Final answer:
To estimate the water loss from a catchment area, multiply the catchment's area by precipitation depth, then subtract the annual discharge volume calculated from the average discharge rate. The difference represents the volume lost to evaporation, transpiration, and percolation. In this case, approximately 2.304 billion cubic meters of water is lost annually due to these processes.
Step-by-step explanation:
To estimate the amount of water lost due to evaporation, transpiration, and percolation to groundwater in a catchment area, first, we calculate the total volume of precipitation by multiplying the catchment area with the precipitation depth. For a catchment area of 2,500 km² receiving 1,300 mm (1.3 m) of precipitation, this equates to a total volume of precipitation of 3.25 billion cubic meters (2,500 km² * 1.3 m). Next, we calculate the annual discharge volume by multiplying the average discharge rate by the number of seconds in a year (30 m³/s * 31,536,000 s = 946.08 billion cubic meters).
The difference between the total volume of precipitation and the annual discharge volume is the volume lost to evaporation, transpiration, and percolation. Subtracting the annual discharge volume from the total precipitation gives us the volume lost: 3.25 billion m³ - 0.946 billion m³ = 2.304 billion m³. Therefore, approximately 2.304 billion cubic meters of water is estimated to be lost annually in the studied catchment area due to these processes.