First Moment Of ERH About Time Origin Divided By Total Effective Rainfall Calculator

Formula Used:

\[ MI_1 = MQ_1 - (n \times K) \]

First Moment of the ERH (MI₁):

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1. What is the First Moment of ERH?

The First Moment of the ERH (Effective Rainfall Hydrograph) about the time origin divided by the total effective rainfall is a key parameter in hydrological analysis. It represents the temporal distribution characteristics of effective rainfall in a catchment area.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ MI_1 = MQ_1 - (n \times K) \]

Where:

\( MI_1 \) — First Moment of the ERH about the time origin divided by the total effective rainfall
\( MQ_1 \) — First Moment of the DRH about the time origin divided by the total direct runoff
\( n \) — Constant for the catchment determined by the effective rainfall
\( K \) — Constant for the catchment determined by flood hydrograph characteristics

Explanation: This formula calculates the first moment of the effective rainfall hydrograph by subtracting the product of constants n and K from the first moment of the direct runoff hydrograph.

3. Importance of First Moment Calculation

Details: Calculating the first moment of ERH is crucial for understanding the timing and distribution of effective rainfall in hydrological modeling, flood forecasting, and watershed management studies.

4. Using the Calculator

Tips: Enter the first moment of DRH (MQ₁), constant n, and constant K. All values must be non-negative numbers. The calculator will compute the first moment of ERH (MI₁).

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the first moment in hydrology?
A: The first moment represents the centroid or average time of the hydrograph, providing important information about the timing characteristics of rainfall or runoff.

Q2: How are constants n and K determined for a catchment?
A: Constants n and K are typically determined through calibration using historical rainfall and runoff data specific to the catchment characteristics.

Q3: What units are used for the first moment calculation?
A: The first moment is typically expressed in time units (hours or minutes) as it represents the temporal distribution of the hydrograph.

Q4: Can this formula be applied to all catchment types?
A: While the formula is generally applicable, constants n and K need to be calibrated specifically for each catchment to ensure accurate results.

Q5: What is the relationship between ERH and DRH?
A: The Effective Rainfall Hydrograph (ERH) represents the rainfall excess that becomes direct runoff, while the Direct Runoff Hydrograph (DRH) represents the catchment's response to this effective rainfall.