Why is the normal ratio method used?

A base station's normal annual rainfall differs from B's by more than 10%

Station B has no normal rainfall

There are only two neighbouring stations

The normal ratio estimate for B is:

Average of (NB/Ni) x Pi over the base stations

2076 Chaitra · 6 marks

Estimating missing precipitation at station B

Short answer

Station normals differ >10%, so normal ratio method is used. Missing rainfall at B = (1/3)[(940/1150)×1000 + (940/1080)×970 + (940/980)×890] = 838.4 mm.

The normal annual rainfall of four stations A, B, C and D in a catchment area is 1150, 940, 1080 and 980 respectively. In a particular year the station B did not work and the rainfall amount of A, C and D were 1000, 970 and 890 respectively. Compute the missing precipitation at point B for that year.

The normal annual rainfall of the base stations A and C differs from that of B by more than 10% (A: 22%; C: 15%; D: 4%), so the normal ratio method is used:

P_B = \frac{1}{n}\left[\frac{N_B}{N_A}P_A + \frac{N_B}{N_C}P_C + \frac{N_B}{N_D}P_D\right]

with $n = 3$ stations, $N_A = 1150$ , $N_B = 940$ , $N_C = 1080$ , $N_D = 980$ and $P_A = 1000$ , $P_C = 970$ , $P_D = 890$ mm.

\begin{aligned} \frac{N_B}{N_A}P_A &= \frac{940}{1150}\times1000 = 817.39\\ \frac{N_B}{N_C}P_C &= \frac{940}{1080}\times970 = 844.26\\ \frac{N_B}{N_D}P_D &= \frac{940}{980}\times890 = 853.67 \end{aligned}

P_B = \frac{817.39 + 844.26 + 853.67}{3} = 838.4\ \text{mm}

Answer: Missing precipitation at station B = 838.4 mm (about 838 mm).

✓ Answer checked by Claude Sonnet 5.5

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