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
Pa = a*Pi+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
Pa = a*Pi+b*P(i-1)+c*P(i-2) --> 0.79*95+0.1*121+0.11*84
Evaluating ... ...
Pa = 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 00.007 seconds)

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Created by Mithila Muthamma PA
Coorg Institute of Technology (CIT), Coorg
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Rainfall Runoff Correlation Calculators

Annual Precipitation in (i-2)th year given Antecedent Precipitation
​ LaTeX ​ 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
​ LaTeX ​ 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
​ LaTeX ​ 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'
Precipitation using Runoff from Exponential Relationship
​ LaTeX ​ Go Rainfall = (Runoff/Coefficient β)^(1/Coefficient m)

Antecedent Precipitation Index Formula

​LaTeX ​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
Pa = a*Pi+b*P(i-1)+c*P(i-2)

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 Pa 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 (Pi), 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 Pa = a*Pi+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 (Pi), 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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