UA/GLOBE III - Antecdent Precipitation Index

Activity: Antecedent Precipitation Index (API)

Purpose

Construct a simple model of the relationship between antecedent precipitation and soil moisture.

Overview

Using self-collected data, data from the data archive or on-line data sets, develop a simple model between precipitation and soil moisture. This will be most meaningful for daily observations of each.
The model, a decaying exponential function, can be represented as a simple mechanical process, a table or spreadsheet computation, or as an exponent of time to make it accessible to a wide range of students. Besides working with integrated data sets, the students can look for characteristic differences between the drying rates in different climates.

Time Required

1-3 class periods, depending upon how much data exploration and analysis is done.

Skill Level

Intermediate-Advanced

Key Concepts and Skills

Concepts: Decay rates, Correlation, Comparison
Skills: Analyzing, Graphing, Modeling

Materials and Tools

Begining: dry kidney beans
Intermediate; paper for tables and graphs, hand calculator
Advanced: spreadsheet program

System Requirements

Data Sets: precipitation, soil bulk density, soil water content
Period: Try to get a time period with several distinct wet-dry cycles. Daily precipitation and soil moisture (gypsum block) data sets are best.
Note: If bulk density is not available, try requesting via GLOBEmail, or assume a bulk density of 1.4 g/cm^3 for a typical loam soil.

Key Words

GLOBE 3; Soil Moisture; Precipitation; Bulk Density; Model; Analysis;

Mathematical Modeling

Basic Concepts

Following a rain, surface soils dry by the combined processes of evaporation and (if vegetation is present) transpiration. A simple approximation to the complex, interactive processes that control evaporation is to assume that a fixed precentage of the previous rainfall (stored in the surface soils) is lost every day. Thus if 5 cm of rain fell and there is a 20% loss rate, the residual soil moisture or Antecedent Precipitation Index (API) is only 4.0 cm and 3.2 cm after one and two days, respectively. It turns out that, given a location and season, this method works reasonably well.
"The rate at which moisture is depleted from a particular basin (or location) under specified meteorological conditions is roughly proportional to the amount in storage. In other words, the soil moisture should decrease logarithmically (or assymptotically) with time during periods of no precipitation" (Linsley, Kohler and Paulhus, 1982)

Mathematical Model

API(t) = API(t=0) * k ^(t)
This equation can be simplified by considering what the index is day-by-day. Thus, t=1 and:
API(t) = API(t-1) * k
The API is reduced by a factor 1-k, where the recession factor (k) typically ranges between 0.85 and 0.98. The initial (t=0) API is just the depth of liquid precipitation (rainfall). Any subsequent rainfall is simply added to the index.

What else you need to know

Estimating near-surface soil moisture storage from a GLOBE soil moisture depth profile

First, find the average soil water content (avg_SWC) from the surface to a depth of 100 cm.
avg_SWC/m = 0.20 * SWC(10) + 0.25 * SWC(30) + 0.30 * SWC(60) + 0.25 * SWC(90)
Now convert this to effective soil water depth by muliplying by the bulk density. Note the units below:
   avg_SWC/m       rho_bulk  1/rho_water

 (wet - dry) wt.    dry wt.      cm^3    10 mm
 --------------- * ---------- * ------ * -----  =   soil water storage [mm]
    dry wt.        sample vol.    1 g     cm

Parameter Definitions

t = Time [days]
z = Depth below the surface [cm]
P = Precipitation [mm]
rho_bulk = soil bulk density [g/cm^3]
SWC = Soil Water Content [g/g]
API = Antecedent Precipitation Index [mm]
k = Recession Factor [unitless]

Basic Assumptions

The recession factor is a calibration "constant", that depends on the location, climate and season.
This formulation assumes runoff is zero or insignificant.
The API should only be related to the total amount of near-surface soil moisture, which will be estimated below from GLOBE observations.

**Model Inputs and Outputs**
Inputs	Outputs	Constants
time precipitation API(t-1) SWC(z) [g/g]	API(t) avg_SWC [mm]	k

Example Applications

Even you youngest students can model the API or soil water storage using kidney beans. Start with 50 beans and help them play the following GAME.
Assume a value of k of .85. Use the data in the following WORKSHEET to complete the table and graph the results of three well-behaved drying cycles. Check your answers HERE.
In order to estimate the Recession Factor (k), use the data in the following TABLE to practice the procedure outlined at the top (often called inversion by scientists). Then get you own data set from the GLOBE data archive and try it again. You might find that the archive data is more variable or "noisier" than the example you just completed. Why might this be so?
Older students should use their calculators or a spreadsheet to calculate the logarithmic decrease in API. An example using MS Excel can be found HERE.

Data Analysis

What to do with your data

Quality Control
Important metadata
What to see in GLOBE visualizations
Entering your data into a table
Data for API Activity
Date: Group Name:

Site Description:

Independent Variable Dependent Variables
time
.... measurement
...
Graphing your data

**Data for API Activity**
Date:	Group Name:
Site Description:
Independent Variable	Dependent Variables
time ....	measurement ...

What to do with other GLOBE data

How to get it
Which sites might be similar
Which sites might show systematic differences
Examples of comparisons

What to do with global data (non-GLOBE)

Posssible data sources
Global activities
Questions you should ask

References

Assessment Requirements

Do the students understand that this can be a predictive model for the period before the next rainfall? Are they overwhelmed by the computation and miss the complementary relationship between precipitation and soil moisture?

Last updated: 12/4/96
Comments? globe@hwr.arizona.edu

Activity: Antecedent Precipitation Index (API)

Purpose

Overview

Time Required

Skill Level

Key Concepts and Skills

Materials and Tools

System Requirements

Key Words

Mathematical Modeling

Basic Concepts

Mathematical Model

What else you need to know

Parameter Definitions

Basic Assumptions

Example Applications

Data Analysis

What to do with your data

What to do with other GLOBE data

What to do with global data (non-GLOBE)

References

Assessment Requirements

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