# 2.7.3.2 Qualitative mathematical model

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For the purposes of this BA, a qualitative mathematical model was developed that described the general dynamics of the aquatic community associated with springs in the zone of potential hydrological change (Figure 13). A critical factor in preserving the aquatic community is the rate of groundwater flow that maintains a damp or submerged state in the spring, such that its surface does not become dry. An increase in water depth above this rate of flow (which is specified as the depth of water in the spring greater than maintaining a damp state (or ‘D>Dam’) in the two signed digraphs for the ‘Springs’ landscape group shown in Figure 13 and Figure 14) supports a wetted-area regime around the perimeter and downstream of the spring that is beneficial to emergent vegetation, the building of peat mounds, tail vegetation (i.e. vegetation at the outfall or tail end of a spring) and groundwater-dependent vegetation. Within the free-water area downstream of a spring, an increase in surface water depth supports an increase in primary production (i.e. phytoplankton, macrophytes and benthic algae), and habitat for aquatic grazers. The growth of macrophytes and benthic algae is mediated by competition for space and light, while emergent vegetation provides a substrate for the growth of benthic algae. Algae (phytoplankton and benthic) are the basal resources for grazers, filter feeders and omnivorous invertebrate predators. Top (vertebrate) predators that rely on these aquatic food resources are also maintained by habitat provided by adjacent groundwater-dependent vegetation. There was uncertainty in the model structure arising from the extent to which benthic algae could (or could not) respond to an increase in surface water depth. This led to two alternative qualitative models, one with (Figure 13) and one without (Figure 14) a positive link from depth of water to benthic algae.

Figure 13 Signed digraph model (Model 1) of the 'Springs' landscape group in the zone of potential hydrological change of the Galilee subregion, which has a positive link between depth of water in a spring (D>Dam) and benthic algae (BA)

Model variables are: benthic algae (BA), depth of spring greater than damp (D>Dam), emergent vegetation (EV), filter feeders (FF), groundwater-dependent vegetation (GDV), grazers (Gra), groundwater depletion (GWD), invertebrate predators (IP), macrophytes (submerged and floating) (MP), nutrients (Nut), peat mound (PM), phytoplankton (PP), subsurface water (SSW), tail vegetation (TV), vertebrate predators (VP), wetted-area regime (WAR).

Data: Bioregional Assessment Programme (Dataset 7)

Figure 14 Signed digraph model (Model 2) of the 'Springs' landscape group in the zone of potential hydrological change of the Galilee subregion, which lacks a positive link between depth of water in a spring (D>Dam) and benthic algae (BA)

Model variables are: benthic algae (BA), depth of spring greater than damp (D>Dam), emergent vegetation (EV), filter feeders (FF), groundwater-dependent vegetation (GDV), grazers (Gra), groundwater depletion (GWD), invertebrate predators (IP), macrophytes (submerged and floating) (MP), nutrients (Nut), peat mound (PM), phytoplankton (PP), subsurface water (SSW), tail vegetation (TV), vertebrate predators (VP), wetted-area regime (WAR).

Data: Bioregional Assessment Programme (Dataset 7)

Surface water and groundwater modelling indicate potential impacts of coal mining to groundwater depletion and subsurface water availability in some parts of the zone of potential hydrological change (see companion product 2.6.1 (Karim et al., 2018b) and companion product 2.6.2 (Peeters et al., 2018) for further details of the surface water and groundwater modelling undertaken, respectively, for the BA of the Galilee subregion). Based on all possible combinations of these potential impacts, three cumulative impact scenarios were developed for qualitative analysis of response predictions (Table 6).

Table 6 Summary of the cumulative impact scenarios (CISs) for the ‘Springs’ landscape group in the Galilee subregion

CIS

GWD

SSW

C1

+

0

C2

0

C3

+

Pressure scenarios are determined by combinations of no-change (0), increase (+) or decrease (–) in the following signed digraph variables: groundwater depletion (GWD) and subsurface water (SSW).

Data: Bioregional Assessment Programme (Dataset 7)

Qualitative analysis of the two signed digraph models in Figure 13 and Figure 14 indicated a zero or ambiguous response prediction (Table 7 and Table 8, respectively) for the majority of biological variables within the ecosystems associated with the ‘Springs’ landscape group as a result of depletion of groundwater and subsurface water. The high level of ambiguity in the response predictions results from the influence of positive feedback in the macrophytes–benthic algae subsystem and the influence of multiple pathways of interaction that have both positive and negative effects on predicted response variables. These ambiguous predictions could be either positive or negative depending on the strength of interactions attributed to the model’s links. The only variable that had a positive response prediction was macrophytes (submerged and floating) which had a positive response in both models to C2 (a decrease in subsurface water). The only variable that had a negative response prediction was benthic algae which had a negative response in both models to C2 (a decrease in subsurface water). Note that the predictions for depletion of groundwater in the cumulative impact scenarios are within the context of still keeping the spring in damp conditions such that the model variables can still persist. With severe depletion and drying of springs, many of the model variables would disappear and the system, as modelled, would no longer exist.

As noted in Section 2.7.2.3 there were no receptor impact models developed for the ‘Springs’ landscape group in the Galilee subregion, despite preliminary efforts by the external experts at the receptor impact modelling workshop. The main reason for not being able to develop receptor impact models for the ‘Springs’ landscape group was the lack of data and knowledge about critical hydrogeological parameters for the various springs (and spring complexes) within the zone of potential hydrological change. In particular, there was insufficient information available about the magnitude of hydraulic pressure (head) from the source aquifers that drives spring flow in the zone, as well as lack of data about the relationship between hydraulic head and various spring discharge characteristics (e.g. volume, timing, variability etc.). As noted during discussions at the receptor impact modelling workshop, these parameters are likely to be unique to each spring complex in the zone (and may even be unique to individual springs within a complex). This means that spring flow data that may be known for other springs in the GAB (e.g. springs near Lake Blanche in South Australia; Keppel et al., 2016) could not be reliably substituted (i.e. for receptor impact modelling purposes) for the springs in the Galilee subregion’s zone of potential hydrological change. Consequently, without specific estimates of these important hydrogeological parameters for the springs in the zone, the critical relationship that the external experts had identified for developing a springs receptor impact model (i.e. the proportion of pressure head decline that would substantially alter the magnitude of spring flow and effectively represent an ecological ‘tipping point’ in the long-term health and condition of the spring) could not be reliably established for any of the springs or spring complexes within the zone.

Although it was not possible to develop a receptor impact model for the ‘Springs’ landscape group in this BA, some preliminary analysis of remotely sensed data relevant to better understanding near-surface hydrological variability for different springs is presented in companion product 3-4 for the Galilee subregion (Lewis et al., 2018). This work, which has leveraged the available Landsat archive provided by Digital Earth Australia, examines temporal variations in various spring parameters (such as wetness and greenness) within the zone of potential hydrological change. The potential for further research opportunities to build upon this preliminary analysis is also discussed in Lewis et al. (2018).

Table 7 Predicted response of the signed digraph variables (Model 1) in the ‘Springs’ landscape group to (cumulative) changes in hydrological response variables in the zone of potential hydrological change of the Galilee subregion

Signed digraph variable

(name)

Signed digraph name

(shortened form)

C1

C2

C3

Tail vegetation

TV

?

0

?

Emergent vegetation

EV

?

0

?

Peat mound

PM

?

0

?

Groundwater-dependent vegetation

GDV

?

?

?

Wetted area regime

WAR

?

0

?

Macrophytes (submerged and floating)

MP

?

(+)

?

Subsurface water

SSW

?

?

?

Grazers

Gra

?

?

?

Vertebrate predators

VP

?

?

?

Invertebrate predators

IP

?

?

?

Filter feeders

FF

?

?

?

Phytoplankton

PP

?

?

?

Nutrients

Nut

0

0

0

Benthic algae

BA

?

(–)

?

Depth of spring greater than damp

D>Dam

?

0

?

Groundwater depletion

GWD

?

0

?

Qualitative model predictions that are completely determined are shown without parentheses. Predictions that are ambiguous but with a high probability (0.80 or greater) of sign determinacy are shown with parentheses. Predictions with a low probability (less than 0.80) of sign determinacy are denoted by a question mark. Zero denotes completely determined predictions of no change.

Data: Bioregional Assessment Programme (Dataset 7)

Table 8 Predicted response of the signed digraph variables (Model 2) in the ‘Springs’ landscape group to (cumulative) changes in hydrological responses variables in the in the zone of potential hydrological change of the Galilee subregion

Signed digraph variable (name)

Signed digraph name

(shortened form)

C1

C2

C3

Tail vegetation

TV

?

0

?

Emergent vegetation

EV

?

0

?

Peat mound

PM

?

0

?

Groundwater-dependent vegetation

GDV

?

?

?

Wetted area regime

WAR

?

0

?

Macrophytes (submerged and floating)

MP

?

(+)

?

Subsurface water

SSW

?

?

?

Grazers

Gra

?

?

?

Vertebrate predators

VP

?

?

?

Invertebrate predators

IP

?

?

?

Filter feeders

FF

?

?

?

Phytoplankton

PP

?

?

?

Nutrients

Nut

0

0

0

Benthic algae

BA

?

(–)

?

Depth of spring greater than damp

D>Dam

?

0

?

Groundwater depletion

GWD

?

0

?

Qualitative model predictions that are completely determined are shown without parentheses. Predictions that are ambiguous but with a high probability (0.80 or greater) of sign determinacy are shown with parentheses. Predictions with a low probability (less than 0.80) of sign determinacy are denoted by a question mark. Zero denotes completely determined predictions of no change.

Data: Bioregional Assessment Programme (Dataset 7)

Last updated:
4 January 2019