D.8 Mass balance - Base Case

Mass balance is a key concept in environmental modelling, especially in the case of catchment pollutant export simulation. In this instance, mass balance requires that the mass of a given pollutant generated on ground from catchment processes equals that delivered downstream to receiving waters (less mass potentially resettled in-catchment). TUFLOW CATCH independently accounts for these two quantities and so comparison of the respective predictions allows for rigorous assessment of the overall model’s mass balance capability. This section presents that performance using Demonstration_008.tcc.

D.8.1 Concept

TUFLOW CATCH run in its Pollutant Export (or Integrated) configuration predicts the release of pollutant from catchment dry stores. This released pollutant is then advected downstream and potentially settled and resuspended en route. Some released pollutant also reaches the catchment outlet and as it exits the domain is tracked by TUFLOW CATCH as mass, concentrations and volumes. Reconciliation of these independent mass predictions (i.e. that released from - or reentering via settling - the catchment dry store and that leaving the domain) was undertaken by applying bespoke post processing tools to the predictions of Demonstration_008.tcc. The intention was to show that the cumulative released mass and the cumulative mass leaving the overall domain are equal.

D.8.2 Configuration

The TUFLOW CATCH simulation Demonstration_008.tcc was configured as follows:

  • Based broadly on Demonstration_003.tcc
  • MGL unit system
  • Pollutant Export configuration
    • Four pollutants
      • Salinity (constant and zero)
      • Temperature (as a timeseries)
      • Tailings
      • PFAS
    • Settling activated for Tailings and PFAS, with PFAS settling velocity set to zero
    • Two export methods
      • Shear1 (applied to Tailings)
      • Washoff1 (applied to PFAS)
    • Infiltration set to off for both Tailings and PFAS
    • Spatial distributions
      • Tailings: uniform
      • PFAS: specific land uses only
    • A downstream receiving polygon specified
  • Hydraulic configuration
    • Model timestep set to 10 seconds
    • Output timestep of map and timeseries set to 10 seconds
    • 10 day simulation period
    • Extended dry periods before and after a major rain event to allow for complete settling of pollutants from remaining surface waters
  • Output
    • Catchment: Cell centred netcdf format to avoid interpolation issues associated with some other formats
    • Polygon timeseries of flow and concentration (see Section C.9.2)
  • This simulation cannot be run in demo mode as it too long due to the time taken in writing the highly temporally resolved outputs. It must therefore be run with a licence

D.8.3 Method

Mass balance was computed separately for tailings and PFAS so as to demonstrate performance over different pollutant generation methods. A slightly different numerical recipe was applied to each:

  • Tailings (Shear1 method)
    1. The net_mass_tailings field of the cell centred netcdf output file was interrogated and the released mass computed at each cell at each timestep. All cell-based released masses were summed for a given timestep to produce a timeseries of liberated mass across the entire domain. This calculation included the effects of erosion and settling for each cell by default
    2. The polygon outflow csv file was interrogated and mass leaving the domain computed at each timestep by computing the product of reported concentration and flow. This provided a timeseries of mass leaving the domain through the downstream polygon
    3. The mass of Tailings in water within the model was also computed at every timestep (by multiplying cell volume by Tailings concentration on a cell by cell basis and summing globally). This produced a further independent timeseries to compare with that computed as the difference of items 1 and 2 above
  • PFAS (Washoff1 method)
    1. The dry_mass_PFAS field of the cell centred netcdf output file was interrogated and the total released mass computed by
    • Computing the total mass of PFAS that was created across time and all cells via the accumulation process, noting that mass is not created at a timestep or cell where washoff is actively occurring
    • Subtracting from this both:
      • The final mass in the dry_mass_PFAS field and
      • The final mass remaining in the model domain in the water phase (e.g. captured in local topographic features)
    • The result was the mass removed from the domain via washoff
    1. As for Tailings, the polygon outflow csv file was interrogated and mass leaving the domain computed at each timestep by computing the product of reported concentration and flow. This provided a timeseries of mass leaving the domain through the downstream polygon
    2. The mass of PFAS in water within the model was also computed at every timestep (by multiplying cell volume by PFAS concentration on a cell by cell basis and summing globally). This was used to provide the final mass of PFAS remaining in the water phase of the domain at the end of the simulation, noting that settling is set to zero for PFAS

D.8.4 Results

In both Shear1 and Washoff1 cases, the key points of comparison are between:

  • The final cumulative released and exiting masses. This is a single number to number comparison, and these need to be equivalent for mass conservation to hold. In the Shear1 case (i.e. tailings), a timeseries comparison between released and exiting mass is also possible
  • The Shear1 method also allows for a timeseries comparison of water borne mass of pollutants, computed indirectly from mass balance and directly from post processing of concentration and volume cell outputs

The MATLAB scripts used to perform all post processing are provided in the Modelling\TUFLOWCATCH\matlab folder in the Demonstration Model download, and are self explanatory. Some functions from the TUFLOW FV MATLAB toolbox are required to execute these scripts.

D.8.4.1 Tailings

For Tailings simulation using the Shear1 export method:

  • Exported tonnage: 451.92 (via the shear1 method)
  • Received tonnage: 451.92 (entering the downstream polygon)

Timeseries of these are presented in Figure D.8. Note that the shape of the export and receiving curves are different (as expected). Specifically:

  • The shift in time between exported and received masses reflects TUFLOW CATCH’s simulation of on-ground hydraulics and associated pollutant transport: time is taken (and explicitly simulated) between upstream pollutant export and subsequent delivery downstream
  • The exported curve is non-monotonic and this reflects dynamic settling of previously released pollutant occurring in the catchment simulation

The final masses between exported and received are the same.

Figure D.8: Tailings mass conservation

As noted above, a complementary measure of mass conservation performance is to compare the timeseries evolution of the total Tailings mass \(M\) in the water column at every timestep \(i\) computed via two independent means, particularly from the:

  • Reported concentrations \(C\) and water volumes \(d\times\)cell area in each computational cell \(j\), summed across the domain at each timestep (“concentration method”):

\[\begin{equation} M_i = \text{cell area} \times \sum^{\text{num cells}}_{j=1} C_j \times depth_j \tag{D.1} \end{equation}\]

and

  • Fluxes \(F\) of tailings mass to and from all wet cells at timestep \(i\) and adding this net flux to the mass at the previous timestep \(i-1\) (assuming an initial mass of zero, “flux method”)

\[\begin{equation} M_i = M_{i-1} + (F_i^{to} - F_i^{from}) \tag{D.2} \end{equation}\]

These two independent calculations of water column mass are presented as timeseries in Figure D.9. The timeseries coincide, confirming that:

  • Mass is conserved
  • The units of concentration (used to compute \(M_i\) via the concentration method) are correct. Similar analyses can be undertaken with other unit systems if desired.

Figure D.9: Tailings mass comparison

D.8.4.2 PFAS

For PFAS simulation using the Washoff1 export method:

  • Generated tonnage: 17.37 (total, via the washoff1 method)
  • Received tonnage: 4.43 (entering the downstream polygon)
  • Remaining dry store tonnage: 12.88 (remaining in the catchment as not washed off after all rainfall has ceased)
  • Remaining water phase tonnage: 0.06 (remaining in the catchment in trapped water after all rainfall has ceased)

The sum of received and remaining (dry and wet) tonnage (4.43 + 12.88 + 0.06 tonnes) equals that generated (17.37 tonnes), as expected. Figure D.10 presents the time evolution of PFAS mass, for completeness, as:

  • Water column mass as an instantaneous value (the “concentration method” above), and
  • Exported cumulative mass exiting through the downstream polygon

Figure D.10: PFAS masses