Yangang Ren

François Bernard

Véronique Daële

Abdelwahid Mellouki
email: mellouki@cnrs-orleans.fr

Atmospheric fate and impact of perfluorinated butanone and pentanone

Keywords: perfluorinated ketones, UV absorption spectrum, IR absorption spectrum, photolysis rates, natural irradiation, atmospheric lifetime, global warming potential

Perfluoroketones, used as replacement to halons and CFCs, are excluded from the Montreal Protocol because they are considered as non-ozone depleting substances.

However, their chemical structure makes them possible greenhouse gases if their atmospheric lifetimes are long enough. To assess that possibility, we investigated the photolysis of perfluoro-2-methyl-3-pentanone (PF-2M3P), and perfluoro-3-methyl-2butanone (PF-3M2B) using outdoor atmospheric simulation chambers. In addition, the photolysis of a non fluorinated pentanone (2-methyl-3-pentanone, 2M3P) was studied.

The results showed that photolysis is the dominant loss pathway of PF-2M3P and PF-3M2B in the troposphere whereas 2M3P is lost by both photolysis and gas phase reaction with atmospheric oxidants. The photolysis effective quantum yields of PF-2M3P, PF-3M2B and 2M3P were estimated and some of the main products identified.

The photolysis of PF-2M3P and PF-3M2B was found to have a minor impact on the atmospheric burden of fluorinated acids. The atmospheric lifetimes of PF-2M3P, PF-3M2B and 2M3P were estimated to 3-11 days, 13 days and 1-2 days, respectively.

Combining the obtained data, it has been concluded that with 100-year time horizon global warming potentials (GWP100) equivalent to <0.21, ~0.29 and ≤1.3×10 -7 for PF-2M3P, PF-3M2B and 2M3P, respectively, these compounds will have a negligible impact on global warming.

Introduction

Along with hydrofluorocarbons (HFCs), perfluorocarbons (PFCs) are non-ozone depleting substances and therefore excluded from the Montreal Protocol. [START_REF] Forrest | Pool Boiling Heat Transfer Performance of a Dielectric Fluid With Low Global Warming Potential[END_REF] However, they are considered as greenhouse gases due to their strong absorption in the infrared spectral region in the atmospheric window combined to their long atmospheric lifetimes. [START_REF] Yao | In-situ measurements of atmospheric hydrofluorocarbons (HFCs) and perfluorocarbons (PFCs) at the Shangdianzi regional background station, China[END_REF] Their atmospheric concentrations have been growing rapidly over last decades and potentially continue to grow. [START_REF] Schaefer | Estimating Future Emissions and Potential Reductions of HFCs, PFCs, and SF₆[END_REF] They have been widely used for the cooling of power electronics over the last decade. Perfluoroketones such as perfluoro-2-methyl-3-pentanone (PF-2M3P, C2F5C(O)CF(CF3)2, Novec 649/1230) and perfluoro-3methyl-2-butanone (PF-3M2B, C2F5C(O)CF(CF3)2, Novec5110) are among the important replacement chemicals to halons and CFCs [START_REF] Hyrenbach | Alternative gas insulation in medium-voltage switchger[END_REF][START_REF] Taniguchi | Atmospheric Chemistry of C2F5C(O)CF(CF3)2: Photolysis and Reaction with Cl Atoms, OH Radicals, and Ozone[END_REF] . PF-2M3P and PF-3M2B are advanced heat transfer perfluorocarbons with high dielectric strength. Up to 30 t of PF-2M3P could be released into the atmosphere each year from fire-protection systems [START_REF] Jackson | Atmospheric Degradation of Perfluoro-2-methyl-3-pentanone: Photolysis, Hydrolysis and Hydration[END_REF] . PF-3M2B is being used as versatile insulating gas for medium and high voltage applications including gas insulated lines, gas insulated switchgear and circuit breakers. [START_REF] Hyrenbach | Alternative insulation gas for medium-voltage switchgear[END_REF] The large production and usage of both chemicals are likely to induce their direct emission into the atmosphere.

Similarly to other volatile organic compounds, PF-2M3P and PF-3M2B may be potentially removed from the atmosphere through photolysis, gas phase chemical reactions with the main atmospheric oxidants, hydrolysis and deposition. The atmospheric fate of PF-2M3P has been subject to a limited number of investigations.

Photolysis studies were based on the use of artificial and natural irradiations. [START_REF] Taniguchi | Atmospheric Chemistry of C2F5C(O)CF(CF3)2: Photolysis and Reaction with Cl Atoms, OH Radicals, and Ozone[END_REF][START_REF] Mu | The near-UV absorption cross sections for several ketones[END_REF][START_REF] Ren | Investigation of the reaction of ozone with isoprene, methacrolein and methyl vinyl ketone using the HELIOS Chamber[END_REF] The atmospheric lifetime of PF-2M3P has been found to be controlled by photolysis and reported to be in the range of 4-14 days depending on latitude and period of the year. [START_REF] Jackson | Atmospheric Degradation of Perfluoro-2-methyl-3-pentanone: Photolysis, Hydrolysis and Hydration[END_REF] The gas phase reactions with OH radical and ozone as well as hydrolysis represent minor contribution to the total removal of PF-2M3P from the atmosphere. [START_REF] Taniguchi | Atmospheric Chemistry of C2F5C(O)CF(CF3)2: Photolysis and Reaction with Cl Atoms, OH Radicals, and Ozone[END_REF][START_REF] Jackson | Atmospheric Degradation of Perfluoro-2-methyl-3-pentanone: Photolysis, Hydrolysis and Hydration[END_REF] To the best of our knowledge, no experimental data on the photolysis of PF-3M2B have been reported. Hence, the present work aims at investigating the photolysis of PF-3M2B under atmospheric conditions and improving the existing data on PF-2M2B in order to evaluate their atmospheric impacts. In addition to the two perfluorinated ketones, a nonfluorinated analogue aliphatic ketone to PF-2M3P, 2-Methyl-3-pentanone (2M3P, C2H5C(O)CH(CH3)2) has been investigated. The UV-Visible and infrared (IR) absorption spectra of PF-2M3P, PF-3M2B and 2M3P were measured. Their photolysis rates were determined using two complementary atmospheric simulation chambers with natural sunlight irradiation. Atmospheric lifetimes and global warming potentials (GWP) for the three studied compounds are reported and discussed in terms of their atmospheric impacts.

Experimental Section

UV absorption spectra

The apparatus used in this work has been described in previous studies [START_REF] Mu | The near-UV absorption cross sections for several ketones[END_REF] and is briefly presented here. The UV-Visible absorption spectra of PF-2M3P, PF-3M2B, and 2M3P were measured using a spectrophotometer equipped with a 1200 grooves mm -1 grating and a charge-coupled device (CCD) camera. The collimated output of a 30 W deuterium lamp passed through a 100 cm long and 2.5 cm diameter Pyrex absorption cell equipped with quartz windows and focused onto the entrance slit of the spectrometer. Measurements were made over the wavelength region 220-400 nm by recording typically three overlapping regions of about 15 nm. Typically, each measurement consisted of 8-13 scans of diode array. The wavelength scale was calibrated using the emission lines from a low-pressure Hg pen ray lamps (253.7, 313.2, and 365 nm). Absorption cross sections, 𝜎(𝜆) (in cm 2 molecule -1 ) were obtained using the Beer's law:

𝜎(𝜆) = -𝑙𝑛[𝐼(𝜆) 𝐼 0 ⁄ (

Atmospheric simulation chambers

Photolysis studies of PF-2M3P, PF-3M2B and 2M3P were conducted in the large simulation chamber HELIOS. In addition, the photolysis of PF-2M3P was also investigated in a 3.4 m 3 Teflon outdoor chamber. Both HELIOS and the 3.4 m 3 Teflon outdoor chambers allowed photolysis experiments to be performed under natural solar exposure.

HELIOS

The facility consists of a 90 m 3 hemispherical outdoor simulation chamber (47°50'18.39N; 1°56'40.03E) made of FEP Teflon film. This facility has been described previously. [START_REF] Ren | Investigation of the reaction of ozone with isoprene, methacrolein and methyl vinyl ketone using the HELIOS Chamber[END_REF] The light transmission ranges from 88 to 95% over the entire solar spectrum. Two fans installed in the chamber ensure a rapid mixing of reactants PF-2M3P and 2M3P were introduced into the chamber by placing known volumes of liquid in a bubbler and then, flushed by purified air. Their concentrations were derived based on the volume of the liquid introduced, the pressure and the temperature in the chamber using the ideal gas law. PF-3M2B and SF6 were introduced into the chamber by streaming purified air through a calibrated stainless steel cylinder (4.87 L) equipped with capacitance manometers. To compensate sampling flows from analytical instruments and chamber leaks, a flow of purified air (15-25 L/min) was added continuously during all experiments enabling a slight overpressure to be maintained, thus avoiding any contamination from outside air. Dilution of the gas volume in the chamber was determined by monitoring the decay of introduced amount of SF6

(monitored by FT-IR). This decay under dark conditions was found to be in the range of (5 -20) × 10 -6 s -1 .

Background concentrations in the chamber were systematically found to be below the detection limits of analytical instruments (e.g., [NOx]2.5×10 10 , [O3]2.5×10 10 ,

[VOC] 1.3×10 8 molecule cm -3 ).

3.4 m 3 outdoor chamber

Photolysis studies of PF-2M3P were also performed in the 3.4 m 3 ICARE outdoor atmospheric simulation chamber made of ethylene tetrafluoroethylene (ETFE) foil. The light intensity was continuously monitored using a filter radiometer measuring the photolysis frequency of NO2, JNO2 (Meteorologie consult Gmbh, Germany). The temperature and the relative humidity were also continuously measured using a combined probe (Vaisala HMT330 series transmitters). Chemical analysis of the gas mixture was characterized by an infrared spectrometer (Nicolet 550 Magna FT-IR spectrometer) coupled to a White-type multi-pass mirror cell (optical path length 10 meters). Infrared spectra were recorded every 5 minutes by co-adding 130 interferograms at a resolution of 1 cm -1 . Rapid mixing of reactant was insured using a fan made of Teflon mounted into the chamber. The dilution rate was estimated by monitoring the loss of SF6. IR reference spectrum of PF-2M3P was obtained by introducing a known volume of liquid in the chamber. During dark experiments, the chamber was covered by a black and opaque curtain to protect it from sunlight radiation.

The curtain could be removed very quickly for exposure to solar radiation, thus initiating the photolysis process. Experiments were performed at 1013 mbar of purified air and in the temperature range of 306 to 319 K. Initial concentrations of PF-2M3P

were in the range of (0.89-2.7) × 10 14 molecule cm -3 . The gas mixture was exposed to solar irradiation for up to 4 hours.

Photolysis experiments

Under sunlight conditions, the investigated ketones, PF-2M3P, PF-3M2B and 2M3P may be removed by photolysis, dilution and wall loss processes following the reactions:

ketones + h → products J (1)
ketones → dilution and wall loss kL (2)

SF6 → dilution kd ( 3
)
where J (in s -1 ) is their photolysis rate while kL (in s -1 ) is their decay rates under the dark including dilution and wall loss. Under irradiation, the total decays of the investigated ketones are expressed as follows:

ln([ketone]0/[ketone]t) = ktot × t Eq. 2
with [ketone]0 and [ketone]t are the concentrations of PF-2M3P or PF-3M2B or 2M3P at times t0 and t, respectively. ktot (in s -1 ), the total decay rate of the studied compound under irradiation, is formulated as:

ktot = Jmeas + kd,light + (kL-kd,dark) Eq. 3
Jmeas is the photolysis rate obtained from the experiment measurement. kd,dark and kd,light (in s -1 ) are, respectively, the dilution decay rates obtained from SF6 decay in the dark and during irradiation.

The atmospheric photolysis rate coefficient was calculated, Jcalc, as follows:

Jcalc= ∫()()F()d ( = 290-400 nm) Eq. 4

where (), () and F() are the absorption cross-section, the quantum yield of dissociation and the actinic flux over the absorption 290 to 400 nm, respectively. The actinic flux was directly measured by the spectroradiometer placed inside the chamber.

Assuming a quantum yield of unity for the photodissociation process along the absorption region of PF-2M3P or PF-3M2B or 2M3P, the maximum photolytic rate coefficient can be calculated, Jmax = Jcal using Eq. 4. As a result, an effective photodissociation quantum yield can derived: eff = Jmeas/Jmax Eq. 5

Chamber loss correction

The concentrations of the products formed from the photolysis of PF-2M3P, PF-3M2B and 2M3P were corrected to account for dilution and possible photolysis/OH reactions under irradiation using the following equation: 10

[Product]corrected = [Product]measured × F Eq. 6
with F being the correction factor:

F = 1 + Δ[Product]/ [Product]measured
The amount of product lost, Δ[Product] due to secondary reactions, i.e., dilution, reaction with OH radical and photolysis processes is calculated from:

Δ[Product] = ∫(kd,light + Jproduct + [OH]*k) × [Product]measured × dt Eq. 7
The losses of CF3COF, COF2 and CO were only due to dilution and were corrected using F < 1.2. For HCHO, CH3CHO and CH3COCH3, photolysis, reaction with OH radical and dilution were considered and FHCHO < 1.52, FCH3CHO < 1.35 and FCH3COCH3 < 1.30 were used for the corresponding corrections. JHCHO measured by the spectoradiometer and JCH3CHO and JCH3COCH3 were calculated using Eq. 4;

corresponding σ(λ) and Φ(λ) values for CH3CHO and CH3COCH3 were taken from IUPAC database [START_REF] Atkinson | Evaluated kinetic and photochemical data for atmospheric chemistry: Volume II – gas phase reactions of organic species[END_REF] . The OH rate coefficients of CO, HCHO, CH3CHO and CH3COCH3

were extracted from IUPAC kinetic database 11 as 1.65×10 -13 , 8.5×10 -12 , 1.5×10 -11 and 1.8×10 -13 cm 3 molecule -1 s -1 at T = 298 K.

Infrared absorption spectra

The spectra of PF-2M3P, PF-3M2B, and 2M3P were measured at 295±1 K using Fourier transform infrared (FTIR) spectroscopy. Absorption spectra were recorded in 250 co-adds between 700 and 4000 cm -1 at 1 cm -1 resolution (Happ-Genzel apodization).

A Whyte-type multi-pass absorption cell with 10 meters optical path length (KBr windows) was used in the course of these measurements. Absorption spectra, A()

(base e), (or integrated band strengths) were determined using Beer's law:

A() = () × L × [Ketones] Eq. 8
where () is the infrared absorption cross section of the ketones at wavenumber ν, L is the absorption path length, and [ketones] is the PF-2M3P, PF-3M2B, and 2M3P concentration. Measurements were performed using the following concentration ranges (in units of molecule cm -3 ): (1.2-10.8) ×10 [START_REF] Yu | Atmospheric Chemistry of Perfluoro-3-methyl-2butanone[END_REF] for PF-2M3P, (1.6-9.9)×10 [START_REF] Yu | Atmospheric Chemistry of Perfluoro-3-methyl-2butanone[END_REF] for PF-3M2B and (0.6-4.8) ×10 [START_REF] Yu | Atmospheric Chemistry of Perfluoro-3-methyl-2butanone[END_REF] for 2M3P. Over the course of the study, replicate measurements were performed using independently prepared gas mixtures with helium as bath gas.

The absorption spectra (band strengths) were obtained from a linear least-squares fit of A versus [Ketones] that included at least 6 individual spectrum measurements.

Chemicals

The chemicals used in this work and their stated purities were as follows:

perfluoro-2-methyl-3-pentanone (99%, 3M Belgium N.V, Chemical Group-EBC), 2-methyl-3-pentanone (97%, Sigma-Aldrich), perfluoro-3-methyl-2-buytanone (98%, Ugarit Chimie), SF6 (99.9995%, Air Liquide) and O2 (99.9995%, Air Liquide), Helium (99.9995%, Air Liquide). PF-2M3P, PF-3M2B and 2M3P samples were further purified by using several freeze-pump-thaw cycles. GC-MS analysis of the samples did not show any observable impurities.

Results and Discussion

UV absorption cross section

To test the accuracy of the measurement methodology used in this work, the UV absorption spectrum of acetone has been measured and compared to the recommended UV spectrum from NASA/JPL evaluation. [START_REF] Burkholder | Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies[END_REF] As shown in SI (Figure S1), the level of agreement between both measured and recommended spectra is high, within the measurement accuracy of the recommended UV-Vis absorption spectra (8%). This excellent agreement provides confidence in the reliability of the absorption cross section measurement conducted in this work.

The measured UV-Visible absorption spectra of PF-2M3P, PF-3M2B and 2M3P between 220 and 400 nm at (300 ± 2) K are depicted in Figure 1 and absorption cross sections are provided in Table S1. The quoted uncertainties originated from 2 standard deviation (2σ) of the average of individual measurements. The measurements satisfied Beer's law over a wide concentration range (an order of magnitude). The measured absorbance, A (base e) ranged from 0.2 to 1.7 for PF-2M3P, 0.1 to 1.0 for PF-3M2B, 0.3 to 2.0 for 2M3P. Corresponding graphical representations of Beer's law fits are given in Figure S2.

2M3P shows a maximum absorption at 284 nm (σ(284 nm) = (6.99 ± 0.28) × 10 -20 cm 2 molecule -1 ) while PF-2M3P shows a maximum around 305 nm (σ(305 nm) = (6.50 ± 0.28) × 10 -20 cm 2 molecule -1 ) and PF-3M2B exhibits a maximum absorption at 300 nm (σ(300 nm) = (3.46 ± 0.15) × 10 -20 cm 2 molecule -1 ). The UV absorption spectra obtained in this work are compared with those reported in literature when possible and are presented in Figure 1. The absorption spectrum of PF-2M3P is in agreement with the reported one by Taniguchi et al., [START_REF] Taniguchi | Atmospheric Chemistry of C2F5C(O)CF(CF3)2: Photolysis and Reaction with Cl Atoms, OH Radicals, and Ozone[END_REF] within 5%. The absorption cross sections of 2M3P obtained in the present work is higher than that reported by Díaz-de-Mera, et al. [START_REF] Díaz-De-Mera | Photolysis study of fluorinated ketones under natural sunlight conditions[END_REF] by 18% (max). To the best of our knowledge, the experimental UV spectrum of PF-3M2B is reported for the first time here. Prior to this study, the UV spectrum of PF-3M2B was also determined using a theoretical approach and found to be higher compared to this work, within 27% at the maximum cross section. [START_REF] Yu | Atmospheric Chemistry of Perfluoro-3-methyl-2butanone[END_REF] The absorption band of ketones is caused by the dipole forbidden n-π* transition of the C=O group. The maximum absorption of PF-2M3P is red-shifted, i.e. around 20 nm, compared to 2M3P caused by the electronegative substituents in α-α'-positions. 15- 17 In addition, the maximum absorption of PF-2M3P is about 2 times higher than that of PF-3M2B, which is consistent with the results of Mu and Mellouki 8 who observed that the peak UV cross section increased for larger aliphatic ketones.

The actinic flux in HELIOS at 13:00 (± 5 min, local time) on 7 th of September 2013 is also displayed on Figure 1. The integrated absorption cross sections over the actinic flux region for PF-2M3P, 2M3P and PF-3M2B were determined to be 2.61×10 - 18 , 1.22×10 -18 and 1.25×10 -18 cm 2 molecule -1 , respectively, indicating that one could expect JPF-2M3P > J2M3P ≈ JPF-3M2B.

Photolysis of perfluoro-2-methyl-3-pentanone

Photolysis rate measurements. Experiments in the 3.4 m 3 outdoor chamber were conducted in June-July 2010 at (306-319) K and RH<1%. Temporal profiles of PF-2M3P and SF6 concentrations were monitored under the dark for about 4 hours. No discernible loss other than dilution has been observed; the first order decay rates of PF-2M3P and SF6 were in the order of (6.6 -8.1) × 10 -6 s -1 . The chamber was then exposed to solar radiation, thus starting the photolysis. The photolysis rate of PF-2M3P, JPF-2M3P, was obtained by considering the total loss of PF-2M3P (ktot) and that from dilution which was obtained from the loss rate of SF6 (kd) under irradiation. Experimental details and results derived from the four runs conducted are displayed in Table 1. For all experiments, the photolysis rates of NO2 were in the range of (4.4-5.5)×10 -3 s -1 . The consumed fractions of PF-2M3P from photodissociation were between 2.1 and 3.7 % and the derived photolysis rates were (1.7-2.8)×10 -6 s -1 under our experimental conditions (JNO2 = (4.4-5.5)×10 -3 s -1 ). The quoted error corresponds to 2σ obtained from the least square analysis applied on the experimental data. The estimated error on JPF-2M3P was in the range of 7-14 %.

HELIOS experiments were performed during September 2013 at T = 298 -317 K and RH<1%. SF6 and PF-2M3P concentrations were monitored by FT-IR and ATD-GC-MS for typically 2 hours in the dark and under natural irradiation for typically 4 to 7 hours. The loss rates of SF6 and PF-2M3P were found to be similar in the dark, equivalent to (4.8-6.0)×10 -6 s -1 , indicating a minor loss on the chamber wall of PF-2M3P. During irradiation, both FT-IR and ATD-GC-MS instruments showed a slightly higher disappearance rate of PF-2M3P than SF6 which indicated a possible photolysis loss of PF-2M3P (ranging from 1.7 to 7.7 %) under our experimental conditions. The photolysis rate of PF-2M3P, JPF-2M3P was determined to be (1.1-3.8)×10 -6 and (1.1-3.6)×10 -6 s -1 using Eq. 3, from FTIR and GC-MS measurements, respectively, with a recommended range of (1.1-3.8)×10 -6 s -1 (with JNO2 = (3.0-5.6)×10 -3 s -1 ). [START_REF] D'anna | Photolysis Study of Perfluoro-2-methyl-3-pentanone under Natural Sunlight Conditions[END_REF] Díaz-de-Mera, et al. [START_REF] Díaz-De-Mera | Photolysis study of fluorinated ketones under natural sunlight conditions[END_REF] who also conducted experiments under natural irradiation in Spain. In contrast, the experiments conducted under artificial irradiation using black lamps or sunlamps led to lower photolysis rate values [START_REF] Taniguchi | Atmospheric Chemistry of C2F5C(O)CF(CF3)2: Photolysis and Reaction with Cl Atoms, OH Radicals, and Ozone[END_REF] . It should be noted that the measured photolysis rate from this work agreed with the result from the TUV model [START_REF] Madronich | The Role of Solar Radiation in Atmospheric Chemistry[END_REF] run at different seasons of the year (Table S2).

The maximum photolysis rate of PF-2M3P, Jmax-PF-2M3P, was estimated using absorption cross sections and the actinic flux measured in this work (Eq. 4) and found to be in the range of (0.7-1.2)×10 -4 s -1 . Therefore, the observed photolysis rate corresponds to an effective quantum yield of ∅eff =0.015-0.035, which is in agreement with the values reported by D'Anna, et al. [START_REF] D'anna | Photolysis Study of Perfluoro-2-methyl-3-pentanone under Natural Sunlight Conditions[END_REF] and Díaz-de-Mera, et al. [START_REF] Díaz-De-Mera | Photolysis study of fluorinated ketones under natural sunlight conditions[END_REF] , 0.043±0.011 and 0.044±0.006, respectively.

Products and mechanism. Typical IR spectra obtained from the photolysis of PF-2M3P/SF6/air mixture in HELIOS are displayed in SI (Figure S3). CF3COF, COF2 and CO were identified as photolysis products by FTIR analysis from 3.4 m 3 chamber and HELIOS experiments. Perfluoro-propionic acid (CF3CF2C(O)OH, PFPrA) and trifluoro-acetic acid (CF3COOH, TFA) were also identified (m/z 69) among the photolysis products, using the NIST GC-MS library (Figure S4). Temporal profiles of PF-2M3P and its photolysis products are depicted in Figure 2.

The formation yields of products (COF2, CF3COF and CO) were obtained from a linear least-square fit applied to the experimental data as shown in Figure S5 (HELIOS)

and Figure S6 (3.4 m 3 chamber) and summarized in Table S3. The recommended formation yields of products (±2σ) from the photolysis of PF-2M3P are: (74±18)%, (193±84)%, and (204±68)% for CF3C(O)F, COF2, and CO, respectively. The carbon and fluorine budgets were estimated to (90±28)% and (57±18)%, respectively. This suggests a large fraction of unidentified fluorine-containing products. Indeed, Taniguchi, et al. [START_REF] Taniguchi | Atmospheric Chemistry of C2F5C(O)CF(CF3)2: Photolysis and Reaction with Cl Atoms, OH Radicals, and Ozone[END_REF] identified CF3O3CF3 and CF3OH as photolysis products that were not identified in the present work.

A proposed mechanism leading to the formation of the observed products from the photolysis of PF-2M3P is shown in Figure S7. The photodissociation of PF-2M3P may occur through a C-C bond cleavage in the α-position of the carbonyl group to produce perfluoroalkyl and perfluoroacetyl radicals:

CF3CF2C(O)CF(CF3)2 + h → CF3CF2 + C(O)CF(CF3)2 (4) → CF3CF2C(O) + CF(CF3)2 (5)
Perfluoroacetyl radicals are expected to either decompose to give CO and perfluoroalkyl radical:

(CF3)2CFC(O) → (CF3)2CF + CO (6) CF3CF2C(O) → CF3CF2 + CO (7)
or react with O2 leading to the corresponding peroxy radicals:

(CF3)2CFC(O)+ O2 + M → (CF3)2CFC(O)O2 (8) CF3CF2C(O) + O2 + M→ CF3CF2C(O)O2 + M (9)
The high formation yield of CO (204±68)% indicates that the thermal decomposition is an important pathway in the fate of perfluoroacetyl radical over the reaction with O2.

CF3COF and COF2, identified among the photolysis products (74±18)% and (193±84)%, respectively, might originate from the reactions of CF3CF2O2 and (CF3)2CFCO2 radicals with RO2 radicals present in the system leading to the corresponding RO radicals as (CF3)2CFCO and CF3CF2O radicals, which would thermally decompose to form CF3 radicals and the corresponding fluorinated carbonyls CF3C(O)F and COF2. [START_REF] Sehested | UV Absorption Spectrum, and Kinetics and Mechanism of the Self Reaction of CF3CF2O2 Radicals in the Gas Phase at 295 K[END_REF] In addition, CF3CF2OH and CF3OH, formed from CF3CF2O and CF3O radicals reaction with hydrogen-containing compounds present in the chamber (e.g., HCHO desorbing from the chamber walls, impurities in the air diluent, or water), were also reported to transform rapidly into COF2. [START_REF] Wallington | Atmospheric chemistry of trifluoromethoxy radicals: reaction with water[END_REF][START_REF] Young | Overtone-Induced Degradation of Perfluorinated Alcohols in the Atmosphere[END_REF]

Photolysis of 2-methyl-3-pentanone

Photolysis rate measurements. Mixtures of 2M3P/SF6/air were added into HELIOS and left in the dark typically for 2 hours before irradiation by solar light. The loss rates of SF6 and 2M3P in the dark were determined to be (4.8-6.2) ×10 -6 and (5.2-6.8) ×10 -6 s -1 , respectively. The chemical mixture 2M3P/SF6/air was then exposed to solar irradiation for typically 5-6 hours. Under these experimental conditions, the measured loss of 2M3P ranged from 3.9 to 6.3%. The determination of J2M3P from FTIR and GC-MS measurements were in good agreement, within (3-7) %. The experimental conditions and the obtained values of J2M3P are summarized in Table 1.

All the experiments were performed in the absence of OH radical scavenger to avoid spectral interferences in the mid-infrared region with the studied compounds.

Therefore, the gas phase removal of 2M3P during solar exposure might also due to the reaction of OH radicals with 2M3P in addition to its photolysis. Indeed, when the chamber was only filled with purified air and exposed to solar irradiation, separate measurements using a chemical ionization mass spectrometer (CIMS) have shown the presence of OH radicals at concentration ranging from (2.1±0.9)×10 5 occasionally up to 2×10 6 molecule cm -3 could be observed. This implied that under these conditions, the OH reaction contribution to the total loss of 2M3P would have contributed from 30% to 100%. However, it has been also observed that the disappearance rate of 2M3P

during solar exposure during this study was very comparable to those of PF-2M3P and PF-3M2B (Table 1), suggesting that the OH concentration level during these experiments was very low. Therefore, in the absence of OH radical direct measurement during this study, we preferred to be conservative and thus, recommend an upper limit for the photolysis rate of 2M3P, equivalent to (2.6±1.4)×10 -6 s -1 (with JNO2 = 5.6×10 -3 s -1 ).

Based on the integrated UV absorption spectrum over the actinic flux region, the derived maximum photolysis rate constant of 2M3P, Jmax-2M3P, was found to be (6.5-9.6)×10 -6 s -1 . Therefore, the effective photolysis quantum yield is estimated to be ∅eff =≤0.28 under tropospheric sunlight conditions.

Products and mechanism. Products were identified and quantified using FT-IR spectroscopy. The Figure S8 displays the typical spectra acquired before and after the photolysis of 2M3P. Comparison of measured calibrated IR spectra shows the presence of CH3CHO, CO, CH3COCH3 and HCHO among the oxidation products where an example of time-concentration profiles of 2M3P and its products is shown in Figure S9.

These products have been observed to be of primary origin when 2M3P was exposed to natural irradiation (Figure S10). As explained previously, derived formation yields of products, possibly accounted for both contributions of photolysis and OH reactions, were estimated to (81±18)%, (25±6)%, (90±16)% and (98±10)% for CH3CHO, HCHO, CH3COCH3 and CO, respectively. Therefore, due to unquantified contribution of OH reaction to the formation yields of products during this photolysis study, we prefer to conclude qualitatively on the formation of CH3CHO, HCHO, CH3COCH3 and CO among the photolysis products from the irradiation of 2M3P. CO formation indicating the occurrence of at least one of the decomposition channels 12 and 13:

(CH3)2CHC(O) → (CH3)2CH + CO (12) CH3CH2C(O) → CH3CH2 + CO (13)
The reaction of CH3CH2C(O)O2 with HO2 radical has been reported to lead to the formation of CH3CH2C(O)OH and O3. [START_REF] Le Crâne | Atmospheric Chemistry of Propionaldehyde: Kinetics and Mechanisms of Reactions with OH Radicals and Cl Atoms, UV Spectrum, and Self-Reaction Kinetics of CH3CH2C(O)O2 Radicals at 298 K[END_REF] However, the absence of the carboxylic acid and O3 among the photolysis products indicates that the reaction of acetyl peroxy radicals with HO2 was insignificant under our experimental conditions. CH3CH2C(O)O and (CH3)2CHC(O)O radicals are expected to decompose to form the corresponding alkyl radicals, CH3CH2 and (CH3)2CH, respectively. [START_REF] Le Crâne | Atmospheric Chemistry of Propionaldehyde: Kinetics and Mechanisms of Reactions with OH Radicals and Cl Atoms, UV Spectrum, and Self-Reaction Kinetics of CH3CH2C(O)O2 Radicals at 298 K[END_REF][START_REF] Lightfoot | Organic peroxy-radicals-kinetics, spectroscopy and tropospheric chemistry[END_REF] As shown in Figure S11, the subsequent reaction of CH3CH2 and (CH3)2CH with O2 would form the corresponding peroxy radicals, CH3CH2O2 and (CH3)2CHO2. The self-reaction of CH3CH2O2 radical would lead to the formation of CH3CH2O radical (60%) and CH3CHO + CH3CH2OH (40%). [START_REF] Burkholder | Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies[END_REF] In addition, the (CH3)2CHO2 radical selfreaction would lead to the formation of (CH3)2CHO radical (60%) and CH3C(O)CH3 + (CH3)2CHOH (40%). CH3CH2O and (CH3)2CHO alkoxy radicals are expected to react with O2 to form HCHO, CH3CHO and CH3C(O)CH3.

Photolysis of perfluoro-3-methyl-2-butanone

PF-3M2B/SF6/air mixtures were monitored for 2 hours in the dark in HELIOS.

The dark loss rates of SF6 and PF-3M2B were similar and found to be (1.1-1.3) ×10 -5 s -1 . The gas mixture PF-3M2B /SF6/air was exposed to solar irradiation for typically 5-6 hours. PF-3M2B was monitored by FTIR and PTR-TOF-MS (CF3 + and (CF3)2CF3 + ions at m/z 68.986 and m/z 168.970, respectively). The observed loss of PF-3M2B ranged from 1.3 to 2.0% depending on the solar light intensity. The obtained photolysis rate was JPF-3M2B = (9±5)×10 -7 s -1 with JNO2 = (4.2-7.7)×10 -3 s -1 . The experimental conditions and the corresponding results are summarized in Table 1. The TUV model was also used to calculate the PF-3M2B photolysis loss rates at the different period of year, ranging from 2 ×10 -7 s -1 to 1.2 ×10 -6 s -1 . No detectable formation of products was observed from the photolysis of PF-3M2B due to its low photolysis rate and to the detection limits of the analytical techniques used.

The maximum photolysis rate constant of PF-3M2B, Jmax-PF-3M2B, was estimated using the integrated UV absorption spectrum over the actinic flux region and found to be Jmax-PF-3M2B = (2.9-5.6)×10 -5 s -1 . The measured photolysis rate led to an effective photolysis quantum yield estimated to ∅ eff ≤0.037 under tropospheric sunlight conditions.

Infrared absorption and global warming potential (GWP)

The infrared absorption spectra of the PF-2M3P and PF-3M2B measured in this work are characterized by broad diffuse vibrational bands as shown in Figure 3, (digitized absorption spectra are provided in SI as .txt format). The spectra are characterized by strong absorption features in the C-F stretch regions, 1200-1400 cm -1 .

Overall, the larger perfluorinated ketones have greater peak cross sections in this region due, in part, to the greater overlap of vibrational bands. The infrared spectrum of 2M3P is also characterized by broad vibrational band, due to absorption features of C-H stretch regions. The IR spectrum of 2M3P is also characterized by a sharp absorption at 1700 cm -1 , corresponding to C=O stretch vibration (Figure 3). Corresponding graphical representations of Beer's law fits are given in Figures S12, S13 and S14.

The integrated band strengths over the 700-2000 cm -1 region were determined to be 3.68 × 10 -16 , 3.03 × 10 -16 and 1.0 × 10 -16 cm 2 molecule -1 cm -1 (base e) for PF-2M3P, PF-3M2B and 2M3P, respectively. Integrated band strengths of PF-2M3P over the 700-2000 cm -1 IR spectral region reported by Díaz-de-Mera, et al. [START_REF] Díaz-De-Mera | Photolysis study of fluorinated ketones under natural sunlight conditions[END_REF] (3.94 × 10 -16 cm 2 molecule -1 cm -1 ) and D'Anna, et al. [START_REF] D'anna | Photolysis Study of Perfluoro-2-methyl-3-pentanone under Natural Sunlight Conditions[END_REF] (4.05 × 10 -16 cm 2 molecule -1 cm -1 ) are in agreement with the present results, within 7% and 9%, respectively. To the best of our knowledge, IR spectra of PF-3M2B and 2M3P are reported for the first time in this work.

The radiative efficiencies (RE) for the investigated ketones were calculated using the experimentally measured spectra and the method given in Hodnebrog, et al. [START_REF] Hodnebrog | Global warming potentials and radiative efficiencies of halocarbons and related compounds: A comprehensive review[END_REF] . The RE values obtained in this work are 0.357, 0.304 and 1.78×10 -6 W m -2 ppbv -1

for PF-2M3P, PF-3M2B and 2M3P, respectively for atmospherically well-mixed conditions and + 10% stratospheric temperature correction.

However, the radiative forcing for the present ketones is expected to be minor due to their expected short atmospheric lifetimes, < 13 days, and low atmospheric abundances. Therefore, lifetime-adjusted RE, accounting for non-uniform horizontal and vertical mixing for very short-lived compounds, was preferred and calculated to be 0.012-0.036, ~0.036 and ≤4×10 -8 W m -2 ppbv -1 for PF-2M3P, PF-3M2B and 2M3P, respectively. Corresponding GWPs (for 100 years horizon) were found to be <0.21, ~0.29 and ≤1.3×10 -7 for PF-2M3P, PF-3M2B and 2M3P, respectively, showing a minor contribution of the studied ketones to the global warming potential. As shown in Table S4, GWP of PF-2M3P is in good agreement with the studies of Díaz-de-Mera, et al. [START_REF] Díaz-De-Mera | Photolysis study of fluorinated ketones under natural sunlight conditions[END_REF] and Hodnebrog, et al. [START_REF] Hodnebrog | Global warming potentials and radiative efficiencies of halocarbons and related compounds: A comprehensive review[END_REF] .

Atmospheric implications

The photolysis rate of PF-2M3P was measured in September 2013 and July 2010 under natural irradiation and found to be (1.1-3.8) ×10 -6 s -1 and (1.7-2.8) ×10 -6 s - 1 , respectively (JNO2 = (3.3-5.6)×10 -3 s -1 ) leading to an atmospheric lifetime of PF-2M3P

with respect to photolysis in the range of 3-11 days considering that the photolysis occurs during the daytime, which is in good agreement with the literature results, i.e., 4-14 days. 5-6, 13, 18 The hydrolysis as removal process was demonstrated to be too slow to be considered of atmospheric importance. [START_REF] Taniguchi | Atmospheric Chemistry of C2F5C(O)CF(CF3)2: Photolysis and Reaction with Cl Atoms, OH Radicals, and Ozone[END_REF][START_REF] Jackson | Atmospheric Degradation of Perfluoro-2-methyl-3-pentanone: Photolysis, Hydrolysis and Hydration[END_REF] Besides, due to a high air-water partition coefficient, [START_REF] Rayne | Prediction of the air-water partition coefficient for perfluoro-2-methyl-3-pentanone using high-level Gaussian-4 composite theoretical methods[END_REF] very low quantities of PF-2M3P will be present in the cloud droplets.

Based on the upper limits for the reaction rate coefficients (in units of cm 3 molecule -1 s -1 ) with OH radical (<5 × 10 -16 ), O3 (<4 × 10 -22 ) and Cl atoms (<1.7 × 10 -19 ) taken from Taniguchi, et al. [START_REF] Taniguchi | Atmospheric Chemistry of C2F5C(O)CF(CF3)2: Photolysis and Reaction with Cl Atoms, OH Radicals, and Ozone[END_REF] and typical global average tropospheric concentrations (in molecule cm -3 ) of OH  2 × 10 6 , 27 Cl  10 4 , [START_REF] Saiz-Lopez | Reactive halogen chemistry in the troposphere[END_REF] and O3  7 × 10 11 , [START_REF] Monks | Atmospheric composition changeglobal and regional air quality[END_REF] the tropospheric lifetime towards OH, Cl and O3 reactions is equivalent to > 30 years. Thus, it is concluded that the photolysis will be the dominant atmospheric loss process for PF-2M3P.

Based on the photolysis rate measurement of PF-3M2B under natural irradiation (JPF-3M2B = (9±5)×10 -7 s -1 ), an atmospheric lifetime with respect to photolysis of ~13 days was derived. To the best of our knowledge, this work provides the first photolysis study of PF-3M2B. By analogy with PF-2M3P, other processes such as reactions with OH radical, Cl and O3 and hydrolysis would not contribute significantly to the atmospheric removal of PF-3M2B.

Using the photolysis rates of 2M3P measured under natural irradiation (J2M3P = ≤(2.6±1.4)×10 -6 s -1 ), an atmospheric lifetime with respect to photolysis of ≥4 days was derived. In addition to photolysis, gas phase reactions with OH radical and Cl atom could also contribute significantly to the tropospheric loss of 2M3P. Indeed, tropospheric lifetimes towards OH and Cl reactions were derived to be  4 (OH rate coefficient estimated from SAR) [START_REF] Kwok | Estimation of hydroxyl radical reaction rate constants for gas-phase organic compounds using a structure-reactivity relationship: An update[END_REF] and 11 days 31 , respectively. Thus, both photolysis and gas phase loss processes will contribute to the loss of 2M3P in the troposphere.

Therefore, the tropospheric lifetime, tot, defined as Based on the present study, the photolysis of PF-2M3P has been found to produce CF3C(O)F, COF2, TFA, PFPrA, and CO under natural conditions. In the atmosphere, CF3C(O)F will mainly hydrolyze to give trifluoroacetic acid (TFA, CF3C(O)OH). In the lower atmosphere, COF2 will be lost through hydrolysis, [START_REF] Houde | Biological Monitoring of Polyfluoroalkyl Substances: A Review[END_REF][START_REF] Hanson | The loss of CF2O on Ice, Nat, and Sulfuricacid-solutions[END_REF] whereas in the stratosphere, the photolysis is the dominant pathway producing CO2 and HF, [START_REF] Nolle | Determination of quantum yields in the UV photolysis of COF2 and COFCl[END_REF] leading to a local lifetime of 5-10 days. [START_REF]WMO (World Meteorological Organization) Scientific Assessment of Ozone Depletion: 2010[END_REF] The photolysis of 2M3P in the troposphere will lead to the formation of CH3C(O)CH3, CH3CHO, HCHO and CO. The major atmospheric loss of CH3C(O)CH3, CH3CHO and HCHO is controlled by photolysis and reaction with OH radical. Their photolysis are a source of HOX (OH, HO2) in the upper troposphere. [START_REF] Simpson | Halogens and their role in polar boundary-layer ozone depletion[END_REF][START_REF] Jaegle | Chemistry of HOx radicals in the upper troposphere[END_REF] Finally, the low GWP values and the short atmospheric lifetimes for the studied ketones may not lead to a large impact on the global warming of the Earth's atmosphere but may have some impact regarding the formation of other fluorinated species.

ASSOCIATED CONTENT

Supporting Information

UV absorption cross section of PF-2M3P, PF-3M2B and 2M3P are provided in Table S1 and Beer's law fits in Figure S2; UV absorption spectra of acetone is displayed in Figure S1; Seasonal dependence of the photolysis rate of PF-2M3P, PF-3M2B and 2M3P simulated using TUV Model is tabulated in Table S2; Figures S3 andS4 represents the FTIR spectra and GC-MS spectrum, respectively and were used to obtain the products yield as shown in Figures S5 andS6. Formation yields from the photolysis of PF-2M3P are summarized in Table S3. Corresponding photolysis pathway is proposed in Figure S7; Figure S8 presents the FTIR spectra from irradiation of 2M3P. Figure S10 presents the data used to derive the formation yield of products from the loss of 2M3P (Figure S9). Corresponding proposed photolysis pathway is given in Figure S11. Infrared absorption cross sections of 2M3P, PF-2M3P and PF-3M2B (.txt format) used to calculate radiative efficiencies (RE) and GWPs (100 years) (Table S4) and the fitting according to Beer's law (Figure S12, Figure 13 and Figure S14).

Table 1. Experimental conditions and obtained results for the photolysis of perfluoro-2-methyl-3-pentanone (PF-2M3P), perfluoro-3-methyl-2-butanone (PF-3M2B) and 2methyl-3-pentanone (2M3P).

[ketone] J NO2 Photolysis loss Irradiation period J (10 -6 s -1 ) (10 13 molecule cm -3 ) (10 a Recommended value obtained from the weighted average of each individual measurement: Jav=(w1J1+ w2J2 + …)/( w1+ w2+…), where w=1/σ 2 , etc. The error, is given by: 2σav=(σ1 2 +σ2 2 + …) 0.5 b measured using GC-MS c measured using PTR-TOF-MS 1

where

  L is the path length of absorption cell (in cm), and C is the concentration of the studied compound (in molecule cm -3 ). I0(λ) and I(λ) are the light intensities in the absence and in the presence of the compound in the absorption cell, respectively. The concentration of the species of interest in the absorption cell was obtained from the measured pressure using a 0-10 Torr capacitance manometer. Measurements of the PF-2M3P, PF-3M2B and 2M3P UV absorption spectra were performed at T = (292±1) K using the concentration ranges [PF-2M3P] = (0.29 -2.7) × 10 17 , [PF-3M2B] = (0.27 -3.0) × 10 17 and [2M3P] = (0.43 -2.9) × 10 17 molecule cm -3 .

(

  within less than 90 seconds). Solar actinic flux (290-660 nm) and photolysis frequencies of H2O2, HONO, HCHO, NO3, NO2 and O( 1 D) were measured by a spectroradiometer (Meteorologie Consult GmbH 6007). Pressure, relative humidity and temperature were continuously monitored by a three-axis Ultrasonic Anemometer (Delta Ohm, HD 2003) installed in the center of the chamber. The temperature distribution was also measured using six thermocouples (PT-100) spatially and equally distributed inside the chamber. A mobile protective housing kept the chamber under the dark and can be easily moved to fully expose the chamber to sunlight within 30 seconds. The experimental duration under irradiation was between 3 and 7 hours, in which the temperature typically increased by 10 °C. Between experiments, the chamber was cleaned by flushing pure air through for at least 12 hours. Organic compounds were monitored via in situ Fourier transform infrared spectrometry (FT-IR, Bruker Vertex70 spectrometer) coupled to a White-type multipass cell (302.6 m optical path length). Infrared spectra were recorded every 3 minutes by co-adding 250 interferograms with a resolution of 0.4 cm -1 . The gas phase mixture was also analyzed using a gas chromatography coupled to a mass spectrometer (GC-MS, PekinElmer Clarus 600 C). Gas samples were collected from the chamber at low temperature (-30°C) onto Air Toxics tubes and analyzed through a thermal desorber (TurboMatrix™ 150 ATD), with split mode, followed by a thermal desorption at 300 °C (5 min) delivering the sample to a 60-m column (GasPro diameter 0.320mm). The O3 and NO-NOx concentrations were continuously monitored by UV absorption (HORIBA, APOA 370) and chemiluminescence analyzer (HORIBA, APNA 360), respectively. PF-3M2B was also monitored by PTR-TOF-MS (Proton Transfer Reaction -Time of Flight-Mass Spectrometer, IONICON 8000). The fragment CF3 + (m/z 68.986) and (CF3)2CF3 + (m/z 168.970) were used to monitor the temporal behavior of PF-3M2B during the photolysis.

Figure

  FigureS11shows the proposed mechanistic pathways leading to the formation of

  the corresponding lifetimes with respect to photolysis and OH radical and Cl reactions, respectively, was estimated to be 1-2 days.

1 Figure 1 . 2 Figure 2 .

 1122 Figure 1. UV absorption spectra of perfluoro-2-methyl-3-pentanone (PF-2M3P), perfluoro-3-methyl-2-butanone (PF-3M2B) and 2-methyl-3-pentanone (2M3P) and compared with those from literature. The shaded area in yellow represents the solar spectral irradiance measured inside HELIOS (13:00 local time, 27 September 2013).

Table 2

 2

summarizes the photolysis rates of PF-2M3P obtained in this work and those reported in the literature. The values from this work were lower than those reported by D'Anna, et al.

Table 2 .

 2 Photolysis rate of perfluoro-2-methyl-3-pentanone (PF-2M3P), perfluoro-3-methyl-2-butanone (PF-3M2B) and 2-methyl-3pentanone (2M3P) obtained in this work and compared to the reported data from the literature.

	Ketone	[Ketone] 0	Chamber	Date	Irradiation	J	J NO2	Atmospheric	Reference
								Lifetime
		(10 13 molecule cm -3 )				(s -1 )	(s -1 )	(days)
		3.0-3.8	HELIOS	Sept 2013 Solar irradiation (1.1-3.8)×10 -6	(3.0-5.6)×10 -3	3-11	This work
		8.9-27	3.4 m 3 chamber	July 2010 Solar irradiation (1.7-2.8) ×10 -6	(4.4-5.5)×10 -3	4-7	This work
		8-64	Toledo, Spain	June-July 2013/2014	Solar irradiation (6.8±0.8)×10 -6		5.5±1.9	Díaz-de-Mera, et al. 13
		2.5	Euphore	July 2003 Solar irradiation (6.4±0.3)×10 -6	7.85×10 -3	~7	D'Anna, et al. 18
	PF-2M3P	(0.55-6.5)×10 3	140-L Pyrex reactor		14 blacklamps 8 sunlamps	(1.0±0.1)×10 -7 (6±2)×10 -7		7-14	Taniguchi, et al. 5
		47° N and 1° E a	a	TUV model	(0.4-2.8)×10 -6			This work
		39.9° N and 4° W a	a	TUV model	(2.1±0.8)×10 -6		5.5±1.9	Díaz-de-Mera, et al. 13
		Different latitude a	a	TUV model	(0.82-3.1)×10 -6		4-14	Jackson, et al. 6
	2M3P	3.0-3.4	HELIOS	Oct 2013	Solar irradiation ≤(2.6±1.4)×10 -6 (2.2-5.6)×10 -3	1-2	This work
		47° N and 1° E a	a	TUV model	(0.3-2.8)×10 -6			This work
	PF-3M2B	3.0-3.4	HELIOS	July 2017 Solar irradiation	(9±5)×10 -7

Acknowledgments

This work is supported by Labex Voltaire (ANR-10-LABX-100-01), ARD PIVOTS program (supported by the Centre-Val de Loire regional council), and the European Union's Horizon 2020 research and innovation programme through the EUROCHAMP-2020 Infrastructure Activity under grant agreement No. 730997.

AUTHOR INFORMATION

Corresponding Author *Tel: 33 (0)2 38 25 76 12; e-mail: mellouki@cnrs-orleans.fr. ORCID Yangang Ren: 0000-0001-5770-5050 François Bernard: 0000-0002-6116-3167 Véronique Daële: 0000-0003-2509-4077 Abdelwahid Mellouki: 0000-0002-6594-5262


Raphael Perez

Christian Fournier

Llorenç Cabrera-Bosquet

Simon Artzet

Christophe Pradal

Nicolas Brichet

Tsu-Wei Chen

Romain Chapuis

Claude Welcker

Francois Tardieu
email: francois.tardieu@inra.fr

Raphaël P A Perez

François Tardieu

François Tardieu

Changes in the vertical distribution of leaf area enhanced light interception efficiency in maize over generations of selection

Keywords: Architectural traits, breeding, high-throughput phenotyping, light interception, maize (Zea mays L.)

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Plant architecture, i.e. the arrangement of plant leaf area in space and time, affects light interception and the way in which plants make use of the intercepted light for photosynthesis.

For instance, a rapid coverage of the inter-row increases the amount of light intercepted by the canopy and depends on the horizontal distribution of leaf area, e.g. via a change with time of leaf orientation in relation to the plant row [START_REF] Girardin | Effects of intraspecific interference on maize leaf azimuth[END_REF]. Increased leaf erectness tends to decrease the proportion of incident light intercepted by the canopy, butt improves light use efficiency by the canopy [START_REF] Niinemets | A review of light interception in plant stands from leaf to canopy in different plant functional types and in species with varying shade tolerance[END_REF]. This is because the relationship between incident light and photosynthesis is non-linear. Erect architectures avoid upper leaves receiving saturating light and allow lower leaves in the canopy to receive more light [START_REF] Long | Can improvement in photosynthesis increase crop yields?[END_REF].

Overall, traits involved in plant 3D architecture tend to have smaller effects on light interception than leaf area but their effects increase with phenological stages and becomes appreciable at canopy closure, when self and/or mutual shading occur [START_REF] Perez | Designing oil palm architectural ideotypes for optimal light interception and carbon assimilation through a sensitivity analysis of leaf traits[END_REF]Chen et al. 2018a).

Furthermore, the metabolic cost of changes in architecture is negligible compared with that of increasing leaf area in terms of nitrogen and carbon resources, so even small increases in the use of incident light obtained by optimizing plant architecture may have a beneficial effect on biomass accumulation.

Four conditions are necessary for any trait to have an interest in breeding [START_REF] Sadras | Improvement of crop yield in dry environments: Benchmarks, levels of organisation and the role of nitrogen[END_REF]. First, the considered architectural trait needs to result in an appreciable effect on total light interception and/or on the distribution of light interception in the canopy. Secondly, it needs a high genetic variability and heritability in the current genetic diversity. Thirdly, alleles of interest should not have been fixed so a genetic variability remains in current breeding populations after generations of selection. Finally, breeding is highly facilitated if the considered trait has a minimum trade off with other traits, so its improvement correlates with yield in a simple way ('scalability', [START_REF] Sadras | Improvement of crop yield in dry environments: Benchmarks, levels of organisation and the role of nitrogen[END_REF]. The multiple criteria for sorting out architectural traits make it difficult to establish a hierarchy of their interests for breeding, which inevitably depends on the weight that one places on each criterion. An alternative is to consider a posteriori the trends of each of these traits over generations of selection [START_REF] Duvick | Post -Green Revolution Trends in Yield Potential of Temperate Maize in the United States[END_REF].

Breeders essentially select based on yield but, doing so, they can indirectly select for traits that contribute to it, often termed secondary traits [START_REF] Reynolds | Physiological breeding[END_REF]. This can happen if the effect of the considered trait is positive regardless of environmental scenarios. We have argued that most traits involved in adaptation to abiotic stresses do not belong to this category because positive alleles change from year to year so they cannot be selected based on yield [START_REF] Tardieu | The Physiological Basis of Drought Tolerance in Crop Plants : A Scenario-Dependent Probabilistic Approach[END_REF]. Conversely, if the four above-mentioned criteria were met for architectural traits, one would expect a trend in these traits over generations of selection.

The emergence of phenotyping platforms now allows measuring complex traits on thousands of plants, in particular leaf area and biomass [START_REF] Furbank | Phenomics -technologies to relieve the phenotyping bottleneck[END_REF][START_REF] Tardieu | Plant Phenomics, From Sensors to Knowledge[END_REF], but also light interception [START_REF] Cabrera-Bosquet | Highthroughput estimation of incident light, light interception and radiation-use efficiency of thousands of plants in a phenotyping platform[END_REF], plant competitiveness (Chen et al. 2018a) or stomatal conductance (Alvarez [START_REF] Prado | Phenomics allows identification of genomic regions affecting maize stomatal conductance with conditional effects of water deficit and evaporative demand[END_REF]. In particular, it is now possible to dissect biomass accumulation of hundreds of genotypes into components of the Monteith equation, thereby giving the possibility of detection of genomic regions associated with these traits (Chen et al. 2018a). Images can be taken from different directions, so 3D plant reconstructions can be built for mimicking each plant in the greenhouse every day of the plant cycle. This potentially allows calculating architectural traits, but also their consequences on light interception either in conditions in which plants were grown, or in field virtual canopies composed of 3D virtual plants.

We tested if, and which architectural traits were indirectly selected by breeders in a panel involving 60 maize hybrids released in the last sixty years (1950 to 2015), which displays an increasing yield over generations of selection of about 100 kg ha -1 year -1 (Welcker et al unpublished data), similar to that in another panel [START_REF] Hammer | Can Changes in Canopy and/or Root System Architecture Explain Historical Maize Yield Trends in the U.S. Corn Belt?[END_REF]. This panel was analysed in a phenotyping platform, while the interest of architectural traits for light interception was analysed in virtual canopies made of 3D plants, after assessing the validity of such canopies in comparison to a field experiment. We also tested if the observed trends also apply to plants subjected to water deficit. Besides, light interception by hybrids belonging to each generation of selection was also considered at different plant densities, because it has been argued that a major cause of genetic progress of maize yield is the ability of recent hybrids to grow at high densities [START_REF] Duvick | The Contribution of Breeding to Yield Advances in maize (Zea mays L.)[END_REF][START_REF] Assefa | Analysis of Long Term Study Indicates Both Agronomic Optimal Plant Density and Increase Maize Yield per Plant Contributed to Yield Gain[END_REF].

Materials and Methods

Plant material and experiments

The panel consisted of 60 maize (Zea mays. L.) hybrids released in Europe from 1950 and 2015, which were the most successful in their generation according to the Arvalis database (https://www.arvalisinstitutduvegetal.fr) and experts in the field. These hybrids belonged to midearly/mid-late maturity groups, with leaf number from 14 to 18, and originated from the programmes of selection of different breeding companies based in Europe.

3D reconstruction of plants in the greenhouse

The estimation of architectural phenotypic traits was based on 3D plant reconstructed from images analysis [START_REF] Cabrera-Bosquet | Highthroughput estimation of incident light, light interception and radiation-use efficiency of thousands of plants in a phenotyping platform[END_REF][START_REF] Brichet | A robot-assisted imaging pipeline for tracking the growths of maize ear and silks in a high-throughput phenotyping platform[END_REF]. Virtual 3D reconstructions were generated every day for each of the 1680 plants of the platform by analysing RGB (2056 x 2454) plant images taken from 13 views (12 lateral views from 30° rotational difference and one top view) (for details see [START_REF] Cabrera-Bosquet | Highthroughput estimation of incident light, light interception and radiation-use efficiency of thousands of plants in a phenotyping platform[END_REF][START_REF] Brichet | A robot-assisted imaging pipeline for tracking the growths of maize ear and silks in a high-throughput phenotyping platform[END_REF]. Plant pixels were distinguished from the background via threshold algorithms and morphological operators using OpenCV libraries [START_REF] Bradski | Learning OpenCV: Computer vision with the OpenCV library[END_REF] http://opencv.org) and converted into mm 2 by calibrating camera positions using reference objects. Total plant leaf area was obtained every day via calibration curves constructed using multiple linear regression models based on processed images taken in <="" span="">13 directions against measurements of leaf area at different stages [START_REF] Brichet | A robot-assisted imaging pipeline for tracking the growths of maize ear and silks in a high-throughput phenotyping platform[END_REF]. Virtual 3D representations were computed using a space carving algorithm [START_REF] Kutulakos | Theory of shape by space carving[END_REF] and represented by a set of 3D voxels of 0.512 cm 3 each. This voxel set was then transformed into a triangular mesh using the marching cube algorithm [START_REF] Lorensen | Marching cubes: A high resolution 3D surface construction algorithm[END_REF]) and a 90% decimation [START_REF] Schroeder | Decimation of triangle meshes[END_REF]) implemented in a VTK library [START_REF] Schroeder | The Visualization Toolkit: an Object Oriented approach to 3D graphics[END_REF]. This transformation into triangular meshes was achieved in order to obtain a 3D surface reconstruction that conserved the plant leaf area estimated by regressions with pixel number. The open-source software pipeline Phenomenal (https://github.com/openalea/phenomenal; [START_REF] Fournier | Phenomenal : a software framework for model-assisted analysis of high throughput plant phenotyping data[END_REF] processed the images, stored intermediate results and distributed the computation on the grid via the cyber-infrastructure

InfraPhenoGrid [START_REF] Pradal | InfraPhenoGrid: A scientific workflow infrastructure for plant phenomics on the Grid[END_REF]) embedded in the scientific workflow system OpenAlea [START_REF] Pradal | OpenAlea: a visual programming and component-based software platform for plant modelling[END_REF].

Vertical distribution of plant area in the greenhouse

Plant height (hplant) was estimated as the highest pixel of a plant. The whorl height (hwhorl) was estimated as the highest point of the vertical axis including the plant central axis (Table 1), detrmined using the 3D coordinates of the centres of gravity of each voxel structuring the considered 3D plant. First, 3D coordinates of these centres of gravity were projected on the horizontal plan (x,y) and the number of voxels located (vertically) at each (x,y) coordinate was For each plant, the vertical distribution of plant area was described by two variables (rhPAD and bPAD, Table 1) computed based on the number of plant voxels per horizontal layer of the canopy

Horizontal distribution of plant area in the greenhouse

The projection of 3D plants on the horizontal plane, combined with the detection of the position of the plant central axis on this plane, allowed expressing the position of each voxel in polar coordinates, with a specific azimuth (az) and radius (r). Plant radius (Table 1) was estimated as the 95 th quantile of the distribution of voxels radiuses (Fig. SI 2A). The estimation of traits related to plant azimuthal dispersion (σaz) and orientation(Δrow) were performed by i) detecting leaf tips by analysing peripheral voxel and isolating radial peaks (see supplementary material appendix A and Fig. SI 3 for the detailed procedure). Voxels with r < 25% of the maximum radius were removed as they were considered as artefacts, not distant enough from the stem to be considered as leaf tips (Fig. SI 2 B); ii) grouping leaves into azimuthal directions by applying a cluster analysis based on matrix distance of voxel azimuths, and considering the azimuth of the detected radial peaks as cluster medoids (medoids with difference in azimuth below 15° were merged to form a unique cluster) (Fig. SI 2C). Each group was characterized by the number of voxels forming it, an azimuth (median azimuth of the grouped voxel) and a radius (median radius of the grouped voxels); iii) clustering the groups into two main azimuthal directions using a hierarchical cluster analysis (hclust procedure of the R software; R Core Team, 2017) applied on group azimuths weighted by the number of voxels per group (Fig. SI 2D). This clustering analysis allowed estimation of σaz, which was computed as the mean difference between group azimuths with the associated main direction. As a result, σaz can be viewed as the average deviation from a distichous phyllotaxy, i.e the higher σaz the more a plant is dispersed in azimuth (Fig. SI 4A). Finally, Δrow was estimated as the mean difference between the azimuth and the direction of plant rows; the higher Δrow, the more perpendicular were the leaves in relation to plant rows (Fig. SI 4B).

In addition to comparing hybrids at given days after sowing (DAS), we also performed analyses at comparable phenological stages. For that, the number of visible and ligulated leaves were counted twice a week, and the date of tassel appearance was recorded for each plant. In particular, comparisons were performed at the date on which the ligules were visible on half of leaves that eventually emerged, i.e. when no tassel was visible in any of the studied hybrids (see Fig. SI 5). This was done to ensure that the architectural differences observed among hybrids at a given day after sowing were not the result of difference in phenological stages .

Imaging in the field experiment

In the field experiment, vertical upward-looking hemispherical images (2640 × 1760) were taken using a Sigma SD-14 camera equipped with a fisheye lens of 8 mm focal. For each micro-plot and date, 10 images were taken early in the morning (before 8 am). At each sampling date (June 15 th , June 21 st , June 29 th , and July 19 th ), the camera was oriented North with the lens kept horizontally towards the sky and images were distributed over two diagonal segments placed between the two central rows of each micro-plot as detailed in [START_REF] Baret | Leafrolling in maize crops: From leaf scoring to canopy-level measurements for phenotyping[END_REF]. Images are available at http://www.phis.inra.fr/ under an Open Source license (CC-BY-NC-SA). Images were analysed using the Ilastik (Ilastik software, version 1.21.7) [START_REF] Sommer | Ilastik: Interactive learning and segmentation toolkit[END_REF]) built-in pixel classification machine learning procedure based on a training set of contrasting images involving micro-plots of different hybrids at different dates. For each image, total pixels corresponding to vegetation were extracted from background (sky) using a random forest classification method based on colour (Gaussian smoothing of 5 px) and texture (structure tensor eigenvalues of 1.6 px)

The ground cover (ratio of vegetation pixel to total pixel numbers, i.e. reciprocal of gap fraction, Average values of ground cover corresponding to every micro-plot were obtained using images taken at the central positions of each micro-plot. Ground cover (i.e. reciprocal of gap fraction) measured in the field at the four sampling dates was then compared to the RIE of the same hybrids in the greenhouse experiments, with comparisons performed for plants at the same phenological stage in both conditions.

Simulation of light interception and radiative variables in virtual canopies

Radiation interception efficiency (RIE) was estimated considering the 3D representation of each plant in a virtual toric field to represent a homogeneous canopy under three contrasting plant densities (5.5, 9 and 12.5 plants m -2 ) with 0.8 m row spacing. The toricity allows one to remove border effects as if the canopy was infinite. Light interception was estimated using the Caribu light propagation model [START_REF] Chelle | The nested radiosity model for the distribution of light within plant canopies[END_REF], combined with a sky radiance distribution model mixing SOC [START_REF] Moon | Illumination from a non-uniform sky[END_REF] and clear sky [START_REF] Perez | A new operational model for satellite-derived irradiances: description and validation[END_REF] distributins according the mixing ratio proposed by [START_REF] Mardaljevic | Daylight simulation: validation, sky models and daylight coefficients[END_REF]. These models were calibrated with daily meteorological data to reproduce appropriate sun path over a day (segmented into 46 directions).

The extinction coefficient (k) was calculated following the Beer-Lambert equation and was used to assess the penetration of light within the virtual canopy [START_REF] Monsi | On the Factor Light in Plant Communities and its Importance for Matter Production[END_REF]):

Assessing the contribution of architectural traits to light interception

The contribution of architectural traits to light interception was calculated for each virtual canopy via a regression model:

(eq5)
where ε is the residual effect. The absence of multi-collinearity between explanatory variables (traits) was checked using variance inflation factors (VIF<5). This procedure was performed between 9 and 35 DAS when all the plants were presented in the platform, and allowed the decomposition of model variance into its constitutive explanatory variables using the 'calc.relimp' function of the 'relaimpo' R package [START_REF] Grömping | R package relaimpo: relative importance for linear regression[END_REF].

Genotypic means of RIE for each hybrid in virtual canopies

Fourteen virtual canopies were built for each hybrid and water treatment grown in the greenhouse. Each virtual canopy involved replicated 3D representations of one of the 14 plants observed in the greenhouse for the corresponding hybrid and water treatment, positioned in the virtual canopy with its exact architecture and azimuthal position as in the greenhouse. RIE was calculated for the 14 virtual canopies, and its mean value was considered as the genotypic mean for the considered hybrid.

We challenged the validity of this method, first by comparing it with another method based on the random distribution of the 14 plant representations of each hybrid in a single virtual canopy, second by comparing the outputs of both methods with the results obtained for the 11 hybrids in the field experiment. In the alternative method for building a virtual canopy, the fourteen 3D representations corresponding to the studied hybrid were randomly distributed in a single virtual canopy. This was replicaed seven times to account for the effect of randomness of permutations.

The mean RIE for these replications was considered as the genotypic mean for the considered hybrid. Finally, the genotypic means obtained with both methods for the 11 hybrids were compared with the ground covers (reciprocal of gap fraction based on hemispherical images in the field) of the same hybrids in the field experiment.

Heritability

Heritabilities were estimated using the following mixed-effect model for each variable:

(eq2)
Where Yijsd is the phenotypic value of the considered variable for plant i for the water scenario s and the day d, µsd is the overall mean, Gjsd is the effect of genotype j and Eijsd the residual effect. Models were fitted for each water scenario and every day after sowing. Broad sense heritabilities on plant leaf area (LA) and the seven architectural traits (hwhorl, θ, rhPAD, bPAD, radius, σaz and Δrow) were calculated as:

(eq3)
The variance components were estimated using the 'lmer' procedure of the 'lme4' R package (R Core Team, 2017).

Results

A high genetic variability and heritability for architectural traits describing the vertical distribution of leaf area.

The first category of architectural traits was associated to the vertical distribution of leaf area, in particular the relative altitude in the canopy at which half of leaf area was cumulated (rhPAD), the concentration of leaf area at this altitude (bPAD) and leaf erectness (θ). The relative altitude rhPAD and erectness were correlated (r=-0.64, Table 2), meaning that the leaf area of most erect plants was concentrated at lower relative positions of the canopy than in less erect plants. This somewhat counter-intuitive result is linked to the fact that rhPAD is calculated relative to plant height that increases with erectness (Table 2). The index rhPAD tended to increase with time, whereas the concentration of leaf area at the altitude rhPAD (bPAD) increased during the plant cycle (Fig. 2). Leaf erectness tended to decrease with time for all hybrids, with a large genetic variability at each date (Fig. 2). The intra-genotypic variability was lower than inter-genotypic variability for these three variables, which presented a high heritability during the whole growth cycle with maximum of 0.83, 0.80 and 0.58, respectively, at 20-25 days for leaf erectness and rhPAD and at 30 days for bPAD (Fig. 3). They defined the second axis of a principal component analysis (PCA) and showed either weak or no correlation with other variables (Table 2 and Fig.

SI 8).

The second category of architectural traits described plant vigour, in particular leaf area (LA), the height of the whorl (hwhorl) and plant radius that all increased with time and presented a high genetic variability (Fig 2 & Fig. SI 9). These variables defined the first axis of the PCA, (Fig. SI 8), were highly correlated at all phenological stages (Table 2) and had a medium to high heritability that increased with time (Fig. 3).

The third category described the orientation of the projections of leaves over a horizontal plane, namely the azimuthal dispersion (σaz) and the orientation of plants in relation to the row along the plant cycle (Δrow). These two variables increased with time (Fig. SI 9). The increase in σaz meant that the vertical plane of plants, easy to identify at the beginning of the plant cycle, tended to be less and less obvious at later stages. The increase of Δrow meant that the average vertical plane of plants tended to orient towards a direction perpendicular to plant rows. Indeed, at the beginning of the experiment (9 days after sowing), the proportion of plants with orientation toward the inter row (Δrow>45°) was 50%, and progressively increased with canopy closure to reach up to 80% 35 days after sowing (Fig. SI 10). A high plant-to-plant variability was observed for these variables (Fig. SI 9), with very low heritability (Fig. 3), thereby suggesting a low genetic control for plant orientation in relation to the plant row.

The genetic progress affected the vertical distribution of leaf area

Modern hybrids tended to show a markedly different vertical distribution compared with older hybrids, together with a slightly lower leaf area. The variables describing the vertical distribution of leaf area were the most correlated with the year of release of considered hybrids (r = -0.72, -0.44 and 0.44 for rhPAD, bPAD and leaf erectness respectively in both WW and water deficient plants of the panel, Table 3). Leaf area correlated negatively with year of release in both water treatments, meaning that leaf area tended to slightly decrease with genetic progress (Table 3).

However, this tendency disappeared if plants were compared at a given leaf stage rather than at a given date (Fig. SI 11). The plant radius and whorl height were either independent or weakly correlated with year of release. As expected because of its low heritability, the reorientation of the vertical plane of leaves in relation to plant rows (Δrow) was not associated with genetic progress (Table 3).

Hence, leaves tended to be more concentrated at low relative altitudes of the canopy (decreasing values of rhPAD), and distributed more evenly with height (decreasing values of bPAD) over generations of selection (Fig. 4 and Table 3). These changes were observed in both wellwatered and water deficit plants, with parallel positive relationships without significant difference in slopes.

Modern hybrids presented improved light penetration and distribution in the canopy, thereby increasing the amount of light absorbed in the canopy layer

where ears are located.

Virtual canopies, simulating plants in the field, were built to calculate the genotypic means of light interception efficiency for each hybrid. They involved 3D representations of the 14 plants observed in the greenhouse for the corresponding hybrid. Genotypic means of RIE were calculated either by averaging the RIE of fourteen virtual canopies involving every plant replication of the considered hybrid, or calculating the RIE of a virtual canopy involving the same 14 virtual plants placed at random. The genotypic means of RIE obtained by both methods were closely correlated (Fig. 5, inset), suggesting that neither method appreciably biases the tendencies for genetic progress. The correlations between RIE and genotypic means of ground cover observed in the field were slightly better with the first than with the second method (Fig. SI 12), with satisfactory correlations at the four studied dates (r=0.53, 0.57, 0.62 and 0.75 for June , June 21 st , June 29 th , and July 19 th , respectively Fig 5). Correlation coefficients increased with phenological stage, probably because the gap fraction method has a precision that increases with leaf area. As a consequence, further paragraphs only refer to the first method that was considered as adequately representing the genotypic means of RIE translated to the field.

The total amount of light intercepted by virtual canopies was essentially maintained throughout generations of selection with the usual density of 9 plants m -2 , with a slight decrease over generations due to the decrease in leaf area (Fig. SI 13). Variations in light interception efficiency were largely explained by the traits proposed in this study, the latter contributing to 82 -95% of the total variance depending on days after sowing (Fig. 6). Leaf area was the main determinant of light interception during the whole plant cycle (50% contribution) whereas architectural variables, considered jointly, accounted for 40% of light interception. The cumulated contributions to light interception of leaf erectness, rhPAD and bPAD ranged from 5% at the beginning of the plant cycle (9 DAS) to 22% at the 12-leaf stage (35 DAS). Regarding the contribution of architectural traits to the proportion of light intercepted in the layer between 40 and 70% of plant height (RIE 0.4-0.7; Fig 6), it sarply increased over time to reach 80%, rhPAD and leaf erectness accounting for respectively around 60% and 20% of the associated explained variability.

Because leaf area was located lower in the canopy of recent hybrids, one observed a decrease over generations of the relative altitude in the canopy at which 50% of incident light is absorbed (ZrelI, Fig. 7B). Consistently, the extinction coefficient (k) was lowest in recent hybrids, suggesting a better penetration of light within the canopy (Fig. 7A). In old hybrids, the upper 10% of the canopy intercepted 50% of the incident light (ZrelI= 0.9) for the usual plant density of 9 plants m -2 .

In modern hybrids, this upper canopy layer allowed better light penetration, so 50% of incident light was still available in the canopy layers located below 80% of the canopy height. Furthermore, light was intercepted more evenly in the canopy, with a significant decrease in variance of the amount of light intercepted per unit leaf area by the different triangular meshes of the canopy (σEi, Fig. 7C). The increased light penetration in the canopy of recent hybrids was linked to the lower proportion of leaves in the upper canopy layer (Fig. 4A and Fig. 6b), but also to more erect leaves that intercept less light per unit leaf area (Fig. 4B). Similar tendencies were observed if plants were compared at a given leaf stage rather than at a given date (Fig. SI 14).

The increased light penetration in the canopy may have two advantages.

-First, because the relationship between light and photosynthesis is markedly non-linear, a better distribution of light in the canopy allows better radiation-use efficiency by avoiding that the upper 10% of the canopy presents light-saturated photosynthesis whereas the lower layers receive low light.

-Second, because the carbon supply to the ear essentially comes from the leaves located around it [START_REF] Palmer | Patterns of translocation, respiratory loss, and redistribution of C in maize labelled after flowering[END_REF]. The proportion of incident light intercepted in this layer was calculated here as that between the altitudes in the canopy ranging from 40 to 70% of plant height, regardless of generations (Fig. SI 7). It largely increased over generations of selection, from 5% up to 20% in oldest and most recent hybrids, respectively (Fig. 7D). In addition, the leaf area in the same layer increased over generations of selection (Fig. SI 14). Hence, the amount of photosynthates accumulated by the canopy was probably more available to the ear over generations of selection. This was attributable to a change in the vertical distribution of leaf area rather than to a change in ear height (Figure SI 7).

The improved distribution of absorbed light applied to low and high densities

We performed simulations with three plant densities because it has been stated that part of the genetic progress originates from the plant ability to grow at high densities. Studied densities were 9 plants m -2 , common in Europe, plus a high density, 12.5 plants m -2 , increasingly used for silage, and a low density of 5.5 plants m -2 that was used at the beginning of XX th century in southern regions. These simulations were performed with the 3D representations of plants in the greenhouse regardless of plant density, thereby neglecting the adaptation of plant architecture in the considered range of plant densities. Indeed, calculations performed on datasets collected on previous studies suggested a low interaction between these adaptations and generations of selection [START_REF] Sangoi | Response of Brazilian maize hybrids from different eras to changes in plant density[END_REF][START_REF] Ma | Changes in the morphological traits of maize genotypes in China between the 1950s and 2000s[END_REF] or genotypes derived from distinct maize germplasm groups (Ku et al. 2016) (Fig. SI 15). Overall, the relationships between studied variables and generations were essentially parallel for the three studied densities (Fig. 7). In view of the absence of appreciable interaction between generations and adaptation of architecture, this parallelism probably holds in spite of our simplifying hypothesis of neglecting adaptation of architecture. The high density allowed interception of a large amount of light in the canopy layer that includes ears, so modern hybrids could make the best use of incident light even at high densities. Besides, a steeper slope of progress can be visualized at 9 plants m -2 for the extinction coefficient (k) and the variance of irradiance within the canopy (σEi) (Fig. 7 A &C).

Our analysis therefore suggests that changes in canopy architecture were favourable at all densities, thereby allowing the use of high densities without penalty, with a specific advantage of genetic progress at the common plant density rather than higher or lower densities.

Discussion

The recent development of methods allowing in situ characterization of plant architecture, in combination with light models, enables one to explore the capacity of plant to intercept light [START_REF] Burgess | Exploring Relationships between Canopy Architecture, Light Distribution, and Photosynthesis in Contrasting Rice Genotypes Using 3D Canopy Reconstruction[END_REF]). Here we demonstrate that such approach applied to a phenotyping platform [START_REF] Cabrera-Bosquet | Highthroughput estimation of incident light, light interception and radiation-use efficiency of thousands of plants in a phenotyping platform[END_REF], helps to overcome the technical bottleneck of conducting genetic analysis on architectural traits [START_REF] Tardieu | Plant Phenomics, From Sensors to Knowledge[END_REF]. Comparatively to modelling studies based on architectural models, our approach is based on accurate and actual 3D reconstructions avoiding any change in the phenotypic correlation among architectural traits that may emerge from uncontrolled combinations of allometries used in these models.

The dissection of 3D reconstruction allowed identification of novel traits related to either vertical or horizontal distribution of leaf area. The trait that underwent the clearest indirect selection by breeders was the vertical distribution of leaf area (rhPAD) that appreciably contributed to light penetration in the canopy. The change in vertical distribution over generations of selection allowed optimizing the utilization of light in the different canopy layers, and a better interception by the layer containing the leaves that mainly supply carbon to the ear [START_REF] Palmer | Patterns of translocation, respiratory loss, and redistribution of C in maize labelled after flowering[END_REF] . This is in agreement with the plausible enhancement of yield trough improved photosynthesis at ear height, as suggested in previous studies [START_REF] Long | Can improvement in photosynthesis increase crop yields?[END_REF][START_REF] Hammer | Can Changes in Canopy and/or Root System Architecture Explain Historical Maize Yield Trends in the U.S. Corn Belt?[END_REF]. Another advantage of more even leaf area and light distribution along the canopy is to reduce the stomatal limitation to photosynthesis and save water, especially under stress condition (Chen et al. 2018b). In addition, a deeper penetration of light within the canopy may optimize nitrogen supply, thus enhancing phtotosynthetic capacity [START_REF] Mantilla-Perez | Differential manipulation of leaf angle throughout the canopy: Current status and prospects[END_REF].

Interestingly, the changes in vertical distribution of either leaf area or light interception were essentially continuous over generations of selection, without clear breaking point or step, suggesting that they were obtained via rearrangement of a large number of allelic values rather than via the introduction of key novel alleles.

The correlation between vertical distribution of leaf area and leaf erectness suggests that the latter has appreciably contributed to the former. Leaf erectness has been identified as a heritable trait and a key component of high-yielding varieties in cereals species [START_REF] Mantilla-Perez | Differential manipulation of leaf angle throughout the canopy: Current status and prospects[END_REF]. We confirm here that erectness largely contributes to light interception and its penetration within the canopy [START_REF] Truong | Harnessing Genetic Variation in Leaf Angle to Increase Productivity of Sorghum bicolor[END_REF][START_REF] Burgess | Exploring Relationships between Canopy Architecture, Light Distribution, and Photosynthesis in Contrasting Rice Genotypes Using 3D Canopy Reconstruction[END_REF], and that it has been indirectly selected by breeders. Erectness was empirically selected over generations of selection, which corroborate with morphological changes observed in maize hybrids selected in American [START_REF] Duvick | Post -Green Revolution Trends in Yield Potential of Temperate Maize in the United States[END_REF] and Chinese programs [START_REF] Ma | Changes in the morphological traits of maize genotypes in China between the 1950s and 2000s[END_REF].

We also estimate a new indicator related to the horizontal arrangement of leaf area (σaz and Δrow).

As previously indicated by [START_REF] Drouet | Spatial re-orientation of maize leaves affected by initial plant orientation and density[END_REF], we observed a non-random distribution of azimuths, with maize leaves turning toward inter-row spaces over time and thus ensuring a better capture of the available incident light [START_REF] Maddonni | Light interception of contrasting azimuth canopies under square and rectangular plant spatial distributions: Simulations and crop measurements[END_REF]. Traits related to leaf horizontal orientations were not heritable, suggesting either the absence of genetic variability of such traits or that the alleles related to leaf re-orientation were already fixed before selection programs. This outcome contradicts the genetic variability of phytochrome-mediated responses to low red to far-red ratio (R/FR) as suggested by [START_REF] Maddonni | Maize Leaves Turn Away from Neighbors[END_REF].

Finally, the enhancement of light penetration over generations of selection occurred for all planting densities, with a slightly better progression at 9 plants m -2 , density considered as the current agronomic optimum plant density [START_REF] Assefa | Analysis of Long Term Study Indicates Both Agronomic Optimal Plant Density and Increase Maize Yield per Plant Contributed to Yield Gain[END_REF]. This suggests that selected changes in plant architecture were driven to fulfil the physiological trade-off imposed by a specific agronomic management. However, light simulations were performed under virtual canopy that did not integrate plant-plant interactions and thus overlooked the potential architectural plasticity under contrasting densities. Because of the absence of appreciable interaction between this plasticity and generation of selection, the relative differences in yintercepts of each regression lines were likely to be underestimated in this study, but the main result, namely common response to density regardless of generations of selection probably holds.

  counted(Fig 1A). The central axis of the plant was defined as the (xc,yc) coordinate with the maximal voxel count. Whorl height was estimated as the z coordinate of the topmost voxel xc-yc located on the central axis (Fig.1Band Fig.SI 1A).

(

  1 voxel/8 mm thickness) extracted from 3D plant reconstructions (Munier-Jolain et al. 2013) zrel) is the cumulated leaf area (expressed relatively to total plant leaf area) from plant base to the height zrel in the canopy. zrel is the ratio between the absolute altitude of the considered voxel and the plant height. rhPAD is the relative height in the canopy where the cumulated leaf area reached half of the total leaf area (f(rhPAD)=0.5). High values of rhPAD indicate a concentration of plant area towards the top of the plant (Fig. SI 1B). bPAD is an index of concentration of leaf area around zrel = rhPAD, with high values of bPAD indicating a high concentration of plant area around rhpad, whereas low values of bPAD indicate an evenly distributed area in horizontal layers of the canopy. rhPAD and bPAD were estimated using the 'nls' function of R software (R Core Team 2017). Leaf erectness (θ) was calculated as the mean of elevation angles (θp) of the triangular meshes composing the 3D reconstructions (Fig 1D). High values of θ indicate more erect leaves (Fig. SI 1C).

Fig

  Fig. SI 6) was calculated in every micro-plot corresponding to each of the 11 studied hybrids.

  using the 'nls' function of R software (R Core Team 2017) based on estimations of RIE and leaf area index (LAI) from 0 to 35 DAS for each of the 1680 simulated canopies. The amount of light intercepted by each component (triangular mesh) of the reconstructed plants in the canopy allowed estimating three radiative variables: ZrelI, the depth above which half of the incident light was intercepted; RIE0.4-0.7, the proportion of incident light intercepted by the canopy layer located between 40% and 70% of the canopy height (layer where ears are located; Brichet et al, 2017, Fig. SI 7) and σEi, the standard deviation of the proportion of incident light intercepted per unit leaf area of plant components.

  The panel was tested in two experiments performed in controlled and field conditions. The

	to contrasting phenotypes (erectness, total leaf area) and year of release, were sown on 19 May
	2017 in plots of 16.7 m² with four 5.2 m long rows 0.8 m apart and grown under irrigation, with
	two replications for each hybrid.
	platform	experiment		was	conducted	at	the	PhenoArch	installation
	(https://www6.Montpellier.inra.fr/lepse_eng/M3P/PHENOARCH-platform; (Cabrera-Bosquet et
	al.	2016)	hosted	at	the	Montpellier	Plant	Phenotyping	Platforms,	M3P
	distance of 40cm and an inter-plant distance of 20 cm within the row). One replicate of each
	hybrid was randomly positioned within each line, leading to a total of 14 replicates per hybrid and
	per irrigation treatment. Air temperature and relative humidity were measured at eight positions
	in the greenhouse every 15 min (Rotronic, HC2A, Bassersdorf, Switzerland). Temperature was
	maintained at 26 ± 3°C during the day and 18 ± 1 °C during the night. The amount of incident
	light at each plant position was estimated using hemispherical images and the outside incident
	photosynthetic photon flux density (PPFD) measured every 15 min with a sensor on the top of
	the glasshouse (for details see Cabrera-Bosquet et al. 2016). Additional incident light was
	provided by lamps when external solar radiation was below 300 W m -2 or to extend the
	photoperiod with 400 W HPS Plantastar lamps (OSRAM, Munich, Germany) with 0.4 lamps
	m -2 . All experimental, environmental and 3D collected data were stored in the PHIS information
	system (Neveu et al. 2019).
	A	field	experiment	was	hosted	at	DIAPHEN	(https://www.phenome-
	fppn.fr/phenome_eng/Facilities/Montpellier-Field) at INRA Mauguio (southeast of France, 43°36ʹ
	N, 03°58ʹE) between May and September 2017. Eleven hybrids of the panel, selected according

(https://www6.montpellier.inra.fr/lepse/M3P) in spring 2017 (from April 6 th to May 31 th ). Plants were subjected to two levels of soil water content, either well-watered (WW) or water deficit (WD) (for details see

[START_REF] Brichet | A robot-assisted imaging pipeline for tracking the growths of maize ear and silks in a high-throughput phenotyping platform[END_REF]

. Seeds were sown in 9-l pots (0.19 m diameter, 0.4 m high) filled with a 30:70 (v/v) mixture of a clay and organic compost, and thinned to one plant per pot at the 3 appeared leaf stage. Pots were arranged in 28 rows of 60 plants (with an inter-row

Table 1 :

 1 Overview of the phenotypic traits estimated from 3D reconstructions

	Symbols Units	Traits	area
				arrangement
	LA	m 2	Plant leaf area	-
	hwhorl	cm	Whorl height	vertical
	θ	degrees Leaf erectness	vertical	&
				horizontal
	rhPAD	-	Plant relative height where half plant leaf	vertical
			area is reached
	bPAD	-	Distribution of leaf area along plant height vertical
	radius	cm	Plant radius	horizontal	&
				vertical
	σaz	degrees Azimuthal dispersion	horizontal
	Δrow	degrees Azimuthal deviation from row	horizontal

Table 2 :

 2 Pearson correlation coefficients between architectural traits 35 days after sowing. Data originate from well-watered plants. Correlation is based on individual plant values (Correlation when the ligules were visible on half of leaves that eventually emerged is

	presented Table S2)
		LA	hwhorl	hplant	radius	Θ	σaz	Δrow	rhPAD	bPAD
	LA	1
	hwhorl	0.65 *** 1
	hplant	0.60***	0.78***	1
	radius	0.51***	0.44***	0.68***	1
	θ	-0.17*** 0.05 n.s 0.34***	0.09**	1
	σaz	0.11***	0.00 n.s -0.09**	-0.15*** -0.16*** 1
	Δrow	-0.15*** -0.17*** -0.22*** -0.05*	-0.06 n.s -0.21*** 1
	rhPAD	0.30***	0.25***	-0.14*** -0.03 n.s -0.64*** 0.21***	-0.01 n.s 1
	bPAD	0.11***	-0.19*** -0.25*** -0.07*	-0.22*** 0.14***	0.07*	0.09**	1

Table 3 :

 3 Pearson correlation coefficients between the studied variables and year of release among water treatments (35 days after sowing). Correlation is based on average values of all replicates per hybrid.

	Architectural traits	WW	WD
	LA	-0.48 ***	-0.49 ***
	hwhorl	-0.33 **	-0.28 *
	radius	0.15 n.s	0.21 n.s
	θ	0.44 ***	0.43 ***
	σaz	-0.42 ***	-0.48 ***
	Δrow	-0.02 n.s	0.04 n.s
	rhPAD	-0.72 ***	-0.76 ***
	bPAD	-0.44 ***	-0.58 ***

Acknowledgements

This work was supported by the "Infrastructure Biologie Santé" Phenome funded by the National Research Agency (ANR-11-INBS-0012) and the Agence Nationale de la Recherche project ANR-10-BTBR-01 (Amaizing). FT was also supported by the EU project H2020 731013 (EPPN 2020 ). We are grateful to all members at the DIAPHEN and PhenoArch platforms for providing technical support, conducting the experiments and collecting data.