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Runoff Rainfall Regression by Logarithmic Transformation Formula

GoEquation of Straight-line Regression between Runoff and Rainfall Formula

GoExponential Relationship for Larger Catchments Formula

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Runoff is usually measured is either seasonal measured or annual measured. Check FAQs

R = m \cdot \exp (\ln (P)) + \exp (\ln (β))

R - Runoff?m - Coefficient m?P - Rainfall?β - Coefficient β?

Runoff Rainfall Regression by Logarithmic Transformation Example

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With units

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Here is how the Runoff Rainfall Regression by Logarithmic Transformation equation looks like with Values.

Here is how the Runoff Rainfall Regression by Logarithmic Transformation equation looks like with Units.

Here is how the Runoff Rainfall Regression by Logarithmic Transformation equation looks like.

26.5 = 0.3 \cdot \exp (\ln (75)) + \exp (\ln (4))

26.5cm = 0.3 \cdot \exp (\ln (75cm)) + \exp (\ln (4))

26.5 = 0.3 \cdot \exp (\ln (75)) + \exp (\ln (4))

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Runoff Rainfall Regression by Logarithmic Transformation Solution

Follow our step by step solution on how to calculate Runoff Rainfall Regression by Logarithmic Transformation?

FIRST Step Consider the formula

R = m \cdot \exp (\ln (P)) + \exp (\ln (β))

Next Step Substitute values of Variables

∴

R = 0.3 \cdot \exp (\ln (75cm)) + \exp (\ln (4))

Next Step Prepare to Evaluate

∴

R = 0.3 \cdot \exp (\ln (75)) + \exp (\ln (4))

Next Step Evaluate

∴

R = 0.265m

LAST Step Convert to Output's Unit

∴

R = 26.5cm

Runoff Rainfall Regression by Logarithmic Transformation Formula Elements

Variables

Functions

Runoff

Runoff is usually measured is either seasonal measured or annual measured.

Symbol: R

Measurement: LengthUnit: cm

Note: Value should be greater than 0.

Formulas to find Runoff

Coefficient m

Coefficient m in Logarithmic Transformation which reduces or removes the skewness of our original data.

Symbol: m

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Coefficient m

Rainfall

Rainfall is measured here is the annual rainfall in a particular year.

Symbol: P

Measurement: LengthUnit: cm

Note: Value should be greater than 0.

Formulas to find Rainfall

Coefficient β

Coefficient β in Logarithmic Transformation reduces or removes the skewness of our original data.

Symbol: β

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Coefficient β

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: 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.

Syntax: exp(Number)

Other Formulas to find Runoff

Go Equation of Straight-line Regression between Runoff and Rainfall

R = a \cdot P + (B)

Go Exponential Relationship for Larger Catchments

R = β \cdot P^{m}

Other formulas in Rainfall Runoff Correlation category

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

P (i-2) = \frac{P a - a \cdot P i - b \cdot P (i-1)}{c}

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

P (i-1) = \frac{P a - a \cdot P i - c \cdot P (i-2)}{b}

Go Annual Precipitation in i-th year given Antecedent Precipitation

P i = \frac{P a - b \cdot P (i-1) - c \cdot P (i-2)}{a}

Go Precipitation using Runoff from Exponential Relationship

P = {(\frac{R}{β})}^{\frac{1}{m}}

How to Evaluate Runoff Rainfall Regression by Logarithmic Transformation?

Runoff Rainfall Regression by Logarithmic Transformation evaluator uses Runoff = Coefficient m*exp(ln(Rainfall))+exp(ln(Coefficient β)) to evaluate 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 evaluate Runoff Rainfall Regression by Logarithmic Transformation using this online evaluator? To use this online evaluator for Runoff Rainfall Regression by Logarithmic Transformation, enter Coefficient m (m), Rainfall (P) & Coefficient β (β) and hit the calculate button.

FAQs on Runoff Rainfall Regression by Logarithmic Transformation

What is the formula to find Runoff Rainfall Regression by Logarithmic Transformation?

The formula of Runoff Rainfall Regression by Logarithmic Transformation is expressed as Runoff = Coefficient m*exp(ln(Rainfall))+exp(ln(Coefficient β)). Here is an example- 2650 = 0.3*exp(ln(0.75))+exp(ln(4)).

How to calculate Runoff Rainfall Regression by Logarithmic Transformation?

With Coefficient m (m), Rainfall (P) & Coefficient β (β) we can find Runoff Rainfall Regression by Logarithmic Transformation using the formula - Runoff = Coefficient m*exp(ln(Rainfall))+exp(ln(Coefficient β)). This formula also uses Natural Logarithm (ln), Exponential Growth (exp) function(s).

What are the other ways to Calculate Runoff?

Here are the different ways to Calculate Runoff-

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

Can the Runoff Rainfall Regression by Logarithmic Transformation be negative?

No, the Runoff Rainfall Regression by Logarithmic Transformation, measured in Length cannot be negative.

Which unit is used to measure Runoff Rainfall Regression by Logarithmic Transformation?

Runoff Rainfall Regression by Logarithmic Transformation is usually measured using the Centimeter[cm] for Length. Meter[cm], Millimeter[cm], Kilometer[cm] are the few other units in which Runoff Rainfall Regression by Logarithmic Transformation can be measured.

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