RMF Calculator

Open RMF Calculator

Estimate the Regional Maximum Flood (RMF) peak discharge for Southern African catchments using the Kovacs / Francou-Rodier envelope methodology. This guide covers the 27 K-value regions, the three flood zones (Storm, Transition, Flood), the 500 m river-segment override rule, the three K-value determination modes, and how to interpret the result as an upper-bound check flood for dam safety and critical infrastructure.

Overview

The RMF Calculator estimates the Regional Maximum Flood (RMF) peak discharge for a catchment using the Francou-Rodier envelope methodology. Originally developed by Francou and Rodier (1967) using over 1 200 recorded flood peaks worldwide, this method was adapted for Southern Africa by Kovacs (1988) and subsequently revised in the RMF-2023 update.

The tool divides Southern Africa into 27 K-value regions based on flood envelope characteristics, with K-values ranging from below 2.8 (arid Kalahari) to 5.8 (high-rainfall coastal zones). Additionally, 63 river segments with verified K-values are overlaid on the regional map to provide more precise estimates near specific rivers where observed flood data justify a departure from the surrounding regional envelope.

What is RMF?

The Regional Maximum Flood provides an upper-envelope estimate of the maximum flood peak discharge that can be expected at a given catchment, based on regional flood characteristics. It represents the most severe flood event considered plausible for a given catchment size and hydrological region — not a probabilistic quantile.

When to use RMF

RMF is commonly used as a check flood or upper-bound estimate in dam safety assessments, spillway sizing, road and bridge design for critical links, and other high-consequence infrastructure. It provides a deterministic (non-probabilistic) estimate that represents the maximum credible flood for a region, and is typically compared against the Probable Maximum Flood (PMF) derived from the PMP Calculator and the probabilistic quantiles from the Flood Frequency Analysis or Index Flood Calculator.

The K-value is the key regional parameter. Higher K-values indicate regions with greater flood-producing potential relative to catchment size:

• K < 3.0 — Arid regions with low flood potential (Kalahari, Central Botswana)
• K = 3.0 – 4.5 — Interior regions with moderate flood potential
• K = 4.5 – 5.0 — Highveld regions with significant rainfall
• K > 5.0 — Coastal and high-rainfall regions with high flood potential
• K = 6.5 — World-recorded flood peak envelope (Francou-Rodier global upper bound)

K-value regions

Southern Africa is divided into 27 K-value regions, each representing a hydrologically homogeneous zone with a characteristic K-value. These regions were established based on analysis of the 300 highest recorded flood peaks in South Africa (1894 – 1979) by Kovacs (1988), and subsequently updated in the RMF-2023 revision.

Region map

The interactive map in the RMF Calculator displays all 27 K-value regions with a sequential colour scale from yellow (low K) to purple (high K). River segments with verified K-values are shown as dashed lines overlaid on the regions, so you can see at a glance where a river-specific override will apply.

K-value ranges by region

Region description	K-value range
Central Botswana (special zone)	< 2.8
West Coast Namibia	2.8 – 3.4
SA Kalahari / Interior	3.6 – 4.0
Northern Interior / Limpopo	4.2 – 4.4
SA Highvelds	4.6 – 5.0
Southeastern Coastal Belt	5.0 – 5.4
High-rainfall Coastal	5.6 – 5.8

Special zones

Regions with K < 2.8 (Central Botswana) represent very arid zones with minimal flood potential. For calculation purposes, K = 2.8 is used as the minimum value.

Calculation methodology

The RMF is calculated using the Francou-Rodier envelope formula, which relates the maximum flood peak discharge to catchment area and a regional K-value coefficient. The method identifies three distinct flood zones based on catchment size.

Francou-Rodier formula

The fundamental relationship for the Flood Zone (A > 100 km²):

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

Francou-Rodier envelope formula

Where $Q_0 = 10^6$ m³/s is the reference discharge, $A_0 = 10^8$ km² is the reference area, $A$ is the catchment area in km², and $K$ is the regional K-value coefficient.

Substituting the reference values:

$$Q \;=\; 10^6 \cdot \left(\frac{A}{10^8}\right)^{1 - 0.1K}$$

Francou-Rodier formula (simplified)

Note that as $K$ increases, the exponent $(1 - 0.1K)$ decreases, which flattens the Q-A curve — more flood-prone regions produce larger floods from smaller catchments relative to the global envelope.

Flood zones

The Francou-Rodier diagram identifies three distinct zones on the Q-A plane:

Zone	Area range	Description
Storm Zone	< 1 km²	Peak discharge depends primarily on rainfall intensity
Transition Zone	1 – 100 km²	Smooth transition between Storm and Flood-zone envelopes
Flood Zone	> 100 km²	Standard Francou-Rodier formula applies directly

The calculator automatically selects the correct zone formulation based on the catchment area you supply and reports the zone alongside the peak flow.

River K-value override

Some river reaches have verified K-values that differ from their surrounding regional K-value, typically based on observed flood peaks on that specific river. The calculator includes 63 such river segments with K-values of 4.2, 4.4, 4.6, and 5.4.

500 m proximity rule

If the outlet point is within 500 metres of a river segment with a different K-value than the surrounding region, the river K-value is automatically applied. A prominent warning is displayed showing both the regional and river K-values so you can decide whether to accept the override or revert to the regional value.

Input parameters

Parameter	Unit	Range	Description
Catchment Area (A)	km²	> 0	Total catchment area upstream of the outlet
K-value	—	2.8 – 5.8	Regional flood envelope coefficient
Outlet Point	lat, lng	Within SA / SADC	Location for K-value lookup (click map or enter coordinates)

Two calculation modes

K-value lookup only: Determine the K-value for a location without calculating the flood discharge. Useful for quick regional checks during site selection.

Full RMF calculation: Provide both K-value and catchment area to calculate the peak discharge $Q$ in m³/s.

K-value determination

The calculator offers three ways to determine the K-value for your catchment.

Manual / map click

Click directly on the interactive map to place your outlet point, or enter latitude and longitude coordinates manually. The tool will automatically look up the K-value from the regional map and check for nearby rivers within 500 m. You can also select a K-value from the dropdown to override the auto-detected value if you have local information.

Polygon upload

Upload a GeoJSON or Shapefile containing your catchment boundary polygon. The tool will calculate the polygon’s centroid and use it to determine the K-value. The catchment area will also be calculated automatically from the polygon geometry — useful when you already have a delineated boundary from GIS work.

Supported formats

GeoJSON files (.geojson, .json) and Shapefiles (.shp, with sidecars) are supported. The polygon must be in WGS84 (EPSG:4326) coordinates.

From watershed

If you have previously saved a watershed delineation using the Watershed Delineation tool, you can select it directly. The outlet point and catchment area will be loaded automatically, and the K-value will be determined from the outlet location. This is the most efficient workflow when the RMF is part of a larger design-flood analysis.

Interpreting results

The calculator produces several outputs:

• Peak discharge $Q$ (m³/s) — the Regional Maximum Flood peak discharge for your catchment. This is a deterministic upper-envelope estimate, not a probabilistic design flood.
• K-value source — shows whether the K-value came from the regional map, a nearby river override, or manual selection.
• Flood zone — indicates which of the three zones (Storm, Transition, or Flood) your catchment falls into based on its area.
• Q vs K comparison table — shows the RMF discharge for all standard K-values, allowing you to see how sensitive the result is to the K-value choice.

Important consideration

The RMF is an upper-envelope estimate representing the maximum credible flood for a region. It should not be used directly as a design flood for routine infrastructure — that would lead to grossly over-sized structures. For probabilistic design floods, use the Flood Frequency Analysis, Index Flood Calculator, Rational Method, or SDF Method with appropriate return periods, and use the RMF only as a check against the largest quantile from those methods.

Saving and exporting

Results can be saved to your account for future reference and downloaded as CSV files. The CSV includes methodology references, input parameters, K-value source information, and the calculated discharge — suitable for inclusion in a design report appendix.

Limitations

• Southern Africa only — the K-value regionalisation is calibrated against the SA / Southern African flood record and cannot be transferred to other continents.
• Deterministic envelope — the method provides no associated probability or return period; it is a “worst plausible” value, not a quantile.
• Sensitivity to K — a 10% change in K can shift the RMF by a factor of ~2 for large catchments, so the K-value override check at river segments is important.
• Age of the underlying data — the Kovacs envelopes are based on floods observed up to 1979; more recent extremes may or may not remain below the published envelope.

References

• Francou, J. & Rodier, J.A. (1967). Essai de classification des crues maximales observées dans le monde. Cahiers ORSTOM, Série Hydrologie, IV(3), 19 – 46.
• Kovacs, Z.P. (1988). Regional Maximum Flood Peaks in Southern Africa. Technical Report TR137, Department of Water Affairs, Pretoria. 519 sites analysed (354 from South Africa), 300 highest flood peaks (1894 – 1979).
• RMF-2023 Revision. Updated Regional Maximum Flood methodology for Southern Africa. Includes revised K-value zones, special zones (K < 2.8 for Central Botswana, K < 3.4 for West Coast Namibia), and river-specific K-value adjustments.
• Alexander, W.J.R. (2002). The Standard Design Flood. Journal of the South African Institution of Civil Engineering, 44(1), 26 – 30.
• SANCOLD. (1991). Guidelines on Safety in Relation to Floods. South African National Committee on Large Dams, Pretoria.

---

Open RMF Calculator