As hydrologists, we often need to convert 24‑hour daily rainfall into shorter durations (e.g., 1‑hour or 30‑minute intensities) to design drainage systems or run hydrological models.
The standard tool is the scaling relationship:
I(t) = I₂₄ × (24/t)ⁿ
But here is the critical question: How do you derive that exponent 'n'?
There are two fundamentally different approaches and they give very different answers:
🔴 Method 1: Global Max (Sliding Window)
Takes your entire rainfall time series and slides a window across every timestep.
Picks the absolute maximum depth for each duration (20min, 1h, 6h, 24h).
Fits one regression line to those extreme points.
✅ Result: A steep, high exponent (my case, n ≈ 0.75).
📌 this can be used for: Extreme event design – IDF curves, stormwater drains, dam spillways, bridge scour. This captures the worst storm on record.
🔵 Method 2: Storm‑Based (Event Separation)
Splits the time series into individual storm events using a dry threshold (e.g., 6 hours of no rain).
Calculates 'n' for each storm separately, then takes the median of all storms.
✅ Result: A milder, lower exponent (my case, n ≈ 0.605).
📌 this can be used for: Continuous hydrological simulation, average runoff estimation, soil moisture accounting, reservoir yield studies. This captures the behaviour of a typical storm.
⚠️ THE DANGEROUS MISTAKE
Many practitioners think that 'n' is a fixed catchment parameter a physical constant. It is not.
The exponent you derive depends entirely on how you select the data:
The Global Max selects the top 1% most extreme events.
The Storm‑Based averages across 100% of events.
If you use the mild storm‑based n (0.608) to design a 100‑year culvert, you will underestimate the 1‑hour peak intensity by a large margin. Your infrastructure will be undersized. When the real extreme event arrives, it will fail.
Conversely, if you use the steep extreme n (0.75) for average runoff modelling, you will grossly overestimate daily flows and mismanage reservoir releases.
🧠 Key takeaway:
"A catchment’s average hydrological behaviour is NOT the same as its design storm behaviour."
The scaling factor is a tool, not a truth. Match your methodology to your objective:
