---
title: "Procedure of Thiessen mean rainfall"
subject: "Engineering Hydrology"
chapter: 2
key: "semester_5/engineering_hydrology:thiessen-procedure"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/thiessen-procedure
site: BCT Engineering
---

# Procedure of Thiessen mean rainfall

Engineering Hydrology · Chapter 2: Precipitation

- Asked in: 2080 Bhadra, 4 marks
- Video: [Thiessen Polygon method to determine average rainfall of a catchment area in hydrology](https://www.youtube.com/watch?v=RV0Tw-O5oIA) — ENG-School
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/thiessen-procedure
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-2

## Question

Describe the procedure of estimation of mean rainfall over an area using Thiessen Mean Method.

## Short answer

Join adjacent gauges to form triangles, draw perpendicular bisectors to create polygons. Measure polygon areas A_i; weight = A_i/A. Mean rainfall = Σ A_i P_i / Σ A_i. It improves on arithmetic mean for uneven spread but ignores orography and requires polygon redraw if gauges change.

## Answer

The Thiessen polygon method gives the mean rainfall by weighting each gauge by the area nearest to it.

#### Procedure
1. Draw the catchment boundary to scale and mark the positions of all rain gauges (inside, and a few just outside).
2. Join adjacent stations by straight lines to form a network of triangles (avoid very acute triangles).
3. Draw the perpendicular bisector of each side. The bisectors meet at the circumcentres of the triangles and form a polygon around each station.
4. Each polygon is the area closer to its station than to any other. Trim the polygons at the catchment boundary.
5. Measure the area $A_i$ of each polygon inside the catchment (planimeter, grid or coordinates).
6. Find the weight $W_i = A_i/A$, where $A = \sum A_i$ is the catchment area.
7. Mean rainfall:

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

```text
        *1
       /|\
      / | \     perpendicular bisectors
   *2---+---*3   form polygons around
      \ | /     each station
        *4
```

#### Remarks
It is better than the arithmetic mean for uneven gauge spread, but it does not include orographic effects. The polygons must be redrawn when a gauge is added or fails.

## Check yourself

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

1. What forms the polygons?
   A. Lines joining stations
   B. Isohyets
   C. Perpendicular bisectors of lines joining adjacent stations
   D. Parallel lines
   Answer: C. They meet at circumcentres. (Key point: Bisectors)

2. How is the weight W_i defined?
   A. P_i / sum P
   B. 1/n
   C. A / A_i
   D. A_i / A
   Answer: D. Polygon area over catchment area. (Key point: Weights)

3. What is a limitation?
   A. Does not include orographic effects; redraw if gauge changes
   B. Needs no map
   C. Ignores gauge positions
   D. Only for hills
   Answer: A. Not suitable for orographic variation. (Key point: Limitation)

## 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
- [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×
- [DAD curve procedure and isohyetal area data](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Adad-curve-procedure-isohyetal) — Engineering Hydrology, chapter 2
- [Principle and procedure of slope-area method](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aslope-area-principle-procedure) — Engineering Hydrology, chapter 4
- [Thiessen weights for semicircular catchment](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Athiessen-weights-semicircle) — Engineering Hydrology, chapter 2

## Related in other subjects

- [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
- [Advantages of interval over point estimation](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Aadvantages-interval-estimation-over-point) — Probability and Statistics, chapter 6
- [Oxidation pond and area procedure](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Aoxidation-pond-area-procedure) — Sanitary Engineering, chapter 7
- [Arithmetic mean and Thiessen average precipitation](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Aarithmetic-thiessen-numerical) — Hydro Power, chapter 2