---
title: "Attenuation and lag of peak in routing"
subject: "Engineering Hydrology"
chapter: 7
key: "semester_5/engineering_hydrology:attenuation-lag-peak"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/attenuation-lag-peak
site: BCT Engineering
---

# Attenuation and lag of peak in routing

Engineering Hydrology · Chapter 7: Flow Routing

- Asked in: 2081 Bhadra, 2 marks; 2071 Shrawan, 4 marks (asked 2 times)
- Video: [Lecture on Flood Routing : Attenuation and Lag](https://www.youtube.com/watch?v=GO2jPh1k8Xs) — Mrinmoy Majumder
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/attenuation-lag-peak
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-7

## Question

Explain the concept of attenuation and lag of peak due to routing with sketch.

## Short answer

Attenuation is the reduction in peak outflow compared to peak inflow due to storage filling during rising limb. Lag is the time delay of the outflow peak relative to inflow peak; peak outflow occurs where outflow curve crosses inflow curve (maximum storage).

## Answer

When a flood wave passes through a reach or reservoir, its shape changes. The hydrograph is flattened and delayed.

#### Concept

- **Attenuation of peak:** the peak outflow is lower than the peak inflow, $\Delta Q_p = I_{max} - O_{max}$. During the rising limb, part of the inflow fills the storage ($I > O$), so the outflow is smaller than the inflow. The stored water drains later, so the falling limb is stretched out.
- **Lag of peak:** the peak outflow occurs later than the peak inflow, $t_{lag} = t_{p,out} - t_{p,in}$.
- The peak outflow always occurs where the outflow curve crosses the inflow curve, because there $dS/dt = I - O = 0$ (storage is maximum).

#### Sketch

```text
 Q
 |      inflow
 |       /\
 |      /  \      outflow
 |     /   /‾‾\
 |    /   /    \
 |   /   /      \__
 |  /___/__________\___
 +--------------------------> t
     t_pI  t_pO
     |<--lag-->|
 Attenuation = I_peak - O_peak
```

#### Why it occurs

- In a **reservoir**, the water surface is level, so storage is a function of outflow alone and the peak is cut by surcharge storage.
- In a **river reach**, the wedge and prism storage (Muskingum) delays the flood, and friction and floodplain storage flatten it. The wave peak decreases with distance travelled.

Attenuation and lag increase with the storage constant $K$ and are important in design of spillways, flood-control reservoirs, and in forecasting arrival times of a flood downstream.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is attenuation of peak?
   A. The peak outflow is later than the peak inflow
   B. The peak outflow is lower than the peak inflow
   C. The flood volume is reduced
   D. The base flow is removed
   Answer: B. Attenuation = I_max - O_max, a reduction in peak. (Key point: Attenuation)

2. What is lag of peak?
   A. The delay between the inflow peak and outflow peak
   B. The difference between peak flows
   C. The time from rain start to inflow peak
   D. The recession time of the outflow
   Answer: A. Lag = time of peak outflow - time of peak inflow. (Key point: Lag)

3. Where does the outflow peak occur, and why?
   A. At the inflow peak, since I is maximum
   B. At the start of the rising limb
   C. At the end of recession, where storage is empty
   D. Where the outflow curve crosses the inflow curve, since dS/dt = I - O = 0 and storage is maximum
   Answer: D. Outflow rises while I > O and falls when O > I, so it peaks at I = O when storage is maximum. (Key point: Where outflow peaks)

## Related in Engineering Hydrology

- [Muskingum routing, K=10, x=0.20](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Amuskingum-k10-x0-2-5to40) — Engineering Hydrology, chapter 7, asked 2×
- [Muskingum routing, K=12 h, X=0.20](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Amuskingum-k12-x0-2) — Engineering Hydrology, chapter 7, asked 2×
- [Derive UH from storm, peak flow from two storms](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Auh-from-storm-then-peak-two) — Engineering Hydrology, chapter 5
- [Reservoir routing through spillway, 6-hr inflow](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Areservoir-routing-spillway-6hr) — Engineering Hydrology, chapter 7
- [Muskingum routing, K=36 hr, x=0.15](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Amuskingum-k36-x0-15) — Engineering Hydrology, chapter 7

## Related in other subjects

- [Current chopping overvoltage at zero and peak](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Achopping-overvoltage-7a) — High Voltage Engineering, chapter 3