Understanding the local and global impacts of model physics changes

Transcription

1 ECMWF Annual Seminar 2008 MJR 1 Understanding the local and global impacts of model physics changes Mark Rodwell Work with Thomas Jung 4 September 2008 Thanks to:

2 MJR 2 Motivation The real world and GCMs are complex systems Can use hierarchy of simpler models to understand processes and develop parametrizations. But The fully complex system may behave differently. For example due to interactions. It is the fully complex system that is used to produce the forecast! Hence There is a need to develop diagnostics that help us understand the physics, dynamics and interactions within the fully complex system.

3 MJR 3 Talk Outline Annual cycle of the global circulation Systematic errors in seasonal integrations Introduction to the case study: aerosol change Statistically significant global changes Understanding the local physics Analysis Increments and Initial Tendencies Perturbed physics example: reducing climate change uncertainty Understanding the tropic-wide response Tropical waves Coupling with convection Understanding the extra-tropical response The tropical control of the divergent wind Balances in the vorticity equation Extra-tropical physics and PV Pedagogical! See Rodwell & Jung (2008)

4 MJR 4 Annual Cycle of the Global Circulation

5 MJR 5 Mean Annual Cycle: Precipitation, V 925 & Z 500 INTER-TROPICAL CONVERGENCE ZONE MONSOONS SEASONAL CYCLE OF RAINS CONVECTIVE HEATING SUBTROPICAL ANTICYCLONES DUALITY WITH MONSOON HEATING RADIATIVELY IMPORTANT STRATOCUMULUS DEEP CONVECTION (SPCZ ETC) EXTRATROPICAL STORMTRACKS STRONG VORTICITY GRADIENTS SENSITIVITY TO TROPICAL FORCING JJA DJF mm day E m/s Precipitation: Xie-Arkin 1979/ /99 V 925 : ERA Z 500 : ERA , CI=10 dam

6 MJR 6 Old and New Aerosol Optical Thickness OLD (NO ANNUAL CYCLE) NEW (JULY) OPTICAL DEPTH d AT 550nm SOIL DUST IS IMPORTANT SOIL DUST ABSORBS AS WELL AS SCATTERS Old: C26R1 (Tanre et al. 1984), New: C26R3 (Tegen et al. 1997). ATTENUATION FACTOR = e -d SINGLE SCATTERING ALBEDO FOR DESERT AEROSOL 0.9

7 MJR 7 June August Precipitation, v925 and Z500 (a) JJA OBS mm day m/s (b) JJA OLD - OBS 10% sig. mm day -1 5 m/s E E 180 (c) JJA NEW - OLD 10% sig. mm day -1 5 m/s (d) JJA NEW - OBS 10% sig. mm day -1 5 m/s E E 180 Precip: Xie-Arkin V925, Z500: ERA , (a) 10, (b)-(d) 2 dam. 26R3 seasonal data for the same period

8 MJR 8 Understanding the Local Physics

9 MJR 9 DJF T500 Medium-range Mean Forecast Error UNIT=0.1K Unit = D+1 NON-SIG. 5% SIG. 0.9m/s Unit = 0.1K D+2 2.0m/s Unit = 0.1K m/s D+5 D+10 Unit = 0.1K m/s Based on DJF 2006/7 operational analyses and forecasts. Significant values (5% level) in deep colours.

10 MJR 10 Data Assimilation Cycle: Perfect Model T Observations Analysis Mean Analysis Increment = 0 Analysis increment First guess forecast Time (cycles) (Imperfect, unbiased observations)

11 MJR 11 Data Assimilation Cycle: Imperfect Model T Observations Analysis Mean Analysis Increment 0 Analysis increment First guess forecast Time (cycles) Mean Analysis Increment = Mean Net Initial Tendency ( I.T. in, e.g., Kcycle -1 ) = Mean Convective I.T. + Mean Radiative I.T. + + Mean Dynamical I.T. (summed over all processes in the model)

12 MJR 12 MAM Mean Analysis Increments: T and (v,w) Unit=0.01K T799L91 0.5m/s McICA and changes to SW rad, linear cloud & conv, ice particle size. (Also apparent JJA 2007, before 32R3) O N 60 O N 40 O N 20 O N 0 O 20 O S 40 O S 60 O S 80 O S 80 O N 60 O N 40 O N 20 O N 0 O 20 O S 40 O S 60 O S 80 O S

13 MJR 13 MAM Mean Forecast Error D+5: T and (v,w) Unit = 0.1K Unit = 0.1K m/s O N 60 O N 40 O N 20 O N 0 O 20 O S 40 O S 60 O S 80 O S 80 O N 60 O N 40 O N 20 O N 0 O 20 O S 40 O S 60 O S 80 O S

14 UNIT=0.01K Unit 0.01K m/s Diagnostics MJR 14 Confronting models with observations T500 Analysis Increment UNIT=0.01K See Rodwell & Jung, ECMWF Newsletter Autumn 2008 Observed First Guess Brightness Temperature AIRS ch 215 (~T500) DJF 2007/8

15 MJR 15 Amazon Initial Process Tendencies Approx. Pressure (hpa) CONTROL PERFECT MODEL (ALMOST!) Kday -1 (K for bias) ENTRAIN/5 REDUCED ENTRAINMENT IMPERFECT MODEL Kday -1 (K for bias) Dyn Rad V.Dif Con LSP Tot Net Bias (D+5) PROCESS TENDENCIES BALANCE WELL LEADING TO A SMALL NET TENDENCY IMBALANCE LEADS TO LARGE NET TENDENCIES INDICATIVE OF PHYSICS ERROR Amazon = [300 o E-320 o E, 20 o S-0 o N]. Mean of 31 days X 4 forecasts per day X 12 timesteps per forecast (January 2005). 70% confidence intervals are based on daily means. CONTROL model = 29R1,T159,L60,1800S.

16 MJR 16 JJA Precipitation, v925 and Z500. New-Old mm day % Sig. 5 m/s E 180

17 MJR 17 North Africa Jul 2004 T Tendencies (New-Old) New-Old e INITIAL D Kday -1 Kday -1 f Pressure (hpa) Dyn Rad V.Dif Con LSP Tot RADIATIATION CHANGES DESTABILISE PROFILE AND LEAD TO MORE CONVECTION BUT ULTIMATELY LEAD TO MORE DESCENT AND LESS OVERALL PRECIPITATION North Africa = [5 o N-15 o N, 20 o W-40 o E]. Mean of 31 days X 4 forecasts per day X 12 timesteps per forecast. 70% confidence intervals are based on daily means. CONTROL model = 29R1,T159,L60,1800S.

18 MJR 18 Local Response to Aerosol Reduction CONVECTION (FAST RESPONSE) RADIATION LESS ABSORPTION DYNAMICS (SLOW RESPONSE) IMPORTANCE OF SEMI-DIRECT EFFECT(?) DRYING

19 MJR 19 Understanding the Tropic-wide Response

20 MJR 20 Tropical Waves: Outgoing Long-wave Radiation 5 o S-5 o N 7.5 o S-17.5 o N 30 W 28 M 26 S 70 AUG AUG 24 T 22 T 20 S F8 W6 M4 S T0 T8 S F4 W2 31 M 29 S 27 T 25 T 23 S TIME JUL JUN MADDEN-JULIAN OSCILLATION: EASTWARD PROPAGATING, DAY ( 10ms -1 ) MJO JUL JUN 21 F W9 M7 S5 T3 T1 S9 F7 W5 M3 S1 29 T 27 T 25 S 23 F 21 W M9 S7 T5 T3 S1 F9 WESTWARD PROPAGATING WAVES Wm o W 0 o 100 o E 150 O W 100 O W 50 O W 0 O 50 O E 100 O E 150 O E LONGITUDE W7 M5 S3 T1 100 o W 0 o 100 o E Plots from Thomas Jung. OLR data from NOAA -70

21 MJR 21 Shallow Water Equations on the β-plane (Here, for understanding tropical atmospheric waves) Baroclinic mode: βyv ε η u u u 1 2 v v v 1 2 ε («H 2 ) LAYER 2 v 2 Momentum: H 2 ρ 2 u 2 u t η β yv + g x 0 η («H 1 ) v t η + β yu + g y 0 HH c g gh c 20 to 80ms c H 1 ρ g g ρ e e e H1+ H2 e y x 2 1 "reduced gravity" LAYER 1 ρ 1 is the propagation speed of a barotropic gravity wave in single layer of depth H e v 1 u 1 Continuity: 1 1 η u v H1 H2 t x y Solving for v: v v v v t t x y x β yv c 0 2 e + c 2 2 eβ =

22 MJR 22 Free Equatorial Waves V=0: V 0: 2 y 2 ik( x cet ) = East propagating Kelvin Wave u u e e 0 v = vˆ( y) e i kx t ( ω ) Non-dispersive In geostrophic balance Substitute into equation for v Structures (Meridional structures are solutions to Schrodinger s simple harmonic oscillator) 1 2y 2 4y 1 vy ˆ( ) = 3 8y 12y Hn ( y) e y 2 2 Hermite Polynomials: H ( ) n y Each successive polynomial has one more node Modes alternate asymmetric / symmetric about equator Dispersion (How phase speed is related to spatial scale) k 2 = ( 2n+ 1) ce ω ce ( n = 0,1,2,...) 2 ω 2 βk β For n 0: 3 values of ω for each k West propagating Rossby Wave E & W propagating Gravity Wave For n=0: 2 values of ω for each k E & W prop. Mixed Rossby-Gravity y has been non-dimensionalised by the factor ( β ) 1/ 2 /c e

23 MJR 23 Wave Spotting Colours show height perturbation (red positive, blue negative), arrows show lower-level winds

24 MJR 24 Interpretation of Free Equatorial Waves 5 Dispersion Diagram 4 Gravity C ω = - β/2k C ω(βc e ) -1/2 3 2 SUGGESTS METHOD OF COMPARISON BETWEEN OBSERVATIONS AND MODEL n=1 n=2 n=3 Kelvin n=-1 φ (c=c e tanφ) 1 Rossby Mixed n=0 C=ω/k (phase speed) C g =dω/dk (group velocity) 0 r 2 =1 r 2 =3 r 2 = k(c /β) 1/2 e

25 MJR 25 Symmetric waves. Observed OLR (NOAA) 5 Waves with v Symmetric about the Equator 4 Gravity C ω = - β/2k C ω(βc e ) -1/2 3 2 n=1 n=3 Kelvin n=-1 1 Rossby Wave Power c 20ms -1 φ (c=c e tanφ) C=ω/k (phase speed) C g =dω/dk (group velocity) r 0 2 = k(c /β) 1/2 AGREEMENT WITH THEORY IF OLR IS A e STRONG CONVECTIVE COUPLING FOR SLAVE TO THE FREE WAVES, LINEARITY ETC. MJO AS IT DOESN T LIE ON ANY LINE(?) DJF Following Wheeler and Kiladis (1999). Convective coupling generally reduces phase speed

26 MJR 26 Symmetric waves. Simulated OLR (ECMWF) 5 Waves with v Symmetric about the Equator 4 Gravity C ω = - β/2k C ω(βc e ) -1/2 3 2 n=1 n=3 Kelvin n=-1 Wave Power φ (c=c e tanφ) 1 Rossby C=ω/k (phase speed) C g =dω/dk (group velocity) r 0 2 = k(c /β) 1/2 e TOO MUCH POWER GENERALLY AT LOW FREQUENCIES Model cycle: 32R3, resolution: T159L91, DJF

27 MJR 27 Asymmetric waves. Observed OLR (NOAA) 5 Waves with v Asymmetric about the Equator 4 Gravity C ω = - β/2k C 3 ω(βc e ) -1/2 2 n=2 Wave Power φ (c=c e tanφ) 1 Rossby Mixed n=0 C=ω/k (phase speed) C g =dω/dk (group velocity) r 0 =1 r 2 = MIXED ROSSBY-GRAVITY k(c /β) 1/2 e ALIASING DUE TO SAMPLING BY OBSERVATIONS DJF

28 MJR 28 Asymmetric waves. Simulated OLR (ECMWF) 5 Waves with v Asymmetric about the Equator 4 Gravity C ω = - β/2k C 3 ω(βc e ) -1/2 2 n=2 Wave Power φ (c=c e tanφ) 1 Rossby Mixed n=0 C=ω/k (phase speed) C g =dω/dk (group velocity) r 0 2 =1 r 2 = k(c /β) 1/2 e MIXED ROSSBY-GRAVITY NOT AS EVIDENT AS IN THE OBSERVATIONS Model cycle: 32R3, resolution: T159L91, DJF

29 MJR 29 Gill s steady solution to monsoon heating DAMPING/HEATING TERMS TAKE THE PLACE OF THE TIME DERIVATIVES EXPLICITLY SOLVE FOR THE X-DEPENDENCE GOOD AGREEMENT WITH THE AEROSOL CHANGE RESULTS (OPPOSITE SIGN): NORTH ATLANTIC SUBTROPICAL ANTICYCLONE CONVECTIVE COUPLING IN KELVIN WAVE REGIME Colours show perturbation pressure, vectors show velocity field for lower level, contours show vertical motion (blue = -0.1, red = 0.0,0.3,0.6, ) Following Gill (1980). See also Matsuno (1966)

30 MJR 30 JJA Precipitation, v925 and Z500. New-Old mm day % Sig. 5 m/s E 180

31 MJR 31 Understanding the Extra-tropical Response

32 MJR 32 Upper Troposphere Divergent Wind Anomaly 1.0m/s New minus Old aerosol. Anomaly is integrated between 100 and 300 hpa

33 MJR 33 The Vorticity Equation Motivation (2D flow) : ζ z v u = x y ( kˆ ) z v kˆ is the unit vertical vector and is the horizontal curl operator z z v y x u δ x δ y ζ z u + δ u v + δ v Curl of the 3D momentum equation in absolute frame of reference: d ζ dt ( ) ( ) 12 = ζ u + ζ u + ρ p + F Lagrangian Divergence Tilting Baroclinic Friction tendency in absolute p vorticity ρ ρ NEGLECT THESE TERMS u

34 MJR 34 Barotropic Vorticity Equation Making the shallow atmosphere approximations and assuming barotropic, frictionless, horizontal flow ζ t + v ζ = ψ ( v χζ ) = ζ v v ζ χ χ "Rossby W ave Source" Application to simple models: Sardeshmukh and Hoskins (1988). For use in complex GCMs, it is found here to be useful to vertically integrate this equation between 100 and 300 hpa. Is the extra-tropical mean response a linear stationary-wave solution? v ζ + v ζ ζ v v ζ ψ ψ χ χ (?)

35 MJR 35 JJA Balance in Vorticity Equation New-Old Rossby Wave Source ζ + Near linear balance for stationary response. Note that the stationary wavelength is longer in the SH where jet is stronger s -2 + Sig. 10% Non sig. (c) Advection Rotational Advection by (Anomalous Rotational wind) Wind Advection of Anomalous Vorticity (d) Rotational Advection (Anomalous vorticity) Upstream Propagation Downstream Advection

36 MJR 36 JJA New-Old RWS, v χ,ψ and mean ζ s -2 Unit: 1e-11 s m/s Rossby wave paths agree beautifully with those predicted by Hoskins and Ambrizzi (1995)

37 MJR 37 JJA Precipitation, v925 and Z500. New-Old mm day % Sig. 5 m/s E 180

38 MJR 38 The December February Season

39 MJR 39 DJF Precipitation, v925 and Z500 (a) DJF OBS mm day m/s (b) DJF OLD - OBS 10% sig. mm day -1 5 m/s E E 180 (c) DJF NEW - OLD 10% sig. mm day -1 5 m/s (d) DJF NEW - OBS 10% sig. mm day -1 5 m/s E E 180 Precip: Xie-Arkin V925, Z500: ERA , (a) 10, (b)-(d) 2 dam. 26R3 seasonal data for the same period

40 MJR 40 DJF New-Old RWS, v χ,ψ and mean ζ Unit: e-11 ss m/s Precipitation / RWS agreement suggests possibility for interaction with extra-tropical physics Rossby wave path agrees with that predicted by Hoskins and Ambrizzi (1993)

41 MJR 41 Summary Physics changes have global implications! Statistical tests can reveal which aspects are attributable to a change To understand why, a set of diagnostic tools is needed Analysis Increments and Initial Tendencies Useful to help understand local physics changes (and subsequent interactions) Different from climate simulations and single column experiments Equatorial waves Help explain the mean tropic-wide response Linear waves can set the scene Coupling with convection enhances the response Extra-tropical Rossby waves Help explain the mean extra-tropical response Understanding is aided by linearity Extra-tropical interaction with physics could be studied with PV approach