PROBLEM $1$:

The figure below shows a watershed with three rainfall gauges nearby. The table below gives the coordinate of the three gauges and the rainfall observed at these gauges for a given storm. Determine total volume of rainfall $($in ${10}^6$ cubic meters$)$ over the watershed using $($a$)$ the arithmetic mean method and $($b$)$ the inverse distance method with a weighting factor $($exponent$)$ of $2.$ HINT: Use the center of each grid as the location for interpolation for each grid AND make sure to consider that some of the grids do not contribute their entire area to the watershed.

Figure $1.--$Location of watershed and rain gages for problem $1.$

Table $1.-$Location of rain gages and measured depth of rain for problem $1.$

$\backslash$table$[[,,,],[$Gauge$,$Easting $(km),$Northing $(km),$Rainfall $(cm)$