1. Diagnostics MJR 1 ECMWF Training Course 2009 – NWP-PR Atmospheric Variability & Error: Tropics Mark Rodwell 18 March 2009

2. Diagnostics 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. Diagnostics 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

4. Diagnostics MJR 4 Annual Cycle of the Global Circulation

5. Diagnostics MJR 5 Historical Perspective MEDIEVAL MAP SHOWING TRADE ROUTES FROM ARABIAN PENINSULA TO INDIA KNOWLEDGE OF METEOROLOGY WAS ESSENTIAL PERSIAN PAINTING (1240 AD) SHOWING DHOW WITH BROKEN MAST AND ROWERS!

6. Diagnostics MJR 6 JJA DJF mm day -1 Precipitation: Xie-Arkin 1979/80 – 1998/99 V 925 : ERA40 1962-01 Z 500 : ERA40 1962-01, CI=10 dam 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

7. Diagnostics MJR 7 Old and New Aerosol Optical Thickness Old: C26R1 (Tanre et al. 1984), New: C26R3 (Tegen et al. 1997). SOIL DUST IS IMPORTANT SOIL DUST ABSORBS AS WELL AS SCATTERS NEW (JULY) OLD (NO ANNUAL CYCLE) OPTICAL DEPTH d AT 550nm ATTENUATION FACTOR = e -d SINGLE SCATTERING ALBEDO FOR DESERT AEROSOL 0.9

8. Diagnostics MJR 8 June – August Precipitation, v925 and Z500 Precip: Xie-Arkin 1980–1999. V925, Z500: ERA40 1962-01, (a) 10, (b)-(d) 2 dam. 26R3 seasonal data for the same period mm day -1 10% sig.

9. Diagnostics MJR 9 Local Physics

10. Diagnostics MJR 10 T500 Forecast Error as function of lead-time D+1 D+5 D+2 Based on DJF 2007/8 operational analyses and forecasts. Significant values (5% level) in deep colours. x0.01K x0.1K D+10

11. Diagnostics MJR 11 Data Assimilation Cycle: Perfect Model (Imperfect, unbiased observations) Mean Analysis Increment = 0

12. Diagnostics MJR 12 Data Assimilation Cycle: Imperfect Model Mean Analysis Increment 0 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)

13. Diagnostics MJR 13 AIRS CH 215 OBS-FG T500 ANALYSIS INCREMENTD+1 T500 FORECAST ERROR Confronting models with observations OBSERVED – FIRST GUESS BRIGHTNESS TEMPERATURE AIRS CH 215 (~T500) UNIT=0.01K Based on DJF 2007/8 operational analyses and forecasts. Significant values (5% level) in deep colours.

14. Diagnostics MJR 14 Parameter Uncertainties in Climate Sensitivity ParameterPhysicsLowMiddleHigh Droplet to rain conversion rate (s -1 )Cloud0.5x10 -4 1.0x10 -4 4.0x10 -4 Relative humidity for cloud formationCloud0.60.70.9 Cloud fraction at saturation (free trop.)Cloud0.50.70.8 Entrainment rate coefficientConvection0.63.09.0 Time-scale for destruction of CAPE (h)Convection1.02.04.0 Effective radius of ice particles (μm)Radiation253040 Diffusion e-folding time (h)Dynamics61224 Roughness length parameter (Charnock)Boundary0.0120.0160.02 Stomatal conductance dependent on CO 2 LandOff-On Ocean-to-ice heat transfer (m -2 s -1 )Sea Ice2.5x10 -5 1.0x10 -4 3.8x10 -4 Representative selection of parameters and uncertainties used by Murphy et al., 2004: Nature, 430, 768-772. MANY UNCERTAINTIES ARE ASSOCIATED WITH FAST PHYSICS. … WHICH IS ALSO IMPORTANT IN NWP

15. Diagnostics MJR 15 Amazon January 2005 Initial T Tendencies 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. 70% confidence intervals are based on daily means. CONTROL model = 29R1,T159,L60,1800S. Reduced Entrainment model is out of balance: reject or down-weight? IMPERFECT MODELPERFECT MODEL (ALMOST!)

16. Diagnostics MJR 16 JJA Precipitation, v925 and Z500. New-Old mm day -1. 10% Sig.

17. Diagnostics MJR 17 North Africa Jul 2004 T Tendencies (New-Old) 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. RADIATIATION CHANGES DESTABILISE PROFILE AND LEAD TO MORE CONVECTION … …BUT ULTIMATELY LEAD TO MORE DESCENT AND LESS OVERALL PRECIPITATION

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

19. Diagnostics MJR 19 Tropical Waves

20. Diagnostics MJR 20 Tropical Waves: Outgoing Long-wave Radiation 5 o S-5 o N JUN AUG JUL 2006 100 o W0o0o 100 o E MJO MADDEN-JULIAN OSCILLATION: EASTWARD PROPAGATING, 30-60 DAY (10ms -1 ) Data from NOAA Wm -2 WESTWARD PROPAGATING WAVES 7.5 o S-17.5 o N JUN AUG JUL 100 o W0o0o 100 o E TIME LONGITUDE

21. Diagnostics MJR 21 Shallow Water Equations on the β-plane (Here, for understanding tropical atmospheric waves) Note: No coupling with convection in this model Momentum: (1) Continuity: u1u1 u1u1 v1v1 v1v1 (2) Solving for v: (3)

22. Diagnostics MJR 22 V=0: V0: Structures (Meridional structures are solutions to Schrodingers simple harmonic oscillator) Dispersion (How phase speed is related to spatial scale) Free Equatorial Waves East propagating Kelvin Wave Non-dispersive In geostrophic balance 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 Hermite Polynomials: Each successive polynomial has one more node Modes alternate asymmetric / symmetric about equator Substitute into equation for v

23. Diagnostics MJR 23 Interpretation of Free Equatorial Waves Dispersion Diagram SUGGESTS METHOD OF COMPARISON BETWEEN OBSERVATIONS AND MODEL

24. Diagnostics MJR 24 Wave Power OLR DJF 1990-05 NOAA & 32R3 AGREEMENT WITH SHALLOW WATER THEORY IF OLR IS A SLAVE TO THE FREE WAVES, LINEARITY ETC. ROSSBY KELVIN c20ms -1 (a) Observed Symmetric (c) Simulated Symmetric(d) Simulated Asymmetric (b) Observed Asymmetric MIXED ROSSBY MJO CONVECTIVELY COUPLED(?) ALIASING OF 12H OBSERVATIONS TOO MUCH LOW FREQUENCY POWER n=1 n=3 n=2 n=0 n=-1

25. Diagnostics MJR 25 Wave Spotting Colours show height perturbation (red positive, blue negative), arrows show lower-level winds To re-start movie, escape and start slide show again

26. Diagnostics MJR 26 Wave Spotting Answers Colours show height perturbation (red positive, blue negative), arrows show lower-level winds To re-start movie, escape and start slide show again

27. Diagnostics MJR 27 WaveKelvin Mixed Rossby- Gravity Rossby Eastward Gravity Westward Gravity 1 2 3 4 5 6 7 8 9 10 11 12 Wave spotting: Your Answers

28. Diagnostics MJR 28 Gills steady solution to monsoon heating 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,…) 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 Following Gill (1980). See also Matsuno (1966)

29. Diagnostics MJR 29 JJA Precipitation, v925 and Z500. New-Old mm day -1. 10% Sig. The Extratropical Response will be explained in the next lecture!

30. Diagnostics MJR 30 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