Case Study Gwydir Wetlands

The Gwydir wetlands and floodplains cover 3000 km2 in the Gwydir catchment, New South Wales, Australia (Figure 1). The wetlands rely on flooding from a regulated river system (a working river) with large headwater storage, diversions, and extractions for irrigated agriculture. Rainfall varies from over 800mmyr_1 in the upper parts of the catchment to less than 450mmyr_1 over the wetlands, while potential evapotranspiration can exceed 1400mmyr~ . Ecological values include the welfare of vegetation communities, colonial nesting birds, and other water-dependent fauna, with sites listed under both national and international conventions for wetland protection.

A model to represent the ecological response to flooding is required to improve water management. It is important to remember that a model is a simplified and imperfect representation of a system, describing only the features essential for the model's purpose. It is crucial for model acceptance and credibility that the modeling process is transparent and follows best practice. The ten-step approach to model development provides a good-practice framework for this case study.

Step 1: Define the Model Purpose

Models can be used to

• improve qualitative understanding of the system,

• elicit and review knowledge and reveal system properties,

• reveal weaknesses in our knowledge and set research priorities,

• generate and test scientific hypotheses,

• provide a focus for discussion of a problem or simulate further questions about system behavior,

• forecast or predict outcomes under a range of scenarios, and

• educate and learn about the system.

The crucial question in the wetlands case study is 'What flood regimes are required to maintain the ecological values of the wetland system?' For water management, this amounts to asking how environmental water can be delivered for greatest ecological benefit.

The stakeholders were identified through liaison with an Environmental Advisory Committee, representing a range ofgovernment departments, local landowners, independent scientists, and other interest groups. The committee advises on the management of environmental water for the Gwydir

Figure 1 Location and major features of the Gwydir wetlands.

wetlands. Funding organizations, technical experts, and data suppliers may also need to be considered stakeholders.

Ultimately, stakeholders may want the model to forecast outcomes (flood extent and duration and vegetation response) for a range of environmental flow scenarios. The spatial and temporal resolutions must be decided relative to that purpose. Water for the environment is in limited supply and delivery can be both technically and politically difficult. The ability to model a range of water-delivery scenarios provides greater assurance of beneficial outcomes while observing practical constraints.

The first model attempt revealed gaps in knowledge of flood patterns, vegetation response to flooding, and triggers for water-bird breeding, and highlighted the need for further research. The results of that research should allow better definition of the model type, structure, and complexity. This is a cycle of iteration: tentative choices of model scope, type, structure, and resolution determine data needs, which when filled allow refinement of those choices (which may then reveal further needs). The process also includes revision of stakeholder expectations as what is practicable becomes clearer.

There are other outcomes of the modeling exercise benefiting all stakeholders, such as better understanding of the system. Partial answers, at least, are obtained for broad questions such as

1. How do floods behave and how does flooding affect the vegetation communities?

2. What are the interactions between flooding, vegetation response, and fauna, and which of these processes are of interest to water managers?

Finally, model development has provided a focus for discussion of the problem. It has enabled a range of stakeholders to define the system and its problems, incorporate prior knowledge, and concentrate on the problems rather than being distracted by matters outside their boundaries.

Step 2: Model Context

The model process was introduced to stakeholders through meetings, position papers, and one-to-one discussion to gain acceptance and elicit advice on specific questions and model boundaries. Questions to which the stakeholders expected answers from the model included:

1. How much water is required to inundate specific areas (ecological 'assets' including bird breeding areas, specific vegetation communities, and water holes) for a specified length of time?

2. What was the flooding pattern and vegetation response in each 'asset' prior to and after river regulation?

3. Is it just a matter of water volume entering the system, or does timing (e.g., the daily flow pattern) influence the flood pattern and vegetation response?

Model development included the opportunity for stakeholders to continue to refine their objectives through meetings, focus-group discussions, and individual responses. It may be necessary to revisit the original model objectives at this point.

Spatial and temporal boundaries and scales were also considered. Vegetation response to inundation is measured in days to weeks, while the ecological community structure is a product of longer-term flood patterns (frequency and depth). Spatially the smallest vegetation community covers an area of approximately 3 km2, but other ecological assets can be smaller. A choice whether the model should be confined to the frequently flooded core wetlands or should include the broader floodplain is yet to be made. The question is whether to start small (spatially) and build up the model or start larger and refine the model.

Resources such as people, time, and effort available for the modeling must be identified. In this instance a 3-year period is allowed, with one researcher. The financial resources available preclude additional staff, expensive or extensive monitoring programs, or expansion of the project significantly beyond the identified scope within the 3 years. There may be opportunities for model development at the end of the initial 3 years, and for collaboration with other research, so the modeling process allows for critical areas of further development to be identified as part of the project.

Step 3: Conceptualize System, Data, and Prior Knowledge

A conceptual model can be used as a step in model development, and may be a useful tool on its own. It is used as an abstraction of reality in ecosystems to delineate the level of organization that best meets the objectives of the model. It captures the state variables, forcing functions, and their connections. A range of conceptual tools is helpful in this process as summarized in Table 1.

With the model objectives and context in mind, the model concept was initially based on a semilumped water-balance approach as shown in Figure 2. This concept defines the most important drivers of the flood patterns and identifies spatially distributed components that represent different flood dynamics and ecological responses.

The next step is to incorporate vegetation response. A number of possible concepts may be considered. Important vegetation species may be modeled in detail if there is sufficient information about their requirements. In Australian inland wetlands, prior monitoring and research has provided information about the response of specific plant species to inundation depth, duration, and seasonality. The flood dependence of each stage (e.g., germination, establishment, growth, reproduction, and

Table 1 Conceptualization methods

Method

Description

1. Word models

2. Picture models

3. Box models

4. Input/output models

5. Matrix conceptualization

6. Forrester diagrams

7. Computer flow chart

8. Signed digraph models

9. Energy circuit diagrams

A purely verbal description

A pictorial representation of the system

Boxes represent components; arrow represent processes

Same as 'box models' except values for input to and output from the boxes are added Using matrices to assess possible interactions between components

Symbolic language representing variable, parameters, sources/sinks, flows and rate equations Flow chart to show the sequence of events in a process

Plus and minus signs used to represent positive and negative reactions between system components in a matrix

Designed to give information on thermodynamic constraints, feedback mechanisms, and energy flows

Modified from Jorgensen SE and Bendoricchio G (2001) Fundamentals of Ecological Modeling. Amsterdam: Elsevier.

Outflow to next channel

Outflow = inflow to next channel, flowpath, or core wetland

Figure 2 Conceptual flowchart of channels, flowpaths, and habitats that can be used to create a semidistributed model of flooding, soils moisture, and vegetation response across a floodplain system.

Outflow to next channel

Outflow = inflow to next channel, flowpath, or core wetland

Figure 2 Conceptual flowchart of channels, flowpaths, and habitats that can be used to create a semidistributed model of flooding, soils moisture, and vegetation response across a floodplain system.

death) has to be represented and some measure of success devised, based on successful recruitment to the seedbank or sufficient storage in rhizomes. This approach requires two temporal scales to be considered: the 'within-event' scale where day-to-week inundation patterns and vegetation response are important, and multiple 'events' which influence the functional groups that respond to many events, ultimately influencing the community structure of the system. The information may be incorporated into a response model as a surrogate for whole-community response, or in conjunction with the functional group approach. An example of a similar approach is a grid-based model (Figure 3), which represents individual species response to season and water level and runs temporally.

A simpler approach is based on primary productivity response (or a surrogate such as a vegetation index based on remote sensing). This approach quantifies the vegetation (community) response through green-up, maturity, senescence, and dormancy. Applying this

Figure 3 Conceptual flow chart of plant response to flooding.

concept to the study area, multitemporal remote-sensing analysis of a flood event clearly demonstrated the vegetation response pattern - not only detecting the green-up, maturity, and senescence stages, but also the initial flooding of the area (Figure 4). Linking the phenology over a range of floods to vegetation functional groups may provide the basis for understanding vegetation community response.

Julian day (2004)

Figure 4 Vegetation response curve (mean ± standard deviation) for a wetland site. The initial flooding is shown as normalized difference vegetation index (NDVI) values of less than 0 on day 22. Response to maximum greenness is rapid.

Julian day (2004)

Figure 4 Vegetation response curve (mean ± standard deviation) for a wetland site. The initial flooding is shown as normalized difference vegetation index (NDVI) values of less than 0 on day 22. Response to maximum greenness is rapid.

Step 4: Select Model Features and Families

The selection of model features and families depends on the items of interest and the form of the model output. For example, is it a long-term mean, an extreme value, a probability distribution, or a spatial and/or temporal pattern.? Model families and features include:

• Empirical, data-based, statistical models such as parametric or nonparametric time-series models, regressions and their generalizations such as autoregressive moving-average exogenous models, power laws, and neural networks. Such models have detailed structure and parameter values determined exclusively by observational data, rather than selected in advance on the basis of prior scientific knowledge, expert judgment, or custom.

• Stochastic, general-form but highly structured models which can incorporate prior knowledge, for example, state-space models and hidden Markov models.

• Specific 'theory-based or process-based models' (usually deterministic, i.e., not probabilistic and thus not directly allowing for uncertainty), as often used in environmental physics and economics, for example, specific types of partial or ordinary differential or difference equations.

• Conceptual models based on assumed structural similarities to the system, for example, Bayesian (decision) networks, compartmental models, cellular automata.

• Agent-based models allowing locally structured emergent behavior, as distinct from models representing regular behavior that is averaged or summed over large parts of the system.

• Rule-based models, for example, expert systems, decision trees.

• A spectrum of models which represents dynamics (time-spread responses to the inputs at any given instant) in differing degrees of detail. This spectrum spans instantaneous (static, nondynamical, algebraic) models, discrete-event and discrete-state models, lumped but continuous-valued dynamical models, and distributed and delay-differential models with infinite state dimension.

• A corresponding spectrum of spatial treatments, comprising nonspatial, 'region-based', or 'polygon-based' spatial, and more finely (in principle continuously) spatially distributed models.

The selection of model feature and families for the case study depends on the results of remote-sensing analysis, as well as the model outputs expected. In our example, outputs include temporal and spatial flood dynamics and measures of frequency or probability distribution of the flood patterns. If a good relationship between observed flow and flood dynamics is found, then a regression-based model may be sufficient. However a combination of regression analysis and a process-based deterministic model (e.g., distributed water balance) may be a better choice. Similarly, vegetation response may be based on regression analysis of the remotely sensed response to flooding. Other options may be a specific theory-based response model, such as the example shown in Figure 3, or a simple rule-based model such as a decision tree or a conceptual model. Here, as often in environmental modeling, the complexity of the behavior to be modeled and of the purposes make it likely that the model will be a hybrid, including features of several model families.

Spatially the final model is most likely to be lumped or semilumped, with regions or polygons representing areas of similar behavior. Alternatively, a grid structure might be evaluated. In view of the large volume of information and high model complexity consequent on a grid with resolution as in Figure 3, categorization then lumping of responses is desirable; an immediate research aim is to find out what coarsest resolution is adequate to capture the responses. To match the level of detail of available data and the outputs required of the model, temporal resolution is likely to be around a day and temporal extent at least a year.

Step 5: Choose How the Model Structure and Parameter Values Are to be Found

In finding the structure, prior science-based theoretical knowledge might be enough to suggest the form of the relations between the variables in the model. In the flood dynamics component of this model, there are insufficient data to allow empirical modeling from scratch, so existing water-balance principles will be used. Through a parallel data-acquisition exercise (remote-sensing analysis as well as field-based assessment), the principles will be re-examined and the structure may be simplified or altered to accommodate new knowledge.

There are a number of possible model structures for the vegetation response component (see step 3). Some parameters will be estimated by optimizing the fit of model outputs to observed outputs such as measured water depth at a location, vegetation surveys, or results of remote sensing that provide NDVI response as a surrogate for productivity. This approach will be used with caution, as experience shows that the system has been manipulated during past floods, with channel structures altered during the course of a flood or vegetation cleared, grazed, or burnt. If theoretical understanding is one of the model objectives, and some prior knowledge of system processes exists, then an approach that does not determine model structure solely according to fit to observed data should be favored. Such an approach is very likely to produce a model structure which is an uneconomical summary of the behavior observed in the data, as the structure is partly or wholly dictated by prior knowledge (an empirical modeler would say 'prejudice'). Such prior fixing of model structure can impose realistic constraints on possible behavior and may make interpretation of the model parameters much easier, but there is often a conflict between making the structure reflect what is known in advance and making it identifiable (through testable parameter values) from observations. In this project many parameters, particularly in the vegetation response component, are unlikely to be optimized through fitting but may be estimated using expert opinion. Experts in the field of wetland vegetation or ecological response in similar systems can be called upon to check vegetation response parameters and model structures. There is little safeguard against misjudgment on their part, however.

Degree of spatial aggregation will be determined by a mapping approach based on identified ecological 'assets', major vegetation communities, and remote-sensing analysis to identify major flowpaths and flood areas. The result should be relatively homogeneous units (in respect of flood frequency, depth, duration, and vegetation response for both functional groups and primary productivity), but as large (lumped) as practicable to match the objectives of the research and the resolution of the input data.

Step 6: Choose the Performance Criteria and Parameter-Estimation Techniques

The criteria by which the model performance is judged should reflect the desired properties of the estimates. This is particularly important in this case study, which must gain the acceptance of a group of nonmodeler stakeholders. Demonstrated lack of bias is important, as there will be significant input from stakeholders who may be perceived to have particular viewpoints or desired outcomes. It is best achieved through acceptable prediction performance. This may be a challenge in view of the dynamics of the system discussed in step 5; a solution might be to discuss the results with the stakeholders, employing collective memory of past events as well as hard data.

Step 7: Identify the Model Structure and Parameter Values

The final model structure should balance sensitivity with complexity and represent the dominant responses of the system at the time and spatial scales of concern. The structure should also ensure that system descriptors such as numbers of variables and processes are aggregated where this makes the representation more efficient. As discussed in step 5, aggregation may be spatial or temporal, or it may be in the way in which vegetation response is modeled, focusing on functional groups or total productivity rather than individual species.

To test for overparametrization, analysis of the sensitivity of the model outputs to the parameters is useful. It can be performed on the individual components (e.g., the flood dynamics and the vegetation response), but ideally should be performed on the integrated model. Sensitivity assessment will also help to identify critical parameters whose values may need refining, scope for further lumping, nonlinearities which affect the nature of the responses, and behavior inconsistent with expert knowledge. As a result of this analysis it may be necessary to modify the model structure and even the model family.

Finally, the structure should not be overflexible as that may result in unrealistic behavior, ill-conditioning, and poor identifiability (inability to find well-defined parameter values). This should be tested in step 8 if performance criteria are well chosen and verification properly carried out.

Step 8: Verification

Verification of the model structure and parametrization ensures that the model adequately reproduces the observed behavior with regard to the original purpose and context. Figure 5 illustrates a simple comparison of model outputs (the inundation depth) against the observed behavior of a nearby depth gauge. Here measures of model fit such as the root mean square error would indicate a poor fit, but the errors are largely due

Figure 5 Modeled and observed depth of inundation for a wetland site.

to mistiming. The matching of extent, rates, and pattern of response may be considered acceptable for the purpose and context. If not, these expectations can be revisited, alternate model concepts proposed, or different model families and structures tested. Testing should also examine the robustness of the model outputs to insignificant changes to data and assumption.

Assumed physical properties should be plausible, defensible, and consistent with prior knowledge (if we are clear about what prior knowledge is genuinely known and what is assumed). In the water-balance model, for example, assumptions about the behavior of soil moisture have been made according to plausible physical processes, but they must be tested and modified as required. Soil moisture and inundation over a flood-plain can be modeled but there is no observed data set to verify. Instead, stakeholders examined the results in the light of personal experience and judged the results to be plausible and consistent with their expectations. Iteration of the model development is likely throughout the modeling process, particularly in the ecological components of the vegetation response.

It is also important that the model is tested against statistical knowledge and assumptions, for example, that residuals do not disagree significantly with statistical assumptions, such as absence (or atmost a tolerable level) of systematic structure or significant correlation with the inputs. It is also desirable to confirm that parameter estimates have converged, although with short or sparse data sets this may not be possible. Excessive variation of parameters with time or location may expose shortcomings of the model structure or the observations. As discussed previously, the entire modeling process must conform with the purpose and context of the model; the verification step is no exception. At this stage, the assumptions and boundaries within which the model seems valid must be clearly established.

Step 9: Quantify the Uncertainty

Primary sources of uncertainty in the model include errors and finite sample size in the observations, experimental or subjective error in supplied parameter values, and approximation error in the model algorithms and structure. This last source includes both error deliberately incurred in exchange for model simplicity or reduced data needs and, importantly, intrinsic variability in the processes modeled, due to finer-grained processes in which there is no realistic prospect of modeling. In the present example, this source is prominent and ineradicable.

Although it is possible to incorporate quantification of uncertainty within the model structure itself (as in stochastic models), the model structures for this study do not allow one to do so. Uncertainty testing is thus a separate item. To establish which variables and what types of uncertainty are significant for the model purpose, the results of sensitivity assessment have to be examined, together with estimates of the parameter uncertainties and unmodeled inputs. Some parameter-estimation algorithms (e.g., least squares and its recursive generalizations) provide estimates of parameter uncertainty in the form of error covariances, and can account for observation errors and responses to unknown inputs as 'noise' with assumed or estimated statistical properties. Alternatively, fitted parameters can be estimated from different sections of the records and the variation in the parameter values and the output residuals assessed (or approximate probability densities found by resampling, as in the bootstrap). Cross-validation by comparing residuals across various subsamples of the records (see below) is an instance of this process.

Ideally one would consider a number of model structures (as in some of the options for the vegetation component) to assess the uncertainty associated with the model structure.

Step 10: Evaluate and Test the Model

Finally the model can be evaluated on an independent data set with different input series to test the predictive performance (or cross-validated using a range of subsam-ples of the original data, in which case steps 9 and 10 are intimately linked). The practical difficulties mentioned in step 5 and 6, arising from channel or vegetation manipulation in past floods altering the behavior modeled, are typical. Changes in the system (as distinct from its inputs) are common in environmental modeling yet hard to represent, being often episodic and not unambiguously identifiable from the primary records. Auxiliary sources of information, for example, aerial photographs at long intervals, vegetation monitoring (Figure 6), and the memories of stakeholders, may be critical in identifying and understanding the changes.

In the context of this project, some uncertainties are not readily characterized, especially those following from omission or overaggregation of significant behavior, and from incomplete observation records. Moreover, the main performance criteria of the model are its effectiveness as a guide to what water flow regimes will achieve the required ecological values and its value in increasing understanding of the effects of floods and regulated flows. Neither is adequately measured by exclusively statistical or other formal means. Consequently, an important approach to model testing (although not the only one) is to look for, explain, and if possible rectify anomalies in the outputs produced for realistic input data sets; for example, dummy input flow and climate series may be constructed to test the flood dynamics. The opinions of expert stakeholders are to be sought on the plausibility of the responses at selected locations

Figure 6 Vegetation monitoring in the Gwydir wetlands. Monitoring of vegetation response following flooding along fixed transects provides additional information to evaluate the model outputs.

(e.g., floodplains), in crucial periods and overall. Where the results are implausible, the model must be re-examined. Conversely, results accepted as plausible may raise confidence in the fitness of the model for evaluating environmental flow-delivery scenarios.

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