diagnostics mjr 1 ecmwf training course 2009 – nwp-pr atmospheric variability & error: tropics...
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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
T
S
M
W
F
S
T
T
S
M
W
F
S
T
T
S
M
W
F
S
T
T
S
M
W
F
S
T
T
S
M
W
F
S
T
T
S
M
W
F
S
T
T
S
M
W
1JUN
2006
3
5
7
9
11
13
15
17
19
21
23
25
27
29
1JUL
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
2AUG
4
6
8
10
12
14
16
18
20
22
24
26
28
30
150 OW 100 OW 50OW 0O 50OE 100 OE 150 OE
Daily OLR: NOAA JJA 2006 (-5-5)
-70
-60
-50
-40
-30
-20
-10
10
20
30
40
50
60
70
F
S
T
T
S
M
W
F
S
T
T
S
M
W
F
S
T
T
S
M
W
F
S
T
T
S
M
W
F
S
T
T
S
M
W
F
S
T
T
S
M
W
F
S
T
T
2JUN
2006
4
6
8
10
12
14
16
18
20
22
24
26
28
30
2JUL
4
6
8
10
12
14
16
18
20
22
24
26
28
30
1AUG
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
150 OW 100 OW 50OW 0O 50OE 100 OE 150 OE
Daily OLR: FC D+1 JJA 2006 (-5-5)
-70
-60
-50
-40
-30
-20
-10
10
20
30
40
50
60
70
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
T
S
M
W
F
S
T
T
S
M
W
F
S
T
T
S
M
W
F
S
T
T
S
M
W
F
S
T
T
S
M
W
F
S
T
T
S
M
W
F
S
T
T
S
M
W
1JUN
2006
3
5
7
9
11
13
15
17
19
21
23
25
27
29
1JUL
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
2AUG
4
6
8
10
12
14
16
18
20
22
24
26
28
30
100OW 50OW 0O 50OE
Daily OLR: NOAA JJA 2006 (7.5-17.5)
-70
-60
-50
-40
-30
-20
-10
10
20
30
40
50
60
70
F
S
T
T
S
M
W
F
S
T
T
S
M
W
F
S
T
T
S
M
W
F
S
T
T
S
M
W
F
S
T
T
S
M
W
F
S
T
T
S
M
W
F
S
T
T
2JUN
2006
4
6
8
10
12
14
16
18
20
22
24
26
28
30
2JUL
4
6
8
10
12
14
16
18
20
22
24
26
28
30
1AUG
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
100OW 50OW 0O 50OE
Daily OLR: FC D+1 JJA 2006 (7.5-17.5)
-70
-60
-50
-40
-30
-20
-10
10
20
30
40
50
60
70
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