This blog builds on the previous post; looking at the runoff coefficient approach to modelling losses and the implications for representing impervious surfaces in the RORB model.

In addition to the IL/CL model discussed in the previous post, RORB can be run using an initial loss / runoff coefficient model, where the runoff coefficient specifies the proportion of rainfall lost in each time step after the initial loss is satisfied. This reason these different loss models are of interest is that the new version of Australian Rainfall and Runoff is recommending that the IL/CL model is used in place of the runoff coefficient model (Book 5, Section 3.3.1). In some areas, modelling approaches will need to change and this will have implications for flood estimates.

The runoff coefficient loss model is selected as shown in Figure 1.

Figure 1: A runoff coefficient loss model can be selected in RORB

The user inputs the runoff coefficient, *C*, for a pervious surface. For an impervious surface, there is no opportunity to specify the runoff coefficient which is hard-wired in RORB as 0.9. For mixed sub-areas, the runoff coefficient is scaled, the equations from the RORB manual are:

Where *C*_{i} is the runoff coefficient for the i^{th} sub-area.

Example: For a fraction impervious, and

The initial loss is calculated as as a weighted average of the pervious and impervious initial losses as shown in the previous post. The impervious initial loss is always set to zero in RORB.

Let’s do the calculations for a 100% impervious surface. RORB will set and . Using the 6 hour, 1% rainfall as before, the rainfall excess hyetograph is shown in Figure 2.

Figure 2: Rainfall excess hyetograph for an impervious surface using the runoff coefficient model. RORB sets IL to zero and the the runoff coefficient to 0.9 so 10% of rain is lost at each time step

Example calculation:

As explained in the previous post, the rainfall between 1.5 hour and 2 hour is 19.4 mm. With a runoff coefficient of 0.9, the rainfall excess will be: 0.9 x 19.4 = 17.5 mm.

The rainfall excess hydrograph from a 10 km^{2} impervious sub-area can be calculated from the rainfall excess hyetograph using the method described in the previous post. The peak flow corresponding to the 17.5 mm rainfall peak is 97.2 m^{3}s^{-1} (see the previous post for sample calculations).

The key point is that we have changed the peak flow from an impervious surface, just by changing the loss model. With the IL/CL model, both initial and continuing loss for a 100% impervious surface are hard-wired to zero. The peak runoff was 107.8 m^{3}s^{-1}. For the runoff coefficient model, initial loss is hard-wired to zero, but the runoff coefficient is hard-wired to 0.9, i.e. we have some loss from the impervious surface. This changes the hydrograph as shown in Figure 3.

Figure 3: Comparison of rainfall excess hydrographs from a 100% impervious surface; same rainfall, different loss model

The value of the runoff coefficient for an impervious surface is noted in the RORB manual:

The impervious area runoff coefficient *C*_{imp} is set by the program to 0.9, reflecting the fact that losses occur even on nominally impervious surfaces in urban areas.

This is reasonable, but inconsistent with the treatment of the continuing loss when the IL/CL loss model is used. In this case, *CL* is hard-wired to zero so there are no losses from impervious surfaces; a feature of RORB for modellers to be aware of.

Also note Equation 3.6 above. This suggests that if the user inputs a runoff coefficient larger than the impervious coefficient (i.e. larger than 0.9) then a value of 0.9 will be used. This isn’t actually implemented. If a runoff coefficient of 1 is input, there is a direct conversion of rainfall to runoff i.e. there is no loss. It is even possible to input runoff coefficients greater than 1.

Equation 3.6 may just be the result of a typo. Some experimenting suggests the behaviour in the model is represented the combination of equation 3.5, above and the following in place of equation 3.6:

That is, the runoff coefficient for an impervious surface is 0.9 unless the runoff coefficient input by the user is larger than 0.9.

Calculations are available via a gist.