Reduced Variate 'Y' in Gumbel's Method 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%

✖Reduced Variate 'Y' is a transformed variable that allows for the Gumbel distribution to be used to model extreme values.ⓘ Reduced Variate 'Y' in Gumbel's Method [y]

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Reduced Variate 'Y' in Gumbel's Method Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
y = ((1.285*(x_T-x_m))/σ)+0.577
This formula uses 4 Variables

Variables Used

Reduced Variate 'Y' - Reduced Variate 'Y' is a transformed variable that allows for the Gumbel distribution to be used to model extreme values.
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

y = ((1.285*(x_T-x_m))/σ)+0.577 --> ((1.285*(9.43-0.578))/1.25)+0.577

Evaluating ... ...

y = 9.676856

STEP 3: Convert Result to Output's Unit

9.676856 --> No Conversion Required

FINAL ANSWER

9.676856 <-- Reduced Variate 'Y'

(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 'Y' in Gumbel's Method Formula

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
y = ((1.285*(x_T-x_m))/σ)+0.577

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 'Y' in Gumbel's Method?

Reduced Variate 'Y' in Gumbel's Method calculator uses 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 to calculate the Reduced Variate 'Y', The Reduced Variate 'Y' in Gumbel's Method formula is defined as the dimensionless variable in Gumbel's Method, one of the most widely used probability distribution functions for extreme values in hydrologic and meteorological studies for prediction of flood peaks. Reduced Variate 'Y' is denoted by y symbol.

How to calculate Reduced Variate 'Y' in Gumbel's Method using this online calculator? To use this online calculator for Reduced Variate 'Y' in Gumbel's Method, 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 Reduced Variate 'Y' in Gumbel's Method calculation can be explained with given input values -> 9.6748 = ((1.285*(9.43-0.578))/1.25)+0.577.

FAQ

What is Reduced Variate 'Y' in Gumbel's Method?

The Reduced Variate 'Y' in Gumbel's Method formula is defined as the dimensionless variable in Gumbel's Method, one of the most widely used probability distribution functions for extreme values in hydrologic and meteorological studies for prediction of flood peaks and is represented as y = ((1.285*(x_T-x_m))/σ)+0.577 or 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. 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 Reduced Variate 'Y' in Gumbel's Method?

The Reduced Variate 'Y' in Gumbel's Method formula is defined as the dimensionless variable in Gumbel's Method, one of the most widely used probability distribution functions for extreme values in hydrologic and meteorological studies for prediction of flood peaks is calculated using 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. To calculate Reduced Variate 'Y' in Gumbel's Method, 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.

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