A few last-minute things…. Rossby wave breaking

A few last-minute things…

Rossby wave breaking...

http://www.atmos.washington.edu/cgi-bin/wxloop.cgi?/home/user_www/hakim/tropo/330/+all

EOF analyses, eigenvectors etc.

•Eigenvectors & eigenvalues arise as solutions to physical problems

•For an operator A, an eigenfunction (f) satisifies: A f = f ,

where is the corresponding eigenvalue.

•Example:

•Eigenfunctions in this case are sines and cosines, and we write the general solution as a sum of these, multiplied by weights.

2 22 2

2 20,

d dm or m

dz dz

EOF analyses, eigenvectors etc.

•Consider the 500 mb height field.

•Take (500) at a certain latitude and time.

•We can project this onto sines and cosines in longitude.

•The process works since sine and cosine functions are orthogonal to each other.

•We can take this idea into 2D if we know the proper basis functions.

•For the sphere, the basis functions are a product of sines or cosines in x (longitude) and Hough functions in y (latitude).

•A Hough function is an infinite sum of Associated Legendre polynomials.

EOF analyses, eigenvectors etc.

•Suppose we don’t know what the basis functions are.

•OR suppose we only care about the underlying patterns that account for variance (in time) of a field.

•For example, consider the NH SLP pattern evolving over a winter, say. What is the structure of underlying patterns (if any)?

•EOFs provide this information.

•The EOFs are developed based on the amount of variance in the field they explain (the first EOF explains the most variance, and so forth).

•http://ncas-cms.nerc.ac.uk/content/view/102/123/

EOF analyses, eigenvectors etc.

•The EOFs are orthogonal (good).

•It is possible to find “rotated” EOFs which:

•Are no longer orthogonal

•Better explain the variance pattern

•Example: Wallace & Gutzler

•Example:

Reanalysis...

•We have seen about a million references now to “reanalysis data” – what is this?

•Quoting from the original BAMS 1996 reanalysis paper:

Reanalysis...

•Why?

Reanalysis...

•How?

Reanalysis...

•How?

Reanalysis...

•How?

Reanalysis...

•How?

Reanalysis...

•Input data…

•Global rawinsonde data

•COADS surface marine data

•Aircraft data

•Surface land synoptic data

•Satellite sounder data

•SSM/I surface wind speeds

•Satellite cloud drift winds

Reanalysis...

•What is Assimilation

•A process of assimilating all data into one, accurate, gridded analysis.

•Using a model! The same model as is used for forecasting.

•Source data will be from non-gridded locations and may be sparse (e.g., radiosonde data).

•Source data is also assimilated in time (4D), e.g., surface obs versus satellite data.

•http://en.wikipedia.org/wiki/Data_assimilation

•http://www.metoffice.gov.uk/research/nwp/analysis/

•http://web.unbc.ca/~ytang/assimilation.html