---
title: "Methods of average rainfall over catchment"
subject: "Engineering Hydrology"
chapter: 2
key: "semester_5/engineering_hydrology:avg-rainfall-methods"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/avg-rainfall-methods
site: BCT Engineering
---

# Methods of average rainfall over catchment

Engineering Hydrology · Chapter 2: Precipitation

- Asked in: 2078 Kartik, 6 marks; 2075 Asoj, 6 marks; 2071 Chaitra, 6 marks (asked 3 times)
- Video: [Methods of Finding Average Rainfall Data - Hydrology - Water Resource Engineering 1](https://www.youtube.com/watch?v=U8AAU19CgB0) — Ekeeda
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/avg-rainfall-methods
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-2

## Question

Discuss three different methods of determining the average depth of rainfall over a catchment.

## Short answer

Three methods: arithmetic mean (simple average for flat areas with uniform gauges), Thiessen polygon (area-weighted by polygon around each gauge, for uneven distribution), and isohyetal (averaging between isohyets, most accurate for hilly terrain).

## Answer

Rainfall measured at a gauge is point rainfall. To find the average depth over a catchment, three methods are used.

#### 1. Arithmetic mean method
The average of rainfall of all gauges in the area:

$$
\bar P = \frac{P_1 + P_2 + \dots + P_n}{n}
$$

Suitable for flat areas with uniform gauge distribution and little variation of rainfall. It is simple but ignores the position of gauges and topography.

#### 2. Thiessen polygon method
Gauge stations are joined to form triangles, perpendicular bisectors of the sides are drawn, and the polygon around each station is the area closest to it. Each gauge is weighted by its polygon area:

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

It considers non-uniform gauge density and is more accurate than the arithmetic mean. It does not account for orographic effects, and the polygons must be redrawn if a gauge is added or fails.

#### 3. Isohyetal method
Isohyets (lines of equal rainfall) are drawn using gauge values. The average rainfall between two successive isohyets is taken as their mean, and weighted by the area between them:

$$
\bar P = \frac{\sum A_i \dfrac{P_i + P_{i+1}}{2}}{\sum A_i}
$$

It is the most accurate, particularly for hilly regions, as it accounts for topography and storm pattern, but requires many gauges and judgement.

```text
   15 cm   10 cm   5 cm   (isohyets)
   ( (  ( o ) ) )    A1, A2, A3 = inter-isohyet areas
```

## Check yourself

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

1. Arithmetic mean suits:
   A. Flat areas with uniform gauge spread and little variation
   B. Hilly regions
   C. Non-uniform gauges
   D. Very large areas
   Answer: A. Ignores position. (Key point: Arithmetic mean)

2. Thiessen weights each gauge by:
   A. Its elevation
   B. The area of its polygon
   C. Its rainfall rank
   D. Time of record
   Answer: B. Perpendicular bisectors make polygons. (Key point: Thiessen)

3. The isohyetal method is the:
   A. Least accurate
   B. Simplest
   C. Most accurate, especially in hilly regions
   D. Only for flat land
   Answer: C. Includes topography and storm pattern. (Key point: Isohyetal accuracy)

4. A limitation of Thiessen is:
   A. Ignores gauge density
   B. Needs no map
   C. Gives unweighted mean
   D. Does not account for orographic effects
   Answer: D. Polygons must be redrawn if a gauge changes. (Key point: Thiessen limit)

## Related in Engineering Hydrology

- [Average rainfall methods with merits and demerits](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aavg-rainfall-methods-merits) — Engineering Hydrology, chapter 2, 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
- [Thiessen average rainfall, four gauges at rectangle corners](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Athiessen-rectangle-four-gauges) — Engineering Hydrology, chapter 2
- [Empirical flood formula, 100 sq km catchment](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aempirical-flood-100sqkm) — Engineering Hydrology, chapter 6
- [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×

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