117 Boundary conditions

I have had several discussions over the last year on how to model the boundary conditions of high watercourse levels limiting the discharge of flow from sewerage systems and so increasing flood risk.  This applies to storm overflow discharges from combined systems, outfalls from surface water sewers and potentially outfalls for treated effluent at wastewater treatment works.

Opinions that I have heard have ranged from the ridiculous to the sublime.

·         One was that there was no need to consider boundary conditions as the water level in the watercourse was not the responsibility of the sewerage utility and so could be ignored.

·         The other extreme was that it was essential to have a fully integrated model of the sewerage system and the watercourses and analyse it for a long time series of rainfall to ensure that critical conditions were identified.

So what is a practical approach to river boundary conditions?

Existing guidance

Let’s start with the guidance published by CIWEM Urban Drainage Group.

The modelling bible is the Code of Practice for the Hydraulic Modelling of Urban Drainage Systems published in 2017.

This sets out that

• The possibility of restricted outflow due to boundary conditions should be considered for all outfalls.
• If there is no better information then start by assuming that the watercourse is at bank full or at the level indicated by national flood map outlines.  If this would increase flood risk then investigate further.
• If peak water levels are available from an existing river model then test if this would increase flood risk and if so a boundary conditions is required.
• The representation of the boundary condition depends on the relative times of concentration of the watercourse and the sewerage systems.  There are three options.

1. A fully integrated sewerage and river model responding to the same rainfall.
2. A partially integrated sewerage and river model where the upstream river boundary is represented by a steady start inflow hydrograph.
3. A stand-alone sewerage model that represent the boundary condition is represented as a steady state river level.

The CoP refers to further guidance in the CIWEM UDG Integrated Urban Drainage Modelling Guide updated in 2021.  However that guide adds lots of detail without changing the basic concepts.

Other guidance

Some useful additional guidance was given in the Scottish Water specification for building and verifying urban drainage models.  Unfortunately this is not available on-line but I have extracted a few key paragraphs below.

This sets out the criteria for using each of the three modelling approaches described above.

Fast Response Watercourses

These respond to rainfall similarly to the sewerage elements. Typically in just a few hours because of their small size, irrespective of whether their catchment is urban or rural.

If the critical duration for the watercourse is similar to the critical duration in the urban catchment (less than 12 hours’ difference), then these parts of the catchment should be treated as a fast response watercourse.

These watercourses should be represented by a fully integrated model because the response times of the watercourse and urban system are similar, and allow for two-way interaction as described in the IUD Guide.

Intermediate Response Watercourses

Here the response time of the rural catchment is significantly longer than that of the sewerage system, but the urban contribution to the river flow is significant.

These watercourses would be represented as an integrated model for the urban component of flow in the river, using a steady state boundary condition for the rural inflow. This allows for two-way interaction in the urban part of the model.

Slow Response Watercourses

Here the response time of the rural catchment is significantly longer than that of the urban system, and the relatively rapid urban discharge to the river is typically a small percentage of the total river flow.  

These watercourses would generally be represented using a steady state boundary condition derived from a stand-alone river model.

There are challenges with this approach.  For flat lowland rivers, the level may not vary much along a reach and one hydrograph can be used for a group of outfalls, but more usually it will be necessary to derive a separate level hydrograph for each outfall location.  It may therefore be simpler to use the intermediate approach with a simplified representation of the river channel to automatically give the appropriate level hydrographs.

Joint probability

For a type 1 (fast) model approach there is no need to consider joint probability.  All of the system responses are driven by the same rainfall.

For type 2 (intermediate) and 3 (slow) models, joint probability should be considered when selecting the boundary conditions.  This needs to consider the differing times of concentration of the river and sewerage system and the probability of systems responding at the same time.  This depends on the duration of the storm used for the sewerage system analysis and on whether it is summer or winter.

Short duration storms are less likely to coincide with river conditions of the same return period.  The annual average river flow or level is therefore probably appropriate.  Ideally this should be derived separately for summer and winter and the appropriate one used to match the rainfall applied to the sewerage system.

For longer duration storms the river system and sewerage system could be responding to the same rainfall and so river flows or levels of the same return period as the urban storm should be used.

There is clearly a need for site specific assessment of the appropriate conditions.