---
title: "Arithmetic mean, Thiessen, isohyetal methods compared"
subject: "Engineering Hydrology"
chapter: 2
key: "semester_5/engineering_hydrology:arith-thiessen-isohyetal-diff"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/arith-thiessen-isohyetal-diff
site: BCT Engineering
---

# Arithmetic mean, Thiessen, isohyetal methods compared

Engineering Hydrology · Chapter 2: Precipitation

- Asked in: 2081 Bhadra, 5 marks
- 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/arith-thiessen-isohyetal-diff
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-2

## Question

Differentiate Arithmetic Mean, Thiessen Polygon and Isohyetal Methods.

## Short answer

Arithmetic mean ignores gauge location; Thiessen polygon assigns area weights to each gauge; isohyetal method uses isohyets and considers topography, best for hilly areas. Accuracy and effort increase in that order.

## Answer

| Point | Arithmetic mean | Thiessen polygon | Isohyetal |
|---|---|---|---|
| Principle | Simple average of gauge values | Weighted average with weights equal to polygon areas | Weighted average using areas between isohyets |
| Formula | $\bar P = \sum P_i / n$ | $\bar P = \sum A_i P_i / \sum A_i$ | $\bar P = \sum A_i \bar P_i / \sum A_i$ |
| Map needed | No | Yes (polygons) | Yes (isohyets) |
| Gauge position | Ignored | Considered | Considered |
| Topography / orography | Ignored | Not considered | Considered |
| Suitable for | Flat area, uniform gauges | Plains, moderate relief, uneven gauges | Hilly/mountainous areas, large catchments |
| Accuracy | Lowest | Better | Highest |
| Effort | Very small | Moderate; redraw if gauge changes | Most; needs judgement and many gauges |

## Check yourself

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

1. What does the arithmetic mean method ignore?
   A. Gauge position and topography
   B. The number of gauges
   C. Rainfall values
   D. Units
   Answer: A. It is a simple average. (Key point: Arithmetic mean)

2. What are Thiessen weights based on?
   A. Isohyet areas
   B. Polygon areas around gauges
   C. Elevation
   D. Equal share
   Answer: B. Weighted by area nearest to each gauge. (Key point: Thiessen weights)

3. For which terrain is the isohyetal method best?
   A. Flat areas with uniform gauges
   B. Single gauge
   C. Hilly/mountainous large catchments
   D. Urban
   Answer: C. It considers orography and has highest accuracy. (Key point: Isohyetal suitability)

## Related in Engineering Hydrology

- [Thiessen polygon mean rainfall, pentagon catchment](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Athiessen-pentagon-pqrs) — 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

## Related in other subjects

- [Arithmetic mean and Thiessen average precipitation](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Aarithmetic-thiessen-numerical) — Hydro Power, chapter 2
- [Thiessen polygon method with rainfall data](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Athiessen-polygon-explain-numerical) — Hydro Power, chapter 2