First Moment of ERH given Second Moment of DRH Calculator

Formula Used:

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

Second Moment of the DRH (MQ2):

Second Moment of the ERH (MI2):

Constant n:

Constant K:

First Moment of the ERH (MI1):

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1. What is the First Moment of ERH?

The First Moment of the Effective Rainfall Hyetograph (ERH) about the time origin divided by the total effective rainfall is a key parameter in hydrological analysis. It helps in understanding the temporal distribution of effective rainfall and its impact on runoff generation.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( MI1 \) — First Moment of the ERH
\( MQ2 \) — Second Moment of the DRH about the time origin divided by the total direct runoff
\( MI2 \) — Second Moment of the ERH about the time origin divided by the total excess rainfall
\( n \) — Constant for the catchment determined by the effective rainfall
\( K \) — Constant for the catchment determined by flood hydrograph characteristics

Explanation: This formula establishes the relationship between moments of direct runoff hydrograph (DRH) and effective rainfall hyetograph (ERH) using catchment-specific constants.

3. Importance of First Moment Calculation

Details: Calculating the first moment of ERH is crucial for hydrological modeling, flood forecasting, and understanding the temporal characteristics of rainfall-runoff processes in a catchment area.

4. Using the Calculator

Tips: Enter all required parameters - Second Moment of DRH, Second Moment of ERH, Constant n, and Constant K. Ensure all values are positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for Constant n and K?
A: Constant n typically ranges from 1 to 5, while Constant K varies based on catchment characteristics and can range from 1 to 10 hours.

Q2: How are the moments of DRH and ERH determined?
A: Moments are calculated from measured or simulated hydrograph and hyetograph data using statistical moment calculations about the time origin.

Q3: What is the significance of the first moment in hydrology?
A: The first moment represents the centroid or average time of the distribution, providing information about the timing characteristics of rainfall or runoff.

Q4: Can this formula be applied to all catchments?
A: The formula is generally applicable but constants n and K need to be calibrated for specific catchment characteristics.

Q5: What are the units of the calculated first moment?
A: The first moment has units of time (e.g., hours) and represents the average time offset of the effective rainfall distribution.