A Bayesian approach to the ecosystem inverse problem

Assessing Ecosystem State Space Models: Identifiability and Estimation

Hierarchical probability models are being used more often than non-hierarchical deterministic process models in environmental prediction and forecasting, and Bayesian approaches to fitting such models are becoming increasingly popular. In particular, models describing ecosystem dynamics with multiple states that are autoregressive at each step in time can be treated as statistical state space models (SSMs). In this paper, we examine this subset of ecosystem models, embed a process-based ecosystem model into an SSM, and give closed form Gibbs sampling updates for latent states and process precision parameters when process and observation errors are normally distributed. Here, we use simulated data from an example model (DALECev) and study the effects changing the temporal resolution of observations on the states (observation data gaps), the temporal resolution of the state process (model time step), and the level of aggregation of observations on fluxes (measurements of transfer rates on the state process). We show that parameter estimates become unreliable as temporal gaps between observed state data increase. To improve parameter estimates, we introduce a method of tuning the time resolution of the latent states while still using higher-frequency driver information and show that this helps to improve estimates. Further, we show that data cloning is a suitable method for assessing parameter identifiability in this class of models. Overall, our study helps inform the application of state space models to ecological forecasting applications where (1) data are not available for all states and transfers at the operational time step for the ecosystem model and (2) process uncertainty estimation is desired.

Pipeline Leakage Detection and Localization Using a Reliable Pipeline-Mechanism Model Incorporating a Bayesian Model Updating Approach

Pipeline transportation is widely used in industrial production and daily life. In order to reduce the waste of resources and economic losses caused by pipeline leakage, effective pipeline leakage detection and localization technology is particularly important. Among the many leakage detection methods, the model-based method for pipeline leakage detection and localization is widely used. However, the key to the method is how to obtain an accurate and reliable pipeline model to ensure and improve the detection accuracy. This paper proposes a novel method to obtain a reliable pipeline-mechanism model that fused data and mechanism models based on Bayesian theory. Moreover, in the process of Bayesian fusion, the complexity and calculations in the mechanism models were greatly reduced by establishing a surrogate model. After that, the multidimensional posterior distribution was sampled by the Markov chain Monte Carlo-differential evolution adaptive metropolis (ZS) (MCMC-DREAM (ZS)) algorithm, and the uncertainty in the model was updated to obtain a reliable pipeline-mechanism model. Subsequently, the pipeline resistance coefficient, which could be calculated based on the reliable pipeline-mechanism model, was proposed as an indicator for detecting whether the pipeline leaked or not. Finally, the pipeline leak model was used to determine the location of the leak. The reliable pipeline-mechanism model was applied in an experimental device to validate its performance. The results showed that the proposed method improved the accuracy and reliability of the mechanism model, and, in addition, the leakage could be accurately located.

Water Environmental Capacity Analysis of Taihu Lake and Parameter Estimation Based on the Integration of the Inverse Method and Bayesian Modeling

An integrated approach using the inverse method and Bayesian approach, combined with a lake eutrophication water quality model, was developed for parameter estimation and water environmental capacity (WEC) analysis. The model was used to support load reduction and effective water quality management in the Taihu Lake system in eastern China. Water quality was surveyed yearly from 1987 to 2010. Total nitrogen (TN) and total phosphorus (TP) were selected as water quality model variables. Decay rates of TN and TP were estimated using the proposed approach. WECs of TN and TP in 2011 were determined based on the estimated decay rates. Results showed that the historical loading was beyond the WEC, thus, reduction of nitrogen and phosphorus input is necessary to meet water quality goals. Then WEC and allowable discharge capacity (ADC) in 2015 and 2020 were predicted. The reduction ratios of ADC during these years were also provided. All of these enable decision makers to assess the influence of each loading and visualize potential load reductions under different water quality goals, and then to formulate a reasonable water quality management strategy.

Space, time and complexity in plant dispersal ecology

Dispersal of pollen and seeds are essential functions of plant species, with far-reaching demographic, ecological and evolutionary consequences. Interest in plant dispersal has increased with concerns about the persistence of populations and species under global change. We argue here that advances in plant dispersal ecology research will be determined by our ability to surmount challenges of spatiotemporal scales and heterogeneities and ecosystem complexity. Based on this framework, we propose a selected set of research questions, for which we suggest some specific objectives and methodological approaches. Reviewed topics include multiple vector contributions to plant dispersal, landscape-dependent dispersal patterns, long-distance dispersal events, spatiotemporal variation in dispersal, and the consequences of dispersal for plant communities, populations under climate change, and anthropogenic landscapes.

Bayesian learning and predictability in a stochastic nonlinear dynamical model

Bayesian inference methods are applied within a Bayesian hierarchical modeling framework to the problems of joint state and parameter estimation, and of state forecasting. We explore and demonstrate the ideas in the context of a simple nonlinear marine biogeochemical model. A novel approach is proposed to the formulation of the stochastic process model, in which ecophysiological properties of plankton communities are represented by autoregressive stochastic processes. This approach captures the effects of changes in plankton communities over time, and it allows the incorporation of literature metadata on individual species into prior distributions for process model parameters. The approach is applied to a case study at Ocean Station Papa, using particle Markov chain Monte Carlo computational techniques. The results suggest that, by drawing on objective prior information, it is possible to extract useful information about model state and a subset of parameters, and even to make useful long-term forecasts, based on sparse and noisy observations.

Combined Bayesian statistics and load duration curve method for bacteria nonpoint source loading estimation

Nonpoint source load estimation is an essential part of the development of the bacterial total maximum daily load (TMDL) mandated by the Clean Water Act. However, the currently widely used watershed-receiving water modeling approach is usually associated with a high level of uncertainty and requires long-term observational data and intensive training effort. The load duration curve (LDC) method recommended by the EPA provides a simpler way to estimate bacteria loading. This method, however, does not take into consideration the specific fate and transport mechanisms of the pollutant and cannot address the uncertainty. In this study, a Bayesian statistical approach is applied to the Escherichia coli TMDL development of a stream on the Eastern Shore of Virginia to inversely estimate watershed bacteria loads from the in-stream monitoring data. The mechanism of bacteria transport is incorporated. The effects of temperature, bottom slope, and flow on allowable and existing load calculations are discussed. The uncertainties associated with load estimation are also fully described. Our method combines the merits of LDC, mechanistic modeling, and Bayesian statistics, while overcoming some of the shortcomings associated with these methods. It is a cost-effective tool for bacteria TMDL development and can be modified and applied to multi-segment streams as well.

A Bayesian approach for estimating bacterial nonpoint source loading in an estuary with limited observations

Large uncertainty in the estimation of bacterial nonpoint sources often results in the poor simulation of bacteria concentration in estuaries using a deterministic model. To better quantify the uncertainty in bacterial modeling, a Bayesian approach was incorporated into a tidally averaged estuarine model for estimating bacterial loading using in-stream observations. This was accomplished by using Bayes' theorem to develop a joint probability distribution for nonpoint source loadings based on the bacteria observations in the estuary. To overcome the geometry variation along the estuary for a non-linear transport problem with no analytical solution, the approach was implemented on a finite difference model. The approach was applied to Holdens Creek, a tidal river of the Pocomoke Sound of the Chesapeake Bay, to explore the feasibility of estimating bacteria sources and to develop an allowable load for the Creek to attain water quality standards. Further experiments were conducted to investigate the convergence for loading estimation, and the errors and uncertainties associated with load estimation using different data sets with varied sample sizes. With the use of limited observations, the nonpoint source loads can be estimated within an acceptable error range by selecting appropriate prior loading distributions. Because of the high spatial correlations among observations in the estuary, the errors in loading estimation at adjacent watersheds compensated each other, resulting in a good estimation of loads for the entire watershed. The approach not only provides an efficient methodology to assess the nonpoint source contribution for watershed management, but also has the additional advantage of addressing the problems of the uncertainty and error associated with bacterial simulation in the estuary.

Water quality modeling for load reduction under uncertainty: a Bayesian approach

A Bayesian approach was applied to river water quality modeling (WQM) for load and parameter estimation. A distributed-source model (DSM) was used as the basic model to support load reduction and effective water quality management in the Hun-Taizi River system, northeastern China. Water quality was surveyed at 18 sites weekly from 1995 to 2004; biological oxygen demand (BOD) and ammonia (NH(4)(+)) were selected as WQM variables. The first-order decay rate (k(i)) and load (L(i)) of the 16 river segments were estimated using the Bayesian approach. The maximum pollutant loading (L(m)) of NH(4)(+) and BOD for each river segment was determined based on DSM and the estimated parameters of k(i). The results showed that for most river segments, the historical loading was beyond the L(m) threshold; thus, reduction for organic matter and nitrogen is necessary to meet water quality goals. Then the effects of inflow pollutant concentration (C(i-1)) and water velocity (v(i)) on water quality standard compliance were used to demonstrate how the proposed model can be applied to water quality management. The results enable decision makers to decide load reductions and allocations among river segments under different C(i-1) and v(i) scenarios.