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.

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Diagnostics I

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Diagnostics i

Diagnostics I

Mark Rodwell

Meteorological Training Course

Predictability, Diagnostics and Extended-Range Forecasting

ECMWF

9 May 2012


Diagnostics i

Talk outline

  • Aspects of diagnostics

  • The need for diagnostics research

  • Seamless diagnostics

  • Equatorial wave diagnostics


Diagnostics i

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


Diagnostics i

The need for diagnostics research

Temporal variance of D+1 error of Z500

  • Error identification

Total wavenumber

From Adrian Simmons


Diagnostics i

The need for diagnostics research

  • Error identification

Number of observations assimilated (106 day-1)

  • Observation volume

From Peter Bauer and Jean-Noel Thepaut


Diagnostics i

The need for diagnostics research

  • Error identification

Physical processes represented in the IFS model

  • Observation volume

  • Model complexity

From Peter Bechtold


Diagnostics i

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


Diagnostics i

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.


Diagnostics i

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


Diagnostics i

‘Seamless’ diagnostics


Diagnostics i

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.


Diagnostics i

Data assimilation: Perfect model

Mean Analysis Increment = 0

(Imperfect, unbiased observations)


Diagnostics i

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)


Diagnostics i

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


Diagnostics i

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.


Diagnostics i

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.


Diagnostics i

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.


Diagnostics i

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).


Diagnostics i

JJA Precipitation, v925 and Z500. New-Old

mm day-1. 10% Sig.


Diagnostics i

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.


Local response to aerosol reduction

CONVECTION

(FAST RESPONSE)

DYNAMICS

(SLOW RESPONSE)

DRYING

Local Response to Aerosol Reduction

RADIATION

IMPORTANCE OF SEMI-DIRECT EFFECT(?)

LESS

ABSORPTION


Diagnostics i

Wind and humidity errors: 850 hPa, JJA 2009


Diagnostics i

Diagnostics Explorer: Seamless & Accessible


Diagnostics i

Equatorial wave diagnostics


Diagnostics i

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


Diagnostics i

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


Diagnostics i

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)


Diagnostics i

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)


Diagnostics i

Interpretation of Free Equatorial Waves

Dispersion Diagram

SUGGESTS METHOD OF COMPARISON BETWEEN OBSERVATIONS AND MODEL


Diagnostics i

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.


Diagnostics i

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)


Diagnostics i

JJA Precipitation, v925 and Z500. New-Old

The Extratropical Response will be explained in the next lecture!

mm day-1. 10% Sig.


Diagnostics i

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


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