---
title: "Average rainfall methods with merits and demerits"
subject: "Engineering Hydrology"
chapter: 2
key: "semester_5/engineering_hydrology:avg-rainfall-methods-merits"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/avg-rainfall-methods-merits
site: BCT Engineering
---

# Average rainfall methods with merits and demerits

Engineering Hydrology · Chapter 2: Precipitation

- Asked in: 2082 Baisakh, 2+4 marks; 2072 Kartik, 3+3 marks (asked 2 times)
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/avg-rainfall-methods-merits
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-2

## Question

Explain the different methods of determining the average rainfall over a catchment due to a storm. Discuss the relative merits and demerits of the various methods.

## Short answer

Arithmetic mean is simplest but ignores spatial variation. Thiessen polygon weights gauges by area and is objective, but ignores orography. Isohyetal method is most accurate as it incorporates topography and storm pattern, but requires dense gauges and skilled plotting.

## Answer

Rain gauges give point rainfall. The mean rainfall over a catchment due to a storm is found by three methods.

#### 1. Arithmetic mean method
$$
\bar P = \frac{P_1+P_2+\dots+P_n}{n}
$$
The simple average of the gauges inside the catchment. Used for flat areas with uniformly spread gauges and rainfall that varies little.

#### 2. Thiessen polygon method
1. Plot the gauges on the catchment map and join adjacent gauges to form triangles.
2. Draw perpendicular bisectors of the sides; they form a polygon around each gauge.
3. Measure the area $A_i$ of each polygon inside the catchment.
4. Compute

$$
\bar P = \frac{\sum A_i P_i}{\sum A_i}
$$

#### 3. Isohyetal method
1. Draw isohyets (lines of equal rainfall) by interpolating between gauge values.
2. Find the area $A_i$ between consecutive isohyets and the mean of their values $\bar P_i$.
3. Compute $\bar P = \sum A_i \bar P_i / \sum A_i$.

#### Merits and demerits
| Method | Merits | Demerits |
|---|---|---|
| Arithmetic mean | Very simple, quick, needs no map | Ignores gauge position and relief; poor for uneven gauges or storms |
| Thiessen polygon | Weights gauges by area; objective; good for moderately uneven gauge spread | Ignores orography; polygons must be redrawn when a gauge is added or missing; assumes rainfall is the same over the polygon |
| Isohyetal | Most accurate; includes relief and storm pattern; gives rainfall pattern | Needs a dense network and skill; more time; subjective drawing of isohyets |

For hilly catchments such as those in Nepal, the isohyetal method is preferred if enough gauges exist; otherwise Thiessen is used.

## Check yourself

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

1. Arithmetic mean demerit:
   A. Ignores gauge position and relief
   B. Needs dense network
   C. Is subjective
   D. Needs isohyets
   Answer: A. But it is very simple. (Key point: Arithmetic demerit)

2. Thiessen demerit:
   A. Needs isohyets
   B. Polygons must be redrawn when a gauge is added or missing
   C. Is the most accurate
   D. Weights by elevation
   Answer: B. Also ignores orography. (Key point: Thiessen demerit)

3. Isohyetal demerit:
   A. Ignores relief
   B. Is very quick
   C. Needs dense network and skill; subjective
   D. Needs no map
   Answer: C. But it is most accurate. (Key point: Isohyetal demerit)

4. For hilly catchments the preferred method is:
   A. Arithmetic mean
   B. Always Thiessen
   C. None
   D. Isohyetal if enough gauges exist
   Answer: D. Otherwise Thiessen. (Key point: Preference)

## Related in Engineering Hydrology

- [Methods of average rainfall over catchment](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aavg-rainfall-methods) — Engineering Hydrology, chapter 2, asked 3×
- [Runoff and effective rainfall, 4-hr storm, 80 km2](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Arunoff-80km2-subbasins-phi) — Engineering Hydrology, chapter 3, asked 2×
- [Thiessen polygon mean rainfall, pentagon catchment](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Athiessen-pentagon-pqrs) — Engineering Hydrology, chapter 2
- [Average rainfall by isohyetal method, Bagmati basin](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aisohyetal-bagmati-442) — Engineering Hydrology, chapter 2
- [Total rainfall, net runoff, W-index of 140-min storm](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aphi-w-index-140min-storm) — Engineering Hydrology, chapter 3, asked 2×
- [Total rainfall, net runoff, W-index of 120-min storm](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aphi-w-index-120min-storm) — Engineering Hydrology, chapter 3, asked 2×

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- [Techniques for average depth of rainfall](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Aaverage-rainfall-techniques) — Hydro Power, chapter 2
- [Cofferdam types, uses, merits and demerits](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Acofferdam-types-merits) — Foundation Engineering, chapter 5, asked 7×
- [Merits and demerits of interconnected system](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Ainterconnection-merits-demerits) — Power System Analysis II, chapter 1, asked 3×