Problem #3: Mean Areal Precipitation with Thiessen Polygons Figure 1 below is a schematic of a...

 

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Problem #3: Mean Areal Precipitation with Thiessen Polygons Figure 1 below is a schematic of a watershed with an established set of precipitation gages. The precipitation that was observed during a storm is listed in Table 1 for each gage. Table 1: Rain gage station IDs and observed precipitation for a storm. Station ID Storm #1 PPT (mm) kilometers A 35.1 B 24.4 C 19.2 D 39.5 100 90 D 80 70 A C 60 50 40 30 20 10 B 10 20 30 40 50 60 70 80 90 100 110 120 130 140 kilometers Figure 1: Location of four precipitation gages for an idealized watershed. a) Compute the areal average precipitation for storm #1 using an arithmetic mean approach. b) Compute the areal average precipitation for storm #1 using a Thiessen polygon approach by constructing the polygons by-hand and "counting squares" for each polygon area on Figure 1 (you can do this by hand or on an iPad, tablet, etc). Draw your polygons very carefully. You should be precise - there is an exact solution. Consider only the area inside the basin. Be sure to turn in your figure showing the polygons as part of your solution and make your figures neat. c) Calculate the percent difference between the two estimates from part (a) and (b). d) Discuss the difference in the two areal averages you found for the watershed. Which method do you think provides the most accurate estimate of the mean precipitation over the basin? Why? Problem #3: Mean Areal Precipitation with Thiessen Polygons Figure 1 below is a schematic of a watershed with an established set of precipitation gages. The precipitation that was observed during a storm is listed in Table 1 for each gage. Table 1: Rain gage station IDs and observed precipitation for a storm. Station ID Storm #1 PPT (mm) kilometers A 35.1 B 24.4 C 19.2 D 39.5 100 90 D 80 70 A C 60 50 40 30 20 10 B 10 20 30 40 50 60 70 80 90 100 110 120 130 140 kilometers Figure 1: Location of four precipitation gages for an idealized watershed. a) Compute the areal average precipitation for storm #1 using an arithmetic mean approach. b) Compute the areal average precipitation for storm #1 using a Thiessen polygon approach by constructing the polygons by-hand and "counting squares" for each polygon area on Figure 1 (you can do this by hand or on an iPad, tablet, etc). Draw your polygons very carefully. You should be precise - there is an exact solution. Consider only the area inside the basin. Be sure to turn in your figure showing the polygons as part of your solution and make your figures neat. c) Calculate the percent difference between the two estimates from part (a) and (b). d) Discuss the difference in the two areal averages you found for the watershed. Which method do you think provides the most accurate estimate of the mean precipitation over the basin? Why?