Antecedent Precipitation Index Calculator

✖Coefficient 'a' in straight-line regression between runoff and rainfall. The sum of other coefficients will be unity and found by trial and error.ⓘ Coefficient 'a' [a]			+10% -10%
✖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.ⓘ Precipitation in (i)th Year [P_i]			+10% -10%
✖Coefficient 'b' with their sum equal to unity.ⓘ Coefficient 'b' [b]			+10% -10%
✖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.ⓘ Precipitation in (i-1)th Year [P_(i-1)]			+10% -10%
✖Coefficient 'c' with their sum equal to unity.ⓘ Coefficient 'c' [c]			+10% -10%
✖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.ⓘ Precipitation in (i-2)th Year [P_(i-2)]			+10% -10%

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

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Formula

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Antecedent Precipitation Index

Formula

`"P"_{"a"} = "a"*"P"_{"i"}+"b"*"P"_{"(i-1)"}+"c"*"P"_{"(i-2)"}`

Example

`"96.39cm"="0.79"*"95cm"+"0.1"*"121cm"+"0.11"*"84cm"`

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Antecedent Precipitation Index Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
P_a = a*P_i+b*P_(i-1)+c*P_(i-2)
This formula uses 7 Variables

Variables Used

Antecedent Precipitation Index - (Measured in Centimeter) - Antecedent Precipitation Index is a running day by day measure of catchment wetness based on the rainfall that has occurred over preceding days.
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.
Precipitation in (i)th Year - (Measured in Centimeter) - 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.
Coefficient 'b' - Coefficient 'b' with their sum equal to unity.
Precipitation in (i-1)th Year - (Measured in Centimeter) - 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.
Coefficient 'c' - Coefficient 'c' with their sum equal to unity.
Precipitation in (i-2)th Year - (Measured in Centimeter) - 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.

STEP 1: Convert Input(s) to Base Unit

Coefficient 'a': 0.79 --> No Conversion Required
Precipitation in (i)th Year: 95 Centimeter --> 95 Centimeter No Conversion Required
Coefficient 'b': 0.1 --> No Conversion Required
Precipitation in (i-1)th Year: 121 Centimeter --> 121 Centimeter No Conversion Required
Coefficient 'c': 0.11 --> No Conversion Required
Precipitation in (i-2)th Year: 84 Centimeter --> 84 Centimeter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_a = a*P_i+b*P_(i-1)+c*P_(i-2) --> 0.79*95+0.1*121+0.11*84

Evaluating ... ...

P_a = 96.39

STEP 3: Convert Result to Output's Unit

0.9639 Meter -->96.39 Centimeter (Check conversion here)

FINAL ANSWER

96.39 Centimeter <-- Antecedent Precipitation Index

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Engineering Hydrology » Runoff » Runoff Volume » Rainfall-Runoff Correlation and Strange's Tables » Rainfall-Runoff Correlation » Antecedent Precipitation Index

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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

Antecedent Precipitation Index Formula

What is the use of Antecedent Rainfall?

Many improvements of the basic rainfall-runoff correlation by considering additional parameters such as soil moisture and antecedent rainfall have been attempted. Antecedent rainfall influences the initial soil moisture
and hence the infiltration rate at the start of the storm.

What does Precipitation mean?

Precipitation is any product of the condensation of atmospheric water vapor that falls under gravitational pull from clouds. The main forms of precipitation include drizzling, rain, sleet, snow, ice pellets, graupel and hail.

How to Calculate Antecedent Precipitation Index?

Antecedent Precipitation Index calculator 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 calculate 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 calculate Antecedent Precipitation Index using this online calculator? To use this online calculator 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. Here is how the Antecedent Precipitation Index calculation can be explained with given input values -> 9639 = 0.79*0.95+0.1*1.21+0.11*0.84.

FAQ

What is 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 and is represented as P_a = a*P_i+b*P_(i-1)+c*P_(i-2) or 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. Coefficient 'a' in straight-line regression between runoff and rainfall. The sum of other coefficients will be unity and found by trial and error, 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, Coefficient 'b' with their sum equal to unity, 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, Coefficient 'c' with their sum equal to unity & 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.

How to calculate 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 is calculated using 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 calculate Antecedent Precipitation Index, you need 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)). With our tool, you need to enter the respective value for Coefficient 'a', Precipitation in (i)th Year, Coefficient 'b', Precipitation in (i-1)th Year, Coefficient 'c' & Precipitation in (i-2)th Year and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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