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Keywords:

  • Bayesian network;
  • Decision support system;
  • Integrative modeling;
  • Uncertainty analysis;
  • River rehabilitation

Abstract

  1. Top of page
  2. Abstract
  3. EDITOR'S NOTE
  4. INTRODUCTION
  5. DESCRIPTION OF METHOD
  6. MODEL DEVELOPMENT
  7. MODEL APPLICATION
  8. DISCUSSION
  9. CONCLUSIONS
  10. Acknowledgements
  11. REFERENCES

As rehabilitation of previously channelized rivers becomes more common worldwide, flexible integrative modeling tools are needed to help predict the morphological, hydraulic, economic, and ecological consequences of the rehabilitation activities. Such predictions can provide the basis for planning and long-term management efforts that attempt to balance the diverse interests of river system stakeholders. We have previously reported on a variety of modeling methods and decision support concepts that can assist with various aspects of the river rehabilitation process. Here, we bring all of these tools together into a probability network model that links management actions, through morphological and hydraulic changes, to the ultimate ecological and economic consequences. Although our model uses a causal graph representation common to Bayesian networks, we do not limit ourselves to discrete-valued nodes or conditional Gaussian distributions as required by most Bayesian network implementations. This precludes us from carrying out easy probabilistic inference but gives us the advantages of functional and distributional flexibility and enhanced predictive accuracy, which we believe to be more important in most environmental management applications. We exemplify model application to a large, recently completed rehabilitation project in Switzerland. Integr Environ Assess Manag 2012; 8: 462–472. © SETAC


EDITOR'S NOTE

  1. Top of page
  2. Abstract
  3. EDITOR'S NOTE
  4. INTRODUCTION
  5. DESCRIPTION OF METHOD
  6. MODEL DEVELOPMENT
  7. MODEL APPLICATION
  8. DISCUSSION
  9. CONCLUSIONS
  10. Acknowledgements
  11. REFERENCES

This paper represents 1 of 7 review and case study articles generated as a result of a workshop entitled “Scenario and decision analysis in environmental management using Bayesian Belief Networks” (1–2 October 2009, Oslo, Norway) hosted by the Norwegian Institute for Nature Research (NINA) and the Strategic Institute Project “Nature 2020+” and funded by the Research Council of Norway. The main aim of the workshop was to compare Bayesian network applications to different environmental and resource management problems from around the world, identifying common modeling strategies and questions for further research.

INTRODUCTION

  1. Top of page
  2. Abstract
  3. EDITOR'S NOTE
  4. INTRODUCTION
  5. DESCRIPTION OF METHOD
  6. MODEL DEVELOPMENT
  7. MODEL APPLICATION
  8. DISCUSSION
  9. CONCLUSIONS
  10. Acknowledgements
  11. REFERENCES

Many rivers worldwide have been channelized to extend agricultural, industrial, or residential land use, facilitate river navigation, and reduce flood risk (Rosgen 1994; Buijse et al. 2002). These engineering projects have resulted in straight, often erosive, rivers lined by artificial flood levees. Thus, riparian zones are homogenized and natural dynamics are lost (Ward et al. 2001), decreasing the habitat quality for organisms living in or near the river. This is often reflected in a reduction in the abundance and diversity of resident terrestrial and aquatic organisms (Ward 1998). Human recreational opportunities, such as fishing, bird watching, and swimming or wading are also usually diminished, leading to an underappreciation of the ecosystem services that the river has the potential to provide (Millennium Ecosystem Assessment 2005).

In recent years, the rehabilitation of channelized systems has become increasingly common, with some countries spending billions of dollars to improve the ecological condition of rivers while maintaining flood protection for adjacent land uses (Buijse et al. 2002; Shields et al. 2003; Peter et al. 2005). This may involve the creation of localized “river widenings” in which the levees are moved back to allow natural channel movement within a limited area (Rohde et al. 2005). Within the widened reach, the river might shift and adjust, possibly reestablishing the range of riparian habitats that could be found before channelization (Ernst et al. 2010). This can certainly enhance local recreational opportunities, and, if enough reaches are addressed, overall river ecosystem health may improve (Naiman et al. 1993).

Despite the increasing number and expense of restoration projects, there are few attempts to provide integrative assessments of the benefits that various rehabilitation options are likely to incur. Most models designed to support the restoration process do so in a limited manner, focusing exclusively on hydraulic changes (Liu et al. 2004), gravel transport dynamics (Singer and Dunne 2006), or single targeted species (Tyler and Rutherford 2007; Noble et al. 2009). We have previously developed and reported on a number of such models ourselves (Borsuk et al. 2006; Schweizer et al. 2007a, Schweizer et al. 2007b) with intended application primarily to large, midland rivers in Switzerland.

Here, we bring all of our previous efforts together into an integrative model that links potential management actions, through morphological and hydraulic changes, to ecological and economic consequences. To do this, we use the structure of a graphical probability network (often referred to as a Bayesian network) because of the method's consistency with the decision analytic paradigm (Reichert et al. 2007). Specifically, the ability to represent and propagate uncertainty through multiple models that are based on varying types and scales of knowledge is essential for evaluating candidate decision alternatives according to a probabilistic assessment of their anticipated outcomes.

As the specific model components have largely been published elsewhere, the goal of the present article is to describe how these components have been linked together using the graphical probability network formalism. Specifically, we use a directed acyclic graph to represent causal relationships that are characterized by conditional probability distributions. However, we do not require that the model be used to carry out probabilistic inference (using Bayes' theorem), as this task leads to many practical limitations and is not necessary for our purpose. In fact, true Bayesian inference in fully integrated networks is required in only a small minority of environmental management applications, and the common software requirements of discrete-valued nodes or conditional Gaussian distributions can be restrictive and introduce unnecessary ambiguity. Bayesian inference is still important to our effort but only in characterizing the submodel relationships, and it is performed as an offline step in separate software. We exemplify application of our model to a large, recently completed rehabilitation project in Switzerland. This gives us the opportunity to test some model predictions and the model's potential use for providing decision support.

DESCRIPTION OF METHOD

  1. Top of page
  2. Abstract
  3. EDITOR'S NOTE
  4. INTRODUCTION
  5. DESCRIPTION OF METHOD
  6. MODEL DEVELOPMENT
  7. MODEL APPLICATION
  8. DISCUSSION
  9. CONCLUSIONS
  10. Acknowledgements
  11. REFERENCES

A (Bayesian) probability network is a directed acyclic graph that leads to a compact representation of the joint probability distribution of a set of variables in a system of interest (Pearl 2000). Graphically, system variables are represented by nodes, and dependences between nodes are represented by arrows. These arrows indicate patterns of probabilistic dependence and not the flow of mass or process control.

Importantly, the absence of a directly connecting arrow between any 2 nodes in a Bayesian network implies that the 2 variables are conditionally independent, given the values of any intermediate nodes. This means that the probability distribution of any variable Xi in any state of the network can be determined by knowing only the values of its immediate predecessors (called its parents, PAi), without regard to the values of any other variables. In this way, the joint probability distribution for the entire network can be written as the product of a limited number of conditional distributions using the chain rule of probability calculus

  • equation image(1)

Nodes without any parents are called roots and are specified by marginal (i.e., unconditional) distributions.

The interpretation of a Bayesian network in terms of causality is not necessary for extracting the conditional dependence relations. However, it is usually the causal interpretation that allows the structure of the network to be determined. That is to say that appropriate experts can construct a graphical network based on straightforward, qualitative notions of cause and effect (that are the basic building blocks of scientific knowledge) without necessarily being fluent in probabilistic reasoning. The network then defines the appropriate factorization of all relevant variables in the system into conditional distributions that can be used to generate the necessary consequence probabilities (Eqn. 1). In other words, the full diagram can be modularized to allow the characterization of individual subnetworks to proceed independently without regard to the broader context. This means that each subnetwork can be specified using an approach suitable for the type and scale of information available (Borsuk et al. 2004). This is a property of which we take particular advantage in the model described here.

Most published examples of Bayesian network models have used either inherently discrete variables or continuous variables that have been discretized into a finite number of categories. When all variables in a Bayesian network are discrete, then the relationships are specified by conditional probability tables for each node that provide the probability of it being in a particular state (or category), given any combination of states of its parents. This simplifies the probability calculus involved in probabilistic (Bayesian) inference of the states of ancestor nodes, given observed states of descendants. This possibility for inference is the basis for the term Bayesian network.

Inferring the states of some nodes, given the observed states of some descendants (a process referred to as diagnosis), may be useful in some river management contexts. For example, if a network model is constructed to represent the relationship between past disturbances (e.g., floods, drought, pollutant spills) and particular ecosystem responses, then, when such a response is observed in the future, the process of inference can help determine which disturbance was likely to have been the cause. In most cases of rehabilitation assessment however, the primary task is to forecast the likely results of a potential management action, rather than to diagnose the cause of a symptom.

When the possibility for easy inference is not a requirement of the model, then an alternative to constructing networks entirely of discrete variables related by conditional probability tables is to use continuous variables connected by functional equations. Probabilities are introduced through the assumption that certain variables or parameters in the equations are uncertain or unobserved. In many ways, this is more consistent with the semideterministic way that causal models are conceived and used in biology, physics, and engineering. In its most general form, a probabilistic functional equation for a variable Xi consists of an equation of the form

  • equation image(2)

where PAi are the parents of Xi, and Ui are the disturbances caused by omitted variables or random effects (Pearl 2000). This conceptualization can be considered a nonlinear version of the more familiar linear structural equation models (Shipley 2002).

With all the conditional distributions of a Bayesian network specified, generation of the distribution of final outcome nodes is straightforward and can generally proceed most effectively using Monte Carlo–type simulation (Borsuk et al. 2004). Each marginal node is set to a value specifying a decision alternative or a distribution describing uncertain background conditions. A large random sample is then generated for the probabilistic marginal nodes, which is used as input to the functions defining that node's descendants, along with samples from any other uncertain variables that are required by the functions. This generates a sample of the first generation of descendants, which is propagated further along the causal direction in an analogous manner until the final outcome nodes are reached. The marginal distributions of each of the outcome nodes then represent the (probabilistic) predictions of the consequences of the specified decision alternative.

MODEL DEVELOPMENT

  1. Top of page
  2. Abstract
  3. EDITOR'S NOTE
  4. INTRODUCTION
  5. DESCRIPTION OF METHOD
  6. MODEL DEVELOPMENT
  7. MODEL APPLICATION
  8. DISCUSSION
  9. CONCLUSIONS
  10. Acknowledgements
  11. REFERENCES

Consistent with the decision analytic approach, our model building process started with the construction of a comprehensive objectives hierarchy concerning the goals of river rehabilitation (Reichert et al. 2007). This process was undertaken in collaboration with a collection of organized stakeholder groups for a river rehabilitation project in Switzerland, as described by Hostmann et al. (2005a, 2005b). Measurable attributes describing the achievement of the lower-level objectives of the hierarchy then provide the set of variables that should ideally be predicted by the probabilistic outcome model. The key variables resulting from this process, in our case, in addition to the obvious ones of flood protection level and rehabilitation cost, included: river morphology, hydraulic habitat characteristics, erosion potential, siltation of riverbed, benthic population diversity and biomass, riparian community abundance, fish population abundance and age structure, local employment potential, and adjacent land use impacts (see Hostmann et al. 2005a for details). These variables are related to each other and to input variables describing rehabilitation alternatives as shown in the schematic network model of Figure 1. As most of the submodels delineated by the dotted boxes in Figure 1 have been described elsewhere, we will describe them only briefly in the following subsections.

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Figure 1. Schematic probability network relating input variables describing catchment characteristics and rehabilitation alternatives (upper left) to submodels predicting key decision attributes.

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Morphology and hydraulics submodel

Hydraulics and river morphology influence all other variables of interest (Figure 1). Therefore, model construction began with this submodel (Schweizer et al. 2007b). Important attributes include river morphology, erosion potential, hydraulic diversity, and riverbed siltation. Modules to predict these attributes are briefly described in the following subsections. Schweizer et al. (2007b) provide details.

Channel morphology and erosion potential

A river's morphology depends on the balance between stream power, external width constraints, and gravel supply (van den Berg 1995). We developed a stepwise procedure to consider these factors (Figure 2). The procedure starts with the application of the logistic regression model of Bledsoe and Watson (2001) predicting the probability of a river being single- or multithreaded based on valley slope, mean annual flood discharge, and median gravel diameter. Next, the impact of channel width constraints is considered. This is done by predicting the natural width for the indicated morphology using the results of a regression of bankfull width on mean annual flood discharge and median gravel diameter. This predicted natural width is then compared against any constraints (e.g., levees) expected to remain after rehabilitation. If the constrained width is larger than the natural width, then single-threaded rivers are predicted to be sinuous with alternating side bars, otherwise they are predicted to be straight.

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Figure 2. Flow chart of channel morphology determination.

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Rivers predicted to be multi-threaded according to the logistic regression may yet be single-threaded if width constraints are too severe. The pattern diagram of da Silva (1991) indicates whether a river will be braided, meandering, alternating, or straight for given gravel size, channel geometry, and mean depth at bankfull discharge. For single-thread rivers, the mean depth is estimated iteratively using the equation of Strickler (1923), and for braided rivers the iterative method of Zarn (1997) is applied. Finally, the gravel transport capacity within the reach is calculated to check whether the upstream gravel supply is sufficient to allow the predicted morphological structures to develop. These calculations are based on the method of Meyer-Peter and Müller (1948) with corrections based on Zarn (1997). When net annual erosion is predicted, we assume that a straight, incising channel will result. When there is net deposition, we assume that the morphologies predicted by the previous calculations will develop.

Hydraulics

Spatial variation in flow depth and velocity over a river reach is a key determinant of ecosystem structure and function (Allan 1995). We developed an empirical model for the joint distribution of depth and velocity using survey data from 92 stream reaches (Schweizer et al. 2007a). We found that the bivariate distribution of relative velocity and relative depth can be described by a mixture of 2 end-member distributions, 1 normal and the other lognormal, each with fixed parameters. The relative contribution of each distribution can then be predicted from a combination of the dimensionless characteristics: the reach mean Froude number, the reach mean relative roughness, and the ratio of actual discharge to mean discharge. We apply this method to alternating gravel bar and braided morphologies. The joint distribution of relative velocity and relative depth in a straight river, on the other hand, is described by beta-distributed marginals with fixed parameters that are correlated with a rank correlation coefficient of 0.94, as fit to survey data from a set of reaches in Switzerland (see Schweizer et al. 2007a for details). The relative frequency of hydraulic units, such as pools, runs, and riffles are calculated from the predicted bivariate distributions of depth and velocity (Jowett 1993).

Riverbed siltation

Fish and benthic species use the gravel bed matrix as cover and to provide egg incubation habitat. Therefore, siltation and clearance of the interstices are important ecological processes. Conceptually, we model gravel bed siltation as a process that occurs at low to medium discharges at a rate that depends on hydraulic and bed characteristics. As a result of this process, the percent of fines in the river bed increases and the hydraulic conductivity is reduced. When the deposition and resuspension of particles are in equilibrium, siltation of a river bed stops. The temporal progression of the build up of fines is modeled according to the methods of Schälchli (1995).

Occasionally, a high discharge event will flush the river bed, restoring the original gravel structure and size distribution. The discharge sufficient to clear the river bed is calculated according to comparisons of the dimensionless shear stress with bed stability according to Günther (1971). The frequency of this discharge, together with the siltation rate, determines the temporal extent and severity of siltation.

Because of spatial differences in the bottom shear stress, we apply the siltation equations of Schälchli (1995) separately to average conditions in pools and runs. We assume that significant siltation will not occur in riffles due to the very high filter velocities.

Benthic population submodel

Periphyton and invertebrates are important components of river ecosystems due to their ability to produce organic material, decompose detritus, and serve as a food source for organisms at higher trophic levels. We developed a set of simple data-based models to describe the biomass of periphyton, total invertebrates, and 3 invertebrate functional feeding groups (collector-gatherers, predators, and scrapers) as a function of time since the last bed-moving flood, mean water depth, grain size, mean flow velocity, and season (time within the year) (Schweizer 2006). Parameters were estimated from a statistical fit to survey data from as many as 8 sites in 3 rivers. The statistical approach made it easier to derive reliable relationships across different rivers and sites than would have been possible with a strictly mechanistic modeling approach.

Considering the diversity of data sets and the simplicity of the formulations, the models lead to a remarkably good agreement with time series of measurements (Schweizer 2006). Because of the larger data set available, this was particularly true for the periphyton model.

Riparian community submodel

Our riparian community model focuses on riparian arthropods, a significant contributor to overall riverine biodiversity and a functionally important component of river ecosystems. The model predicts the abundance of 3 major groups (spiders, ground beetles, and rove beetles) as a function of river morphology and riparian siltation. Both of these variables are outputs of the “Morphology and Hydraulic” submodel described above.

Using the data of Paetzold et al. (2008), we carried out multiple regression analyses to relate the variation in species abundance to the abiotic predictor variables (Figure 3). We found that for all species there were significant differences between natural and channelized morphologies. In addition, siltation reduced the abundance of all species similarly in both types of morphologies, except for spiders at channelized sites that were already so low that siltation had no further effect. Uncertainty was accounted for through the inclusion of a probabilistic error term, derived from the distribution of residuals from the regression model.

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Figure 3. Predicted and observed abundance of (a) spiders, (b) rove beetles, and (c) ground beetles as a function of riparian siltation and river morphology. Squares represent data from channelized rivers and circles represent data from rivers with natural morphology.

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Fish submodel

The core of our fish submodel is a dynamic, age-structured population simulation (Borsuk et al. 2006). Because our model was initially developed for application to midland rivers in Switzerland, our focal species is brown trout, a desirable sport fish and indicator of river ecosystem health (Lasne et al. 2007).

We represent 5 major stages of the brown trout life cycle in the model: eggs, newly emergent fry, late summer fry, immature juveniles, and adult spawners. The distinction between emergent and late summer fry was made to differentiate the period of greatest density dependence. The number of individuals in each life stage is determined by the number in the previous life stage, as well as relevant population parameters, such as survival and reproductive rates. These parameters are influenced, in turn, by intermediate variables, such as body size and growth rate, or by external controls relevant to rehabilitation measures, such as including substrate and habitat quality, stocking practices, angling, prey resources, and competing species (Figure 4).

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Figure 4. Graphical probability network of brown trout population model. Dark shaded nodes indicate life cycle stages. Light shaded nodes indicate variables likely to be influenced by rehabilitation measures.

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Consistent with the Bayesian viewpoint that probabilities represent subjective degrees of belief, conditional probabilities in a Bayesian network may be based on any available information, including experimental or field results, process-based models, or the elicited judgment of experts. Many of the relationships in the fish submodel were based on expert elicitations (see Borsuk et al. 2006 for details).

Socioeconomic submodel

The socioeconomic submodel estimates the direct and indirect effects of river rehabilitation on the local economy (Spörri et al. 2007). The basic model is expressed in terms of an input–output matrix (Miller and Blair 1985), tracking goods and service flows between various sectors of the economy. This matrix is then used to calculate the direct and indirect changes in economic output and jobs per sector resulting from the direct changes in demand associated with the rehabilitation project (e.g., in the construction, real estate, and other involved industries). We account for uncertainty in the data and in some of the model assumptions using a probabilistic formulation and propagating these probabilities through the model equations (see Spörri et al. 2007 for details).

Model users can input into the model a local input–output matrix, if available, or modify a national matrix using, for example, local employment statistics (the location quotient method; Miller 1998). The input–output method can also be used to estimate the longer-term effects on the local economy of changes in tourism and recreation expected to result from rehabilitation.

Model implementation

The submodels described in the above sections were implemented in Analytica, a commercially available software program for propagating uncertainty through models formulated as graphical networks (Lumina 1997). In principle, the model could be implemented using other software; we chose Analytica because it allows for a wide variety of probability distributions and functional model forms.

The inputs required to run the integrative river rehabilitation model consist of both site-specific characteristics (e.g., discharge statistics, reach slope, gravel size, water temperature patterns) and rehabilitation design criteria (e.g., project expenditures, dike height and spacing, land use changes, revegetation plans, fish stocking). The former can generally be determined from historical or site survey data for the river reach of interest, and the latter should be viewed as decision variables to be set to values corresponding to current conditions, specific design alternatives, or scenarios used for sensitivity analysis.

In Analytica, each input variable is specified by either a fixed value, a probability density function, or, in the case of a discrete variable, a probability table. Input nodes can also be specified as multivariate joint distributions if the uncertainty of 2 or more variables cannot be assumed to be independent. Each child node is then defined by a conditional probability table or, more generally, by a functional expression of the form of Equation 1, derived from submodels such as those described in the sections above. In the latter case, model parameters and error terms are represented explicitly as marginal nodes that serve as parents of a child node along with that variable's predictors. Covariance in model parameters is included by using appropriate multivariate distributions.

Once all model variables, parameters, and relationships are specified, a large sample of realizations is drawn for each marginal node using random Latin hypercube sampling (McKay et al. 1979). These realizations are then propagated through the functional expressions defining the conditional distribution of each child node. These children then serve as parents of the next set of nodes in the network, and their uncertainty is propagated accordingly. The distributions of final model endpoints thus convey the combined uncertainty and variability coming from their entire set of ancestors. This process of Monte Carlo–type simulation is implemented in many other software packages, but to our knowledge, Analytica is the only commercial software that provides a graphical diagramming interface consistent with the Bayesian network concept. Analytica also allows for the inclusion of decision and objective nodes, making it easy to implement a description of stakeholder preferences to yield decision analytic results (e.g., Hostman et al. 2005a; Reichert et al. 2007).

The process of integrating our various submodels into a cohesive network required some additional assumptions. For example, whereas sufficient knowledge and data exist to build the benthic population submodel at a flow–dynamic scale (days to weeks), the fish population model focuses on life cycle transitions at a longer time scale (months to years). Thus, for estimating brown trout prey availability, the seasonal average benthic biomass was used, neglecting shorter term fluctuations. In other network models, we have faced the opposite situation, needing to express changes in highly dynamic variables as functions of more slowly evolving variables (Borsuk et al. 2004), a technique referred to as “variable speed splitting” (Walters and Korman 1999). Either of these methods may be necessary for cross-scale modeling with Bayesian networks.

Another challenge comes with reconciling the spatial scales of the various submodels. For example, although the physical processes of siltation can be described mathematically at a fine spatial and temporal scale, the brown trout spawning model required the reach-wide seasonal average as input. Therefore, we decided that a reasonable simplifying procedure would be to: 1) assume spatially homogeneous conditions within each hydraulic unit (i.e., runs, pools, riffles), 2) simulate the siltation dynamics under each of these sets of conditions, then 3) calculate the seasonal average siltation level for each hydraulic unit, and finally 4) calculate the weighted average siltation level for the reach using the modeled proportions of each type of hydraulic unit. Similar assumptions concerning homogeneity within hydraulic units were also necessary for other variables, including water depth and velocity, gravel size, and habitat suitability.

MODEL APPLICATION

  1. Top of page
  2. Abstract
  3. EDITOR'S NOTE
  4. INTRODUCTION
  5. DESCRIPTION OF METHOD
  6. MODEL DEVELOPMENT
  7. MODEL APPLICATION
  8. DISCUSSION
  9. CONCLUSIONS
  10. Acknowledgements
  11. REFERENCES

Case study description

To demonstrate application of the model, we use a case study at the Thur River, Switzerland. The catchment of the Thur River originates 2500 m above sea level and the river flows 130 km before entering the Rhine River at 350 m above sea level, giving a total catchment area of 1750 km2. Regular flooding of the Thur prevented settlement of its floodplains until 1890, when the first river correction project occurred. The meandering river was straightened and levees were built, flanking the river at widths of 30 to 50 m. However, the corrections could not contain the largest floods and also gave rise to new problems. In the straightened channel, water flowed more quickly and with a greater depth than before, increasing its erosive power and undercutting the levees. The monotonous stream with uniform bed morphology also offered few breeding or spawning areas for birds, fish, or aquatic organisms.

After a series of large floods between 1960 and 1980, authorities realized that the condition of the Thur was not sustainable and decided to dedicate funds and effort to improving flood protection while simultaneously enhancing ecosystem health (Amt für Umwelt 1999). As a result, local rehabilitation measures have been taking place at some reaches along the length of the river for the past 15 y.

Our case study focuses on a rehabilitation project conducted on the Thur River in 2004 near the cantonal border of Thurgau and Zürich (Figure 5). The median discharge at this location is 49 m3/s with an annual flood value of approximately 570 to 725 m3/s. Median water temperature is 10.5 °C with a maximum of approximately 22.4 °C. Channel constraints were widened from an average of 40 m to 120 m over a 1.5-km stretch by reducing floodplain height and returning this area to the river. To protect nearby residences from large floods, the historical dikes were maintained at a width of 200 m. No retention basins or side channels were constructed. The widening project cost 9.9 million Swiss Francs (Sfr) and removed approximately 3 ha from agricultural production. Gravel bed characteristics and transport estimates for this section of the Thur are available from Schälchli et al. (2005), and time series data of discharge, suspended particle concentration, and water temperature come from unpublished sources. We generate model results for pre- and postrehabilitation conditions to estimate the morphological, hydraulic, ecological, and economic effects of the project. For some attributes, limited measurements are available for comparison.

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Figure 5. The Thur River at the location of rehabilitation. (Top) Map of Thur watershed. (Bottom left) June 2001, before the river was widened. (Bottom right) May 2004, after the river was widened. Data source: swisstopo: Vector25©2006, DHM25©20036, GG25©2006 (reproduced with permission of swisstopo/JA 100119). Photographs: C. Herrmann, BHAteam, Frauenfeld.

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Case study results

If the study section of the Thur River were to be of sufficient length and free of any width constraints, the model predicts that the natural river form is much more likely to be single-threaded (i.e., straight, meandering, or alternating gravel bars with 89% probability) than multi-threaded (i.e., braided with 11% probability). However, the actual constrained channel morphology will depend on the gravel supply, as well as the severity of width constraints, as predicted by the pattern diagram of da Silva (1991) (Figure 2).

With the actual rehabilitated width of 150 m and length of 1.5 km, there is a negligible chance of braiding, a 56% chance of alternating gravel bars, and a 44% chance that the river might still be straight. The model estimates that gravel transport out of the study section is sufficiently reduced to yield gravel deposition rather than incising. Thus, gravel supply should not be a limiting factor in the formation of bank structures at this width. Indeed, since the 2004 rehabilitation, the river at this section has gone from highly channelized to forming significant gravel bar structures.

The model can be used to predict the mean flow depth and velocity, as well as the distribution of habitat units (i.e., pools, riffles, runs), for any discharge below bankfull. To illustrate the difference in hydraulic conditions between the historically straight and a rehabilitated alternating gravel bar morphology, we used the modal discharge (Q = 28 m3/s). We find that the 2 morphologies do not differ considerably with respect to mean depth and velocity, but a substantial increase in the variability of velocity and depth is predicted for the alternating form, as reflected in the anticipated spatial distribution of habitat units (Figure 6). For a straight morphology, the hydraulic conditions are extremely homogeneous (mostly runs, with pools and riffles almost absent), whereas for an alternating form, approximately 40% of the river stretch will consist of either pool or riffle habitat.

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Figure 6. Predicted spatial frequency of habitat units by morphological type.

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Model results indicate that flushing events will occur less frequently after widening, due to the lower water depths and thus lower dimensionless shear forces for a given discharge compared to a constrained river. This leads to an average fine particle content (assuming an alternating gravel bar form) of 7% (90% interval of 3% to 11%). Although siltation conditions appear to worsen as a result of rehabilitation, it is important to note that a widened river reach will contain 20% to 30% more riffles than a constrained river, and these can be expected to remain clear of fines due to their hydraulic conditions.

The total invertebrate biomass is expected to vary seasonally, with median predicted values after widening ranging from 1 to 23 g dry mass m−2 with an uncertainty factor of approximately 2 (Figure 7). Measurements taken in June at this location led to total invertebrate biomass estimates of 2.8 to 5.3 g dry mass/m−2 (P. Baumann, personal communication). Periphyton biomass is expected to stabilize at approximately 16 g dry mass/m−2 (results not shown). Bed-moving floods are expected to be rare in the rehabilitated condition, leading to little disruption of the benthic population.

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Figure 7. Predicted total invertebrate mass by day of year. Lines represent bounds on indicated predictive intervals. Jagged lower edges are the result of a rarely occurring bed-moving flood disturbing the benthic population.

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Total riparian arthropod abundance is predicted to be 26.5 ± 6.5 individuals/m2 with the majority consisting of spiders and ground beetles. This is a significant improvement relative to the 16.8 ± 5.8 individuals/m2 predicted for the channelized state of the river.

The study region of the Thur River lies in the transition zone between ecoregions supporting grayling and barbell fish species (Huet 1959). Thus, resident brown trout are not expected in this reach. Indeed, electrofishing over 40 sections in this area found only 19 brown trout (Schager and Peter 2005). Fortunately, the brown trout portion of the model has been tested successfully in a variety of other river reaches, both channelized and natural (Borsuk et al. 2006).

Finally, for the 9.9 million Sfr spent on the project, one can expect a total of 13.8 ± 0.4 million Sfr in increased output and 78 ± 4 new full-time equivalent (fte) employment positions. However, these short-term job gains will be partially offset by the long-term loss of approximately 3.0 fte agricultural positions, and 0.4 ± 0.6 million SwF in lost economic output per year, as a result of taking 3 ha of agricultural land out of production to provide for the wider river corridor.

DISCUSSION

  1. Top of page
  2. Abstract
  3. EDITOR'S NOTE
  4. INTRODUCTION
  5. DESCRIPTION OF METHOD
  6. MODEL DEVELOPMENT
  7. MODEL APPLICATION
  8. DISCUSSION
  9. CONCLUSIONS
  10. Acknowledgements
  11. REFERENCES

A variety of models and analyses have been developed to anticipate the outcomes of river rehabilitation measures such as corridor widening. However, to our knowledge, the model described here is the first attempt to combine models of multiple features into an integrative forecasting tool. Having a model that links actions to outcomes using the language of probabilities is essential for making rational choices according to a decision theoretic framework (Reichert et al. 2007). We believe that our model is applicable to rivers similar to those from which the data used to estimate our submodels originated. Specifically, we believe it is appropriate to apply the model to gravel bed rivers in mid latitudes, with a relatively natural flow regime, mean discharge between 1 and 60 m3/s, and slope less than 2%.

The case study application of our model to a recently rehabilitated section of the Thur River at the cantonal border of Thurgau and Zürich, Switzerland, shows that the results can yield useful information for rehabilitation planning. Specifically, the model predicts (correctly) that, after widening of the channel at this location from 40 to 120 m, gravel transport out of the reach would be reduced and alternating gravel side bars would develop. This morphology is judged to be more attractive by stakeholders and likely to increase recreational use (Hostmann et al. 2005b).

As a result of this more natural morphology, the variability of flow velocity and depth is expected to increase and a significant number of pools and riffles are expected to develop. This is likely to lead to greater siltation in some areas, but overall a more diverse mosaic of silted and clean gravel conditions will exist. Although the total invertebrate population is not expected to change dramatically, the model predicts a near doubling in the riparian arthropod community, thus providing increased food for birds, fish, and other riverine fauna. Although brown trout, a desirable species, is not expected to reside in this section of the river, grayling and barbel populations are likely to improve as a result of the added prey resources and more diverse habitat (Weber et al. 2009).

Economically, rehabilitation of the Thur appears to be a good investment. A 40% return, in the form of indirect stimulation of other sectors of the local economy is expected. In addition, new employment of approximately 80 fte is anticipated during the construction phase, which is only partially offset by the loss of 3 fte/y in agricultural positions.

Although in our case study our model was used retrospectively, we anticipate the model being used to complement stakeholder assessments in providing decision support for managers (Reichert et al. 2007). Such a procedure can help guide selection of reach-specific rehabilitation measures. In addition, we are extending our reach-oriented model to one that can support prioritization decisions at the regional or catchment scale over an entire river network.

Methodologically, our model is distinct in the Bayesian network literature in using functional equations to link continuous variables, rather than employing discrete variables and conditional probability tables. Representing all variables in an influence diagram as being discrete does have the advantage that software is readily available to handle all possible calculations one would want to make with such a model, including inference against the direction of arrows. However, discretizing variables that are inherently continuous is often a subjective process that introduces a degree of imprecision into the model that would otherwise not exist. This is because of the vagueness that arises from assigning all values within a specified range of a continuous variable to the same discrete state.

Another problem associated with discretization is that it encourages vagueness in variable definitions. For example, many studies have been published that define states of variables to be low, medium, and high, without giving precise quantitative definitions. This opens up the possibility for model developers or users to have very different ideas of what the variable and its different states represent. This can lead to errors in assessing the probabilities required of the model or in applying the results for decision making. Therefore, although we lose the ability to infer the values of ancestors from observed values of descendants, we generally prefer to build networks of continuous variables, described by flexible distributional forms, and linked by functional causal expressions.

Although we do not benefit from the inferential strength of Bayesian networks, the effort of model building was significantly facilitated by the use of the graphical network structure. By highlighting subnetworks (referred to as cliques) that are relatively independent of other parts of the full network, the causal graph encourages decomposition of the larger modeling problem into manageable submodels. As discussed in the Model Implementation section, however, special attention needs to be given to address any potential discrepancies in spatial or temporal scale.

CONCLUSIONS

  1. Top of page
  2. Abstract
  3. EDITOR'S NOTE
  4. INTRODUCTION
  5. DESCRIPTION OF METHOD
  6. MODEL DEVELOPMENT
  7. MODEL APPLICATION
  8. DISCUSSION
  9. CONCLUSIONS
  10. Acknowledgements
  11. REFERENCES

We have brought a variety of submodels relevant to river rehabilitation planning together into a graphical probability network that links management alternatives to ecological and economic consequences. Although we have adopted the causal graph formalism common to Bayesian networks, we have not made probabilistic inference a priority, providing us with added flexibility in functional and conditional distributional representation. This improves forecasting precision, which we believe to be a more important model attribute in environmental management applications than the possibility of performing causal diagnosis. Our case study exemplifies the potential use of the model in addressing socioeconomic and ecological consequences of rehabilitation, in addition to strictly morphological and hydraulic impacts. The former are usually the concerns of greatest interest to stakeholders and therefore model predictions of these consequences can be an influential factor in supporting local rehabilitation decisions.

Acknowledgements

  1. Top of page
  2. Abstract
  3. EDITOR'S NOTE
  4. INTRODUCTION
  5. DESCRIPTION OF METHOD
  6. MODEL DEVELOPMENT
  7. MODEL APPLICATION
  8. DISCUSSION
  9. CONCLUSIONS
  10. Acknowledgements
  11. REFERENCES

This study was supported by the Rhone-Thur project, which was initiated and funded by the Swiss Federal Office for the Environment (BAFU), the Swiss Federal Institute for Environmental Science and Technology (Eawag), and the Swiss Federal Institute for Forest, Snow and Landscape Research (WSL). We thank Rosi Siber for producing the map in Figure 5.

REFERENCES

  1. Top of page
  2. Abstract
  3. EDITOR'S NOTE
  4. INTRODUCTION
  5. DESCRIPTION OF METHOD
  6. MODEL DEVELOPMENT
  7. MODEL APPLICATION
  8. DISCUSSION
  9. CONCLUSIONS
  10. Acknowledgements
  11. REFERENCES
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