CE 374K Hydrology, Spring 2004                             Precipitation

# Homework #3

3.2.1 (Problem on atmospheric water)

3.3.2 (Problem on Precipitation, terminal velocity)

3.4.3 (Problem on Precipitation, rainfall hyetograph)

3.4.7 (Problem on Precipitation, spatial interpolation)

Additional reading for Precipitation: Sections 3.4, 3.5, 3.6, and 3.7 from Handbook of Hydrology.

Reading for the next class (Evaporation): Sections 3.5 and 3.6 from Applied Hydrology.

Precipitation on the web:

Animated precipitation map for the United States from NOAA.

Animated rainfall and Snowfall map for the United States from Intellicast.com

Global monthly precipitation (mm/month) based on satellite precipitation estimates over ocean areas and rain gage data over land regions.

CE 374K Hydrology, Spring 2004

Spatial Interpolation Methods:

This information is in addition to what you have in the textbook.

Thiessen Polygon Applet on the web:

http://www.cs.cornell.edu/Info/People/chew/Delaunay.html

# Inverse Distance Weighting:Inverse distance weighting is based on the assumption that the interpolating surface should be influenced most by the nearby points and less by the more distant points. The interpolating surface is a weighted average of the scatter points and the weight assigned to each scatter point diminishes as the distance from the interpolation point to the scatter point increases. Mathematically, IDW is computed as below: Where is the estimate at any required location, Pi is the measured/observed value at the ith location, di is the distance between , and N is the total number of measured points that are included in the interpolation process. This particular formula is called Squared Inverse Distance Weighting because di is raised by a power of two. The power could be any value, but two is commonly used.

There are more methods for interpolation, such as Splines and Kriging, but these methods are beyond the scope of this class. If you need more information on these methods, please write an email to me (vmmerwade@mail.utexas.edu).

Extra Credit!

In problem 3.4.7, find an interpolated precipitation value for a point A (6, 7) using the squared inverse distance weighting method.