Frequency Factor given Variate 'x' concerning Return Period 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%
✖Mean of the Variate X of a random hydrologic series with a return period.ⓘ Mean of the Variate X [x_m]			+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%

✖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 given Variate 'x' concerning Return Period [K_z]

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Formula

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Frequency Factor given Variate 'x' concerning Return Period

Formula

`"K"_{"z"} = ("x"_{"T"}-"x"_{"m"})/"σ"`

Example

`"7.0816"=("9.43"-"0.578")/"1.25"`

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

Frequency Factor given Variate 'x' concerning Return Period Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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).
Variate 'X' with a Recurrence Interval - Variate 'X' with a Recurrence Interval of a random hydrologic series with a return period.
Mean of the Variate X - Mean of the Variate X of a random hydrologic series with a return period.
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
Mean of the Variate X: 0.578 --> No Conversion Required
Standard Deviation of the Z Variate Sample: 1.25 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K_z = (x_T-x_m)/σ --> (9.43-0.578)/1.25

Evaluating ... ...

K_z = 7.0816

STEP 3: Convert Result to Output's Unit

7.0816 --> No Conversion Required

FINAL ANSWER

7.0816 <-- Frequency Factor

(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

Frequency Factor given Variate 'x' concerning Return Period Formula

Frequency Factor = (Variate 'X' with a Recurrence Interval-Mean of the Variate X)/Standard Deviation of the Z Variate Sample
K_z = (x_T-x_m)/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 Frequency Factor given Variate 'x' concerning Return Period?

Frequency Factor given Variate 'x' concerning Return Period calculator uses Frequency Factor = (Variate 'X' with a Recurrence Interval-Mean of the Variate X)/Standard Deviation of the Z Variate Sample to calculate the Frequency Factor, The Frequency Factor given Variate 'x' concerning Return Period formula is defined as a factor used to compare and relate results and attach probabilities to several sets of maximum rainfall data. K is primarily a function of the recurrence interval for a particular probability distribution. Frequency Factor is denoted by K_z symbol.

How to calculate Frequency Factor given Variate 'x' concerning Return Period using this online calculator? To use this online calculator for Frequency Factor given Variate 'x' concerning Return Period, enter Variate 'X' with a Recurrence Interval (x_T), Mean of the Variate X (x_m) & Standard Deviation of the Z Variate Sample (σ) and hit the calculate button. Here is how the Frequency Factor given Variate 'x' concerning Return Period calculation can be explained with given input values -> 7.08 = (9.43-0.578)/1.25.

FAQ

What is Frequency Factor given Variate 'x' concerning Return Period?

The Frequency Factor given Variate 'x' concerning Return Period formula is defined as a factor used to compare and relate results and attach probabilities to several sets of maximum rainfall data. K is primarily a function of the recurrence interval for a particular probability distribution and is represented as K_z = (x_T-x_m)/σ or Frequency Factor = (Variate 'X' with a Recurrence Interval-Mean of the Variate X)/Standard Deviation of the Z Variate Sample. Variate 'X' with a Recurrence Interval of a random hydrologic series with a return period, Mean of the Variate X of a random hydrologic series with a return period & Standard Deviation of the Z Variate Sample follows a certain probability distribution of a hydrologic model.

How to calculate Frequency Factor given Variate 'x' concerning Return Period?

The Frequency Factor given Variate 'x' concerning Return Period formula is defined as a factor used to compare and relate results and attach probabilities to several sets of maximum rainfall data. K is primarily a function of the recurrence interval for a particular probability distribution is calculated using Frequency Factor = (Variate 'X' with a Recurrence Interval-Mean of the Variate X)/Standard Deviation of the Z Variate Sample. To calculate Frequency Factor given Variate 'x' concerning Return Period, you need Variate 'X' with a Recurrence Interval (x_T), Mean of the Variate X (x_m) & 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, Mean of the Variate X & 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 Frequency Factor?

In this formula, Frequency Factor uses Variate 'X' with a Recurrence Interval, Mean of the Variate X & Standard Deviation of the Z Variate Sample. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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