GATE 2023 ES – Question 51
The catchment Q–S–U–T–Q and gauge positions are shown. Rainfalls P, Q, R, S, U, V are20,25,30,15,22,18 mm. Find Thiessen-weighted mean rainfall in mm, to two decimals.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 20.00 to 22.00
Explanation
Use coordinates P(0,0),Q(2,0),R(6,0),S(0,2),U(2,4),V(6,4),with T(4,2). The catchment comprises the upper radius2 km semicircle over S–T and the lower S–Q–T triangle, total area $2\pi+4=10.283185$ km². Intersect nearest-gauge polygons with this boundary. Nonzero areas are Q:3,S:$1+\pi/2=2.570796$,U:$3\pi/2=4.712389$ km²; P, R, V have zero area. Weighted mean is $[25(3)+15(2.570796)+22(4.712389)]/10.283185=\mathbf{21.13}$ mm.