E Calais

L Dong

M Wang

Z Shen

M Vergnolle

Continental Deformation in Asia from a Combined GPS Solution

After decades of research on continental tectonics, there is still no consensus on the mode of deformation of continents or on the forces that drive their deformation. In Asia the debate opposes edge-driven block models, requiring a strong lithosphere with strain localized on faults, to buoyancy-driven continuous models, requiring a viscous lithosphere with pervasive strain. Discriminating between these models requires continent-wide estimates of lithospheric strain rates. Previous efforts have relied on the resampling of heterogeneous geodetic and Quaternary faulting data sets using interpolation techniques.

We present a new velocity field based on the rigorous combination of geodetic solutions with relatively homogeneous station spacing, avoiding technique-dependend biases inherent to interpolation methods. We find (1) unresolvable strain rates (< 3 × 10 9 /yr) over a large part of Asia, with current motions well-described by block or microplate rotations, and (2) internal strain, possibly continuous, limited to high-elevation areas.

Introduction

Geodetic measurements at sites located far enough away from active plate boundaries show that horizontal surface motions on most of our planet can be described by simple rotations of a limited number of rigid plates, as predicted by plate tectonics (e.g., [START_REF] Argus | Plate motion and crustal deformation estimated with geodetic data from the Global Positioning System[END_REF]. In deforming continents such as Asia or the Western U.S., however, the ability of plate tectonic concepts to describe horizontal motions is still questioned [START_REF] Thatcher | GPS constraints on the kinematics of continental deformation[END_REF]. Indeed, observations and models of actively deforming continents such as Asia 1 have led to two opposing interpretations. For some, continental lithosphere deforms as a mosaic of rigid lithospheric blocks bounded by fast-slipping faults affecting the entire thickness of the lithosphere. In that view, deformation is solely driven by boundary forces due to the India-Eurasia collision (e.g., [START_REF] Tapponnier | Propagating extrusion tectonics in Asia: New insights from simple experiments with plasticine[END_REF]Peltzer and Tapponnier, 1988;[START_REF] Peltzer | Present-day kinematics of Asia derived from geological fault rates[END_REF]. For others, deformation is pervasive and continents can be treated as a continuously deforming viscous medium where faults play a minor role. In that view, deformation is driven for a large part by buoyancy forces resulting from crustal thickening in response to the India-Eurasia collision (e.g., [START_REF] England | Finite strain calculations of continental deformation, 2. Comparison with the India-Asia collision zone[END_REF][START_REF] Houseman | Crustal thickening versus lateral expulsion in the India-Asian continental collision[END_REF].

In some instances, space geodetic studies have provided insight into this debate. For instance, GPS measurements show that the central part of the Altyn Tagh fault accumulates strain at a rate of 9 mm/yr [START_REF] Bendick | Geodetic evidence for a low slip rate in the Altyn Tagh fault system[END_REF][START_REF] Shen | Crustal deformation along the Altyn Tagh fault system, western China, from GPS[END_REF]Wallace et al., 2004), inconsistent with edge-driven block models that require slip rates at least a factor of two larger [START_REF] Peltzer | Present-day kinematics of Asia derived from geological fault rates[END_REF]. Geodetic measurements of the eastward velocity of south China at 8 to 10 mm/yr (e.g., [START_REF] Wang | Present-Day Crustal Deformation in China Constrained by Global Positionning System Measurements[END_REF] match block models and continuous deformation models equally well [START_REF] Peltzer | Present-day kinematics of Asia derived from geological fault rates[END_REF]Molnar and Gipson, 1996) but proved wrong early models of extrusion that required at least 10-15 mm/yr of eastward motion of south China [START_REF] Avouac | Kinematic model of deformation in central Asia[END_REF]. At a continent-wide scale, [START_REF] Flesch | Dynamics of the India-Eurasia collision zone[END_REF], used an interpolated velocity field derived from heterogeneous GPS data and Quaternary fault slip rates to show that large parts of Asia undergo little internal deformation and that gravitational potential energy (GPE) contributes up to 50% to the force balance. [START_REF] England | Late Quaternary to decadal velocity fields in Asia[END_REF], using similar data but a different spatial resampling technique, argue that continuous deformation dominates.

Here, we combine geodetic solutions in Asia to produce a new velocity field with continent-wide coverage and relatively homogeneous station spacing, removing the need for spatial resampling, necessarily model-dependent. The kinematic analysis of this continent-wide data set shows unresolvable strain rates over a large part of Asia, while significant strain rates, possibly associated with continuous deformation, are limited to the high-elevation areas of the Himalaya, Tibet, Pamir-Tien Shan, and Western Mongolia.

GPS data

In order to obtain a geodetically consistent velocity field covering Asia, we combined three GPS solutions. Asia with data spanning from 1991 to 2002 [START_REF] Socquet | India and Sunda plates motion and deformation along their boundary in Myanmar determined by GPS[END_REF]. Although Socquet et al.'s (2006) original solution contains 191 sites, those located within active plate boundary zones in eastern Indonesia (Sulawesi, Timor, Irian Jaya) and the Philipines were not considered here.

The first one covers

For the first two data sets, we processed the pseudorange and phase GPS data single-day solutions, together with 16 reference stations of the International GPS Service (IGS) to serve as ties with the International Terrestrial Reference Frame (ITRF). Details on the data processing procedure can be found in [START_REF] Wang | Contemporary crustal deformation of Chinese continent and blocking motion model[END_REF] and [START_REF] Calais | GPS measurements of crustal deformation in the Baikal-Mongolia area (1994-2002): Implications for current kinematics of Asia[END_REF] and are not repeated here. The resulting least squares adjustment vector and its corresponding variance-covariance matrix for station positions and orbital elements estimated for each independent daily solution were then combined with global So-X -3 lution Independent Exchange format (SINEX) files from the IGS daily processing routinely done at Scripps Institution of Oceanography (http://sopac.ucsd.edu) into a single, unconstrained, global solution using the combination method described in [START_REF] Dong | Estimating Regional Deformation from a Combination of Space and Terrestrial Geodetic Data[END_REF]. The velocity error model includes a 2 mm/ √ yr random walk component to account for colored noise in GPS uncertainties. We imposed the reference frame by minimizing the position and velocity deviations of 25 core IGS stations with respect to the ITRF2000 [START_REF] Altamimi | ITRF2000: A New Release of the International Terrestrial Reference Frame for Earth Science Applications[END_REF] while estimating an orientation and translation (and their rate-of-change) transformation (12 parameters). These glacial isostatic adjustment effects [START_REF] Calais | GPS measurements of crustal deformation in the Baikal-Mongolia area (1994-2002): Implications for current kinematics of Asia[END_REF].

The resulting GPS velocity field describes horizontal surface motions at 188 sites in Asia with a precision ranging from 0.5 to 3.5 mmr/yr (Figure 1 2 ). In the following, we discard from the intrepretation sites with velocity uncertainties larger than 1.5 mm/yr. These sites, mostly located in the Mongolia-Altay-Baikal area, are consistently campaign sites with less than 3 observations epochs.

Velocity field

The combined GPS velocity field (Figure 1) and velocity profiles (Figure 2 an F-test [START_REF] Stein | Statiistical tests of additional plate boundaries from plate motion inversions[END_REF]. The F-statistics, defined as (χ 2 1plate -χ 2 2plates /3)/(χ 2 2plates /72) is 2.3, implying that the χ 2 decrease is significant at the 92% level.

The data is therefore better fit by a splitting North and South China into two separate plates, although not at a very high significance level.

Our rotation pole for Sunda is located southwest of Australia, with a clockwise rotation with respect to Eurasia. These parameters differ significantly from those of Chamot-Rooke and Le Pichon (1999), possibly because of different definition of the Eurasia frame. They also differ from those of [START_REF] Bock | Microplate Tectonics of Indonesia from Global Positioning System Measurements, 1989-1994[END_REF], but these authors considered Sunda and South China as a single block. Using a F-test, we find that the χ 2 decrease when splitting Sunda and South China compared to treating them as a single block is significant at the 99.9% confidence level, indicating that our data is fit significantly better by a two-plate model.

Strain distribution

The above analysis in terms of block rotations is limited by the a priori choice of block boundaries and site

subsets. An alternative approach consists of calculating horizontal strain rates over the study area. To do so, we discretize the study area using a Delaunay triangulation and calculate, for each triangle, the strain rate tensor with its covariance matrix, its level of significance, the principal strain rates, and the second invariant of the strain rate tensor -or effective strain rate -given by

Ė = ( ˙ ij ˙ ij )/2
, where ˙ ij are the components of the strain rate tensor and summing over repeated subscripts applies.

The resulting maps (Figure 3) show that strain rates are significant at the 95% confidence in the Himalayas, Tibet, Pamir-Tien Shan, Altay and Gobi Altay, with principal compressional axis consistent with shortening perpendicular to these structures. Within Tibet, principal strains show a combination of NNE-SSW compression and WNW-ESE extension, consistent with previous results [START_REF] Wang | Present-Day Crustal Deformation in China Constrained by Global Positionning System Measurements[END_REF][START_REF] Zhang | Continuous deformation of the Tibetan Plateau from global positioning system data[END_REF] and geologic observations of widespread extension on NStrending normal faults in Tibet (e.g., [START_REF] Armijo | Quaternary extension in southern Tibet: Field observations and tectonic implications[END_REF][START_REF] Yin | Significant late Neogene east-west extension in northern Tibet[END_REF][START_REF] Kapp | Indian punch rifts Tibet[END_REF]. Strain rates are also significant in the Baikal rift zone and directly west and southwest of it in the Hovsgol, Darkhat, and Busingol grabens, with extensional maximum principal strain perpendicular to the major normal faults.

Effective strain rates in all these regions are larger than 3×10 -9 /yr and reach maximum values of 2-3×10 -8 /yr in the Himalayas, Burma, and along the eastern edge of the Tibetan plateau.

Strain rates are not significant at the 95% confidence level in the rest of Asia (including the Tarim basin, central and eastern Mongolia, north and south China, and Sunda). These regions also show effective strain rates less than 3×10 -9 /yr, which corresponds to the current precision level of the GPS data set (average triangle dimension ∼ 300 km, velocity precision ∼ 1 mm/yr). These regions of unresolvable strain rate, at the current precision of the GPS data, are consistent with the major blocks or microplates defined above. Strain rates in a significant part of Asia (about 60% of the area considered in this study) are therefore comparable to stable plate interiors (less than 3×10 -9 /yr) and not resolvable at the current precision level of GPS measurements in Asia.

Our findings contrast with [START_REF] England | Late Quaternary to decadal velocity fields in Asia[END_REF] conclusion that continuous deformation dominates in Asia, while block-like motions are restricted to the Tarim basin and small portions of north and south China.

The difference likely results from England and Molnar's modeling approach, which resamples heterogeneous GPS data sets and Quaternary fault slip rates over a coarse triangular grid with linear shape functions. Our results match Flesch et al.'s (2001) interpolated kinematic model better, which however does not fit the observed east to southeastward velocities in Mongolia and North China.

However, we do find, like [START_REF] Flesch | Dynamics of the India-Eurasia collision zone[END_REF] and [START_REF] England | Late Quaternary to decadal velocity fields in Asia[END_REF], a radial pattern in principal compressional strain rate directions around Tibet aligned with gradients of gravitational potential energy, an argument used by [START_REF] England | Late Quaternary to decadal velocity fields in Asia[END_REF] to support the idea that buoyancy forces play a significant role in driving present-day deformation in Asia.

Conclusion

The debate on continental deformation in Asia opposes edge-driven block models, requiring a strong lithosphere with strain localized on faults, to buoyancy-driven continuous models, requiring a viscous lithosphere with pervasive strain. As shown here, block-or plate-like motions appear to provide an accurate kinematic description of surface deformation for most of Asia. Similar conclusions have been drawn at a smaller scale for Tibet [START_REF] Thatcher | Present-Day Microplate Tectonics of Tibet and its Relation to Rheological Stratification and Flow in the Lithosphere[END_REF] r is the chi-squared per degree of freedom (dof). λ and φ are the latitude and longitude, respectively, of the Euler pole describing the block rotation with respect to Eurasia (in decimal degrees). σ maj and σ min are the semi-major and semi-minor axes of the pole error ellipse in degrees. θ is the direction of the semi-major axis in degrees counterclockwise from East. Ang. is the rotation rate in degrees per Ma. WRMS is the weighted root mean square of residual velocities for each block.

  Mongolia, the Baikal rift zone, and the Russian Altay. It contains 110 survey sites, of which 64 have been observed at least 3 times from 1994 to 2004, and 3 continuous stations. The second one includes 83 stations in China measured between 1998 and 2005, of which 27 became continuous in 1999. The 56 other are measured annually, with 10 observation-days per site each year. The third one includes 41 sites in Southeast

  25 reference stations, globally distributed, were chosen for having velocity uncertainties less that 2 mm/yr on the horizontal and 5 mm/yr on the vertical components in the ITRF2000 definition. The post-fit f ¯weighted root-meansquare (WRMS) of the reference frame stabilization is 2.0 mm in position and 0.6 mm/yr in velocity. We then combined the resulting solution with that of Socquet al. (2006) for Southeast Asia, by estimating a 7-parameter transformation (translation, rotation, and scale) based on 12 IGS stations common to the two solutions. The WRMS of the velocity differences at the common sites is 1.2 mm/yr. We mapped the resulting velocities (in ITRF2000) into a Eurasia-fixed frame by minimizing velocities at 15 sites distributed across the Eurasian plate (YAKT, IRKT, KSTU, ARTU, ZWEN, GLSV, GRAZ, WSRT, POTS, WTZR, KOSG, CAGL, NRIL, NVSK, VILL), while propagating the variance of the ITRF2000-Eurasia angular velocity to the individual site velocities. These 15 reference sites are chosen to cover the entire stable part of the Eurasian plate and are located away from areas potentially affected by tectonic deformation or significant

  ) illustrate the known convergence between India and the Tarim basin, the eastward motion of Tibet and south China and the clockwise rotation of eastern Tibet around the eastern Himalayan syntaxis. Convergence between India and Eurasia occur at 38 mm/yr (from velocities at sites Bangalore and Hyderabad in southern India), consistent with GPS-derived plate motion parameters for India[START_REF] Paul | The motion and active deformation of India[END_REF][START_REF] Sella | REVEL: A model for recent plate velocities from Space Geodesy[END_REF]. The western velocity profile shows consistent NNE-directed azimuths with velocity magnitudes steadily decreasing northward, indicative of NNE-SSW shortening. About 20 mm/yr of the total shortening is accommodated in the Himalayas, as previously reported byBilham et al. (1997), while the remaining 17 mm/yr are distributed from Tibet to the Siberian platform, mostly taken up in the Tien Shan (17 mm/yr in the west, decreasing eastward to less than 10 mm/yr).On the central profile (Figure2B), horizontal velocities show a more complex pattern, with about 20 mm/yr of shortening accommodated in the Hymalayas and Ti-bet, but no shortening north of the Qilin Shan. This NNE-SSW shortening is accompanied, in Tibet, by up to 17 mm/yr of ESE-ward motion. North of the Qilin Shan, across western Mongolia and all the way to the Baikal rift zone velocities are directed ESE-ward at 3 to 5 mm/yr.On the eastern profile (Figure2C), horizontal motions are mostly directed to the east or southeast, with a steady increase in magnitude from 0 to about 9 mm/yr from north to south across north and south China. This consistent pattern of east-to southeastward motions from eastern Mongolia, north China, and south China, is a striking feature of this velocity field and had not yet been documented at that scale.To separate block rotations from distributed strain, we attempt to describe the horizontal velocity field in terms of rotations of non-deforming blocks or microplates. To do so, we use the trace of major active faults in Asia (Figure1) to divide the velocity field into 6 subsets of sites, representing the following blocks: North China (or "Amurian plate" of Zonenshain and Zavostin, 1981), South China, Sunda (e.g., Chamot-Rooke and Le Pichon, 1999;[START_REF] Bock | Microplate Tectonics of Indonesia from Global Positioning System Measurements, 1989-1994[END_REF], Tarim basin, Qaidam basin, and Central Tibet. In Tibet, we limit our analysis to two blocks, Qaidam and Central Tibet, bounded by the Altyn Tagh, Kunlun, and Jiali faults[START_REF] Chen | A deforming block model for the presentday tectonics of Tibet[END_REF] because the low density of sites in our solution does not provide the resolution necessary to investigate kinematics at smaller spatial scales. Also, we omit GPS sites located within actively deforming structures in the Himalayas, the Tien Shan, western Mongolia (Altay and Gobi Altay), Eastern Tibet (Karakorum and Pamir), Western Tibet (Longmen Shan), and in the Ordos, possibly affected by non-secular deformation processes on these active tecctonic structures (e.g., interseismic strain accumulation or postseismic deformation). For the same reason, we omit sites located within 500 km of the Andaman-Sumatra-Java subduction, where elastic loading effects are significant (Chamot-Rooke and Le Pichon, 1999). We then solve for block angular rotations with respect to Eurasia by inverting the model that relates horizontal site velocities to plate angular velocity. Table1shows the resulting angular rotations and corresponding statistics, while Figure 1 (bottom) shows residual velocities after subtracting the estimated rotations.The fit to a block rotation is good for most site subsets, with reduced chi-squared close to unity, except for the Qaidam and Central Tibet subsets. The fit in Tibet is not improved by considering Qaidam and Central Tibet as a single block, consistent with previous reports of block motions and internal deformation from denser GPS measurements in Tibet[START_REF] Chen | A deforming block model for the presentday tectonics of Tibet[END_REF]. The fit to a rigid rotation is particularly good for South China, with a weighted velocity residual RMS of 0.4 mm/yr. For North China, the resulting angular velocity is consistent with a recent estimate by[START_REF] Apel | Independent Active Microplate Tectonics of Northeast Asia from GPS Velocities and Block Modeling[END_REF], based on a similar dataset. It is significantly different from previous estimates from Kreemer et al. (2003), Sella et al. (2003), and Prawirodirdjo and Bock (2004), but those were constrained by 3 sites only. The rotation poles for North and South China are located in eastern Siberia and associated with a counter-clockwise rotation with respect to Eurasia. The linear gradient in eastward velocities from north to south on Profile C (Figure 2) and the lack of offset at the boundary between North and South China may suggest that they constitute a single plate. We tested the significance of the χ 2 decrease from a solution where North and South China are treated as a single block to a solution where they are treated as two separate blocks using CALAIS ET AL.: CONTINENTAL DEFORMATION IN ASIA FROM GPS X -5

Figure 1 .

 1 Figure 1. Top: Horizontal GPS velocities shown with respect to Eurasia. Large velocities at sites on adjacent plates are shown transparent for a sake of readability. The dashed boxes show the domains included in the 3 profiles (A, B, C) shown on Figure 2. Bottom: Residual velocities after subtracting rigid block rotations (see explanations in text). Dots show the location of all GPS sites. Major blocks used here are shown with color background. White areas were not included in the block analysis. Error ellipses are 95% confidence interval on both figures.

Figure 2 .

 2 Figure 2. Velocity profiles: GPS velocity components projected into profile-parallel (along-track) and profile-perpendicular (cross-track) directions. The profile locations and sites included are shown on Figure 1 (top).

Table 1 .

 1 Angular velocities. χ 2

	Acknowledgments. We thank our collaborators in Rus-
	sia (Institute of the Earth Crust, Irkutsk and Institute of
	Geology, Geophysics, and Mineralogy, Novosibirsk, Siberian
	Branch of the Russian Academy of Sciences), Kazakhstan (In-
	stitute for High Temperatures), Mongolia (Research Center for
	Astronomy and Geophysics), for their invaluable contribution
	to the collection and processing of the GPS data. We thank A.
	Socquet and C. Vigny for making their GPS results available
	in advance of publication. Insightful reviews by P. Molnar and
	an anonymous reviewer and discussions with L. Flesch signifi-
	cantly helped improve the manuscript. This work was funded
	by NSF under award EARXXXX, CNRS-INSU ("Intérieur de
	la Terre" Program).
	Notes
	1. Supplemental Material is available at ftp://ftp.agu.org/apend/gl/2006GL28433
	2. See Supplemental materials

and the Western U.S. (e.g.,

[START_REF] Meade | Block models of crustal deformation in southern California constrained by GPS measurements[END_REF]

. Although these results apparently favor block models, they do not rebut continuous deformation models, provided that significant lateral variations in lithospheric strength exist. This is supported by results from

[START_REF] Flesch | Dynamics of the India-Eurasia collision zone[END_REF]

, who show that vertically averaged effective viscosity in Asia varies laterally by up to 3 orders of magnitude. The GPS velocity field presented here does not resolve, by itsef, the debate on continental deformation but provides new quantitative information to validate physical theories on driving forces.


Saleem Hamady
email: shamady@laas.fr

Frédéric Morancho
email: morancho@laas.fr

Bilal Beydoun

Patrick Austin
email: austin@laas.fr

Mathieu Gavelle
email: mathieu.gavelle@cea.fr

Normally-Off AlGaN/GaN HEMT using fluorine implantation below the channel

Keywords: TCAD simulation, normally-off, Gallium Nitride (GaN), High electron mobility transistor (HEMT), fluorine implantation

RESUME

-AlGaN/GaN HEMTs are very promising candidates for high frequency applications with high power and low noise. Unfortunately, while switching applications strongly demand normally-off operation, conventional HEMTs are normally-on. For the sake of achieving normally-off HEMTs, several structures have been proposed. One of the major normally-off HEMTs uses fluorine implantation in the AlGaN layer. We suggest in this work the implantation of fluorine ions under the AlGaN/GaN interface only below the gate electrode rather than implanting in the AlGaN layer. Simulation results show that the proposed method is capable of achieving normallyoff operation and more effective when it comes to the fluorine concentration required to obtain the desired threshold voltage. Neither the vertical breakdown voltage, nor the off-state current are affected by this approach.

INTRODUCTION

The High Electron Mobility Transistor (HEMT) is a field effect transistor in which two layers of different bandgaps and polarization fields are grown upon one another. As a consequence of the discontinuity in the polarization field, surface charges at the heterointerface are created. If the induced charge is positive, electrons will tend to compensate the induced charge resulting in the formation of a two dimensional electron gas (2DEG) [START_REF] Chen | Enhanced device performance of AlGaN/GaN HEMTs using thermal oxidation of electron-beam deposited aluminum for gate oxide[END_REF]. Thanks to the GaN properties and the HEMT's topology, AlGaN/GaN HEMTs are now promising devices for high frequency applications with high power and low noise, such as microwave and millimeter wave communications, imaging and radars [START_REF] Mishra | AlGaN/GaN HEMTs-an overview of device operation and applications[END_REF].

In the conventional HEMT, the energy levels of the triangular quantum well, formed in the GaN layer below the AlGaN/GaN interface, are below the Fermi level at equilibrium. This will make the channel populated with electrons at zero gate voltage, hence making the HEMT normally-on. However, for power switching applications, normally-off operation is strongly required [START_REF] Kambayashi | High field-effect mobility normally-off AlGaN/GaN hybrid MOS-HFET on Si substrate by selective area growth technique[END_REF]. In order to achieve normally-off operation, the energy levels must be lifted above the Fermi level. Several structures have been proposed

for the realization of normally-off AlGaN/GaN HEMT such as recessed gate structures [START_REF] Burnham | Gate-recessed normally-off GaN-on-Si HEMT using a new O2-BCl3 digital etching technique[END_REF], fluorine ion treatment [START_REF] Chen | Self-aligned enhancement-mode AlGaN/GaN HEMTs using 25 keV fluorine ion implantation[END_REF], pn junction gate structures [START_REF] Hu | Enhancement mode AlGaN/GaN HFET with selectively grown pn junction gate[END_REF], thin AlGaN barrier [START_REF] Ohmaki | Enhancement-Mode AlGaN/AlN/GaN High Electron Mobility Transistor with Low On-State Resistance and High Breakdown Voltage[END_REF], AlN/GaN structure [START_REF] Higashiwaki | Enhancement-Mode AlN/GaN HFETs Using Cat-CVD SiN[END_REF] and conventional HEMT with InGaN cap layer [START_REF] Mizutani | AlGaN/GaN HEMTs With Thin InGaN Cap Layer for Normally Off Operation[END_REF]. In the normally-off HEMT reported in [START_REF] Chen | Self-aligned enhancement-mode AlGaN/GaN HEMTs using 25 keV fluorine ion implantation[END_REF], fluorine ions are implanted in the barrier layer (AlGaN layer). When this approach is used, small amount of fluorine ions penetrate into the channel formed at the AlGaN/GaN interface, presenting themselves as impurities that lead to mobility degradation [START_REF] Chen | Physics of fluorine plasma ion implantation for GaN normally-off HEMT technology[END_REF]. In this paper, we propose to implement the ions below the channel (in the GaN layer) under the AlGaN/GaN interface, and that only below the gate electrode. To obtain this structure, the following can be done: after growing the buffer and GaN layers, fluorine ions will be implanted. Then the channel layer of GaN (15 nm) will be introduced, and above all comes the AlGaN layer (barrier layer). This way, no scattering will occur between the 2DEG and the fluorine ions since the fluorine ions are below the channel region.

SIMULATION STRATEGY ATLAS, a physically-based TCAD simulation tool from

Silvaco, is used to analyze the new HEMT structure. Physical models of the simulator are based on Shockley-Read Hall recombination, Fermi-Dirac statistics and field-dependent mobility [START_REF] Silvaco | ATLAS User's Manual DEVICE SIMULATION SOFTWARE[END_REF]. The simulator is calibrated by using real parameters of a normally-on HEMT device, as shown in figure 1. Add "cm-3" after 10 15 and 10 16 in the figure 1.

In figure 2, the simulation results are presented and compared with the experimental transfer characteristics I d (V gs ). A good match is observed for the threshold voltage (V th ) and the transconductance (g m ). During calibration, the energy and the concentration of the acceptor traps as well as the density of the 2DEG were tuned. In Table 1, some of the parameters used for the simulation are illustrated.

Table 1: HEMT simulation parameters

To simulate the effect of the implanted fluorine ions, negative charge was added inside the GaN (or AlGaN) layer. To do that using ATLAS, the GaN (or AlGaN) layer was split into two layers. This will generate an interface (GaN/GaN or AlGaN/AlGaN homo-interface) inside the layer. At this interface, a fixed negative charge is added. Although the profile of the fluorine ions concentration, resulting from this approach, differs from the profile experimentally obtained, its effect on the transfer characteristics can be imitated by varying the concentration of negative charge at the interface.

SIMULATION RESULTS

Fluorine implantation in AlGaN layer

Figure 3 shows the transfer characteristics of the conventional normally-on HEMT of figure 1 ("Null") and HEMTs with fluorine implanted in AlGaN (figure 4) at various concentrations (from 4 × 10 12 to 1.4 × 10 13 cm -2 ). The distance between the fluorine ions and the AlGaN/GaN interface is taken 15 nm. It is clear that, at a certain fluorine concentration (1.4 × 10 13 cm -2 ), this technique is capable of shifting the threshold voltage to a positive value (0.5 V), making the HEMT normally-off.

Fluorine implantation in the GaN layer

Figure 5 shows the transfer characteristics of the conventional normally-on HEMT of figure 1 ("Null") and HEMTs with It can be seen from figures 3 and 5 that although the same threshold voltage (0.5 V) was achieved after implantation in both cases, the fluorine concentration required to achieve the desired threshold voltage is lower (8×10 12 < 14×10 12 ) when implantation is performed in the GaN layer rather than in the AlGaN layer, making our proposed technique more efficient.

ENERGY BAND DIAGRAM

To further explore the consequences of the two different techniques, the band diagrams for the two structures are shown in figure 7. It can be concluded from this figure that the implantation in GaN is more effective: since HEMTs attain Schottky gates, the conduction band at the top of the AlGaN layer is pinned at a fixed energy equals to the Schottky barrier. If it was not for that pinning, the conduction band in AlGaN would have risen higher when fluorine is implanted, causing a higher shift in the threshold voltage. Moreover, it can be noted, from the band diagram, that the confinement of the 2DEG under the gate is superior in the case of Fluorine implanted in GaN (see zoom in Figure 7).

BREAKDOWN AND OFF-STATE CURRENT

To examine the off-state current and the breakdown voltage, the structure shown in figure 6 was studied. However, an x-mole fraction of 0.15 was used instead (YOU HAVE TO EXPLAIN HERE, IN ONE SENTENCE, WHY YOU HAVE CHANGED THE X-MOLE FRACTION). In this case, a fluorine concentration of 4.2 × 10 12 cm -2 is necessary to achieve normally-off operation with a threshold voltage of 0.5 V. The same HEMT with no fluorine implantation attains a threshold voltage of -2 V.

Figure 8 shows the variation of the drain current with the applied drain to source voltage I d (V ds ). The applied gate to source voltage is: V gs = V th -1 V, in order to study the two HEMTs in the off-state, i.e. below their threshold voltage. It is clear that neither the vertical breakdown voltage, nor the offstate current are affected by the implanted fluorine ions. A breakdown voltage of 280 V was obtained in both cases.

CONCLUSION

In this work, for the sake of obtaining a normally-off HEMT, we suggest the implantation of fluorine ions in the GaN layer, under the AlGaN/GaN interface only below the gate electrode, rather than the implantation in the AlGaN layer as previously proposed in other papers. Using numerical simulations, we have shown that this approach is capable of shifting the threshold voltage to positive values. In addition to that, this technique is more effective when it comes to the concentration required to achieve normally-off operation. Moreover, with this technique, the channel electrons will be better confined below the gate and scattering with fluorine ions will vanish, since fluorine is implanted below the channel layer. Finally, the implantation of fluorine ions below the channel does not affect the vertical breakdown voltage and the off-state current.

ACKNOWLEDGMENT

Fig. 1 .

 1 Fig. 1. Schematic cross-section of the normally-on HEMT structure used for the calibration of the TCAD simulations.

Fig. 2 .

 2 Fig. 2. Comparison of experimental and simulated Id(Vgs) transfer characteristics showing a clear match for the threshold voltage and transconductance.

Fig. 3 .

 3 Fig. 3. Id (Vgs) transfer characteristics of the conventional normally-on HEMT and HEMTs with fluorine implanted in AGaN at various concentration.

Fig. 4 .

 4 Fig. 4. Schematic cross-section of the simulated HEMT with fluorine implanted in the AlGaN layer.

Fig. 5 .

 5 Fig. 5. Id (Vgs) transfer characteristics of the conventional normally-on HEMT and HEMT with fluorine implanted in GaN at various concentration.

Fig. 6 .

 6 Fig. 6. Schematic cross-section of the simulated HEMT with fluorine implanted in the GaN layer

Fig. 7 :

 7 Fig. 7: Band diagrams of HEMT with fluorine implanted in AlGaN at concentration 1.4×10 13 cm -2 and HEMT with fluorine in GaN at concentration 8×10 12 cm -2 ; both HEMTs attain a threshold voltage of 0.5 V.

This work was funded by the Laboratory for Analysis and Architecture of Systems (LAAS -CNRS/France) and by GET/EDST/UL-AZM & SAADA association.


The sensitivity of the variability of an eddy-driven jet to the upper-and lower-level baroclinicity of the mean state is analyzed using a three-level quasi-geostrophic model on the sphere. The model is forced by a relaxation in temperature to a steady, zonally symmetric profile with varying latitude and intensity of the maximum baroclinicity. The leading EOF of the zonally-and vertically-averaged zonal wind is characterized by a meridional shift of the eddy-driven jet. While changes in the upper-level baroclinicity have no significant impact on the persistence of this leading EOF, an increase in lower-level baroclinicity leads to a reduced persistence. For small lower-level baroclinicity, the leading EOF follows a classical zonal index regime, for which the meridional excursions of the zonal wind anomalies are maintained by a strong positive eddy feedback. For strong lower-level baroclinicity, the jet enters a poleward propagation regime, for which the eddy forcing continuously acts to push the jet poleward and prevents its maintenance at a fixed latitude. The enhanced poleward propagation when the lower-level baroclinicity increases is interpreted as resulting from the broader and weaker potential vorticity gradient which enables the waves to propagate equatorward and facilitates the poleward migration of the critical latitude. Finally, the decrease in EOF1 persistence as the lower-level baroclinicity increases is shown not to result from the impact of changes in the mean climatological jet latitude.

Introduction

Eddy-driven jets and storm tracks have a key role in mid-latitude surface weather and it is important to understand how they might respond to climate change. Results from the CMIP project experiments show a robust poleward shift of the jet in the Southern Hemisphere (Kidston and Gerber 2010), but the picture is more complicated in the Northern Hemisphere ocean basins (Barnes and Polvani 2013; Simpson et al. 2014;[START_REF] Vallis | Response of the Large-Scale Structure of the Atmosphere to Global Warming[END_REF]. In particular, there are competing influences of the local warming maxima in the upper tropical troposphere [START_REF] Seager | Mechanisms of Hemispherically Symmetric Climate Variability[END_REF][START_REF] Lu | Response of the Zonal Mean Atmospheric Circulation to El Niño versus Global Warming[END_REF]) and near the surface in the Arctic [START_REF] Oudar | Respective Roles of Direct GHG Radiative Forcing and Induced Arctic Sea Ice Loss on the Northern Hemisphere Atmospheric Circulation[END_REF], which change the meridional temperature gradient in opposite directions at different levels in the vertical, and therefore have opposite effects in terms of jet shifts (Butler et A change of the mean jet latitude can change its variability; as the mean jet moves poleward, its leading mode of variability -usually characterized by a latitudinal wobbling -often becomes less persistent, possibly because of a weaker positive eddy feedback [START_REF] Barnes | Effect of Latitude on the Persistence of Eddy-Driven Jets[END_REF]; Kidston and Gerber 2010; Arakelian and Codron 2012, see Fig. 5e), even if some studies with comprehensive models suggest that this relationship may not be as robust as initially thought (Simpson et al. 2013a; [START_REF] Simpson | Revisiting the relationship between jet position, forced response, and annular mode variability in the southern midlatitudes[END_REF]. Moreover, the dominant mode of variability may change its nature for high-latitude jets and become characterized more by a pulse in amplitude than by a latitudinal shift [START_REF] Barnes | Rossby Wave Scales, Propagation, and the Variability of Eddy-Driven Jets[END_REF]. The jet variability seems also strongly sensitive to the latitude of wave excitation, either the latitude of stochastic stirring in a barotropic model [START_REF] Barnes | Effect of Latitude on the Persistence of Eddy-Driven Jets[END_REF] or that of oceanic fronts in aquaplanet General Circulation Models (GCMs) experiments [START_REF] Michel | Sensitivity of the Position and Variability of the Eddy-Driven Jet to Different SST Profiles in an Aquaplanet General Circulation Model[END_REF][START_REF] Ogawa | Importance of Midlatitude Oceanic Frontal Zones for the Annular Mode Variability: Interbasin Differences in the Southern Annular Mode Signature[END_REF]. In these studies, the persistence of the leading mode of variability decreases as the wave excitation zone is shifted poleward, in agreement with the sensitivity to the jet latitude.

The impacts on the jet variability of changes in the mean temperature gradient or baroclinicity have been comparatively less studied. Son andLee (2005, 2006) performed sensitivity numerical experiments in a dry GCM by varying the tropical heating and high-latitude cooling rates of the radiative equilibrium temperature profile used to force their model. The intensity of the tropical heating controlled the strength of the subtropical jet while the high-latitude cooling largely determined the width and strength of the mid-latitude baroclinic zone. For large tropical heating and small polar cooling, a single jet appeared and the leading mode was a latitudinal wobbling of the jet (also referred to as the zonal index regime). In the opposite range of the parameter space (small tropical heating and large polar cooling), a double-jet structure emerged at upper levels and zonal wind anomalies tended to propagate poleward (also referred to as the poleward propagation regime). The interpretation mainly relied on the shape of the time-mean potential vorticity gradient [START_REF] Lee | A Mechanism for the Poleward Propagation of Zonal Mean Flow Anomalies[END_REF]; [START_REF] Son | Time Scale and Feedback of Zonal-Mean-Flow Variability[END_REF]). When it is strong and sharp as in the first case (zonal index), waves are meridionally trapped and mainly converge momentum into the jet core, leading to a strong positive eddy feedback. When it is weak and broad as in the second (propagating) case, waves propagate more easily equatorward and push the jet poleward. Similar arguments will be used in the present study when analyzing the sensitivity of the jet variability to the strength of the baroclinicity using a quasi-geostrophic model on the sphere. It is important to underline that our numerical setup significantly differs from the previously cited studies as the subtropical jet is weak in our quasi-geostrophic framework. Also, the originality of the present paper lies in the distinction made between the effects of changes in lower-level and upper-level baroclinicity.

Changes in the vertical structure of the baroclinicity are known to have an effect on jet position [START_REF] Butler | The Steady-State Atmospheric Circulation Response to Climate Change-like Thermal Forcings in a Simple General Circulation Model[END_REF][START_REF] Rivière | A Dynamical Interpretation of the Poleward Shift of the Jet Streams in Global Warming Scenarios[END_REF]) and eddy intensity (Held and O'Brien 1992; Yuval and Kaspi 2016) but its effect on the jet variability has not apparently been studied so far.

The idealized quasi-geostrophic model used in the present study has three vertical levels, which is the minimal framework to separate the baroclinicity into lower-and upper-level components. This model is thus well suited to study in particular the effect of opposite tendencies in lowerand upper-level temperature gradients, as occurs in global warming scenarios (Held and O'Brien 1992; Rivière 2011). The model is described in section 2, together with the different experiments.

The results describing the changes in the jet variability and eddy feedbacks when modifying the lower and upper-level baroclinicity are presented in section 3, together with a dynamical interpretation and sensitivity experiments to check the robustness of the results. Concluding remarks are provided in section 4.

Model and diagnostics

a. Numerical model

The model used is the dry quasi-geostrophic model on the sphere of [START_REF] Marshall | Toward a Dynamical Understanding of Planetary-Scale Flow Regimes[END_REF] at a T42 resolution. It has three pressure levels in the vertical at 200, 500 and 800 hPa. The model is governed by the following equations for the quasigeostrophic potential vorticity (PV) q i at levels i = 1, 2, 3:

∂ q i ∂t + J(ψ i , q i ) = S i -D i , q i = f + ∆ψ i + ψ i -ψ i+1 R 2 i - ψ i-1 -ψ i R 2 i-1 , (1)
where ψ i is the streamfunction (ψ 0 = ψ 1 and ψ 4 = ψ 3 ), R i is the deformation radius between levels

i and i + 1, S i -D i
S 1 -D 1 = -c H ∇ 8 (q 1 -f ) + 1 τ R1 ψ 1 -ψ 2 -ψ1 + ψ2 R 2 1 , S 2 -D 2 = -c H ∇ 8 (q 2 -f ) - 1 τ R1 ψ 1 -ψ 2 -ψ1 + ψ2 R 2 1 + 1 τ R2 ψ 2 -ψ 3 -ψ2 + ψ3 R 2 2 , S 3 -D 3 = -c H ∇ 8 (q 3 -f ) - 1 τ R2 ψ 2 -ψ 3 -ψ2 + ψ3 R 2 2 - 1 τ E ∇ 2 ψ 3 .
The first term on the right-hand-side (rhs) of the equation represents a scale-selective horizontal diffusion such that the damping time scale of the shorter waves at T42 truncation is 0.02 days.

The next term on the rhs represents a Newtonian relaxation in temperature toward a fixed profile (denoted with a tilde) using two timescales at the two interfaces. Finally, a linear drag with a timescale of τ E = 3 days is applied to the third level.

The restoration temperature profile is zonally-symmetric and in thermal wind balance with a Gaussian zonal jet given by :

ũi (λ , ϕ) = U i exp - (ϕ -ϕ 0 ) 2 dϕ 2 , ( 2
)
where ϕ 0 = 30 • N, and dϕ = 20 • are the control values of the mean position and width of the jet.

Control values of the restoration wind amplitude U i are set to U 1 = U 0 , U 2 = 0.5U 0 and U 3 = 0.2U 0 where U 0 = 50 m s -1 . In the rest of the paper, we define the baroclinicity by the vertical shear of the zonal wind divided by the radius of deformation at the interface because the static stability is a constant at each interface. The upper-level (lower-level) baroclinicity refers to

(u 1 -u 2 )/R 1 ((u 2 -u 3 )/R 2 ) and its restoration counterpart is ( ũ1 -ũ2 )/R 1 (( ũ2 -ũ3 )/R 2 )
. The simulations are 15 years long to ensure significant results and the first year is discarded before the analysis, as in RRC17.

Different series of simulations have been performed to investigate the impact of changes of the upper-and lower-level baroclinicity. These series are shown in Table 1. Experiments where the upper-level baroclinicity is varied (denoted as UB) are obtained by fixing the equilibrium lowerlevel wind amplitude U 2 and U 3 to their respective control values and varying U 1 from 0.8U 0 to 1.2U 0 , corresponding to an upper-level baroclinicity factor (U 1 -U 2 )/U 0 varying from 0.3 to 0.7.

That means that there is a factor of about 2.3 between the smallest and greatest values of the upper-level vertical shear of the restoration zonal wind. Similarly, experiments where the lowerlevel baroclinicity changes are obtained by fixing U 1 and U 2 and varying U 3 from 0.3U 0 to 0.1U 0 .

This corresponds to a baroclinicity factor (U 2 -U 3 )/U 0 varying from 0.2 to 0.4 and a lower-level vertical shear varying by a factor of 2.

The study is mainly focused on sensitivity experiments for which the relaxation time scales are set to τ R1 = τ R2 = 25 days. This enables a systematic comparison between the effects of changes in upper-and lower-level baroclinicity as the relaxation time scales are the same at the two interfaces.

These series are hereafter denoted as UB25 and LB25. Another set of sensitivity experiments is made with different time scales at the upper and lower interfaces (τ R1 = 40 days and τ R2 = 15 days), as used in RRC17, hereafter denoted as UB40 and LB40. Finally, a series of simulation JP25 with fixed baroclinicity but changes in the jet position ϕ 0 is run to help assess the respective impacts of changes in the baroclinicity and jet latitude.

Results

a. Time-mean versus restoration baroclinicity

Changes in the baroclinicity of the restoration temperature field do not necessarily induce the same changes in the simulated climatology because of the dynamical adjustment. Figure 1 shows the climatological upper-and lower-level baroclinicity fields obtained for the UB25 and LB25

experiments. An increase in the upper-or lower-level restoration baroclinicity indeed leads to an increase of the corresponding climatological mean baroclinicity, as shown in Figs. 1a andd. We note that the upper-level baroclinicity maxima differ by a factor of 2 between the extreme cases in UB25 (Fig. 1a), which is a bit less than the range of the restoration baroclinicity. There is however little impact on the lower-level baroclinicity, with only a slight decrease and shift toward the pole.

For the LB25 series, the climatological mean lower-level baroclinicity also fluctuates over a smaller range of maxima than the restoration baroclinicity (Fig. 1b); but unlike the UB25 case the increase in the lower-level baroclinicity in LB25 simulations leads to a decrease in the upper-level one. This change in upper-level baroclinicity is due to the fact that the upper-level wind does not change as the lower-level baroclinicity is increased, while the middle-and lower-level winds increase (not shown). The increase in both the lower-and middle-level winds can be interpreted as follows. When the lower-level baroclinicity is increased, eddy energy increases but as the dissipation is acting at the low-level only, the low-level wind must increase. This also leads to an increase in the middle-level wind because the forcing is such that the baroclinicity at the interface between the low-and middle-level increases. These opposite changes in the two baroclinicities need to be kept in mind while interpreting the results. Similar results are obtained for UB40 and LB40 (not shown).

b. Persistence of the leading mode and eddy feedbacks persistence very much (Fig. 2a); however an increase in the lower-level baroclinicity causes a clear decrease in persistence (Fig. 2b). After 20 days, the PC1 autocorrelation for strong lowerlevel baroclinicity (U 2 -U 3 ≥ 0.34U 0 ) drops to 0.25 on average, whereas for weak lower-level baroclinicity (U 2 -U 3 ≤ 0.26U 0 ), it remains above 0.5.

The tendency of the vertically and zonally averaged zonal wind [u] satifies the following equation (RRC17):

∂ [u] ∂t = - 1 a cos 2 ϕ ∂ ∂ ϕ [u * v * ] cos 2 ϕ - [u 3 ] 3τ E , (3)
where u 3 is the zonal wind in the lower level of the model, the operators and [] correspond to the vertical and zonal average respectively and

u * = u -[u] and v * = v -[v]
are departures of the zonal and meridional wind from their zonal mean. The factor 1/3 in the second term of the right-hand-side of Eq. ( 3) is due to the vertical integration of the momentum equation and the fact that the Ekman dissipation is only acting in the lowest level. By projecting each term of Eq. ( 3) onto EOF1, we get the tendency equation for PC1:

dPC1 dt = m + d, ( 4
)
where m is the eddy momentum forcing (i.e. the projection of the eddy momentum flux convergence) and d is the projection of the surface drag. To get growth rates at a given time t, we compute the time-lag cross-correlation between PC1 and each term of Eq. ( 4), then we divide them by the

autocorrelation function of PC1 A 1 (t 0 ) = ∑ t PC1(t)PC1(t 0 + t): 1 A 1 dA 1 dt = 1 τ m + 1 τ d . (5)
where:

τ -1 m (t 0 ) = ∑ t PC1(t)m(t 0 + t) A 1 (t 0 ) , τ -1 d (t 0 ) = ∑ t PC1(t)d(t 0 + t) A 1 (t 0 ) .
The left-hand side of Eq. ( 5), which is the instantaneous rate of change of the PC1 autocorrelation, is driven by two distinct contributions. On one hand, τ -1 m corresponds to the forcing due to momentum flux convergence. On the other hand, τ -1 d corresponds to the effect of the drag. The benefit of Eq. ( 5) when modifying the upper-level baroclinicity (Fig. 3a). One notable feature is the strong oscillation for U 1 -U 2 = 0.6U 0 which is probably due to successive wave reflections (Rivière et al.

is that τ -1 d is almost constant. Indeed, [u 3 ] is roughly proportional to [u]

2016, RRC17

). Conversely, Fig. 3b shows a gradual increase in the eddy momentum contribution at positive lags when the lower-level baroclinicity is decreased. At short positive lags (+2 to +3 days), the negative values found for large baroclinicity disappear and become positive for small baroclinicity. At longer positive lags (+5 to +20 days), the eddy momentum contribution is near zero for large baroclinicity and becomes positive for small baroclinicity.

Figure 4 compares each term of Eq. ( 5) for two extreme values of the lower-level baroclinicity.

As expected, the contribution of the drag is constant and similar for both simulations. For weak lower-level baroclinicity (Fig. 4a), the eddy momentum contribution is significantly positive at all positive lags. But for strong lower-level baroclinicity (Fig. 4b), it is first negative at short positive lags, then becomes slightly positive between lag +5 and +12 days and finally decreases and becomes again negative after lag +16 days. Hence, at all positive lags, the eddy momentum contribution τ -1 m is stronger in the weak baroclinicity case.

Since the seminal work of [START_REF] Lorenz | Eddy-Zonal Flow Feedback in the Southern Hemisphere[END_REF], the positive correlation between m and PC1 at long positive lags (greater than 5 days) is considered as the signature of a positive synoptic eddy feedback. Following this interpretation, the first main conclusion from Figs. 3 and4 is that this positive feedback is weaker and less durable for stronger lower-level baroclinicity. The second conclusion is that at short positive lags (less than 5 days), the negative feedback exerted by planetary waves as revealed in Rivière et al. ( 2016) and RRC17 becomes less effective for weak baroclinicity. These two changes go in the same direction, namely a decrease in persistence of the leading mode of jet variability with increased lower-level baroclinicity. The next section will be dedicated to investigate the underlying causes.

c. Dynamical interpretation

The aim of this section is to interpret the clear drop in PC1 persistence when the lower-level baroclinicity is increased. Fig. 5 shows the lagged regressions of the momentum flux convergence and zonal wind anomalies on PC1 for weak and strong lower-level baroclinicity. We first note that wind anomalies have more than three times higher amplitudes for stronger baroclinicity. This is logical as the lower-level baroclinicity largely determines the eddy growth rate (Lindzen and Farrell 1980; Hoskins and Valdes 1990) and so the higher amplitude of eddies for stronger baroclinicity lead to stronger momentum flux convergence and jet fluctuations. More interestingly, zonal wind anomalies propagate poleward for strong lower-level baroclinicity while they stay more or less at the same latitude for weak lower-level baroclinicity. For example, for the weak lower-level baroclinicity simulation, the maximum of negative wind anomalies (dashed contours on Fig. 5a) is around 32 • N for a lag of -10 days and around 34 • N for +20 days. In contrast, for a strong lower-level baroclinicity, the same anomalies peaks at 35 • N for a lag of -10 days and around 44 • N for +20 days. This difference can explain the eddy momentum contribution to A PC1 rate of change seen on Fig. 4b. Indeed, the poleward-shifted zonal wind anomalies of Fig. 5b are due to poleward-shifted eddy momentum convergence patterns after lag +5 days which end up becoming orthogonal to EOF1 due to its poleward propagation and can eventually project negatively onto it. Thus, the low or negative values of the cross covariance between m and PC1 in the strong lower-level baroclinicity case correspond to a response of the eddies that does not maintain the jet shift associated with EOF1 but rather makes the jet propagate polewards.

The poleward propagation regime was found to emerge and dominate in the simulations of Son • a wave generated in the jet core, which propagates equatorwards, induces momentum convergence near the jet core and a divergence on its equatorward flank.

• The momentum flux divergence decelerates the zonal wind near the critical latitude, which moves it poleward.

• The next equatorward propagating wave will therefore break slightly further away from the Equator, its momentum convergence and divergence patterns are shifted poleward compared to the first wave. Thereby, the jet is further pushed poleward and so on.

This mechanism needs the Rossby waves to reach a critical latitude on the equatorward flank of the jet and to strongly decelerate the westerlies there. This is unlikely to happen when waves do not propagate away from the jet and the jet somehow acts as a wave guide. This assertion can be tested by comparing the structure of Rossby waves between a weak and strong lower-level baroclinicity simulation. Figure 6 shows one point correlation maps of the meridional wind for both simulations with different lags : -2 days, 0 day and +2 days. On the one hand, the weak lower-level baroclinicity simulation (Fig. 6a, c ande) shows a prevalence of zonal wavenumber k = 6. The waves are slightly anticyclonically tilted, as expected from spherical geometry and the quasi-geostrophic model bias [START_REF] Rivière | The Effect of Latitudinal Variations in Low-Level Baroclinicity on Eddy Life Cycles and Upper-Tropospheric Wave-Breaking Processes[END_REF]. Therefore, Rossby wave propagation is almost zonal, waves staying confined into the jet (compare Figs. 6a ande) which mainly acts as a waveguide.

On the other hand, the strong lower-level baroclinicity simulation (Figs. 6b, d andf) is dominated by wavenumber k = 4 and the observed wave structure has more pronounced tilts: a cyclonic tilt for the negative lag (Fig. 6b) and an even more pronounced anticyclonic tilt at the positive lag (Fig. 6f). At lag zero (Fig. 6d), waves seem to exhibit both tilts, cyclonic west from the reference ). This picture is confirmed by Fig. 7 which shows the time-mean zonal wind and PV gradient for LB25. The width of the jet increases while its peak amplitude stays roughly constant when the baroclinicity increases (Fig. 7a). For all simulations, the PV gradient has two peaks (Fig. 7b), a strong one located near the jet core and a weaker one closer to the Equator. The two peaks are stronger when the lower-level baroclinicity decreases and they also seem to be sharper. To confirm the latter statement, an estimation of the width at half maximum was computed for each simulation (Fig. 8c). It clearly shows a broader PV gradient as the lower-level baroclinicity increases. If the same computation is made for the UB25 simulations (Fig. 8a), the PV gradient is found to have a constant width, which supports our interpretation and the fact that changes in upper-level baroclinicity does not influence the poleward propagation.

However, one may argue that the broader climatological mean jet and PV gradient is due to smearing by the larger meridional incursions when poleward propagation of zonal wind anoma- In their case, the poleward propagation regime associated with the broader and weaker PV gradient logically emerges when the baroclinic zone is forced to be broader by a stronger cooling rate at high latitudes. In our case, it is not straightforward to explain why the PV gradient and the jet broaden when the restoration baroclinicity is intensified and the meridional width of the restoration baroclinicity is kept unchanged.

Two possible mechanisms explaining how a stronger low-level (but not upper-level) baroclinicity leads to a broader jet can be put forward. The first one relies on baroclinic instability arguments.

The development of baroclinic instability requires a change of sign of the PV gradient in the vertical; given that this gradient is always positive at upper levels, this is equivalent to having a negative PV gradient in the lower troposphere. An increase in lower-level baroclinicity will tend to enhance the negative low-level PV gradient, and therefore widen the latitudinal band in which it is negative, as shown in Figs. 9c andd for different restoration profiles (see Eq. ( 2)) for their definition). In contrast, a change in upper-level baroclinicity does not affect the width of the region where the PV gradient changes sign in the vertical, as it remains positive at upper-levels (Figs. 9a andb). So, the latitudinal band in which baroclinic waves might be unstable increases in width only when the lower-level baroclinicity increases. This will in turn increase the width of the latitudinal band of eddy momentum deposition in the upper troposphere and thus the width of the eddy-driven jet.

The second potential explanation relies on changes in eddy wavelengths. There is a clear shift toward larger eddy lengthscales for stronger lower-level baroclinicity (compare Fig. 6 right and left columns). Figure 10 confirms it by showing the spectrum of the squared meridional wind as function of latitude and wavenumber for a weak and a strong lower-level baroclinicity simulation.

This figure also confirms the assumption that waves are trapped in the jet for a weak lower-level baroclinicity (Fig. 10a), whereas they can escape and propagate meridionally for a stronger baroclinicity (Fig. 10c). Moreover, waves tend to reach higher amplitudes for a stronger lower-level baroclinicity, and at all latitudes (compare Figs. 10b andd). The increase in eddy horizontal scale when the baroclinicity increases is consistent with similar quasi-geostrophic or primitive-equation simulations (Whitaker and Barcilon 1995; Chai and Vallis 2014). However, there are different competing mechanisms to explain this result and the mechanism at play may depend on the range of the baroclinicity (or criticality) values. One possible explanation might be the upscale nonlinear energy transfer. Indeed, an increase in the lower-level baroclinicity enhances wave generation of the most unstable synoptic waves. This intensifies non-linear interaction among synoptic waves that lead to more energy transfer toward large waves. There are also linear and alternative nonlinear arguments that may explain this result which are particularly more relevant when discussing weakly nonlinear regimes, as discussed in the two previously cited studies. So one possible interpretation for the broader jet in the presence of the stronger lower-level baroclinicity is the fol-

We have checked that the upper-level baroclinicity has a less drastic effect on eddy length scales in the present simulations (not shown).

Finally, this shift towards smaller wavenumbers for strong lower-level baroclinicity could explain another result: the stronger negative values of eddy momentum forcing at short positive lags observed (Fig. 3b). Smaller wavenumbers means more planetary waves which tend to reflect near the jet flank and induce a negative eddy momentum forcing (Rivière et al. 2016, RCC17). It could seem paradoxical that more reflections occur for strong lower-level baroclinicity when the jet acts less as a wave guide. However in that case, equatorward propagating planetary waves may reflect or be absorbed depending on the situation. The pronounced tilt observed on Fig. 6f (and to a lesser extent on Fig. 6d) is consistent with an increase in the wave-mean flow interaction described in experiments. This strongly suggests that the impact of the lower-level baroclinicity onto the EOF1 persistence cannot be simply explained by the latitudinal displacement of the jet.

2) SENSITIVITY TO RELAXATION TIMESCALES

To check the robustness of the results, the same series of simulations as LB25 and UB25 has been run but with the relaxation time scales set to the same values as in RRC17: τ R1 = 40 days and τ R2 = 15 days. These setups, denoted as LB40 and UB40 (cf. Table 1), are also more similar to the Held and Suarez (1994)'s benchmark. Figure 12 shows the PC1 autocorrelation for these new series of simulations. As for LB25, the persistence of the leading EOF generally increases by decreasing the lower-level baroclinicity while, as for UB25, this persistence is not impacted by a change in upper-level baroclinicity. There is only one exception for the very weak baroclinicity ((U 2 -U 3 )/U 0 equal to 0.20 and 0.22) for which the persistence suddenly decreases from 0.22 to 0.20. The general increased persistence as the baroclinicity decreases can be explained by the increased eddy momentum forcing τ -1 m (Fig. 13b) as for the LB25 experiments. Only the marginal cases for lower-level baroclinicity factors from 0.22 to 0.20 show an abrupt reversal of the tendency. Similar to UB25, the eddy momentum forcing does not show significant change in average when the upper-level baroclinicity is increased (Fig. 13a). In conclusion, the results found previously for τ R1 = 25 days and τ R2 = 25 days are still valid here, except for the very weak lower-level baroclinicity simulations.

Conclusions

The impact of changes in upper-and lower-level baroclinicity on the eddy-driven jet variability has been investigated using a three-level quasigeostrophic model on the sphere. This study focused on the persistence of the leading EOF of the zonally-and vertically-averaged zonal wind. We found that its sensitivity to the upper or lower baroclinicity is very different: an increase in the upper-level baroclinicity has no significant effect whereas an increase in lower-level baroclinicity tends to decrease the EOF1 persistence.

When the lower-level baroclinicity increases, the EOF1 also becomes more characterized by a poleward propagation of zonal wind anomalies. Using the terminology introduced by Son and [START_REF] Son | Preferred Modes of Variability and Their Relationship with Climate Change[END_REF], the zonal index regime is progressively replaced by the poleward propagation regime.

In the zonal index regime, the meridional excursion of the jet is maintained by a strong positive eddy feedback. In the poleward propagation regime, the eddies instead deposit their momentum poleward of the current jet position, leading to its propagation. The interpretation is provided in terms of PV gradient. For strong lower-level baroclinicity, the PV gradient is broad and weak enough to favor an equatorward propagation of the waves. Then, the waves decelerate the zonal winds on the equatorward flank of the jet when they break and displace the critical latitude further poleward. This tends to shift the eddy momentum flux convergence / divergence patterns and the zonal wind anomalies poleward with time. For weak lower-level baroclinicity, the PV gradient is so strong and sharp that the jet acts as a waveguide, waves are trapped and the deceleration of the zonal winds on the equatorward flank of the jet is too weak to modify the location of the critical latitudes. The interpretation is similar to [START_REF] Lee | A Mechanism for the Poleward Propagation of Zonal Mean Flow Anomalies[END_REF] and [START_REF] Son | Time Scale and Feedback of Zonal-Mean-Flow Variability[END_REF] but the setup of the numerical experiments is different. In the previous studies, a broader PV gradient logically appears as the width of the forced baroclinic zone increases. In our case, an intensification of the restoration baroclinicity without changing its meridional width is enough to lead to the same effect.

Two explanations are provided. The first one is based on a baroclinic instability argument. When the lower-level baroclinicity increases, the latitudinal band where baroclinic instability is likely to occur increases which enlarges the region of momentum deposit by the waves and hence widens the jet. The second one is based on the increased wavelength when the lower-level baroclinicity increases. As larger waves deposit momentum over a larger latitudinal band, the eddy-driven jet becomes broader.

Another effect of the increased wavelength when the lower-level baroclinicity increases is seen on shorter timescales. In the strong lower-level baroclinicity cases, the wave scale becomes larger and waves are more inclined to be reflected onto the equatorward side of the jet, reinforcing the negative eddy feedback a few days after the peak of PC1 (Rivière et al. 2016, RRC17). This constitutes an additional reason for the weaker persistence of PC1 for stronger lower-level baroclinicity.

The present idealized study provides dynamical diagnoses to further investigate the persistence of annular modes in future climate projections obtained with the CMIP (Climate Model Intercomparison Project) exercises. In addition to the sensitivity to the jet latitude sensitivity already discussed in several papers (Kidston and Gerber 2010; Arakelian and Codron 2012; Barnes and Polvani 2013), the sensitivity to the lower-level baroclinicity and to the width of the PV gradient should be examined, especially during autumn and early winter when the polar amplification is expected to be the strongest in the Northen Hemisphere. LIST OF FIGURES

  al. 2010; Rivière 2011; Chavaillaz et al. 2013; Harvey et al. 2014; Shaw et al. 2016).

  the source and dissipative terms, ∆ denotes the Laplacian operator, and f = 2Ω sin(ϕ) the Coriolis parameter. The deformation radii are set to R 1 = 660 km and R 2 = 400 km as in Rivière (2009) and Robert et al. (2017), hereafter RRC17.

Following

  [START_REF] Lorenz | Eddy-Zonal Flow Feedback in the Southern Hemisphere[END_REF] and RRC17, Empirical Orthogonal Functions (EOF) of the zonally and vertically averaged zonal wind are computed for each simulation of UB25 and LB25. The autocorrelation function of the principal component (PC) of the leading EOF, hereafter named PC1 and EOF1, of each experiment is plotted in Fig.2. As in RRC17, the autocorrelation has systematically a shoulder shape marked by a fast decay rate during the first few days followed by a slower decay rate at longer lags. On average, the e-folding time is around 20 days, which is of the same order of the timescales of the Southern Hemisphere annular mode in comprehensive models as they vary between 15 and 30 days during summer (Kidston and Gerber 2010; Arakelian and Codron 2012). It is however larger than the observed ones, which are closer to 10 days efolding(Simpson et al. 2013b; Simpson and Polvani 2016), as is often the case in comprehensive and idealized models. A change in upper-level baroclinicity does not seem to impact the EOF1

  , so we expect d to evolve in line with PC1. Therefore, changes in the instantaneous rate of change of the PC1 autocorrelation should mainly be caused by changes in the eddy momentum forcing τ -1 m . Figure 3 shows τ -1 m as a function of time lag and the baroclinicity factors (U 1 -U 2 )/U 0 and (U 2 -U 3 )/U 0 . In general, this quantity is very similar to the time-lag cross-covariance between PC1 and the eddy momentum forcing (i.e ∑ t PC1(t)m(t 0 + t)). It exhibits strong positive values at short negative lags which correspond to the triggering of the event by a strong projection of the convergence of eddy momentum onto the EOF. Then, at short positive lags it has negative values in most cases. This was shown to come mainly from the negative feedback ex-back (e.g., Lorenz and Hartmann 2001, 2003; Zurita-Gotor 2014, RRC17). Even though the eddy momentum contribution to A PC1 rate of change follows these different steps in most cases, differences among the various cases exist and are worth analyzing. As expected from Fig. 2, the values of the eddy momentum contribution shows almost no monotonic or consistent changes

  and[START_REF] Son | Preferred Modes of Variability and Their Relationship with Climate Change[END_REF],[START_REF] Lee | A Mechanism for the Poleward Propagation of Zonal Mean Flow Anomalies[END_REF] and[START_REF] Son | Time Scale and Feedback of Zonal-Mean-Flow Variability[END_REF] forced by a strong high-latitude cooling rate, that is when the mid-latitude baroclinic zone was reinforced and enlarged. This is consistent with our simulations which show the dominance of the poleward propagation regime when the mid-latitude lower-level baroclinicity is increased. The rationale for the poleward propagation regime provided by[START_REF] Lee | A Mechanism for the Poleward Propagation of Zonal Mean Flow Anomalies[END_REF] is the following :

  point and anticyclonic east of it. This could indicate wave reflections occurring on the northern flank ot the jet, which is consistent with the change in sign of the momentum flux convergence at short positive lags in Fig. 5b (Rivière et al. 2016). In any case, Fig. 6 reveals that waves tend to propagate more meridionally for the strong lower-level simulation. The stronger anticyclonic tilt observed there induces zonal wind deceleration on the equatorward side of the jet as needed in the above mechanism of poleward propagation.This difference in wave structures can be related to the shape of the jet. Meridionally propagating waves are more likely to occur within broader jets for which the PV gradient is smoother and does not decrease too fast on the flanks of the jet while meridionally trapped waves are confined in welldefined regions of strong PV gradient[START_REF] Co;2. Martius | Tropopause-Level Waveguides[END_REF]

  lies occur. It is thus not clear if a wider climatological mean jet necessarily means a wider jet at different times of the simulation. To address this issue, the width of the zonally-averaged PV gradient has been computed at each day of the simulations and then averaged. The result is shown in Fig. 8d (and Fig. 8b for UB25), which still clearly shows that the averaged width at half maximum also increases with the lower-level baroclinicity and not with the upper-level baroclinicity. Therefore, a stronger lower-level baroclinicity leads to a broader jet and a smoother PV gradient, enabling the poleward propagation regime to become the dominant mode of variability. It confirms the interpretation provided by Lee et al. (2007) and Son et al. (2008).

  [START_REF] Rivière | A Short-Term Negative Eddy Feedback on Midlatitude Jet Variabilty due to Planetary Waves Reflections[END_REF], leading sometimes to the appearence of reflecting levels before the wave reaches the critical latitude. This well-marked equatorward wave propagation which may result in reflection or absorption does not appear for weak lower-level baroclinicity where waves are more systematically trapped in the jet core by the sharp PV gradient (Figs.6c et e).d. Additional sensitivity experiments1) BAROCLINICITY INTENSITY VERSUS LATITUDEAs recalled in the introduction, changes in the persistence of the leading mode of jet variability have been linked to changes in the mean jet latitude (e.g., Kidston and Gerber 2010; Arakelian and Codron 2012) and one may argue that the results from the LB25 experiments could also be due to changes in the mean jet latitude. To check this, the LB25 series is compared to JP25, a series of simulations where the intensity of the restoration baroclinicity is fixed but its latitude is varied. To compare these two series, we compute the instantaneous rate of change of the autocorrelation function due to the eddy momentum forcing (term τ -1 m from Eq. (5)). Its averaged value between lag +5 and +15 days is plotted on Fig. 11 for all simulations. We first recover in the JP25 experiments the classical result (Barnes et al. 2010; Arakelian and Codron 2012) that as the latitude of the mean jet increases, the eddy feedback coefficient decreases (black squares). The LB25 experiments indicate that as the lower-level baroclinicity increases, the jet moves slightly poleward, consistent with Butler et al. (2010) and Rivière (2011).For these experiments, the eddy feedback also decreases as the jet moves poleward but with a much steeper slope than for the JP25

Fig. 1 .Fig. 2 .Fig. 3 . 1 mFig. 4 .Fig. 5 .Fig. 6 .Fig. 7 .Fig. 8 .Fig. 9 .Fig. 11 .Fig. 12 .Fig. 13 .FIG. 1 .FIG. 2 .FIG 1 )FIG. 4 . 1 FIG. 5 .FIG. 7 .

 12314567891112131214157 Fig. 1. Climatological mean of (left panels) upper-and (right panels) lower-level baroclinicity, respectively (U 1 -U 2 ) and (U 2 -U 3 ), for (upper panels) UB25 and (lower panels) LB25. The baroclinicity factors correspond to (U 1 -U 2 )/U 0 and (U 2 -U 3 )/U 0 respectively. . . . . . 29 Fig. 2. Autocorrelation function of PC1 for (a) UB25 and (b) LB25 for which the baroclinicity factors are (U 1 -U 2 )/U 0 and (U 2 -U 3 )/U 0 respectively. . . . . . . . . . . . 30 Fig. 3. eddy momentum contribution to the rate of change of the PC1 autocorrelation function (τ -1 m of Eq. (5)), as a function of lag and baroclinicity factors for (a) UB25 and (b) LB25. The baroclinicity factors in (a) and (b) correspond to (U 1 -U 2 )/U 0 and (U 2 -U 3 )/U 0 respectively. . . . . . . . . . . . . . . . . . . . . . . . . 31 Fig. 4. Rate of change of the PC1 autocorrelation function (left-hand-side of Eq. (5)), in green), and its momentum (τ -1 m of Eq. (5), in black) and drag contribution (τ -1 m of Eq. (5), in blue), for two simulations of LB25 : (a) weak baroclinicity (U 2 -U 3 = 0.2U 0 ) and (b) strong baroclinicity (U 2 -U 3 = 0.4U 0 ). . . . . . . . . . . . . . . . . . 32 Fig. 5. Lagged regression onto PC1 of anomalous zonally and vertically-averaged eddy momentum flux convergence (in shading) and zonal wind (in contours, interval: 0.5 m s -1 ) as a function of lag and latitude for two simulations of LB25 : (a) weak baroclinicity (U 2 -U 3 = 0.2U 0 ) and (b) strong baroclinicity (U 2 -U 3 = 0.4U 0 ). The black dashed-dotted lines indicate the meridional extension of the mean jet (taken as ±10 • around jet maximum). . . . . . . 33 Fig. 6. Lagged one point correlation map of the meridional wind for (left panels) weak lower-level baroclinicity (U 2 -U 3 = 0.2U 0 ) and (right panels) strong lower-level baroclinicity (U 2 -U 3 = 0.4U 0 ). These correlations maps have been plotted with a lag of (a,b) -2 days, (c,d) 0 day and (e,f) +2 days. The reference point, plotted using a white cross, is in each simulation close to the maximum of zonal wind. . . . . . . . . . . . . . . . . 34 Fig. 7. Climatological mean of (a) the zonally averaged zonal wind and (b) zonally averaged PV gradient at 200hPa for LB25, the baroclinicity factor being (U 2 -U 3 )/U 0 . . . . . . . 35 Fig. 8. (a,c) Full width at half maximum of the main peak of zonally averaged zonal wind (solid line) and PV gradient (dashed line) at 200hPa and (b,d) averaged full width at half maximum of the daily peak of the same quantities as a function of (a,b) the upper-level baroclinicity factor (U 1 -U 2 )/U 0 for each simulation of UB25 and (c,d) the lower-level baroclinicity factor (U 2 -U 3 )/U 0 for each simulation of LB25 (plotted with their respective color). . . . 36 Fig. 9. Vertical cross-section of the zonal wind (in shadings) and PV gradient (in contours, interval: 2 10 -11 m -1 s -1 ) of the restoration basic states for (a) weak upper-level baroclinicity (U 1 -U 2 = 0.4U 0 ), (b) strong upper-level baroclinicity (U 1 -U 2 = 0.7U 0 ), (c) weak lower-level baroclinicity (U 2 -U 3 = 0.2U 0 ) and (d) strong lower-level baroclinicity (U 2 -U 3 = 0.4U 0 ). . . 37 Fig. 10. (a,c) Spectrum of the squared meridional wind as a function of latitude and zonal wave number and (b,d) its integral over wavenumber for (a,b) a weak lower-level baroclinicity (U 2 -U 3 = 0.2U 0 ) and (c,d) a strong lower-level baroclinicity (U 2 -U 3 = 0.4U 0 ). . . . . 38 Fig. 11. Feedback coefficient as a function of mean jet position for the JP25 series (in black squares) and the LB25 series (in colored diamonds), the baroclinicity factor being (U 2 -U 3 )/U 0 . . . . 39 Fig. 12. As Fig. 2 but for UB40 and LB40 series. . . . . . . . . . . . . . . . 40

FIG. 9 .

 9 FIG. 9. Vertical cross-section of the zonal wind (in shadings) and PV gradient (in contours, interval: 2 10 -11 m -1 s -1 ) of the restoration basic states for (a) weak upper-level baroclinicity (U 1 -U 2 = 0.4U 0 ), (b) strong upper-level baroclinicity (U 1 -U 2 = 0.7U 0 ), (c) weak lower-level baroclinicity (U 2 -U 3 = 0.2U 0 ) and (d) strong lower-level baroclinicity (U 2 -U 3 = 0.4U 0 ).

  FIG. 10. (a,c) Spectrum of the squared meridional wind as a function of latitude and zonal wave number and (b,d) its integral over wavenumber for (a,b) a weak lower-level baroclinicity (U 2 -U 3 = 0.2U 0 ) and (c,d) a strong lower-level baroclinicity (U 2 -U 3 = 0.4U 0 ).

FIG. 11 .FIG

 11 FIG. 11. Feedback coefficient as a function of mean jet position for the JP25 series (in black squares) and the LB25 series (in colored diamonds), the baroclinicity factor being (U 2 -U 3 )/U 0 .

Table 1 .

 1 Sensitivity experiment description table. . . . . . . . . . . . . 26

	533

TABLE 1 .

 1 Sensitivity experiment description table.

Acknowledgments. he authors would like to thank Jian Lu and two anonymous reviewers for their relevant and helpful remarks.