Runoff Rainfall Regression by Logarithmic Transformation Calculator

✖Coefficient m in Logarithmic Transformation which reduces or removes the skewness of our original data.ⓘ Coefficient m [m]			+10% -10%
✖Rainfall is measured here is the annual rainfall in a particular year.ⓘ Rainfall [P]			+10% -10%
✖Coefficient β in Logarithmic Transformation reduces or removes the skewness of our original data.ⓘ Coefficient β [β]			+10% -10%

✖Runoff is usually measured is either seasonal measured or annual measured.ⓘ Runoff Rainfall Regression by Logarithmic Transformation [R]

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Formula

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Runoff Rainfall Regression by Logarithmic Transformation

Formula

`"R" = "m"*exp(ln("P"))+exp(ln("β"))`

Example

`"26.5cm"="0.3"*exp(ln("75cm"))+exp(ln("4"))`

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Download Rainfall-Runoff Correlation and Strange's Tables Formulas PDF PDF Image

Runoff Rainfall Regression by Logarithmic Transformation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Runoff = Coefficient m*exp(ln(Rainfall))+exp(ln(Coefficient β))
R = m*exp(ln(P))+exp(ln(β))
This formula uses 2 Functions, 4 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)
exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)

Variables Used

Runoff - (Measured in Centimeter) - Runoff is usually measured is either seasonal measured or annual measured.
Coefficient m - Coefficient m in Logarithmic Transformation which reduces or removes the skewness of our original data.
Rainfall - (Measured in Centimeter) - Rainfall is measured here is the annual rainfall in a particular year.
Coefficient β - Coefficient β in Logarithmic Transformation reduces or removes the skewness of our original data.

STEP 1: Convert Input(s) to Base Unit

Coefficient m: 0.3 --> No Conversion Required
Rainfall: 75 Centimeter --> 75 Centimeter No Conversion Required
Coefficient β: 4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R = m*exp(ln(P))+exp(ln(β)) --> 0.3*exp(ln(75))+exp(ln(4))

Evaluating ... ...

R = 26.5

STEP 3: Convert Result to Output's Unit

0.265 Meter -->26.5 Centimeter (Check conversion here)

FINAL ANSWER

26.5 Centimeter <-- Runoff

(Calculation completed in 00.004 seconds)

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< 9 Rainfall-Runoff Correlation Calculators

Annual Precipitation in (i-2)th year given Antecedent Precipitation

Go Precipitation in (i-2)th Year = (Antecedent Precipitation Index-Coefficient 'a'*Precipitation in (i)th Year-Coefficient 'b'*Precipitation in (i-1)th Year)/Coefficient 'c'

Annual Precipitation in (i-1)th year given Antecedent Precipitation

Go Precipitation in (i-1)th Year = (Antecedent Precipitation Index-Coefficient 'a'*Precipitation in (i)th Year-Coefficient 'c'*Precipitation in (i-2)th Year)/Coefficient 'b'

Annual Precipitation in i-th year given Antecedent Precipitation

Go Precipitation in (i)th Year = (Antecedent Precipitation Index-Coefficient 'b'*Precipitation in (i-1)th Year-Coefficient 'c'*Precipitation in (i-2)th Year)/Coefficient 'a'

Antecedent Precipitation Index

Go Antecedent Precipitation Index = Coefficient 'a'*Precipitation in (i)th Year+Coefficient 'b'*Precipitation in (i-1)th Year+Coefficient 'c'*Precipitation in (i-2)th Year

Runoff Rainfall Regression by Logarithmic Transformation

Go Runoff = Coefficient m*exp(ln(Rainfall))+exp(ln(Coefficient β))

Precipitation using Runoff in Straight Line Regression between Runoff and Rainfall

Go Rainfall = (Runoff-(Coefficient 'B' in Straight-line Regression))/Coefficient 'a'

Equation of Straight-line Regression between Runoff and Rainfall

Go Runoff = Coefficient 'a'*Rainfall+(Coefficient 'B' in Straight-line Regression)

Precipitation using Runoff from Exponential Relationship

Go Rainfall = (Runoff/Coefficient β)^(1/Coefficient m)

Exponential Relationship for Larger Catchments

Go Runoff = Coefficient β*Rainfall^Coefficient m

Runoff Rainfall Regression by Logarithmic Transformation Formula

Runoff = Coefficient m*exp(ln(Rainfall))+exp(ln(Coefficient β))
R = m*exp(ln(P))+exp(ln(β))

What is Regression Analysis?

Regression Analysis is used to identify factors governing flood generation and routing, and to predict flow volumes and flood peaks as functions of rainfall input and antecedent wetness.

What is Runoff?

Runoff can be described as the part of the water cycle that flows over land as surface water instead of being absorbed into groundwater or evaporating. According to the U.S. Geological Survey (USGS), runoff is that part of the precipitation, snow melt, or irrigation water that appears in uncontrolled surface streams, rivers, drains, or sewers.

How to Calculate Runoff Rainfall Regression by Logarithmic Transformation?

Runoff Rainfall Regression by Logarithmic Transformation calculator uses Runoff = Coefficient m*exp(ln(Rainfall))+exp(ln(Coefficient β)) to calculate the Runoff, The Runoff Rainfall Regression by Logarithmic Transformation formula is defined as the reduced linear form of the equation for runoff for large catchments with an exponential relationship. Runoff is denoted by R symbol.

How to calculate Runoff Rainfall Regression by Logarithmic Transformation using this online calculator? To use this online calculator for Runoff Rainfall Regression by Logarithmic Transformation, enter Coefficient m (m), Rainfall (P) & Coefficient β (β) and hit the calculate button. Here is how the Runoff Rainfall Regression by Logarithmic Transformation calculation can be explained with given input values -> 2650 = 0.3*exp(ln(0.75))+exp(ln(4)).

FAQ

What is Runoff Rainfall Regression by Logarithmic Transformation?

The Runoff Rainfall Regression by Logarithmic Transformation formula is defined as the reduced linear form of the equation for runoff for large catchments with an exponential relationship and is represented as R = m*exp(ln(P))+exp(ln(β)) or Runoff = Coefficient m*exp(ln(Rainfall))+exp(ln(Coefficient β)). Coefficient m in Logarithmic Transformation which reduces or removes the skewness of our original data, Rainfall is measured here is the annual rainfall in a particular year & Coefficient β in Logarithmic Transformation reduces or removes the skewness of our original data.

How to calculate Runoff Rainfall Regression by Logarithmic Transformation?

The Runoff Rainfall Regression by Logarithmic Transformation formula is defined as the reduced linear form of the equation for runoff for large catchments with an exponential relationship is calculated using Runoff = Coefficient m*exp(ln(Rainfall))+exp(ln(Coefficient β)). To calculate Runoff Rainfall Regression by Logarithmic Transformation, you need Coefficient m (m), Rainfall (P) & Coefficient β (β). With our tool, you need to enter the respective value for Coefficient m, Rainfall & Coefficient β 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 Runoff?

In this formula, Runoff uses Coefficient m, Rainfall & Coefficient β. We can use 2 other way(s) to calculate the same, which is/are as follows -

Runoff = Coefficient 'a'*Rainfall+(Coefficient 'B' in Straight-line Regression)
Runoff = Coefficient β*Rainfall^Coefficient m

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