Calculating Irrigation Trigger Point

This problem requires calculating the specific soil moisture percentage at which irrigation should begin, based on the field capacity (FC), permanent wilting point (PWP), and a specified depletion level.

Understanding Key Soil Moisture Terms

• Field Capacity (FC): The maximum amount of water the soil can hold against gravity. Given as 42%.
• Permanent Wilting Point (PWP): The soil moisture level at which plants can no longer extract water and wilt permanently. Given as 19%.
• Available Moisture (AM): The difference between FC and PWP, representing the water available for plants.
• Depletion Level: The percentage of AM that is allowed to be used before irrigation is triggered. Given as 40%.

Step-by-Step Calculation

1. Calculate Available Moisture (AM):

   AM is the difference between FC and PWP.

   $ \text{AM} = \text{FC} - \text{PWP} $ $ \text{AM} = 42\% - 19\% = 23\% $

2. Calculate the Depletion Amount:

   Irrigation is needed when 40% of the AM is depleted.

   $ \text{Depletion Amount} = 40\% \times \text{AM} $ $ \text{Depletion Amount} = 0.40 \times 23\% = 9.2\% $

3. Determine the Irrigation Trigger Point:

   Subtract the depletion amount from the Field Capacity.

   $ \text{Irrigation Trigger Point} = \text{FC} - \text{Depletion Amount} $ $ \text{Irrigation Trigger Point} = 42\% - 9.2\% = 32.8\% $

Therefore, irrigation should be initiated when the soil moisture reaches 32.8%.