Mean of Variate in Flood Frequency Studies Calculator

✖Variate 'X' with a Recurrence Interval of a random hydrologic series with a return period.ⓘ Variate 'X' with a Recurrence Interval [x_T]			+10% -10%
✖Frequency Factor which varies between 5 to 30 according to rainfall duration is a function of recurrence interval (T) and the coefficient of skew (Cs).ⓘ Frequency Factor [K_z]			+10% -10%
✖Standard Deviation of the Z Variate Sample follows a certain probability distribution of a hydrologic model.ⓘ Standard Deviation of the Z Variate Sample [σ]			+10% -10%

✖Mean of the Variate X of a random hydrologic series with a return period.ⓘ Mean of Variate in Flood Frequency Studies [x_m]

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Formula

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Mean of Variate in Flood Frequency Studies

Formula

`"x"_{"m"} = "x"_{"T"}-"K"_{"z"}*"σ"`

Example

`"0.68"="9.43"-"7"*"1.25"`

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Download Gumbel's Method for Prediction of Flood's Peak Formulas PDF

Mean of Variate in Flood Frequency Studies Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mean of the Variate X = Variate 'X' with a Recurrence Interval-Frequency Factor*Standard Deviation of the Z Variate Sample
x_m = x_T-K_z*σ
This formula uses 4 Variables

Variables Used

Mean of the Variate X - Mean of the Variate X of a random hydrologic series with a return period.
Variate 'X' with a Recurrence Interval - Variate 'X' with a Recurrence Interval of a random hydrologic series with a return period.
Frequency Factor - Frequency Factor which varies between 5 to 30 according to rainfall duration is a function of recurrence interval (T) and the coefficient of skew (Cs).
Standard Deviation of the Z Variate Sample - Standard Deviation of the Z Variate Sample follows a certain probability distribution of a hydrologic model.

STEP 1: Convert Input(s) to Base Unit

Variate 'X' with a Recurrence Interval: 9.43 --> No Conversion Required
Frequency Factor: 7 --> No Conversion Required
Standard Deviation of the Z Variate Sample: 1.25 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

x_m = x_T-K_z*σ --> 9.43-7*1.25

Evaluating ... ...

x_m = 0.68

STEP 3: Convert Result to Output's Unit

0.68 --> No Conversion Required

FINAL ANSWER

0.68 <-- Mean of the Variate X

(Calculation completed in 00.004 seconds)

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< 14 Gumbel's Method for Prediction of Flood's Peak Calculators

Reduced Variate 'Y' in Gumbel's Method

Go Reduced Variate 'Y' = ((1.285*(Variate 'X' with a Recurrence Interval-Mean of the Variate X))/Standard Deviation of the Z Variate Sample)+0.577

Reduced Variate 'Y' for given Return Period

Go Reduced Variate 'Y' for Return Period = -(0.834+2.303*log10(log10(Return Period/(Return Period-1))))

Mean Variate given Variate 'x' with Recurrence Interval for Practical Use

Go Mean of the Variate X = Variate 'X' with a Recurrence Interval-(Frequency Factor*Standard Deviation of the Sample of Size N)

Frequency Factor given Variate 'x' concerning Return Period

Go Frequency Factor = (Variate 'X' with a Recurrence Interval-Mean of the Variate X)/Standard Deviation of the Z Variate Sample

Gumbel's Variate 'x' with Recurrence Interval for Practical Use

Go Variate 'X' with a Recurrence Interval = Mean of the Variate X+Frequency Factor*Standard Deviation of the Sample of Size N

General Equation of Hydrologic Frequency Analysis

Go Variate 'X' with a Recurrence Interval = Mean of the Variate X+Frequency Factor*Standard Deviation of the Z Variate Sample

Mean of Variate in Flood Frequency Studies

Go Mean of the Variate X = Variate 'X' with a Recurrence Interval-Frequency Factor*Standard Deviation of the Z Variate Sample

Reduced Variate when Frequency Factor and Standard Deviation is Considered

Go Reduced Variate 'Y' with Respect to Frequency = Frequency Factor*Standard Deviation of the Sample of Size N+Reduced Mean

Reduced Variate concerning Return Period

Go Reduced Variate 'Y' for Return Period = -(ln(ln(Return Period/(Return Period-1))))

Reduced Mean when Frequency Factor and Standard Deviation are Considered

Go Reduced Mean = Reduced Variate 'Y' for Return Period-(Frequency Factor*Reduced Standard Deviation)

Reduced Standard Deviation when Variate and Reduced Mean is Considered

Go Reduced Standard Deviation = (Reduced Variate 'Y' for Return Period-Reduced Mean)/Frequency Factor

Frequency Factor in Gumbel's Equation for Practical Use

Go Frequency Factor = (Reduced Variate 'Y' for Return Period-Reduced Mean)/Reduced Standard Deviation

Reduced Variate for Return Period when Frequency Factor is Considered

Go Reduced Variate 'Y' with Respect to Frequency = (Frequency Factor*1.2825)+0.577

Frequency Factor as applicable to Infinite Sample Size

Go Frequency Factor = (Reduced Variate 'Y' for Return Period-0.577)/1.2825

Mean of Variate in Flood Frequency Studies Formula

Mean of the Variate X = Variate 'X' with a Recurrence Interval-Frequency Factor*Standard Deviation of the Z Variate Sample
x_m = x_T-K_z*σ

What is Flood Frequency Analysis?

Flood Frequency Analysis is a technique used by hydrologists to predict flow values corresponding to specific return periods or probabilities along a river. After choosing the probability distribution that best fits the annual maxima data, flood frequency curves are plotted.

What is Peak Discharge?

In Hydrology, the term Peak Discharge stands for the highest concentration of runoff from the basin area. The concentrated flow of the basin greatly exaggerates and overtops the natural or artificial bank, and this might be called a flood.

How to Calculate Mean of Variate in Flood Frequency Studies?

Mean of Variate in Flood Frequency Studies calculator uses Mean of the Variate X = Variate 'X' with a Recurrence Interval-Frequency Factor*Standard Deviation of the Z Variate Sample to calculate the Mean of the Variate X, The Mean of Variate in Flood Frequency Studies formula is defined as the mean value of the variate X of a random hydrologic series with a return period in the Hydrologic Frequency Analysis. Mean of the Variate X is denoted by x_m symbol.

How to calculate Mean of Variate in Flood Frequency Studies using this online calculator? To use this online calculator for Mean of Variate in Flood Frequency Studies, enter Variate 'X' with a Recurrence Interval (x_T), Frequency Factor (K_z) & Standard Deviation of the Z Variate Sample (σ) and hit the calculate button. Here is how the Mean of Variate in Flood Frequency Studies calculation can be explained with given input values -> 0.678 = 9.43-7*1.25.

FAQ

What is Mean of Variate in Flood Frequency Studies?

The Mean of Variate in Flood Frequency Studies formula is defined as the mean value of the variate X of a random hydrologic series with a return period in the Hydrologic Frequency Analysis and is represented as x_m = x_T-K_z*σ or Mean of the Variate X = Variate 'X' with a Recurrence Interval-Frequency Factor*Standard Deviation of the Z Variate Sample. Variate 'X' with a Recurrence Interval of a random hydrologic series with a return period, Frequency Factor which varies between 5 to 30 according to rainfall duration is a function of recurrence interval (T) and the coefficient of skew (Cs) & Standard Deviation of the Z Variate Sample follows a certain probability distribution of a hydrologic model.

How to calculate Mean of Variate in Flood Frequency Studies?

The Mean of Variate in Flood Frequency Studies formula is defined as the mean value of the variate X of a random hydrologic series with a return period in the Hydrologic Frequency Analysis is calculated using Mean of the Variate X = Variate 'X' with a Recurrence Interval-Frequency Factor*Standard Deviation of the Z Variate Sample. To calculate Mean of Variate in Flood Frequency Studies, you need Variate 'X' with a Recurrence Interval (x_T), Frequency Factor (K_z) & Standard Deviation of the Z Variate Sample (σ). With our tool, you need to enter the respective value for Variate 'X' with a Recurrence Interval, Frequency Factor & Standard Deviation of the Z Variate Sample and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Mean of the Variate X?

In this formula, Mean of the Variate X uses Variate 'X' with a Recurrence Interval, Frequency Factor & Standard Deviation of the Z Variate Sample. We can use 1 other way(s) to calculate the same, which is/are as follows -

Mean of the Variate X = Variate 'X' with a Recurrence Interval-(Frequency Factor*Standard Deviation of the Sample of Size N)

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