7.3 Flow duration curves and low flow analysis

Flow Duration Curves

Flow duration curves (FDCs) show how often different streamflow levels occur at a given location. They're one of the most widely used tools in hydrology because they compress an entire streamflow record into a single graph that reveals water availability, flow variability, and drought risk at a glance.

Low flow analysis builds on this by focusing specifically on dry-period conditions. Indices like 7Q10 and 95% exceedance flow give water managers standardized benchmarks for setting discharge permits, protecting aquatic ecosystems, and planning for droughts.

Flow Duration Curves

Flow duration curves in water management

An FDC plots the percentage of time a specific flow is equaled or exceeded. The x-axis shows exceedance probability (how often), and the y-axis shows the corresponding discharge (how much). Together, they capture the full range of flow conditions a stream experiences.

FDCs are used to:

• Assess water availability for irrigation, hydropower generation, and municipal water supply
• Evaluate habitat suitability by identifying whether a stream maintains enough flow to support aquatic life
• Design hydraulic structures such as culverts, bridges, and spillways, where engineers need to know the range of flows a structure must handle
• Detect changes over time by comparing FDCs before and after land-use changes, water withdrawals, or shifts in climate

Construction of flow duration curves

Building an FDC is straightforward once you have a continuous streamflow record:

1. Gather streamflow data for the location and time period of interest (daily mean discharge is most common).
2. Rank all flow values from highest (rank 1) to lowest (rank $n$).
3. Calculate exceedance probability for each ranked value using the Weibull plotting position formula:

$P = \frac{m}{n+1} \times 100$

• $P$ = exceedance probability (%)
• $m$ = rank of the flow value (1 = highest flow)
• $n$ = total number of flow values

1. Plot the results with exceedance probability on the x-axis and discharge on the y-axis. Both axes are typically shown on logarithmic scales so the full range of flows is visible.

Interpreting the curve shape

The shape of an FDC tells you a lot about the watershed:

• A steep curve means the stream is "flashy," with large differences between high and low flows. This is common in small, urbanized, or impervious catchments.
• A flat curve indicates more stable, sustained flow, often driven by strong groundwater (baseflow) contributions or regulation by lakes and reservoirs.
• The lower tail (right side, high exceedance percentages) is especially important for low flow analysis because it shows how much water the stream provides during dry periods.

Low Flow Analysis

Low flow analysis for water availability

Low flow conditions occur when streamflow drops well below average, typically during prolonged dry weather or when upstream withdrawals reduce discharge. Understanding these conditions matters because:

• Ecosystems depend on minimum flows to maintain water temperature, dissolved oxygen, and habitat connectivity for fish.
• Water supply systems need to know the worst-case flows they'll have to work with.
• Regulators set effluent discharge limits based on low flows, since pollutant concentrations rise as dilution decreases.

Statistical methods for low flow indices

Low flow indices give you standardized numbers to compare drought severity across different streams and time periods. The two most common are 7Q10 and 95% exceedance flow.

7Q10: Lowest 7-day average flow with a 10-year return period

The 7Q10 is the lowest 7-day average flow expected to occur once every 10 years on average. It's widely used in the U.S. for setting wastewater discharge permits. To calculate it:

1. For each year in the record, find the minimum 7-day running average of daily flows.
2. Rank these annual minimum 7-day averages from lowest (rank 1) to highest (rank $n$).
3. Assign a non-exceedance probability to each using the Weibull formula:

$P = \frac{m}{n+1}$

• $P$ = non-exceedance probability
• $m$ = rank (1 = lowest flow)
• $n$ = number of years of record

1. The 7Q10 corresponds to a non-exceedance probability of 0.1 (10%). Interpolate between the two ranked values whose probabilities bracket 0.1, or fit a frequency distribution (such as the log-Pearson Type III) and read the value at $P = 0.1$.

A longer period of record produces a more reliable 7Q10 estimate. With only a few years of data, the result can be quite uncertain.

95% exceedance flow

This is the discharge equaled or exceeded 95% of the time. You read it directly off the flow duration curve at the 95% mark on the x-axis. It's simpler to obtain than the 7Q10 and is commonly used internationally for water resource planning and environmental flow requirements.