Double Mass Curve Technique in Hydrology

Double Mass Curve Technique

• Used to check for inconsistency in a raingauge station's record.
• The technique relies on the principle that consistent rainfall data originates from the same parent population.
• Steps:
  • Select a group (5-10) of base stations near the station in question (X).
  • Arrange the annual (or monthly/seasonal) rainfall data for station X and the average rainfall data for the base stations in reverse chronological order.
  • Calculate the accumulated precipitation for station X (∑ Px) and the accumulated average precipitation for the base stations (∑ Pb) starting from the latest record.
  • Plot ∑ Px against ∑ Pb for consecutive time periods.
  • A break in the plot's slope indicates a change in the precipitation regime at station X.
  • Correct precipitation values beyond the regime change using the formula: Pcx = Px * (Mc/Ma), where:
    • Pcx = corrected precipitation at time period t1 at station X.
    • Px = original recorded precipitation at time period t1 at station X.
    • Mc = corrected slope of the double mass curve.
    • Ma = original slope of the double mass curve.

Causes of Inconsistency in Rainfall Record

• Shifting of a raingauge station to a new location.
• Significant changes in the station's surrounding environment.
• Ecosystem changes due to events like forest fires or landslides.
• Observational errors from a specific date onward.

Mean Precipitation Over an Area

• Determines the average precipitation depth over a specific area.
• Factors affecting reliability of rainfall measurements at a single gauge:
  • Distance from the gauge to the area's center.
  • Area size.
  • Topography.
  • Nature of the rainfall event.
  • Local storm pattern characteristics.

Methods to Calculate Areal Average Precipitation

• Arithmetic Mean Method:
  • Simplest method.
  • Considers only stations within the watershed boundary.
  • Average precipitation (P) = ∑(Pi) / N
    • Pi = rainfall at the ith raingauge station.
    • N = total number of raingauge stations.
• Thiessen Polygon Method:
  • Assigns weightage to each station's rainfall based on its corresponding area.
  • Procedure:
    • Draw the catchment area to scale.
    • Mark raingauge station positions on the map.
    • Connect stations to form triangles.
    • Construct perpendicular bisectors for each triangle side, forming polygons around each station.
  • P = (A1 * P1 + A2 * P2 + ... + An * Pn) / (A1 + A2 + ... + An)
    • Ai = Area of the polygon around station i.
    • Pi = Rainfall at station i.
• Isohyetal Method:
  • Draws isohyets (lines of equal rainfall) based on rainfall data.
  • Calculates the area enclosed between each pair of isohyets.
  • Average precipitation is determined by weighing the precipitation at the center of each area by the area's size.
• Inverse Distance Weighting:
  • Uses the inverse of the distance between a station and the area's point of interest to weight the station's rainfall value.
  • Closer stations have a higher weight.

Additional Terms

• Point rainfall: Rainfall measured at a single station.
• Moving average: A technique to smooth out high-frequency fluctuations in a time series.
• Hyetograph: A graphical representation of rainfall intensity over time.
• Mass Curve of Rainfall: A graph that shows the cumulative rainfall over time.
• Normal Ratio Method: A method used to estimate the annual rainfall at a station when normal annual precipitation values vary significantly.

This quiz explores the Double Mass Curve Technique used to assess inconsistencies in rainfall data from gauging stations. Participants will learn the methodology for plotting accumulated precipitation data, identifying regime changes, and applying corrections to recorded values. Test your understanding of this vital hydrological analysis tool.