2015-05-12 Japanese-French modelstudies of planetary atmospheres

Cloud tracking using sequential
images from Venus Express VMC
Takeshi Horinouchi, Shinichi Ikegawa(Hokkaido Univ)
Paper: Ikegawa & Horinouchi (2015) Icarus, submitted: IH15
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Venusian atmosphere:
Remaining Frontier of GFD• General circulation– Super-rotation– Meridional circulation– (Angular) momentum
transport/balance• Waves, instabilities, turbulence,…
• Need observations for soundscientific progresses (althoughobservation is inherently limited, ofcourse)

Schubert,1983

Venus is covered with cloudsTayler(1998)

Cloud tracking• Long history– Mariner 10, Feb 1974 (fly-by)– Pioneer Venus Orbiter, 1979-1986– Galileo, Feb 1994 (fly-by)– Venus Express, 2006-2014– ground-based observations• Coverage– Day-side: reflected sunlight (UV: 65-70 km; NIR ~1μm:~60 km)– Night-side: shadow of clouds from low-level thermalemission (IR ~2μm: ~45 km)– (day&night: thermal infrared)

Cloud tracking studies with Venus Express(VEX)• Mean winds & thermal tides (Sanchez-Lavega et al2008; Moissl et al 2009; Hueso et al 2012; Khatuntsev et al2013; Hueso et al 2014. – mostly based on manualtracking)– Also some case studies• Planetary-scale waves (Kouyama et al 2013 – withautomated digital tracking)Tracking methods• Manual– by human eyes
– labor-intensive– supposed to be more reliable than automatedtracking– resultant vectors tend to be sparse• Digital (automated)– by using the cross-correlation method– produces many errors  need screening (e.g.
Rossow et al 1990) or correction (e.g., Kouyama 2012)– provides dense data (whether reliable or not)

cross-correlation (CC) method

From Kouyama et al. (2012)7

Kouyama et al (2012)
Example of results from Galileo images (violet)
Deviation fromthe mean

Simple CC

Zonal mean U

Corrected by selectingpeaks

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Purpose of this study• To improve the CC method by jointly using
many (not just two) images to derive cloud
motion vectors (CMVs).
• To develop methods to estimate the quality ofeach CMVDatafrom Titov (2012)• VEX VMC (VenusMonitoringCamera) V 2.0– Used: 365 nm (UV).
512x512 px– At apogee, Δx =~ 50
km at the subspacecraft point• VEX:– orbital period: 24 h– observation during
ascending nodes
10Corrected VMC images (Titov et al 2012)
Raw imageCorrected; published data…

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VMC 2.0 data
• Corrected, but noise still remains (sometimes only
partially & faintly, sometimes largely & significantly)• Noise patterns often have similar scales tosignal scales  sometimes makes tracking
difficult⇒ We need a noise tolerant method

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Example of the CC surfaces with multiple
peaks （VMC orbit #246, Δt = 3h20m）
Template size ６x６

Maximum:wrong match

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How to use multiple images• Superpose the CC surfaces between 2 images
for all combinations with Δt >= Δtmin (=40 minin this study)– Point: superpose with respect to velocity (u,v)#246 (20min internval)

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Time interval

Initial time15

Superposeall16

Δt greater ⇒ Search region wider
Rectangles：regions overwhich the center oftarget region is swept
when Δt=1,2,3 h
70 m/sCenter oftemplate(at t0)

70 m/s

200 m/s
Template size：6x60 m/s
17Corresponding velocity when Δt=3 h

Essence of the CC superposition
𝑟 𝑥, 𝑦, 𝑡

1=𝑃

𝑓 ′ 𝑥 + 𝑢𝑡1 , 𝑦 + 𝑣𝑡1 , 𝑡 + 𝑡1 𝑓′ 𝑥𝑡1 ,𝑡2 )+ 𝑢𝑡2 , 𝑦 + 𝑣𝑡2 , 𝑡 + 𝑡2 )–: average over small x&y ranges (6x 6 in IH15)– 𝑃 : the number of the 𝑡1 , 𝑡2 ) combinations– 𝑓 ′ : normalized brightness deviation– 𝑢 and 𝑣 : the velocity to be derived.

(Traditional one-pair method: 𝑃 = 1 & 𝑡1 = 0, 𝑡2 = ∆𝑡)18

Why does the superposition enhance (reduce)
the correct (wrong) peak(s)?
• For match with actual similar features– Suppose (at 𝑡 = 𝑡0 ) similar cloud features A around 𝑥, 𝑦)
and B around 𝑥 + 𝑐, 𝑦 + 𝑑); both are advected by 𝑢, 𝑣)(assume a common velocity, since they are nearby)– Correlation between A at 𝑡0 and B at 𝑡0 + ∆𝑡  peaks atvelocity = 𝑢 + 𝑐/Δ𝑡, 𝑣 + 𝑑/Δ𝑡)• Varies by Δ𝑡 unless 𝑐 = 𝑑 = 0  peak reduced(𝑐 = 𝑑 = 0 means correct match)• Point: to have various Δ𝑡 values• Match by noise or error– is also reduced by superposition, if noise/error isindependent among images (regardless Δ𝑡 values)

19Why does the superposition increase theaccuracy too?
• Because it reduces the random peak shift bynoise and pixel discretization

The 1/ 𝑁 effect20

Spatial superposition (~running mean) of
CC surfaces (additional; STS in IH15)• Adequate when thedesired spatial resolution
is coarser than thetemplate size.
• Overlay the 5 CC surfaces
before deriving velocity– Trade off between spatialresolution and accuracy– The default procedure inIH15 (used in what follows)21

Error estimation: Necessity• Crucial! Needed to judge what we can do (to whatextent) with the data!
– error level sets the effective resolution.
– Clouds are some times featureless: accuracy varies
significantly.

• Previous studies used 𝜎 (std.dev.; e.g. against zonal mean),which includes natural (true) variability.
2
2 , it’s safe to use 𝜎, but it is– Since 𝜎 2 = 𝜎natural+ 𝜎err
22useless as a measure of error if 𝜎err
≪ 𝜎natural, but toachieve it is the very thing that we need to study
atmospheric disturbances.

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Error evaluation 1 (precision)• Utilize the lower confidence bound of CC– Use the effective degree of freedom.
– Covers streaky clouds （then CC surfaces are alsostreaky）– Applicable to one-pair estimates– Cannot tell anything about peak selection(drawback)23

CC surface above the lowerconfidence bound (90%) is fit by
1. Elliptic paraboloid (forslantwise streaks)
2. Parabolas along cross sections
at peak along u and v axes

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𝜀2𝑉

𝜀1𝑉𝜀1𝑉

𝜀2𝑉
𝜀2𝑈
𝜀1𝑈

𝜀2𝑈 𝜀1𝑈𝜀 = max 𝜀1𝑈 , 𝜀1𝑉 , 𝜀2𝑈 , 𝜀2𝑈 ) : the worst of the four params.
Caveat: confidence percentage (90%, here) is only applicable to CC.
Cannot be converted to the confidence level of (u,v).
But 𝜀 may be used as a relative measure of the precision of (u,v).
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Error evaluation 2Group A#246

0200time

Group B
0200time– Use the rms between
the two.
– Note: B & C are expected
to have greater error thanA, since the number ofpairs are smallerGroup C20• Entire images (A) are
divided into 2 groups(B,C) and winds are
estimated from each

160
time

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From IH15

(P, PA, PB : the number of pairs in the groups A,B,C)⇒

Expected error (here, the factor of 1.96 is for the 95% confidence level)

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Characteristics of χ
• Merit: Direct measure of errors in (u, v)• Limitation: Deals with peak selection, but only
partially (peaks in B and C may differ, though agreement
does not guarantee correctness).

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Our screening• Made by
1. Peak CC value: rmax ≥ 0.6
2. Mapped CC lower bound: ε ≤ 20 m/s
3. Error form 2-group comparison: χ ≤ 10 m/s• No correction of erroneous vectors (can beintroduced, but simply not have been tried)

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Result example (Orbit 246)

Our estimation is limited down to 45S

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Added a uniform zonal flow: (90,0) m/s

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Ref： Kouyama et al (2012) Example of wind from
Galileo images (violet)
Deviation fromthe mean

Simple CC

Zonal mean U

Corrected by selectingpeaks

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Error evaluation(#246)Max CC rmax

0.620 m/s

Mapped CClower bound εError from 2-groupcomparison χ

10 m/s

20 m/s
10 m/s340

Screened on by rmax

10-50 80

div & rot
A群

A群

B群

B群

C群

C群

200

Good correspondence even though div,rot enhances
small scale features (though not all features are reliable)

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Summary of the error estimates （After the screening.
χ (from 2-group diff.)

Orbits 243-267）

ε (from CC confidence)• In general, χ < ε• If measured by χ, typical error is 2 m/s. (Too good for manual (humaneye) verification. Q: actually good beyond the limit of manual tracking, or χ istoo good?)• Low lat (EQ-30S) better than mid lat (30S-45S)• χ : median < rms （∵big values are outliers）

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Results (#200s)• 10 orbits from 243 to 267– Other orbits (in this period) are not available since the numberof images ＜4– For each of the 10 orbits, 8-11 images are used.
– Caveat (from subjective verification)： some results (vectors) arelikely invalid beyond the χ value.

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Orbit 243

Local time=13 h

Local time=11 h38

Orbit 246

Local time=13 h

Local time=11 h39

Orbit 250Cannot be justified manually.
Screened out if ε threshold is set to 10 m/s

Local time=13 h

Local time=11 h40

Orbit 257

Local time=13 h

Local time=11 h41

Orbit 258

Local time=13 h

Local time=11 h42

Orbit 260

Local time=13 h

Local time=11 h43

Orbit 263

Local time=13 h

Local time=11 h44

Orbit 265

Local time=13 h

Local time=11 h45

Orbit 266

Local time=13 h

Local time=11 h46

Orbit 267

Local time=13 h

Local time=11 h47

Comparison with earlier studies (mean zonal wind)Note: longitudinal coverage in these studies are unknown  comparison limited48

Time sequence of zonal winds (avg: 20S-EQ,LT11-13h)
U•

VExists day-by-day fluctuation– No obvious periodicity 
unable to explain by asingle planetary-scale wave
– U, V fluctuations: similar
magnitude– 〇 : Confirms the rapid
intensification pointed outby Moissl et al (2009)49

Tidal components (time average as func of LT&lat)
UV

#200s

#200s

#400s

#400s

• Mean zonal wind : Period 2 (200s) > Period 3 (400s)• Roughly speaking, consistent with preceding studies
50Summary，Problems，Future outlook• Improved the digital cloud tracking by superposing CC
surfaces (significantly better than preceding studies).
– It’s always nice to use all good data than to throw a part away.

• Developed methods to evaluate the accuracy of each CMV.
– Mapped CC lower bound (ε) and error from 2-groupcomparison (χ). Can be used together for screening.
– Results of VEX 200s  Typical value of χ is 2 m/s. Typical εvalue is 8 m/s at low latitude & much greater at mid latitude.
– Epoch making, if the error is as small as χ  enables one tostudy atmospheric disturbances (mom flux; waves; turbulence…)• Question: Is this really so? (manual impression is closer to ε)• Improve the algorithm (Vary the template size and select according
to ε and χ. Alternative peak selection as done by Koyama. Iteration, etc.）• Further development of error estimation
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