Jan Mandel/Blog/2013 Jan Mar

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Contents

January 1: Revising the KS4DVAR paper

January 7: Running on Janus cluster

  • To build the fire code on Janus: Before doing anything,
ssh janus-compile4
source /projects/jmandel/intel.rc
  • Configure for the intel compiler. This is the only one on Janus that can build the full code (including WRF-Chem) with MPI. The user documentation is now quite good and you can find it at https://www.rc.colorado.edu/crcdocs/start
  • Build your codes in the /projects file system. Run large problems in the /lustre file system. I suggest the janus-short or janus-small queue unless there is a reason otherwise.
  • Allocation is needed to submit jobs. Check if you were added by
use Crc-allocations
check_allocation.py
  • To transfer files push them from the outside
rsync -arvzuP your_file_or_directory login.rc.colorado.edu:/projects/your_user_name_on_janus

January 7: LETKF analysis

Formulation

Transformations that preserve exchangeability

  • An important component in our EnKF convergence proof Mandel-2011-CEK doi ucd was that the ensemble is exchangeable. It stands to reason that it should be. Is the ensemble exchangeable for the square root ensemble Kalman filter? If X=[x1,...,xN] exchangeable random elements, what about their linear combinations XT? Such T form an ideal containing all permutation matrices and the matrix of all ones, but is there anything else? The EAKF can be interpreted as AX which is always exchangeable (except for the little trouble when X is rank deficient, not sure what then)
  • Dean-1990-LTP doi ucd, Commenges-2003-TPE doi ucd The only constant matrices T with the property "if X is exchangeable then XT is exchangeable" are aI + bE. (I=identity, E=all ones)
  • But of M(x1,...,xN)=(y1,...,yN) is permutation invariant mapping that is PM(X)=M(PX) then X exchangeable implies P(X) exchangeable
  • When is the mapping X to XT(X) permutation invariant? Compare with partial orthogonalization in Mandel-1990-TDD. Linear combinations of a collection of functions into orthogonal in a permutation-invariant is essentially the same as combining ensemble to get identity covariance. Then generalize to prescribed covariance. In either case the key to permutation invariance is using matrix square roots not Cholesky.

January 7-10: AMS 93rd Annual Meeting

Our papers

Other sessions and talks of interest

Monday January 7

Tuesday January 8

Wednesday January 9

17th Conference on Integrated Observing and Assimilation Systems for the Atmosphere, Oceans, and Land Surface (IOAS-AOLS)

Thursday January 10

Joint Math Meeting

January 9: Proofs of GMD FireFlux paper

January 11: Proofs of Adaptive-multilevel BDDC paper

January 15: Intel MIC

January 18: GMD paper published in Discussions

January 22: Adaptive multilevel paper published online in Computing

February 2: EnKS-4DVAR

  • revised the paper, added formulation of algorithms - was too brief, deceptively simple with things missing
  • current draft paper and files

February 17-22: Hybrid 4DVAR and nonlinear EnKS method without tangents and adjoints

February 23: Google Docs

February 27: Numerical wildfires

March 1: NIH project report

March 2: SIAM Front Range Student Conference

March 3: Curvelets

  • From curvelet.org: The Curvelet transform is a higher dimensional generalization of the Wavelet transform designed to represent images at different scales and different angles. Curvelets enjoy two unique mathematical properties, namely:
    • Curved singularities can be well approximated with very few coefficients and in a non-adaptive manner - hence the name "curvelets."
    • Curvelets remain coherent waveforms under the action of the wave equation in a smooth medium.
  • Wikipedia: Curvelet
  • What is a curvelet?

March 5: Data assimilation seminar: White noise on Hilbert space

March 7: CAS project

March 21: Stochastic expansions

March 21: Moisture data assimilation

March 24: Balancing teaching and research

March 25: Graduate student support

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