Figure 2.1 shows a map of the Schoharie Creek, NY watershed (113.5 km) and the nine...

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Figure 2.1 shows a map of the Schoharie Creek, NY watershed (113.5 km²) and the nine rain gauges in or near the watershed. Construct the Thiessen polygons for the watershed using all nine rain gauges. Table 2.1 shows the rainfall for a particular storm which occurred over the Schoharie Creek, NY watershed and the area associated with each of the nine Thiessen polygons. Determine the average rainfall over the watershed during the storm by (a) the arithmetic mean of all nine rain gages, (b) the arithmetic mean of only the rain gages within the watershed boundary, (c) the Thiessen polygon method with all nine rain gages, and (d) the isohyetal method using the interval and area shown in Table 2.2. Please also show the isohyets. Compare the results of the four methods and discuss reasons for any differences. [7 points] Table 2.1 Gauge data and Thiessen polygon area Rain gauge Polygon area Rainfall number (km²) (inches) 1 2 3 4 5 6 7 8 9 10.2 8.1 14.3 4.0 15.8 19.1 17.1 7.2 17.7 8.23 4.49 3.05 2.22 3.38 3.89 5.47 5.78 7.85 Table 2.2. Area for the isohyetal method Rain gauge Rainfall range % Area number A1 A2 A3 A4 A5 A6 A7 Total (inches) 8-9 7-8 6-7 5-6 4-5 3-4 2-3 8.2 9.3 10.7 11.8 16.6 20.1 23.3 100.0 Schoharie Creek, NY watershed 8.23 1 7.85 1 km 9 5.78 4.49 2 5.47 Q 3.05 3 $6 3.89 5 3.38 4 2.22 Figure 2.1 shows a map of the Schoharie Creek, NY watershed (113.5 km²) and the nine rain gauges in or near the watershed. Construct the Thiessen polygons for the watershed using all nine rain gauges. Table 2.1 shows the rainfall for a particular storm which occurred over the Schoharie Creek, NY watershed and the area associated with each of the nine Thiessen polygons. Determine the average rainfall over the watershed during the storm by (a) the arithmetic mean of all nine rain gages, (b) the arithmetic mean of only the rain gages within the watershed boundary, (c) the Thiessen polygon method with all nine rain gages, and (d) the isohyetal method using the interval and area shown in Table 2.2. Please also show the isohyets. Compare the results of the four methods and discuss reasons for any differences. [7 points] Table 2.1 Gauge data and Thiessen polygon area Rain gauge Polygon area Rainfall number (km²) (inches) 1 2 3 4 5 6 7 8 9 10.2 8.1 14.3 4.0 15.8 19.1 17.1 7.2 17.7 8.23 4.49 3.05 2.22 3.38 3.89 5.47 5.78 7.85 Table 2.2. Area for the isohyetal method Rain gauge Rainfall range % Area number A1 A2 A3 A4 A5 A6 A7 Total (inches) 8-9 7-8 6-7 5-6 4-5 3-4 2-3 8.2 9.3 10.7 11.8 16.6 20.1 23.3 100.0 Schoharie Creek, NY watershed 8.23 1 7.85 1 km 9 5.78 4.49 2 5.47 Q 3.05 3 $6 3.89 5 3.38 4 2.22