Hydrograph and flow duration curve

Hydrograph

A hydrograph is a graph of river discharge plotted against time in calendar order (hours, days or months). It shows when high and low flows occur, e.g. the monsoon peak in July–August and the dry-season low in March–April for Nepalese rivers.

 Q (m3/s)
  |            __
  |           /  \
  |          /    \
  |         /      \__
  |  _____/            \______
  +---------------------------> Month
   Jan  Mar  May  Jul  Sep  Nov

Flow duration curve (FDC)

An FDC is a graph of discharge against the percentage of time it is equalled or exceeded. It is made by sorting the same flow data in descending order and plotting each value against its exceedance $P = \dfrac{m}{n+1}\times 100\%$. Time order is lost, but the duration of each flow is shown.

 Q (m3/s)
  |\
  | \
  |  \___
  |      \______
  |             \__________
  +--------------------------> % time exceeded
  0     45   65       95  100

Applicability of the hydrograph

1. Seasonal energy: monthly flows give month-wise energy, needed for wet/dry season tariff and PPA.
2. Flood design: peak flood hydrographs size spillways, cofferdams and diversion works.
3. Storage design: the mass curve (cumulative hydrograph) gives the reservoir or pondage volume needed to meet demand.
4. Construction and maintenance planning: plan works and unit outages in low-flow months.
5. Sediment planning: high-flow months carry most sediment, guiding desander operation.

Applicability of the FDC

1. Design discharge: chosen at a set exceedance, e.g. $Q_{40}$–$Q_{45}$ for ROR in Nepal.
2. Installed capacity and annual energy: area under the FDC up to the design flow gives energy; plant factor is found from it.
3. Firm power: from $Q_{90}$–$Q_{95}$.
4. Number and size of units: shows how often the plant runs at part load.
5. Riparian release: from the low-flow tail.
6. Comparison of sites: a flat FDC means steady flow, ideal for ROR; a steep FDC means storage is needed.