Diagnostics MJR 1 ECMWF Training Course 2009 – NWP-PR Atmospheric Variability: Extratropics Mark Rodwell 19 March 2009.

Diagnostics

MJR 1ECMWF Training Course 2009 – NWP-PR

Atmospheric Variability: Extratropics

Mark Rodwell

19 March 2009

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

Diagnostics

MJR 3Free Barotropic Rossby Waves

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


4.0m/s

Unit: 1e-10 s-2

-14 -10 -6 -2 2 6 10 14


4.0m/s

Unit: 1e-10 s-2

-14 -10 -6 -2 2 6 10 14


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

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

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

Rossby Wave

MJR 7


4.0m/s

Unit: 1e-10 s-2

-14 -10 -6 -2 2 6 10 14


4.0m/s

Unit: 1e-10 s-2

-14 -10 -6 -2 2 6 10 14


4.0m/s

Unit: 1e-10 s-2

-14 -10 -6 -2 2 6 10 14


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

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



?

-15 -5 -3 -1 1 3 5 13 -15 -5 -3 -1 1 3 5 13



?

-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

Rossby Wave

MJR 9The Rossby Wave Source

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

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)

Rossby Wave

MJR 12



JJA Balance in Vorticity Equation New-OldRossby Wave Source

Advection by Anomalous Rotational Wind Advection of Anomalous Vorticity



?

-15 -5 -3 -1 1 3 5 13 -15 -5 -3 -1 1 3 5 13



?

-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

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)

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.

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)

Rossby Wave

MJR 16Diabatic Processes

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

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

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

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


-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


-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


-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

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(?)

Rossby Wave


PV=2 SURFACE

V850

CYCLONE “KURT”


0Z, 26 DEC1999 TROPOPAUSE FOLD NOW ALSO ASSOCIATED WITH LOTHAR

Wernli et al. (2002) Fig. 7b

Rossby Wave


PV=2 SURFACE

V850

CYCLONE “KURT”


6Z, 26 DEC1999

UPPER AND LOWER PV ANOMALIES NEARLY JOIN

INTENSE WINDS KILL 50

Wernli et al. (2002) Fig. 7c

Rossby Wave

MJR 24


4.0m/s

Unit: 1e-10 s-2

-14 -10 -6 -2 2 6 10 14


4.0m/s

Unit: 1e-10 s-2

-14 -10 -6 -2 2 6 10 14


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.

Rossby Wave

MJR 25Precipitation

Rossby Wave

MJR 26

Deterministic Scores: Z500, θPV=2 & Precip

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

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?

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)

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)

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

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

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

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

Diagnostics MJR 1 ECMWF Training Course 2009 – NWP-PR Atmospheric Variability: Extratropics Mark Rodwell 19 March 2009.

Documents

rossby wave mjr

rossby wave source slide

rossby wave paths

rossby wave source theory

clearer view of rossby

sustaining wave

stationary rossby waves

hpa slide