Understanding Irrigation Requirements and Efficiency

In irrigation engineering, it's important to understand the different terms used to describe the amount of water needed for crops. Two key terms are Net Irrigation Requirement (NIR) and Field Irrigation Requirement (FIR). Water application efficiency ($\text{h}_\text{a}$) connects these two concepts.

What are Net Irrigation Requirement (NIR) and Field Irrigation Requirement (FIR)?

• Net Irrigation Requirement (NIR): This is the actual amount of water required to bring the soil moisture content in the root zone up to the field capacity. It's the water directly used by the crop to meet its needs after considering effective rainfall.
• Field Irrigation Requirement (FIR): This is the total amount of water that needs to be delivered to the field. It is always greater than or equal to NIR because it accounts for losses that occur during the application of water in the field, such as percolation losses, surface runoff, and evaporation from the field surface.

Water Application Efficiency ($\text{h}_\text{a}$)

Water application efficiency ($\text{h}_\text{a}$) measures how effectively the water delivered to the field is stored in the root zone where the crop can use it. It is defined as the ratio of the water stored in the root zone to the water delivered to the field.

The formula for water application efficiency is:

$$\text{h}_\text{a} = \frac{\text{Water stored in the root zone}}{\text{Water delivered to the field}}$$

Assuming the water stored in the root zone is approximately equal to the Net Irrigation Requirement (NIR) and the water delivered to the field is the Field Irrigation Requirement (FIR), the formula can be written as:

$$\text{h}_\text{a} = \frac{\text{NIR}}{\text{FIR}}$$

Relating NIR and FIR using $\text{h}_\text{a}$

We want to find the relationship that expresses NIR in terms of FIR and $\text{h}_\text{a}$. We can rearrange the efficiency formula:

$$\text{h}_\text{a} = \frac{\text{NIR}}{\text{FIR}}$$

To isolate NIR, we multiply both sides of the equation by FIR:

$$\text{NIR} = \text{h}_\text{a} \times \text{FIR}$$

This equation shows that the Net Irrigation Requirement is equal to the Field Irrigation Requirement multiplied by the water application efficiency. Since efficiency is usually less than 1 (or 100%), FIR will be greater than NIR, accounting for application losses.

Analyzing the Given Options

Let's look at the provided options and compare them with our derived relationship:

• Option 1: NIR=FIR /ha ($\text{NIR} = \frac{\text{FIR}}{\text{h}_\text{a}}$) - This would imply NIR is greater than FIR if $\text{h}_\text{a} < 1$, which is incorrect.
• Option 2: NIR=FIR +h a ($\text{NIR} = \text{FIR} + \text{h}_\text{a}$) - This doesn't represent a standard relationship based on efficiency.
• Option 3: NIR=FIR –h a ($\text{NIR} = \text{FIR} - \text{h}_\text{a}$) - This doesn't represent a standard relationship based on efficiency.
• Option 4: NIR=ha × FIR ($\text{NIR} = \text{h}_\text{a} \times \text{FIR}$) - This matches our derived relationship.

Based on the definition of water application efficiency, the correct relationship between Net Irrigation Requirement (NIR) and Field Irrigation Requirement (FIR) is $\text{NIR} = \text{h}_\text{a} \times \text{FIR}$.