A Martinez

R Modolo

F Leblanc

J Y Chaufray

O Witasse

N Romanelli

Y Dong

T Hara

J Halekas

R Lillis

J Mcfadden

F Eparvier

L Leclercq

J Luhmann

S Curry

B Jakosky

Influence of the solar wind dynamic pressure on the ion precipitation: MAVEN observations and simulation results

Using the data from the SWIA and STATIC instruments on board Mars Atmosphere and Volatile EvolutioN (MAVEN) and LatHyS (Latmos Hybrid Simulation) simulations, we investigate the heavy ion precipitation into the Martian atmosphere. We discuss the influence of the solar wind dynamic pressure on the ion precipitation using observations performed by MAVEN from 04 June 2014 to 20 July 2017. The increase of the dynamic pressure from 0.63 to 1.44nPa is clearly associated with an increase of the same order of magnitude of the precipitating oxygen ion energy flux measured by MAVEN/STATIC from 9.9 to 20.6 × 10 eV. cm . sr . s at low energy (from 30 to 650 eV). In the same way, from 650 eV to 25000 eV, MAVEN/SWIA (all species) observed an increase from 22.4 to 42.8 × 10 7 eV. cm -2 . sr -1 . s -1 of the precipitating ion energy flux.

Performing two simulations using the average solar wind conditions for both solar dynamic pressure regimes observed by MAVEN as input in the LatHyS model, we reproduce some of the key characteristics of the observed oxygen ion precipitation. We characterize the oxygen ions simulated by LatHyS by their energy and time of impact, their time of injection in the simulation and initial position and the mechanism by which these ions were created. The model suggests that the main cause of the increase of the heavy ion precipitation during an increase of the solar dynamic pressure is the increase of the ion production by charge exchange, proportional to the increase of the solar wind flux, which becomes the main contribution to the ion precipitation at high energy.

Introduction

In the absence of a global magnetic field, Mars' upper atmosphere interacts directly with the solar wind. Planetary neutral species (mainly carbon dioxide molecules, hydrogen and oxygen atoms) are ionized by photoionization, electronic impact or charge exchange and are accelerated by the motional electric field of the solar wind. These charged particles can precipitate into Mars' atmosphere with energy up to several keV and induce a cascade of collisions, transferring enough energy to atmospheric particles to exceed the Martian escape velocity [START_REF] Luhmann | Dayside pick-up oxygen ion precipitation at Venus and Mars: Spatial distributions, energy deposition and consequences[END_REF][START_REF] Johnson | Plasma-induced sputtering of an atmosphere[END_REF]. While this process, named atmospheric sputtering, may have led to significant atmospheric escape in its early history, as suggested by [START_REF] Luhmann | Evolutionary impact of sputtering of the Martian atmosphere by O + pickup ions[END_REF], its contribution is nowadays minor compared to other neutral escape processes like Jeans escape (Anderson and Hord, 1971;[START_REF] Krasnopolsky | Detection of molecular hydrogen in the atmosphere of Mars[END_REF] and photochemical escape [START_REF] Lillis | Characterizing Atmospheric Escape from Mars Today and Through Time, with MAVEN[END_REF]2017), or ion escape process like pick-up ions [START_REF] Luhmann | A model of the ion wake of Mars[END_REF][START_REF] Fang | Escape probability of Martian atmospheric ions: Controlling effects of the electromagnetic fields[END_REF][START_REF] Dong | Seasonal variability of Martian ion escape through the plume and tail from MAVEN observations[END_REF] and ion outflow [START_REF] Lundin | ASPERA/ Phobos measurements of the ion outflow from the Martian ionosphere[END_REF][START_REF] Andersson | The Combined Atmospheric Photochemistry and Ion Tracing code: reproducing the Viking Lander results and initial outflow results[END_REF].

Atmospheric escape induced by sputtering at the present epoch is expected to be small compared to other mechanisms [START_REF] Leblanc | On the origins of Mars' exospheric nonthermal oxygen component as observed by MAVEN and modeled by HELIOSARES[END_REF] and therefore difficult to quantify from direct measurements. However, since heavy planetary ion precipitation (which we define as having mass larger or equal to the mass of carbon atom) is the primary driver of atmospheric sputtering [START_REF] Johnson | The sputtering of an oxygen thermosphere by energetic O +[END_REF][START_REF] Wang | Modeling of the O + pickup ion sputtering efficiency dependence on solar wind conditions for the Martian atmosphere[END_REF]2015), it is essential to constrain the dependence of the precipitating ion flux on present solar wind conditions in order to, potentially, extrapolate the effect of this mechanism, over the Martian history. In situ measurements of precipitating ions began with Mars Express (MEX) spacecraft, in orbit around Mars since December 2003, (e.g., [START_REF] Chicarro | The Mars Express mission: An overview, in Mars Express: A European Mission to the Red Planet[END_REF][START_REF] Barabash | The analyzer of space plasmas and energetic atoms (ASPERA-3) for the Mars Express mission[END_REF]. [START_REF] Hara | Heavy-ion flux enhancement in the vicinity of the Martian Ionosphere during CIR passage: Mars Express ASPERA-3 observations[END_REF] reported that MEX observed enhancements of precipitating heavy ions (e.g. 𝑂 and 𝑂 ) during the passage of Corotating Interaction Region (CIR) solar wind structures. This observation suggests that heavy ion precipitation is highly variable and depends on the upstream solar wind conditions at Mars. Thanks to Mars Atmosphere and Volatile EvolutioN (MAVEN) measurements, observations of heavy ion precipitation during quiet solar wind conditions have been reported by [START_REF] Leblanc | Mars heavy ion precipitating flux as measured by Mars Atmosphere and Volatile EvolutioN[END_REF], suggesting that atmospheric sputtering occurs almost continuously at Mars. Several investigations, either from observational or modeling studies, have highlighted the influence of the plasma properties on the Martian environment. [START_REF] Edberg | Plasmas boundary variability at Mars as observed by Mars Global Surveyor and Mars Express[END_REF], [START_REF] Hall | Annual variations in the Martian bow shock location as observed by the Mars Express mission[END_REF], [START_REF] Halekas | Structure, dynamics, and seasonal variability of the Mars-solar wind interaction: MAVEN Solar Wind Ion Analyzer in-flight performance and science results[END_REF] and [START_REF] Ramstad | Solar wind-and EUV-dependent models for the shapes of the Martian plasma boundaries based on Mars Express measurements[END_REF] have shown that the solar EUV irradiance and the solar wind dynamic pressure have an influence on the position of plasma boundaries such as the Magnetic Pileup Boundary (MPB) and the Bow Shock (BS). Indeed, the newly created exospheric ions can act to slow the solar wind flux, which can move the bow shock position away from the planet [START_REF] Hall | Annual variations in the Martian bow shock location as observed by the Mars Express mission[END_REF].

Moreover, [START_REF] Lundin | Solar forcing and planetary ion escape from Mars[END_REF] also showed that the size of the Martian obstacle (estimated as proportional to the BS position) influences the ion atmospheric escape rate.

The statistical study by Hara et al. (2017a) has showed that precipitating ion fluxes observed by MAVEN [START_REF] Jakosky | The Mars Atmosphere and Volatile Evolution (MAVEN) Mission[END_REF] vary at least by an order of magnitude (typically between 10 𝑐𝑚 . 𝑠 𝑠𝑟 and 10 𝑐𝑚 . 𝑠 𝑠𝑟 for ions with energies higher than 25 eV) depending on the upstream solar wind conditions such as the dynamic pressure, the magnitude of the interplanetary magnetic field, and the motional electric field direction E ⃗ = -V ⃗ × B ⃗ with V ⃗ the solar wind velocity and B ⃗ the interplanetary magnetic field vector. Indeed, it has been shown by several theoretical studies [START_REF] Luhmann | Dayside pick-up oxygen ion precipitation at Venus and Mars: Spatial distributions, energy deposition and consequences[END_REF][START_REF] Chaufray | Mars solar wind interaction: Formation of the Martian corona and atmospheric loss to space[END_REF][START_REF] Curry | Response of Mars 0+ pickup ions to the 8 March 2015 ICME: Inferences from MAVEN data-based models[END_REF] that the orientation of the motional electric field may influence the energy and intensity of ion precipitation on Mars. These studies suggested that the integrated total precipitating ion fluxes are globally larger in the -𝐸 ⃗ hemisphere than in the +𝐸 ⃗ hemisphere. Pickup oxygen ions formed in the -𝐸 ⃗ hemisphere are accelerated towards Mars and can precipitate while oxygen ions formed in the +𝐸 ⃗ hemisphere are accelerated away from Mars and can escape. Such results have been observed by Martinez et al. (2019a) and Hara et al. (2017a) thanks to MAVEN. [START_REF] Curry | Response of Mars 0+ pickup ions to the 8 March 2015 ICME: Inferences from MAVEN data-based models[END_REF] have studied the response of Mars O + pickup ions to an ICME (March 8 th , 2015) with a test-particle approach and found that the oxygen ion precipitation depends on the phase of the ICME with a maximum of precipitation during the shock. After the passage of the ICME shock, the precipitating flux of the ejecta phase decreases but still remains greater than the precipitating flux during the pre-ICME phase. Based on a similar approach, [START_REF] Fang | The importance of pickup oxygen ion precipitation to the Mars upper atmosphere under extreme solar wind conditions[END_REF] have shown that oxygen ion precipitation can vary by at least one order of magnitude due to the variation in dynamic pressure during ICME or CIR solar wind events. Similar conclusions have been reported by [START_REF] Hara | Heavy-ion flux enhancement in the vicinity of the Martian Ionosphere during CIR passage: Mars Express ASPERA-3 observations[END_REF] with Mars Express observation or by Martinez et al. (2019a) with MAVEN observations during the September 2017 solar events (Lee et al. 2018).

Complementary to observations, models can provide an extended set of information to better characterize the physical processes under investigations. By being able to take into account a wide variety of physical processes in time and space, models can be used to reproduce observations and investigate the resulting mechanisms. They provide a three-dimensional context for the observations.

At the beginning of Martian exploration, with Mariner 4 or Phobos 2, computer simulations have been found very useful for investigating the physic mechanisms of the atmospheric escape [START_REF] Luhmann | Dayside pick-up oxygen ion precipitation at Venus and Mars: Spatial distributions, energy deposition and consequences[END_REF]Luhmann, Jonhson & Zhang, 1992;[START_REF] Johnson | Plasma-induced sputtering of an atmosphere[END_REF][START_REF] Leblanc | Sputtering of the Martian atmosphere by solar wind pick-up ions[END_REF][START_REF] Leblanc | Role of molecules in pick-up ion sputtering of the Martian atmosphere[END_REF]Dubinin & Lundin, 1995;[START_REF] Fang | Escape probability of Martian atmospheric ions: Controlling effects of the electromagnetic fields[END_REF]. Some studies also make it possible to model the present and past contributions of these mechanisms to atmospheric escape [START_REF] Chassefière | Mars atmospheric escape and evolution; interaction with the solar wind[END_REF].

Combining MEX observations and sophisticated global model simulations, [START_REF] Diéval | A case study of proton precipitation at Mars: Mars Express observations and hybrid simulations[END_REF] have

shown that the precipitating protons originate from both the solar wind and the planetary exosphere.

Here, we use model to simulate the potential effects of the solar dynamic pressure on the ion precipitation.

In this paper, we further analyze the role of the solar dynamic pressure on the ion precipitation by performing a detailed analysis of MAVEN measurements combined with the simulation of its potential effects. The LATMOS Hybrid Simulation (LatHyS) model [START_REF] Modolo | Mars-solar wind interaction: LatHyS, an improved parallel 3-D multispecies hybrid model[END_REF] is used to constrain the processes that may control the ion precipitation. The instruments and data used to perform this analysis, as well as the methodology developed are described in section II. The model is described in section III whereas section IV present the main results and lessons derived from the simulation/measurement comparisons and section V the conclusions.

II.

MAVEN measurements of the solar wind conditions and precipitating ion flux

A. Instruments and Data

The large set of MAVEN instruments [START_REF] Jakosky | The Mars Atmosphere and Volatile Evolution (MAVEN) Mission[END_REF] allows us to characterize the precipitating ion flux as well as the upstream solar wind conditions and also to constrain the atmospheric and plasma properties of the Martian environment. In this study, we use measurements performed by the Solar Wind Ion Analyzer (SWIA; [START_REF] Halekas | The Solar Wind Ion Analyzer for MAVEN[END_REF], the SupraThermal and Thermal Ion Composition (STATIC;McFadden et al., 2015), the Magnetometer (MAG; Connerney et al., 2015a;2015b) and the Solar Extreme Ultraviolet Monitor (EUVM; [START_REF] Eparvier | The Solar Extreme Ultraviolet Monitor for MAVEN[END_REF]. The MAVEN/SWIA instrument is an energy and angular ion spectrometer. In this work, we use the SWIA coarse survey data product, covering an energy range between 25 eV/q and 25 keV/q with 48 energy steps logarithmically spaced, a field of view (FOV) of 360° x 90° with 64 angular bins and 4s time resolution. The MAVEN/STATIC instrument is an energy, mass and angular ion spectrometer. We used the STATIC "D1" data product, covering an energy range between 0.1 eV/q and 35 keV/q with 32 energy steps logarithmically spaced, a field of view (FOV) of 360° x 90° on 64 angular bins and 8 mass bins covering a mass range from 1 amu to 80 amu with a 4s time resolution.

We mainly based our study on MAVEN/SWIA despite the lack of mass resolution because MAVEN/STATIC operates mostly in conic mode (McFadden et al. 2015) below 350 km in altitude leading to a limited coverage for ions with energy larger than 650 eV. In the following, we use MAVEN/STATIC to refine our analysis for energies below 650 eV. Moreover, in order to avoid any potential bias in the measurement due to spacecraft charging, we only consider precipitating ions with energies larger than 30 eV. Although MAVEN/SWIA does not have mass resolution, it can be used to estimate the evolution of heavy ion precipitation for the high energy range. Pickup ions can be accelerated by the motional electric field up to a maximum energy limit [START_REF] Jarvinen | Energization of planetary pickup ions in the solar system[END_REF][START_REF] Rahmati | MAVEN insights into oxygen pickup ions at Mars[END_REF] which is:

𝐸 (𝑀 ) = 4 * 𝑚 * 𝑈 * 𝑠𝑖𝑛 (𝜃 ) = 4 * 𝐸 * ( 𝑚 𝑚 ) * 𝑠𝑖𝑛 (𝜃 ) (1)
Where M + is the species with a mass 𝑚 and 𝜃 is the angle between the solar wind velocity and the interplanetary magnetic field, 𝑚 is the proton mass and 𝐸 is the energy of the solar wind proton.

The maximum energy is 4 times that of the solar wind, that is, typically around four times 800 eV to 1 keV for nominal conditions for planetary protons and four times 2.4 keV to 4 keV for planetary helium ions. Therefore, any ions precipitating with energy larger than few keV are most probably planetary ions with masses larger than the proton and helium masses.

The MAVEN/EUVM measures the solar irradiance in three bands from the soft X-ray to the EUV range (in three spectral bands 0.1-7 nm, 17-22 nm and 121-122 nm) with a temporal resolution of 1s. To characterize the solar EUV irradiance, we use MAVEN/EUVM channel A which measures solar irradiance between 17 and 22 nm.

The solar wind density, solar wind velocity, and Interplanetary Magnetic Field (IMF) vectors are measured by MAVEN/SWIA and MAVEN/MAG and averaged on an orbit-by-orbit basis while MAVEN is in the pristine solar wind [START_REF] Halekas | Structure, dynamics, and seasonal variability of the Mars-solar wind interaction: MAVEN Solar Wind Ion Analyzer in-flight performance and science results[END_REF]. In this work, we use the Mars Solar Electric (MSE) coordinate system in which the X-axis points toward the Sun, the Z-axis is aligned with the solar wind motional electric field and the Y-axis completes the right hand system [START_REF] Fedorov | Structure of the Martian wake[END_REF].

B. Upstream and planetary conditions

To investigate the dependence of the precipitating ion flux with respect to the solar wind dynamic pressure, we used the method developed by [START_REF] Dong | Seasonal variability of Martian ion escape through the plume and tail from MAVEN observations[END_REF] and Martinez et al. (2019b). In absence of permanent solar wind monitoring, we assume that the averaged solar wind parameters, measured by MAVEN when inside the solar wind, are constant during the whole orbit as explained in Martinez et al. (2019b). Solar wind parameters on an orbit-by-orbit basis, when MAVEN was in the solar wind, are then used to determine the average solar wind parameters for a given set of measurements.

We organize MAVEN data into two sets of measurements corresponding to two different solar wind dynamic pressure conditions: a low dynamic pressure case with values between 0.3 and 1.0 nPa and a high dynamic pressure case with values between 1.0 and 2.6 nPa. The IMF strength (𝐵 ) is also imposed between 2.2 and 6.7 nT. The solar wind dynamic pressure is defined as 𝑃 = 𝑚 𝑛 𝑉 ,

where 𝑚 is the mass of the proton, 𝑛 and 𝑉 the solar wind density and velocity. For both sets of measurements, we determine the mean solar wind conditions and calculate the norm of the solar wind motional electric field defined as 𝐸 = 𝑉 ⃗ × 𝐵 ⃗ , the solar wind particle flux defined as 𝐹 = 𝑛 𝑉 , the Alfven Mach number defined as 𝑀 = (with the VA the Alfvén speed), the magnetosonic Mach number 𝑀 as defined in [START_REF] Edberg | Magnetosonic Mach number effect of the position of the bow shock at Mars in comparison to Venus[END_REF] and the MSE angle as defined in Martinez et al., (2019a). The MSE angle corresponds to the anticlockwise angle between the MAVEN's location in MSE coordinates during it measurements of the precipitating ion flux and the East MSE direction (MSE longitude equal to +180° and latitude equal to 0°).

These parameters are displayed in Table 1. The last column of Table 1 presents the coverage distribution, as defined in Martinez et al, (2019b), showing the percentage of common distribution for a given parameter between the two dynamic pressure groups. Except for the solar wind density and flux, and obviously for the dynamic pressure, all solar wind properties show similar variations with about 70 %, or more, of the distribution of each of these parameters in common. In other words, the EUV irradiance, IMF intensity, Alfven and magnetosonic Mach numbers, solar wind speed and MSE angle are similar during these two set of measurements. The spatial coverage of the ion precipitation measurements, characterized by the MSE angle and the solar zenith angle, is also similar during these two set of measurements.

The presence of crustal magnetic fields [START_REF] Acuña | Global distribution of crustal magnetization discovered by the Mars Global Surveyor MAG/ER Experiment[END_REF]Connerney et al., 2005) can influence locally the precipitating ion flux, as shown by Hara et al. (2017b). In order to limit the potential influence of the crustal fields [START_REF] Leblanc | On the origins of Mars' exospheric nonthermal oxygen component as observed by MAVEN and modeled by HELIOSARES[END_REF]Hara et al. 2017b), we also only consider measurements performed when the average magnetic field between 200 and 350 km was less than 60 nT. Moreover, to further limit the potential role of the crustal fields on the precipitation, we also consider only MAVEN measurements performed when the main crustal field region (centered at 180° GEO East longitude and -50° GEO latitude) was in the nightside, meaning when the subsolar point has a GEO longitude from -60° to 60°.

High

C. MAVEN's ion precipitation measurements

In order to reconstruct the precipitating ion energy flux, we use the method developed by Leblanc et al. (2015) and Martinez et al (2019a). We use MAVEN observations of the two sets of measurements performed between 200 and 350 km. Within such altitude range, any ions moving toward the planet in a cone of less than 75° with respect to the local nadir direction has a very large probability to impact Mars' atmosphere. Therefore, to reconstruct the precipitating flux, we sum all measurements of SWIA (and STATIC) anodes with a FOV corresponding to a cone of less than 75° from the local zenith direction. Moreover, in order to exclude the reconstructed precipitating flux with poor coverage, we only consider measurements during which the total FOV of SWIA (and STATIC) anodes covers more than 65 % of the 75° solid angle cone centered on the zenith direction. In the case of MAVEN/SWIA measurements, which has a low signal-to-noise ratio at high energy, we adapted the method from Martinez et al. (2019a) to remove an average background induced by Solar Energetic Particles (SEP).

Compared to MAVEN/SWIA, MAVEN/STATIC is less sensitive to SEPs because its measurements technique is based on double coincidence (McFadden et al., 2015). In case of intense SEP events or background level, STATIC measurements with poor quality were flagged and systematically excluded from our analysis. So, the background level of MAVEN/STATIC is assumed to be negligible.

In this study, MAVEN observations obtained from June 4 th , 2015 to July 20 th , 2017 have been categorized into two groups with similar spatial coverage: high dynamic pressure with 1.44 nPa averaged on 226 ion precipitation spectra by MAVEN/SWIA, and low dynamic pressure with 0.63 nPa averaged on 454 ion precipitation spectra by MAVEN/SWIA.

III. LatHyS Model

In order to simulate the Martian environment and the precipitating heavy ion flux, we choose to use the hybrid approach which describes ions with a kinetic approach while the electrons are treated as a fluid [START_REF] Modolo | Mars-solar wind interaction: LatHyS, an improved parallel 3-D multispecies hybrid model[END_REF]). The hybrid model called LatHyS is a 3-D multispecies parallelized model that simulates the interaction of the solar wind plasma with the neutral environment of the planet, characterizing all plasma regions in the vicinity of the planet. A detailed description of the LatHyS model can be found in [START_REF] Modolo | Influence of the solar EUV flux on the Martian plasma environment[END_REF]2016). The model uses as inputs a 3-D density description of H, O and CO2 representing the thermosphere and exosphere. The neutral species description is modeled from the LMD -Global Circulation Model [START_REF] Forget | Improved general circulation models of the Martian atmosphere from the surface to above 80 km[END_REF][START_REF] Chaufray | Three-dimensional Martian ionosphere model: II. Effect of transport processes due to pressure gradients[END_REF]) and the Exospheric Global Model [START_REF] Yagi | Mars exospheric thermal and non-thermal components: Seasonal and local variations[END_REF][START_REF] Leblanc | On the origins of Mars' exospheric nonthermal oxygen component as observed by MAVEN and modeled by HELIOSARES[END_REF]. The state of the neutral environment corresponds to solar longitude Ls = 270°. The spatial resolution of the LatHyS results presented in this paper is Δx = 57 km, and a mean solar activity is assumed for all the models (LatHyS, EGM, LMD-GCM) and for the two solar wind dynamic pressure cases.

Simulations are set up with typical solar wind parameters based on the orbit-by-orbit average solar wind parameters for the two groups of solar wind dynamic pressure, from Table 1. To facilitate the interpretation of the simulated precipitation fluxes, the interplanetary magnetic field is taken with only a 𝐵 component. For the period of high dynamic pressure we have: 𝑛 = 4.7 𝑐𝑚 , 𝑉 = 450 𝑘𝑚. 𝑠 and 𝐵 = 4.0 𝑛𝑇. For the period of low dynamic pressure we have: 𝑛 = 2.2 𝑐𝑚 , 𝑉 = 424 𝑘𝑚. 𝑠 and 𝐵 = 3.2 𝑛𝑇. Simulations are performed with a sub-solar longitude at 0° and a subsolar latitude at -23°, meaning that the main crustal field region is located in the nightside.

To further analyze simulation results, for each particle we record the information of the injection position, the ionization mechanism of the particle, the injection time, the precipitation time and its precipitating energy. Three main sources of ions are implemented in the simulation model. A simplified set of ionospheric chemistry equations is included (below 350 km) and particles created in this region are labeled as ionospheric particles. Particles can also be produced by photo-ionization above 350 km, where the optical depth is negligible, or undergo charge exchange reactions. Information concerning the ionization processes are detailed in [START_REF] Modolo | Mars-solar wind interaction: LatHyS, an improved parallel 3-D multispecies hybrid model[END_REF].

In this study, we consider only oxygen ions. Heavier ions (such as 𝐴𝑟 , 𝑂 and 𝐶𝑂 ) are not considered because of their much lower density at high altitude according to [START_REF] Fox | Response of the Martian thermosphere/ionosphere to enhanced fluxes of solar soft X rays[END_REF] so that their contribution to atmospheric sputtering should be very limited in intensity. Once a steady state of the simulation is achieved, O + ion precipitating (𝑉 < 0) below 250 km in altitude are recorded in order to construct an energy flux map on a 4.5° x 4.5° longitude-by-latitude grid. To have meaningful statistics on the precipitating O + ions, the accumulation is performed over 100 solar wind proton gyro-periods (about 6-7 transit times of the simulation box). Each energy spectra corresponding to the impacting O + flux is computed with an energy resolution of = ~ 17 % for energy larger than 2 eV. With more than one million precipitating numerical particles for each simulation, the modelled sample is large enough to be statistically significant. The stationarity of the solution has been checked by comparing energy spectra at each grid point of the map for various accumulation intervals. We found a temporal standard deviation of 15-20 % indicating that the simulation converged to a stable solution.

In order to compare simulation and observation, a similar methodology to reconstruct the simulated precipitation as for MAVEN measurements have been used:

-For each sequence of observation, the portion of MAVEN trajectory during which the precipitating flux was measured (between 200 km and 350 km in altitude) is reconstructed in the simulated MSE reference frame.

-The simulated energy spectra of the precipitating flux along each of these portions of MAVEN trajectory are then reconstructed and averaged. If, for a given energy bin, the simulated flux is lower than the threshold corresponding to MAVEN/SWIA background, the simulated precipitated ion energy flux, for this energy bin, is not considered to calculate the average. For energy larger than a few keVs, as explained in section II.A, MAVEN/SWIA observed ion precipitation should be in large proportion composed of O + ions. Above 3 to 4 keV, there is a clear increase of the measured and simulated precipitating fluxes from the low dynamic pressure case to the high dynamic pressure case. The gap between the MAVEN/SWIA curves (all species) and those of the model (only oxygen ions) between 300 eV and 3-4keV can be explained by the contribution of other species in the observed ion precipitation (mainly protons, in particular around the solar wind energy, probably produced in the hydrogen corona).

IV. LatHyS simulated precipitation and MAVEN precipitating measurements

Table 2 shows the integrated precipitating ion energy flux for each dynamic pressure case and two energy ranges: low energy [30-650] eV) and high energy eV. The ion precipitation increases when the dynamic pressure of the solar wind increases, as previously observed by Hara et al. (2017a) with MAVEN/SWIA and MAVEN/STATIC measurements. It increases by a factor between 1.7 and 2.0 at low energy and by factor 1.9 to 2.1 at high energy. Both simulation and observation agree relatively well when comparing the two dynamic pressure cases, even if the simulation predicts a systematic factor 4 lower integrated flux with respect to SWIA observed precipitation for both solar dynamic pressure cases and energy ranges. At high energy, this factor can be partially explained by the fact that the modelled precipitating ion energy flux becomes lower than the MAVEN/SWIA background and so, the energy ion flux is not considerate, which slightly underestimate the modelled ion precipitation. In other words, even if the simulation did not perfectly reproduce the absolute intensity of the observed precipitation, the simulated variation of the precipitating flux with increasing pressure might be driven by a similar mechanism to the one controlling the dependency of this flux in MAVEN observations. and MAVEN/SWIA (all species) and modelled by LatHyS (only oxygen ion) for each period. The last three line correspond to the ratio between the high pressure period values and the low pressure period values for each instrument. In brackets, the 1-sigma standard deviation (uncertainty) of the precipitating ion energy flux values. The integrated ion precipitation unit is in 𝑒𝑉. 𝑐𝑚 . 𝑠𝑟 . 𝑠 . preventing photo-ionizations. The precipitating ions with energy higher than the solar wind (800 eV -1 keV) are formed in the southern hemisphere MSE and their final energy depends on their altitude of creation (by ionization). This energy-altitude injection relation is consistent with [START_REF] Jarvinen | Oxygen ion energization at Mars: Comparison of MAVEN and Mars express observations to global hybrid simulation[END_REF] and can be explained by the time spent by an ion in the high electric field regions (essentially the solar wind and the magnetosheath). In the northern hemisphere, it can also be seen that precipitating ions are mainly formed within or downstream of the pile-up magnetic region. The high-energy ions precipitate mainly in the Southern hemisphere and on the Martian dayside (not shown) as simulated in [START_REF] Luhmann | Dayside pick-up oxygen ion precipitation at Venus and Mars: Spatial distributions, energy deposition and consequences[END_REF]. This distribution of the origin position of precipitating ions and their impact energy can be explained by the intensity of the electric field and its direction [START_REF] Chaufray | Mars solar wind interaction: Formation of the Martian corona and atmospheric loss to space[END_REF][START_REF] Curry | Response of Mars 0+ pickup ions to the 8 March 2015 ICME: Inferences from MAVEN data-based models[END_REF]. In the upstream solar wind and the magnetosheath, the newly born ions will be accelerated in the direction of the convective electric field. Ions formed in the northern hemisphere MSE will be moved away Mars, while ions formed in the southern hemisphere MSE will be accelerated toward Mars, as observed in Hara et al. (2017a). This is why for high X > 0 and 𝜌 > -0.5 in Figure 2, there are almost no precipitating ions formed upstream the bow shock. The ions formed inside the magnetosheath will see a disturbed electric field direction which may lead them to precipitate. To summarize, this result indicates that oxygen ions created above the ionosphere in the -E hemisphere can more easily precipitate toward the planet rather than those created in the +E hemisphere, in good agreement with previous numerical simulations [START_REF] Chaufray | Mars solar wind interaction: Formation of the Martian corona and atmospheric loss to space[END_REF][START_REF] Fang | Escape probability of Martian atmospheric ions: Controlling effects of the electromagnetic fields[END_REF][START_REF] Curry | Response of Mars 0+ pickup ions to the 8 March 2015 ICME: Inferences from MAVEN data-based models[END_REF]. As a matter of fact, the main difference between the two modelled dynamic pressure cases can be described as a global shift in energy, associated with a change in the local electric field intensity, and an increase of the intensity of the precipitating ions. As an example, in the case of the ionospheric ions (red lines in Figure 3), there is a significant increase of the precipitating flux with increasing dynamic pressure above 50 eV, as observed by the MAVEN/STATIC. In the same way, in the case of the ions produced by photoionization Figure 3, there is globally an increase in energy of the precipitating ions due to the increase of the electric field close to Mars when increasing the dynamic pressure. However, in the case of the ion produced by charge exchange, a higher dynamic pressure induces not only a gain of energy of the precipitating particle but also an increase in the charge exchange ionization rate between solar wind protons and O atmospheric neutral particles which should be proportional to the solar wind particle flux ~ 𝑛 𝑉 . The ionization rate by charge exchange should increase by a factor ~ 2.3 which is the ratio between the solar wind flux in the high dynamic pressure case to the solar wind flux in the low dynamic pressure case. This ratio is very close to the ratio of the precipitating fluxes of the ions produced by charge exchange between the high and low dynamic pressure cases (equal to ~ 2.7). On the other hand, the production rates of ion in the ionosphere or by photo-ionization are not or only in a limited way influenced by the change of the solar wind dynamic pressure. As shown in Figure 3 in the case of the high dynamic pressure (dark blue line), the precipitating flux is dominated by ions produced by charge exchange above 1 keV. In the low dynamic pressure case, charge exchange and photo-ionization produces roughly the same amount of ions according to the simulation.

Integrated precipitating ion energy flux

B. Origins and parameters controlling the simulated precipitating fluxes

The main lessons from the simulation are:

-An increase of the dynamic pressure should lead to a global increase of the energy of the ion precipitating in the atmosphere, roughly proportionally with the change of the motional electric field in the undisturbed solar wind.

-An increase of the dynamic pressure should lead to an increase of the charge exchange rate in a proportion roughly equivalent to the increase in solar wind flux. This effect should be observable at high energy, above typically 1 keV, where the contribution of the charge exchange mechanism on the production of the precipitating ion starts to dominate.

-Below 1 keV, the precipitating ion energy flux should be dominated by the ionospheric ions which are poorly described by LatHyS due to a limitation in spatial resolution.

We also evaluated the impact of the dynamic pressure on the plasma boundaries (essentially on the bow shock position) by comparing the precipitating flux of oxygen ions produced by photo-ionization upstream of the bow shock for both cases. With a small difference between the two cases, we concluded that the precipitating ion flux is only weakly influenced by the compression of the bow shock with increasing solar dynamic pressure (see supplementary document). The average solar conditions of each period are then used to simulate Mars' environment using LatHyS hybrid model [START_REF] Modolo | Mars-solar wind interaction: LatHyS, an improved parallel 3-D multispecies hybrid model[END_REF]. These two simulations are realized for the same solar extreme ultra-violet conditions, the same season of the Martian atmosphere (LS = 270°), with the same orientation of the Interplanetary Magnetic Field and the main crustal field placed in the nightside. A method is also developed in order to reconstruct the oxygen ion precipitation from both simulations using the same approach as when analyzing MAVEN measurements.

V. Summary and Conclusion

The precipitating ion energy flux measured by MAVEN/STATIC and MAVEN/SWIA increases with the increase of the solar wind dynamic pressure, which is consistent with previous studies (Hara et al., 2017a). The increase of the dynamic pressure from 0.63 to 1.44 nPa is clearly associated with an increase at the same order of the precipitating oxygen ion energy flux measured by MAVEN/STATIC from 9.9 to 20.6 × 10 eV. cm . sr . s (a ratio of ~ 2.1) for the low energy range (from 30 to 650 eV). From 650 eV to 25000 eV, observations by MAVEN/SWIA show an increase from 22.4 to 42.8 × 10 7 eV. cm -2 . sr -1 . s -1 (a ratio of ~ 1.9) with a similar order as the increase in solar wind dynamic pressure.

Such increase can be explained, according to the simulation results by several mechanisms. The increase of the dynamic pressure leads to a global increase of the energy and intensity of the ion precipitating into the atmosphere. In terms of energy differential precipitating flux, this is equivalent to a shift in energy of the flux proportional to the increase of the solar wind convective electric field intensity upstream to Mars, and an increase of the intensity of the energy differential precipitating flux, proportional to the increase of the solar wind flux because an increase of the solar wind flux also implies a change of the charge exchange rate between the incident solar wind ions and the planetary exosphere. Such effect is particularly observable above 1 keV in the simulated precipitating ion energy flux where the flux is in a large proportion composed of planetary oxygen ions formed by charge exchange.

A.

  Figure1shows the comparison of the spectrum of the average precipitating ion energy flux for

Figure 1 :

 1 Figure 1: Average precipitating ion differential energy spectra as measured by MAVEN/SWIA

Figure 2

 2 Figure 2 displays the impact energy of the precipitating oxygen ions (of ionospheric origin, created by

Figure 2 :

 2 Figure 2: Map of the origin position of the precipitating ions produced either in the ionosphere (below

Figure 3

 3 Figure 3 displays the energy distribution of the simulated precipitating oxygen ion energy flux averaged

Figure 3 :

 3 Figure 3: Simulated precipitating oxygen ion differential energy spectra. Solid line: high dynamic

  Solar wind observations around Mars from the MAVEN spacecraft from 04 June 2015 to 20 July 2017 are organized into two sets of measurements corresponding to two periods of significantly different solar dynamic pressure. Beside different solar wind conditions, all other parameters that could potentially influence the state of Mars' atmosphere and magnetosphere are carefully estimated in order to be equivalent in both samples (by selecting only observations with the same solar conditions and geographic coverage). From these two periods, we then use MAVEN portions of orbit between 350 and 200 km in altitude to reconstruct the precipitating ion energy fluxes from SWIA[START_REF] Halekas | The Solar Wind Ion Analyzer for MAVEN[END_REF] and STATIC(McFadden et al. 2015) measurements following the method developed in[START_REF] Leblanc | Mars heavy ion precipitating flux as measured by Mars Atmosphere and Volatile EvolutioN[END_REF] andMartinez et al. (2019a).

Table 1 :

 1 Mean µ, standard deviation , first quartile Q25 and third quartile Q75 of the solar zenith angle and each solar planetary parameter distribution for the two sets of precipitating flux measurement. The last column provides the percentage of the area in common between the two distributions.

			Pdyn	Low Pdyn	Common
			[1.0,2.6] nPa	[0.3,1.0] nPa	coverage (%)
		𝜇 ± 𝜎	0.22 ± 0.04	0.22 ± 0.03
	EUV Flux (𝒎𝑾. 𝒎 𝟐 )	Q25	0.19	0.20	85.5
		Q75	0.24	0.23
	Dynamic	𝜇 ± 𝜎	1.44 ± 0.41	0.63 ± 0.19
	pressure	Q25	1.13	0.46	0.0
	(𝒏𝑷𝒂)	Q75	1.63	0.79
		𝜇 ± 𝜎	96 ± 28	96 ± 28
	Solar Zenith Angle (°)	Q25	80	77	89.7
		Q75	115	118
		𝜇 ± 𝜎	1.44 ± 0.55	1.04 ± 0.45
	Electric field (𝒎𝑽. 𝒎 𝟏 )	Q25	1.00	0.74	68.6
		Q75	1.77	1.20
		𝜇 ± 𝜎	3.90 ± 1.12	3.23 ± 0.95
	IMF (𝒏𝑻)	Q25	2.92	2.50	69.1
		Q75	4.52	3.60
		𝜇 ± 𝜎	448 ± 80	423 ± 78
	Speed (𝒌𝒎. 𝒔 𝟏 )	Q25	376	370	80.1
		Q75	495	467
		𝜇 ± 𝜎	4.67 ± 1.93	2.25 ± 0.97
	Density (𝒄𝒎 𝟑 )	Q25	3.28	1.49	40.9
		Q75	5.69	2.78
		𝜇 ± 𝜎	178 ± 110	203 ± 110
	MSE angle(°)				86.2
		Q25	94.7	153

Table 2 :

 2 Integrated precipitating ion energy flux as measured by MAVEN/STATIC (only oxygen ion)

	Low energy	High energy
	[30-650] eV	[650-25000] eV

Acknowledgements

This work was supported by the DIM ACAV and the ESA/ESTEC faculty. This work was also supported by CNES "Système Solaire" program and by the "Programme National de Planétologie" and "Programme National Soleil-Terre". This work is also part of HELIOSARES Project supported by the ANR (ANR-09-BLAN-0223), ANR MARMITE (ANR-13-BS05-0012-02) and ANR TEMPETE (ANR-17-CE31-0016).

Spacecraft data used in this paper are archived and available in the Planetary Data System Archive (https://pds.nasa.gov/). Numerical simulation results used in this article can be found in the simulation database (http://impex.latmos.ipsl.fr).


Christophe Maurel
email: christophe.maurel@cnrs.fr

Philippe Nacry

acclimation to changing water availability

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

Introduction

Water is certainly the most limiting environmental factor for agricultural production, whether in arid or temperate areas. Climate change exacerbates this threat by inducing increasingly frequent and intense drought episodes. While droughts can dramatically alter plant productivity and survival, water excess is not a lesser evil [START_REF] Voesenek | Flood adaptive traits and processes: an overview[END_REF] . With notable exceptions such as rice and Rumex, complete submergence of the plant results in a full growth arrest [START_REF] Voesenek | Flood adaptive traits and processes: an overview[END_REF] and under waterlogging conditions several plant species exhibit a paradoxical wilting phenotype due to transpiration while root water uptake capacity has been reduced 2 . Thus, both water deficit and excess negatively impact agriculture and result in significant economical loses. For instance, a global analysis including drylands and nondrylands worldwide showed that crops as important as wheat and maize show a yield reduction by 21% and 39%, respectively, at approximately 40% water reduction [START_REF] Daryanto | Global synthesis of drought effects on maize and wheat production[END_REF] . According to recent estimates, Europe loses up to 5 billion euros of agricultural harvests every year, due to river overflows. These losses may double by 2080 due to climate change [START_REF] Hirabayashi | Global flood risk under climate change[END_REF] . Thus, understanding the overall modes of response of plant to water availability is of upmost agronomic importance [START_REF] Voesenek | Flood adaptive traits and processes: an overview[END_REF] . Several directions are currently followed, regarding water use. Foremost is irrigation, which has traditionally been used to counteract insufficient precipitation, although it is associated with significant economic and environmental costs. Soil drainage is also central to combat the detrimental effects of waterlogging [START_REF] Manik | Soil and crop management practices to minimize the impact of waterlogging on crop productivity[END_REF] . Although novel water management and predictive practices [START_REF] Manik | Soil and crop management practices to minimize the impact of waterlogging on crop productivity[END_REF][START_REF] Du | Deficit irrigation and sustainable water-resource strategies in agriculture for China's food security[END_REF][START_REF] Kirkegaard | Improving water productivity in the Australian Grains industry-a nationally coordinated approach[END_REF] have been explored to increase the efficiency of water usage [START_REF] Davies | Achieving more crop per drop[END_REF] , developing drought-or flood-tolerant crop cultivars promises to be another main path to progress [START_REF] Voesenek | Flood adaptive traits and processes: an overview[END_REF][START_REF] Davies | Achieving more crop per drop[END_REF][START_REF] Tester | Breeding technologies to increase crop production in a changing world[END_REF] . In particular, drought-tolerant crops are plants that are adapted to water-challenged climates that, most importantly, maintain a stable yield despite annual variations in precipitation. To reach this goal, breeders have focused on exploiting plant phenology as a means to protect the reproductive stage (the most drought-sensitive developmental stage in some crops). Breeding work has also been aimed at transpiration or leaf growth in order to prevent water loss, thereby achieving significant genetic progress in plant resistance to drought [START_REF] Millet | Genome-wide analysis of yield in Europe: Allelic effects vary with drought and heat scenarios[END_REF] . In contrast, most breeders have avoided the selection of root traits, although they fulfil key functions for the plant such as soil water uptake, which is absolutely essential during droughts and is challenged under waterlogging conditions. One reason is that roots vary with soil type and rainfall and require considerable investment for functional assays or growth monitoring in the field. Efforts to phenotype root systems in real soils, using X-ray computed tomography or shovelomics, or in adapted devices such as rhizotrons or transparent soils have led to significant technical progresses on how to capture the complexity and dynamics of root architecture and anatomy (see [START_REF] Atkinson | Uncovering the hidden half of plants using new advances in root phenotyping[END_REF] for a recent review). Yet, the functionality of root systems cannot be fully addressed using these phenotyping devices. In the present Perspective, we point to recent fundamental advances in root biology that open exciting avenues in several directions related to water uptake and ultimately crop improvement.

Elucidating root hydraulic architecture

Roots fulfil their anchoring and foraging functions through continuous growth and branching, thereby producing a highly complex and specialized network, the so called root system architecture (RSA) (Fig. 1a). Experimentally, RSA can be defined by length (depth) of the main root(s), the density and elongation of lower order roots, their gravitropic setpoint angle, and the possible presence of crown roots or adventitious roots. A large body of research has addressed the elementary mechanisms that determine each of these individual traits and emphasized the role of hormones, including auxin, abscisic acid (ABA), cytokinins and ethylene [START_REF] Jung | Getting to the roots of it: Genetic and hormonal control of root architecture[END_REF][START_REF] Lavenus | Lateral root development in Arabidopsis: fifty shades of auxin[END_REF][START_REF] Petricka | Control of Arabidopsis root development[END_REF] . Other studies have addressed the adaptive significance of varying RSA. In a search for root ideotypes that could provide cereal crops with an adaptive advantage under drought, deep rooting has been proposed as a key trait, as it permits access to unexploited water resources when the soil surface desiccates [START_REF] Lynch | cheap and deep: an ideotype to optimize water and N acquisition by maize root systems[END_REF] . Yet, this ideotype may not be optimal for quick recovery after drought in seasonal precipitation regimes [START_REF] Ogura | Root system depth in Arabidopsis is shaped by EXOCYST70A3 via the dynamic modulation of auxin transport[END_REF] , or for acquisition of nutrients such as phosphate [START_REF] Shahzad | Food for thought: how nutrients regulate root system architecture[END_REF] . One initial approach to investigate the role of roots during drought consisted of searching for correspondences between Quantitative Trait Loci (QTLs) for specific root morphological traits and whole-plant performance under water deficit [START_REF] Tuberosa | Identification of QTLs for root characteristics in maize grown in hydroponics and analysis of their overlap with QTLs for grain yield in the field at two water regimes[END_REF][START_REF] Ruta | QTLs for the elongation of axile and lateral roots of maize in response to low water potential[END_REF] . In grasses, for instance, suppression of crown roots was found to promote drought tolerance [START_REF] Gao | Reduced crown root number improves water acquisition under water deficit stress in maize (Zea mays L.)[END_REF][START_REF] Sebastian | Grasses suppress shoot-borne roots to conserve water during drought[END_REF] . In addition, plant geneticists have recently succeeded in cloning such critical genes as rice DRO1, which determines root growth angle and thereby enhances rice performance under drought by favoring deep rooting [START_REF] Uga | Control of root system architecture by DEEPER ROOTING 1 increases rice yield under drought conditions[END_REF] . A natural variation approach, but in Arabidopsis, led to identification of EXOCYST70A3, an exocyst factor which also interferes with root growth orientation and root system depth by acting on expression of auxin efflux carriers in the root tip [START_REF] Ogura | Root system depth in Arabidopsis is shaped by EXOCYST70A3 via the dynamic modulation of auxin transport[END_REF] . Although the two studies point to the central role of auxin in regulating RSA, they identify opposite and species-specific strategies for soil exploration under water deficit. More generally, much of the physiological and genetic components that shape the adaptive value of RSA under natural conditions are as yet unknown. To address these, elaborate time-lapse 3D imaging and mathematical modelling approaches are under development to capture the great complexity of RSA, and its intra-and interspecific variations [START_REF] Jiang | Three-dimensional time-lapse analysis reveals multiscale relationships in maize root systems with contrasting architectures[END_REF][START_REF] Band | Multiscale systems analysis of root growth and development: modeling beyond the network and cellular scales[END_REF][START_REF] Rellan-Alvarez | Environmental control of root system biology[END_REF] .

Water uptake is not simply a matter of root growth. It is also critically determined by the intrinsic water transport capacity of the roots, i.e. their hydraulics (Fig. 1b). Water is first transported radially from the soil to the stele, through concentric layers of root cells, loaded into xylem vessels, and then transported axially up to the shoots. Our biophysical and physiological understanding of these processes has made significant progress in the last two decades [START_REF] Maurel | Aquaporins in plants[END_REF][START_REF] Bramley | Roles of morphology, anatomy, and aquaporins in determining contrasting hydraulic behavior of roots[END_REF] . Molecular physiological studies have shown that water channel proteins named aquaporins facilitate water diffusion across cell membranes and therefore contribute to cell-to-cell transport [START_REF] Maurel | Aquaporins in plants[END_REF][START_REF] Hachez | Localization and quantification of plasma membrane aquaporin expression in maize primary root: a clue to understanding their role as cellular plumbers[END_REF] . Yet, many other components of root hydraulics are to be discovered. For instance, the crucial role of lignified and suberized barriers differentiated in the walls of exo-and endodermal cells has long remained elusive but can now be explored using genetic materials recently arising from sharp molecular dissection of these barriers [START_REF] Barberon | Adaptation of root function by nutrient-induced plasticity of endodermal differentiation[END_REF] . Such studies have revealed however the intricate regulatory pathways connecting the cell wall (apoplastic) and cell-to-cell (aquaporin-dependent) water transport paths [START_REF] Wang | Surveillance of cell wall diffusion barrier integrity modulates water and solute transport in plants[END_REF] . While root growth or leaf water relation traits have been the subject of extensive direct genetic analyses, it is only recently that these approaches have been extended to root hydraulics. For instance, QTL analysis of a biparental recombinant population of Arabidopsis led to the molecular cloning of Hydraulic Conductivity of Root 1 (HCR1) [START_REF] Shahzad | A potassium-dependent oxygen sensing pathway regulates plant root hydraulics[END_REF] . HCR1 encodes a raf-like MAP3K protein kinase which characterization has revealed unexpected hydraulic regulation under the combined effects of potassium and oxygen (O 2 ) availabilities (see below) (Fig. 2a,b). With respect to the strategy used for HCR1 mapping and cloning, Genome Wide Association Studies (GWAS) have recently provided a more direct approach for isolating genes controlling root hydraulic conductivity [START_REF] Tang | Natural variation at XND1 impacts root hydraulics and trade-off for stress responses in Arabidopsis[END_REF] . These studies uncovered XYLEM NAC DOMAIN 1 (XND1), a transcription factor that acts as a negative regulator of xylem differentiation and as a consequence of root hydraulics, thereby providing novel insights into the long-lasting debate on the possibly limiting role of xylem vessels in axial water transport (Fig. 1b).

In relation with its effects on root water transport, XND1 negatively acts on drought stress tolerance [START_REF] Tang | Natural variation at XND1 impacts root hydraulics and trade-off for stress responses in Arabidopsis[END_REF] (Fig. 2c). Overall, natural variation at HCR1 and XND1 points to the critical role of root hydraulics in plant adaptation to water excess or deficit in natural habitats. More broadly, these studies indicate how root hydraulics contributes to integrative response of plants to combined abiotic and biotic stresses (Fig. 2). Future development of such genetic approaches in crops will be crucial for dissecting and possibly improving root hydraulic performance under agricultural conditions. Full comprehension of the ability of roots to capture soil water requires consideration of the root architecture and hydraulics as a whole. Mathematical modelling approaches have therefore attempted to integrate root local water transport properties within the RSA, thereby representing the so-called root hydraulic architecture [START_REF] Doussan | Modelling of the hydraulic architecture of root systems: an integrated approach to water absorption -Distribution of axial and radial conductances in maize[END_REF][START_REF] Doussan | Modelling of the hydraulic architecture of root systems: an integrated approach to water absorption -Model description[END_REF][START_REF] Lobet | A modeling approach to determine the importance of dynamic regulation of plant hydraulic conductivities on the water uptake dynamics in the soil-plant-atmosphere system[END_REF] . Several recent works have aimed at a better match between root anatomy and architecture and water transport properties [START_REF] Couvreur | Going with the flow: multiscale insights into the composite nature of water transport in roots[END_REF][START_REF] Meunier | Towards quantitative root hydraulic phenotyping: novel mathematical functions to calculate plant-scale hydraulic parameters from root system functional and structural traits[END_REF][START_REF] Zarebanadkouki | Visualization of root water uptake: quantification of deuterated water transport in roots using neutron radiography and numerical modeling[END_REF] . Nevertheless, there is still too little experimental data to support or challenge these models [START_REF] Bramley | Roles of morphology, anatomy, and aquaporins in determining contrasting hydraulic behavior of roots[END_REF][START_REF] Zarebanadkouki | Visualization of root water uptake: quantification of deuterated water transport in roots using neutron radiography and numerical modeling[END_REF][START_REF] Pierret | Spatio-temporal variations in axial conductance of primary and first order lateral roots of a maize crop as predicted by a model of the hydraulic architecture of root systems[END_REF][START_REF] Draye | Model-assisted integration of physiological and environmental constraints affecting the dynamic and spatial patterns of root water uptake from soils[END_REF] . Consequently, although this is a crucial integrative trait for plant performance, root hydraulic architecture has largely been neglected by plant breeding efforts. In addition to RSA phenotyping, crude evaluation of root water uptake capacity in breeding materials, by direct measurements in pot or hydroponically grown plants [START_REF] Matsuo | Genotypic differences in root hydraulic conductance of rice (Oryza sativa L.) in response to water regimes[END_REF] , or indirectly through transpiration in grafted species [START_REF] Marguerit | Rootstock control of scion transpiration and its acclimation to water deficit are controlled by different genes[END_REF] , would certainly help estimate the potentialities of these materials. Another key issue is the interconnection between hydraulics and growth. While it is well supported in shoots, it is just emerging in roots. For instance, auxincontrolled aquaporins allow directing water flows in lateral primordia thereby reducing the mechanical resistance of overlaying cells and favoring the emergence of the newly formed lateral roots [START_REF] Péret | Auxin regulates aquaporin function to facilitate lateral root emergence[END_REF] . This study establishes a unique physiological link between root hydraulics and branching.

Root plasticity under varying water availability

Root growth and hydraulics are both highly plastic, and are continuously adjusted in response to a large variety of soil signals with potentially antagonistic or synergistic effects. For instance, water and phosphorus deprivation can induce the formation of deep or shallow roots, respectively, while they both down-regulate aquaporins (root hydraulic conductivity) [START_REF] Rellan-Alvarez | Environmental control of root system biology[END_REF][START_REF] Maurel | Aquaporins in plants[END_REF] . In addition, water and mineral resources are far from uniform and can dramatically vary between soil patches or strata. A key enigma in root research is therefore to resolve how plant roots, which lack a centralized information processing system, can integrate signals from a heterogeneous environment to design the optimal short-and long-term strategies for soil resource acquisition.

There is no need to say that, due to their great agronomical importance, these questions have been raising a strong interest. A large body of literature shows that water availability exerts multiple short-or long-term effects on root growth and hydraulics, with a sharp dose-dependency. For instance, moderate water deprivation enhances primary root growth and lateral root formation, whereas a strong water deficit exerts opposite inhibitory effects [START_REF] Jung | Getting to the roots of it: Genetic and hormonal control of root architecture[END_REF][START_REF] Deak | Osmotic regulation of root system architecture[END_REF][START_REF] Dinneny | Developmental responses to water and salinity in root systems[END_REF] . In addition, sensitivity of these responses can vary between the primary root and lateral roots of different orders, or between segments of a same axial root 46 . Root hydraulics is also dynamically regulated by water deficit, with species-or cultivar-specific profiles and, in most cases, an early inhibition of aquaporin function [START_REF] Vandeleur | Role of aquaporins in root responses to irrigation[END_REF][START_REF] Hachez | Short-term control of maize cell and root water permeability through plasma membrane aquaporin isoforms[END_REF] .

In maize, root aquaporins can also integrate diurnal changes in shoot water demand (transpiration), through a circadian regulation mechanism that shows a higher response amplitude under soil water deficit [START_REF] Caldeira | Circadian rhythms of hydraulic conductance and growth are enhanced by drought and improve plant performance[END_REF] . On a longer term, drought acts on root hydraulics by enhancing suberization of the endodermis, or interfering with xylem differentiation (Fig. 1a). For instance, water deficit triggers in the Arabidopsis root a non-cell-autonomous pathway involving endodermal ABA signaling. The hormone enhances the accumulation of microRNA165, which migrates into the stele to act on transcription factors determining xylem identity [START_REF] Ramachandran | Continuous root xylem formation and vascular acclimation to water deficit involves endodermal ABA signalling via miR165[END_REF] .

Recently, there have been attempts to understand how these responses integrate with each other to determine whole root functionality. Analysis of both root architecture and hydraulics under exogenous-ABA treatments and in ABA-biosynthesis and signalling mutants has revealed striking parallels indicating that ABA, that accumulates under water deficit, acts as an integrator of root responses to the associated stress 46 . Yet, the picture is definitely more complex as ABA acts within a hormonal interaction network involving auxin, ethylene and cytokinins [START_REF] Rowe | Abscisic acid regulates root growth under osmotic stress conditions via an interacting hormonal network with cytokinin, ethylene and auxin[END_REF][START_REF] Li | The biphasic root growth response to abscisic acid in Arabidopsis involves interaction with ethylene and auxin signalling pathways[END_REF] . Future studies will also have to address the issue of local heterogeneity in water availability, which, besides overall water deficit, can occur in the absence of any water stress for the plant. Indeed, local variations can orient root growth (hydrotropism) [START_REF] Moriwaki | Molecular mechanisms of hydrotropism in seedling roots of Arabidopsis thaliana (Brassicaceae)[END_REF] or lateral root formation (hydropatterning) [START_REF] Bao | Plant roots use a patterning mechanism to position lateral root branches toward available water[END_REF][START_REF] Von Wangenheim | Early developmental plasticity of lateral roots in response to asymmetric water availability[END_REF] (Fig. 1a). Orman-Lipeza et al. [START_REF] Orman-Ligeza | The xerobranching response represses lateral root formation when roots are not in contact with water[END_REF] recently described a related response, called xerobranching, which reflects the repression of lateral root formation when a root grows through a large air-filled soil macropore, thereby feeling a transient water deficit. In all cases, root tip growth and root branching are positioned towards regions of higher water availability (Fig. 1a). While much mechanistic details are being uncovered from laboratory experiments [START_REF] Dinneny | Developmental responses to water and salinity in root systems[END_REF] , it will be fascinating to understand how these tropic responses mutually interact and operate during growth of roots in real, drying soils and how they allow optimizing soil foraging and water uptake.

Water excess reduces root hydraulic conductivity in most plant species, with early effects being mediated through proton-dependent gating of aquaporins due to metabolically-induced cell acidosis [START_REF] Tan | Plant water transport and aquaporins in oxygen-deprived environments[END_REF][START_REF] Tournaire-Roux | Cytosolic pH regulates root water transport during anoxic stress through gating of aquaporins[END_REF] . On a longer term, water excess exerts profound effects on root anatomy and ultimately RSA. In some wetland species, hypoxia promotes suberin and lignin deposition in the outer layers of the roots (rhizodermis) to create a barrier for lateral diffusion of O 2 from the root to the water logged soil [START_REF] Sauter | Root responses to flooding[END_REF] . More generally, and to facilitate root aeration, roots differentiate internal air spaces called aerenchyma, which can be either constitutive in species such as rice or inducible by hypoxia.

While the role of ethylene and ROS in aerenchyma induction under hypoxic stress is now well assessed, a central role of auxin in constitutive aerenchyma formation was recently uncovered [START_REF] Yamauchi | Fine control of aerenchyma and lateral root development through AUX/IAA-and ARF-dependent auxin signaling[END_REF] .

Interestingly, the auxin pathway involved shares commonalities with the AUX/IAA-and ARFdependent pathway responsible for lateral root formation. Yet, the two responses are somewhat distinct since auxin operates in two adjacent cell territories, e.g. cortex and pericycle. Concerning root growth, hypoxia can induce root slanting, to possibly escape from deeper layers in water logged soils [START_REF] Eysholdt-Derzso | Root bending is antagonistically affected by hypoxia and ERF-mediated transcription via auxin signaling[END_REF] , due in part to a recently uncovered cytokinin-dependent mechanism that delays the gravitropic response of lateral roots [START_REF] Waidmann | Cytokinin functions as an asymmetric and anti-gravitropic signal in lateral roots[END_REF] . More severe O 2 deprivation can result in tip growth arrest if not death, and inhibition of lateral root formation [START_REF] Voesenek | Flood adaptive traits and processes: an overview[END_REF][START_REF] Sauter | Root responses to flooding[END_REF] . To possibly alleviate defects of the primary root system, flooding also promotes the formation of adventitious roots at the shoot basis of floodtolerant species, a process that is primarily induced by tissue accumulation of ethylene 1 . While effects of energy depletion on transport activities in hypoxic roots have been largely identified [START_REF] Shabala | Membrane transporters mediating root signalling and adaptive responses to oxygen deprivation and soil flooding[END_REF] , the significance with respect to water uptake of hypoxia-induced root developmental reprogramming is as yet unclear. Thus, the notion of root hydraulic architecture in flooded plants will require as much attention as in droughted plants.

Sensing water availability

The molecular and cellular mechanisms underlying the early perception of water availability by roots and downstream signalling processes have become a crucial area in plant research. Interestingly, candidate genes involved in sensing water deficit are now emerging [START_REF] Yuan | OSCA1 mediates osmotic-stress-evoked Ca 2+ increases vital for osmosensing in Arabidopsis[END_REF][START_REF] Hamilton | Mechanosensitive channel MSL8 regulates osmotic forces during pollen hydration and germination[END_REF] and associated signalling events involving ROS and calcium are being elucidated [START_REF] Martiniere | Osmotic stress activates two reactive oxygen species pathways with distinct effects on protein nanodomains and diffusion[END_REF][START_REF] Shkolnik | MIZ1 regulates ECA1 to generate a slow, long-distance phloem-transmitted Ca 2+ signal essential for root water tracking in Arabidopsis[END_REF] . These studies, which deal with local effects of water deficit, typically relate to root responses to pronounced drought. Yet, the capacity of roots to acclimate to heterogeneous water resources or changing water demands of shoots, indicate that roots must continuously emit or sense systemic signals transferred within the root system or between roots and shoots [START_REF] Puertolas | Local root abscisic acid (ABA) accumulation depends on the spatial distribution of soil moisture in potato: implications for ABA signalling under heterogeneous soil drying[END_REF][START_REF] Mclean | Root hydraulic conductance and aquaporin abundance respond rapidly to partial root-zone drying events in a riparian Melaleuca species[END_REF] . A dehydration-induced peptide that relays root ABA signalling towards shoots was recently uncovered [START_REF] Takahashi | A small peptide modulates stomatal control via abscisic acid in longdistance signalling[END_REF] but other physical (e.g. hydraulic) or chemical (e.g. hormones, ions, ROS) signals are surely serving in root responses to heterogeneous or varying water availabilities .

Robbins and Dinneny [START_REF] Robbins | Growth is required for perception of water availability to pattern root branches in plants[END_REF] have recently explored the initial steps of hydropatterning and used a thoughtful modelling approach to show that perception of water availability is necessarily linked to growth. In brief, they showed that growth allows to locally sustain a water potential gradient across the root radial plane whereas such gradient rapidly dissipates in a non-growing zone. These findings echo an independent experimental work showing that signal perception triggering the hydrotropic response of Arabidopsis roots occurs in the elongating cortex [START_REF] Dietrich | Root hydrotropism is controlled via a cortex-specific growth mechanism[END_REF] . Thus, the general principles governing root responses to water availability are emerging and we now know where to look for 'water sensing' and early signalling mechanisms! A first significant step was recently taken by Orosa-Puente et al. [START_REF] Orosa-Puente | Root branching toward water involves posttranslational modification of transcription factor ARF7[END_REF] . These authors showed how the hydropatterning response relies on a chain of negative regulations which locally repress lateral root formation. In brief, local water deficit acts on SUMO protease function to enhance sumoylation of auxin response factor ARF7, which in turn accumulates and represses the downstream expression of root-inducing transcription factor LBD16.

It is still disputed whether xerobranching is an extreme case of hydropatterning or would involve a fully distinct mechanism [START_REF] Dinneny | Developmental responses to water and salinity in root systems[END_REF][START_REF] Orman-Ligeza | The xerobranching response represses lateral root formation when roots are not in contact with water[END_REF] . The authors showed that xerobranching can be mimicked by a transient ABA accumulation and response due to local water deficit, which would somewhat antagonize constitutive auxin-dependent root branching. However, this model awaits validation using ABA signaling mutants [START_REF] Dinneny | Developmental responses to water and salinity in root systems[END_REF] . Nevertheless, this hormonal regulation is different from previously described root responses to long-term exposure to ABA or water deficit. In all cases, a deep interconnection between ABA and auxin is emerging [START_REF] Dinneny | Developmental responses to water and salinity in root systems[END_REF] .

The perception of water excess relies on a completely different mechanism involving a class (class VII) of transcription factors which are homologous to Ethylene Responsive Factors (ERF) and are specifically oxidized and degraded by the O 2 and nitric oxide (NO) sensing branch of the PROTEOLYSIS 6 (PRT6) N-degron pathway [START_REF] Voesenek | Flood adaptive traits and processes: an overview[END_REF][START_REF] Holdsworth | The plant N-degron pathways of ubiquitin-mediated proteolysis[END_REF] . Under flooding (O 2 deprivation) conditions, these socalled ERF-VII factors are stabilized to trigger a core anaerobic transcriptional response. Recent work indicate that this core mechanism is itself regulated by multiple hormonal and environmental cues.

For instance, ethylene, which accumulates in the early phases of submergence and pre-acclimates plant to hypoxia stress, was shown to stabilize ERF-VII factors by increasing the expression of PHYTOGLOBIN1, which in turn scavenges NO [START_REF] Hartman | Ethylene-mediated nitric oxide depletion pre-adapts plants to hypoxia stress[END_REF] . The HCR1 protein kinase was also shown to stabilize one such factor (RAP2.12), specifically in the presence of K + , thereby potentiating this response, and promoting by as yet unknown mechanisms the inhibition of root hydraulic conductivity [START_REF] Shahzad | A potassium-dependent oxygen sensing pathway regulates plant root hydraulics[END_REF] . What might be the significance of this joint response pathway to O 2 and K + availability? Whereas O 2 deprivation directly reports on the intensity of flooding stress, K + availability could reflect the growth capacity of the plant depending on soil washing [START_REF] Manik | Soil and crop management practices to minimize the impact of waterlogging on crop productivity[END_REF] . As a major intracellular cation, K + indeed contributes to turgor maintenance and thereby growth. In this context, HCR1 activation in the presence of K + would promote the plant's metabolic acclimation to flooding stress, thereby providing an enhanced growth capacity during the recovery phase (Fig. 2b). Depending on its intensity, flooding can result in soil water logging or full plant submergence that impact with different extent the water status and growth of plants [START_REF] Voesenek | Flood adaptive traits and processes: an overview[END_REF] . It was proposed that natural alleles of HCR1 with distinct functionalities may have distinct adaptive values in these different scenarios.

ERF-VII transcription factors also play a role in the growth responses of Arabidopsis roots to hypoxia by repressing the slanting response of the primary root to hypoxia [START_REF] Eysholdt-Derzso | Root bending is antagonistically affected by hypoxia and ERF-mediated transcription via auxin signaling[END_REF] and promoting elongation of adventitious roots [START_REF] Eysholdt-Derzso | Hypoxia and the group VII ethylene response transcription factor HRE2 promote adventitious root elongation in Arabidopsis[END_REF] . We also note that the capacity of plant roots to sense and accclimate to O 2 availability goes beyond their responses to flooding stress. Hypoxic niches that naturally occur under aerobic conditions were recently shown to play significant roles in root development. Starting from the observation that hypoxic-responsive genes are induced during the late phases of lateral root formation, Shukla et al. [START_REF] Shukla | Endogenous hypoxia in lateral root primordia controls root architecture by antagonizing auxin signaling in Arabidopsis[END_REF] showed how ERF-VII transcription factors bind to auxin-responsive transcriptional complexes to repress the expression of master regulators of lateral root formation, thereby contributing to the termination of this process.

Conclusions

Roots can be seen as a biological network integrating three main functions: growth, water transport, and water perception and signalling. The first two functions yield the root hydraulic architecture, an underexplored yet key trait. One main question is to understand how this architecture evolves in time and space by integrating local and systemic signals reporting on the availability of water. The present review indicates that the modes and mechanisms of response of roots to water deficit or excess are fundamentally distinct. While ABA emerges as a coordinator of root hydraulic architecture under drought 46 , we miss corresponding information on integrative hydraulic responses of roots to flooding stress. Also, a large focus has been made on aquaporin regulation under drought, whereas the significance of suberization and xylem differentiation with respect to root hydraulics remains disputed. More generally, future research will have to uncover the main principles and variety of strategies used by plant roots to optimize soil water uptake and maintain the plant water status under varying water availabilities. In these respects, mathematical modeling will be crucial to integrate functional and architectural components of whole root systems. In particular, a specific challenge will be to determine and possibly design root genotypes which are the best adapted to specific drought or flooding scenarios or culture practices such as deficit irrigation or partial root zone drying. More generally, a better integration of root functions and their relations to soil in crop models would certainly aid crop improvement.

Recent progress in plant molecular genetics now makes it possible to directly address these issues in the most relevant crops. Besides genome editing using CRISPR-Cas9 which now offers a powerful approach to knock down genes of interest [START_REF] Char | An Agrobacterium-delivered CRISPR/Cas9 system for high-frequency targeted mutagenesis in maize[END_REF] , GWAS provide a potentially direct and rapid approach to the identification of genes controlling a trait of interest. For instance, this approach has been successfully used to isolate genes contributing to drought tolerance in crop plants with complex genomes such as maize [START_REF] Wang | Genetic variation in ZmVPP1 contributes to drought tolerance in maize seedlings[END_REF][START_REF] Mao | A transposable element in a NAC gene is associated with drought tolerance in maize seedlings[END_REF] and it can now be used to target specific root traits. Cereals which display an elaborate embryonic and postembryonic root developmental program also hold promises for exciting discoveries in root functionalization.

Figure legends

Fig. 1| The water uptake capacity of a root system is determined by both its architecture and hydraulics.

a) The root system architecture is determined in part by soil water availability which can be highly heterogeneous depending on soil layers. As shown in the inset, these local heterogeneities can orientate root tip growth (hydrotropism) and lateral root formation (hydropatterning). b) Water uptake can be decomposed in radial water transport from the soil to the root stele and axial transport along the xylem vessels. Aquaporins, which contribute to transcellular water flows during radial transport, determine to a large extent the root hydraulic conductivity. Suberized and lignified endodermis or exodermis (not shown) can also impact radial transport.

Fig. 2|

 2| Fig. 2| Quantitative genetics allowed the identification of novel genes involved in the regulation of root hydraulics under composite stress conditions. a) Optimal growth and transpiration of a plant in a fully aerated (O 2 ), irrigated (H 2 O) and fertilized(K + ) soil. The load of soil pathogenic bacteria (bacteria) is maintained at a minimum. The water uptake capacity of the root system is accounted for by its hydraulic conductivity (Lp r ). b) Flooding results in oxygen deficiency (hypoxia) of the root system. In the presence of nutriments (K + ), induction of the Hydraulic Conductivity of Root 1 (HCR1) pathway enhances the core anaerobic transcriptional response (anaerobic metabolism) and inhibits water uptake (Lp r ). These responses promote plant acclimation to submergence and a better growth during the recovery phase. c) The Xylem NAC Domain 1 (XND1) transcription factor negatively regulates xylem differentiation and as a consequence Lp r . Pathogenic bacteria can penetrate the root and move axially through its vasculature. They also enhance the expression of XND1. Reduced xylem differentiation is detrimental under water deficit (brown) and results in plant wilting. Yet, it restricts the proliferation of vascular pathogens and therefore diminishes the susceptibility of the plant to bacterial wilt. Thus, XND1 determines a trade-off between responses to abiotic and biotic stresses.

Acknowledgements

This work was supported in part by the Agence Nationale de la Recherche (ANR-11-BSV6-018) and the European Research Council (ERC-2017-ADG-788553).

Contributions

C.M. wrote this article which was discussed with and corrected by P.N.

Corresponding author

Correspondence to Christophe Maurel

Competing interests

The authors declare no competing interests