990s and decreases since then. Seasonal changes in concentrations and loads were also apparent with increases since approximately 1990 in March phosphorus concentrations and loads. These documented changes in phosphorus, nitrogen, and suspended solids likely reflect changing land-use practices. Knowledge of these patterns should facilitate efforts to better manage ongoing eutrophication problems in western Lake Erie.

Mining web-based data to assess public response to environmental events.

We explore how the analysis of web-based data, such as Twitter and Google Trends, can be used to assess the social relevance of an environmental accident. The concept and methods are applied in the shutdown of drinking water supply at the city of Toledo, Ohio, USA. Toledo's notice, which persisted from August 1 to 4, 2014, is a high-profile event that directly influenced approximately half a million people and received wide recognition. The notice was given when excessive levels of microcystin, a byproduct of cyanobacteria blooms, were discovered at the drinking water treatment plant on Lake Erie. Twitter mining results illustrated an instant response to the Toledo incident, the associated collective knowledge, and public perception. The results from Google Trends, on the other hand, revealed how the Toledo event raised public attention on the associated environmental issue, harmful algal blooms, in a long-term context. Thus, when jointly applied, Twitter and Google Trend analysis results offer complementary perspectives. Web content aggregated through mining approaches provides a social standpoint, such as public perception and interest, and offers context for establishing and evaluating environmental management policies.

Are chlorophyll a-total phosphorus correlations useful for inference and prediction?

Correlations between chlorophyll a and total phosphorus in freshwater ecosystems were first documented in the 1960s and have been used since then to infer phosphorus limitation, build simple models, and develop management targets. Often these correlations are considered indicative of a cause-effect relationship. However, many scientists regard the use of these associations for modeling and inference to be misleading due to their potentially spurious nature. Using data from Saginaw Bay, Lake Huron, we examine the relationship among chlorophyll a, total phosphorus, and algal biomass measurements. We apply graphical models and recently developed "structure learning" principles that use conditional dependencies to help identify causal relationships among observational data. The spurious relationship suspected by some is not supported by our data, whereas a direct relationship between chlorophyll a and total phosphorus is always supported, and an additional indirect relationship with an algal biomass intermediary is plausible under some circumstances. Thus, we conclude that these correlations are useful for simple model building but encourage the use of modern statistical methods to avoid common model-assumption violations.

Do invasive mussels restrict offshore phosphorus transport in Lake Huron?

Dreissenid mussels were first documented in the Laurentian Great Lakes in the late 1980s. Zebra mussels (Dreissena polymorpha) spread quickly into shallow, hard-substrate areas; quagga mussels (Dreissena rostriformis bugensis) spread more slowly and are currently colonizing deep, offshore areas. These mussels occur at high densities, filter large water volumes while feeding on suspended materials, and deposit particulate waste on the lake bottom. This filtering activity has been hypothesized to sequester tributary phosphorus in nearshore regions reducing offshore primary productivity. We used a mass balance model to estimate the phosphorus sedimentation rate in Saginaw Bay, a shallow embayment of Lake Huron, before and after the mussel invasion. Our results indicate that the proportion of tributary phosphorus retained in Saginaw Bay increased from approximately 46-70% when dreissenids appeared, reducing phosphorus export to the main body of Lake Huron. The combined effects of increased phosphorus retention and decreased phosphorus loading have caused an approximate 60% decrease in phosphorus export from Saginaw Bay to Lake Huron. Our results support the hypothesis that the ongoing decline of preyfish and secondary producers including diporeia (Diporeia spp.) in Lake Huron is a bottom-up phenomenon associated with decreased phosphorus availability in the offshore to support primary production.

Phosphorus load estimation in the Saginaw River, MI using a Bayesian hierarchical/multilevel model.

We propose the use of Bayesian hierarchical/multilevel ratio approach to estimate the annual riverine phosphorus loads in the Saginaw River, Michigan, from 1968 to 2008. The ratio estimator is known to be an unbiased, precise approach for differing flow-concentration relationships and sampling schemes. A Bayesian model can explicitly address the uncertainty in prediction by using a posterior predictive distribution, while in comparison, a Bayesian hierarchical technique can overcome the limitation of interpreting the estimated annual loads inferred from small sample sizes by borrowing strength from the underlying population shared by the years of interest. Thus, by combining the ratio estimator with the Bayesian hierarchical modeling framework, long-term loads estimation can be addressed with explicit quantification of uncertainty. Our study results indicate a slight decrease in total phosphorus load early in the series. The estimated ratio parameter, which can be interpreted as flow-weighted concentration, shows a clearer decrease, damping the noise that yearly flow variation adds to the load. Despite the reductions, it is not likely that Saginaw Bay meets with its target phosphorus load, 440 tonnes/yr. Throughout the decades, the probabilities of the Saginaw Bay not complying with the target load are estimated as 1.00, 0.50, 0.57 and 0.36 in 1977, 1987, 1997, and 2007, respectively. We show that the Bayesian hierarchical model results in reasonable goodness-of-fits to the observations whether or not individual loads are aggregated. Also, this modeling approach can substantially reduce uncertainties associated with small sample sizes both in the estimated parameters and loads.