Conceptual models

​​Natural systems are complex. To understand and manage them, we are often required to make simplifying assumptions. We can do this by portraying the system as a conceptual model.

A conceptual model sets out the collective knowledge, experience and perspectives on the system of interest. The model illustrates your assumptions about how the system functions and what you believe to be the important or dominant processes and their linkages. This includes the factors that are perceived to be driving the changes in the system and the consequences of changes in these factors.

We can use conceptual models to help identify:

• key processes and their interactions
• key pressures and associated stressors acting on the system
• key ecosystem receptors
• cause–effect relationships
• important questions to be addressed
• spatial boundaries
• valid measurement parameters for the processes of concern (what to measure, degree of precision)
• site selection
• temporal and seasonal considerations.

Check with local authorities in your jurisdiction who might have established conceptual models you can use.

Application in the Water Quality Management Framework

Development of conceptual models is a critical component of the Water Quality Management Framework, at Step 1, to examine cu​rrent understanding.

In a robust and logical way, conceptual models classify the important features of the waterway in relation to how the system works and underlying drivers and causal relationships among significant components for the issue of interest.

Conceptual models also have application in other steps of the framework. For instance, they can be used to (adapted from DEHP 2012):

• clarify the vision and management goals of stakeholders for the waterway (Step 2 o​f the framework)
• develop objectives for monitoring or assessment programs (Step 2 of the framework)
• identify indicators for monitoring or assessment programs (Step 3 of the framework)
• identify most appropriate management actions (Step 8 of the framework)
• communicate outcomes of monitoring or assessment programs (Step 10 of the framework).

We provide guidance on how to follow a logical approach to develop conceptual models for managing and assessing water/sediment quality issues.

Types of conceptual models

Conceptual models can represent the observed world in many ways, such as descriptive text, tables, box-and-arrow diagrams, or pictorial conceptual models. Each of these kinds of models has its advantages and disadvantages.

Text descriptions of an issue can range from succinct statements to comprehensive descriptions, and are often easy to understand. They should accompany all conceptual models, as they help explain and justify the conceptualisation.

Diagrams are usually necessary to clearly communicate linkages. These may comprise boxes and arrows to represent key components and processes, or a pictogram format where boxes are replaced with a representation of the component under discussion.

Box-and-arrow conceptual models are often the precursor to more detailed quantitative modelling. Pictorial forms are generally more useful for communication purposes.

In the Water Quality Guidelines, we have adapted the conceptual modelling guidance of Gross (2003), which was originally developed to support the US National Park Service’s Inventory and Monitoring Program. This guidance is considered useful, appropriate within the Water Quality Management Framework and sufficiently comprehensive for most steps of the conceptual modelling process. The steps have been compared with existing Australian modelling approaches and found to be consistent, after allowing for differences in terminology.

In keeping with the approach of Gross (2003), we refer to 2 types of conceptual models for managing and assessing water/sediment quality issues: process models (or ‘control models’) and stressor models.

A process model is a conceptualisation of the actual controls, feedback and interactions responsible for system dynamics, represented in a mechanistic way.

A stressor model is designed to articulate causal pathways: the relationships between pressures, their associated stressors and receptors. These models depict the pressure–stressor–(ecosystem) receptor (PSR) concept embedded in our water/sediment quality management and assessment guidance in the Water Quality Guidelines, especially in the use of the weight-of-evidence process. Although we often refer to ‘ecosystem’ receptors, this is specifically in the context of the aquatic ecosystems community value. Receptors could equally be identified for other community values. For example, specific crops, livestock or secondary consumers for the primary industries community value.

The intent of a stressor model is to illustrate sources of stress and the relevant ecological responses of the system. Stressor models normally do not represent feedbacks. They include only a very selective subset of system components pertinent to the issue, and usually relate directly to an associated monitoring or assessment program.

The PSR-type stressor modelling approach that we recommend is broadly consistent with approaches used for integrated environmental assessments by some key international jurisdictions or bodies, although there are some differences that are worth highlighting.

The OECD recommends assessment of environmental issues using a conceptual Pressure-State-Response model (OECD 2003). This approach identifies environmental pressures, both direct and indirect, the environmental conditions (i.e. physical, chemical and biological states) that result from the pressures, and the associated societal responses, including management and policy changes.

The European Environment Agency (EEA) and the European Water Framework Directive apply a similar, albeit slightly expanded, ‘driving forces, pressures, states, impacts and responses’ (DPSIR) modelling approach (Smeets & Weterings 1999, Borja et al. 2006).

Our recommended approach for developing stressor models is similar to the Queensland Government’s conceptual modelling approach for water quality management and assessment, which establishes cause-and-effect linkages amongst pressures, stressors and ecological responses (DNRM 2013). It differs from the above international approaches in that it focuses on causal pathways within ecosystems, outside of management responses. It is our preferred approach to stressor models because it is conceptually simple and captures all the key causal pathway elements required to effectively define a water quality issue and determine the associated requirements for monitoring and assessment programs that will inform management strategies. However, management strategies can be included in the models if this aids the process.

Level of complexity

While conceptual modelling depends on using the best available information for the system under investigation, a good conceptual model does not attempt to explain all possible processes and relationships. Instead it tries to simplify reality by only containing the most relevant information.

Too much information can conceal important aspects of the model. Too little information leads to a higher likelihood that the portrayal is not accurate and contrary to what is observed.

The level of conceptual model development that is appropriate will depend on the nature of the issue being addressed and the scale of the systems to be considered. For complex systems and issues, several conceptual models that vary in scope, detail, spatial extent, relevant time frame and focus may be necessary to fully reflect the complexity of the system, and to maximise usability. For very simple systems or issues, for example, potential impacts of point source waste discharges, a simple box and arrow model or even a text description alone may be sufficient.

For any given issue, it may be necessary to develop both or either a process model/s and a stressor model/s. However, to reiterate, the model should only be as complex as is necessary, and always proportional to the nature and scale of the issue being assessed. This approach has been referred to as ‘requisite simplicity’ (Stirzaker et al. 2010), an important aid to negotiating complex problems.

When creating a model, check that it is not too complex by asking yourself these questions:

• What is the problem or issue of concern? (e.g. nutrients, metal loads, bioavailable metals)
• What subsystem (including ecosystem type) should the model describe? (e.g. freshwater, marine waters, estuarine waters, wetland, seagrass bed, mangroves)
• What are the appropriate temporal and spatial scales for the issue of concern?
• Which state should the model describe? (e.g. base flow, flood event)

Assumptions and modifications

All models are a simplification of reality and involve personal judgment.

Often the conceptual model will be based on accumulated wisdom as opposed to actual data. It is important to articulate the assumptions underlying the model and to identify the gaps in information supporting these assumptions. The assumptions need to be critically reviewed because incorrect assumptions may lead to incorrect conclusions being drawn about information needs. One objective of the monitoring program may then be to collect data to validate these assumptions.

Sometimes a conceptual model developed from the current understanding might be wrong.

Monitoring or assessment data that seem inconsistent can be important, leading to significant scientific breakthroughs from which new and more powerful conceptual models can evolve when the study’s results are reviewed and used to refine the current understanding (Step 1 of the framework).

As you collect and review the data, take the time to modify the conceptual process or stressor models. Then you can validate, and change if necessary, the assumptions underlying the notional conceptual model, to reflect any new perspectives.

Key elements of a conceptual model

Conceptual models should include certain specific elements in order to adequately serve their purposes.

Process models

For process models, inclusion of the key processes that dictate how the system works and what is driving or influencing it is critical. The interactions between processes, and the feedbacks to how they affect the system should also be included.

Major processes that affect water quality can be broadly classified as biological, chemical, hydrodynamic and physical, and include:

• bioturbation and bioirrigation
• contaminant transformation, degradation, adsorption, desorption, precipitation and dissolution
• contaminant transport, sedimentation, burial, resuspension and diffusion
• nutrient recycling, loss, transformation, recycling, ammonification, nitrification and denitrification
• organism growth, primary productivity, grazing and succession
• precipitation, evaporation, wet and dry deposition
• sulfate reduction, methanogenesis and organic diagenesis
• transport, flow, turbulence, flushing, mixing and stratification.

Stressor models

Stressor models need to depict causal relationships. So it is critical to identify and include the key causal pathway elements (pressures, associated stressors, ecosystem receptors) that may be exposed and potentially affected by the stressors. It may also be relevant and useful to include the pathways by which the stressors enter the environment and interact with the receptors, including the relevant compartments (e.g. water column, sediment, biota).

These elements are fundamental to correctly understanding the issue and formulating appropriate objectives for monitoring or assessment programs. This will help ensure the study design accounts for those processes and drivers. For example, by measuring the appropriate indicators at the appropriate locations and times that account for these factors, and ensuring the management goals are addressed.

Examples of conceptual models

We provide a few examples of conceptual models and how they might be interpreted, as well as links to other conceptual models that may help guide the development of your own conceptual model.

At a broad scale, your team might be concerned with the sources and transport of contaminants from a catchment to streams, rivers and estuaries. These form the basis of process-based transport models, as shown for nutrients (Figure 1) and metals (Figure 2).

The model in Figure 1 shows potential sources and transport of nutrients in the landscape. A more specific model might focus on a single water body and the issue of concern in that water.

Figure 2 represents a high level stressor model that shows the various pressures that can input metals to aquatic ecosystems. It does not provide details of pathways and links to ecosystem receptors.

Typically, smaller more specific models would be developed to depict the causal pathways for specific toxicants in specific ecosystem types and possibly to specific taxa groups. Keeping stressor models smaller and more specific typically leads to a more useful model with respect to informing aspects such as objectives and indicator selection.

For example, Figure 3 depicts a stressor model for inorganic toxicants (uranium, magnesium, manganese) arising from a uranium mine in northern Australia (Bartolo et al. 2017).

The model shows:

• the pressure (mining activity)
• sources of toxicants (ore and waste rock stockpiles and on-site waterbodies)
• surface water pathways whereby the toxicants can enter the off-site aquatic ecosystems
• affected environmental compartments in the off-site environment
• potential ecosystem receptors
• measurement endpoints (or indicators) that are used to assess or monitor the issue.

Figure 4 illustrates a simplified model for phosphorus cycling in a stratified lake in relation to algal growth.

By looking at the model in Figure 4, where and at what time of the year would you best measure critical phases in the development of an algal bloom and key inputs that will support its development if you want to determine the extent of the bloom? If you wish to measure phosphorus concentrations in the water column, should you take the samples from the epilimnion or hypolimnion, or both? In this example, chlorophyll a would probably be measured because it is a reliable measure of algal biomass, and the samples would be taken from the epilimnion because this is where algal growth occurs. Also, monitoring effort for measuring chlorophyll a would be best focused during the summer months, when sunlight, temperature and flow conditions typically favour algal growth, whereas measurement of nutrients would be done year-round in order to estimate loads.

Conceptual models in the various climatic and geographic regions of Australia and New Zealand may differ. For example, climatic factors and timing will differ significantly between conceptual models developed for the wet tropics, the seasonally dry monsoonal tropics, the arid interior, the temperate wet and the temperate Mediterranean regions.

Capturing climatic and geographic factors in conceptual models is important, because they can significantly affect study design, especially sampling strategies. For example, access to sampling sites during the wet season can be very challenging and unreliable in the tropics. The monitoring or assessment program may need flexibility of timing to mobilise sampling teams.

Examples of conceptual models for aquatic ecosystems

These examples illustrate the broad use and application of conceptual models in a variety of settings. They will help you to understand how conceptual models can be used in the Water Quality Management Framework.

• Pictures Worth a Thousand Words: A Guide to Pictorial Conceptual Modelling, Queensland Department of Environment and Heritage, 2012
• Guidelines for Risk Assessment of Wastewater Discharges to Waterways, Environment Protection Authority Victoria, 2009
• The Application of Conceptual Models to Ecosystem Restoration (PDF, 1.1MB), US Army Corps of Engineers — Engineer Research & Development Center Environmental Laboratory, 2008
• Developing Conceptual Models for Monitoring Programs (PDF, 2,262KB), US National Park Service Science & Nature, 2003
• An Integrated Monitoring Framework for the Great Barrier Reef World Heritage Area, Australian Government Department of the Environment and Energy, 2013
• Conceptual models, OzCoasts, Australian Government Geoscience Australia, 2015
• Sediments: conceptual site models, US Environmental Protection Agency, last updated 2017.

Testable hypotheses and conceptual models

A monitoring or assessment objective is often framed as a testable hypothesis, based on the conceptual model. This applies particularly to cause-and-effect studies. A hypothesis can underpin monitoring for comparison with regulatory standards and even State of the Environment monitoring.

Hypothesis testing is actually a test of the conceptual model.

Hypotheses usually take the form of statements or suppositions; for example:

• variable A in a specified area (or over a given time) does not differ from a given baseline by more than some pre-defined difference
• variable A in a specified area is not changed by more than some pre-defined amount per unit time
• variable A (cause) is controlling variable B (effect).

Details of cause–effect relationships between stressors and ecosystem receptors are usually better specified in the conceptual stressor model than in the conceptual process model.

Some hypotheses relevant to nutrient sampling might include:

• phosphorus concentration is below (or above) the specified water quality guideline
• phosphorus loading is controlling algal biomass
• bioavailable phosphorus and nitrogen are limiting algal growth
• phosphorus and nitrogen are being released from benthic sediments into the water column
• in-flowing phosphorus is adsorbed by particles that settle to the bed of the lake
• catchment activities have led to an increase in the annual phosphorus load to a lake.

Statistical hypotheses

A statistical hypothesis is a supposition based on available facts that can be subjected to a statistical evaluation, after further data have been obtained, to determine if it can be accepted or rejected. This sort of hypothesis is written in such a way that 2 outcomes are possible: either rejection or acceptance.

The null hypothesis (no significant difference) can never be proved to be correct but can be rejected, with known risks of doing so, by using statistical power analysis (Fairweather 1991).

Any assumptions made when establishing hypotheses must be stated because their validity must be examined as part of the sampling design.

If the hypothesis is rejected, the conceptual model may need to be refined unless that outcome was predicted by the model.

Some people debate about the need to formulate a hypothesis. Monitoring or assessment are not always undertaken to overtly test some statistical hypothesis, although it almost always has a stated objective. The requirement that such studies be reduced to a null hypothesis and an alternative hypothesis is an artefact of classical statistical inference.

Hypothesis testing often forces the researcher to try to establish a significant difference between locations, say, instead of attempting to describe interesting spatial trends over a river reach, although the absence of such a trend could be stated as the null hypothesis.

Your team must decide which of these approaches to adopt in such cases because this will affect the data that need to be collected.

Although most inquiry is based on an implicit or explicit ‘model’, a good conceptual model should be explicit and written down for anyone to see and discuss.

How to develop conceptual models for water quality

Ideally, all team members should develop their own concepts of the system, and then discuss and integrate these conceptual models. It should not be left to one stakeholder, however experienced, because the differences between individual models can help to clarify the real issues and questions when setting objectives.

Developing a conceptual model benefits from a logical approach. We outline the key considerations that you might apply to develop a conceptual model. Follow our guidance in a step-wise fashion, or use it as a checklist if the model has been initially developed in a more organic way.

Depending on the issue under consideration, not all these factors will be relevant.

Although conceptual model development is important in water management issues for all community values, it is of greater complexity when considering protection of aquatic ecosystems. This is the main emphasis of our discussion.

Many conceptual models have been developed to cover most of the common water quality issues. Instead of starting from scratch, your first approach should be to check the literature to see if a suitable conceptual model exists for your purpose.