Reduced Variate concerning Return Period Calculator

✖Return Period [Years] is an average time or an estimated average time between events such as earthquakes, floods, landslides, or a river discharge flows to occur.ⓘ Return Period [T_r]

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✖Reduced Variate 'Y' for Return Period is a transformed variable allowed for Gumbel distribution used to model extreme values and return period T is expected years that a certain event will occur.ⓘ Reduced Variate concerning Return Period [y_T]

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Reduced Variate concerning Return Period

Formula

`"y"_{"T"} = -(ln(ln("T"_{"r"}/("T"_{"r"}-1))))`

Example

`"5.007293"=-(ln(ln("150"/("150"-1))))`

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

Reduced Variate concerning Return Period Solution

STEP 0: Pre-Calculation Summary

Formula Used

Reduced Variate 'Y' for Return Period = -(ln(ln(Return Period/(Return Period-1))))
y_T = -(ln(ln(T_r/(T_r-1))))
This formula uses 1 Functions, 2 Variables

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Reduced Variate 'Y' for Return Period - Reduced Variate 'Y' for Return Period is a transformed variable allowed for Gumbel distribution used to model extreme values and return period T is expected years that a certain event will occur.
Return Period - Return Period [Years] is an average time or an estimated average time between events such as earthquakes, floods, landslides, or a river discharge flows to occur.

STEP 1: Convert Input(s) to Base Unit

Return Period: 150 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

y_T = -(ln(ln(T_r/(T_r-1)))) --> -(ln(ln(150/(150-1))))

Evaluating ... ...

y_T = 5.00729266429358

STEP 3: Convert Result to Output's Unit

5.00729266429358 --> No Conversion Required

FINAL ANSWER

5.00729266429358 ≈ 5.007293 <-- Reduced Variate 'Y' for Return Period

(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 concerning Return Period Formula

Reduced Variate 'Y' for Return Period = -(ln(ln(Return Period/(Return Period-1))))
y_T = -(ln(ln(T_r/(T_r-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 Reduced Variate concerning Return Period?

Reduced Variate concerning Return Period calculator uses Reduced Variate 'Y' for Return Period = -(ln(ln(Return Period/(Return Period-1)))) to calculate the Reduced Variate 'Y' for Return Period, The Reduced Variate concerning Return Period 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 the prediction of flood peaks. Reduced Variate 'Y' for Return Period is denoted by y_T symbol.

How to calculate Reduced Variate concerning Return Period using this online calculator? To use this online calculator for Reduced Variate concerning Return Period, enter Return Period (T_r) and hit the calculate button. Here is how the Reduced Variate concerning Return Period calculation can be explained with given input values -> 5.007293 = -(ln(ln(150/(150-1)))).

FAQ

What is Reduced Variate concerning Return Period?

The Reduced Variate concerning Return Period 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 the prediction of flood peaks and is represented as y_T = -(ln(ln(T_r/(T_r-1)))) or Reduced Variate 'Y' for Return Period = -(ln(ln(Return Period/(Return Period-1)))). Return Period [Years] is an average time or an estimated average time between events such as earthquakes, floods, landslides, or a river discharge flows to occur.

How to calculate Reduced Variate concerning Return Period?

The Reduced Variate concerning Return Period 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 the prediction of flood peaks is calculated using Reduced Variate 'Y' for Return Period = -(ln(ln(Return Period/(Return Period-1)))). To calculate Reduced Variate concerning Return Period, you need Return Period (T_r). With our tool, you need to enter the respective value for Return Period 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' for Return Period?

In this formula, Reduced Variate 'Y' for Return Period uses Return Period. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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