Page Comparison

Water surface elevation (WSE or "Reduced level")

The Cells Model approach assumes that the movement of water within a wetland is related to the head difference between the water bodies that make up the wetland. To enable this in Source, the water surface elevation (WSE) is determined for nodes in a wetland cluster.

Wetlands Hydraulic Connector nodes and boundary conditions

Boundary conditions are points at which water can flow in to or out of a wetland. In Source, these points are at either a Wetlands Hydraulic Connector node or a Storage node’s inlet or outlet link (Figure 1). The Wetlands Hydraulic Connector node is used to represent situations where a wetland interacts with a river reach and the inflows and outflows are too small to have an effect on the water surface elevation in the river.

Figure 2 shows a representation of this type of wetland in Source, where the wetland’s boundary is modelled at the Wetlands Hydraulic Connector node.

If the outlet of a Storage node in a wetland cluster is connected to a conventional link then that storage is a boundary of the wetland cluster. Examples in the Murray include:

• Lock 3, which could be modelled as a Storage node at a boundary of a wetland system that includes Lake Bonney, and;
• Euston Weir, modelled as a Storage node at a boundary of the Euston Lakes wetland system.

Figure 3 shows a representation of this type of wetland in Source, where the wetland boundary is modelled at the Storage node’s outlet.

The rules governing outflow from a boundary depend on the type of node:

Wetlands Hydraulic Connector nodes:

• Mass balance: Downstream flow is the difference between upstream inflow and total flow in connected wetland links.
• Flow in each connected wetland link is a function of water surface elevation (WSE) at the hydraulic connector node and the node at the other end of the link. See the Wetland Links (Connectors) section for more information.
• The modeller specifies a relationship between upstream inflow and WSE at the hydraulic connector node.

Storage nodes:

• If the storage node is a weir, and this is within its target operating range, releases are set so that the storage remains at the same volume where possible.
• When there is a spillway, there is a minimum volume "spilled". This amount varies with water surface elevation.
• The release from a storage is determined by the volume ordered, and is limited by outlet capacity (which varies with water surface elevation). It also takes into account spill.

In a Cells Model, connectors allow water to move between cells. In Source, connectors are represented by the wetland link. Flow rate in a connector can be described as a function of water surface elevation (WSE) at each end of the link:

Equation 1	Image Modified

where:

fQ_c is a function that returns flow rate along connector c.

Q_c is the flow rate along connector c. A positive value indicates a flow from WSE₁ to WSE₂.

WSE₁ and WSE₂ are the water surface elevations at each end of connector c.

Flow in a wetland link can be in either direction (unless the modeller specifies otherwise). The default flow direction is set when the modeller selects one node before the other when creating the wetland link. It is indicated by the direction of the arrow on the link in the Schematic Editor. Flow that moves in the default direction is represented by a positive number, while flow in the other direction is represented by a negative number.

Channel

Currently Source has only one type of wetland link function implemented to represent a channel. The specific form of wetland link flow function for a channel implemented in Source is:

Equation 2	Image Modified

where:

Q_c is the wetland link’s flow rate (m³/s).

C() is the modified conveyance relationship, this is the hydraulic conveyance divided by the square root of the channel length (m^2.5/s).

ΔWSE is the drop (m) in surface water elevations along the channel.

In cases where ΔWSE<0.01m, the flow function is adjusted to prevent computational issues due to an infinite slope of the curve at the point where ΔWSE approaches zero. This adjusted function is:

Equation 3	Image Modified

The value for hydraulic conveyance will vary according to where it is calculated. To model this, a piecewise relationship between modified conveyance c and water surface elevation (sometimes referred to as reduced level) is configured using the wetland link’s feature editor. The WSE_c at the point at which the modified conveyance is calculated is estimated as:

Equation 4	Image Modified

where:

WSE₁ is the water surface elevation at the originating node

WSE₂ is the water surface elevation at the destination node

weighting is a spatial weighting factor configured by the modeller in the wetland link’s feature editor. It is specified in relationship to the from end of the link.

Source interpolates between points in the defined modified conveyance versus water surface elevation relationship to find the value of C that corresponds to WSE_c. The originating and destination nodes are defined by the modeller by which direction they drag the wetland link into their system and is shown as an arrow on the link.

Source models regulated flows in wetland links by allowing the modeller to specify a target flow rate. This limits the rate of flow on the wetland link to the target value. It is assumed that regulated flow has a specific direction, ie. if a positive target flow rate is configured, Source will not permit flow in the opposite direction on the wetland link (ie. the value will be set to zero if the flow calculation returns a negative value, and vice versa). The following calculations adjust the channel flow rate to implement the regulated channel.

Where target flow rate Q_target ≥ 0

Equation 5	Image Modified

Where target flow rate Q_target < 0

Equation 6	Image Modified

In Source, storage nodes are used to represent the "cells" or wetland compartments in which water can be stored. A storage node has a relationship between water surface elevation and surface area that can be used to represent the spatial distribution of water in a wetland. Another function relates its water surface elevation WSE_ws to the volume of water stored:

Equation 8	Image Modified

where:

A_ws is the surface are area of storage node ws.

S_ws is the volume stored in storage node ws.

fA_ws is a function that relates surface area to water surface elevation of the storage node ws.

fS_ws is a function that relates storage volume to water surface elevation of the storage node ws.

WSE_ws is the water surface elevation of storage node ws.

The functions above are based on relationships configured by the modeller in the Storage node Dimensions table (in the Storage node's Feature Editor). The Level parameter found in this table is translated into WSE by addition of the node's Elevation parameter (set in the same dialog).

Mass balance equations are used to model the behaviour of a storage node as a cell within a wetland cluster’s cells model. As an implicit Eulerian numerical scheme is used, for each storage node the mass balance over an arbitrary time period is:

Equation 9	Image Modified

or

Equation 10	Image Modified

where:

S₁^ws is the volume of water stored in storage node ws at the start of the period

S₂^ws is the volume of water stored in storage node ws at the end of the period

In_ws is the volume that flowed into storage node ws over the period

Out_ws is the volume that flowed out of storage node ws over the period.

The storage node’s WSE is an input parameter to its cells model calculations (the process by which this is ascertained is described later starting at Model Initialisation). Elements of each storage node’s mass balance equation are calculated as follows:

End of time-step storage volume S₂^ws is determined using the function described above that relates this attribute to WSE.

Volume of inflow to the storage node:

Equation 11	Image Modified

where:

I_ws is the volume of upstream inflow entering storage node ws from outside the wetland cluster (ie. via its inlet link).

Groundwater_ws(Level_ws) is the groundwater flow volume over the time-step in storage node ws. The relationship between groundwater and level is defined in the Seepage table, configured by the modeller on the storage node. WSE is converted to Level by subtracting the base Elevation.

NetEvaporation_ws is the net evaporation flow volume for the time-step in storage node ws. This is a combination of the Rainfall and Evaporation functions configured by the modeller on the storage node. These would usually have surface area A_ws as a parameter.

WetlandFlow_ws is the total flow volume over the time-step on wetland links connected to storage node ws. See the Wetland Links (Connectors) section.

Volume of downstream outflow from the storage node (leaving the wetland cluster): This calculation depends on whether the storage node represents a weir, and if so, where the weir’s WSE is in relation to its operating range:

• Weir: If WSE_ws ≤ minimum target WSE, downstream outflow is zero.
• Weir: If WSE_ws ≥ maximum target WSE, downstream outflow is set to the same volume the maximum of the orders and volume as upstream inflow (entering the node via the inlet link).

Where the storage node is not a weir, or the weir’s WSE_ws is within its target range:

Equation 12	Image Modified

where:

dt is the length of the time-step.

f_omax() is the outlet path capacity relationship that relates the storage node’s WSE to the maximum flow rate that can be made through the outlet path. Note that this capacity includes a spill rate that is also determined by WSE.

f_Spillo() is the spillway relationship for outlet path o that relates the storage node’s WSE to the flow rate leaving the storage node over the spillway.

no_ws is the number of outlet paths from storage node ws.

o is a storage node outlet path.

Order_o is the flow rate ordered to go down outlet path o.

Anchor
Wetlands ordering Wetlands ordering

Wetlands and ordering

Orders can be placed on behalf of a wetland. This may be modelled in Source by connecting a water user node with an in-stream demand model to a supply point node upstream of the wetland cluster for which the water is to be ordered, and using "target flow" expressions on the wetland links to move the water into the wetland once it arrives.

The order processing for both the above configurations is described in the Scientific Reference Guide entries for the water user node, supply point node and ordering system.

Storage nodes on the boundary of a wetland cluster may also be used to supply downstream orders. The interaction of the storage node and ordering system are described under Scientific Reference Guide entries for these items.

Conservative constituents in wetlands

Source treats all water bodies modelled using the storage node as fully mixed. This is discussed in more detail in the Scientific Reference Guide entry on the Storage node. Conservative constituent modelling in wetland links is not yet implemented.

At the start of the scenario run, the schematic network analyser works from upstream to downstream to identify the nodes and links that make up each wetland cluster (representing a wetland). The following rules are used:

• Node types that may belong to a wetland cluster include the hydraulic connector and the storage node. A node is a part of a wetland cluster only if it has a wetland link connected to it.
• Each node can only belong to one wetland cluster.
• If a node has not been assigned to a cluster yet, and is connected via a wetland link to another node that has been assigned, it is assigned to the same cluster as that node.

Source keeps track of the number of nodes that are in each wetland cluster, referred to as NodesInCluster.

When the schematic network analyser encounters a node in a wetland cluster during the flow phase, it processes the cluster together as a unit before running the model for individual nodes and links that make up the cluster. The component that performs the cluster’s Cells Model processing will be referred to here as the "cluster processor".

Cluster processing results in an estimate of the water surface elevation in each storage node and the direction and rate of flow in each wetland link. The model that is later run for each individual storage node determines the node’s final water surface elevation for the time-step. The storage node model is described in the Scientific Reference Guide entry for the Storage node.

As the order of execution of model components cannot be specified, the cluster processor may need to process storage and hydraulic connector nodes for which the current time-step’s inflow rate has not yet been calculated. In these cases, the previous time-step’s inflow values are used.

Flow phase processing of each wetland cluster will only occur once in every time-step, no matter how many connections there are between wetlands or rivers modelled.

The cluster processor uses an iterative method to find and return a set of water surface elevations that satisfy the mass balance equation for every one of its storage nodes. The initial iteration uses the following initial values for WSE:

• Hydraulic connector nodes: The Reduced Level value for the current rate of inflow in the piecewise relationship between Average Inflow and Reduced Level specified by the modeller.
• Storage nodes: The WSE at the end of the previous time-step.

At each subsequent iteration a new set of trial values is created and fed into storage node mass balance equations. This involves the following steps:

• The trial WSEs are used to determine flow rate and direction in the cluster’s wetland links as described under Wetland Links (Connectors).
• The mass balance equation is evaluated for every storage node in the cluster. This equation is described under Storage Nodes (Cells).
• The precision of the solution is determined and compared to the cluster’s convergence limit.
• Precision is calculated as the root mean square of storage node mass balance volumes:

Equation 13	Image Modified

where:

ws is a storage node in the wetland cluster

MassBalance_ws is the result of the mass balance equation for storage node ws.

n_ws is the number of storage nodes in the wetland cluster

The wetland cluster’s convergence limit is calculated based on the scenario’s wetland node convergence limit that was specified by the modeller. 

Precision is compared to the cluster’s convergence limit to determine whether a solution was found:

• If the Precision < ClusterConvergenceLimit, or the maximum number of iterations has been reached, the process of solving the cluster is finished.
• If the Precision ≥ ClusterConvergenceLimit and more iterations are allowed, parameters for each storage node in the cluster are adjusted ready for the next iteration:
• The mass balance error is subtracted from the end of time-step storage volume estimate
• The corresponding WSE for the adjusted storage volume is determined using the Storage Dimensions relationship (between storage volume and level).

Image Modified The solution technique implemented in Source allows other types of node to be used within wetland clusters that like the hydraulic connector node have a WSE that is not impacted by wetland link flow. At present this functionality is not used as the only types of node that may be connected by wetland links are storage nodes and hydraulic connector nodes.

Input data

All input data is configured via user interfaces. The parameters are summarised in the following tables:

These parameters are accessed via the scenario Edit menu, and apply to all wetland clusters in the scenario.

If log diagnostics are required, there are also parameters that determine the location of the log file, the time-steps to be logged, and whether to only log those in which no acceptable Cells Model solution could be found. These parameters are described in more detail in the Source User Guide.

Note that this information is also available in the Schematic Editor on the node’s tool tip.

Use of these parameters is described in Storage Nodes (Cells). For a full list of Storage Node parameters, see the Source User Guide.

Output data

Output data is viewed using the Recording Manager. The recorded attribute values (results) are reported for each time-step of the model run. Results relevant to wetland Cells Model processing are summarised in the following tables:

For a full list of output data for wetland nodes and links, refer to the Source User Guide.

Reference list

Zanobetti, D., Lorgeré, H., Preissmann, A., & Cunge, J.A., 1970, Mekong Delta mathematical model program construction, J. Waterways and Harbors Division, American Society of Civil Engineers, vol.96, no.2, pp.181-199.