Mesoscale -

what is scale?

1. size of a bounded object (if boundaries well defined) cloud

2. sizes of "patches" in a continuum (defined how?)

3. Wavelength (for fluctiations of a continuous field)

What is mesoscale?

Other folks: Markowski and Richardson Ch 1 (upcoming book)

0. Conventional: "a few times 100-102 km in space, minutes to a day (or an inertial period) in time.

1. Dynamical 1: Space scales between aspect ratio 1 and Rossby deformation radius

1a. Dynamical 1a: Time scales between 1/N and 1/f

2. Dynamical 2: Pretty well hysrostatic, but not quite geostrophic.

3. Dynamical 3: You can't ignore Coriolis forces (like for small scales), nor ageostrophic advection (like for synoptic/ large scales).

How do we deal with (describe, formalize) the problem of multiple scales (a continuum of scales)?

Fourier analysis

Definitions

http://en.wikipedia.org/wiki/Fourier_series

From bottom of wikipedia - graphs of converging series

http://mathworld.wolfram.com/FourierSeries.html

Intuitive (image processing oriented)

http://cns-alumni.bu.edu/~slehar/fourier/fourier.html

Table of FFT pairs - Gaussian is of special interest

http://mathworld.wolfram.com/FourierTransform.html

Lecture on image processing (too much)

http://www.archive.org/details/Lectures_on_Image_Processing