Transcript Statistical relationships between integral parameters of

The RadOn method and
associated error analysis
Delanoë J., Protat A., Bouniol D., Testud J.
Centre d’étude des Environnements Terrestre et Planétaires
CloudNET meeting : Paris
4/5th April 2005
Julien Delanoë
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Outline
• RadarOnly Algorithm
• Error analysis
• Retrieval
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Radar Only Algorithm
RadOn
Principle of the radar retrieval
method
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Principle of the Radar Algorithm (1)
Z
Doppler Velocity
Vd=Vt+w
Vt retrieval
 Density law and Area diameter relationships
Dm(Vt)
N0*=f(Dm,Z)
IWC, a, re , t
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First step : Retrieval of VT from VD
Vd=w+Vt
Hypothesis (*) : for a long enough time span
w  V t
2 methods:
•Vt-Z : Statistical relationship between Vd and Z
Assuming (*), we obtain Vt from Z (Vt=aZb)
New approach
•Running Window:
Every 30s we compute the mean Vd over ±10 minutes
(like Matrosov) for each radar gate.
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Retrieval of terminal fall velocity with different methods
04/14/03 Palaiseau
Running Window (20min)
Advantages:
•Better resolution than Matrosov
method
•More variability of Vt than Vt-Z
But instability of RadOn when
Vt<5cm.s-1
Vt from Vt-Z relationship
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Principle of the Radar Algorithm (2)
Z
Doppler Velocity
Vd=Vt+w
Vt retrieval
 Density and Area diameter relationships
Dm(Vt)
N0*=f(Dm,Z)
IWC, a, re , t
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Principle of the radar retrieval method (2)
Second step : estimate of the particle density r(D) and area
A(D) from VT-Z relationship
• Vt-Z relationship obtained from radar is compared to microphysical
Vt-Z relationships with different density and area laws.
• Microphysical Vt-Z relationships :
r(D)=arDbr and v(D)=f(m(D),A(D),ad,bd) (Mitchell 1996)
Where m(D)=(p/6) ar D3+br , A=g Ds and ad, bd are the continuous
drag coefficients (Khvorostianov and Curry 2002).
From coefficients of Vt-Z radar relationship we estimate the best
density diameter and area diameter relationships.
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Example : 04/14/2003 Palaiseau
•black: Vt-Z obtained by the
radar
•red: The best density and
Area relationships
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Principle of the Radar Algorithm (3)
Z
Doppler Velocity
Vd=Vt+w
Vt retrieval
 Density and Area diameter relationships
Dm(Vt)
N0*=f(Dm,Z)
Step unchanged
(see Delft presentation)
IWC, a, re , t
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Principle of the Radar Algorithm (4)
Z
Doppler Velocity
Vd=Vt+w
Vt retrieval
 Density law and Area diameter relationships
Dm(Vt)
IWC, a, re , t
N0*=f(Dm,Z)
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Step unchanged
*
N

0
(see Delft presentation)
Direct relationship:
Kw
p 51018
4


Z e   F ( D / Dm )s bsc dD 


1
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Principle of the Radar Algorithm (5)
Z
Doppler Velocity
Vd=Vt+w
Vt retrieval
 Density and Area diameter relationships
Dm(Vt)
N0*=f(Dm,Z)
IWC, a, re , t
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Clouds parameters
Using Dm N0* and Gamma shape => Clouds parameters
IWC 
a  210
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3 IWC
re 
2 a
N
pr w
4
*
0
4
N 0* Dm 4
s
F ( D / Dm )g D dD
t 
zmax
zmin
a (s)ds
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Evaluation of RadOn using
the microphysical database
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Evaluation of RadOn using the microphysical database
• Dataset: CLARE 98,
CARL 99, EUCREX,
ARM SGP, FASTEX,
CEPEX,
CRYSTALFACE
We compute Vt, Z, IWC, a and re from the insitu measurements, assuming A(D) and r(D)
Entries of the
algorithm :Vt
and Ze from in
situ data
• We impose a density law
and area diameter
relationships for a radar at
35 and 95GHz:
A(D)=gDs with several
couples of coefficients
r(D)=aDb with several
couples of coefficients
RadOn Algorithm
IWC, a, re microf
IWC, a, re from RadOn
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bias + std
bias
bias - std
5 « Area diameter relationships»
4 « Density diameter relationships »: b=-1.4, -1.1, -0.8, -0.5
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bias + std
bias
bias - std
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bias + std
bias
bias - std
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RadOn Retrieval:
•14th April 2003: Palaiseau
Deep ice cloud
•15th April 2003: Palaiseau
Cirrus case
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IWC r(D)=0.022D2 -0.6
A(D)=p/4D
N0*
Retrieval 14th April 2003
re
a
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r(D)=0.0005D-1.3
A(D)=0.05D1.4
IWC
N0*
Retrieval 15th April 2003
re
a
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Future work
•
Refine the error analysis
•
Run Radon on all the CloudNET sites, for all frequencies
•
Statistical study of density, IWC, a, re….
•
Comparison with Radar/Lidar and other Radar algorithm
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IWC retrieval from different method
1. RadOn with running window
2. RadOn with Vt-Z
3. IWC-Z-T R.J Hogan
4. IWC-Z Protat et al.
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1
2
With running window
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Vt-Z
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IWC-Z-T RJH
IWC-Z Protat et al.
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