What is the regional maximum flood?

It is an upper-envelope flood peak for a catchment of a given size in a given flood region. Kovács (1988) grouped the highest recorded floods in Southern Africa into regions with a characteristic K-value and drew envelope curves above them. Du Plessis & Masule (2023) revised the regions and fitted new region-specific curves. The result is a single discharge, used as a check on design floods rather than as one.

What return period does the RMF have?

None is assigned. The RMF is an envelope, not a quantile of a frequency distribution. Du Plessis & Masule (2023) estimated the return periods implied by their revised envelopes at gauged sites and found a median of about 1:5 000 years, with individual stations ranging from under 1:100 to over 1:500 000 years. Do not attach a return period to an RMF in a report.

What changed between Kovács (1988) and RMF 2023?

Kovács used one continuous Francou-Rodier formula in which K sets the exponent. Du Plessis & Masule (2023) checked it against a larger flood-peak database, redrew the K-regions and replaced the single formula with a transition-zone and a flood-zone power curve for each K, each valid over its own area range. Studio's calculator evaluates the 2023 curves; a design flood estimate reports both revisions.

How is the K-value chosen?

K is read from the K-region polygon that contains the outlet, or the catchment centroid if you only supply a polygon. If one of the seven mapped river reaches with its own K lies within 500 m of that point and its K differs from the region's, the reach value is used and both are shown. You can override K by hand where a local study justifies it.

Can I design a structure for the RMF?

Not for routine drainage. An RMF-sized culvert or bridge would be far larger than a 1:50 or 1:100-year design requires. Use the RMF to check that your design floods sit sensibly below the envelope, and in dam safety work, where SANCOLD guidance uses it alongside the probable maximum flood to set the safety evaluation flood.

Regional Maximum Flood (RMF): K-Regions and Envelope Curves

How the regional maximum flood works

Francou and Rodier (1967) plotted the largest recorded floods in the world against catchment area and found that, on log scales, the envelope of each hydrologically similar region converges towards a common point. Kovács (1988) applied the idea to Southern Africa in DWA Technical Report TR 137. He grouped the highest recorded flood peaks into regions and gave each a K-value: the higher the K, the larger the floods a catchment of a given size has produced. His envelope took the Francou-Rodier form

Q = Q_0 \left( \frac{A}{A_0} \right)^{1 - 0.1K}

with $Q_0$ and $A_0$ the Francou-Rodier reference discharge and area.

Du Plessis and Masule (2023) checked that formula against an extended flood-peak database, found it inconsistent across catchment sizes, and replaced it. Each K now has two power curves fitted 15 % above the highest observed peak in its region, one for a transition zone of smaller catchments and one for a flood zone of larger ones:

Q_{RMF} = C \, A^{\,n}

Symbol	Meaning	Units
$Q_{RMF}$	Regional maximum flood peak	m³/s
$A$	Catchment area	km²
$C$	Envelope coefficient for the K-region and zone	m³/s, with $A$ in km²
$n$	Envelope exponent for the K-region and zone	–
$K$	Regional flood envelope value, 2.8 to 5.8	–

There is no area-dependent curve below 1 km² (the storm zone), so a catchment smaller than that is reported at the 1 km² value of its transition curve.

The 2023 envelope curves (Du Plessis & Masule Table 6)

These are the curves Studio evaluates. Regions mapped below 2.8 use the K = 2.8 curves.

K	Transition zone	Transition range (km²)	Flood zone	Flood range (km²)
2.8	$Q = 10.3\,A^{0.44}$	1 – 500	$Q = 1.7\,A^{0.72}$	500 – 600 000
3.4	$Q = 12.6\,A^{0.52}$	1 – 500	$Q = 5.3\,A^{0.66}$	500 – 600 000
3.6	$Q = 15.1\,A^{0.53}$	1 – 500	$Q = 7.6\,A^{0.64}$	500 – 10 000
3.8	$Q = 17.7\,A^{0.54}$	1 – 500	$Q = 11.0\,A^{0.62}$	500 – 80 000
4.0	$Q = 20.2\,A^{0.56}$	1 – 500	$Q = 15.9\,A^{0.60}$	500 – 80 000
4.2	$Q = 22.8\,A^{0.58}$	1 – 200	$Q = 22.9\,A^{0.58}$	200 – 80 000
4.4	$Q = 26.1\,A^{0.61}$	1 – 200	$Q = 33.1\,A^{0.56}$	200 – 80 000
4.6	$Q = 29.5\,A^{0.63}$	1 – 200	$Q = 47.9\,A^{0.54}$	200 – 80 000
4.8	$Q = 32.8\,A^{0.69}$	1 – 80	$Q = 69.2\,A^{0.52}$	80 – 80 000
5.0	$Q = 36.1\,A^{0.73}$	1 – 80	$Q = 100.0\,A^{0.50}$	80 – 80 000
5.2	$Q = 39.1\,A^{0.78}$	1 – 80	$Q = 144.5\,A^{0.48}$	80 – 10 000
5.4	$Q = 42.8\,A^{0.87}$	1 – 50	$Q = 208.9\,A^{0.46}$	50 – 10 000
5.6	$Q = 46.1\,A^{0.92}$	1 – 50	$Q = 302.0\,A^{0.44}$	50 – 10 000
5.8	$Q = 49.4\,A^{0.98}$	1 – 50	$Q = 436.5\,A^{0.42}$	50 – 10 000

The boundary between the zones moves with K, from 500 km² in the arid regions to 50 km² in the wettest. A catchment larger than the flood-zone range is extrapolated, and the result says so.

Inputs and where they come from

The calculator needs two things: the catchment area and the K-value.

Area: enter it, upload the catchment as GeoJSON or Shapefile (the area is computed from the polygon), or pick a saved watershed delineation.
K-value: read automatically from the K-region map at the outlet, or at the centroid when only a polygon is given. The map is the NaFSAT 2.0 RMF layer: 27 polygons in 15 K classes, from below 2.8 in the arid west to 5.8 on parts of the coast.
River reaches: seven reaches carry their own K where recorded floods justify it: the Riet (4.2 in a 3.6 region), the Orange (4.4 in 3.4), the Sand (4.6 in 4.4), the Vet (4.4 in 4.2), the Mooi (4.6 in 3.6) and two reaches of the Modder (4.2, and 5.4 in a 5.0 region). If the lookup point is within 500 m of a reach whose K differs from the region’s, the reach K is applied and both values are reported.

Worked example

A catchment in the KZN Midlands

A hypothetical 85 km² catchment has its outlet near 29.62° S, 30.12° E. The lookup returns K-region 5.0 and no differing river reach within 500 m.

For K = 5.0 the transition zone ends at 80 km², so 85 km² is in the flood zone:

Q_{RMF} = 100.0 \times 85^{0.50} = 100.0 \times 9.22 = 922 \text{ m}^3/\text{s}

The calculator also tabulates the RMF at the same area for neighbouring K-values:

K	4.6	4.8	5.0	5.2	5.4
$Q_{RMF}$ (m³/s)	485	697	922	1 219	1 612

One K step either side moves the answer by 24 to 32 %. If the outlet were close to a region boundary, that table is the honest statement of uncertainty to put in the report.

When a river reach overrides the region

A point on the Mooi River reach just south of Potchefstroom sits in K-region 3.6, but the reach carries K = 4.6. Evaluated at 1 000 km² for comparison, the region value gives 632 m³/s and the reach value gives 1 997 m³/s, a factor of 3.2. The 500 m rule exists because recorded floods on that river exceed what its surrounding region would suggest, so check which value applies before you sign off.

Using the RMF alongside design floods

The RMF bounds the other methods; it does not replace them. Compare it with the 1:100 and 1:200-year peaks from a design flood estimation, the QRT calculator or the Index Flood method. A 1:100-year estimate close to or above the RMF usually means an input is wrong (area, rainfall or coefficient) or the catchment is unusual for its region.

In dam safety work the RMF is one of the two bases SANCOLD guidance uses for the safety evaluation flood, the other being the probable maximum flood built from the probable maximum precipitation. The dam safety evaluation can set its safety evaluation discharge on either basis, linking a saved RMF calculation for the RMF basis.

Limitations

The K-regions come from the Southern African flood record and cannot be transferred to other continents. The Studio calculator runs for sites in South Africa.
The envelope has no return period, and the implied return periods vary by orders of magnitude between gauges.
One step in K changes the RMF by tens of percent, so a region boundary or a nearby river reach matters more than any decimal in the area.
Each curve is validated up to its flood-zone maximum, between 10 000 and 600 000 km² depending on K. Larger catchments are extrapolated and flagged.
Below 1 km² no area-dependent curve exists, so very small catchments all get the 1 km² value.
The 2023 K-region boundaries differ from the 1988 map in places, so an older report may quote a different K for the same site.

What the full Studio tool adds

The calculator shows the K-regions and river reaches on a map, takes the outlet from a click, typed coordinates, an uploaded polygon or a saved watershed, and offers a K-only lookup when you just need the region during site selection. The result states the K source, the zone, the exact equation evaluated, any extrapolation warning and the Q-versus-K table. Calculations save to your projects and export to CSV, Word and Excel.

Inside a design flood estimation the RMF is reported in both revisions, Kovács (1988) and RMF 2023, with the same K provenance, zone and sensitivity table, so the envelope sits next to every other method’s peak for the catchment.

Regional maximum flood calculator

How the regional maximum flood works

The 2023 envelope curves (Du Plessis & Masule Table 6)

Inputs and where they come from

Worked example

A catchment in the KZN Midlands

When a river reach overrides the region

Using the RMF alongside design floods

Limitations

What the full Studio tool adds

Common questions

References

Keep the whole study in one place

Regional maximum flood calculator

How the regional maximum flood works

The 2023 envelope curves (Du Plessis & Masule Table 6)

Inputs and where they come from

Worked example

A catchment in the KZN Midlands

When a river reach overrides the region

Using the RMF alongside design floods

Limitations

What the full Studio tool adds

Common questions

References

Related tools

Keep the whole study in one place