---
title: "Rainfall-runoff relationship, factors affecting runoff"
subject: "Engineering Hydrology"
chapter: 4
key: "semester_5/engineering_hydrology:rainfall-runoff-relation-factors"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/rainfall-runoff-relation-factors
site: BCT Engineering
---

# Rainfall-runoff relationship, factors affecting runoff

Engineering Hydrology · Chapter 4: Surface Runoff

- Asked in: 2080 Bhadra, 3+3 marks
- Video: [Runoff, It's Type, Factors Affecting on Runoff - Hydrology - Water Resource Engineering 1](https://www.youtube.com/watch?v=BlKYOc5DNZs) — Ekeeda
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/rainfall-runoff-relation-factors
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-4

## Question

Establish relationship between rainfall and resulting runoff for a large catchment. Point out the factors affecting runoff from a basin.

## Short answer

Runoff R relates to rainfall P via regression (R = aP + b), runoff coefficient (R = CP), Khosla's formula, or SCS curve number method. Runoff is affected by climatic factors (rainfall intensity, duration, antecendent moisture), catchhment characteristics (size, slope, soil, land use), channel properties, and human activities

## Answer

#### Rainfall-runoff relationship for a large catchment
For a large catchment, runoff $R$ (depth, cm) depends on rainfall $P$ (cm) mainly through losses. Relations are established from records of the catchment, as follows.

**1. Correlation (regression) method**
- Collect annual or seasonal values of $P$ (catchment average rainfall by Thiessen or isohyetal method) and the corresponding $R$ (observed flow converted to depth).
- Plot $R$ against $P$; fit a straight line by least squares:
$$
R = aP + b
$$
where $a=\dfrac{N\sum PR-\sum P\sum R}{N\sum P^2-(\sum P)^2}$ and $b=\bar R - a\bar P$. A correlation coefficient $r$ near 1 shows a reliable relation.
- Where the relation is curved, use $R = aP^{n}$ or a polynomial.

```text
 R |            . . /
   |        . . /
   |     .  /      best-fit line
   |   . /
   | /
   +----------------- P
```

**2. Runoff coefficient:** $R = CP$ (or $Q_p=CiA/360$ for peak flow), where $C$ depends on land use, soil and slope.

**3. Khosla's formula (monthly):** $R_m = P_m - L_m$, with loss $L_m = 0.48T_m$ (cm) for mean temperature $T_m>4.5\ ^\circ$C.

**4. SCS curve-number method (storm):**
$$
R=\frac{(P-0.2S)^2}{P+0.8S},\qquad S=\frac{25400}{CN}-254\ \text{(mm)}
$$

#### Factors affecting runoff from a basin
- **Climatic:** rainfall intensity, duration, distribution, antecedent moisture, storm movement, evaporation, temperature.
- **Catchment:** size, shape, slope, land use and vegetation, soil type and geology, drainage density, depression and lake storage.
- **Channel:** cross-section, roughness and slope.
- **Human:** dams, diversions, urbanisation, irrigation.

The larger the catchment, the lower the specific runoff from short storms because of storage and attenuation.

## Check yourself

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

1. How is the linear rainfall-runoff relation fitted?
   A. R = P always
   B. R is read from the stage
   C. R = P^2
   D. R = aP + b by least squares from catchment records, with r near 1 showing reliability
   Answer: D. Annual or seasonal P and R are regressed. (Key point: Regression)

2. What does the SCS curve number method give?
   A. R = (P - 0.2S)^2/(P + 0.8S) with S = 25400/CN - 254 mm
   B. R = CP
   C. R = P - 0.48T
   D. R = aP + b
   Answer: A. It relates storm runoff to rainfall and the catchment's curve number. (Key point: SCS method)

3. What is Khosla's formula?
   A. Rm = CiA/360
   B. Rm = Pm - Lm, with Lm = 0.48 Tm cm for Tm > 4.5 deg C
   C. Rm = Pm + Lm
   D. Rm = 0.2 Pm
   Answer: B. Monthly loss depends on mean temperature. (Key point: Khosla's formula)

## Related in Engineering Hydrology

- [Catchment and factors affecting runoff](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Acatchment-runoff-factors) — Engineering Hydrology, chapter 4
- [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×
- [Total rainfall, runoff and peak discharge with phi-index](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aphi-index-50ha-2-5) — Engineering Hydrology, chapter 3
- [Rating curve and factors affecting runoff](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Arating-curve-runoff-factors) — Engineering Hydrology, chapter 4
- [Total rainfall and phi-index, 100 km2 basin](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Atotal-rainfall-phi-100km2) — Engineering Hydrology, chapter 3
- [Phi-index, excess rainfall hyetograph, runoff volume](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aphi-hyetograph-5km2) — Engineering Hydrology, chapter 3

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