Rainfall Estimation for Station A

To estimate the rainfall at station A when it was non-operational, we use the data from the other operational stations (B, C, D, E). The method assumes that the ratio of recorded rainfall to average annual rainfall is consistent across the stations in the basin for that particular year.

Calculate Total Average Rainfall (B, C, D, E)

Sum the average annual rainfall for stations B, C, D, and E:

$ R_{B-E} = R_B + R_C + R_D + R_E $

$ R_{B-E} = 810 \text{ mm} + 675 \text{ mm} + 940 \text{ mm} + 780 \text{ mm} = 3205 \text{ mm} $

Calculate Total Recorded Rainfall (B, C, D, E)

Sum the rainfall recorded by stations B, C, D, and E in the particular year:

$ r_{B-E} = r_B + r_C + r_D + r_E $

$ r_{B-E} = 890 \text{ mm} + 725 \text{ mm} + 980 \text{ mm} + 850 \text{ mm} = 3445 \text{ mm} $

Determine Rainfall Ratio

Calculate the ratio of the total recorded rainfall to the total average rainfall for these stations:

$ \text{Ratio} = \frac{r_{B-E}}{R_{B-E}} = \frac{3445 \text{ mm}}{3205 \text{ mm}} $

$ \text{Ratio} \approx 1.07488 $

Estimate Rainfall for Station A

Apply this ratio to the average annual rainfall of station A ($R_A = 1020$ mm) to estimate its rainfall ($r_A$) for that year:

$ r_A = R_A \times \text{Ratio} $

$ r_A = 1020 \text{ mm} \times \frac{3445}{3205} $

$ r_A = 1020 \text{ mm} \times \frac{689}{641} \approx 1096.38 \text{ mm} $

The calculated value is approximately 1096.38 mm. The closest option provided is 1098 mm.