Reduced Variate when Frequency Factor and Standard Deviation is Considered Calculator

✖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 Sample of Size N is the quantity expressed by how much it differs from the mean value for the group and also the square root of its variance.ⓘ Standard Deviation of the Sample of Size N [σ_n-1]			+10% -10%
✖Reduced Mean, a function of sample size N in Gumbel's Extreme Value distribution.ⓘ Reduced Mean [y_n]			+10% -10%

✖Reduced Variate 'Y' with Respect to Frequency Factor is a transformed variable that allows for the Gumbel distribution to be used to model extreme values.ⓘ Reduced Variate when Frequency Factor and Standard Deviation is Considered [y_tf]

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Reduced Variate when Frequency Factor and Standard Deviation is Considered Solution

STEP 0: Pre-Calculation Summary

Formula Used

Reduced Variate 'Y' with Respect to Frequency = Frequency Factor*Standard Deviation of the Sample of Size N+Reduced Mean
y_tf = K_z*σ_n-1+y_n
This formula uses 4 Variables

Variables Used

Reduced Variate 'Y' with Respect to Frequency - Reduced Variate 'Y' with Respect to Frequency Factor is a transformed variable that allows for the Gumbel distribution to be used to model extreme values.
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 Sample of Size N - Standard Deviation of the Sample of Size N is the quantity expressed by how much it differs from the mean value for the group and also the square root of its variance.
Reduced Mean - Reduced Mean, a function of sample size N in Gumbel's Extreme Value distribution.

STEP 1: Convert Input(s) to Base Unit

Frequency Factor: 7 --> No Conversion Required
Standard Deviation of the Sample of Size N: 1.28 --> No Conversion Required
Reduced Mean: 0.577 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

y_tf = K_z*σ_n-1+y_n --> 7*1.28+0.577

Evaluating ... ...

y_tf = 9.537

STEP 3: Convert Result to Output's Unit

9.537 --> No Conversion Required

FINAL ANSWER

9.537 <-- Reduced Variate 'Y' with Respect to Frequency

(Calculation completed in 00.004 seconds)

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

Reduced Variate 'Y' in Gumbel's Method

LaTeX 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

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

Reduced Variate concerning Return Period

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

Frequency Factor as applicable to Infinite Sample Size

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

Reduced Variate when Frequency Factor and Standard Deviation is Considered Formula

LaTeX Go

Reduced Variate 'Y' with Respect to Frequency = Frequency Factor*Standard Deviation of the Sample of Size N+Reduced Mean
y_tf = K_z*σ_n-1+y_n

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 Reduced Variate when Frequency Factor and Standard Deviation is Considered?

Reduced Variate when Frequency Factor and Standard Deviation is Considered calculator uses Reduced Variate 'Y' with Respect to Frequency = Frequency Factor*Standard Deviation of the Sample of Size N+Reduced Mean to calculate the Reduced Variate 'Y' with Respect to Frequency, The Reduced Variate when Frequency Factor and Standard Deviation is Considered formula is defined as a dimensionless variable in Gumbel's method, the most widely used probability distribution's function values for extreme hydrologic and meteorological studies for prediction of flood peaks. Reduced Variate 'Y' with Respect to Frequency is denoted by y_tf symbol.

How to calculate Reduced Variate when Frequency Factor and Standard Deviation is Considered using this online calculator? To use this online calculator for Reduced Variate when Frequency Factor and Standard Deviation is Considered, enter Frequency Factor (K_z), Standard Deviation of the Sample of Size N (σ_n-1) & Reduced Mean (y_n) and hit the calculate button. Here is how the Reduced Variate when Frequency Factor and Standard Deviation is Considered calculation can be explained with given input values -> 9.537 = 7*1.28+0.577.

FAQ

What is Reduced Variate when Frequency Factor and Standard Deviation is Considered?

The Reduced Variate when Frequency Factor and Standard Deviation is Considered formula is defined as a dimensionless variable in Gumbel's method, the most widely used probability distribution's function values for extreme hydrologic and meteorological studies for prediction of flood peaks and is represented as y_tf = K_z*σ_n-1+y_n or Reduced Variate 'Y' with Respect to Frequency = Frequency Factor*Standard Deviation of the Sample of Size N+Reduced Mean. 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 Sample of Size N is the quantity expressed by how much it differs from the mean value for the group and also the square root of its variance & Reduced Mean, a function of sample size N in Gumbel's Extreme Value distribution.

How to calculate Reduced Variate when Frequency Factor and Standard Deviation is Considered?

The Reduced Variate when Frequency Factor and Standard Deviation is Considered formula is defined as a dimensionless variable in Gumbel's method, the most widely used probability distribution's function values for extreme hydrologic and meteorological studies for prediction of flood peaks is calculated using Reduced Variate 'Y' with Respect to Frequency = Frequency Factor*Standard Deviation of the Sample of Size N+Reduced Mean. To calculate Reduced Variate when Frequency Factor and Standard Deviation is Considered, you need Frequency Factor (K_z), Standard Deviation of the Sample of Size N (σ_n-1) & Reduced Mean (y_n). With our tool, you need to enter the respective value for Frequency Factor, Standard Deviation of the Sample of Size N & Reduced Mean 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 Reduced Variate 'Y' with Respect to Frequency?

In this formula, Reduced Variate 'Y' with Respect to Frequency uses Frequency Factor, Standard Deviation of the Sample of Size N & Reduced Mean. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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