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Diagnostics I

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Diagnostics I

Mark Rodwell

Meteorological Training Course

Predictability, Diagnostics and Extended-Range Forecasting

ECMWF

9 May 2012

Talk outline

- Aspects of diagnostics
- The need for diagnostics research
- Seamless diagnostics
- Equatorial wave diagnostics

Aspects of diagnostics

- Understanding the circulation

Lorenz Energy Cycle

- Understanding casestudies

The October Storm

- Understanding error
- (observation, analysis or forecast error)

Radiosonde first-guess departures

The need for diagnostics research

Temporal variance of D+1 error of Z500

- Error identification

Total wavenumber

From Adrian Simmons

The need for diagnostics research

- Error identification

Number of observations assimilated (106 day-1)

- Observation volume

From Peter Bauer and Jean-Noel Thepaut

The need for diagnostics research

- Error identification

Physical processes represented in the IFS model

- Observation volume

- Model complexity

From Peter Bechtold

The need for diagnostics research

- Error identification

- Observation volume

Met Office rainfall radar 2009/11/29 at 10:30

Met Office rainfall radar 2009/11/29 at 10:30

Met Office rainfall radar 2009/11/29 at 10:30

Met Office rainfall radar 2009/11/29 at 10:30

Met Office rainfall radar 2009/11/29 at 10:30

Met Office rainfall radar 2009/11/29 at 10:30

- Model complexity

- ‘Gray-zone’ resolution

TL96

TL799

TL256

TL2047

TL511

TL1279

The need for diagnostics research

- Error identification

m2s-1

Shading: spread Ψ250 D+4

- Observation volume

- Model complexity

mm

- ‘Gray-zone’ resolution

Shading: RMSE Ψ250 D+4

- Uncertainty estimation

Contours: analysed Ψ250. Squares:obs. precip.

The need for diagnostics research

- Error identification

- Observation volume

- Model complexity

AMSRE ch7 (~q850) Variational Bias Correction JJA 2010

- ‘Gray-zone’ resolution

- Uncertainty estimation

- 4D-Var: obsvs model

‘Seamless’ diagnostics

T500 forecast error as function of lead-time

D+1

D+2

x0.01K

x0.1K

D+5

D+10

x0.1K

x0.1K

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

Data assimilation: Perfect model

Mean Analysis Increment = 0

(Imperfect, unbiased observations)

Data assimilation: 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)

Confronting models with observations

UNIT=0.01K

D+1 T500 FORECAST ERROR

T500 ANALYSIS INCREMENT

- Every 1o square has data every cycle
- ~6 Million data values

- Independent vertical modes of information:
- IASI / AIRS:~ 15
- HIRS / AMSUA:~ 5 (~ 2 IN TROP)

- Anchors (not bias corrected):
- Radiosonde
- AMSUA-14
- Radio Occultation

AIRS CH 215 OBS-FIRST GUESS

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

AIRS CH 215 BRIGHTNESS TEMPERATURE ~T500

Parameter Uncertainties in Climate Sensitivity

MANY UNCERTAINTIES ARE ASSOCIATED WITH “FAST PHYSICS”.

… WHICH IS ALSO IMPORTANT IN NWP

Representative selection of parameters and uncertainties used by Murphy et al., 2004: Nature, 430, 768-772.

Amazon January 2005 initial T tendencies

PERFECT MODEL

(Almost!)

IMPERFECT MODEL

(12K Warming)

( Net = Minus the mean

analysis increment )

Reduced Entrainment model is out of balance. Reject or down-weight?

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.

Vertically integrated absolute net tendencies

CONTROL

ENTRAIN/5

T (Kday-1)

q (kgm-2day-1)

Can be the basis for a “process metric”

(as opposed to the more widely used circulationmetrics)

Mean of 31 days X 4 forecasts per day X 12 timesteps per forecast. Mass-weighted vertical integrals.

CONTROL model = 29R1,T159,L60,1800S.

Old and New Aerosol Optical Thickness

OLD

(NO ANNUAL CYCLE)

OPTICAL

DEPTH d AT 550nm

NEW

(JULY)

ATTENUATION FACTOR = e-d

SINGLE SCATTERING ALBEDO FOR DESERT AEROSOL ≈ 0.9

- SOIL DUST IS LARGE COMPONENT
- SOIL DUST ABSORBS AS WELL AS SCATTERS

Old: C26R1 (Tanre et al. 1984), New: C26R3 (Tegen et al. 1997).

JJA Precipitation, v925 and Z500. New-Old

mm day-1. 10% Sig.

North Africa Jul 2004 T Tendencies (New-Old)

RADIATIATION CHANGES DESTABILISE

PROFILE AND LEAD TO MORE CONVECTION …

…BUT ULTIMATELY LEAD TO MORE DESCENT

AND LESS OVERALL PRECIPITATION

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.

CONVECTION

(FAST RESPONSE)

DYNAMICS

(SLOW RESPONSE)

DRYING

RADIATION

IMPORTANCE OF SEMI-DIRECT EFFECT(?)

LESS

ABSORPTION

Wind and humidity errors: 850 hPa, JJA 2009

Diagnostics Explorer: Seamless & Accessible

Equatorial wave diagnostics

Tropical Waves: Outgoing Long-wave Radiation

AUG

AUG

WESTWARD PROPAGATING WAVES

MADDEN-JULIAN OSCILLATION: EASTWARD PROPAGATING,

30-60 DAY (≈10ms-1)

JUL

JUL

MJO

JUN

JUN

100oW

0o

100oE

7.5oS-17.5oN

5oS-5oN

2006

Wm-2

TIME

100oW

0o

100oE

LONGITUDE

Data from NOAA

Equatorial Waves

(Use of the shallow water equations on the β-plane (f=βy) for understanding tropical atmospheric waves)

Momentum:

(1)

Continuity:

v1

u1

u1

(2)

v1

Solving for v:

(3)

Note: No coupling with convection in this model

Limiting solutions

η & v

η tendency

Phase speed

Kelvin waves:v≡0, u in geostrophic balance with meridional pressure gradient

Equator

Gravity waves:Fast, pressure gradient force dominates

Rossby waves:Slow, Coriolis affect important, closer to geostrophic

balance, less convergence. Take curl of (1)

Free Equatorial Waves

V=0:

V≠0:

Structures

(Meridional structures

are solutions to

Schrodinger’s simple

harmonic oscillator)

Dispersion

(How phase speed

is related to spatial scale)

East propagating Kelvin Wave

- Non-dispersive
- In geostrophic balance

Substitute into equation for v

Hermite Polynomials: Hn(y)

- Each successive polynomial has one more node
- Modes alternate asymmetric / symmetric about equator

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

(Gravity: associated with first two terms on lhs, Rossby: with last two terms on lhs, Mixed: all three terms)

Interpretation of Free Equatorial Waves

Dispersion Diagram

SUGGESTS METHOD OF COMPARISON BETWEEN OBSERVATIONS AND MODEL

Wave Power OLR DJF 1990-05 NOAA & 32R3

MJO

CONVECTIVELY COUPLED(?)

ALIASING OF 12H OBSERVATIONS

TOO MUCH LOW FREQUENCY POWER

(a) Observed Symmetric

(b) Observed Asymmetric

KELVIN

c≈20ms-1

MIXED

ROSSBY

ROSSBY

(c) Simulated Symmetric

(d) Simulated Asymmetric

n=-1

n=0

n=1

n=2

n=3

AGREEMENT WITH SHALLOW WATER THEORY IF OLR IS A “SLAVE” TO THE FREE WAVES, LINEARITY ETC.

Gill’s steady solution to monsoon heating

- GOOD AGREEMENT WITH THE AEROSOL
- CHANGE RESULTS (OPPOSITE SIGN):
- NORTH ATLANTIC SUBTROPICAL ANTICYCLONE
- CONVECTIVE COUPLING IN KELVIN WAVE REGIME

DAMPING/HEATING TERMS TAKE THE PLACE OF THE TIME DERIVATIVES

EXPLICITLY SOLVE FOR THE X-DEPENDENCE

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,…)

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

JJA Precipitation, v925 and Z500. New-Old

The Extratropical Response will be explained in the next lecture!

mm day-1. 10% Sig.

Summary

- Aspects of diagnostics
- Understanding: the circulation, case-studies, error

- The need for diagnostics research
- Smaller errors, more observations, model complexity, gray-zone, uncertainty, model vs observation

- Seamless diagnostics
- Errors that grow are likely to be model problems
- Initial tendencies highlight root causes before process interactions
- Process-oriented metrics for climate models

- Equatorial wave diagnostics
- Natural modes of tropical variability
- Good way to understand error and uncertainty