z:\teaching\atm_150\hwk03.doc
ATM 150 - Fall 2003
Name:________________
Problem 9
THIS PROBLEM SET IS OPTIONAL
ALL POINTS ARE “EXTRA CREDIT”
Short answer questions related to Fourier series:
1. (1 pt) What symmetry property do Fourier (exponentials) coefficients have for a pure real
function?
2. (1 pt) A forward transform takes an integral over what independent variable?
3. (6 pts) A climate model has 121 distinct grid points along the equator, a domain periodic over a
distance of 2π*6367 km.
a. What is the largest wavenumber the model could resolve along the equator?
b. What is the largest alias free wavenumber along the equator?
c. What is the shortest alias free wavelength along the equator?
4. (1 pt) Why are finite differences used instead of spectral methods in nearly all mesoscale
models (e.g. MM5, WRF or Eta)? Hint: think of a property that is difficult to transform accurately
using Fourier series.
5. (3 pts) Prove the orthogonality of the basis functions of fourier exponentials eikx for the domain
0 ≤ x ≤ 2. Hint: k is NOT an integer.
Due: 10 December 03 by 5 pm. No credit given after that time.