SME
Physical Geography · Problem type
Water a root zone can hold for plants
Use this for “A loam holds 0.32 at field capacity and 0.15 at wilting point. How much water is available in a 60 cm root zone?”
Chart
Held too tightly: 9 cm
Available: 10.2 cm
This is an example. Type your own values to start a new problem.
θₐ
=
θfc
−
θwp
AW (cm)
=
θₐ
×
D (cm)
θₐ is the share of the soil’s volume that plants can use, and D is how deep the roots reach.
Wfc
Water at field capacity
worked out (not typed) · cm
Wwp
Water at wilting point
worked out (not typed) · cm
Formulas
θₐ = θfc − θwp
0.17 = 0.32 − 0.15
AW
=
θₐ
×
D
10.2 = 0.17 × 60
Wfc
=
θfc
×
D
19.2 = 0.32 × 60
Wwp
=
θwp
×
D
9 = 0.15 × 60
Assumptions
•
Field capacity θfc is the water left a day or two after soaking, once gravity has drained the big pores.
•
At the wilting point θwp the water left is held too tightly for roots, and plants wilt for good.
•
Both are by volume (cm³ of water per cm³ of soil), so θ times the depth is centimeters of water.
•
One soil through the whole root zone; plants use the water between the two limits.
Step-by-step
WE KNOW
θfc = 0.32, θwp = 0.15, D = 60 cm
FIND
available water content (θₐ), available water (AW), water at field capacity (Wfc), water at wilting point (Wwp)
Step 1 · Find available water content (θₐ)
Use θₐ = θfc − θwp
Plants can draw the soil down from field capacity to the wilting point, and no further.
θₐ = 0.32 − 0.15
θₐ = 0.17
Step 2 · Find available water (AW)
Use AW = θₐ × D
Each centimeter of soil holds θₐ cm of usable water, so multiply by the depth.
AW = 0.17 × 60
AW = 10.2 cm
Step 3 · Find water at field capacity (Wfc)
Use Wfc = θfc × D
All the water the root zone holds once drained: the top of the bar.
Wfc = 0.32 × 60
Wfc = 19.2 cm
Step 4 · Find water at wilting point (Wwp)
Use Wwp = θwp × D
The water roots cannot pull out: the bottom of the bar, under the available water.
Wwp = 0.15 × 60
Wwp = 9 cm
Check
Put the numbers back in. Both sides should match.
0.17 = 0.32 − 0.15 ✓
10.2 = 0.17 × 60 ✓
19.2 = 0.32 × 60 ✓
9 = 0.15 × 60 ✓
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