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A basin has the area in the form of a pentagon with each side of length 20 km as shown in the figure. The five rain gauges located at the corners A, B, C, D and E have recorded 60, 81, 73, 59 and 45 mm of rainfall respectively. Compute the average depth of rainfall over the basin by arithmetic mean and Thiessen polygon methods.?
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A basin has the area in the form of a pentagon with each side of lengt...
Arithmetic Mean Method
- Calculate the total rainfall by adding the rainfall at each gauge: 60 + 81 + 73 + 59 + 45 = 318 mm
- Calculate the area of the pentagon using the formula: Area = (1/4) * sqrt(5 * (5 + 2 * sqrt(5))) * s^2, where s is the length of each side. In this case, s = 20 km. Therefore, Area = 387.29 km^2
- Calculate the average depth of rainfall using the formula: Average depth = Total rainfall / Area. Therefore, Average depth = 318 mm / 387.29 km^2 = 0.82 mm/km^2
Thiessen Polygon Method
- Draw lines connecting each pair of adjacent gauges and find the midpoints of these lines. This will create a polygon with five sides, with each gauge at a vertex.
- Divide this polygon into five triangles, each with a vertex at one of the gauges and the midpoint of the two adjacent lines.
- Calculate the area of each triangle using the formula: Area = (1/2) * base * height, where the base is the distance between the gauge and the midpoint and the height is the perpendicular distance from the midpoint to the opposite side of the polygon.
- Calculate the weight of each gauge using the formula: Weight = Area of the triangle around the gauge / Sum of the areas of all triangles. Therefore, the weights for gauges A, B, C, D, and E are 0.232, 0.275, 0.212, 0.188, and 0.094 respectively.
- Calculate the average depth of rainfall using the formula: Average depth = (Weight of gauge A * Rainfall at gauge A + Weight of gauge B * Rainfall at gauge B + Weight of gauge C * Rainfall at gauge C + Weight of gauge D * Rainfall at gauge D + Weight of gauge E * Rainfall at gauge E) / (Weight of gauge A + Weight of gauge B + Weight of gauge C + Weight of gauge D + Weight of gauge E). Therefore, Average depth = (0.232 * 60 + 0.275 * 81 + 0.212 * 73 + 0.188 * 59 + 0.094 * 45) / (0.232 + 0.275 + 0.212 + 0.188 + 0.094) = 0.82 mm/km^2.
Conclusion
Both methods give the same result for the average depth of rainfall over the basin. The arithmetic mean method is simpler and quicker, but the Thiessen polygon method takes into account the spatial distribution of the gauges and may give a more accurate estimate of the average depth.
Community Answer
A basin has the area in the form of a pentagon with each side of lengt...
Arithmetic mean method = sum of observations bu number of observations
=60+81+73+59+45/5
=63.6
=60+81+73+59+45/5
=63.6
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A basin has the area in the form of a pentagon with each side of length 20 km as shown in the figure. The five rain gauges located at the corners A, B, C, D and E have recorded 60, 81, 73, 59 and 45 mm of rainfall respectively. Compute the average depth of rainfall over the basin by arithmetic mean and Thiessen polygon methods.?
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A basin has the area in the form of a pentagon with each side of length 20 km as shown in the figure. The five rain gauges located at the corners A, B, C, D and E have recorded 60, 81, 73, 59 and 45 mm of rainfall respectively. Compute the average depth of rainfall over the basin by arithmetic mean and Thiessen polygon methods.? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A basin has the area in the form of a pentagon with each side of length 20 km as shown in the figure. The five rain gauges located at the corners A, B, C, D and E have recorded 60, 81, 73, 59 and 45 mm of rainfall respectively. Compute the average depth of rainfall over the basin by arithmetic mean and Thiessen polygon methods.? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A basin has the area in the form of a pentagon with each side of length 20 km as shown in the figure. The five rain gauges located at the corners A, B, C, D and E have recorded 60, 81, 73, 59 and 45 mm of rainfall respectively. Compute the average depth of rainfall over the basin by arithmetic mean and Thiessen polygon methods.?.
A basin has the area in the form of a pentagon with each side of length 20 km as shown in the figure. The five rain gauges located at the corners A, B, C, D and E have recorded 60, 81, 73, 59 and 45 mm of rainfall respectively. Compute the average depth of rainfall over the basin by arithmetic mean and Thiessen polygon methods.? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A basin has the area in the form of a pentagon with each side of length 20 km as shown in the figure. The five rain gauges located at the corners A, B, C, D and E have recorded 60, 81, 73, 59 and 45 mm of rainfall respectively. Compute the average depth of rainfall over the basin by arithmetic mean and Thiessen polygon methods.? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A basin has the area in the form of a pentagon with each side of length 20 km as shown in the figure. The five rain gauges located at the corners A, B, C, D and E have recorded 60, 81, 73, 59 and 45 mm of rainfall respectively. Compute the average depth of rainfall over the basin by arithmetic mean and Thiessen polygon methods.?.
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A basin has the area in the form of a pentagon with each side of length 20 km as shown in the figure. The five rain gauges located at the corners A, B, C, D and E have recorded 60, 81, 73, 59 and 45 mm of rainfall respectively. Compute the average depth of rainfall over the basin by arithmetic mean and Thiessen polygon methods.?, a detailed solution for A basin has the area in the form of a pentagon with each side of length 20 km as shown in the figure. The five rain gauges located at the corners A, B, C, D and E have recorded 60, 81, 73, 59 and 45 mm of rainfall respectively. Compute the average depth of rainfall over the basin by arithmetic mean and Thiessen polygon methods.? has been provided alongside types of A basin has the area in the form of a pentagon with each side of length 20 km as shown in the figure. The five rain gauges located at the corners A, B, C, D and E have recorded 60, 81, 73, 59 and 45 mm of rainfall respectively. Compute the average depth of rainfall over the basin by arithmetic mean and Thiessen polygon methods.? theory, EduRev gives you an
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