Urban percentage runoff estimation methods (PR URB )

Historically many models have been developed to represent the urban rainfall-runoff process within hydrological, hydraulic and engineering design calculations. These models are available within commercially available software and are used for surface water drainage design calculations on a routine basis (MicroDrainage, 2011). Here their formulation is taken from Woods-Ballard et al. (2007) and the models are implemented by developing MS Excel spreadsheets.

Current methods for runoff modelling split the above ground (hydrological) and below ground (hydraulic) phases of runoff generation in urban areas to represent the different processes that control runoff generation on urban surfaces, and the hydraulic routing of runoff through surface water drainage systems (Kellagher, 2000). The Wallingford

Procedure, described by Kidd and Lowing (1979) is a methodology developed in the

UK for designing and simulating surface water drainage systems. The method is implemented in a number of different software packages that are used extensively in the UK engineering industry to design and simulate new and existing surface water drainage systems (e.g. Microdrainage, InfoWorks etc.). The above ground, hydrological phase of the modelling process calculates the percentage runoff (PRURB) of an event and the below ground hydraulic phase routes runoff volume into an event hydrograph. This study focusses on the various above ground hydrological models for percentage runoff estimation that are available.

3.9.2.1 Original Fixed UK Runoff Model

The original rainfall-runoff model derived in 1979 for the above ground phase of runoff generation is a regression model (Equation 3.11) linking the percentage runoff of an event to metrics describing the percentage imperviousness of a catchment (PIMP), the antecedent wetness of an event (UCWI) and the soil type (SOIL) as

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defined by the Winter Rainfall Acceptance Potential (WRAP) (Kidd and Lowing, 1979).

𝑃𝑅 = 0.829 ∗ 𝑃𝐼𝑀𝑃 + 25.0 ∗ 𝑆𝑂𝐼𝐿 + 0.078 ∗ 𝑈𝐶𝑊𝐼 − 20.7 Equation 3.11 Measurements of PIMP can be made through the analysis of surface types within urban areas, whilst SOIL values are derived through the analysis of published maps (Kellagher, 2013). The Urban Catchment Wetness Index is derived by the following equation:

𝑈𝐶𝑊𝐼 = 125 + 8 ∗ 𝐴𝑃𝐼5 − 𝑆𝑀𝐷 Equation 3.12

Where API5 = five day antecedent precipitation index (mm) and SMD = soil moisture deficit (A data setcurrently produced by the UK Met Office (MetOffice, 2017)).

Event specific values of UCWI are derived using the following method for simulation purposes:

(i) Sum the rainfall depth totals for each of the five days prior to an event. (ii) The API5 for 09:00 of the day of an event is given by:

𝐴𝑃𝐼5₉ = ∑ 𝑃_−𝑛𝐶_𝑝𝑛=0.5

𝑛=1,5 Equation 3.13

Where P-n = rainfall depth on day n before an event and Cp = a decay coefficient of

0.5.

(iii)The API5 at the time of an event is then given by:

𝐴𝑃𝐼5 = 𝐴𝑃𝐼59𝐶𝑝(𝑡

′_−9)/24

+ 𝑃_𝑡′₋₉𝐶_𝑝(𝑡 ′_−9)/48

Equation 3.14

Where t’= Time (hours) of the beginning of an event, and Pt-9 = rainfall depth between

time t’ and 09:00.

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𝑆𝑀𝐷 = 𝑆𝑀𝐷₉ − 𝑃_𝑡′₋₉ Equation 3.15

Where SMD9 = Soil Moisture Deficit at 09:00 on the day of an event and Pt’-9 = rainfall depth between time t’ and 09:00. The SMD describes the depth of rainfall required to return soil storage to field capacity (Butler and Davies, 2004). The UCWI is therefore a weighted metric of the wetness of the preceding five days before an event, where the rainfall closest to the event has the greatest influence on UCWI values. Design values of UCWI have been recommended for areas across the UK, in relation to the Standard Averaged Annual Rainfall (SAAR) for both winter and summer conditions and these are used in design practice (Kellagher, 2000).

3.9.2.2 New Variable UK Runoff Model

An alternative runoff model, called the Variable UK Runoff Model (or “New” Runoff model) was devised in 1990 to account for increased wetness and runoff generation as rainfall-runoff events elapse. The model was developed by John Packman of CEH, however no single paper reports its development and thus a direct citation is not possible. The Variable UK Runoff Model is recommended over the original regression equation in modern surface water modelling guidance, however, both models are still available within surface water drainage design software packages and are widely used (Woods-Ballard et al., 2015). The UK Variable Runoff Model is sensitive to the fact that not all impervious surfaces are connected to the surface water drainage system as the model contains an Effective Impervious Factor (IF) parameter to split impervious surfaces into connected and disconnected surfaces. Non-connected surfaces are lumped together with permeable surfaces and the runoff generated from these surface types increases as an event elapses and the catchment wetness increases. The percentage runoff from the connected surfaces remains unchanged throughout an event (assumed to be 100%). The Variable UK Runoff Model takes the form:

𝑃𝑅 = 𝐼𝐹 ∗ 𝑃𝐼𝑀𝑃 + (100 − 𝐼𝐹 ∗ 𝑃𝐼𝑀𝑃) ∗ 𝑁𝐴𝑃𝐼

𝑃𝐹 Equation 3.16

Where PR = Percentage Runoff (%), IF = the effective paved area factor (%), PF = soil storage depth and NAPI = the 30 day antecedent precipitation index (similar to

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API5, over a longer preceding period). Design values of NAPI and PF are available in design guidance, whilst PIMP and IF need estimating based upon assessments of surface cover and connectivity.

3.9.2.3 ReFH2

An urban extension to ReFH2 (Section 3.9.1) described by Kjeldsen (2009) includes a method to estimate the impacts of urbanisation on runoff volume generation. The urban extension splits an urban area into two components, (i) rural and (ii) urban, and a runoff volume is defined from a design event for each component. The urban percentage runoff is modelled with Equation 3.17 (simplified from the equations described in Kjeldsen 2009):

𝑃𝑅 = 𝑃𝐼𝑀𝑃 ∗ 𝐼𝐹 ∗ 𝑃𝑅𝑢𝑟𝑏 Eq. 3.17

Where PIMP = the percentage impervious area, IF = the proportion of impervious surfaces connected to a drainage system and PRurb = the percentage runoff of connected impervious surfaces. Default design values are used to represent large-scale urban development within fluvial catchments (PIMP=30%, IF = 70% and PRurb=100%) and whilst the urban extension is intended for the large-scale estimation of the impacts of urbanisation in fluvial catchments the method is also recommended for use on plot scale assessments of runoff (Woods-Ballard et al., 2007; WHS, 2016).

3.9.2.4 SuDS Method

A simple method for estimating the additional runoff volume following urbanisation of a development plot is described by Kellagher (2013). Here the volume of runoff that must be attenuated on site (either through infiltration or storage) for an urban development is estimated using Equation 3.18, this is a version of Equation 3.10 under specific assumptions, and here it is termed the “SuDS Method” given that its details are provided within the SuDS design manual (Woods-Ballard et al., 2007):

𝑉𝑜𝑙_𝑥𝑠= 𝑅𝐷 ∗ 𝐴 ∗ 10 ∗ [𝑃𝐼𝑀𝑃₁₀₀ (𝛼0.8) (1 −𝑃𝐼𝑀𝑃₁₀₀) (𝛽𝑆𝑃𝑅) − 𝑆𝑃𝑅] Equation 3.18

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Volxs = Extra runoff volume resulting from urbanisation (m3) RD = rainfall depth for the 100yr 6hr rainfall event (mm) PIMP = percentage impermeable area (as a proportion) A = Catchment area (ha)

SPR = SPR index for the SOIL or HOST class (this specifies the percentage runoff

from permeable surfaces).

α = proportion of impervious surfaces connected to the surface water drainage network

0.8 = assumed percentage runoff from connected impervious surfaces

β = proportion of pervious surfaces connected to a surface water drainage system.

Equation 3.18 has been copied directly from Woods-Ballard et al. (2007), however inspection of the equation indicates that the text contains a typographical error, therefore, the following modification is made (Equation 3.19) within this study:

𝑉𝑜𝑙_𝑥𝑠= 𝑅𝐷 ∗ 𝐴 ∗ 10 [(𝑃𝐼𝑀𝑃₁₀₀ (𝛼0.8) + (1 −𝑃𝐼𝑀𝑃₁₀₀) 𝛽𝑆𝑃𝑅) − 𝑆𝑃𝑅] Equation. 3.19

Where parameter values have the same meaning as those in equation 3.18.

To apply this model, the areas of connected and disconnected impervious and pervious surfaces are determined and the percentage runoff from impervious surfaces estimated (default value of 0.8). This model includes the SPRHOST catchment characteristic from the FEH (CEH, 1999) to represent the likely percentage runoff of a development site under greenfield conditions. It is possible to modify the equation to include an alternative greenfield model so that SPR is derived from ReFH2 as follows:

𝑉𝑜𝑙_𝑥𝑠 = 𝑅𝐷 ∗ 𝐴 ∗ 10 [(𝑃𝐼𝑀𝑃₁₀₀ (𝛼0.8) + (1 −𝑃𝐼𝑀𝑃₁₀₀) 𝛽_{𝑅𝐸𝐹𝐻2}) − 𝑃𝑅_{𝑅𝑒𝐹𝐻2}] Eq.3.20

All parameters are identical to those defined for equation 3.18 and PRReFH2 is the greenfield percentage runoff as defined by the plot scale ReFH2 method described in Section 3.9.1.

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