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*(xT-xm))/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*(xT-xm))/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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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

Reduced Variate 'Y' in Gumbel's Method Formula

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*(xT-xm))/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 (xT), Mean of the Variate X (xm) & 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*(xT-xm))/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 (xT), Mean of the Variate X (xm) & 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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