Irrigation Depth Calculation

This calculation determines the gross amount of water needed for irrigation to restore soil moisture to field capacity.

Given Soil and Irrigation Parameters:

• Field Capacity (Moisture Content, FC): $32\%$
• Wilting Point (Moisture Content, WP): $12\%$
• Soil Bulk Density ($\rho_b$): $1.5 \text{ g cm}^{-3}$
• Crop Root Zone Depth (D): $50 \text{ cm}$
• Field Water Application Efficiency ($\eta_a$): $75\% = 0.75$
• Irrigation Trigger Point: Available soil water drops to $60\%$ of total capacity.

Step 1: Calculate Total Available Water (AW)

The total available water is the difference between the moisture content at field capacity and wilting point.

$ AW = FC - WP $

$ AW = 32\% - 12\% = 20\% $

Step 2: Determine Current Available Water Level

Irrigation is needed when the available water reduces to $60\%$ of the total AW.

$ \text{Current AW} = 0.60 \times AW $

$ \text{Current AW} = 0.60 \times 20\% = 12\% $

Step 3: Calculate Current Soil Moisture Content

The current moisture content ($\theta_{\text{current}}$) is the sum of the wilting point and the current available water, expressed by mass.

$ \theta_{\text{current}} = WP + \text{Current AW} $

$ \theta_{\text{current}} = 12\% + 12\% = 24\% \quad (\text{by mass}) $

Step 4: Calculate Moisture Deficit

The moisture deficit ($\Delta \theta$) represents the amount of water needed (by mass) to bring the soil back to field capacity.

$ \Delta \theta = FC - \theta_{\text{current}} $

$ \Delta \theta = 32\% - 24\% = 8\% \quad (\text{by mass}) $

Step 5: Calculate Net Irrigation Depth

Convert the moisture deficit from mass percentage to depth (cm). Assume the density of water ($\rho_w$) is $1 \text{ g cm}^{-3}$.

$ \Delta d_{\text{net}} = D \times \frac{\Delta \theta (\text{by mass})}{100} \times \frac{\rho_b}{\rho_w} $

$ \Delta d_{\text{net}} = 50 \text{ cm} \times \frac{8}{100} \times \frac{1.5 \text{ g cm}^{-3}}{1 \text{ g cm}^{-3}} $

$ \Delta d_{\text{net}} = 50 \times 0.08 \times 1.5 = 6 \text{ cm} $

Step 6: Calculate Gross Irrigation Depth

Adjust the net depth for the field water application efficiency ($\eta_a$) to find the total water to be applied.

$ \Delta d_{\text{gross}} = \frac{\Delta d_{\text{net}}}{\eta_a} $

$ \Delta d_{\text{gross}} = \frac{6 \text{ cm}}{0.75} = 8 \text{ cm} $

Result

The gross depth of irrigation required is 8 cm.