PMP Calculator

Open PMP Calculator

Look up the 1-day Probable Maximum Precipitation for any location in South Africa. This guide covers the definition of PMP, the four main estimation methods (WMO hydrometeorological, Hershfield statistical, HRU 1/72 generalised, and the SA gridded dataset), depth-duration-area relationships, moisture maximisation and storm transposition, temporal and spatial distribution of PMP storms, the use of PMP to derive the Probable Maximum Flood (PMF) for dam-safety applications, climate-change caveats, and a worked example for a KwaZulu-Natal dam site.

Overview

Probable Maximum Precipitation (PMP) is defined by the World Meteorological Organization (WMO Manual No. 1045, 2009) as “the greatest depth of precipitation for a given duration that is physically possible over a given size storm area at a particular geographic location at a certain time of year.” PMP is a theoretical upper bound — not a statistical return-period value. It has no formally assigned probability of exceedance, though practical PMP estimates are sometimes informally associated with annual exceedance probabilities in the range 1 × 10⁻⁵ to 1 × 10⁻⁷ for large areas and long durations.

PMP is used in the design of hydraulic structures where the consequences of failure are catastrophic: the Probable Maximum Flood (PMF) derived from PMP is the design flood standard for nuclear power plant cooling systems, for the Safety Evaluation Flood (SEF) of Category II and III dams in South Africa (per SANCOLD Report 4, 1991), and for the upper-bound check on spillway and auxiliary-spillway capacity for high-hazard civil infrastructure. It is not used for routine stormwater design, small bridges, or culverts — those are governed by return-period events from the Design Rainfall IDF curves.

The HydroDesign PMP Calculator is a 1-day PMP lookup tool: it returns the 24-hour PMP depth at any point in South Africa by querying a gridded dataset of 45 499 points covering the country at approximately 2 to 5 km spacing. Sub-daily and multi-day PMP values can be derived from the 1-day PMP using empirical depth-duration relationships described below.

PMP is a design ceiling, not a forecast

PMP is the theoretical maximum precipitation under idealised atmospheric conditions — full saturation, the maximum observed precipitation efficiency, and the maximum dew point for the season. It is a ceiling on what is considered physically possible, not a statement that such a storm has occurred or is expected. Actual observed storms are typically 40 to 80 percent of the co-located PMP; storms exceeding 100 percent of the published PMP at any point do occur occasionally and trigger re-estimation of the PMP at that location.

When to use PMP

PMP and the PMF derived from it are required for:

• Dam safety evaluation of high-hazard (Category III) dams — the SEF is expressed as a fraction of the PMF, up to 1.1 × PMF for large high-hazard dams. See the Dam Safety Evaluation guide for the SANCOLD tabulation.
• Medium-hazard (Category II) dam SEF — 0.5 to 1.0 × PMF depending on size / hazard combination.
• Nuclear power plant cooling systems and critical process water — regulatory bodies (the NNR in South Africa, NRC in the US) require PMF-level protection.
• Major industrial hazardous-materials facilities — stormwater containment at chemical plants, tailings storage facilities with long-term environmental risk.

PMP is not used for:

• Stormwater pipes, culverts, small bridges — use 1:10 to 1:100 year Design Rainfall.
• Routine channel design — use 1:50 to 1:100 year IDF.
• Small farm dams (SANCOLD Category I) — the SEF is a fraction of PMF ranging from 0.2 to 0.7, but the PMF itself is the computational input.

Right-sizing is an ethical obligation

Using PMP for a problem that calls for a return-period event produces comically oversized infrastructure and wastes public / client money. Using a return-period event for a problem that calls for PMP produces inadequate infrastructure that can fail catastrophically. The SANCOLD Category and the regulatory framework determine which is appropriate — use them. If you are unsure, err on the side of the more rigorous method and document the choice.

Definition and physical basis

PMP at a location depends on four physical inputs:

1. Moisture availability — the maximum atmospheric water vapour content that could be advected into the storm area, usually characterised by the maximum persisting 12-hour 1000-mb dew point.
2. Precipitation efficiency — the fraction of advected water vapour that actually precipitates during a storm event; controlled by lifting mechanism, condensation efficiency, and microphysics.
3. Wind and inflow — the rate at which moist air is advected into the storm area, determined by synoptic-scale wind patterns and the orientation of the storm relative to moisture sources.
4. Topography and geographic setting — orographic lift enhances precipitation on windward slopes; rain shadows depress it on leeward slopes.

The precipitable water in an atmospheric column is related to the surface dew point temperature via a near-exponential relationship:

$$W_p \;\approx\; 2.18 \cdot \exp(0.0614 \cdot T_d) \qquad (mm, T_d \text{ in } ^\circ C)$$

Precipitable water from dew point (WMO 1045, Annex 1)

This is the foundation of moisture maximisation: if a historical storm occurred with dew point $T_{d,\text{obs}}$ and produced rainfall depth $P_{\text{obs}}$, and the maximum persisting dew point at that location is $T_{d,\text{max}}$, then the moisture-maximised depth is:

$$P_{\text{max}} \;=\; P_{\text{obs}} \cdot \frac{W_p(T_{d,\text{max}})}{W_p(T_{d,\text{obs}})}$$

Moisture maximisation ratio

Moisture maximisation is the most physically-defensible of the PMP estimation methods and is the basis of the WMO hydrometeorological procedure.

Estimation methods

Four main methods are used to estimate PMP, each with different data requirements, applicability, and accuracy.

WMO Hydrometeorological method

The WMO Manual No. 1045 (2009) outlines the hydrometeorological approach — the most rigorous and data-intensive PMP estimation method. The procedure:

1. Identify major historical storms in the region or in meteorologically-similar regions (within a few hundred kilometres).
2. Depth-area-duration (DAD) analysis of each storm: extract the maximum rainfall depth as a function of area covered and duration.
3. Moisture maximisation of each storm using the observed dew point and the climatological maximum persisting 12-hour dew point.
4. Storm transposition — shift the storm geographically to the site of interest, with an adjustment for elevation and moisture differences.
5. Envelope the transposed and maximised DAD values to produce the site-specific PMP.

This method produces physically-meaningful upper-bound estimates but requires (a) a substantial historical storm database, (b) reliable dew-point records across the region, and (c) skilled meteorological judgement. It is the method used in the generalised PMP studies for the Mississippi River Basin (US HMR reports), the Indian subcontinent (CWC), and parts of Southern Africa.

Hershfield statistical method

Developed by David Hershfield (1961, 1965) and embedded in Chow, Maidment, and Mays (1988) as a rapid alternative where hydrometeorological data are sparse. PMP is estimated as:

$$P_{\mathrm{PMP}} \;=\; \bar{P}_n \;+\; K_m \cdot s_n$$

Hershfield statistical PMP

where $\bar{P}_n$ and $s_n$ are the mean and standard deviation of the annual maximum $n$-hour rainfall series, and $K_m$ is the Hershfield frequency factor. Hershfield (1961) found $K_m = 15$ from a global sample of annual maximum 24-hour storms; subsequent work (Hershfield 1965, Koutsoyiannis 1999) refined this to:

$$K_m \;=\; f(\bar{P}_n, n)$$

Koutsoyiannis-refined Hershfield factor

with tabulated values depending on the mean and duration (typically 10 to 20).

The Hershfield method is statistically simple — you need only the daily rainfall record — but does not reference physical upper bounds on atmospheric moisture. It is best regarded as an upper-bound frequency estimate rather than a true PMP in the WMO sense, and it is known to underestimate PMP in data-sparse regions.

When Hershfield overestimates

In regions with unusually long, homogeneous rainfall records and a few severe outlier events, the Hershfield PMP can exceed the hydrometeorological PMP. This usually means the outlier events are, themselves, near-PMP storms. Do not reject the Hershfield estimate without meteorological investigation of the outlier events — they may be the key calibration data for a local hydrometeorological PMP.

HRU 1/72 and SA generalised PMP

The Hydrological Research Unit Report 1/72 (1972) — Design Flood Determination in South Africa — contains the original country-wide generalised PMP maps for South Africa. The method combined:

• 1-day PMP maps produced by the South African Weather Bureau (now SAWS) via moisture-maximisation of historical storms.
• Storm-transposition adjustments between homogeneous meteorological regions.
• Depth-duration curves derived from regional storm data.

The HRU 1/72 1-day PMP maps are the basis of SA dam-safety practice, predating the current gridded dataset by four decades. The maps were extensively updated by SAWS and subsequent research (Smithers, Schulze, and colleagues — WRC Report 1060/1/03; Gericke and Du Plessis 2011) to produce the modern gridded product.

Gridded 1-day PMP dataset

The HydroDesign PMP Calculator queries a gridded dataset of 45 499 points covering South Africa at approximately 2 to 5 km resolution. The underlying data are:

• 1-day duration only — other durations must be derived via the depth-duration relations described below.
• Point values — the gridded PMP is a point estimate; for catchment-area averages, an areal-reduction factor (ARF) must be applied.
• Based on SA generalised studies combining WMO hydrometeorological and HRU 1/72 methodology, with updates through 2015.
• Coordinate system — WGS84 lat/lon; nearest-point lookup via geodesic (Haversine) distance, no spatial interpolation between grid points.

Dataset attribute	Value
Grid points	45 499
Approximate spacing	2 – 5 km
Duration	1 day (24 hour)
Spatial extent	South Africa terrestrial
Coordinate system	WGS84
Update cycle	Periodic (5 – 10 years)

The tool returns:

• The 1-day PMP depth (mm) at the nearest grid point to the user’s selected location.
• The coordinates of that grid point and the Haversine distance to the user’s click location.

Sub-daily and multi-day PMP at the site are estimated from the 1-day value using the depth-duration-frequency relationships described in the next section.

Depth-Duration relationships

PMP at durations other than 1 day is estimated from empirical depth-duration curves. For South African PMP estimation, the following relations are commonly used:

$$P_D \;=\; P_{24} \cdot (D / 24)^{m}$$

Generic PMP depth-duration (power-law)

where $P_D$ is the PMP depth for duration $D$ (hr), $P_{24}$ is the 1-day PMP, and $m$ is the duration-scaling exponent. Typical values:

Duration $D$ (hr)	Typical $P_D / P_{24}$ ratio	Equivalent $m$
0.25 (15 min)	0.15 – 0.20	0.40
0.5 (30 min)	0.20 – 0.27	0.40
1	0.28 – 0.38	0.36
2	0.40 – 0.50	0.33
6	0.65 – 0.75	0.28
12	0.82 – 0.88	0.26
24	1.00	—
48	1.15 – 1.25	0.20
72	1.25 – 1.35	0.17

These ratios are coarse and regionally-variable — for critical dam design, consult the SA generalised PMP maps (HRU 1/72 as updated by Smithers et al.) for location-specific ratios.

For multi-day PMP ($D > 24$ hr), the ratios reflect the persistence of synoptic-scale systems over the catchment; in South Africa, tropical low pressure systems can produce near-1-day PMP every day for 2 to 3 days, giving a 72-hour PMP depth roughly 1.3 × the 1-day PMP.

Depth-Area relationships and Areal Reduction Factor

Point PMP decreases with increasing catchment area because any actual storm produces its peak depth over a small core area and progressively less rainfall at greater distances. The Areal Reduction Factor (ARF) is the ratio of the areal-average depth to the point depth:

$$\mathrm{ARF}(A, D) \;=\; \frac{P_\text{areal}(A, D)}{P_\text{point}(D)}$$

Areal Reduction Factor definition

ARF is a function of both area $A$ and duration $D$: it decreases with area (larger catchments sample more spatial variability) and increases with duration (longer-duration storms are spatially larger).

For SA PMP applications:

Area (km²)	ARF for 24-hour PMP	ARF for 6-hour PMP
10	0.98	0.95
50	0.94	0.88
100	0.91	0.83
500	0.82	0.68
1000	0.76	0.58
5000	0.60	0.40

See the ARF Calculator for a dedicated tool with Bell, NERC, and Smithers ARF models for SA catchments.

PMP is a point value — adjust for your catchment

The gridded PMP dataset returns a point value. For any catchment larger than approximately 10 km², applying the point PMP without ARF adjustment is non-conservative on inflow volume but approximately correct on peak discharge. For PMF computation, apply ARF explicitly before convolution with the unit hydrograph — the resulting PMF will be 5 to 40 percent lower than the unadjusted value depending on catchment size.

Temporal distribution of PMP storms

PMP is a depth (mm). To compute PMF you also need the time distribution of rainfall through the PMP event — how the total depth is distributed across the storm duration. Three standard distributions are used:

SCS Type distributions

The SCS developed four dimensionless 24-hour distributions (Type I, IA, II, III) based on US rainfall climatology. Type II is the most intense — 50 percent of the 24-hour depth falls in the central 1-hour block — and is widely used for PMP applications where a severe, front-loaded storm is desired. The tool can apply the Type II distribution automatically when generating a PMP hyetograph for convolution via the Hydrograph Generator.

Alternating block

Constructed from an IDF curve (or a PMP-depth-duration curve), the alternating-block method places the highest-intensity block at the centre of the storm and alternates successively-lower blocks on either side. This produces a severe, centre-weighted storm consistent with the design-storm philosophy for spillway adequacy.

Huff quartile distributions

Huff (1967) developed median distributions of cumulative rainfall depth vs cumulative time for each storm quartile (1st, 2nd, 3rd, 4th) based on Illinois data. Huff 1st-quartile distributions are front-loaded (peaks early) and 4th-quartile are rear-loaded (peaks late). For PMF, the 2nd- or 3rd-quartile distribution is typically used as the most realistic representation of storm evolution. Regional Huff-type distributions exist for South Africa (Smithers and Schulze 2003).

Distribution choice matters

For a given 24-hour PMP depth, the PMF peak can vary by 20 to 40 percent depending on the temporal distribution chosen. A front-loaded Type II on a wet-AMC catchment produces the highest peak because early rainfall saturates the soil and routes efficiently to the outlet. A centre-weighted alternating-block produces slightly lower peaks but shorter time-to-peak. Document your distribution choice and run a sensitivity analysis.

Spatial distribution of PMP storms

For large catchments (> 500 km²), the PMP event must be distributed spatially — the storm core is placed at a specific location within the catchment, and depths diminish radially outward to the edge. Standard approaches:

• Centroid-centred — storm core at the catchment centroid, radial decay via the depth-area relation.
• Worst-case positioning — the storm is oriented to maximise the PMF peak, typically by aligning the storm axis with the catchment’s longest dimension and placing the core upstream of the outlet to minimise travel-time attenuation.
• Climatological orientation — storm transposed with a fixed meteorologically-reasonable orientation (e.g., storm axes parallel to the dominant moisture-inflow direction).

The WMO manual recommends climatological orientation for physically-defensible estimates; worst-case positioning is used for conservative upper-bound analyses where design life and consequences warrant the conservatism.

Derivation of PMF from PMP

The Probable Maximum Flood (PMF) is the flood hydrograph produced when the PMP storm falls on a catchment in its most flood-producing state. Standard workflow:

1. Extract PMP at the catchment centroid for the durations of interest (typically 24-hour, possibly 48 or 72-hour for large catchments).
2. Apply ARF if the catchment exceeds ~10 km² — see ARF Calculator.
3. Construct the PMP hyetograph using an appropriate temporal distribution (Section above).
4. Apply a loss model — typically SCS-CN with a wet-AMC curve number (AMC III), or a low φ-index. The saturated-soil assumption is physically consistent with the PMP assumption that antecedent conditions maximise runoff.
5. Convolve with a unit hydrograph — use the Hydrograph Generator with either the SCS dimensionless UH (Type II) or a site-calibrated UH. For very large catchments, consider a distributed rainfall-runoff model or a basin-subdivided convolution.
6. Add baseflow — for long-duration PMP events, a moderate baseflow contribution is appropriate; use regional recession analysis.
7. Route through the reservoir if the application is dam-safety — see Flood Routing.

The resulting PMF peak is used in the SANCOLD SEF tabulation (see Dam Safety Evaluation) multiplied by the applicable SEF factor (0.2 to 1.1 depending on Category).

Loss modelling under PMP conditions

PMP scenarios produce extreme rainfall depths. Loss modelling must reflect that by design:

• Antecedent Moisture Condition — AMC III (wet antecedent) is the SANCOLD convention for PMF derivation. The curve number is adjusted upward from the normal AMC II value via the SCS AMC conversion table (CN_III ≈ CN_II + 15 for typical agricultural CN).
• Initial abstraction — the standard $I_a = 0.2 \, S$ is often replaced with $I_a = 0.05 \, S$ for PMP / PMF work (the modern research-based value), reflecting near-saturated starting conditions.
• Constant loss rate — for φ-index applications, a low value (5 to 10 mm/hr) is typical for saturated soils.

The combination of wet antecedent, low initial abstraction, and extreme rainfall means that PMF runoff coefficients commonly exceed 0.8 — effectively all rainfall becomes runoff. This is physically reasonable under PMP assumptions.

Climate change and PMP non-stationarity

The foundational assumption of PMP estimation — that atmospheric moisture and precipitation efficiency are stationary in time — is being challenged by anthropogenic climate change. Three lines of evidence:

• Global Clausius-Clapeyron scaling predicts that atmospheric water-holding capacity increases by approximately 7 percent per degree of warming. Global-mean surface warming of 1.1 °C (2020 relative to preindustrial) implies a ~7.5 percent increase in precipitable water, which translates directly into a PMP increase of similar magnitude in moisture-maximised methods.
• Observed increases in extreme rainfall — the IPCC AR6 concluded that extreme precipitation frequency has increased at the global scale and in most regions since 1950, with high confidence. For Southern Africa, the evidence is mixed — some regions show trends, others do not — but the direction is towards more intense short-duration extremes.
• Projected increases — CMIP6 projections for Southern Africa under SSP2-4.5 show median increases in 99th-percentile daily rainfall of 10 to 25 percent by 2070, with larger increases in the eastern escarpment regions.

Published PMP values are dated

Most published SA PMP maps (including the HRU 1/72 / SA generalised product underlying the gridded dataset) predate the majority of observed global warming. Engineering judgement suggests adding a climate-change safety factor of 10 to 20 percent to the tabulated 1-day PMP for dams commissioned now with design lives past 2070. DWS (2019) climate-change guidance recommends a 20 percent PMF uplift for high-hazard dams. This is handled outside the PMP Calculator — in the subsequent PMF derivation — by scaling the effective rainfall or the PMF peak.

Historical context and critiques

The “probable” in “Probable Maximum Precipitation” has long been controversial. A brief history of the key critiques:

• No formal probability assignment. PMP is a physical upper bound, not a quantile of a distribution. Attempts to assign return periods (e.g., 1 in 10⁷) rely on frequency-based extrapolation that the original WMO framework does not support.
• Historical exceedances. Storms exceeding 90 percent of co-located PMP have been observed repeatedly; a few storms have exceeded 100 percent of the published PMP at points within their footprint. Examples include Tropical Storm Allison (2001) over Houston, Hurricane Harvey (2017), and in South Africa, the floods associated with Cyclone Domoina (1984) and the April 2022 KwaZulu-Natal floods.
• Non-stationarity. As discussed in the previous section, climate change makes the very notion of a fixed PMP problematic.
• Conservative bias. Because PMP is intentionally an upper bound, designs based on full PMF are extremely conservative relative to probabilistic risk-based design. For low-hazard dams this is economically unjustifiable; for high-hazard dams it is often appropriate.

Modern practice recognises these limitations by:

• Using Category-based SEF factors (0.2 to 1.1 × PMF per SANCOLD) to calibrate the conservatism to the hazard.
• Computing PMF alongside RMF-based SEF values and reconciling the two.
• Applying explicit climate-change adjustments where appropriate.
• Monte Carlo or scenario sensitivity analysis around the deterministic PMF.

Worked example — 1-day PMP at a KZN dam site

The following example walks through a complete PMP-to-PMF derivation for a hypothetical dam site near Estcourt in KwaZulu-Natal.

Given information

• Dam site: 28.98° S, 29.87° E (near Estcourt, KZN foothills).
• Catchment area: 500 km², elongated north-south, mean elevation 1 300 m.
• Time of concentration $T_c$ = 5.2 hr.
• SCS CN (AMC II): 72 (mixed cultivated and natural veldt on hydrologic soil group C).
• Design goal: 1:1.0 PMF × PMP for the SEF of a Category III dam.

Step 1 — Look up 1-day PMP at the catchment centroid

Using the PMP Calculator with the catchment centroid coordinates, the gridded 1-day PMP is 620 mm at the nearest grid point (distance to click: 1.8 km).

Step 2 — Apply ARF

Catchment area 500 km². From the ARF table (or the ARF Calculator), $\mathrm{ARF}(500 \text{ km}^2, 24 \text{ hr}) \approx 0.82$.

Catchment-average 1-day PMP: $P_{24} = 620 \times 0.82 = 508$ mm.

Step 3 — Extract sub-daily PMP for hyetograph construction

Using the depth-duration relation ($m \approx 0.33$) and the catchment-average 1-day PMP:

Duration (hr)	Depth ratio	PMP depth (mm)
0.5	0.25	127
1	0.33	168
2	0.42	213
6	0.65	330
12	0.82	417
24	1.00	508

Step 4 — Construct the PMP hyetograph

Using the SCS Type II distribution (appropriate for severe South African convective events) applied to the 508 mm 24-hour depth, the hyetograph places ≈ 60 percent of the depth in the central 3 hours. The 15-minute maximum-intensity block peaks at 0.41 × P_1hr / 0.25 = ~ 275 mm/hr.

Step 5 — Apply losses

Convert CN_II = 72 to CN_III (wet) using the SCS AMC conversion: CN_III ≈ 87. $S = 25400/87 - 254 = 38.0$ mm. $I_a = 0.05 \, S = 1.9$ mm (research-based value).

Applying the SCS-CN equation cumulatively to the 508 mm total:

$$P_e \;=\; \frac{(508 - 1.9)^2}{508 - 1.9 + 38.0} \;\approx\; 471 \ \mathrm{mm}$$

Runoff fraction: 471 / 508 = 0.93 — consistent with saturated-soil assumption under PMF conditions.

Step 6 — Convolve with unit hydrograph

Using the Hydrograph Generator with the SCS dimensionless UH method, $T_c$ = 5.2 hr, PRF = 484, and the 471 mm effective hyetograph over 500 km², the PMF peak is approximately 2 850 m³/s at $t_p \approx 14$ hr from storm start.

Step 7 — Apply climate-change safety factor

Applying a 20 percent PMF uplift per DWS (2019) climate-change guidance: PMF = 3 420 m³/s.

Step 8 — Use in SEF

For a Category III large high-hazard dam, SEF = 1.1 × PMF = 3 760 m³/s. This is the inflow peak that the reservoir must route, with the spillway and freeboard analysis as per the Dam Safety Evaluation guide.

Sensitivity envelope

The deterministic PMF of 2 850 m³/s (or 3 420 m³/s with climate uplift) has a realistic uncertainty of ± 30 percent from PMP, ARF, loss, and UH contributions combined. For a Category III design, compute the PMF at the 10 / 50 / 90 percentile inputs and use the 90 percentile for spillway sizing — this yields a physically-justified conservatism that survives peer review.

Limitations of the gridded PMP tool

• 1-day duration only. Sub-daily and multi-day PMP must be derived using depth-duration relations, which are regionally-variable and carry their own uncertainty.
• Nearest-point lookup, no interpolation. Grid-point spacing is 2 to 5 km, so the nearest-point error can be up to ~3 km in the worst case. For point values this is usually immaterial; for critical applications, consider averaging over several surrounding grid points.
• South Africa only. The gridded dataset covers the country’s terrestrial extent; selections outside South Africa return the nearest border grid point.
• No explicit uncertainty. The tool returns a single value per grid point with no confidence interval. Practical uncertainty is ± 20 percent on the tabulated value.
• Static data. The dataset is updated periodically but between updates reflects the meteorological data as of the most recent refresh. Climate-change adjustments must be applied externally.
• Point, not areal. ARF must be applied externally for any catchment larger than a few km².
• Not a substitute for site-specific study. For Category III dams in critical settings, a site-specific PMP study following the WMO 1045 hydrometeorological procedure may be required by the DWS Dam Safety Office. The gridded lookup is a screening tool and an input to routine safety evaluations.

Regulatory hierarchy

Published PMP maps and gridded datasets are screening tools. For Category III dams, and for any dam where the safety evaluation is being contested, the DWS Dam Safety Office has the authority to require a bespoke site-specific PMP study carried out by a qualified meteorologist using the full WMO 1045 procedure. Always confirm with the DWS Dam Safety Office whether a site-specific PMP is required for your application.

Related tools and cross-references

• Dam Safety Evaluation — use the PMP to derive the PMF and then the SEF via the SANCOLD category matrix.
• Hydrograph Generator — convolve the PMP hyetograph with a unit hydrograph to produce the PMF hydrograph.
• Flood Routing — route the PMF through the reservoir for the spillway adequacy check.
• Design Storm — construct the PMP hyetograph using SCS, alternating-block, or Huff distributions.
• ARF Calculator — apply the areal-reduction factor to convert point PMP to catchment-average PMP.
• Design Rainfall — return-period rainfall for routine design (not a substitute for PMP).
• Daily Rainfall Data — historical daily rainfall records used in frequency analysis and storm studies.
• RMF Calculator — the Kovács Regional Maximum Flood, an alternative upper-bound used alongside PMF in SANCOLD SEF formulation.
• Flood Frequency Analysis — gauged flood-frequency methods used for RDD.
• SCS Method — the standard SA design flood method using SCS-CN losses and unit hydrograph.

References

• WMO. (2009). Manual on Estimation of Probable Maximum Precipitation (PMP). World Meteorological Organization, WMO-No. 1045, Geneva. (The authoritative international standard.)
• WMO. (1986). Manual for Estimation of Probable Maximum Precipitation (2nd ed.). World Meteorological Organization, Operational Hydrology Report No. 1, Geneva. (Previous edition, still cited.)
• Hershfield, D.M. (1961). Estimating the probable maximum precipitation. Proceedings of ASCE, Journal of the Hydraulics Division, 87(HY5), 99 – 116.
• Hershfield, D.M. (1965). Method for estimating probable maximum precipitation. Journal of the American Water Works Association, 57, 965 – 972.
• Koutsoyiannis, D. (1999). A probabilistic view of Hershfield’s method for estimating probable maximum precipitation. Water Resources Research, 35(4), 1313 – 1322.
• Hydrological Research Unit. (1972). Design Flood Determination in South Africa. HRU Report 1/72, University of the Witwatersrand, Johannesburg. (The original SA PMP / generalised flood study.)
• South African Weather Bureau. (1972). A Study of the Estimation of Probable Maximum Rainfall Depths in South Africa. Technical Report 102, SAWB, Pretoria.
• Gericke, O.J. & Du Plessis, J.A. (2011). Evaluation of the standard design flood method in selected basins in South Africa. Journal of the South African Institution of Civil Engineering, 53(2), 46 – 56.
• Smithers, J.C. & Schulze, R.E. (2003). Design Rainfall and Flood Estimation in South Africa. Water Research Commission Report 1060/1/03, Pretoria. (Modern SA rainfall / flood reference.)
• Smithers, J.C. (2012). Methods for design flood estimation in South Africa. Water SA, 38(4), 633 – 646.
• Pegram, G. & Parak, M. (2004). A review of the regional maximum flood and rational formula using geomorphological information and observed floods. Water SA, 30(3), 377 – 388.
• WRC. (2017). Guidelines for Climate Change Adaptation in the South African Water Sector. Water Research Commission Report TT 716/17, Pretoria.
• IPCC. (2021). Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report, Cambridge University Press. Chapter 11 (Extremes), Chapter 12 (Regional Information), Africa Atlas sections.
• Clausius, R. (1850). Über die bewegende Kraft der Wärme. Annalen der Physik, 79, 368 – 397. (The Clausius-Clapeyron thermodynamic relation underlying atmospheric moisture scaling.)
• Cullis, J., Alton, T., Arndt, C., et al. (2015). An uncertainty approach to modelling climate change risk in South Africa. WIDER Working Paper 2015/045, United Nations University.
• US NWS. (1978 – 1994). Hydrometeorological Reports (HMR). HMR 51, 52, 55A, 57, 58, 59, National Weather Service. (Generalised US PMP studies — methodological references for the hydrometeorological approach.)
• Graham, W.J. (1999). A Procedure for Estimating Loss of Life Caused by Dam Failure. US Bureau of Reclamation DSO-99-06, Denver.
• SANCOLD. (1991). Guidelines on Safety in Relation to Floods. SANCOLD Report 4, Pretoria.
• DWS. (2019). Adaptation of South African Dam Safety to Climate Change — Guidance Note. Department of Water and Sanitation, Directorate Dam Safety, Pretoria.
• Ohlsson, L. (2017). Review of methods for Probable Maximum Precipitation estimation and application in southern Africa. Progress in Physical Geography, 41(6), 744 – 770.

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