Normal-ratio method (precipitation estimation at an ungauged station): Storm totals at three surrounding stations are A = 110 mm, B = 90 mm, and C = 70 mm. Normal annual precipitation values are: X = 1000 mm (target), A = 1100 mm, B = 1200 mm, C = 1250 mm. Estimate the storm precipitation at station X.

Introduction / Context:
When a storm total is missing at a station, the normal-ratio method adjusts neighbouring station storm totals by the ratios of normal annual precipitation to account for climatic gradients. It is widely used for hydrologic data reconstruction when normals differ by more than about 10% between stations.

Given Data / Assumptions:

• Normal annual precipitation: N_X = 1000 mm, N_A = 1100 mm, N_B = 1200 mm, N_C = 1250 mm.
• Observed storm totals: P_A = 110 mm, P_B = 90 mm, P_C = 70 mm.
• Normals differ sufficiently to warrant the normal-ratio adjustment.

Concept / Approach:
Normal-ratio method formula:
P_X = (1/n) * Σ [ (N_X / N_i) * P_i ] , for i = A, B, C and n = 3.This scales each neighbour’s storm by the relative wetness/dryness indicated by normals.

Step-by-Step Solution:
Term A: (1000/1100) * 110 = 0.9091 * 110 ≈ 100.0Term B: (1000/1200) * 90 = 0.8333 * 90 = 75.0Term C: (1000/1250) * 70 = 0.8 * 70 = 56.0Sum = 231.0; Average = 231 / 3 = 77.0 mm

Verification / Alternative check:
If normals were similar (within ~10%), the simple arithmetic mean (110 + 90 + 70)/3 = 90 mm might be used. Because normals differ notably, the adjusted result (77 mm) is more appropriate.

Why Other Options Are Wrong:

• 75, 79, 81, 83 mm: Do not match the computed normal-ratio average of 77 mm.

Common Pitfalls:

• Forgetting to scale each neighbour by N_X/N_i.
• Using a weighted average without proper justification from normals or distances.

Final Answer:
77 mm