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Remote Sensing Letters

ISSN: 2150-704X (Print) 2150-7058 (Online) Journal homepage: http://www.tandfonline.com/loi/trsl20

Use of the quasi-analytical algorithm toretrieve backscattering from in-situ data in theMediterranean Sea

Jaime Pitarch, Marco Bellacicco, Gianluca Volpe, Simone Colella & RosaliaSantoleri

To cite this article: Jaime Pitarch, Marco Bellacicco, Gianluca Volpe, Simone Colella &Rosalia Santoleri (2016) Use of the quasi-analytical algorithm to retrieve backscatteringfrom in-situ data in the Mediterranean Sea, Remote Sensing Letters, 7:6, 591-600, DOI:10.1080/2150704X.2016.1171922

To link to this article: http://dx.doi.org/10.1080/2150704X.2016.1171922

Published online: 13 Apr 2016.

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Use of the quasi-analytical algorithm to retrievebackscattering from in-situ data in the Mediterranean SeaJaime Pitarcha, Marco Bellaciccoa,b, Gianluca Volpea, Simone Colellaa

and Rosalia Santoleria

aDipartimento Scienze del Sistema Terra e Tecnologie per l’Ambiente, Istituto di Scienze dell’Atmosfera edel Clima (ISAC)-CNR, Rome, Italy; bDipartimento di Scienza e Tecnologia, Università degli Studi di Napoli‘Parthenope’, Naples, Italy

ABSTRACTWe evaluate retrieval of particle backscattering at 555 nm (bbp(555)) in the Mediterranean Sea with the quasi-analytical algorithm(QAA), using new in-situ concurrent data of remote-sensing reflec-tance (Rrs) and inherent optical properties (IOP). When Rrs is cor-rected for Raman scattering, retrieved bbp(555) are reducedbetween ~7% in open waters and ~3% in coastal waters. AfterRaman effect is accounted for, partitioned statistics within the dataset for cruise and water type are rather homogeneous. QAA-retrieved bbp(555) slightly underestimates our in-situ bbp(555),thus contradicting the few previous studies, in which high over-estimation was either reported or suggested. Retrieval errors aremostly caused by the Rrs-IOP model. The ‘new’ Rrs-IOP model thatseparates the influences of water and particle phase functionsproduces mean bias ~–3% for open waters and ~–7% for coastalwaters. In contrast, the ‘old’ model, ambiguous with respect tothe phase function, produces a bias ~–5% for open waters and ~–9% for coastal waters. It is also shown that regional calibration canvirtually suppress bias. In all cases, RMS error remains ~19% andaccounts for all errors involved.

ARTICLE HISTORYReceived 25 November 2015Accepted 21 March 2016

1. Introduction

Retrieval of water inherent optical properties (IOPs) from satellite-derived remote-sensing reflectance (Rrs) ranges from biological (Behrenfeld et al. 2005) and physical(Yang, Arnone, and Jolliff 2015) applications. We focus here on the specific case of theMediterranean Sea, whose bio-optics has not been directly studied yet, although speci-ficities have been pointed out (Volpe et al. 2007). In-situ data represents a requirement,but there is a great absence of publicly available optical data in the Mediterranean Sea.Here, we use new Rrs-IOP data from two oceanographic cruises performed in threedifferent areas of the Mediterranean Sea: the Tyrrhenian Sea, the Ionian Sea and theAdriatic Sea, adding up to a total of 95 stations.

CONTACT Jaime Pitarch j.pitarch@isac.cnr.it Istituto di Scienze dell’Atmosfera e del Clima (ISAC)-CNR, ViaFosso del Cavaliere 100, 00133 Rome, Italy

REMOTE SENSING LETTERS, 2016VOL. 7, NO. 6, 591–600http://dx.doi.org/10.1080/2150704X.2016.1171922

© 2016 Informa UK Limited, trading as Taylor & Francis Group

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The QAA (Lee, Carder, and Arnone 2002) retrieves spectral absorption a(λ) andparticulate backscatter bbp(λ), where λ is the wavelength in vacuum. Hereafter, werefer the newest version QAA V6 (Lee and Huot 2014) as simply QAA. It is a multi-levelalgorithm that concatenates a sequence of empirical, analytical and semi-analyticalsteps. First, an analytical Rrs-IOP model is inverted. Second, separated combination ofempirical and analytical relationships are applied to estimate a(λ) and bbp(λ) (Lee, Carder,and Arnone 2002; Lee, Carder, and Du 2004; Lee et al. 2011; Lee 2014).

Former published works suggested a great bbp overestimation by the QAA. Huot et al.(2008) compared satellite chl (chlorophyll concentration; OC3M algorithm) to QAA-retrieved bbp. The resulting scatter plot (their Figure A1) was far above an independentchl–bbp relationship from in-situ data. For bbp < 10–3 m−1, the scatter cloud appearedabove ~200% the in-situ relationship, tending to reduce the distance for higher bbpvalues. This result indirectly suggests great QAA overestimation, although other factorshad an effect, like chl algorithm or atmospheric correction issues. Brewin et al. (2012)reported similar results. These cited studies lacked in-situ bbp, which was replaced by anestimation from satellite-derived chl and application of a bio-optical model chl-bbp.Elsewhere (Mélin et al. 2011), application of the QAA to satellite Rrs showed a bias of+16.4% respect to in-situ bbp in the Adriatic Sea. Input Rrs were from satellite, whichprevented the estimation of the part of the error that is solely due to the QAA. Using thefully in-situ data set NOMAD (Werdell and Bailey 2005), a + 38% bbp(443) overestimationby the QAA respect to the measured value was reported (Werdell et al. 2013).With in-situdata, a bias +2.5–8.8% was found for the QAA-derived bbp(λ) in artic waters, and +9.5%to +16.4% in low-latitude waters (Zheng, Stramski, and Reynolds 2014). Higher errors forclear waters than for more turbid or eutrophic were found. Other studies showed severeissues for extremely clear (Lee and Huot 2014) and turbid (Zhu and Yu 2013) waters. TheQAA depends on empirically derived coefficients despite being an IOP-based algorithm.To date there is not a single study documenting QAA performance in the MediterraneanSea fully based on in-situ data. We focus onto one question: how accurately can thebackscattering coefficient be retrieved in the Mediterranean Sea using several versionsof the QAA, and which are the major sources of errors in this retrieval.

2. Methods

2.1. Backscattering retrieval with the QAA

We study two versions of the QAA that differ in how Rrs and the IOPs relate, that is the‘Rrs-IOP model’. In the ‘old’ model, the sub-surface reflectance rrs (Lee, Carder, andArnone 2002) has a quadratic dependence on the quasi-single scattering albedo:

rrs ¼ g0uþ g1u2 (1)

Here, u = bb/(a + bb) and bb is the total backscattering equal to that of particles (bbp)and seawater (bbw), bb = bbw + bbp. The coefficients (g0, g1) are second-order quantitiesand depend little on both a and bb. Instead, they are more dependent on the phasefunction and illumination conditions. Several values for (g0, g1) have been published(Gordon et al. 1988; Lee et al. 1999; Lee, Carder, and Arnone 2002; Aurin and Dierssen2012). See also the short review provided by Li et al. (2013).

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Lee, Carder, and Du (2004) pointed out that the ‘old’ model is ambiguous withrespect to the phase function: different proportions of water and particle backscatteringcould be found such that that the same u is obtained. However, as the total phasefunction would be different, different (g0, g1) values would be needed for each case. Tosolve this issue, they developed a new Rrs-IOP model, separating between uw and up,where uw = bbw/(a + bb) and up = bbp/(a + bb). Lee et al. (2011) developed an invertibleRrs-IOP model, called ‘new’ in this article.

Rrs ¼ Gw0 uw þ Gw

1 u2w þ Gp

0up þ Gp1u

2p (2)

The Hydrolight software (Mobley and Sundman 2008) was used to simulate reflec-tances from a synthetic IOP data set, from which the coefficients ðGw

0 ;Gw1 ;G

p0 ;G

p1Þ ¼

ð0:0604; 0:0406; 0:0402; 0:1310Þ were obtained.

2.2. Raman scattering effect correction

The QAA was designed neglecting Raman scattering, but this has an effect on Rrs and mustbe taken into account. In fact, Lee and Huot (2014) estimated a mean overestimation of theretrieved bbp by ~0.00022m

−1 if Raman effects were neglected. Lee et al. (2013) presented asimple empirical correction that should be applied to Rrs prior to QAA inversion:

Rrs;corr λð Þ ¼ Rrs λð Þ1þ F λð Þ (3)

where Rrs,corr(λ) stands for Raman-corrected Rrs(λ). The factor F(λ) (Lee et al. 2013) is

F λð Þ ¼ α λð Þ Rrs 443ð ÞRrs 555ð Þ þ β1 λð ÞRrs 555ð Þβ2 λð Þ (4)

2.3. In-situ data

Data belong to two field campaigns (Figure 1): the first one (wb13) was conducted inApril 2013 in the Tyrrhenian Sea. The second one (cs15) was conducted in April 2015 inthe Ionian and Adriatic Seas. We differentiate between open waters and coastal watersby setting the threshold Rrs(664) = 4 × 10–4 sr−1. Optically, the stations range from veryoligotrophic at the Ionian Sea towards mesotrophic at the Tyrrhenian and lower AdriaticSea to eutrophic waters at the northern Adriatic Sea. In turn, coastal waters are stronglyinfluenced by river run-off and sediment resuspension.

Measurements were normally performed between 8:30 h and 16:00 h UTC, encompass-ing conditions from clear sky to fully cloudy. IOPs and Rrs were collected sequentially at eachstation, with a maximum delay of ~1 hour and ship drift of maximum few hundreds ofmetres. This methodology might have an effect in coastal waters, where waters are morepatchy, which further motivates the differentiation of derived statistics by water type.Hyperspectral absorption and attenuation at visible wavelengths were measured with anac-s (WET Labs, Inc.) and corrected following standard NASA recommendations, includingcorrection for differences in temperature and salinity, drift correction and residual scatter ofthe absorption tube correction (Pegau et al. 2003). Backscattering was measured with anECO-VSF3 (WET Labs, Inc.) at wavelengths 470, 530 and 660 nm. bbp(555) was estimated

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after subtracting backscattering of particle-free sea water (Zhang, Hu, and He 2009) andspectrally interpolating with a power law. IOPs were vertically averaged from the surfaceuntil the deepest point available, always deep enough to ensure negligible truncationeffects. The function K(λ,z) = a(λ,z) + bb(λ,z) was used as a rough estimation of the diffuseattenuation coefficient (Lee, Du, and Arnone 2005), where z and z’ are depth in the watercolumn, increasing downwards. The weighting function

f λ; zð Þ ¼ exp �2ð0zK λ; z0ð Þ dz0

� �(5)

was used to obtain representative quantities for remote sensing in the case of a non-homogeneous water column (Gordon and Clark 1980). Bottom effects were assumed tobe negligible. Radiometry was performed with OCR-507 radiometers (Satlantic, Inc.), withbands centred at the bands 412, 443, 490, 510, 556, 665, 865 nm. In-water upwellingradiance at nadir (Lu) sensor was mounted onto a free-falling T-shaped structure, withthe multicast technique. Above-water downwelling irradiance (Ed) sensor was mountedat the top of the ship’s deck. Data were processed and Rrs was derived followingstandard NASA protocols (Pegau et al. 2003; Zibordi, D’Alimonte, and Berthon 2004).

In-situ Rrs and vertically weighted IOPs (non-water absorption anw = a − aw andparticle backscattering bbp, aw is absorption of pure water) are shown in Figure 2. Inopen (and clearer) waters, the expected step-wise shape for Rrs can be seen, while incoastal waters (more turbid and productive), the overall magnitude increases and aspectral peak in the green tends to develop. In these coastal waters, productivity ishigher, as evidenced by the secondary absorption peak at ~676 nm. In its turn, bbpshows the classic power-law-like spectral shape, at least for the three availablewavelengths.

5° E 10° E 15° E 20° E35° N

40° N

45° N

Ionian Sea

Adriatic Sea

Tyrrhenian Sea

Figure 1. Study area with measurement stations. Cruise wb13 (N = 35 stations) of 2013 in theTyrrhenian Sea. Cruise cs15 (N = 58 stations) of 2015 in the Ionian and Adriatic Seas. Coastal andopen waters are divided based on the threshold Rrs(664) = 4 × 10–4 sr−1. Dot colours are: wb13-openin blue, cs15-open in red, wb13-coastal in green and cs15-coastal in brown.

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2.4. Statistics

Backscattering retrievals were compared in-situ measurements via the following statistics:Mean relative bias and mean relative root-mean square error:

bias ¼ 1N

XNi¼1

yi � xixi

; RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1N

XNi¼1

yi � xixi

� �2vuut (6)

Here, xi stands for the in-situ bbp(555), whereas yi is the value retrieved by the QAA. Thebest linear fit by the least squares method was calculated. The corresponding coefficientof determination (R2), slope (m) and intercept (n) are also shown.

3. Results

The ‘old’ QAA was applied to our Rrs data to derive bbp(555) (until made explicitbelow, the ‘old’ model is applied). Results (statistics in Table 1) highlight a QAAunderestimation of ~2% with respect to in-situ bbp(555), and RMSE ~19%. Statisticsare presented for all data, and also separated by cruise and water type. With the firstseparation, we detect any possible deviation caused by instrument calibration. Withthe second separation, we explore possible different behaviour of both QAA and in-situ data caused by water type. RMSE is higher in coastal waters. Here, the largestsource of errors is mismatch between water type measured by the IOP package and

Table 1. Statistics of bbp inversion with QAA, old Rrs model and standard QAA coefficients, Ramanscattering not corrected. ‘wb13’ stands for measurements of 2013, ‘cs15’ are measurements of 2015,‘Open’ are measurements in open waters and ‘Coastal’ are in coastal waters.

R2 Bias (%) RMSE (%) m n

All, N = 93 0.93 −2.1 19.2 0.89 0.0003wb13, N = 35 0.93 −3.7 17.0 0.70 0.0014cs15, N = 58 0.94 −1.1 20.5 0.92 0.0002Open, N = 45 0.58 1.4 15.1 0.51 0.0013Coastal, N = 48 0.90 −5.3 22.4 0.89 0.0005

400 500 600 7000

0.005

0.010

0.015

0.020

λ (nm)

Rrs

(sr-1

)

400 500 600 7000

0.1

0.2

0.3

0.4

λ (nm)

a nw (m

-1)

400 500 600 7000

0.02

0.04

λ (nm)

b bp (m

-1)

Figure 2. In-situ remote-sensing reflectance (Rrs), non-water absorption (anw) and particle back-scattering (bbp) spectra. Cruise wb13 (N = 35 stations) of 2013 in the Tyrrhenian Sea. Cruise cs15(N = 58 stations) of 2015 in the Ionian and Adriatic Seas. Coastal and open waters are divided basedon the threshold Rrs(664) = 4 × 10–4 sr−1. Curve colours are: wb13-open in blue, cs15-open in red,wb13-coastal in green and cs15-coastal in brown.

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the radiometers. The QAA tends from slight overestimation (+1%) at open waters tounderestimation (−5%) at coastal waters.

Posteriorly, measured Rrs are Raman-corrected and the QAA is applied again. Table 2shows resulting statistics. Related scatter plots are graphically shown in Figure 3(a,b).The application of Raman Scattering correction results in a smaller retrieved bbp. Thus,biases are made more negative so match is worsened. However, we have applied theQAA here to a Rrs theoretically unaffected by Raman Scattering, as assumed in thealgorithm development. Thus, in Table 1 retrieval overestimation due to not consideringRaman scattering was compensating QAA underestimation.

On the other hand, the sources of error in the bbp retrieval are two: first, the Rrs-IOP model (Equation (1) or Equation (2)), and second, how the contributions ofscattering and absorption are separated. To distinguish between these error sources,we have replaced the QAA-estimated u with the actually measured u, and thenapplied the QAA only to separate between a and bb. Statistics (not shown) presenteda bias ~0% and RMSE was reduced to less than half with respect to Table 2. Thus, thelargest error source in the bbp retrieval lays in the Rrs-IOP model. Consequently, werecommend efforts to be focused here so that errors are reduced to the minimumpossible.

As an attempt to find a more regionalized old Rrs-IOP model, we have found thebest quadratic fit between rrs and u, forcing the intercept to zero (hereafter, thecorrection for Raman scattering according to Lee et al. (2013) is always performed).Resulting coefficients are (g0, g1) = (0.0920, 0.0191), R2 = 0.89. Our (g0, g1) values areable to reduce biases; see Table 2 and graphics in Figure 3(c,d). Improvement is minor

Table 2. Statistics of bbp inversion with QAA, old and new Rrs models. Rrs previously corrected forRaman scattering effects (Lee et al. 2013). ‘wb13’ stands for measurements of 2013, ‘cs15’ aremeasurements of 2015, ‘Open’ are measurements in open waters and ‘Coastal’ are in coastal waters.

R2 Bias (%) RMSE (%) m n

Old Rrs model, standard coefficientsAll, N = 93 0.93 −7.1 20.0 0.87 0.0002wb13, N = 35 0.93 −8.5 17.9 0.68 0.0012cs15, N = 58 0.94 −6.2 20.7 0.90 7.3 × 10–5

Open, N = 45 0.58 −5.4 15.3 0.50 0.0011Coastal, N = 48 0.90 −8.7 23.0 0.87 0.0003

Old Rrs model, optimized coefficientsAll, N = 93 0.92 −1.4 20.8 0.93 0.0003wb13, N = 35 0.90 −3.2 17.4 0.70 0.0014cs15, N = 58 0.93 −0.3 22.6 0.97 0.0002Open, N = 45 0.58 −2.5 14.6 0.53 0.0011Coastal, N = 48 0.88 −0.4 25.2 0.91 0.0008

New Rrs model, standard coefficientsAll, N = 93 0.94 −5.2 18.6 0.90 0.0001wb13, N = 35 0.95 −5.9 16.6 0.73 0.0011cs15, N = 58 0.94 −4.7 19.7 0.93 −1.5 × 10–5

Open, N = 45 0.58 −3.3 14.7 0.53 0.0011Coastal, N = 48 0.91 −6.9 21.6 0.90 0.0001

New Rrs model, optimized coefficientsAll, N = 93 0.93 1.2 21.0 0.99 9.3 × 10–5

wb13, N = 35 0.92 0.05 17.4 0.77 0.0013cs15, N = 58 0.94 1.9 22.9 1.05 −8.051 × 10–5

Open, N = 45 0.58 −1.5 14.8 0.58 0.0010Coastal, N = 48 0.89 3.8 25.5 0.98 0.0005

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in open waters, as a change in the coefficients has a higher effect at high u values, thatis in coastal areas.

Next, we evaluate the ‘new’ Rrs-IOP model (Equation (2)). Input Rrs is previouslycorrected for Raman scattering. Results appear improved (Figure 4(a,b)) with respectto the old Rrs-IOP model (Figure 3(a,b)).

Although the presented results would be satisfactory in the evaluation of an algo-rithm, we have attempted a regionalization of the coefficients also here. Our last resultstarts from the new Rrs–IOP relationship. The optimization is multilinear in this case, withðGw

0 ;Gw1 ;G

p0 ;G

p1Þ as optimizable coefficients. In principle, ðGw

0 ;Gw1 Þ are most dependent

(but not exclusively) on the properties of pure water. We therefore have left their valuesunchanged and set ðGp

0 ;Gp1Þ as optimizable. Our results areðGp

0 ;Gp1Þ ¼ ð0:0425; 0:0458Þ,

R2 = 0.89. Table 2 and Figure 4(c,d) show results for this slight optimization of the ‘new’Rrs-IOP model. In general, the small underestimation found for Lee’s coefficients iscompensated. Contributions by the different error sources to RMSE are always additive.The final RMSE of ~20% seems rather good.

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(c) (d)

Figure 3. Backscattering bbp(555), old Rrs model, Raman corrected, compared to in-situ backscatter-ing. Cruise wb13 (N = 35 stations) of 2013 in the Tyrrhenian Sea. Cruise cs15 (N = 58 stations) of2015 in the Ionian and Adriatic Seas. Coastal and open waters are divided based on the threshold Rrs(664) = 4 × 10–4 sr−1. (a) and (b) Using standard (g0,g1) coefficients; (c) and (d) using optimizedcoefficients; (a) and (c) scatter cloud and 1:1 line; (b) and (d) relative retrieval error. Dot colours are:wb13-open in blue, cs15-open in red, wb13-coastal in green and cs15-coastal in brown.

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The Hydrolight simulations used to calibrate the QAA, in the old and new formula-tions, assumed a cloud-free sky. As resulting coefficients are dependent on theseboundary conditions, it is worth questioning whether or not QAA application to in-situRrs-IOP matchups might lead to biased results. For this reason, we have selected stationswith a cloud cover not higher than 2/8. QAA application to these stations (N = 50) leadsto R2 = 0.93, bias = 1.0% and bias = 20.0% for the ‘old’ model, and R2 = 0.93, bias = 3.2%and 20.0% for the ‘new’ model, in both cases, using the standard coefficients. Comparingthese to Table 2, bias becomes more positive ~+8%, while RMSE remains fairlyunchanged. However, it is not possible to guess how much of this change in thestatistics is caused by algorithm functioning or by data set subsampling, given its limitedsize.

4. Conclusions

The range of bbp(555) values presented here (1.4 × 10–3 m−1 to 6 × 10–2 m−1) encom-passes the majority of cases to be found in oceanic and coastal waters (Antoine et al.

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) ret

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(c) (d)

Figure 4. Backscattering bbp(555) retrieval with QAA, new Rrs model, Raman corrected, compared toin-situ backscattering. Cruise wb13 (N = 35 stations) of 2013 in the Tyrrhenian Sea. Cruise cs15(N = 58 stations) of 2015 in the Ionian and Adriatic Seas. Coastal and open waters are divided basedon the threshold Rrs(664) = 4 × 10–4 sr−1. (a) and (b) Using standard ðGp

0; Gp1Þ coefficients; (c) and (d)

using optimized coefficients; (a) and (c) scatter cloud and 1:1 line; (b) and (d) relative retrieval error.Dot colours are: wb13-open in blue, cs15-open in red, wb13-coastal in green and cs15-coastal inbrown.

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2011). The ‘new’ and ‘old’ Rrs-IOP models are able to provide reasonably low biases, andregional calibrations are possible if sufficient in-situ data are available. Statistics aresomewhat altered when only cloud-free stations are selected, but in any case, thehypothesis of high bbp(555) overestimation in the Mediterranean Sea is rejected. TheQAA appears suitable for backscattering retrieval in the Mediterranean Sea as far as ouranalysis indicates.

Acknowledgments

The crew of the research vessel ‘Minerva Uno’ is thanked for their support during field work.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This research has received funding from the European Union Seventh Framework Programmethrough HORIZON 2020 [grant number 210129802] (Copernicus Marine environment monitoringservice). M.B. is funded by the RITMARE PhD fellowship at the ISAC-CNR.

References

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Aurin, D. A., and H. M. Dierssen. 2012. “Advantages and Limitations of Ocean Color RemoteSensing in CDOM-Dominated, Mineral-Rich Coastal and Estuarine Waters.” Remote Sensing ofEnvironment 125: 181–197. doi:10.1016/j.rse.2012.07.001.

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