Displays

The historical adoption of Bayesian approaches was limited by two main impediments: 1) the requirement for subjective prior information, and 2) the unavailability of analytical solutions for all but a few simple model forms. However, water quality modeling has always been subjective; selecting point values for model parameters, undertaking some “judicious diddling” to adjust them so that model output more closely matches observed data, and declaring the model to be “reasonable” is a long-standing practice. Water quality modeling in a Bayesian framework can actually reduce this subjectivity as it provides a rigorous and transparent approach for model parameter estimation. The second impediment, lack of analytical solutions, has for many applications, been largely reduced by the increasing availability of fast, cheap computing and concurrent evolution of efficient algorithms to sample the posterior distribution. In water quality modeling, however, the increasing computational availability may be reinforcing the dichotomy between probabilistic and “process-based” models. When I was a graduate student we couldn’t do both process and probability because computers weren’t fast enough. However, current computers unimaginably faster and we still rarely do both. It seems that our increasing computational capacity has been absorbed either in more complex and highly resolved, but still deterministic, process models, or more structurally complex probabilistic models (like hierarchical models) that are still light process. In principal, Bayes Theorem is quite general; any model could constitute the likelihood function, but practically, running Monte Carlo-based methods on simulation models that require hours, days, or even longer to run is not feasible. Developing models that capture the essential (and best understood processes) and that still allow a meaningful uncertainty analysis is an area that invites renewed attention.

How to cite: Stow, C.: Process-based or Probabilistic Models?, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-9925, https://doi.org/10.5194/egusphere-egu2020-9925, 2020.

Applications of the Bayesian statistics require specifying a prior distribution for each unknown parameter to be estimated. The commonly used definition of a Bayesian prior distribution, information about an uncertain parameter, does not provide guidance on how to derive and formulate a prior distribution. In practice, we often use "non-informative" priors or priors based on mathematical convenience. I present a normative definition of the prior based on the shared features of the James-Stein estimator, the empirical Bayes method, and the Bayesian hierarchical model. I use the word "normative" to mean "prescriptive". It also reflects the meaning that the definition can be inconsistent with one another insofar as different types of parameters. I present two case studies where this definition guided me to formulate the modeling processes: one on modeling and predicting cyanobacterial toxin concentration in Lake Erie using chlorophyll-a concentrations (Lake Erie example) and the other on improving the accuracy of calibration-curve-based chemical measurement method (calibration-curve example). The Lake Erie example illustrates temporal exchangeable units, while the calibration-curve example showcases the ubiquity of such exchangeable units.

How to cite: Qian, S.: A normative definition of a Bayesian prior, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-17978, https://doi.org/10.5194/egusphere-egu2020-17978, 2020.

To address the wide range of conceptual and operational uncertainties typically characterizing any modelling exercise, the modelling community in Lake Erie opted for a novel multi-model strategy that aimed to capitalize upon the wide variety of both empirical and process-based models of variant complexity that have been developed in the area over the past decade. Being primarily a reflection of our current level of understanding and existing measurement technologies, the multi-model strategy adopted for Lake Erie accommodates the fact that many different model structures and many different parameter sets within a chosen model structure can acceptably reproduce the observed behavior of a complex environmental system. While this very important notion is still neglected in the modelling literature, there are viewpoints suggesting that environmental management decisions relying upon a single, partially adequate, model can introduce bias and uncertainty that is much larger than the error stemming from a single, partially defensible, selection of model parameter values. Importantly, the practise of basing ecological predictions on one single mathematical model implies that a valid alternative model may be omitted from the decision making process (Type I model error), but also that our forecasts could be derived from an erroneous model that was not rejected in an earlier stage (Type II model error). Recognizing that there is no true model of an ecological system, but rather several adequate descriptions of different conceptual basis and structure, the development of model ensembles is a technique specifically designed to address the uncertainty inherent in the model selection process. Instead of picking the single “best-fit” model to draw ecological forecasts, we can use a multi-model ensemble to derive a weighted average of the predictions from different models.

Notwithstanding the voices in the literature asserting that we are still missing rigorous methodological frameworks to develop multi-model ensembles, the basic framework comprises several steps related to the development of "truly" distinct, site-specific conceptual models, selection of the optimal subset of both data-driven and process-based models, effective combination of these models to synthesize predictions, and subsequent assessment of the underlying uncertainty. This methodological procedure involves three critical decisions aiming: (i) to identify the conceptual or structural differences of the existing models (ensemble members), and thus determine the actual diversity collectively characterizing the model ensemble; (ii) to determine the most suitable calibration/validation domain for evaluating model performance in time and space; and (iii) to establish an optimal weighting scheme in order to assign weights to each ensemble member, when integrating over the individual predictions, and determine the most likely outcome along with the associated uncertainty bounds. In this study, I dissect the two model ensembles developed for the Maumee River watershed and the Lake Erie itself and evaluate their compliance with the aforementioned framework. I provide an overview of all the models used in the area by shedding light on their fundamental assumptions, structural features, and general consistency against empirical knowledge from the system. 

How to cite: Arhonditsis, G.: Castles built on sand or predictive limnology in action? The importance of Bayesian ensembles to support our ecological forecasts, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-7836, https://doi.org/10.5194/egusphere-egu2020-7836, 2020.

Ecosystem degradation is usually abrupt and unexpected shifts in ecosystem states that cannot be easily reversed. Some ecosystems might be subject to high risks of irreversible degradation (RID) because of strong undesirable resilience. In this study, we propose a probabilistic method to quantify RID by measuring the probability of the recovering threshold being unattainable under real world scenarios. Bayesian inference was used for parameter estimations and the posteriors were used to calculate the threshold for recovery and thereby the probability of it being unattainable, i.e., RID. We applied this method to lake eutrophication as an example. Our case study supported our hypothesis that ecosystems could be subject to high RID, as shown by the lake having a RID of 72% at the whole lake level. Spatial heterogeneity of RID was significant and certain regions were more susceptible to irreversible degradation, whereas others had higher chances of recovery. This spatial heterogeneity provides opportunities for mitigation because targeting regions with lower RID is more effective. We also found that pulse disturbances and ecosystem-based solutions had positive influences on lowering the RID. Pulse disturbances had the most significant influence on regions with higher RID, while ecosystem-based solutions performed best for regions with moderate RID, reducing RID to almost 0. Our method provides a practical framework to identify sensitive regions for conservation as well as opportunities for mitigation, which is applicable to a wide range of ecosystems. Our findings highlighted the worst scenario of irreversible degradation by providing a quantitative measure of the risk, thus raising further requirements and challenges for sustainability.

How to cite: Liu, Y. and Wu, S.: Resilience indicator for ecosystems subject to high risk of irreversible degradation: a probabilistic method based on Bayesian inference, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-6182, https://doi.org/10.5194/egusphere-egu2020-6182, 2020.

Nutrient recycling from bottom sediments can provide substantial internal loading to eutrophic lakes and reservoirs, potentially exceeding external watershed loads. However, measurements of sediment nutrient fluxes are rare for most waterbodies in the United States, causing many modeling studies to parameterize these fluxes in simplistic ways or else make assumptions about complex sediment diagenetic rates. Here we propose an alternative approach to understanding internal cycling, using a mass-balance model combined with Bayesian inference to rigorously update prior information on nutrient flux parameters. The approach is applied to Jordan Lake, a major water supply reservoir in North Carolina (USA) that has been highly eutrophic since impoundment in the early 1980s, with chlorophyll a concentrations occasionally exceeding 100 µg/L. We simulate monthly nitrogen and phosphorus dynamics in the water column and sediment layer of four longitudinal reservoir segments, forced by watershed flows, nutrient loads, and meteorology. The model is calibrated within the Bayesian framework and validated using a multi-decadal record of surface nutrient concentration data. We compare multiple versions of the model to assess the importance of prior knowledge from previous literature, the multi-decadal calibration period, and the mechanistic formulation for obtaining accurate and robust predictive performance. Overall, the model explains from 40-60% of the variability in observed nutrient concentrations. Model results indicate that a large fraction (>40%) of phosphorus is lost in the upstream reaches of the reservoir, likely due to rapid settling and burial of particulate material. Within the main body of the reservoir, phosphorus recycling rates were found to be higher than expected a priori, particularly in the summer season. Results show how nutrients stored in lacustrine sediment have been an important source of internal loading to the reservoir for multiple decades, and will dampen the effects of external watershed loading reductions, at least in the near term. To better understand potential time scales for reservoir recovery, we perform future simulations over a multi-decadal period and characterize forecast uncertainties.

How to cite: Obenour, D., Del Giudice, D., Aupperle, M., and Sankarasubramanian, A.: Assessing within-lake nutrient cycling through multi-decadal Bayesian mechanistic modeling, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-4232, https://doi.org/10.5194/egusphere-egu2020-4232, 2020.

Cyanobacteria blooms, especially those involving Microcystis, are an increasing problem facing many freshwater systems worldwide. In this study, a Bayesian Network (BN) along with a Structural Equation Model (SEM) were concurrently developed through data-driven learning and expert elicitation in order to better delineate the main pathways responsible for the Microcystis dominance in a Mediterranean semi-arid hypereutrophic reservoir. The resulting two model structures were then compared with regards to the pathways they identified between the physical lake conditions and the nutrient loads on one hand and Microcystis dominance on the other. The two models were also used to predict the probability of bloom formation under different scenarios of climate change and nutrient loading. Both models showed that, given the eutrophic status of the study reservoir, direct temperature effects appear to be the primary driving force behind the Microcystis growth and dominance. Indirect temperature effects, which modulated water column stratification and internal nutrient release, were also found to play an important role in bloom formation. On the other hand, both models revealed that the direct nutrient pathways were less important as compared to the temperature effects, with internal nutrient loads dominating over external loads due to the seasonal variability in river flows, typical of Mediterranean rivers. Nevertheless, the BN model was unable to capture the recursive relationships between Microcystis and its forcings.

How to cite: Alameddine, I. and Deutsch, E.: Understanding Harmful Algal Bloom Dynamics in a Mediterranean Hypereutrophic Reservoir insights from a Bayesian Network and a Structural Equation Model, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-6709, https://doi.org/10.5194/egusphere-egu2020-6709, 2020.

How to cite: Guo, D., Lintern, A., Webb, A., Ryu, D., Bende-Michl, U., Liu, S., and Western, A.: A bayesian hierarchical model to predict spatio-temporal variability in river water quality at 102 catchments, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-4725, https://doi.org/10.5194/egusphere-egu2020-4725, 2020.

Contaminants that cause water pollution are generated from large areas and flow into rivers. It becomes difficult to obtain an accurate prediction of water quality due to the large spatio-temporal variability in a changing climate which in turn leads to considerable uncertainty in the estimation of water quality. Water quality over South Korea highly depends on hydrometeorological conditions due to distinct seasonality. In this context, we explored the use of hydrometeorological variables (i.e., precipitation and temperature) and the autocorrelation structure of water quality parameters in the water quality prediction model within a Bayesian modeling framework. More specifically, we analyzed explored the interdepedencies and correlations between hydrometeorological factors and the water quality parameters for the Mangyeong River basin, and built a hierarchical Bayesian regression model for the TN and TP which are main water quality paramters in South Korea. The result shows that the proposed modeling framework can capture the key aspects of the water quality paramters in terms of seasonality and their uncertainty.

KEYWORDS: Hierarchical Bayesian Model, Meteorological factors, Water Quality prediction

Acknowledgement

This work was funded by the Korea Meteorological Administration Research and Development Program under Grant KMI(KMI2018-01215)

How to cite: Jung, M., Choi, H.-G., Nguyen, D. H., and Kwon, H.-H.: A Hierchcial Bayesian Model for Spatio-Temporal Water Quality Modeling in a Chainging Climate in South Korea, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-21271, https://doi.org/10.5194/egusphere-egu2020-21271, 2020.

Many hydrological systems have a stochastic behavior at the spatiotemporal scales we observe them. The reasons are insufficient quantity or quality of input observations, and model structural errors, the effects of which vary over time. Assuming model parameters as time-dependent, stochastic processes can account for such effects. This approach differs from using deterministic models in combination with a stochastic error term on output and or input. We start from an existing deterministic conceptual bucket model, which was developed and calibrated to jointly predict streamflow and herbicide pollution observed in a small stream with an agricultural catchment in the Swiss midlands. The model considers sorption and degradation of herbicides, as well as fast transport processes such as overland flow to shortcuts and macropore flow to tile drains. Subsequently, the model is made stochastic by replacing selected constant parameter values by time-varying stochastic processes. We perform parameter inference according to the Bayesian approach using a Gibbs-sampler to combine Metropolis sampling of the remaining constant parameters with sampling from an Ornstein-Uhlenbeck process for the time-dependent parameter. A preliminary analysis of the resulting time series of the parameters reveals, for example, model deficits w.r.t. baseflow, in particular during dry conditions. We show that the resulting patterns can inspire model improvements by providing information that can be interpreted by the modeler. These findings indicate that stochastic models with time-dependent parameters are a promising tool for uncertainty quantification of water quality models and for facilitating the scientific learning process, which may ultimately lead to better predictions.

How to cite: Ammann, L., Fenicia, F., Doppler, T., Stamm, C., and Reichert, P.: Patterns in time-dependent parameters reveal deficits of a catchment-scale herbicide transport model, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-9081, https://doi.org/10.5194/egusphere-egu2020-9081, 2020.

I review the experience obtained in using integrative Bayesian models in interdisciplinary analysis focusing on oil spill risk analysis and water quality in the Baltic Sea. We have applied BBN especially to interdisciplinary analysis, which is easily needed in decision analysis. In the environmental risk analysis, we have mainly focused on the oil spills, where the data sets are poor and also the published papers are scarce. More importantly, the aim of the decision analysis here is to avoid seeing the data, i.e. to avoid accidents. Therefore, some of our applications are based mainly on the use of expert knowledge, especially when we consider decision options that have not been applied before.

  In the oil spill risk analysis, we have chosen the state of the threatened species as the decision criteria, as they have a status in other parts of Finnish legislation. There is no single clear objective in oil spill legislation which could be used as a utility function, and our analysis have shown, that the legislation should be updated to include well defined objectives. One of the scientific quality criteria for using the Bayesian decision analysis for management is that the uncertainty estimates are scientifically justified. Especially in cases where society is assumed to be highly risk averse, the uncertainty estimates related to alternative management options may have a crucial role.

   Biology, sociology and environmental economics have their own scientific traditions. Bayesian models are becoming traditional tools in fisheries biology, where uncertainty estimates of management options are frequently required. In sociology, the traditions allow the subjective treatment of the information, which supports the use of prior probability distributions.  Many of the environmental risks have also economic components, or at least actions have a price, which favors the use of quantitative risk analysis. However, the traditions and quality criteria of these three scientific fields are in many respects different. This creates both technical and human challenges to the modeling tasks.

Keywords: Bayesian networks, fisheries management, environmental management, interdisciplinary risk and decision analysis

How to cite: Kuikka, S.: Experiences in applying Bayesian network models in interdisciplinary water quality decision analysis , EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-7270, https://doi.org/10.5194/egusphere-egu2020-7270, 2020.

Diffuse pollution of phosphorus (P) from agriculture is a major pressure on water quality in Ireland. The Agricultural Catchments Programme (ACP) was initiated to evaluate the Good Agricultural Practice measures implemented under the EU Nitrates Directive. Within the ACP, extensive monitoring and research has been made to understand the drivers and controls on nutrient loss in the agricultural landscape. However, tapering P pollution in agricultural catchments also requires informed decisions about the likely effectiveness of measures as well as their spatial targeting.  There is a need to develop Decision Support Tools (DST) that can account for the uncertainty inherently present in both data and water quality models.

Bayesian Belief Networks (BBNs) are probabilistic graphical models that allow the integration of both quantitative and qualitative information from different sources (experimental data, model outputs and expert opinion) all in one model. Moreover, these models can be easily updated with new knowledge and can be applied with scarce datasets. BBNs have previously been used in multiple decision-making settings to understand causal relationships in different contexts. Recently, BBNs were used to support ecological risk-based decision making.

In this study, a prototype BBN was implemented with the Genie software to develop a DST for understanding the influence of land management and P pollution risk in four ACP catchments dominated by intensively farmed land with contrasting hydrology and land use. In the fist stage of the study, the spatial BBN was constructed visualising the ‘source-mobilisation-transport-continuum’, identifying the main drivers of P pollution based on previous findings from the ACP catchments. A second step involved the consultation of experts and stakeholders through a series of workshops aimed at eliciting their input. These stakeholders have expertise ranging from hydrology and hydrochemistry, land management and farm consulting, to policy and environmental modelling.

At present, the BBN is being parameterized for a 12km² catchment with mostly grassland on poorly drained soils, using a high temporal and spatial resolution dataset that includes hydro-chemo-metrics, mapped soil properties (drainage class and Soil Morgan P), landscape characteristics (i.e. land use and management, presence of mitigation measures and presence of point pollution sources). Preliminary results show that the model captures the difference in P loss risk between catchments, probably caused by contrasting hydrological characteristics and soil P sources.

Future research will be focussed on parameterizing and testing the BBN in three other ACP catchments. Such parametrization will be pivotal to testing the model in data sparse catchments and possibly upscaling the tool to regional and national scale. Moreover, climate change and land use change modelled scenarios will be crucial to inform targeting of mitigation measures.  

How to cite: Negri, C., Glendell, M., Schurch, N., Wade, A. J., and Mellander, P.-E.: Modelling phosphorus pollution risk in agricultural catchments using a spatially distributed Bayesian Belief Network, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-555, https://doi.org/10.5194/egusphere-egu2020-555, 2020.

Fluorescence Spectroscopy is a very promising tool for the identification of dissolved organic material (DOM) in aquatic systems. It is rapid, sensitive and relatively inexpensive. Knowledge gaps and challenging interpretation of large and complex datasets are currently hindering the full exploitation of its potential. To cite only few of the most crucial challenges, different fluorophores can contribute to overlapping peaks in the Excitation Emission Matrix (EEM), peaks can be shifted or their intensity can be reduced or enhanced through different environmental factors, and more powerful data processing tools are required. EEM data are typically analyzed by means of Parallel Factor Analysis (PARAFAC), which is a powerful technique that will also be applied here. Nevertheless, PARAFAC and similar analytical tools have a range of limitations. Therefore, we propose to develop and test a novel systemic approach and Bayesian statistical techniques to overcome existing obstacles. Contrary to the above mentioned, Bayesian statistics allow integrating prior information within the analysis in a transparent, formal and reproducible way. In this field, a vast body of knowledge and data has been gathered, which can be formalized in the form of priors and be included in the interpretation of data to make the analysis more powerful and robust. We will explore different applications in an EEM dataset consisting of samples from well-studied water systems with diverse characteristics covering spatial and temporal variability.

How to cite: Peer, S., Zoboli, O., Vybornova, A., Krampe, J., and Zessner, M.: Exploitation of the maximum potential of fluorescence spectroscopy for water resource systems using Bayesian statistical approaches, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-21443, https://doi.org/10.5194/egusphere-egu2020-21443, 2020.

The spatial variation of road construction runoff, and environmental impacts on both the terrestrial and aquatic environment necessitate the monitoring of receiving water quality. The paper proposed an integrated methodology for spatial optimization of the water quality monitoring network (WQMN) using information-theoretic techniques, including the concepts of the Transinformation entropy (TE) and the value of information (VOI). First, based on the correlation analysis, the most significant water quality parameters were selected. Then, using the Canadian Council of Ministers of the Environment (CCME) method, the water quality index (WQI) was computed in each potential monitoring station. After that, the VOI and TE for all potential stations were calculated. To achieve an optimal network among potential stations, the NSGA-II multi-objective optimization model was developed considering three objective functions, including i) minimizing the number of stations, ii) maximizing the VOI in the selected network, and iii) minimizing TE by the selected nodes. The optimization model resulted in a set of optimal solutions for WQMNs, called Pareto-front. Finally, two multi-criteria decision-making models including TOPSIS and PROMETHEE were utilized for choosing the best solution on the Pareto-front space considering various weighing scenarios assigned to objectives. The applicability of the presented methodology was assessed in a WQMN of a road construction site (33 km) in E18 highway, south of Norway. The selected solutions by TOPSIS and PROMETHEE models present the WQMN with maximum VOI and minimum TE among 33, and 28 potential stations, respectively.

How to cite: Ghorbani Mooselu, M., Liltved, H., Nikoo, M. R., Hindar, A., and Meland, S.: Optimal water quality monitoring network during road construction using Bayes and Entropy theories, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-9147, https://doi.org/10.5194/egusphere-egu2020-9147, 2020.

The open source Mobius framework allows for quick develoment of models based on ODE- and discrete-timestep equations. One can build and explore many model structures with only small modifications to the model code. Model run speed is fast, making it feasible to do extensive automated parameter space exploration, for instance using optimizers or MCMC algorithms. The framework can compile models to a format where they are accessible for interaction using the Python scripting language. Moreover, several calibration and uncertainty analysis tools in Python are already set up so that they can be used with any Mobius model. This can then be used to evaluate model structures using Bayesian methods. We show an example of evaluating a few DOC catchment models using this framework. Modelling frameworks are a good alternative to one-size-fits-all models, and we hope Mobius will be a useful tool for promoting more robust modelling.

How to cite: Norling, M.: Rapid development and evaluation of fast process based models in Mobius, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-7326, https://doi.org/10.5194/egusphere-egu2020-7326, 2020.