Second Moment Of DRH About Time Origin Divided By Total Direct Runoff Calculator

Formula Used:

\[ MQ2 = (n \times (n+1) \times K^2) + (2 \times n \times K \times MI1) + MI2 \]

Constant n:

(dimensionless)

Constant K:

(time units)

First Moment of the ERH:

(time units)

Second Moment of the ERH:

(time² units)

Second Moment of the DRH:

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1. What is the Second Moment of DRH?

The Second Moment of the Direct Runoff Hydrograph (DRH) about the time origin divided by the total direct runoff is a statistical measure that characterizes the temporal distribution and spread of the runoff hydrograph. It provides information about the dispersion and timing of the runoff response in a catchment.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ MQ2 = (n \times (n+1) \times K^2) + (2 \times n \times K \times MI1) + MI2 \]

Where:

\( MQ2 \) — Second Moment of the DRH (time² units)
\( n \) — Constant for the catchment (dimensionless)
\( K \) — Constant for flood hydrograph characteristics (time units)
\( MI1 \) — First Moment of the ERH (time units)
\( MI2 \) — Second Moment of the ERH (time² units)

Explanation: This formula relates the second moment of the direct runoff hydrograph to the catchment constants and the moments of the effective rainfall hyetograph.

3. Importance of Second Moment Calculation

Details: Calculating the second moment of DRH is crucial for understanding the temporal distribution of runoff, analyzing catchment response characteristics, and developing accurate hydrological models for flood prediction and water resource management.

4. Using the Calculator

Tips: Enter the constant n (dimensionless), constant K (time units), first moment of ERH (time units), and second moment of ERH (time² units). All values must be non-negative.

5. Frequently Asked Questions (FAQ)

Q1: What do the constants n and K represent?
A: Constant n represents catchment characteristics determined by effective rainfall, while constant K represents flood hydrograph characteristics of the catchment.

Q2: How are the moments of ERH determined?
A: The moments of Effective Rainfall Hyetograph are calculated from rainfall data about the time origin, divided by the total effective rainfall.

Q3: What units are used for the moments?
A: First moment has time units, second moment has time² units. The specific time unit depends on the measurement interval used.

Q4: How is this calculation used in hydrology?
A: This calculation helps in understanding catchment response timing, designing drainage systems, and developing unit hydrographs for flood forecasting.

Q5: Are there limitations to this formula?
A: The formula assumes linear catchment response and may need adjustment for complex catchments with non-linear behavior or significant storage effects.