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

✖Mean of the Variate X of a random hydrologic series with a return period.ⓘ Mean of the Variate X [x_m]			+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 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%

✖Variate 'X' with a Recurrence Interval of a random hydrologic series with a return period.ⓘ Gumbel's Variate 'x' with Recurrence Interval for Practical Use [x_T]

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

STEP 0: Pre-Calculation Summary

Formula Used

Variate 'X' with a Recurrence Interval = Mean of the Variate X+Frequency Factor*Standard Deviation of the Sample of Size N
x_T = x_m+K_z*σ_n-1
This formula uses 4 Variables

Variables Used

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.
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.

STEP 1: Convert Input(s) to Base Unit

Mean of the Variate X: 0.578 --> No Conversion Required
Frequency Factor: 7 --> No Conversion Required
Standard Deviation of the Sample of Size N: 1.28 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

x_T = x_m+K_z*σ_n-1 --> 0.578+7*1.28

Evaluating ... ...

x_T = 9.538

STEP 3: Convert Result to Output's Unit

9.538 --> No Conversion Required

FINAL ANSWER

9.538 <-- Variate 'X' with a Recurrence Interval

(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

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

LaTeX Go

Variate 'X' with a Recurrence Interval = Mean of the Variate X+Frequency Factor*Standard Deviation of the Sample of Size N
x_T = x_m+K_z*σ_n-1

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

Gumbel's Variate 'x' with Recurrence Interval for Practical Use calculator uses Variate 'X' with a Recurrence Interval = Mean of the Variate X+Frequency Factor*Standard Deviation of the Sample of Size N to calculate the Variate 'X' with a Recurrence Interval, The Gumbel's Variate 'x' with Recurrence Interval for Practical Use 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. Variate 'X' with a Recurrence Interval is denoted by x_T symbol.

How to calculate Gumbel's Variate 'x' with Recurrence Interval for Practical Use using this online calculator? To use this online calculator for Gumbel's Variate 'x' with Recurrence Interval for Practical Use, enter Mean of the Variate X (x_m), Frequency Factor (K_z) & Standard Deviation of the Sample of Size N (σ_n-1) and hit the calculate button. Here is how the Gumbel's Variate 'x' with Recurrence Interval for Practical Use calculation can be explained with given input values -> 9.538 = 0.578+7*1.28.

FAQ

What is Gumbel's Variate 'x' with Recurrence Interval for Practical Use?

The Gumbel's Variate 'x' with Recurrence Interval for Practical Use 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 x_T = x_m+K_z*σ_n-1 or Variate 'X' with a Recurrence Interval = Mean of the Variate X+Frequency Factor*Standard Deviation of the Sample of Size N. Mean of the Variate X 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 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.

How to calculate Gumbel's Variate 'x' with Recurrence Interval for Practical Use?

The Gumbel's Variate 'x' with Recurrence Interval for Practical Use 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 Variate 'X' with a Recurrence Interval = Mean of the Variate X+Frequency Factor*Standard Deviation of the Sample of Size N. To calculate Gumbel's Variate 'x' with Recurrence Interval for Practical Use, you need Mean of the Variate X (x_m), Frequency Factor (K_z) & Standard Deviation of the Sample of Size N (σ_n-1). With our tool, you need to enter the respective value for Mean of the Variate X, Frequency Factor & Standard Deviation of the Sample of Size N 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 Variate 'X' with a Recurrence Interval?

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

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

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