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Leo Separovic, Ramon de Elia and Rene Laprise

First results and methodological approach to parameter perturbations in GEM-LAM simulations PART I. Leo Separovic, Ramon de Elia and Rene Laprise. MOTIVATION. Sub-grid parameterization schemes are source of “ parametric uncertainty”:

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Leo Separovic, Ramon de Elia and Rene Laprise

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  1. First results and methodological approach to parameter perturbations in GEM-LAM simulationsPART I Leo Separovic, Ramon de Elia and Rene Laprise

  2. MOTIVATION • Sub-grid parameterization schemes are source of “parametric uncertainty”: - well-known processes that can be exactly represented (e.g. radiation transfer) but need to be approximated so that they do not take excessive computational time; - less-well understood processes (e.g. turbulent energy transfer) that are situation dependent; parameters rely on mixture of theoretical understanding and empirical fitting; - measurable parameters - measurement error, - non-measurable parameters uncertainty associated with representativity. • Tuning can eliminate only reduciblecomponent of the model error. • Parametric uncertainty can be (at least theoretically) quantified by perturbing parameters and measuring the impact on model output.

  3. CONTENTS • Detection of the model response to perturbations of parameters in a large domain - noise: brief analysis of internal variability - signal: sensitivity of seasonal climate to selected perturbations of a trigger parameter of KF convection - statistical significance (signal-to-noise ratio) - trade-off between statistical significance and computational cost • Detections of model response in a small domain - effects of reduction of domain size on magnitude of the signal and noise • Future work - intermediate domain size, next parameter, multiple parameter perturbations

  4. EXPERIMENTAL CONFIGURATION • GEM-LAM 140x140 • DX=0.5 deg (max 55.5 km at JREF=65), NLEV=52

  5. EXPERIMENTAL CONFIGURATION • Five start dates:November 1-5 1992 00GMT • End date: November 30 1993 00GMT 4 seasons DEC01-NOV30 • Time step: 30 min • Nesting data: ERA 40 • PTOPO: npex=4 npey=4 • Estimated time:12hrs/year • Output frequency:once per 6 hours

  6. Physics package Version: RPN-CMC4.5 • RADIA: CCCMARAD • SCHMSOL: ISBA • GWDRAG: GWD86 • LONGMEL: BOUJO • FLUVERT: CLEF • SHLCVT: CONRES, KTRSNT_MG • CONVEC: KFC • KFCPCP: CONSPCPN • STCOND: CONSUN • Stomate: .false. • Typsol: .true. • Snowmelt: .false.

  7. Trigger vertical velocity in KFC scheme • The KFCTRIG values that are deemed to be appropriate at the limits of the resolution interval in which the KFC scheme is to be used (B. Dugas, 2005): KFCTRIG (170 km) = 0.01 KFCTRIG (10 km) = 0.17 • It is assumed that: KFCTRIG (RES) * RES = 1.7 = C (#) • KFCTRIG is a function of the grid-tile area: KFCTRIG = KFCTRIG0 * RES0 / sqrt (DXDY) • At the nominal resolution of 50km (#) gives KFCTRIG=0.034 (REFERENCE) • We performed 2 perturbations (ONE PER TIME): KFCTRIG1=0.020 and KFCTRIG2=0.048 These values would be deemed appropriate at resolution of 85km and 35km.

  8. THREE ENSEMBLES • WKLCL =0.034 (REFERENCE) 5 members • WKLCL=0.029 (-) single 5 members • WKLCL=0.048 (+) single 5 members

  9. Internal variability in the reference 5-member ensembleTA-ESTD-PCP

  10. Internal variability in the reference 5-member ensembleTA-ESTD-PCP normalized

  11. ESTD-TA-PCP

  12. (ESTD-TA-PCP)/(EA-TA-PCP)

  13. ESTD-TA-Tscn

  14. Detection of the model response to parameter perturbations • Signal: difference between the ensemble averages of - reference ensemble XR: nR=5 members - perturbed-parameter ensemble XP:nP= members • Error: sample STD of the ensemble averages: E2(XR)/nRand E2(XP)/nP. • If the true variances of XR and XP are equal then the quantity follows the Student’s distribution with (nR+nP-2) degrees of freedom. • Null hypothesis: The two means are computed from two samples drawn from a unique distribution.

  15. PCP KFCTRIG=0.020 (-)

  16. PCP – level of rejection

  17. Signal (TTscn)

  18. TTscn: rejection level

  19. Trade-off between number of parameter perturbations and significance signal • We need to find a trade-off between P and t • Let’s relate the two ensemble sizes: then Significance t Internal variability σ Computational resources $ No of parameter perturbations P and • One should invest in nR because of its low cost but not more than b=5 (diminishing returns) • np=1 & b>>0 minimizes the cost but also minimizes the signal-to-noise ratio

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