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Antecedent Precipitation Index Formula

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

P a = a \cdot P i + b \cdot P (i-1) + c \cdot P (i-2)

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

Antecedent Precipitation Index Example

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With units

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Here is how the Antecedent Precipitation Index equation looks like with Values.

Here is how the Antecedent Precipitation Index equation looks like with Units.

Here is how the Antecedent Precipitation Index equation looks like.

96.39 = 0.79 \cdot 95 + 0.1 \cdot 121 + 0.11 \cdot 84

96.39cm = 0.79 \cdot 95cm + 0.1 \cdot 121cm + 0.11 \cdot 84cm

96.39 = 0.79 \cdot 95 + 0.1 \cdot 121 + 0.11 \cdot 84

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Antecedent Precipitation Index Solution

Follow our step by step solution on how to calculate Antecedent Precipitation Index?

FIRST Step Consider the formula

P a = a \cdot P i + b \cdot P (i-1) + c \cdot P (i-2)

Next Step Substitute values of Variables

∴

P a = 0.79 \cdot 95cm + 0.1 \cdot 121cm + 0.11 \cdot 84cm

Next Step Prepare to Evaluate

∴

P a = 0.79 \cdot 95 + 0.1 \cdot 121 + 0.11 \cdot 84

Next Step Evaluate

∴

P a = 0.9639m

LAST Step Convert to Output's Unit

∴

P a = 96.39cm

Antecedent Precipitation Index Formula Elements

Variables

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 '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'

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

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

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 Antecedent Precipitation Index?

Antecedent Precipitation Index evaluator uses 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 to evaluate the Antecedent Precipitation Index, The Antecedent Precipitation Index formula is defined as the precipitation falling before, but influencing the runoff yields of, a given rainfall event. Antecedent Precipitation Index is denoted by P_a symbol.

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

FAQs on Antecedent Precipitation Index

What is the formula to find Antecedent Precipitation Index?

The formula of Antecedent Precipitation Index is expressed as 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. Here is an example- 9639 = 0.79*0.95+0.1*1.21+0.11*0.84.

How to calculate Antecedent Precipitation Index?

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

Can the Antecedent Precipitation Index be negative?

No, the Antecedent Precipitation Index, measured in Length cannot be negative.

Which unit is used to measure Antecedent Precipitation Index?

Antecedent Precipitation Index is usually measured using the Centimeter[cm] for Length. Meter[cm], Millimeter[cm], Kilometer[cm] are the few other units in which Antecedent Precipitation Index can be measured.

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Antecedent Precipitation Index Formula

Antecedent Precipitation Index Example

Antecedent Precipitation Index Solution

Antecedent Precipitation Index Formula Elements

Other formulas in Rainfall Runoff Correlation category

How to Evaluate Antecedent Precipitation Index?

FAQs on Antecedent Precipitation Index

Variable Name