# Modelling impervious surfaces in RORB

The previous post looked at rainfall excess hydrographs; here I explore how these hydrographs change when modelling impervious surfaces in RORB.  This post focusses on the initial loss/continuing loss modelling approach.

Usually, losses are reduced for impervious compared to pervious surfaces and RORB sets both initial and continuing loss to zero if a surface is 100% impervious.

As an example, consider the 6 hour 1% rainfall for Melbourne, which is 83.4 mm.  If we use the ARR1987 temporal pattern (see the previous post), the hyetograph is as shown in Figure 1.

Figure 1: The 6 hour 1% rainfall (83.4 mm) multiplied by the ARR1987 temporal pattern.  For an impervious surface, RORB sets both initial and continuing loss to zero

Example calculation:

In the ARR1987 temporal pattern, the time period between 1.5 and 2 hours has 23.3 percent of the rain.  The total rainfall is 83.4 mm so the rain in this period is 83.4 x 23.3% = 19.43 mm which is consistent with Figure 1.

The corresponding rainfall excess hydrograph, for an area of 10 km2, which is 100% impervious, is shown in Figure 2 (Note that Areal Reduction Factors have not been used).

Figure 2: rainfall excess hydrograph for an area of 10 km2

Example calculation:

The instantaneous flow at a 2 hours will be

$\frac{1}{3.6} \times \frac{1}{0.5} \times 19.4 \times 10 = 107.8 \mathrm{m^3 s^{-1}}$

To explain factors at the start of the equation, 1/3.6 is for unit conversion, 1/0.5 is because the temporal pattern has a 0.5 hour time step.   The RORB output matches the calculations (Figure 3).

By default, RORB will show the rainfall excess hyetograph above the calculated hydrograph but this is  based on the initial and continuing loss as provided by the user.  In this case, I’ve specified IL = 10 mm and CL = 2 mm/h for the pervious areas.   These losses, and the hyetograph, are misleading where a sub-catchment has some impervious component.  In this case, for a 100% impervious sub-area, both IL and CL are set to zero by the program.  It would be best not to display the misleading hyetograph, which can be turned off as shown in Figure 4.

FInure 3: RORB output

Figure 4: The hyetograph can be toggled off using the button outlined in pink

If a sub-area is a combination of both impervious and pervious surfaces, this must be specified to RORB as a Fraction Impervious (Fi).  The initial and continuing losses are scaled based on this fraction.

$IL_i = (1 - F_i) I\!L_{perv}$
$CL_i = (1 - F_i) C\!L_{perv}$

Where $I\!L_{perv}$ and $C\!L_{perv}$ are the initial and continuing losses for pervious areas as input by the user.

For example, if the pervious value of IL is set to 10 mm and CL to 2 mm/h, then for a sub-area with a Fraction Impervious value of 60%, the initial and continuing losses will be:

$I\!L = (1 - 0.6) \times 10 = 4 \; \mathrm{mm}$
$C\!L = (1 - 0.6) \times 2 = 0.8 \; \mathrm{mm/h}$

The continuing loss is 0.8 mm/h which is 0.4 mm per 30 min time step.

Running the model with these parameters results in a rainfall excess hydrograph as shown in Figure 5.  Note that the start of the rise of the hydrograph is delayed because of the initial loss.  The peak is reduced by a small amount (from  108 cumec to 106 cumec because of the continuing loss).

Example calculation, flow peak:

$\frac{1}{3.6} \times \frac{1}{0.5} \times (19.4 - 0.4) \times 10 = 105.6 \mathrm{m^3 s^{-1}}$

Figure 5: Rainfall excess hydrograph

For a real catchment with a 60% fraction impervious, we would expect some early runoff from the impervious surfaces that would provide flow directly into the urban drainage system.  RORB doesn’t model this process, which may not matter, depending on the application, but as modellers we need to be aware of this limitation.

Calculations are available as a gist.

## 2 thoughts on “Modelling impervious surfaces in RORB”

1. lukecunninghamwt

Hi Tony,
Great post again. In rainfall on grid hydraulic modelling, we take the rainfall runoff equations from RORB to apply the CL/IL or RoC/IL approach across the model’s grid. As each grid cell is assigned a FI, in the earlier stages of the event when RORB doesn’t show the early runoff, the hydraulic model might show excess runoff starting to form on roads and driveways first, and so on – it can look quite cool and is a good check that your losses are working well. But… as you mentioned, in the scheme of things, it probably makes very little difference to the peaks as the total volume runoff isn’t changing between the methods of course, especially in urban environments where IL is probably pretty low anyway!