Hydrographs

What is a Hydrograph?

A Hydrograph is a plot of discharge ($Q$) versus time ($t$) at a specific section of a river or channel. It represents the integrated response of a catchment to rainfall inputs.

Components of a Single-Peaked Hydrograph:

1. Rising Limb: The ascending portion, influenced by storm character and catchment state.
2. Crest Segment (Peak): The highest point ($Q_p$).
3. Recession Limb: The descending portion, representing the withdrawal of water from storage (surface, channel, and ground).

Baseflow Separation

To analyze the direct response to a storm (Direct Runoff Hydrograph - DRH), Baseflow must be subtracted from the total streamflow hydrograph.

Methods:

1. Straight Line Method: Connects the start of the rising limb to a point on the recession limb.
2. Fixed Base Method: Assumes baseflow recession continues until the peak, then rises.
3. Variable Slope Method: Adjusts baseflow based on recession curves.

Unit Hydrograph Theory

Sherman (1932) introduced the Unit Hydrograph (UH).

Definition: The hydrograph of direct runoff resulting from 1 unit (e.g., 1 cm or 1 inch) of effective rainfall occurring uniformly over the basin at a uniform rate during a specified duration ($D$).

Assumptions:

1. Time Invariance: The DRH for a given effective rainfall is always the same, regardless of when it occurs.
2. Linear Response: Runoff ordinates are proportional to rainfall excess volume. (e.g., 2 cm of rain produces a DRH with ordinates 2x that of the UH).
3. Superposition: Hydrographs from consecutive rainfall bursts can be added (lagged by time).

Deriving DRH from UH:

If we have a $D$-hour Unit Hydrograph ($U$) and a storm of excess rainfall $P$ cm (duration $D$), the resulting DRH ordinates are:

S-Curve Method

Used to convert a Unit Hydrograph of duration $D$ to a Unit Hydrograph of duration $T$. An S-Curve is the hydrograph produced by a continuous effective rainfall at a constant rate for an infinite period.