Lysimeter Water Balance Analysis

The problem involves calculating the potential evapotranspiration (PET) using data from three lysimeters (A, B, C) under different conditions in a paddy field. We use the water balance equation for each lysimeter:

$ \Delta W = P - ET - D $

Where:

• $ \Delta W $ is the change in water stored in the lysimeter (Final Depth - Initial Depth).
• $ P $ is the precipitation received.
• $ ET $ is the evapotranspiration.
• $ D $ is the drainage (percolation).

Initial ponding depth = 12 cm.

Rainfall ($ P $) = 15 mm = 1.5 cm.

Lysimeter A Analysis (Closed bottom, no plant)

The change in water depth ($ \Delta W_A $) = 10.4 cm - 12 cm = -1.6 cm.

Since the bottom is closed, drainage ($ D_A $) = 0.

The water balance equation becomes: $ \Delta W_A = P - ET_A $

$ -1.6 \text{ cm} = 1.5 \text{ cm} - ET_A $

$ ET_A = 1.5 \text{ cm} + 1.6 \text{ cm} = 3.1 \text{ cm} $

This $ ET_A $ represents evapotranspiration from the bare soil surface.

Lysimeter B Analysis (Open bottom, no plant)

The change in water depth ($ \Delta W_B $) = 8.6 cm - 12 cm = -3.4 cm.

The water balance equation is: $ \Delta W_B = P - ET_B - D_B $

$ -3.4 \text{ cm} = 1.5 \text{ cm} - ET_B - D_B $

$ ET_B + D_B = 1.5 \text{ cm} + 3.4 \text{ cm} = 4.9 \text{ cm} $

Assuming evapotranspiration from bare soil is consistent ($ ET_B \approx ET_A $), we get:

$ 3.1 \text{ cm} + D_B \approx 4.9 \text{ cm} $

$ D_B \approx 4.9 \text{ cm} - 3.1 \text{ cm} = 1.8 \text{ cm} $

This $ D_B $ represents percolation through the bare soil.

Lysimeter C Analysis (Open bottom, with paddy plants)

The change in water depth ($ \Delta W_C $) = 7.0 cm - 12 cm = -5.0 cm.

The water balance equation is: $ \Delta W_C = P - ET_C - D_C $

$ -5.0 \text{ cm} = 1.5 \text{ cm} - ET_C - D_C $

$ ET_C + D_C = 1.5 \text{ cm} + 5.0 \text{ cm} = 6.5 \text{ cm} $

$ ET_C $ represents the total evapotranspiration from the cropped lysimeter (crop + soil). Since the lysimeter is ponded, water is not limiting, so $ ET_C $ is a measure of actual ET, approximating potential evapotranspiration (PET).

Estimating Potential Evapotranspiration (PET)

To find $ ET_C $, we need to estimate the drainage $ D_C $. Assuming percolation under the crop is similar to percolation under bare soil ($ D_C \approx D_B $):

$ D_C \approx 1.8 \text{ cm} $

Now, substitute this into the equation for Lysimeter C:

$ ET_C + 1.8 \text{ cm} \approx 6.5 \text{ cm} $

$ ET_C \approx 6.5 \text{ cm} - 1.8 \text{ cm} = 4.7 \text{ cm} $

The calculated weekly evapotranspiration for the paddy crop is approximately 4.7 cm. This value serves as the estimate for potential evapotranspiration (PET).

Note: The calculation yields approximately 4.7 cm. Given the answer range is stated as "between 5 and 5", the intended value is likely 5 cm. The slight difference arises from the assumptions made (e.g., $ D_C \approx D_B $).