Key Features

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Frequency Analysis

Frequency analysis takes a different approach in characterising baseflow by deriving the relationship between the magnitude and frequency of streamflow discharges from the hydrographic record. In its most common application, a flow duration curve (FDC) is generated. Instead of plotting as a time series, a flow duration curve shows the percentage of time that a given flow rate is equalled or exceeded. The FDC is constructed from flow data of fixed time period (eg daily, monthly, annual) by:

  1. Sorting the flow data in order of decreasing flow;
  2. Assigning a unique ranking number m to each flow, starting with 1 for the maximum flow to n for the minimum flow, where n is the number of flow measurements.

  3. The probability P that a given flow will be equalled or exceeded is defined by:

    (Equation 1)

    Mathematical equation
  4. The flow-probability relationship is typically presented as a log-normal plot (Fetter, 1994).

Flow duration curves can be constructed for the entire record of flow measurement, or for specific time periods such as similar calendar months or seasons.

Figure 1: Flow distribution curves for examples of (a) high baseflow and (b) low baseflow streams

Figure 1: Flow distribution curves for examples of (a) high baseflow and (b) low baseflow streams

The FDC provides information on the baseflow component of stream flow. The median flow (Q50) is the discharge which is equalled or exceeded 50% of the time. The part of the curve with flows below the median flow represents low-flow conditions. Baseflow is interpreted to be significant if this part of the curve has a low slope, as this reflects continuous discharge to the stream. A steep slope for these low-flows suggests relatively small contributions from natural storages like groundwater (Figure 1). These streams may cease to flow for relatively long periods. In this way, the shape of the FDC can indicate the hydrogeological characteristics of a catchment (Smakhtin, 2001).

Various indices are used to represent the characteristics of the low-flow regime for a stream. The ratio of the discharge which is equalled or exceeded 90% of the time, to that of 50% of the time (Q90/Q50) is commonly used to indicate the proportion of streamflow contributed from groundwater storage (Nathan and McMahon, 1990). Other low-flow indices include:

  1. One- or n-day discharges that are exceeded at defined percentages of time, say 75, 90 or 95% eg. Q75(7), Q75(10), Q95(10);
  2. The percentage of time the stream is at zero-flow conditions;
  3. The longest recorded period of consecutive zero-flow days (Smakhtin, 2001). A Low-flow Frequency Curve (LFFC) shows the proportion of years when a low-flow rate is exceeded. This depicts the recurrence interval which is the average interval (in years) that the stream discharge falls below a given rate, and can also be used to represent baseflow conditions. The curve is generated from the series of annual minimum flow values extracted from the stream monitoring data. Like the flow duration curve, various indices can be used to indicate baseflow conditions including:
    1. The slope of the LFFC, as the larger the slope indicates more variability in low-flows;
    2. Breaks in the curve near the modal value have been interpreted as representing when streamflow is exclusively from groundwater storage;
    3. Lowest average flows that occur over a set number of consecutive days (eg 3, 7 days) at defined recurrence intervals (eg 2, 10 years), for example 7-day 10-year low flow (7Q10) or 7-day 2-year low flow (7Q2);
    4. The average of the annual series of minimum 7-day average flows, MAM7 or also known as dry weather flow;
    5. Indices of seasonal low flows such as mean 30-day summer low flows (Smakhtin, 2001).

References