Probable maximum precipitation in South Africa

What the calculator returns

The calculator returns a 1-day probable maximum precipitation depth in millimetres. The data are the Johnson and Smithers (2020) point PMP values: 45 499 grid points at about 0.05° spacing (about 5.6 km north to south and 5 km east to west) covering South Africa, Lesotho and Eswatini, with depths from 42.1 mm on the dry west coast to 1 821.9 mm on the Soutpansberg. The Studio tool accepts sites between latitudes 22° S and 35.5° S and longitudes 16° E and 33.5° E.

You choose how the grid is read:

The interpolated value is

In point mode you can switch individual grid points off, for example one that sits across a ridge from your site, and the weights are recomputed from the rest. No areal reduction is applied and no other duration is derived: the output is a 1-day point depth.

When you need a PMP

A probable maximum precipitation depth is needed when a failure would be catastrophic and the design criterion is written in terms of the probable maximum flood. In South Africa that means mainly dams: the safety evaluation of a dam with a safety risk under the Dam Safety Regulations, where the SANCOLD category sets the fraction of the PMF the dam must survive. It is also the starting point for checking an existing spillway that was sized before the current grid existed.

It is not a design input for culverts, bridges, stormwater systems or channels. Those are designed for return-period floods from design rainfall, and using a PMP for them produces structures far larger than any standard requires. Where an upper bound is wanted for a road or bridge, the regional maximum flood is the usual check.

How PMP is estimated

WMO Manual 1045 covers hydrometeorological methods and a statistical method. The hydrometeorological approach takes major observed storms, scales each one up to the maximum moisture the atmosphere could have supplied (moisture maximisation), transposes it to the site and envelopes the results. The statistical approach, from Hershfield (1961), works from long annual-maximum rainfall series:

The derivation of the South African 1-day grid is set out in Johnson and Smithers (2020). Earlier South African practice used generalised PMP maps prepared in the 1970s, so a site’s depth in an old dam safety report may not match the grid.

Reference table: 1-day PMP at selected centres

Interpolated values (the calculator’s default mode, to 0.1 mm) from the grid at the coordinates given. They show how much the depth varies across the country, and why a lookup at your own site matters: Gqeberha and East London are about 240 km apart on the same coast and differ by a factor of more than six.

Worked example: a dam site in the KZN Midlands

The site is at 29.6218° S, 30.1244° E. The four nearest grid points are:

The nearest-point mode would return 1 010.0 mm. The four points span 725 to 1 010 mm within 5.3 km, so for this dam the catchment-average mode over the actual catchment boundary is the better input to a PMF than either point value.

From PMP to the probable maximum flood

The SANCOLD (1986) interim guidelines express the safety evaluation flood for a dam as a fraction of the probable maximum flood, from 0.2 for a small low-hazard dam to 1.0 for medium high-hazard dams and large dams of significant or high hazard. The SANCOLD (1991) guidelines require the PMF itself for those dams and scale it down for the others, so the PMF is the number a dam engineer needs. The calculator stops at the rainfall depth. Turning it into a PMF takes the usual rainfall-runoff steps, each of which needs its own justification in a dam safety report:

1. Convert the 1-day point depth to the storm durations that matter for the catchment, and reduce it for the storm area with an areal reduction factor.
2. Distribute the depth in time with a design storm pattern from the design storm generator.
3. Apply losses for wet antecedent conditions and convert the excess to a flood hydrograph, for example with the unit hydrograph generator.
4. Route the hydrograph through the reservoir and check the spillway and freeboard in a dam safety evaluation.

A Rational-formula PMF needs the PMP for a storm lasting $T_c$. The 1-day depth divided by a $T_c$ of a few hours is not that number and will overstate the peak, so derive the storm-duration depth first.

Limitations

• Only the 1-day duration is available, as a point value. Shorter or longer durations and areal reduction are your responsibility.
• The grid spacing is about 5 km, and neighbouring points can differ by hundreds of millimetres: two adjacent points in the KZN Midlands example differ by 205 mm.
• The grid reflects the historical record used by Johnson and Smithers (2020). Any allowance for climate change is a separate engineering decision.
• For a high-hazard dam, a published grid is a screening input. Confirm with the DWS Dam Safety Office whether a site-specific PMP study is required.
• Coordinates outside latitudes 22–35.5° S and longitudes 16–33.5° E are rejected. Inside that box a site beyond the grid still gets the values of the nearest grid points, however far away (49 km at Maputo), so check the distances the calculator reports.

What the full Studio tool adds

The calculator draws the grid on the map with the points it used and their weights, accepts a point by click or coordinates, or a catchment from an uploaded polygon or a saved watershed delineation. Results save to your projects, export to CSV, Word and Excel, and the grid points used export as GIS points. The depth can be sent straight to the PMF step of a dam safety evaluation, where the regional maximum flood gives the second, independent upper bound.