IntroDiagram (canonical)

ExpliSyT (hierarchical)

CConDoR (separable)

Novel methods to retrieve Doppler spectral widths
from EarthCARE-like spaceborne radars
Ousmane O. Sy
ousmane.o.sy@jpl.nasa.gov

Simone Tanellisimone.tanelli@jpl.nasa.gov

Jet Propulsion Laboratory
California Institute of Technology

November 27, 2023
Copyright 2023. All rights reserved

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EarthCARE CPR: 1st radar of its kind:

ExpliSyT (hierarchical)

CConDoR (separable)

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What Doppler results to expect?

TRMM PR
CloudSat CPR
GPM DPR
RainCube PR
EarthCARE CPR

Launchf

XT scanObservables

1997
2006
2014
2018
2024

Ku
W
Ku, Ka
Ka
WX
×X
××Z
Z
ZZ
Z, V , S

IntroDiagram (canonical)

ExpliSyT (hierarchical)

CConDoR (separable)

ECPR Idealized spectrum

Reference moments: (ZR , VR , SR )Idealized moments: (ZID , VID , SID )NUBF bias:
Spectral broadening:

VID 6= VR
SID  SR

Pulse-pair moments: (ZPP , VPP , SPP )NUBF, broadening
random, noisy

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ExpliSyT (hierarchical)

CConDoR (separable)

Example: ECPR (PRF = 7 kHz) from sub-orbital APR3 in ORACLES (PI: dr. Jens Redemann)

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ExpliSyT (hierarchical)

CConDoR (separable)

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Why no correction for S?

Mean velocity V - NUBF
Tanelli et al. (2002), Durden et al. (2007), Kollias et al. (2014), Sy et al. (2014)

V = (Wwind − Vterm ) + φNUBF(1)

φNUBF ∝ (VSAT , Z) (hierarchical) ⇒ can be corrected
Spectral width S - broadening
Meneghini & Kozu (1990), Tanelli et al. (2002), Kollias et al. (2014)22
2S 2 = (Sturb+ Sshear+ Sterm) + ψBROAD(2)

ψBROAD (VSAT , θ3dB )6= f (Z , V ) (not hierarchical) ⇒ (2) not useable for correction
Resampling Diagram/

ExpliSyT/

CConDoR

IntroDiagram (canonical)

ExpliSyT (hierarchical)

Canonical Doppler resampling: Fading(0), Znubf(0), Vnubf(0)CConDoR (separable)

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ExpliSyT (hierarchical)

Canonical Doppler resampling: Fading(0), Znubf(0), Vnubf(1)CConDoR (separable)

OutroIntroDiagram (canonical)

ExpliSyT (hierarchical)

Canonical Doppler resampling: Fading(0), Znubf(-1), Vnubf(1)CConDoR (separable)

OutroIntroDiagram (canonical)

ExpliSyT (hierarchical)

Canonical Doppler resampling: Fading(0), Znubf(1), Vnubf(1)CConDoR (separable)

OutroIntroDiagram (canonical)

ExpliSyT (hierarchical)

Canonical Doppler resampling: Fading(1), Znubf(1), Vnubf(1)CConDoR (separable)

OutroIntroDiagram (canonical)

ExpliSyT (hierarchical)

Canonical Doppler resampling: Fading(1), Znubf(1), Vnubf(1)CConDoR (separable)

OutroIntroDiagram (canonical)

ExpliSyT (hierarchical)

Canonical Doppler resampling: Fading(1), Znubf(1), Vnubf(-1)

CConDoR (separable)

OutroIntroDiagram (canonical)

ExpliSyT (hierarchical)

CConDoR (separable)

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Idealized ECPR moments

Z

Z

PI (xI ; v ) =UJ (xI − xE )LαX (xE − xA )PA [xA ; v + β(xE − xA )] dxA dxE
X

Doppler moments by integration wrt v

ZID = UJ ∗ αX ∗ ZA = ZR
UJ : along-track integration
αX : antenna pattern(∗): convolution 11Zfor any functions F1 and F2 , F1 (xI ) ∗ F2 (xI ) =F1 (xI − x)F2 (x)dx.
x∈RIntro

Diagram (canonical)

ExpliSyT (hierarchical)

CConDoR (separable)

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Idealized ECPR moments: by v -integration Analytical
VID ∼ VR + φL

φL ∝Z0VSATA2 ID
hSATZID

22SID∼ SR+ ψV,L + ψZ,L

VSAT
0
A2 VID,ChSAT
Z 00

1 + D4 ID
VSAT 2ZID
ψZ,L ∝A2− φ2L
Z 00
hSAT
1 + D2 ID
ZID
ψV,L ∝in uniform beamfilling: ψUBF =VSAThSAT

2A2 ∼ (3.6 m/s)2A2 , D2 , D4 : factors of variance and kurtosis of UJ and αXIntroDiagram (canonical)

ExpliSyT (hierarchical)

CConDoR (separable)

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Example: ECPR idealized scale analysis

Input VAψZ vs ψ(truth)
ECPR SID

corr. only byψZ

ψ(numeric)vsψ(truth)Ref SRcorr. by ψ(numerical)

corr. by ψ(analytical)

ψ(analytic)vsψ(truth)IntroDiagram (canonical)

ExpliSyT (hierarchical)

CConDoR (separable)

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Example: ECPR idealized (VFAD = 7.2 km/s)

Input ZAECPR ZIDECPR VID

ECPR
SID

Corrected
VID

Corrected SID

Ref. VR

Ref. SR

Post
spectra O

Post
spectra ∇IntroDiagram (canonical)

ExpliSyT (hierarchical)

CConDoR (separable)

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Example: ECPR pulse pair (VFAD = 7.2 km/s)

Input ZAECPR ZPP

ECPR VPP

ECPR
SPP

Corrected
VPP

Corrected SPP

Ref. VR

Ref. SR

Post
spectra O

Post
spectra ∇IntroDiagram (canonical)

ExpliSyT (hierarchical)

CConDoR (separable)

CConDoR approach: Complex Convolutional Doppler ResamplingZ

Z
UJ (xI − xE )PI (xI ; v ) =LαX (xE − xA )PA [xA ; v + β(xE − xA )] dxA dxEXInverse Fourier transform wrt v
By deconvolution
QI (xI , τ ) = ΓI (xI , τ ) ∗ QA (xI , τ )NUBF correction

QI = Fv−1 [PI ]: ECPR correlation (lag τ )broadening correction

QA = Fv−1 [PA ]: Input correlation (unaffected by VSAT )hτΓI (x, τ ) = UJ (x) ∗ αX (x)e −i4π λ β(x)iresolution enhancement

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ExpliSyT (hierarchical)

Example from CAMP2 EX 2019/09/16: ECPR pulse pair

CConDoR (separable)

OutroIntroDiagram (canonical)

ExpliSyT (hierarchical)

CConDoR (separable)

Thank you for your attention
References
ExpliSyT: O.O. Sy and S. Tanelli, Recovering the Elusive Spectral Width from Spaceborne Doppler
Profiling Radar Measurements: the “ExpliSyT” Approach, IEEE TGRS, vol. 61, 2023
CConDoR: O.O. Sy and S. Tanelli, Dynamic Retrievals From Spaceborne Doppler Radar
Measurements: the CConDoR Approach, IEEE TGRS, vol. 60, 2022

Acknowledgements
NASA’s Earth Science US PI program
NASA’s ORACLES and CAMP2 EX campaigns (EVS-2 program)

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