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
Mark Rodwell
Meteorological Training Course
Predictability, Diagnostics and Extended-Range Forecasting
ECMWF
9 May 2012
Talk outline
Aspects of diagnostics
Lorenz Energy Cycle
The October Storm
Radiosonde first-guess departures
The need for diagnostics research
Temporal variance of D+1 error of Z500
Total wavenumber
From Adrian Simmons
The need for diagnostics research
Number of observations assimilated (106 day-1)
From Peter Bauer and Jean-Noel Thepaut
The need for diagnostics research
Physical processes represented in the IFS model
From Peter Bechtold
The need for diagnostics research
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
TL96
TL799
TL256
TL2047
TL511
TL1279
The need for diagnostics research
m2s-1
Shading: spread Ψ250 D+4
mm
Shading: RMSE Ψ250 D+4
Contours: analysed Ψ250. Squares:obs. precip.
The need for diagnostics research
AMSRE ch7 (~q850) Variational Bias Correction JJA 2010
‘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
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
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
Substitute into equation for v
Hermite Polynomials: Hn(y)
For n ≠0: 3 values of ω for each k
For n=0: 2 values of ω for each k
(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
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