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CLUSTER Moments: Error Analysis

This paper discusses error analysis in moments calculations, including theory, practice, and software implementation. Examples and to-do tasks are also provided.

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CLUSTER Moments: Error Analysis

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  1. CLUSTER Moments: Error Analysis O. Marghitu CIS Meeting, Paris September 15-17, 2003

  2. Content • General theory • Practice: Comments on N, J, JE, V, P, T • Error computation • S/W implementation • Examples: N, J, JE • To Do

  3. General Theory

  4. A1) N => scalar A2) J, JE => vectors 3 components & absolute value Depend on the reference system: INST (instrument system) GSE B-aligned Practice: N, J, JE, V, P, T A3) P => 2-rank symmetric tensor • 6 components • To compute P one also needs N and J: • Depends on the reference system: • INST • DIAG (P matrix diagonal) • B-aligned A. Primary quantities, obtained by summation: B. Derived quantities: B1) V = J / N B2) T = P / N Complexity of error computation: A1A2B1A3B2

  5. Error computation: N, J, JE

  6. Error computation: V, P, T

  7. S/W Implementation • PLOT_3DMOM_FROM_CRIB, /ERR_S, ... in COD_3DMOM_CRIB • Modified CCAT routines: N_3D_CIS PLOT_3DMOM_FROM_CRIB J_3D_CIS CODIF_MOMENTS JE_3D_CIS COMBINE_3DMOMENTS P_3D_CIS (TBD) CIS_COORD_TRANS

  8. Examples: N & J

  9. Examples: JE

  10. To Do • Error in V - S/W implementation • B-aligned reference system • Error in P and T - S/W implementation • Finite (DE, DW) error

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