Design Rainfall

Open Design Rainfall

Estimate design rainfall depths and Intensity-Duration-Frequency (IDF) relationships for any point in South Africa using the regionalised K5_1060 methodology. This guide covers the underlying L-moment statistics and growth curves, the anchor-duration and log-log interpolation scheme, the 421,027-point grid, confidence bounds, and the AEP/EY terminology used alongside the Australian BOM IFD data source.

Overview

The Design Rainfall tool computes design rainfall depths for any location in South Africa using the methodology described in WRC Report K5_1060 (Smithers & Schulze, 2003). It provides rainfall depths for 23 storm durations (5 minutes to 7 days) across 7 return periods (2 to 200 years), each with lower, mean, and upper 95% confidence bounds.

Under the hood the tool uses a pre-computed grid of 421,027 points covering South Africa at 1-arcminute (~1.85 km) resolution. For any chosen location the nearest grid point is identified and design rainfall values are computed on-the-fly using cached lookup tables and a log-log interpolation algorithm.

Methodology

The K5_1060 methodology is a regionalised, L-moment-based approach to estimating design rainfall for ungauged locations. Three computational layers combine to produce the final depth-duration-frequency (DDF) surface: a regional growth curve, an at-site first L-moment, and log-log interpolation between anchor durations.

K5_1060 report

Design Rainfall Estimation in South Africa (Version 3) was developed by Smithers & Schulze at the University of KwaZulu-Natal for the Water Research Commission (WRC Report No. 1060/1/04). It provides a regionalised approach to estimating design rainfall at ungauged locations using L-moment statistics, growth curve clusters, and regression relationships fitted to an extensive daily rainfall database.

L-moments & growth curves

The methodology uses L-moment ratios to characterise rainfall frequency distributions. South Africa is divided into 78 growth curve clusters, each with a set of dimensionless growth curve factors ($GC$) for return periods of 2, 5, 10, 20, 50, 100, and 200 years. The design rainfall depth for a given duration and return period is computed as:

$$P_{T,D} \;=\; GC_T \cdot L_{1,D}$$

K5_1060 design rainfall formulation

where $L_{1,D}$ is the at-site mean (first L-moment) for duration $D$, and $GC_T$ is the dimensionless growth curve factor for the cluster and return period $T$.

Log-log interpolation

At-site $L_1$ values are computed directly at a limited set of anchor durations using regression equations. For non-anchor durations, values are interpolated in $\log_{10}$-$\log_{10}$ space between adjacent anchors, enforcing a non-negative slope to ensure physically plausible, monotonically increasing depths:

$$\begin{aligned} m &= \max\!\left(\frac{\log_{10} V_{hi} - \log_{10} V_{lo}}{\log_{10} D_{hi} - \log_{10} D_{lo}},\ 0\right) \\[4pt] V_{D} &= 10^{\,\log_{10} V_{hi} \;-\; m \,(\log_{10} D_{hi} - \log_{10} D)} \end{aligned}$$

Log-log interpolation between anchor durations

This scheme guarantees smooth transitions across duration scales and avoids the oscillations that polynomial interpolation can introduce.

Grid data

The underlying dataset consists of 421,027 grid points at 1-arcminute resolution (approximately 1.85 km spacing). Each grid point stores:

• MAP — Mean Annual Precipitation (mm/yr)
• Altitude — Elevation in metres
• Cluster — Growth curve cluster (1–78)
• S-Cluster — Short-duration regression cluster (1–15)
• AV-Cluster — Daily regression region (1–7)
• ADJ_L1_1D — Adjusted first L-moment for 1-day rainfall
• P values — Uncertainty percentages for the confidence bounds at each anchor duration

Duration scales

The tool returns depths for 23 durations spanning short-duration convective storms through multi-day frontal events. Durations are grouped into two regimes, each with its own regression framework and set of anchor points.

Sub-daily (5 min – 24 hr)

16 durations: 5 min, 10 min, 15 min, 30 min, 45 min, 1 hr, 1.5 hr, 2 hr, 4 hr, 6 hr, 8 hr, 10 hr, 12 hr, 16 hr, 20 hr, 24 hr. Anchor points at 5 min, 15 min, 2 hr, and 24 hr.

Anchor points

Sub-daily $L_1$ values at anchors are computed using $L_1 = D_{24h} \cdot \text{XCOEF} + \text{CONST}$, where $D_{24h}$ is the 24-hour estimate derived from the adjusted 1-day $L_1$ and the 24h/1day median ratio.

Daily (1 day – 7 day)

7 durations: 1 day, 2 day, 3 day, 4 day, 5 day, 6 day, 7 day. Anchor points at 1 day, 3 day, and 7 day. Multi-day $L_1$ values are produced by a regional regression with six parameters (UPSILON, KAPPA, RHO, THETA, TAU, SIGMA) across seven rainfall regions.

Return periods

Seven return periods are computed: 1:2, 1:5, 1:10, 1:20, 1:50, 1:100, and 1:200 year. The growth curve factors for each return period are applied to the $L_1$ value at each duration to produce the design rainfall depth.

Common engineering use

For typical stormwater drainage design, the 1:10 to 1:50 year return periods are most commonly used. The 1:100 and 1:200 year values are reserved for critical infrastructure such as bridges, dams, and emergency spillways.

AEP & EY terminology

Since the 2016 revision of Australian Rainfall and Runoff (ARR 2016), design rainfalls in Australia use probability-based terminology instead of the traditional Average Recurrence Interval (ARI) or Return Period (RP). This terminology is now used across the HydroDesign platform when working with Australian BOM IFD data, and is available globally via the RP | AEP notation toggle.

What is AEP?

Annual Exceedance Probability (AEP) is the probability of an event being exceeded in any given year, expressed as a percentage. For example, a 1% AEP rainfall event has a 1% chance (1 in 100) of being exceeded in any single year. This does not mean it occurs once every 100 years — it could occur in consecutive years, or not for 200 years. Each year is independent.

Common misconception

A “1 in 100 year” event does not mean it happens once every 100 years. A 1% AEP event has the same probability of occurring every year. Over a 100-year period, there is actually a 63% chance of experiencing at least one such event.

What is EY?

Exceedances per Year (EY) is used for very frequent events. It represents the average number of times an event of a given magnitude is expected to be exceeded in any year. For example:

• 12 EY — expected ~12 times per year (approximately monthly)
• 6 EY — expected ~6 times per year (approximately every 2 months)
• 2 EY — expected ~2 times per year (approximately every 6 months)
• 0.5 EY — expected about once every 2 years

EY is preferred over AEP for frequent events because AEP percentages above 63.2% become unintuitive (for example, a 2 EY event has an 86.5% AEP).

AEP vs ARI (return period)

The traditional Average Recurrence Interval (ARI), also known as Return Period (RP), is the average time between events of the same magnitude. While still commonly used in South Africa and the USA, Australia has moved to AEP terminology because:

• AEP more clearly communicates the probability nature of extreme events
• AEP avoids the misconception that a “100-year event” happens exactly once in 100 years
• AEP/EY is consistent across the full probability range (frequent to rare)

Important note on conversions

The 50% AEP does not correspond to the 2-year ARI — it corresponds to the 1.44-year ARI. Similarly, the 20% AEP corresponds to the 4.48-year ARI, not 5-year ARI. The exact conversion is $\mathrm{ARI} = -1 / \ln(1 - \mathrm{AEP})$. For rare events (below 10% AEP), ARI and $1/\mathrm{AEP}$ are approximately equal.

Quick reference table

Category	EY	AEP (%)	AEP (1 in x)	ARI (years)	Typical use
Very frequent	12	—	—	—	—
	6	99.75	1.002	0.17	Water-sensitive urban design
	4	98.17	1.02	0.25	—
	3	95.02	1.05	0.33	—
	2	86.47	1.16	0.50	—
Frequent	1	63.2	1.58	1.00	Stormwater / pit & pipe design
	0.69	50	2	1.44	—
	0.5	39.35	2.54	2.00	—
	0.22	20	5	4.48	—
	0.11	10	10	9.49	—
Infrequent	0.05	5	20	19.5	Floodplain management & waterway design
	0.02	2	50	49.5	—
	0.01	1	100	99.5	—
Rare	—	—	1 in 200	200	Dam safety & critical infrastructure
	—	—	1 in 500	500	—
	—	—	1 in 1000	1000	—
	—	—	1 in 2000	2000	—

Source: Bureau of Meteorology / Australian Rainfall and Runoff 2019. Bold values are standard design rainfall probabilities.

Australian BOM IFD

The Design Rainfall tool also provides access to the Australian BOM Intensity-Frequency-Duration data source for projects outside South Africa.

Overview

The Bureau of Meteorology (BOM) provides Intensity-Frequency-Duration (IFD) design rainfall estimates for all of Australia as part of the 2016 revision of Australian Rainfall and Runoff (ARR 2019). These replace both the original ARR87 design rainfalls and the interim 2013 estimates. The 2016 design rainfalls utilise a significantly expanded rainfall database and improved statistical methods.

In HydroDesign, the BOM IFD data source fetches design rainfall depths directly from the Bureau of Meteorology for any location in Australia. Click a point on the map or enter coordinates, and the platform retrieves the complete IFD table.

Estimation methods

The 2016 design rainfalls were derived from observed rainfall data using different methods for each probability range:

Standard IFDs (10% to 1% AEP)

• 8,074 daily-read and 2,280 continuous (sub-daily) rainfall stations
• Minimum record length: 30 years (daily) / 8 years (continuous)
• Annual Maximum Series (AMS) fitted with Generalised Extreme Value (GEV) distribution using L-moments
• Region of Influence regionalisation (500 station years)
• Gridded using ANUSPLIN thin-plate smoothing splines

Very frequent (12 EY to 63.2% AEP)

• 15,364 daily-read and 2,722 continuous stations
• Minimum record length: 5 years
• Partial Duration Series (PDS) with minimum inter-event time for independence
• Generalised Pareto (GPA) distribution fitted using L-moments
• Ratios to 50% AEP gridded using ANUSPLIN

Rare (1 in 200 to 1 in 2000 AEP)

• 3,955 daily-read stations from the Bureau of Meteorology
• Minimum record length: 60 years
• GEV distribution fitted using LH(2)-moments (placing weight on largest observed values)
• Region of Influence regionalisation (minimum 2,000 station years)
• Anchored to more frequent design rainfalls at the 5% AEP
• Sub-daily rare events derived via ratios from 1-day rare estimates

Coverage & durations

BOM IFD data covers all of Australia with gridded estimates available at approximately 2.5 km resolution.

• 29 standard durations: 1, 2, 3, 4, 5, 10, 15, 20, 25, 30, 45 min; 1, 1.5, 2, 3, 6, 12, 24, 48, 72, 96, 120, 168 hours
• 18 probabilities: 12 EY to 1 in 2000 AEP
• Seasonality: Winter factors available for winter-dominated rainfall regions

Note on confidence intervals

Unlike the SA Design Rainfall (which provides lower, mean, and upper bounds) and NOAA Atlas 14 (lower, median, and upper), the BOM IFD system currently provides only best-estimate values without confidence intervals.

Limitations

• Best estimate only: No upper/lower confidence bounds are provided.
• Sub-daily rare events: Derived indirectly from daily data via ratios, not from direct sub-daily observations — higher uncertainty for short-duration rare events.
• Stationarity: Estimates assume rainfall statistics are stationary. Climate change may cause actual extremes to differ.
• Design rainfall ≠ design flood: Design rainfall is only one input. Temporal patterns, areal reduction factors, and losses must also be considered for flood estimation.
• Differences from ARR87: Differences between 2016 and ARR87 estimates reflect improved methods and data — they do not imply rainfall trends over time.

Confidence bounds

Each design rainfall value is provided with three estimates:

• Lower — Lower 95% confidence bound ($GC_{lower} \cdot L_{1,lower}$)
• Mean — Median estimate ($GC_{mean} \cdot L_{1,mean}$)
• Upper — Upper 95% confidence bound ($GC_{upper} \cdot L_{1,upper}$)

The bounds are derived from the uncertainty ($P\%$) in the $L_1$ estimate at each anchor point, combined with the lower/upper growth curve factors for the cluster.

When to use bounds

For conservative design (e.g. dam spillways, flood attenuation), use the upper bound. For economic assessment or typical design, use the mean value. The lower bound represents the minimum plausible design rainfall.

DRE station comparison

The tool also displays the three nearest DRE (Design Rainfall Estimation) stations from a database of 3,946 historical rain gauges across South Africa. These stations have observed daily design rainfall values (1-day to 7-day) that can be compared against the gridded estimates.

Gridded vs station data

The gridded values are spatially interpolated and may differ from individual station observations. When a nearby station has a long record period (30+ years), its observed values may be more reliable for daily durations than the gridded estimate. The gridded approach is most valuable for sub-daily durations where station data is scarce.

How to use

1. Open the Design Rainfall tool from the sidebar or create a new calculation.
2. Select a location by clicking on the map or entering coordinates manually. The tool only works within South Africa’s borders for the K5_1060 data source; use the BOM IFD data source for Australia.
3. The computation runs automatically. Results appear in the right panel showing grid-point information, a rainfall table, and charts.
4. Use the Lower / Mean / Upper toggle to switch between confidence bounds.
5. Switch between the Table, IDF Curves, and Depth Chart tabs to visualise results differently.
6. Check the Nearest DRE Stations panel to compare against observed station data.
7. Click Save to store the calculation, or Export CSV to download results.

Interpreting results

The results table shows rainfall depth in millimetres for each combination of duration and return period. Key things to look for:

• Increasing with duration: Rainfall depth should increase with duration (a 7-day storm produces more total rainfall than a 5-minute burst).
• Increasing with return period: Rarer events (higher return periods) produce larger rainfall depths.
• IDF curves: The Intensity-Duration-Frequency chart shows rainfall intensity (mm/hr) decreasing with duration — short, intense bursts are more intense per hour than long storms.
• Depth chart: The depth vs. duration chart shows the cumulative rainfall depth increasing with duration.

Worked example — reading an IDF table

Consider a location on the Highveld (MAP ≈ 700 mm/yr, cluster typical of summer convective regimes). For the 1:50 year return period and a catchment with a time of concentration of 35 minutes, the procedure is:

1. Pick the coordinates on the map. The tool returns the nearest grid point and the full 23 × 7 depth table.
2. In the Depth table, locate the row for 30 min and the row for 45 min (the bracketing durations for 35 min).
3. Read the mean 1:50 year depths, e.g. 52 mm at 30 min and 62 mm at 45 min.
4. Interpolate in log-log space (or use the IDF Curves tab, which does this automatically) to get a 35 min mean depth of ≈ 56 mm, equivalent to an intensity of $i = 56 / (35/60) \approx 96$ mm/hr.
5. This intensity is the design rainfall input for the Rational Method at the chosen return period.

Practical tip

If the 24 hr mean value seems unusually high or low for the area, check the MAP (Mean Annual Precipitation) value in the grid-point info panel. Low MAP areas (<400 mm/yr) will naturally have lower design rainfall depths.

Exporting data

Click the Export CSV button to download a CSV file containing:

• Header with location coordinates, grid-point info, MAP, and altitude
• The selected statistic (lower, mean, or upper)
• 23 rows (one per duration) with 7 columns (one per return period)

Limitations

• Grid resolution: Values are for the nearest 1-arcminute grid point, not the exact clicked location. In areas with high rainfall gradients (e.g. mountain passes), there may be noticeable differences over short distances.
• Interpolation: Non-anchor durations are interpolated in log-log space. While physically reasonable, the interpolated values are less certain than anchor-point values.
• Sub-daily uncertainty: Sub-daily rainfall estimates have higher uncertainty than daily estimates due to the limited number of high-frequency recording stations used in the original analysis.
• Stationarity assumption: The methodology assumes rainfall statistics are stationary (not changing over time). In a changing climate, actual extreme rainfall may deviate from these estimates.
• Return periods > 200 years: Extrapolation beyond 200 years is not provided and should be treated with extreme caution. For dam-safety and spillway design use the PMP Calculator or a dedicated Flood Frequency Analysis on long observational records.

References

South Africa

• Smithers, J.C. & Schulze, R.E. (2003). Design Rainfall and Flood Estimation in South Africa. WRC Report No. 1060/1/04. Water Research Commission, Pretoria.
• Smithers, J.C. & Schulze, R.E. (2000). Long duration design rainfall estimates for South Africa. WRC Report No. 811/1/00.
• Hosking, J.R.M. & Wallis, J.R. (1997). Regional Frequency Analysis: An Approach Based on L-Moments. Cambridge University Press.

Australia

• Ball, J., Babister, M., Nathan, R., Weeks, W., Weinmann, E., Retallick, M. & Testoni, I. (Eds.) (2019). Australian Rainfall and Runoff: A Guide to Flood Estimation. Commonwealth of Australia.
• Green, J., Xuereb, K., Johnson, F., Moore, G. & The, C. (2015). The Revised Intensity-Frequency-Duration (IFD) Design Rainfall Estimates for Australia — An Overview. 36th Hydrology and Water Resources Symposium.
• Bureau of Meteorology (2016). Design Rainfall Data System. https://www.bom.gov.au/water/designRainfalls/revised-ifd/

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Open Design Rainfall