Why is the unit hydrograph called a linear method?

It assumes that doubling the effective rainfall doubles the runoff (proportionality) and that the responses to successive rainfall increments add up (superposition); these linearity assumptions let any storm's hydrograph be built by convolving rainfall with the unit hydrograph.

What is a synthetic unit hydrograph?

It is a unit hydrograph estimated from catchment characteristics, such as area, slope, and time of concentration, rather than from observed rainfall-runoff data, allowing the method to be applied to ungauged catchments.

The Unit Hydrograph

The unit hydrograph is the runoff response of a catchment to a unit depth of effective rainfall, treating the catchment as a linear system that can be used to predict flood hydrographs.

Definition

The unit hydrograph is the direct-runoff hydrograph resulting from one unit (for example, one centimetre) of effective rainfall applied uniformly over a catchment during a specified duration, used as the catchment's linear response function.

Scope

This topic covers the definition and assumptions of the unit hydrograph, its derivation from observed storms, its use to predict runoff by convolution, and synthetic and instantaneous unit hydrographs. It is the classic linear-systems approach to the rainfall-runoff transformation introduced physically in the runoff-mechanisms topic.

Core questions

What is the unit hydrograph, and what assumptions does it make?
How is a unit hydrograph derived from observed rainfall and runoff?
How is it used to predict the runoff hydrograph from a storm?
What are synthetic and instantaneous unit hydrographs?

Key concepts

Effective (excess) rainfall
Direct runoff
Linearity and superposition
Convolution
Instantaneous unit hydrograph
Synthetic unit hydrographs

Key theories

Unit hydrograph theory: Sherman proposed that direct runoff is proportional to effective rainfall and that the catchment response is fixed and additive, so the hydrograph from any storm can be built by scaling and superposing the unit hydrograph (convolution).
Linear-systems and the instantaneous unit hydrograph: The unit hydrograph was generalized as the impulse response of a linear, time-invariant system, leading to the instantaneous unit hydrograph and conceptual models of catchment response.

Clinical relevance

The unit hydrograph remains a widely used, transparent tool for design-flood estimation and rainfall-runoff prediction in engineering hydrology, including at ungauged sites through synthetic unit hydrographs, and provides the conceptual basis for many catchment models.

History

Sherman introduced the unit-graph method in 1932; subsequent decades formalized it through linear-systems theory, the instantaneous unit hydrograph (Dooge and others), and synthetic unit hydrographs for ungauged catchments, making it a cornerstone of applied hydrology.

Key figures

LeRoy K. Sherman
James C. I. Dooge
Ven Te Chow

Seminal works

sherman1932
chow1988
dooge1959

Frequently asked questions

Why is the unit hydrograph called a linear method?: It assumes that doubling the effective rainfall doubles the runoff (proportionality) and that the responses to successive rainfall increments add up (superposition); these linearity assumptions let any storm's hydrograph be built by convolving rainfall with the unit hydrograph.
What is a synthetic unit hydrograph?: It is a unit hydrograph estimated from catchment characteristics, such as area, slope, and time of concentration, rather than from observed rainfall-runoff data, allowing the method to be applied to ungauged catchments.