# How many sub-catchments does my RORB model need?

First, let’s consider the required minimum number of sub-catchments required for RORB modelling.

If the number of sub-catchments is too small then hydrographs may appear to be too similar to the time series of rainfall inputs i.e. they will appear to fluctuate unrealistically.  The RORB manual (section 7.2, item 11) notes that:

It is recommended that at least 5 sub-areas be placed above any hydrograph printout point to allow sufficient smoothing and attenuation of the rainfall excess hyetographs.

The RORB manual suggests that between 5 and 20 sub-catchments are usually sufficient to allow for areal variation of rainfall, losses, and the effects of varying flow distance to the catchment outlet

Too few sub-catchments can  cause numerical instabilities. Dyer (1994)1 investigated this problem and suggested the following minimum number of sub-catchments as a function of catchment area.

 Area (km2) Minimum number of sub-catchments 44.3 5 153 6 259 6 692 7 1140 10

Boyd (1985)2 also developed a table of the minimum number of sub-catchments which are more conservative than Dyer’s values.

 Area (km2) Minimum number of sub-catchments 0.1 4 10 7 1000 10

A line fitted through Boyd’s three points, provides an approximate indication of the least number of sub-catchments as a function of area:

$S_{min} = 5.20(A)^{0.1}$

Where: Smin is the minimum number of sub-catchments and A is the area is km2.

So there is reasonable guidance on the minimum number of sub-catchments, what about the maximum number? Currently, this is a more significant issue because it is now very easy to generate a large number of sub-catchments using tools such as ArcHydro and CatchmentSim.  One of the drivers for this is that in recent studies, the area where flood mapping is required can be very large.  This is particularly so for the regional studies currently underway in Victoria (Lett and Wilkinson, 2015).  The demand for mapping is also pushing to upstream areas of catchments.  To achieve 3 to 5 sub-catchments upstream of locations where hydrographs are required means a lot of smaller sub-catchments and maintaining a consistent sub-catchment size then requires a large number of sub-catchments across the whole model.

Table 3 contrasts the number of sub-catchments in some older flood studies with those in recent studies.  Although this isn’t a rigorous analysis,  it suggests the number of sub-catchments has increased by an order of magnitude.

Table 3: Sub-catchments in some recent and older studies
Study Year of study Number of
Sub-catchments
Link Location in report
Skipton 2013 104 http://bit.ly/2aE2bm0 p36, Figure 4-1
Castlemaine 2013 420 http://bit.ly/2aE0Rjo Campbells Ck RORB layout
Appendix D1
Rochester 2013 78 http://bit.ly/2aEclmO Section 4.1.1
Strathfieldsaye 1978 11 http://bit.ly/2aEcOFw Figure B.1
Benalla 1984 16 http://bit.ly/2aFl4bN Figure A4
Traralgon Ck 1979 7 to 26 http://bit.ly/2aEgffi Appendix E, E.2
Traralgon Ck 2016 85 http://bit.ly/2aFHxXM Figure 4-1

A key issue is that there is interaction between the number of sub-catchments and RORB parameters such as kc and losses.  Most guides to routing parameters and losses are based on straightforward RORB models with small numbers of sub-catchments.  Hydrologists need to take care when applying recommended values to larger, more complex models.

Weeks, 1980  showed that the number of sub-catchments  can affect model results, in particular, as the number of sub-catchments increased the:

• timing of the flood peak was delayed
• the magnitude of the peak was increased.

Weeks had to increase the kc parameter to maintain the estimated peak discharge when comparing model results with a historical event.

The issue was also investigated in a report on modelling of floods in Traralgon Creek which showed similar results, but work by Yu3 suggests a greater number of sub-catchments could increase or decrease the flood peak depending on how the catchments were connected.  Norris and Haan (1993), showed an initial increase in peak flow as the number of sub-catchments increased and then stable results following further increases.  Boyd et al. (1979) also found that results were stable to further sub-division following initial initial region of change.

In summary, the key messages are:

1. A large number of sub-catchments may delay the flood peak.
2. (A corollary of 1) if the calculated flood appears to be greatly delayed, it may be worth reducing the number of sub-catchments.
3. A large number of sub-catchments may increase or decrease the flood peak depending on the model layout.
4. Changing the kparameter may compensate for the effect of the number of sub-catchments on flood peak.
5. (A corollary of 3) if the number of sub-catchments differs between models, expect to use different kparameter values.
6. Use a minimum of 5 sub-catchments upstream of a location where a hydrograph is to be printed.
7. Ensure you have at least the minimum number of sub-catchments appropriate for the size of the catchment being modelled e.g. those in Table 2.

There are also related guidance in Australian Rainfall and Runoff (1987 edition, Book V, Section 3):

• No sub-catchment should be longer than about one third the length of the main stream.
• Sub-catchments should be all of the same order of size, and none should be larger than about 25% of the total catchment area.

### Acknowledgement

Thank you to Ben Tate for helpful comments.

### References

1. Dyer, B. G. (1994) Regionalisation of parameters for the RORB runoff routing model.  Thesis (PhD). University of Melbourne.
2. Boyd, M. J. (1985) Effect of catchment sub-division on runoff routing models. Civil Engineering Transactions CE27: 403-410.
3. Boyd, M. J., Pilgrim, D. H. and Cordery, I. (1979) A storage routing model based on catchment geomorphology.  Journal of Hydrology 42:209-230. (link)
4. Yu, B. (1994) Effects of catchment subdivision on rainfall-runoff routing results.  8th Queensland Hydrology Symposium. Griffith University, 29-30 June 1994.
5. Lett, R. and Wilkinson, S. (2016) Filling in the gaps – Victoria’s regional flood mapping program.  2016 Floodplain Management Association Conference. (link at FMA) (link at Wayback Machine).