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Annual Precipitation in i-th year given Antecedent Precipitation Formula

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Precipitation in (i)th Year for Antecedent Precipitation Index, a running day by day measure of catchment wetness based on the rainfall that has occurred over preceding days. Check FAQs

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

P_i - Precipitation in (i)th Year?P_a - Antecedent Precipitation Index?b - Coefficient 'b'?P_(i-1) - Precipitation in (i-1)th Year?c - Coefficient 'c'?P_(i-2) - Precipitation in (i-2)th Year?a - Coefficient 'a'?

Annual Precipitation in i-th year given Antecedent Precipitation Example

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Here is how the Annual Precipitation in i-th year given Antecedent Precipitation equation looks like with Values.

Here is how the Annual Precipitation in i-th year given Antecedent Precipitation equation looks like with Units.

Here is how the Annual Precipitation in i-th year given Antecedent Precipitation equation looks like.

95 = \frac{96.39 - 0.1 \cdot 121 - 0.11 \cdot 84}{0.79}

95cm = \frac{96.39cm - 0.1 \cdot 121cm - 0.11 \cdot 84cm}{0.79}

95 = \frac{96.39 - 0.1 \cdot 121 - 0.11 \cdot 84}{0.79}

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Annual Precipitation in i-th year given Antecedent Precipitation Solution

Follow our step by step solution on how to calculate Annual Precipitation in i-th year given Antecedent Precipitation?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

P i = \frac{96.39cm - 0.1 \cdot 121cm - 0.11 \cdot 84cm}{0.79}

Next Step Prepare to Evaluate

∴

P i = \frac{96.39 - 0.1 \cdot 121 - 0.11 \cdot 84}{0.79}

Next Step Evaluate

∴

P i = 0.95m

LAST Step Convert to Output's Unit

∴

P i = 95cm

Annual Precipitation in i-th year given Antecedent Precipitation Formula Elements

Variables

Precipitation in (i)th Year

Precipitation in (i)th Year for Antecedent Precipitation Index, a running day by day measure of catchment wetness based on the rainfall that has occurred over preceding days.

Symbol: P_i

Measurement: LengthUnit: cm

Note: Value should be greater than 0.

Formulas to find Precipitation in (i)th Year

Antecedent Precipitation Index

Antecedent Precipitation Index is a running day by day measure of catchment wetness based on the rainfall that has occurred over preceding days.

Symbol: P_a

Measurement: LengthUnit: cm

Note: Value should be greater than 0.

Formulas to find Antecedent Precipitation Index

Coefficient 'b'

Coefficient 'b' with their sum equal to unity.

Symbol: b

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Coefficient 'b'

Precipitation in (i-1)th Year

Precipitation in (i-1)th Year for Antecedent Precipitation Index, a running day by day measure of catchment wetness based on the rainfall that has occurred over preceding days.

Symbol: P_(i-1)

Measurement: LengthUnit: cm

Note: Value should be greater than 0.

Formulas to find Precipitation in (i-1)th Year

Coefficient 'c'

Coefficient 'c' with their sum equal to unity.

Symbol: c

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Coefficient 'c'

Precipitation in (i-2)th Year

Precipitation in (i-2)th Year for Antecedent Precipitation Index, a running day by day measure of catchment wetness based on rainfall that has occurred over preceding days.

Symbol: P_(i-2)

Measurement: LengthUnit: cm

Note: Value should be greater than 0.

Formulas to find Precipitation in (i-2)th Year

Coefficient 'a'

Coefficient 'a' in straight-line regression between runoff and rainfall. The sum of other coefficients will be unity and found by trial and error.

Symbol: a

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Coefficient 'a'

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}

How to Evaluate Annual Precipitation in i-th year given Antecedent Precipitation?

Annual Precipitation in i-th year given Antecedent Precipitation evaluator uses 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' to evaluate the Precipitation in (i)th Year, The Annual Precipitation in i-th year given Antecedent Precipitation formula is defined as the total precipitation in the current year under consideration for the Antecedent Precipitation index. Precipitation in (i)th Year is denoted by P_i symbol.

How to evaluate Annual Precipitation in i-th year given Antecedent Precipitation using this online evaluator? To use this online evaluator for Annual Precipitation in i-th year given Antecedent Precipitation, enter Antecedent Precipitation Index (P_a), Coefficient 'b' (b), Precipitation in (i-1)th Year (P_(i-1)), Coefficient 'c' (c), Precipitation in (i-2)th Year (P_(i-2)) & Coefficient 'a' (a) and hit the calculate button.

FAQs on Annual Precipitation in i-th year given Antecedent Precipitation

What is the formula to find Annual Precipitation in i-th year given Antecedent Precipitation?

The formula of Annual Precipitation in i-th year given Antecedent Precipitation is expressed as 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'. Here is an example- 8944.304 = (0.9639-0.1*1.21-0.11*0.84)/0.79.

How to calculate Annual Precipitation in i-th year given Antecedent Precipitation?

With Antecedent Precipitation Index (P_a), Coefficient 'b' (b), Precipitation in (i-1)th Year (P_(i-1)), Coefficient 'c' (c), Precipitation in (i-2)th Year (P_(i-2)) & Coefficient 'a' (a) we can find Annual Precipitation in i-th year given Antecedent Precipitation using the formula - 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'.

Can the Annual Precipitation in i-th year given Antecedent Precipitation be negative?

No, the Annual Precipitation in i-th year given Antecedent Precipitation, measured in Length cannot be negative.

Which unit is used to measure Annual Precipitation in i-th year given Antecedent Precipitation?

Annual Precipitation in i-th year given Antecedent Precipitation is usually measured using the Centimeter[cm] for Length. Meter[cm], Millimeter[cm], Kilometer[cm] are the few other units in which Annual Precipitation in i-th year given Antecedent Precipitation can be measured.

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Annual Precipitation in i-th year given Antecedent Precipitation Formula

Annual Precipitation in i-th year given Antecedent Precipitation Example

Annual Precipitation in i-th year given Antecedent Precipitation Solution

Annual Precipitation in i-th year given Antecedent Precipitation Formula Elements

Other formulas in Rainfall Runoff Correlation category

How to Evaluate Annual Precipitation in i-th year given Antecedent Precipitation?

FAQs on Annual Precipitation in i-th year given Antecedent Precipitation

Variable Name