Unit hydrograph convolution calculator

Calculate convolved direct-runoff ordinates JSON and peak direct-runoff discharge with your own figures.

Your numbers

Use the units shown. Results update as you change valid inputs.

Use convolved direct-runoff ordinates JSON and peak direct-runoff discharge to compare changes to your inputs. The method and limits below explain the scope.

Examples

Examples

Try the starting example

Excess rainfall blocks (mm)
5,10,3
Unit hydrograph ordinates (m³/s per mm)
0,1,2,1,0
Convolved direct-runoff ordinates (m³/s) JSON
[0,5,20,28,16,3,0]
Peak direct-runoff discharge (m³/s)
28

Try another scenario

Excess rainfall blocks (mm)
[6, 10, 3]
Unit hydrograph ordinates (m³/s per mm)
[0, 1, 2, 1, 0]
Convolved direct-runoff ordinates (m³/s) JSON
[0,6,22,29,16,3,0]
Peak direct-runoff discharge (m³/s)
29
Calculation method

Calculation method

Convolved direct-runoff ordinates (m³/s) JSON

Discrete convolution with unit hydrograph expressed per 1 mm excess rainfall and matching rainfall-block duration.

Peak direct-runoff discharge (m³/s)

Discrete convolution with unit hydrograph expressed per 1 mm excess rainfall and matching rainfall-block duration.

Symbols and units
a
Excess rainfall blocks (mm)
b
Unit hydrograph ordinates (m³/s per mm)

Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.

Assumptions & limits

Assumptions & limits

  • User-supplied measurements and assumptions; Discrete convolution with unit hydrograph expressed per 1 mm excess rainfall and matching rainfall-block duration. Supported limits: Finite numeric values bounded to 1e9 magnitude; lists and tables contain 1–100 records unless a stricter bound is stated. Inputs use the units shown. Lists explicitly paired by a method must have matching lengths; independent polynomial coefficient vectors may differ. Respect stated physical, interpolation, policy and computational domain limits.
Are these inputs private?

These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.

Further reading

Method reference ↗

Background reading; this does not imply endorsement or independent review of SumFizz.

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