An approach to calculating allowable watershed pollutant loads

To improve the management of discharge pollutants loads in the reservoirs’ watershed, an approach of the allowable pollutants loads calculation and its allocation, based on the water environment model, was proposed. Establishment of the approach framework was described at first. Under the guidance of this framework, two major steps were as follows: modeling and scenario analysis were involved and should be applied to support the decision of discharge loads management; Environmental Fluid Dynamic Code (EFDC) model was selected as the kernel model in this framework. In modeling step, spatial discretization for establishing cell map in model, data preprocessing, parameter calibration and uncertainty analysis (which is considered as the significantly relevant factor of the margin of safety (MOS)), were conducted. As a result of the research, the model-based approach presented as a combination of estimation and precise calculation, which contributed to scenario analysis step. Some integrated modules, such as scenario simulation, result analysis and plan optimization were implemented as cycles in the scenario analysis. Finally, allowable pollutant loads under various conditions were calculated. The Chaihe Reservoir in Liaoning Province, China was used as a case study for an application of the approach described above. Results of the Chaihe reservoir water quality simulation, show good agreement with field data and demonstrated that the approach used in the present study provide an efficient and appropriate methodology for pollutant load allocation.     

Modeling agricultural non-point source pollution in a high-precipitation coastal area of China

Non-point source （NPS） pollution simulation in the high-precipitation coastal areas of China is difficult because varying annual typhoon incidence leads to highly contrasting rainfall patterns in dry years and wet years. An IMPULSE （Integrated Model of Non-point Sources Pollution Processes） based NPS model of the Changtan Reservoir watershed, which is a typical high-precipitation coastal area in China, was established based on the analysis of point and NPS pollution data, a digital elevation model, and data on land-use, soil, meteorology, economy, and agricultural management practice. Pre-processed pre-rain- fall soil moisture levels were introduced during the simulation to model the effects of typhoons on hydrology. Rainfall events were simulated sequentially through the year and the model was calibrated and verified using hydrological and water quality data. Accuracy of the simulated rainfall runoff and water quality in the Changtan watershed was found to be acceptable. The study showed that the NPS modeling system could be applied to the simulation and prediction ofNPS loadings in the Changtan Reservoir watershed.     

The Use of Bayesian Model Averaging to Better Represent Uncertainty in Ecological Models

Abstract:   In conservation biology, uncertainty about the choice of a statistical model is rarely considered. Model-selection uncertainty occurs whenever one model is chosen over plausible alternative models to represent understanding about a process and to make predictions about future observations. The standard approach to representing prediction uncertainty involves the calculation of prediction (or confidence) intervals that incorporate uncertainty about parameter estimates contingent on the choice of a "best" model chosen to represent truth. However, this approach to prediction based on statistical models tends to ignore model-selection uncertainty, resulting in overconfident predictions. Bayesian model averaging (BMA) has been promoted in a range of disciplines as a simple means of incorporating model-selection uncertainty into statistical inference and prediction. Bayesian model averaging also provides a formal framework for incorporating prior knowledge about the process being modeled. We provide an example of the application of BMA in modeling and predicting the spatial distribution of an arboreal marsupial in the Eden region of southeastern Australia. Other approaches to estimating prediction uncertainty are discussed.     

Simulation of water quality in a flood detention area using models of different spatial discretization

Detention areas provide a means to lower peak discharges in rivers by temporarily storing excess water. In the case of extreme flood events, the storage effect reduces the risk of dike failures or extensive inundations for downstream reaches and near the site of abstraction. Due to the large amount of organic matter contained in the river water and the inundation of terrestrial vegetation in the detention area, a deterioration of water quality may occur. In particular, decay processes can cause a severe depletion of dissolved oxygen (DO) in the temporary water body. In this paper, we studied the potential of a water quality model to simulate the DO dynamics in a large but shallow detention area to be built at the Elbe River (Germany). Our focus was on examining the impact of spatial discretization on the model’s performance and usability. Therefore, we used a zero-dimensional (0D) and a two-dimensional (2D) modeling approach in parallel. The two approaches solely differ in their spatial discretization, while conversion processes, parameters, and boundary conditions were kept identical. The dynamics of DO simulated by the two models are similar in the initial flooding period but diverge when the system starts to drain. The deviation can be attributed to the different spatial discretization of the two models, leading to different estimates of flow velocities and water depths. Only the 2D model can account for the impact of spatial variability on the evolution of state variables. However, its application requires high efforts for pre- and post-processing and significantly longer computation times. The 2D model is, therefore, not suitable for investigating various flood scenarios or for analyzing the impact of parameter uncertainty. For practical applications, we recommend to firstly set up a fast-running model of reduced spatial discretization, e.g. a 0D model. Using this tool, the reliability of the simulation results should be checked by analyzing the parameter uncertainty of the water quality model. A particular focus may be on those parameters that are spatially variable and, therefore, believed to be better represented in a 2D approach. The benefit from the application of the more costly 2D model should be assessed, based on the analyses carried out with the 0D model. A 2D model appears to be preferable only if the simulated detention area has a complex topography, flow velocities are highly variable in space, and the parameters of the water quality model are well known.     

A Bayesian hierarchical framework for calibrating aquatic biogeochemical models

Model practitioners increasingly place emphasis on rigorous quantitative error analysis in aquatic biogeochemical models and the existing initiatives range from the development of alternative metrics for goodness of fit, to data assimilation into operational models, to parameter estimation techniques. However, the treatment of error in many of these efforts is arguably selective and/or ad hoc. A Bayesian hierarchical framework enables the development of robust probabilistic analysis of error and uncertainty in model predictions by explicitly accommodating measurement error, parameter uncertainty, and model structure imperfection. This paper presents a Bayesian hierarchical formulation for simultaneously calibrating aquatic biogeochemical models at multiple systems (or sites of the same system) with differences in their trophic conditions, prior precisions of model parameters, available information, measurement error or inter-annual variability. Our statistical formulation also explicitly considers the uncertainty in model inputs (model parameters, initial conditions), the analytical/sampling error associated with the field data, and the discrepancy between model structure and the natural system dynamics (e.g., missing key ecological processes, erroneous formulations, misspecified forcing functions). The comparison between observations and posterior predictive monthly distributions indicates that the plankton models calibrated under the Bayesian hierarchical scheme provided accurate system representations for all the scenarios examined. Our results also suggest that the Bayesian hierarchical approach allows overcoming problems of insufficient local data by “borrowing strength” from well-studied sites and this feature will be highly relevant to conservation practices of regions with a high number of freshwater resources for which complete data could never be practically collected. Finally, we discuss the prospect of extending this framework to spatially explicit biogeochemical models (e.g., more effectively connect inshore with offshore areas) along with the benefits for environmental management, such as the optimization of the sampling design of monitoring programs and the alignment with the policy practice of adaptive management.     

Uncertainty analyses for calibrating a soil carbon balance model to agricultural field trial data in Sweden and Kenya

How do additional data of the same and/or different type contribute to reducing model parameter and predictive uncertainties? Most modeling applications of soil organic carbon (SOC) time series in agricultural field trial datasets have been conducted without accounting for model parameter uncertainty. There have been recent advances with Monte Carlo-based uncertainty analyses in the field of hydrological modeling that are applicable, relevant and potentially valuable in modeling the dynamics of SOC. Here we employed a Monte Carlo method with threshold screening known as Generalized Likelihood Uncertainty Estimation (GLUE) to calibrate the Introductory Carbon Balance Model (ICBM) to long-term field trail data from Ultuna, Sweden and Machang’a, Kenya. Calibration results are presented in terms of parameter distributions and credibility bands on time series simulations for a number of case studies. Using these methods, we demonstrate that widely uncertain model parameters, as well as strong covariance between inert pool size and rate constant parameters, exist when root mean square simulation errors were within uncertainties in input estimations and data observations. We show that even rough estimates of the inert pool (perhaps from chemical analysis) can be quite valuable to reduce uncertainties in model parameters. In fact, such estimates were more effective at reducing parameter and predictive uncertainty than an additional 16 years time series data at Ultuna. We also demonstrate an effective method to jointly, simultaneously and in principle more robustly calibrate model parameters to multiple datasets across different climatic regions within an uncertainty framework. These methods and approaches should have benefits for use with other SOC models and datasets as well.     

Incorporating known sources of uncertainty to determine precautionary harvests of saltwater crocodiles.

It has been demonstrated repeatedly that the degree to which regulation operates and the magnitude of environmental variation in an exploited population will together dictate the type of sustainable harvest achievable. Yet typically, harvest models fail to incorporate uncertainty in the underlying dynamics of the target population by assuming a particular (unknown) form of endogenous control. We use a novel approach to estimate the sustainable yield of saltwater crocodile (Crocodylus porosus) populations from major river systems in the Northern Territory, Australia, as an example of a system with high uncertainty. We used multimodel inference to incorporate three levels of uncertainty in yield estimation: (1) uncertainty in the choice of the underlying model(s) used to describe population dynamics, (2) the error associated with the precision and bias of model parameter estimation, and (3) environmental fluctuation (process error). We demonstrate varying strength of evidence for density regulation (1.3-96.7%) for crocodiles among 19 river systems by applying a continuum of five dynamical models (density-independent with and without drift and three alternative density-dependent models) to time series of density estimates. Evidence for density dependence increased with the number of yearly transitions over which each river system was monitored. Deterministic proportional maximum sustainable yield (PMSY) models varied widely among river systems (0.042-0.611), and there was strong evidence for an increasing PMSY as support for density dependence rose. However, there was also a large discrepancy between PMSY values and those produced by the full stochastic simulation projection incorporating all forms of uncertainty, which can be explained by the contribution of process error to estimates of sustainable harvest. We also determined that a fixed-quota harvest strategy (up to 0.2K, where K is the carrying capacity) reduces population size much more rapidly than proportional harvest (the latter strategy requiring temporal monitoring of population size to adjust harvest quotas) and greatly inflates the risk of resource depletion. Using an iconic species recovering from recent extreme overexploitation to examine the potential for renewed sustainable harvest, we have demonstrated that incorporating major forms of uncertainty into a single quantitative framework provides a robust approach to modeling the dynamics of exploited populations.     

Planning for robust reserve networks using uncertainty analysis

Planning land-use for biodiversity conservation frequently involves computer-assisted reserve selection algorithms. Typically such algorithms operate on matrices of species presence–absence in sites, or on species-specific distributions of model predicted probabilities of occurrence in grid cells. There are practically always errors in input data—erroneous species presence–absence data, structural and parametric uncertainty in predictive habitat models, and lack of correspondence between temporal presence and long-run persistence. Despite these uncertainties, typical reserve selection methods proceed as if there is no uncertainty in the data or models. Having two conservation options of apparently equal biological value, one would prefer the option whose value is relatively insensitive to errors in planning inputs. In this work we show how uncertainty analysis for reserve planning can be implemented within a framework of information-gap decision theory, generating reserve designs that are robust to uncertainty. Consideration of uncertainty involves modifications to the typical objective functions used in reserve selection. Search for robust-optimal reserve structures can still be implemented via typical reserve selection optimization techniques, including stepwise heuristics, integer-programming and stochastic global search.     

A state-dependent model for the optimal management of an invasive metapopulation.

Management of invasive species involves choosing between different management strategy options, but often the best strategy for a particular scenario is not obvious. We illustrate the use of optimization methods to determine the most efficient management strategy using one of the most devastating invasive forest pests in North America, the gypsy moth (Lymantria dispar), as a case study. The optimization approach involves the application of stochastic dynamic programming (SDP) to a metapopulation framework with different infestation patch sizes, with the goal of minimizing infestation spread. We use a novel "moving window" approach as a way to address a spatially explicit problem without being explicitly spatial. We examine results for two cases in order to develop general rules of thumb for management. We explore a model with limited parameter information and then assess how strategies change with specific parameterization for the gypsy moth. The model results in a complex but stable, state-dependent management strategy for a multiyear management program that is robust even under situations of uncertainty. The general rule of thumb for the basic model consists of three strategies: eradicating medium-density infestations, reducing large-density infestations, and reducing the colonization rate from the main infestation, depending on the state of the system. With specific gypsy moth parameterization, reducing colonization decreases in importance relative to the other two strategies. The application of this model to gypsy moth management emphasizes the importance of managing based on the state of the system, and if applied to a specific geographic area, has the potential to substantially improve the efficiency and cost-effectiveness of current gypsy moth eradication programs, helping to slow the spread of this pest. Additionally, the approach used for this particular invasive species can be extended to the optimization of management programs for the spread of other invasive and problem species exhibiting metapopulation dynamics.     

Sensitivity Analyses of Spatial Population Viability Analysis Models for Species at Risk and Habitat Conservation Planning

Abstract:  Population viability analysis (PVA) is an effective framework for modeling species- and habitat-recovery efforts, but uncertainty in parameter estimates and model structure can lead to unreliable predictions. Integrating complex and often uncertain information into spatial PVA models requires that comprehensive sensitivity analyses be applied to explore the influence of spatial and nonspatial parameters on model predictions. We reviewed 87 analyses of spatial demographic PVA models of plants and animals to identify common approaches to sensitivity analysis in recent publications. In contrast to best practices recommended in the broader modeling community, sensitivity analyses of spatial PVAs were typically ad hoc, inconsistent, and difficult to compare. Most studies applied local approaches to sensitivity analyses, but few varied multiple parameters simultaneously. A lack of standards for sensitivity analysis and reporting in spatial PVAs has the potential to compromise the ability to learn collectively from PVA results, accurately interpret results in cases where model relationships include nonlinearities and interactions, prioritize monitoring and management actions, and ensure conservation-planning decisions are robust to uncertainties in spatial and nonspatial parameters. Our review underscores the need to develop tools for global sensitivity analysis and apply these to spatial PVA.     

River water quality management model using genetic algorithm

Conventional mathematical programming methods, such as linear programming, non linear programming, dynamic programming and integer programming have been used to solve the cost optimization problem for regional wastewater treatment systems. In this study, a river water quality management model was developed through the integration of a genetic algorithm (GA). This model was applied to a river system contaminated by three determined discharge sources to achieve the water quality goals and wastewater treatment cost optimization in the river basin. The genetic algorithm solution, described the treatment plant efficiency, such that the cost of wastewater treatment for the entire river basin is minimized while the water quality constraints in each reach are satisfied. This study showed that genetic algorithm can be applied for river water quality modeling studies as an alternative to the present methods.     

Making conservation decisions under uncertainty for the persistence of multiple species.

Population models for multiple species provide one of the few means of assessing the impact of alternative management options on the persistence of biodiversity, but they are inevitably uncertain. Is it possible to use population models in multiple-species conservation planning given the associated uncertainties? We use information-gap decision theory to explore the impact of parameter uncertainty on the conservation decision when planning for the persistence of multiple species. An information-gap approach seeks robust outcomes that are most immune from error. We assess the impact of uncertainty in key model parameters for three species, whose extinction risks under four alternative management scenarios are estimated using a metapopulation model. Three methods are described for making conservation decisions across the species, taking into account uncertainty. We find that decisions based on single species are relatively robust to uncertainty in parameters, although the estimates of extinction risk increase rapidly with uncertainty. When identifying the best conservation decision for the persistence of all species, the methods that rely on the rankings of the management options by each species result in decisions that are similarly robust to uncertainty. Methods that depend on absolute values of extinction risk are sensitive to uncertainty, as small changes in extinction risk can alter the ranking of the alternative scenarios. We discover that it is possible to make robust conservation decisions even when the uncertainties of the multiple-species problem appear overwhelming. However, the decision most robust to uncertainty is likely to differ from the best decision when uncertainty is ignored, illustrating the importance of incorporating uncertainty into the decision-making process.     

Fish dispersal in fragmented landscapes: a modeling framework for quantifying the permeability of structural barriers

Dispersal is a key determinant of the spatial distribution and abundance of populations, but human-made fragmentation can create barriers that hinder dispersal and reduce population viability. This study presents a modeling framework based on dispersal kernels (modified Laplace distributions) that describe stream fish dispersal in the presence of obstacles to passage. We used mark-recapture trials to quantify summer dispersal of brook trout (Salvelinus fontinalis) in four streams crossed by a highway. The analysis identified population heterogeneity in dispersal behavior, as revealed by the presence of a dominant sedentary component (48-72% of all individuals) characterized by short mean dispersal distance (<10 m), and a secondary mobile component characterized by longer mean dispersal distance (56-1086 m). We did not detect evidence of barrier effects on dispersal through highway crossings. Simulation of various plausible scenarios indicated that detectability of barrier effects was strongly dependent on features of sampling design, such as spatial configuration of the sampling area, barrier extent, and sample size. The proposed modeling framework extends conventional dispersal kernels by incorporating structural barriers. A major strength of the approach is that ecological process (dispersal model) and sampling design (observation model) are incorporated simultaneously into the analysis. This feature can facilitate the use of prior knowledge to improve sampling efficiency of mark-recapture trials in movement studies. Model-based estimation of barrier permeability and its associated uncertainty provides a rigorous approach for quantifying the effect of barriers on stream fish dispersal and assessing population dynamics of stream fish in fragmented landscapes.     

Using demography and movement behavior to predict range expansion of the southern sea otter

In addition to forecasting population growth, basic demographic data combined with movement data provide a means for predicting rates of range expansion. Quantitative models of range expansion have rarely been applied to large vertebrates, although such tools could be useful for restoration and management of many threatened but recovering populations. Using the southern sea otter (Enhydra lutris nereis) as a case study, we utilized integro-difference equations in combination with a stage-structured projection matrix that incorporated spatial variation in dispersal and demography to make forecasts of population recovery and range recolonization. In addition to these basic predictions, we emphasize how to make these modeling predictions useful in a management context through the inclusion of parameter uncertainty and sensitivity analysis. Our models resulted in hind-cast (1989-2003) predictions of net population growth and range expansion that closely matched observed patterns. We next made projections of future range expansion and population growth, incorporating uncertainty in all model parameters, and explored the sensitivity of model predictions to variation in spatially explicit survival and dispersal rates. The predicted rate of southward range expansion (median = 5.2 km/yr) was sensitive to both dispersal and survival rates; elasticity analysis indicated that changes in adult survival would have the greatest potential effect on the rate of range expansion, while perturbation analysis showed that variation in subadult dispersal contributed most to variance in model predictions. Variation in survival and dispersal of females at the south end of the range contributed most of the variance in predicted southward range expansion. Our approach provides guidance for the acquisition of further data and a means of forecasting the consequence of specific management actions. Similar methods could aid in the management of other recovering populations.     

Making more out of sparse data: hierarchical modeling of species communities

Community ecologists and conservation biologists often work with data that are too sparse for achieving reliable inference with species-specific approaches. Here we explore the idea of combining species-specific models into a single hierarchical model. The community component of the model seeks for shared patterns in how the species respond to environmental covariates. We illustrate the modeling framework in the context of logistic regression and presence-absence data, but a similar hierarchical structure could also be used in many other types of applications. We first use simulated data to illustrate that the community component can improve parameterization of species-specific models especially for rare species, for which the data would be too sparse to be informative alone. We then apply the community model to real data on 500 diatom species to show that it has much greater predictive power than a collection of independent species-specific models. We use the modeling approach to show that roughly one-third of distance decay in community similarity can be explained by two variables characterizing water quality, rare species typically preferring nutrient-poor waters with high pH, and common species showing a more general pattern of resource use.     

北大港水库调蓄“引江水”水质变化

通过模拟实验研究了北大港水库底泥释放氯离子的规律,建立了数学模型。采用2 0 0 3年第8次“引黄济津”水质监测数据,验证了模型的有效性。最后,利用该数学模型,预测了南水北调“引江水”在水库中调蓄时的水质变化。认为在合理调度运用的情况下,根据工程规划,北大港水库可以满足作为南水北调调蓄水库的水质要求     

Integrating intraseasonal grassland dynamics in cross-scale distribution modeling to support waterbird recovery plans

Despite much discussion about the utility of remote sensing for effective conservation, the inclusion of these technologies in species recovery plans remains largely anecdotal. We developed a modeling approach for the integration of local, spatially measured ecosystem functional dynamics into a species distribution modeling (SDM) framework in which other ecologically relevant factors are modeled separately at broad scales. To illustrate the approach, we incorporated intraseasonal water-vegetation dynamics into a cross-scale SDM for the Common Snipe (Gallinago gallinago), which is highly dependent on water and vegetation dynamics. The Common Snipe is an Iberian grassland waterbird characteristic of European agricultural meadows and a member of one of the most threatened bird guilds. The intraseasonal dynamics of water content of vegetation were measured using the standard deviation of the normalized difference water index time series computed from bimonthly images of the Sentinel-2 satellite. The recovery plan for the Common Snipe in Galicia (northwestern Iberian Peninsula) provided an opportunity to apply our modeling framework. Model accuracy in predicting the species’ distribution at a regional scale (resulting from integration of downscaled climate projections with regional habitat–topographic suitability models) was very high (area under the curve [AUC] of 0.981 and Boyce's index of 0.971). Local water-vegetation dynamic models, based exclusively on Sentinel-2 imagery, were good predictors (AUC of 0.849 and Boyce's index of 0.976). The predictive power improved (AUC of 0.92 and Boyce's index of 0.98) when local model predictions were restricted to areas identified by the continental and regional models as priorities for conservation. Our models also performed well (AUC of 0.90 and Boyce's index of 0.93) when projected to updated water-vegetation conditions. Our modeling framework enabled incorporation of key ecosystem processes closely related to water and carbon cycles while accounting for other factors ecologically relevant to endangered grassland waterbirds across different scales, allowed identification of priority areas for conservation, and provided an opportunity for cost-effective recovery planning by monitoring management effectiveness from space.     

Using global sensitivity analysis of demographic models for ecological impact assessment

Population viability analysis (PVA) is widely used to assess population‐level impacts of environmental changes on species. When combined with sensitivity analysis, PVA yields insights into the effects of parameter and model structure uncertainty. This helps researchers prioritize efforts for further data collection so that model improvements are efficient and helps managers prioritize conservation and management actions. Usually, sensitivity is analyzed by varying one input parameter at a time and observing the influence that variation has over model outcomes. This approach does not account for interactions among parameters. Global sensitivity analysis (GSA) overcomes this limitation by varying several model inputs simultaneously. Then, regression techniques allow measuring the importance of input‐parameter uncertainties. In many conservation applications, the goal of demographic modeling is to assess how different scenarios of impact or management cause changes in a population. This is challenging because the uncertainty of input‐parameter values can be confounded with the effect of impacts and management actions. We developed a GSA method that separates model outcome uncertainty resulting from parameter uncertainty from that resulting from projected ecological impacts or simulated management actions, effectively separating the 2 main questions that sensitivity analysis asks. We applied this method to assess the effects of predicted sea‐level rise on Snowy Plover (Charadrius nivosus). A relatively small number of replicate models (approximately 100) resulted in consistent measures of variable importance when not trying to separate the effects of ecological impacts from parameter uncertainty. However, many more replicate models (approximately 500) were required to separate these effects. These differences are important to consider when using demographic models to estimate ecological impacts of management actions.     

From Adaptive Management to Adjustive Management: A Pragmatic Account of Biodiversity Values

Abstract: The conservation of biodiversity poses an exceptionally difficult problem in that it needs to be effective in a context of double uncertainty: scientific (i.e., how to conserve biodiversity) and normative (i.e., which biodiversity to conserve and why). Although adaptive management offers a promising approach to overcome scientific uncertainty, normative uncertainty is seldom tackled by conservation science. We expanded on the approach proposed by adaptive‐management theorists by devising an integrative and iterative approach to conservation that encompasses both types of uncertainty. Inspired by environmental pragmatism, we suggest that moral values at stake in biodiversity conservation are plastic and that a plurality of individual normative positions can coexist and evolve. Moral values should thus be explored through an experimental process as additional parameters to be incorporated in the traditional adaptive‐management approach. As such, moral values should also be monitored by environmental ethicists working side by side with scientists and managers on conservation projects. Acknowledging the diversity of moral values and integrating them in a process of collective deliberation will help overcome the normative uncertainty. We used Dewey's distinction between adaptation and adjustment to offer a new paradigm built around what we call adjustive management, which reflects both the uncertainty and the likely evolution of the moral values humans attribute to biodiversity. We illustrate how this paradigm relates to practical conservation decisions by exploring the case of the Sacred Ibis (Threskiornis aethiopicus), an alien species in France that is the target of an eradication plan undertaken with little regard for moral issues. We propose that a more satisfying result of efforts to control Sacred Ibis could have been reached by rerouting the traditional feedback loop of adaptive management to include a normative inquiry. This adjustive management approach now needs to be tested in real‐case conservation programs.