Flow Duration Curve Calculator
Compute flow duration curve using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Formula
Exceedance Probability = rank / (n + 1) x 100
For each flow value, sort all values from highest to lowest and assign ranks. The exceedance probability for each rank is calculated using the Weibull plotting position: P = m / (n + 1) x 100, where m is the rank and n is the total number of data points. The flow at any target exceedance is found by interpolation between adjacent ranked values.
Worked Examples
Example 1: Perennial Stream Analysis
Problem: Monthly average flows (m3/s): 120, 95, 80, 65, 50, 40, 30, 22, 15, 8. Find Q80.
Solution: Sort descending: 120, 95, 80, 65, 50, 40, 30, 22, 15, 8\nExceedance probabilities: 9.1%, 18.2%, 27.3%, ..., 90.9%\nQ80 by interpolation falls between 15 and 22 m3/s\nMean flow: 52.5 m3/s | CV: 63.7%
Result: Q80 ~ 17.4 m3/s | Mean: 52.5 | Highly variable stream
Example 2: Hydropower Feasibility
Problem: Design flow at Q30, mean annual flow 50 m3/s, catchment area 100 km2.
Solution: Q30 from FDC gives the flow exceeded 30% of time.\nThis represents the upper range for turbine sizing.\nSpecific discharge = (50/100) x 1000 = 500 L/s/km2\nThe steep FDC slope suggests seasonal generation variability.
Result: Design at Q30 for optimal energy balance | Seasonal operation likely
Frequently Asked Questions
What is a flow duration curve?
A flow duration curve (FDC) is a cumulative frequency curve that shows the percentage of time a given streamflow was equaled or exceeded over a historical period. The x-axis shows the percentage of time (exceedance probability) and the y-axis shows discharge. The curve summarizes the complete range of flow conditions at a site in a single graph. It is one of the most useful tools in hydrology for water supply planning, hydropower design, ecological flow assessment, and water quality management.
What does the slope of a flow duration curve indicate?
A steep FDC slope indicates highly variable flow with large differences between wet and dry periods, typical of flashy catchments with impervious surfaces or steep terrain. A flat FDC slope indicates stable flow with small differences between high and low flows, typical of groundwater-dominated catchments or those with significant reservoir storage. The slope index is often calculated as the difference between log(Q10) and log(Q90) divided by 80, providing a single number that characterizes flow variability across the middle range of the distribution.
How is a flow duration curve used in hydropower design?
For hydropower, the FDC determines the optimal design flow and expected energy generation. The design flow is typically chosen between Q20 and Q40, balancing turbine size against annual energy output. Flow below the minimum turbine operating threshold (usually 30-40% of design flow) cannot generate power. The area under the FDC between the minimum and design flows represents the energy-generating potential. A flat FDC means more consistent power generation, while a steep FDC means seasonal variability requiring storage or grid backup.
Can flow duration curves predict future conditions?
Historical FDCs assume stationarity, meaning past flow patterns will continue. However, climate change, land use change, and water management alterations can shift the FDC significantly. Climate change may flatten or steepen the curve depending on how precipitation patterns shift. Urbanization typically steepens the curve by increasing high flows and reducing baseflow. Reservoir construction flattens the curve by storing high flows and augmenting low flows. Periodically updating FDCs with recent data is essential for reliable water planning.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
Does Flow Duration Curve Calculator work offline?
Once the page is loaded, the calculation logic runs entirely in your browser. If you have already opened the page, most calculators will continue to work even if your internet connection is lost, since no server requests are needed for computation.