Conservation and boundary fluxes in CAM

Transcription

1 Conservation and boundary fluxes in CAM Thomas Toniazzo Uni Research Climate Bjerknes Centre for Climate Research Bergen, Norway AMWRG meeting NCAR, 18 February 2015

2 Part I Energy

3 Ensuring energy conservation We need to enforce this equation:

4 Ensuring energy conservation We enforce this equation: dynamics

5 Ensuring energy conservation We enforce this equation: dynamics physics

6 Ensuring energy conservation We enforce this equation: adjustment dynamics physics

7 Ensuring energy conservation We enforce this equation: adjustment dynamics physics CAM-FV's energy formulation error Williamson et al. 2015, submitted to J.Clim. This talk

8 Ensuring energy conservation We enforce this equation: adjustment Implied conservation law: dynamics physics

9 change in total energy lid work enthalpy flux divergence surface fluxes diabatic sources material change

10 change in total energy lid work dynamics enthalpy flux divergence surface fluxes diabatic sources material change

11 change in total energy lid work dynamics enthalpy flux divergence surface fluxes physics diabatic sources material change

12 change in total energy lid work dynamics enthalpy flux divergence surface fluxes physics diabatic sources hydrost. adjustment material change

13 global energy budget dynamics enthalpy flux divergence surface fluxes physics diabatic sources hydrost. adjustment material change

14 global energy budget dynamics enthalpy flux divergence surface fluxes physics diabatic sources material change

15 Interim summary: Energy conservation requires that pressure work from hydrostatic adjustment associated with material sources and sinks be matched by fluxes of heat corresponding to the total enthalpy held by the exchanged material The rest is details...

16 Details 1 CAM's energy update problem

17 (lagrangian) dynamics phys. par. 1 q,t update 1 phys. par. 2 (eulerian eta) q,t update 2... q,t update N adjustment of p, T Inluding surface fluxes (coupling) Timestepping in CAM: conceptual outline

18 (lagrangian) dynamics phys. par. 1 wrong T updt 1 phys. par. 2 (eulerian eta) wrong T updt 2... wrong T updt N Timestepping in CAM: ugly reality (old)

19 (lagrangian) dynamics phys. par. 1 wrong T updt 1 phys. par. 2 (eulerian eta) wrong T updt 2... wrong T updt N

20 (lagrangian) dynamics phys. par. 1 wrong T updt 1 phys. par. 2 (eulerian eta) wrong T updt 2... wrong T updt N Cumlated T-tendency

21 (lagrangian) dynamics phys. par. 1 wrong T updt 1 phys. par. 2 (eulerian eta) wrong T updt 2... wrong T updt N KLUDGE Cumlated T-tendency

22 (lagrangian) dynamics phys. par. 1 wrong T updt 1 phys. par. 2 (eulerian eta) wrong T updt 2... wrong T updt N KLUDGE adjustment of p no adjustment of T Cumlated T-tendency

23 (lagrangian) dynamics Cure step 1 phys. par. 1 wrong T updt 1 phys. par. 2 (eulerian eta) wrong T updt 2... wrong T updt N KLUDGE adjustment of p no adjustment of T Cumlated T-tendency Correct the update

24 (lagrangian) dynamics Cure step 2 phys. par. 1 q,t update 1 phys. par. 2 (eulerian eta) q,t update 2... q,t update N KLUDGE adjustment of p no adjustment of T Cumlated T-tendency Remove old fixes

25 DLW et al., presentation at AMWG February 2014 TEMPERATURE (K) 10 YEAR ANNUAL AVERAGE CORRECT ENERGY minus ERA40 CAM5.2 minus ERA40

26 DLW et al., presentation at AMWG February 2014 TEMPERATURE (K) 10 YEAR ANNUAL AVERAGE CORRECT ENERGY minus ERA40 CAM5.2 minus ERA40 This was mainly due to an incorrect adjustment

27 DLW et al., presentation at AMWG February 2014 TEMPERATURE (K) 10 YEAR ANNUAL AVERAGE CORRECT ENERGY minus ERA40 CAM5.2 minus ERA40 This was mainly due to an incorrect adjustment (which preserved energy!)

28 Details 2 CAM's erroneous formulation of energy conservation

29 (lagrangian) dynamics Cure step 3 phys. par. 1 q,t update 1 phys. par. 2 (eulerian eta) q,t update 2... q,t update N adjustment of p no adjustment of T Adjustment must also be corrected

30 CAM's hydrostatic mass fixer (dme_adjust) Physics updates layer q and T but NOT layer-interface pressure. (-δq) pk+1 So if e.g. precipitation is formed... then water is removed... pk δq but hydrostatic pressure is not changed... pk-1 which implies that dry mass is added to compensate.

31 CAM's hydrostatic mass fixer (dme_adjust) The dry mass and the hydrostatic pressure both need to be adjusted to ensure conservation of dry air. In all version of CAM, this is done in physics_dme_adjust... pk+1 pk pk-1 p'k+1 p'k p'k-1

32 CAM's hydrostatic mass fixer (dme_adjust) The dry mass and the hydrostatic pressure both need to be adjusted to ensure conservation of dry air. In all version of CAM, this is done in physics_dme_adjust... pk+1 pk pk-1 p'k+1 p'k p'k-1 then T is adjusted to conserve total column energy

33 Work associated with hydrostatic mass adjustment First law of Thermodynamics: d dp = dt dt where ε is the specific internal enthalpy and α the specific volume. pk+1 p'k+1 pk p'k pk-1 p'k-1 Physics parametrisations should keep correct energy budgets. But they don't. So this needs to be done in dme_adjust.

34 TEMPERATURE (K) 10 YEAR ANNUAL AVERAGE CORRECT ENERGY minus ERA40 (a) Pres.adj.(Ф) ERA/I: T CAM5.2 minus ERA40 (b) Original CAM4 ERA/I: T

35 TEMPERATURE (K) 10 YEAR ANNUAL AVERAGE CORRECT ENERGY minus ERA40 CAM5.2 minus ERA40 Consistent adjustment saves model climatology (a) Pres.adj.(Ф) ERA/I: T (b) Original CAM4 ERA/I: T (c) α(δp) ERA/I: T

36 TEMPERATURE (K) 10 YEAR ANNUAL AVERAGE CORRECT ENERGY minus ERA40 (a) Pres.adj.(Ф) ERA/I: T t u B o m n l de on l o CAM5.2 minus ERA40 p p a r a e o c o t s (b) Original CAM4 ERA/I: T r e g e n e l a t Consistent o t adjustment e v r saves model e ns climatology (c) α(δp) ERA/I: T! y rg

37 Details 3 How to fix it

38 global energy budget enthalpy flux divergence surface fluxes physics material change

39 CAM's energy budget enthalpy flux divergence surface fluxes physics mass change this term ignored

40 CAM's energy budget enthalpy flux divergence surface fluxes physics + energy fixer residual, applied uniformly everywhere

41 CAM's energy budget revised [...] mass change

42 CAM's energy budget revised [...] hq mass source with specific enthalpy hq hm h q heat transfer between atmosphere and mass source

43 CAM's energy budget revised hm h q /c p, air Air temperature increment associated with heat transfer between atmosphere and mass source hq Additional boundary heat flux, output diagnostics EFLX Now implemented in physics_dme_adjust atmospheric energy budget closed only if considering EFLX global heat budget closed only if EFLX passed to other ES components

44 hq It should be the job of each specific physics submodel/parametrisation to determine. E.g., how much of its enthalpy does a raindrop retain? all (hq=hm) terminal velocity + thermal other

45 hq It should be the job of each specific physics submodel/parametrisation to determine. E.g., how much of its enthalpy does a raindrop retain? V all ( terminal velocity ~ 300m/s!) terminal velocity + thermal other

46 hq It should be the job of each specific physics submodel/parametrisation to determine. E.g., how much of its enthalpy does a raindrop retain? V all ( terminal velocity ~ 300m/s!) terminal velocity + thermal V other, e.g. ocean and land models assume T q=t surf hq=c p, water T surf

47 Details 4 Implications for surface fluxes

48 Preliminary note on Details 4 All net mass sources and sinks reside at the surface. Therefore the net atmospheric column energy imbalance associated with mass changes must be closed by surface heat fluxes.

49 Surface heat fluxes EC

50 Surface heat fluxes EC ~0.3 W/m² global avg

51 Surface heat fluxes ECx No surface imbalance

52 Details 5 Impacts on simulation results

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59 Summary: energy Correction of energy errors in CAM involves 3 changes: 1. Temperature updating (physics_update) 2. Hydrostatic pressure work of layer mass changes (dme_adjust) 3. Enthalpy fluxes associated with mass and evt heat transfers (eodem) Need to account for boundary fluxes of enthalpy associated with mass exchanges (new diagnostics EFLX) Implementations given for two no-physics assumptions 1. adiabatic 2. mass-less h q=hm h q=c p,water T surf (AMIP) (coupled) Impact on atmosph. mean thermal structure small in AMIP runs Impact on air-sea fluxes and diabatic tendencies NOT negligible Together with COARE boundary flux computation, significant improvements in AMIP and coupled climatologies (NorESM)

60 Conclusions Mass and energy conservation in CAM not exact Code revision necessary to enforce energy conservation Impact on surface fluxes stronger than on mean state in AMIP simulations