diagnostics mjr 1 ecmwf training course 2009 – nwp-pr atmospheric variability: extratropics mark...
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Diagnostics
MJR 1ECMWF Training Course 2009 – NWP-PR
Atmospheric Variability: Extratropics
Mark Rodwell
19 March 2009
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Diagnostics
MJR 2Talk Outline
●Free Barotropic Rossby Waves● Observations
● Theory
●The Rossby Wave Source● Theory
● Explaining the extra-tropical response to the aerosol change
●Diabatic Processes● Potential Vorticity
● Explosive growth of cyclones
● Causes of forecast “busts”
●Precipitation● Deterministic verification
● Combined prediction systems
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Diagnostics
MJR 3Free Barotropic Rossby Waves
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Rossby Wave
MJR 4
20080524 100-300 hPa Rossby.W.Src (Unit: 1e-10 s-2), Meridional wind (CI: 8 ms-1). MJR 2008/09/15
4.0m/s
Unit: 1e-10 s-2
-14 -10 -6 -2 2 6 10 14
Rossby waves. Upper tropospheric vΨ, vχ & RWS
20080527 100-300 hPa Rossby.W.Src (Unit: 1e-10 s-2), Meridional wind (CI: 8 ms-1). MJR 2008/09/15
4.0m/s
Unit: 1e-10 s-2
-14 -10 -6 -2 2 6 10 14
20080525 100-300 hPa Rossby.W.Src (Unit: 1e-10 s-2), Meridional wind (CI: 8 ms-1). MJR 2008/09/15
4.0m/s
Unit: 1e-10 s-2
-14 -10 -6 -2 2 6 10 14
20080526 100-300 hPa Rossby.W.Src (Unit: 1e-10 s-2), Meridional wind (CI: 8 ms-1). MJR 2008/09/15
4.0m/s
Unit: 1e-10 s-2
-14 -10 -6 -2 2 6 10 14
24 May
25 May
26 May
27 May
2008
Group Velocity
Phase Velocity
Contour 8ms-1
10-10s-2
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Rossby Wave
MJR 5The Vorticity Equation
x
zy
ˆz z
v uk v
x y
z
v vv
u
u u
xy is the unit “vertical” vector and
is the horizontal curl operatork̂
z
Motivation (2D flow) :
p
Curl of the 3D momentum equation in absolute frame of reference:
12
Lagrangian Divergence Tilting Baroclinic Frictiontendencyin absolutevorticity
u
du u p F
dt
Shallow atmosphere approximation & assuming non-divergent, horizontal, barotropic, frictionless flow:
0vt
v v v v
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Rossby Wave
MJR 6Free Barotropic Rossby Waves
2xc uk K
2 2 2K k l
We obtain the“dispersion relation”
Where
Rossby waves get advected downstream and propagate upstream
The larger the spatial scale of the wave, the faster the upstream propagation
1SYNOPTIC SYNOPTIC SYNOPTICWavelength 2 6,000km 17 7 ms 0k c
2 20, 0x sc K Ku
For stationary waves
cos 2 2 (winter) to 5 (summer)sm a u Mid-latitude stationaryzonal wavenumbers
Seeking wave-likesolutions …
2kx
2ly
Non-divergent barotropicvorticity equation
-planef
y
f
Where/ 0f
u vt x y
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Rossby Wave
MJR 7
20080527 100-300 hPa Rossby.W.Src (Unit: 1e-10 s-2), Meridional wind (CI: 8 ms-1). MJR 2008/09/15
4.0m/s
Unit: 1e-10 s-2
-14 -10 -6 -2 2 6 10 14
20080526 100-300 hPa Rossby.W.Src (Unit: 1e-10 s-2), Meridional wind (CI: 8 ms-1). MJR 2008/09/15
4.0m/s
Unit: 1e-10 s-2
-14 -10 -6 -2 2 6 10 14
20080525 100-300 hPa Rossby.W.Src (Unit: 1e-10 s-2), Meridional wind (CI: 8 ms-1). MJR 2008/09/15
4.0m/s
Unit: 1e-10 s-2
-14 -10 -6 -2 2 6 10 14
20080524 100-300 hPa Rossby.W.Src (Unit: 1e-10 s-2), Meridional wind (CI: 8 ms-1). MJR 2008/09/15
4.0m/s
Unit: 1e-10 s-2
-14 -10 -6 -2 2 6 10 14
Rossby waves. Upper tropospheric vΨ, vχ & RWS
24 May
25 May
26 May
27 May
2008
Contour 8ms-1
10-10s-2
Group Speed
2
4
2ifgx x
kc c u k l
k K
Phase Speed
2xc uk K
10ms-1 agrees well with theory
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Rossby Wave
MJR 8
(a) Rossby Wave Source (Full) (b) Rossby Wave Source (Anom. wind, Divergence comp.)
(c) Rotational Advection (Anomalous wind) (d) Rotational Advection (Anomalous vorticity)
Stationary Rossby Waves: Vorticity advection
Advection by Anomalous Rotational Wind Advection of Anomalous Vorticity
(a) Rossby Wave Source (Full) (b) Rossby Wave Source (Anom. wind, Divergence comp.)
(c) Rotational Advection (Anomalous wind) (d) Rotational Advection (Anomalous vorticity)
?
-15 -5 -3 -1 1 3 5 13 -15 -5 -3 -1 1 3 5 13
(a) Rossby Wave Source (Full) (b) Rossby Wave Source (Anom. wind, Divergence comp.)
(c) Rotational Advection (Anomalous wind) (d) Rotational Advection (Anomalous vorticity)
?
-15 -5 -3 -1 1 3 5 13 -15 -5 -3 -1 1 3 5 1310-11 s-2
Non sig.Sig. 10%
Upstream Propagation Downstream Advection
40-year mean response to change in aerosol climatology deduced using seasonal-mean data. Results are very similar when daily data are used. Anomalies integrated 100-300 hPa.
Rossby Wave Vorticity Advection Balance
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Rossby Wave
MJR 9The Rossby Wave Source
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Rossby Wave
MJR 10Upper Troposphere Divergent Wind Anomaly
1.0m/s1.0m/s1 m/s
New minus Old aerosol. Anomaly is integrated between 100 and 300 hPa
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Rossby Wave
MJR 11The “Rossby Wave Source”
"Rossby Wave Source"
v v vt
v
When divergent windsare not neglected in thevorticity equation
For use in complex GCMs, it is found here to be useful to vertically integrate this equation between 100 and 300 hPa
Application to barotropic models:Sardeshmukh and Hoskins (1988)
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Rossby Wave
MJR 12
(a) Rossby Wave Source (Full) (b) Rossby Wave Source (Anom. wind, Divergence comp.)
(c) Rotational Advection (Anomalous wind) (d) Rotational Advection (Anomalous vorticity)
JJA Balance in Vorticity Equation New-OldRossby Wave Source
Advection by Anomalous Rotational Wind Advection of Anomalous Vorticity
(a) Rossby Wave Source (Full) (b) Rossby Wave Source (Anom. wind, Divergence comp.)
(c) Rotational Advection (Anomalous wind) (d) Rotational Advection (Anomalous vorticity)
?
-15 -5 -3 -1 1 3 5 13 -15 -5 -3 -1 1 3 5 13
(a) Rossby Wave Source (Full) (b) Rossby Wave Source (Anom. wind, Divergence comp.)
(c) Rotational Advection (Anomalous wind) (d) Rotational Advection (Anomalous vorticity)
?
-15 -5 -3 -1 1 3 5 13 -15 -5 -3 -1 1 3 5 1310-11 s-2
Non sig.Sig. 10%
Upstream Propagation Downstream Advection
40-year mean response to change in aerosol climatology deduced using seasonal-mean data. Results are very similar when daily data are used. Anomalies integrated 100-300 hPa.
The Rossby Wave Source is indeed seen as the tropically induced source of the extratropical stationary Rossby wave response
Wave Initiators
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Rossby Wave
MJR 13
JJA New-Old RWS, vχ,Ψ and mean ζ
Unit: 1e-11 s-2
-7 -5 -3 -1 1 3 5 13 -7 -5 -3 -1 1 3 5 13
1 m/s
10-11 s-2
Rossby wave paths agree beautifully with those predicted by Hoskins and Ambrizzi (1995)
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Rossby Wave
MJR 14
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.
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Rossby Wave
MJR 15
Unit: 1e-11 s-2
-7 -5 -3 -1 1 3 5 7 -7 -5 -3 -1 1 3 5 7
1 m/s
DJF New-Old RWS, vχ,Ψ and mean ζ
10-11 s-2
Extratropical RWS anomaly coincides with precipitation changes. Is upper tropospheric divergent wind directly related to local physics?
Rossby wave path agrees with that shown by Hoskins and Ambrizzi (1993)
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Rossby Wave
MJR 16Diabatic Processes
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Rossby Wave
MJR 17
Adiabatic & Diabatic Contributions to RWS
θ=320K600
300 θ=340K
30oN 90oN60oN
hPa
Account for adiabatic stretching by considering Potential Vorticity (P):
Pv P
t
“Stretching”, Tilting & Advectionby Diabatic Processes (+ Friction)
ADIABATICADIABATIC+ DIABATIC
When averaging over a long period
PV ‘absorbs’ the adiabatic stretching
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Rossby Wave
MJR 18SYNOP Precipitation Anomaly Summer 2007PPT (mm/day) Anomalous: 20070601-20070813
-3.5 - -2.5 -2.5 - -1.5 -1.5 - -0.5 -0.5 - 0.5 0.5 - 1.5 1.5 - 2.5 2.5 - 3.5
Based on 24hr accumulations 20070601-2007813 and our new global SYNOP climatology for the years 1979-2005
-3 -2 -1 0 1 2 3 mm/day
Total rainfall was double the climatological mean
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Rossby Wave
MJR 19Components of a Predictable SignalPPT (mm/day) Anomalous: 20070601-20070813
-3.5 - -2.5 -2.5 - -1.5 -1.5 - -0.5 -0.5 - 0.5 0.5 - 1.5 1.5 - 2.5 2.5 - 3.5
Europe’s wet summer of 2007 could have been the unlucky mean of unpredictable variability. But if not, then this schematic shows some likely building blocks to predictability
-3 -2 -1 0 1 2 3 mm/day
TROPICALPHYSICS?
LOCALPHYSICS?PHYSICS
ALONG WAVE?
DYNAMICAL WAVES?
SCHEMATIC
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Rossby Wave
MJR 20
60°S60°S
30°S 30°S
0°0°
30°N 30°N
60°N60°N
120°E
120°E 150°E
150°E 180°
180° 150°W
150°W 120°W
120°W 90°W
90°W 60°W
60°W 30°W
30°W 0°
0° 30°E
30°E 60°E
60°E
ECMWF Analysis VT:Friday 1 June 2007 00UTC 330K **Potential vorticity
-0.26
-0.22
-0.18
-0.14
-0.1
-0.06
-0.02
0.02
0.06
0.1
0.14
0.18
0.22
0.26
Terms in PV equation @330K
60°S60°S
30°S 30°S
0°0°
30°N 30°N
60°N60°N
120°E
120°E 150°E
150°E 180°
180° 150°W
150°W 120°W
120°W 90°W
90°W 60°W
60°W 30°W
30°W 0°
0° 30°E
30°E 60°E
60°E
ECMWF Analysis VT:Friday 1 June 2007 00UTC 330K **Potential vorticity
-0.26
-0.22
-0.18
-0.14
-0.1
-0.06
-0.02
0.02
0.06
0.1
0.14
0.18
0.22
0.26
60°S60°S
30°S 30°S
0°0°
30°N 30°N
60°N60°N
120°E
120°E 150°E
150°E 180°
180° 150°W
150°W 120°W
120°W 90°W
90°W 60°W
60°W 30°W
30°W 0°
0° 30°E
30°E 60°E
60°E
ECMWF Analysis VT:Friday 1 June 2007 00UTC 330K **Potential vorticity
-0.26
-0.22
-0.18
-0.14
-0.1
-0.06
-0.02
0.02
0.06
0.1
0.14
0.18
0.22
0.26
60°S60°S
30°S 30°S
0°0°
30°N 30°N
60°N60°N
120°E
120°E 150°E
150°E 180°
180° 150°W
150°W 120°W
120°W 90°W
90°W 60°W
60°W 30°W
30°W 0°
0° 30°E
30°E 60°E
60°E
ECMWF Analysis VT:Friday 1 June 2007 00UTC 330K **Potential vorticity
-0.26
-0.22
-0.18
-0.14
-0.1
-0.06
-0.02
0.02
0.06
0.1
0.14
0.18
0.22
0.26
'v P 'v P
Quadratic Diabatic (residual)
Results are based on 0 and 12Z analyses. An over-bar indicates the 2001-2006 climatological mean and a prime indicates the instantaneous 2007 departure from the climatological mean. (June 1 to August 13)
Clearer view of Rossby wave?
Agreement with rainfall anomalies.Important for sustaining wave?
26
18
14
10
6
2
22
-26
-18
-14
-10-6
-2
-22
UNIT = 10-13Km2kg-1s-2
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Rossby Wave
MJR 21Analysis of winter storm “Lothar”
Wernli et al. (2002) Fig. 7a
PV=2 SURFACE
V850
CYCLONE “KURT”
LOW-LEVEL CYCLONE “LOTHAR”
18Z, 25 DEC1999 TROPOPAUSE FOLDING ASSOCIATED WITH KURT AND ISENTROPIC DOWN-GLIDING(?)
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Rossby Wave
MJR 22Analysis of winter storm “Lothar”
PV=2 SURFACE
V850
CYCLONE “KURT”
LOW-LEVEL CYCLONE “LOTHAR”
0Z, 26 DEC1999 TROPOPAUSE FOLD NOW ALSO ASSOCIATED WITH LOTHAR
Wernli et al. (2002) Fig. 7b
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Rossby Wave
MJR 23Analysis of winter storm “Lothar”
PV=2 SURFACE
V850
CYCLONE “KURT”
LOW-LEVEL CYCLONE “LOTHAR”
6Z, 26 DEC1999
UPPER AND LOWER PV ANOMALIES NEARLY JOIN
INTENSE WINDS KILL 50
Wernli et al. (2002) Fig. 7c
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Rossby Wave
MJR 24
20080606 100-300 hPa Rossby.W.Src (Unit: 1e-10 s-2), Meridional wind (CI: 8 ms-1). MJR 2008/09/15
4.0m/s
Unit: 1e-10 s-2
-14 -10 -6 -2 2 6 10 14
20080530 100-300 hPa Rossby.W.Src (Unit: 1e-10 s-2), Meridional wind (CI: 8 ms-1). MJR 2008/09/15
4.0m/s
Unit: 1e-10 s-2
-14 -10 -6 -2 2 6 10 14
20080605 100-300 hPa Rossby.W.Src (Unit: 1e-10 s-2), Meridional wind (CI: 8 ms-1). MJR 2008/09/15
4.0m/s
Unit: 1e-10 s-2
-14 -10 -6 -2 2 6 10 14
RWS, vχ and Meridional wind anomalies
RWS shade interval 10-10 s-2. Meridional wind contour interval 8 ms-1. 100-300 hPa integrals
30 May
5 June
6 June
• Classic example that led to a forecast “bust” over Europe a few days later
• What is the diabatic forcing?• How well does the (first
guess) forecast represent this forcing?
• What are the implications of observation rejection?
Look at developments like this from PV perspective.
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Rossby Wave
MJR 25Precipitation
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Rossby Wave
MJR 26
Deterministic Scores: Z500, θPV=2 & Precip
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Rossby Wave
MJR 27Extratropical Deterministic Precip Scores
1 2 3 4 5 6 7 8 9 10Leadtime (Days)
0.0
0.1
0.2
0.3
0.4
0.5
AC
C
1995 (365dim, 1638spd) 1996 (366dim, 1744spd) 1997 (365dim, 1855spd) 1998 (362dim, 1943spd) 1999 (365dim, 1996spd) 2000 (366dim, 2095spd) 2001 (365dim, 2202spd) 2002 (365dim, 2245spd) 2003 (365dim, 2216spd) 2004 (366dim, 2213spd) 2005 (365dim, 2175spd) 2006 (365dim, 2148spd) 2007 (365dim, 2038spd) 2008 (366dim, 1993spd) 70% Confidence
PPT (SYNOP & nearest gridpoint) ExTrop DET ACC (F/C,O/C)
1995
2008
D+5 forecast in 2008 as good as D+1 forecast in 1995
Area = [SP--30oS & 30oN--NP]
PPT score ,
where forecast
observation at station
climate
i i
i i
i
i
i
f oCOR
c c
f
o i
c
24h Accumulated Precipitation Forecast Scored against SYNOP Observations
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Rossby Wave
MJR 28ECMWF “Meteogram” of Precipitation
Thu 1 Fri 2 Sat 3 Sun 4 Mon 5 Tue 6 Wed 7 Thu 8 Fri 9 Sat 10June 2006
22
24
26
28
30
32
max
min
75%median25% T799 OPS T399 CTRL
2m Temperature reduced to station height (°C) 28m (T799) 26m (T399)
Magics++ 1.1.0
0
2
4
6
8
1010m Wind Speed (m/s)
0
2
4
6
8
10
12
14
16Total Precipitation (mm/6h)
0
2
4
6
8
EPS MeteogramMumbai (26m) 19.1°N 72.9°EDeterministic Forecasts and EPS Distribution Thursday 1 June 2006 00 UTC
Total Cloud Cover (okta)
Thu 1 Fri 2 Sat 3 Sun 4 Mon 5 Tue 6 Wed 7 Thu 8 Fri 9 Sat 10June 2006
22
24
26
28
30
32
max
min
75%median25% T799 OPS T399 CTRL
2m Temperature reduced to station height (°C) 28m (T799) 26m (T399)
Magics++ 1.1.0
0
2
4
6
8
1010m Wind Speed (m/s)
0
2
4
6
8
10
12
14
16Total Precipitation (mm/6h)
0
2
4
6
8
EPS MeteogramMumbai (26m) 19.1°N 72.9°EDeterministic Forecasts and EPS Distribution Thursday 1 June 2006 00 UTC
Total Cloud Cover (okta)
Mumbai
ENSEMBLE CONTROL FORECAST
HIGH RESOLUTION DETERMINISTIC FORECAST
ENSEMBLE PREDICTION SYSTEM
Highly useful product but …… “What should I believe?”• At D+2?• At D+5?
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Rossby Wave
MJR 29Combined Prediction System – Concept
Combining a 10-member ensemble of equally likely members (orange squares) with a single more accurate forecast (yellow rectangle)
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Rossby Wave
MJR 30 Combined Prediction System - Theory
1
K
ij k ijkk
p w p
K = number of forecast systems ( K ≤3 here)wk is the weight applied to system k (independent of location)Find weights that maximize Brier Skill ScoreApply in cross-validated mode(date for year y applied in year y+1)
2
clim1
1 11
j
nij ij
j i Mj ij
p vB
n m b
B = Brier Skill Score averaged over all stationsn = number of datesMj = set of stations reporting on date jmj = number of stations in Mj
pij = CPS probabilityvij = verification (0 or 1)bclim = bclim(location,month) (from climatology)
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Rossby Wave
MJR 31
1 2 3 4 5 6 7 8 9 10Lead-time (days)
0
5
10
15
20
Wei
gh
t (n
um
ber
of
EP
S m
emb
ers)
Weight of Deterministic Forecast within Combined Prediction System
Pp > 1 mm day-1
Pp > 5 mm day-1
Pp > 10 mm day-1
Combined Prediction System - Weights
2001-2005
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Rossby Wave
MJR 32
1 2 3 4 5 6 7 8 9 10Lead-time (days)
0.0
0.1
0.2
0.3
0.4
Bri
er S
kill
Sco
reBrier Skill Score for the event that P
p > x mm day-1
x=1
CPS
EPS
x=5
CPS
EPS
x=10
CPS
EPS
CPS > EPS
5% Significance
Combined Prediction System - Results
2001-2005
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Rossby Wave
MJR 33
Thu 1 Fri 2 Sat 3 Sun 4 Mon 5 Tue 6 Wed 7 Thu 8 Fri 9 Sat 100
20
40
60
Total Precipitation (mm/day) Combined Probability DistributionsOptimized for the critical event the precipitation exceeds 10 mmday-1
Prob > 10 mm/day
Brier Skill Score
100
23
98
19
91
14
70
9
90
5
81
1
45
0
27
0
27
0
43
0
Combined “Meteogram”
Mumbai
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Rossby Wave
MJR 34Summary
●Free Barotropic Rossby Waves●Propagate upstream and get advected downstream
●Larger waves can become stationary (e.g. Blocking)
●The Rossby Wave Source●How the (tropical) divergent flow can influence the extratropics
●Diabatic Processes●May be important for maintaining anomalous flow over a season
●Clearly important for explosively growing cyclones
●Poor representation (over North America) may lead to forecast “busts”
●Precipitation●Deterministic scores show improving trends
●Combined prediction systems can improve probabilistic forecasts