Diagnostics

MJR 1ECMWF Training Course 2009 – NWP-PR

Atmospheric Variability & Error: Tropics

Mark Rodwell

18 March 2009

Diagnostics

MJR 2Motivation

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.

Diagnostics

MJR 3Talk 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

Diagnostics

MJR 4Annual Cycle of the Global Circulation

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!

Diagnostics

MJR 6

15 m/s

0° 90°E 180°

(a) JJA OBS

2 4 6 8 10 12 18

5 m/s

0° 90°E 180°

(b) JJA OLD - OBS

-16 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 16

5 m/s

0° 90°E 180°

(c) JJA NEW - OLD

-10 -5 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 5 10

5 m/s

0° 90°E 180°

(d) JJA NEW - OBS

-16 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 16

15 m/s

0° 90°E 180°

(a) DJF OBS

2 4 6 8 10 12 18

5 m/s

0° 90°E 180°

(b) DJF OLD - OBS

-16 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 16

5 m/s

0° 90°E 180°

(c) DJF NEW - OLD

-10 -5 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 5 10

5 m/s

0° 90°E 180°

(d) DJF NEW - OBS

-16 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 16

JJA

DJF

mm day-1

Precipitation: Xie-Arkin 1979/80 – 1998/99V925: ERA40 1962-01Z500: ERA40 1962-01, CI=10 dam

Mean Annual Cycle: Precipitation, V925 & Z500

• 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

Diagnostics

MJR 7Old 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)

OPTICALDEPTH d AT 550nm

ATTENUATION FACTOR = e-d

SINGLE SCATTERING ALBEDO FOR DESERT AEROSOL ≈ 0.9

Diagnostics

MJR 8

15 m/s

0° 90°E 180°

(a) JJA OBS

2 4 6 8 10 12 18

5 m/s

0° 90°E 180°

(b) JJA OLD - OBS

-16 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 16

5 m/s

0° 90°E 180°

(c) JJA NEW - OLD

-10 -5 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 5 10

5 m/s

0° 90°E 180°

(d) JJA NEW - OBS

-16 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 16

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

mm day-1mm day-1

mm day-1 10% sig.

10% sig.10% sig.

Diagnostics

MJR 9Local Physics

Diagnostics

MJR 10(a) D+1 Unit = 0.01K

-55 -25 -15 -5 5 15 25 65 -55 -25 -15 -5 5 15 25 65

Unit = 0.1K

-9 -5 -3 -1 1 3 5 9 -9 -5 -3 -1 1 3 5 9

(b) D+2

(c) D+5 Unit = 0.1K

-21 -5 -3 -1 1 3 5 15 -21 -5 -3 -1 1 3 5 15

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 (d) D+10 Unit = 0.1K

-34 -10 -6 -2 2 6 10 26 -34 -10 -6 -2 2 6 10 26

x0.1K

x0.1K x0.1K

D+10

Diagnostics

MJR 11

Data Assimilation Cycle: Perfect Model

(Imperfect, unbiased observations)

Schematic diagram of data assimilation / forecast cycle (perfect model)

ObservationsAnalysis

Analysis increment

First guess forecast

0 1 2 3 4Time (cycles)

T

Mean Analysis Increment = 0

Diagnostics

MJR 12

Data Assimilation Cycle: Imperfect ModelSchematic diagram of data assimilation / forecast cycle (imperfect model)

ObservationsAnalysis

Analysis increment

First guess forecast

0 1 2 3 4Time (cycles)

T

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)

Diagnostics

MJR 13

Infrared brightness temperature, weighting function: 700 to 300 hPa.AIRS ch 215 (~T500) FG_DEP, 2008_DJF, Expver=1, Analysis=DCDA, Time=[00,12], Smoothed

Unit = 0.01 K

-86 -10 -6 -2 2 6 10 74

AIRS CH 215 OBS-FG

Analysis Increments: Mean T500, 2008 DJF, Expver=oper 1, Analysis=dcda. Deep colours = 5% significance

0.6m/s0.6m/s

Unit = 0.01K

-52 -20 -12 -4 4 12 20 76 -52 -20 -12 -4 4 12 20 76

T500 ANALYSIS INCREMENT

(a) D+1 Unit = 0.01K

-55 -25 -15 -5 5 15 25 65 -55 -25 -15 -5 5 15 25 65

D+1 T500 FORECAST ERROR

Confronting models with observations

OBSERVED – FIRST GUESSBRIGHTNESS TEMPERATUREAIRS CH 215 (~T500)

UNIT=0.01K

Based on DJF 2007/8 operational analyses and forecasts. Significant values (5% level) in deep colours.

Diagnostics

MJR 14

Parameter Uncertainties in Climate Sensitivity

Parameter Physics Low Middle High

Droplet to rain conversion rate (s-1) Cloud 0.5x10-4 1.0x10-4 4.0x10-4

Relative humidity for cloud formation Cloud 0.6 0.7 0.9

Cloud fraction at saturation (free trop.) Cloud 0.5 0.7 0.8

Entrainment rate coefficient Convection 0.6 3.0 9.0

Time-scale for destruction of CAPE (h) Convection 1.0 2.0 4.0

Effective radius of ice particles (μm) Radiation 25 30 40

Diffusion e-folding time (h) Dynamics 6 12 24

Roughness length parameter (Charnock) Boundary 0.012 0.016 0.02

Stomatal conductance dependent on CO2 Land Off - On

Ocean-to-ice heat transfer (m-2s-1) Sea Ice 2.5x10-5 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

Diagnostics

MJR 15

-6 -3 0 3 6Kday-1 (K for bias)

1296

202

353

539

728

884979

Ap

pro

x. P

ress

ure

(h

Pa)

(a) Control

-6 -3 0 3 6Kday-1 (K for bias)

(b) Reduced Entrainment

Dyn Rad V.Dif Con LSP Net D+5 Bias

Amazon January 2005 Initial T Tendencies

Amazon = [300oE-320oE, 20oS-0oN]. 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!)

Diagnostics

MJR 16

15 m/s

0° 90°E 180°

(a) JJA OBS

2 4 6 8 10 12 18

5 m/s

0° 90°E 180°

(b) JJA OLD - OBS

-16 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 16

5 m/s

0° 90°E 180°

(c) JJA NEW - OLD

-10 -5 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 5 10

5 m/s

0° 90°E 180°

(d) JJA NEW - OBS

-16 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 16

JJA Precipitation, v925 and Z500. New-Old

mm day-1. 10% Sig.

Diagnostics

MJR 17

-0.6 -0.3 0 0.3 0.6Kday-1

1296

202

353

539

728

884979

Ap

pro

x. P

ress

ure

(h

Pa)

(a) Initial

-0.6 -0.3 0 0.3 0.6Kday-1

(b) D+5

Dyn Rad V.Dif Con LSP Net

North Africa Jul 2004 T Tendencies (New-Old)

North Africa = [5oN-15oN, 20oW-40oE]. 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 DESTABILISEPROFILE AND LEAD TO MORE CONVECTION …

… BUT ULTIMATELY LEAD TO MORE DESCENTAND LESS OVERALL PRECIPITATION

Diagnostics

MJR 18Local Response to Aerosol Reduction

CONVECTION(FAST RESPONSE)

RADIATION

DYNAMICS(SLOW RESPONSE)

DRYING

LESSABSORPTION

IMPORTANCE OF SEMI-DIRECT EFFECT(?)

Diagnostics

MJR 19Tropical Waves

Diagnostics

MJR 20

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1JUL

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2AUG

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150 OW 100 OW 50OW 0O 50OE 100 OE 150 OE

Daily OLR: NOAA JJA 2006 (-5-5)

-70

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-40

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-20

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150 OW 100 OW 50OW 0O 50OE 100 OE 150 OE

Daily OLR: FC D+1 JJA 2006 (-5-5)

-70

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-20

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Tropical Waves: Outgoing Long-wave Radiation

5oS-5oN

JUN

AUG

JUL

20

06

100oW 0o 100oE

MJO

MADDEN-JULIAN OSCILLATION: EASTWARD PROPAGATING,30-60 DAY (≈10ms-1)

Data from NOAA

Wm-2

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2006

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100OW 50OW 0O 50OE

Daily OLR: NOAA JJA 2006 (7.5-17.5)

-70

-60

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100OW 50OW 0O 50OE

Daily OLR: FC D+1 JJA 2006 (7.5-17.5)

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WESTWARD PROPAGATING WAVES

7.5oS-17.5oN

JUN

AUG

JUL

100oW 0o 100oE

TIME

LONGITUDE

Diagnostics

MJR 21

The 2-Layer Shallow Water Model

Shallow Water Equations on the β-plane(Here, for understanding tropical atmospheric waves)

Note: No coupling with convection in this model

Momentum:

0u

yv gt x

0v

yu gt y

(1)

2 21 2

1 2

20 to 80ms

is the propagation speed of a barotropic

gravity wave in single layer of depth

e e e

e

e

H Hc g gH c

H H

c

H

2

0'ec u v

t g x y

Continuity:

u1 u1

v1

v1

t

(2)

2 2 22 2 2 2

2 2 20e e

v v v vy v c c

t t x y x

Solving for v:

(3)

Diagnostics

MJR 22

V=0:

V≠0:

Structures(Meridional structures

are solutions to

Schrodinger’s simple

harmonic oscillator)

Dispersion(How phase speed

is related to spatial scale)

Free Equatorial Waves

22

23

1

2

4 1ˆ( )

8 12

( )

y

n

y

yv y e

y y

H y

2

22

2 1

( 0,1,2,...)ee

kk n

cc

n

2 ( )20

eik x c tyu u e e 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

( )ˆ( ) i kx tv v y e

1/2 has been non-dimensionalised by the factor /cey

( )nH y

Substitute into equation for v

Diagnostics

MJR 23

-5 -4 -3 -2 -1 0 1 2 3 4 500k(c

e/)1/2

0

1

2

3

4

5

00

(

c e)-1

/2

(c=cetan)

Equatorial Wave Dispersion Diagram

Gravity

Rossby

Mixed

Kelvinn=-1

n=0

n=1

n=2

n=3

C C

C=/k (phase speed)C

g=d/dk (group velocity)

=

-/

2k

r2=1 r2=3 r2=5

Interpretation of Free Equatorial Waves

Dispersion Diagram

SUGGESTS METHOD OF COMPARISON BETWEEN OBSERVATIONS AND MODEL

Diagnostics

MJR 24

-2 -1 0 1 200k(c

e/)1/2

0

1

00

(

c e)-1/2

(d) Simulated Asymmetric

-2 -1 0 1 200k(c

e/)1/2

0

1

00

(

c e)-1/2

(b) Observed Asymmetric

-2 -1 0 1 200k(c

e/)1/2

0

1

00

(

c e)-1/2

(c) Simulated Symmetric

-2 -1 0 1 200k(c

e/)1/2

0

1

00

(

c e)-1/2

(a) Observed Symmetric

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

c≈20

ms

-1

(a) Observed Symmetric

(c) Simulated Symmetric (d) Simulated Asymmetric

(b) Observed Asymmetric

MIXED

ROSSBYMJOCONVECTIVELY COUPLED(?)

ALIASING OF 12H OBSERVATIONS

TOO MUCH LOW FREQUENCY POWERn=1

n=3

n=2

n=0

n=-1

Diagnostics

MJR 25Wave Spotting

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

To re-start movie, escape and start slide show again

Diagnostics

MJR 26Wave 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

Diagnostics

MJR 27

Wave KelvinMixed

Rossby-Gravity

RossbyEastward Gravity

Westward Gravity

1

2

3

4

5

6

7

8

9

10

11

12

Wave spotting: Your Answers

Diagnostics

MJR 28Gill’s 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,…)

-10 -5 0 5 10 15-4

-2

0

2

4

DAMPING/HEATING TERMS TAKE THE PLACE OF THE TIME DERIVATIVES

EXPLICITLY SOLVE FOR THE X-DEPENDENCE

GOOD AGREEMENT WITH THE AEROSOLCHANGE RESULTS (OPPOSITE SIGN):

• NORTH ATLANTIC SUBTROPICAL ANTICYCLONE• CONVECTIVE COUPLING IN KELVIN WAVE REGIME

Following Gill (1980). See also Matsuno (1966)

Diagnostics

MJR 29

15 m/s

0° 90°E 180°

(a) JJA OBS

2 4 6 8 10 12 18

5 m/s

0° 90°E 180°

(b) JJA OLD - OBS

-16 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 16

5 m/s

0° 90°E 180°

(c) JJA NEW - OLD

-10 -5 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 5 10

5 m/s

0° 90°E 180°

(d) JJA NEW - OBS

-16 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 16

JJA Precipitation, v925 and Z500. New-Old

mm day-1. 10% Sig.

The Extratropical Response will be explained in the next lecture!

Diagnostics

MJR 30Summary

● 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