A new method to inform the distribution of stormwater disconnection within a catchment has been conceived. It is based on ensuring that the peak flow from a catchment at a specified point of interest within the urban drainage network is reduced. The basis of achieving this is the concept of areal co-contribution.
3.2.1 Superposition of Flows from Subcatchments
Consider a linear branch of sewer (Figure 3-1). A single pipe receives flow from a catchment comprising three identical subcatchments. There is a flow monitoring point (A) downstream of the catchment. A symmetrical peaked rainfall event falls uniformly across the catchment, generating stormwater runoff which flows through point A.
Subcatchment ID
A 1
2 3
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The arrival of stormwater runoff at point A is dictated by the time of concentration (tc) of the
subcatchment from which the stormwater was generated. Time of concentration comprises two components; time of entry (te) and time of flow (tf), and is described by Equation 3-1.
𝑡𝑐 = 𝑡𝑒+ 𝑡𝑓 (Equation 3-1)
Let us assume that each subcatchment is identical, and as such possesses equal times of entry. The arrival of stormwater runoff at A is therefore dependent on the time of flow from each subcatchment. For simplicity, each subcatchment may be ascribed consistently incremental values for time of flow. Figure 3-2 shows the disaggregated arrival of stormwater flow at point A. The actual flow through point A may be calculated through application of the theory of superposition.
Figure 3-2: Depiction of stormwater flows through point A in Figure 3-1.
3.2.2 Peak Flow and Sewer Failure
A rainfall event falling on a catchment generates a flow profile, determined by the superposition of the flow profiles of its subcatchments. Any section of an urban drainage network will have an associated conveyance capacity. When the flow rate within the system exceeds the conveyance capacity, surcharge may be observed, leading to flooding events. CSO are set to allow a design flow rate to be retained within the urban drainage network, and excess flow is spilled. Sewer flooding and CSO spills are caused by the exceedance of the conveyance capacity of the sewer system by the flow profile from a catchment. The duration of the flow rate above the conveyance capacity of the system determines the volume of flood
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water and the volume and duration of a CSO spill. The reduction of the peak flow rate is therefore an important objective of stormwater disconnection for urban drainage performance improvement.
3.2.3
Areal Co-Contribution
To achieve the objective of reducing the peak flow rate, it is useful to understand if the generation of peak flows can be ascribed to particular locations in the catchment. This would enable engineers to “target” stormwater disconnection in appropriate parts of the catchment. The characteristics of a catchment affect the flow hydrograph generated by that catchment. Real-world catchments, and therefore the associated flow hydrographs, are heterogeneous. Some examples of heterogeneity are slopes within catchments, the proportion of impermeable to permeable area and the type of urban area found in the catchment, which affects the run- off coefficient of the catchment.
One additional and important characteristic of urban drainage systems is areal co- contribution. Any urban drainage system can be sub-divided through the use of isochrones. Isochrones are imaginary lines that split a catchment into sections based on the time taken for stormwater run-off to flow to a designated point in the system.
An example of an urban drainage catchment split using isochrones is provided in Figure 3-3, showing a catchment of 11 subcatchments. Each subcatchment has a time of entry = 5 minutes. The time of flow from one subcatchment to the downstream subcatchment is 10 minutes. This allows the calculation of the time of concentration (tc = te + tf) for each
subcatchment to Point A. In Figure 3-3, subcatchments with the same time of concentration to A have been split using isochrones.
Areal co-contribution is the concept of disparate areas located within a catchment possessing similar times of concentration to some pre-identified point of interest in the catchment; run- off from these areas will arrive at the point of interest simultaneously. Summing the amount of area within each isochrone segment gives the areal co-contribution at that time of concentration.
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Figure 3-3: A simple catchment split via isochrones.
3.2.4 The Disaggregated Unit Hydrograph
Originally used in the field of natural hydrology, the unit hydrograph describes the hydrograph inherent to the specific catchment under investigation (Shaw, 1998). A unit depth of rainfall is applied uniformly to the catchment at a constant rate for some duration. The resultant hydrograph is the unit hydrograph for the rainfall conditions. The unit hydrograph can subsequently be adjusted to describe the response of the associated catchment to any rainfall event.
The unit hydrograph can theoretically be spatially disaggregated to understand how run-off from different isochrones contributes to it. Figure 3-4 shows the complete and disaggregated unit hydrograph for the catchment presented in Figure 3-3. It can be seen from Figure 3-4 that isochrone 5 produces the greatest peak flow response from any co-contributing area within the catchment, that flow from isochrones 3, 4, and 5 are contemporaneous with the overall peak flow response from the catchment, and that the greatest contribution to the peak flow is associated with isochrones 5. This suggests that stormwater disconnection may be usefully targeted within isochrones with the greatest areal co-contribution.
6 A 1 2 3 4 5 7
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Figure 3-4: The resultant and disaggregated unit hydrograph for the catchment in Figure 3-3.