Step 1: Understanding the Concept:
Water Use Efficiency (WUE) is defined as the ratio of crop yield to the total volume of water used by the crop, including irrigation and rainfall.
Irrigation systems with lower water losses from evaporation, runoff, and deep percolation have higher water use efficiency.
Step 2: Detailed Explanation:
Let us evaluate the water application and conservation efficiency of the listed irrigation systems:
1. Surface irrigation: Methods like flooding and furrow irrigation have the lowest efficiency ($30\text{ to }50\%$) due to high runoff, uneven distribution, and deep percolation losses.
2. Sprinkler irrigation: This pressurized system distributes water through overhead nozzles, improving efficiency ($60\text{ to }75\%$) by reducing runoff and percolation losses, though some water is lost to wind drift and canopy evaporation.
3. Drip irrigation: Applies water directly to the soil surface or subsurface near plant roots through emitters, achieving high efficiency ($80\text{ to }90\%$) by minimizing soil surface evaporation and weed growth.
4. Pitcher pot irrigation: Is a localized, passive capillary system where water seeps through buried unglazed clay pots.
Because water release is driven by the moisture gradient in the surrounding soil, there is virtually no evaporation, deep percolation, or runoff loss.
This system can achieve water use efficiencies exceeding $90\%$ for compatible crops in arid zones.
Therefore, the correct ascending order of water use efficiency is: Surface irrigation $<$ Sprinkler irrigation $<$ Drip irrigation $<$ Pitcher pot irrigation.
Step 3: Final Answer:
The correct increasing order of water use efficiency is Surface irrigation, Sprinkler irrigation, Drip irrigation, Pitcher pot irrigation, which corresponds to Option (A).