A Flower

N Bory

Tribovillard

T Sionneau
email: sionneau.thomas@wanadoo.fr

V Bout-Roumazeilles

G Meunier

C Kissel

B P Flower

A Bory

N Tribovillard

Atmospheric re-organization during Marine Isotope Stage 3 over the North American continent: sedimentological and mineralogical evidence from the Gulf of Mexico

Keywords:

Atmospheric re-organization during Marine Isotope

Stage 3 over the North American continent: sedimentological and mineralogical evidence from the Gulf of Mexico

Introduction

Throughout the last decades, oxygen isotopic studies of Greenland ice cores [START_REF] Dansgaard | A New Greenland deep ice core[END_REF][START_REF] Dansgaard | Evidence for general instability of past climate from 250-kyr ice core record[END_REF][START_REF] Stuiver | GISP2 Oxygen Isotope Ratios[END_REF] revealed important and rapid climatic fluctuations over the North Atlantic during the Marine Isotope Stage 3 (MIS3: 21-55 ka BP). Temperatures of Greenland air masses rose abruptly at the beginning of an interstadial (δ 18 O maxima) and then decreased slowly to a minimum: a stadial (δ 18 O minima).

These millennial-scale climatic oscillations were called Dansgaard-Oeschger cycles. They could be applied to longer-duration cooling cycles called Bond cycles [START_REF] Bond | Correlations between climate records from North Atlantic sediments and Greenland ice[END_REF] with termination often characterized by the collapse of northern hemispheric ice sheets, generating large discharges of icebergs in the North Atlantic known as Heinrich events [START_REF] Heinrich | Origin and consequences of cyclic ice rafting in the Northeast Atlantic Ocean during the past 130,000 years[END_REF][START_REF] Broecker | Origin of the northern Atlantic's Heinrich events[END_REF], followed by a sudden shift from cold to warm temperatures.

Impacts of these climatic fluctuations have been identified in both marine and continental sites all over the world [START_REF] Voelker | Global distribution of centennial scale records for Marine Isotope Stage (MIS) 3: a database[END_REF]. Although some regions may experience warmer and wetter conditions during interstadials compared with stadials [START_REF] Clement | Mechanisms of abrupt climate change of the last glacial period[END_REF], temperatures as well as moisture availability and distribution displayed a pronounced regional heterogeneity. In the Gulf of Mexico (GOM), climatic conditions depend on the respective positions of the Inter-Tropical Convergence Zone, Jet-Stream, Bermuda High and subtropical gyre [START_REF] Forman | Paleoclimatic significance of late Quaternary eolian deposition on the Piedmont and High Plains, central United States[END_REF][START_REF] Liu | Reconstruction of prehistoric landfall frequencies of catastrophic hurricanes in Northwestern Florida from lake sediment records[END_REF][START_REF] Harrison | Mid-Holocene climates of the Americas: a dynamical response to changed seasonality[END_REF][START_REF] Knox | North American palaeofloods and future floods: responses to climate change[END_REF]. [START_REF] Grimm | Evidence for warm wet Heinrich events in Florida[END_REF] suggested that climatic conditions over Florida were warm and wet during the coldest periods of Bond cycles, while cold and dry conditions were predominant in interior North America [START_REF] Wang | Correlation of climate cycles in middle Mississippi Valley loess and Greenland ice[END_REF][START_REF] Jacobs | Lacustrine evidence for moisture changes in the Nebraska Sand Hills during Marine Isotope Stage 3[END_REF][START_REF] Jiménez-Moreno | Millennial-scale variability during the last glacial in vegetation records from North America[END_REF]. The conclusions of [START_REF] Grimm | Evidence for warm wet Heinrich events in Florida[END_REF] are consistent with the hypothesis that decreased North Atlantic Deep Water formation, caused by the calving of icebergs into the North Atlantic during Heinrich events [START_REF] Ganopolski | Rapid changes of glacial climate simulated in a coupled climate model[END_REF], reduced the transport of heat from the GOM to northern high latitudes, leading to the warming of Florida. [START_REF] Hill | Laurentide Ice Sheet meltwater and abrupt climate change during the last glaciation[END_REF] reconstructed the oxygen isotopic composition of the northern GOM seawater during the MIS3 and demonstrated that meltwater pulses from the Laurentide Ice Sheet (LIS) occurred when temperatures over Greenland were cold, in contradiction with the previous theory which stipulated that "Dansgaard-Oeschger" warming corresponds to freshwater routing to the GOM [START_REF] Clark | Freshwater forcing of abrupt climate change during the last glaciation[END_REF]. Understanding climatic and environmental conditions in the North America/GOM system during the MIS3 appears to be all the more difficult since continental evidence for the position of the LIS are very scarce due to glacial re-advance and erosion during the Last Glacial Maximum [START_REF] Dyke | The Laurentide and Innuitian ice sheets during the Last Glacial Maximum[END_REF].

Since the clay mineralogy of the potential main source areas in and around the Mississippi River watershed have been determined [START_REF] Sionneau | Clay mineral distributions in and around the Mississippi River watershed and Northern Gulf of Mexico: sources and transport patterns[END_REF]Fig. 1a), clay mineral records of the northern continental slope of the GOM have provided valuable information on the provenance of freshwater inputs in the GOM during the last deglaciation [START_REF] Montero-Serrano | Sedimentary evidence of deglacial megafloods in northern Gulf of Mexico (Pigmy Basin)[END_REF][START_REF] Sionneau | Provenance of freshwater pulses in the Gulf of Mexico during the last deglaciation[END_REF] and allowed reconstructions of atmospheric circulation shape and humidity transfer patterns over North America during the Holocene and Last Interglacial [START_REF] Montero-Serrano | Changes in precipitation regimes over North America during the Holocene as recorded by mineralogy and geochemistry of Gulf of Mexico sediments[END_REF], 2011).

In this article, we present sedimentological and mineralogical records of terrigenous sediments deposited during the MIS3 in the Orca Basin (26°56.770N, 91°20.740W; northern GOM), which is considered to be an ideal site for high-resolution paleoclimatic studies [START_REF] Flower | Phasing of deglacial warming and Laurentide Ice Sheet meltwater in the Gulf of Mexico[END_REF][START_REF] Hill | Laurentide Ice Sheet meltwater and abrupt climate change during the last glaciation[END_REF][START_REF] Sionneau | Provenance of freshwater pulses in the Gulf of Mexico during the last deglaciation[END_REF], in order to determine a regional paleoatmospheric circulation model that could explain results of previous studies [START_REF] Grimm | Evidence for warm wet Heinrich events in Florida[END_REF][START_REF] Hill | Laurentide Ice Sheet meltwater and abrupt climate change during the last glaciation[END_REF].

Geological settings

Core MD02-2552 (26°56.800N, 91°20.72'W, 2250 m water depth) was recovered from the Orca Basin (Fig. 1b andc) during the IMAGES-PAGE cruise [START_REF] Bout-Roumazeilles | Sedimentologic analysis of cores, recovered from the RV Marion Dufresne cruise in the Gulf of Mexico[END_REF] on board the R/V Marion Dufresne (IPEV) in 2002.

The Orca Basin is a small (∼400 km2), deep (∼2400 m) depression on the northern continental slope of the Gulf of Mexico [START_REF] Shokes | Anoxic, hypersaline basin in the northern Gulf of Mexico[END_REF][START_REF] Sheu | The anoxic Orca Basin (Gulf of Mexico): geochemistry of brines and sediments[END_REF][START_REF] Tribovillard | Paleodepositional conditions in the Orca Basin as inferred from organic matter and trace metal contents[END_REF]. It formed as a consequence of salt tectonics about 50 ka ago. The depression is bordered by sills at ∼2000 m of depth, resulting in a shallow (<200-m-thick) restricted deep water mass. The contact between the bulk of the water mass, being of normal seawater chemistry, and the restricted deep-water mass occurs over a∼50m thick transition zone below ∼2200 m. Across this contact, salinity increases from 35 ppt to ∼260 ppt, density from 27 to 180 (σ t ), dissolved oxygen falls to zero, and hydrogen sulfide rises to >3 µM (peaking at ∼2250 m) before falling to zero in the deepest part of the water column. The exceptionally strong pycnocline limits exchange between the restricted deep water mass and the overlying water column. The high salinity of the deep water mass is maintained through dissolution of salt in shallow subsurface diapirs in the vicinity of the basin [START_REF] Presley | Interstitial water chemistry, Deep Sea Drilling Project Leg 961[END_REF][START_REF] Sheu | Sulfur and oxygen isotopic compositions of dissolved sulfate in the Orca Basin: implications for origin of the high-salinity brine and oxidation of sulfides at the brine seawater interface[END_REF].

Clay mineralogical and sedimentological analysis

The core MD02-2552 was sampled at 5-cm intervals from 19.5 to 30 m (covering 26.9e45.3 ka). This interval was chosen in order to match the time interval studied by [START_REF] Hill | Abrupt Climate Change during the Last Glacial Period: a Gulf of Mexico Perspective (Theses and dissertations[END_REF] in core MD02-2551. A total of 206 samples were analyzed for clay mineralogy.

In this paper, "clay minerals" refer to the major phyllosilicate minerals within the claysize fraction (generally < 2 µm). They are identified by X-Ray Diffraction using the protocol explained in detail in published articles [START_REF] Sionneau | Clay mineral distributions in and around the Mississippi River watershed and Northern Gulf of Mexico: sources and transport patterns[END_REF]. The main northern American drainage basins contributing to GOM clay sedimentation are made up of four distinct mineralogical provinces [START_REF] Sionneau | Clay mineral distributions in and around the Mississippi River watershed and Northern Gulf of Mexico: sources and transport patterns[END_REF]; Table 1): (1) the smectite-rich northwestern Mississippi River watershed (55% smectite on average), (2) the illite and chlorite-rich northeastern Mississippi River watershed and Great Lakes area (77% illite plus chlorite on average), (3) the kaolinite-rich southeastern United States (58% kaolinite on average) and ( 4) the illite and kaolinite-rich southwestern Mississippi River watershed (34% illite and 23% kaolinite on average). Considering that weathering/alteration processes on land are slow [START_REF] Thiry | Paleoclimatic interpretation of clay minerals in marine deposits: an outlook from the continental origin[END_REF], millennial-scale fluctuations of the clay mineralogy of GOM sedimentary deposits reflect changes of the respective contributions of the main mineralogical provinces [START_REF] Sionneau | Provenance of freshwater pulses in the Gulf of Mexico during the last deglaciation[END_REF].

Grain-size and magnetic susceptibility analyses were conducted using procedures detailed in published articles [START_REF] Laj | North Atlantic paleointensity stack since 75 ka (NAPIS-75) and the duration of the Laschamp event[END_REF][START_REF] Sionneau | Provenance of freshwater pulses in the Gulf of Mexico during the last deglaciation[END_REF].

Age model

Cores MD02-2252 and MD02-2551 (26°56.78N, 91°20.75W) are separated by only 62 m in the Orca Basin. Since these cores record rather similar sedimentological context, their correlation has been easily achieved using magnetic susceptibility (Fig. 2). Depth depth relationships between cores were established using the Macintosh AnalySeries-1.2 software [START_REF] Paillard | Macintosh program performs time-series analysis[END_REF]. We used the published age model [START_REF] Hill | Laurentide Ice Sheet meltwater and abrupt climate change during the last glaciation[END_REF] of core MD02-2551 based on 17 AMS 14C dates from monospecific samples of pink G. ruber.

In order to test the stratigraphic control, we plotted on the age model three AMS 14C dates (determined at the Poznan Radiocarbon Laboratory -Poland) from the core MD02-2552, obtained from both G. ruber and mixed Globigerinoides sp. (G. ruber, G. sacculifer, G. trilobus) assemblages (Fig. 2). These three radiocarbon ages were calibrated to calendar years using the Fairbanks0107 online conversion program [START_REF] Fairbanks | Radiocarbon calibration curve spanning 0 to 50,000 years BP based on paired 230TH/234U/238U and 14C dates on pristine corals[END_REF]. The chronostratigraphy was also constrained by the occurrence of a significant directional deviation associated to a low in relative intensity of the earth magnetic field between 26.75 m and 27.47 m in core MD02-2552 corresponding to the Laschamp geomagnetic excursion [START_REF] Laj | North Atlantic paleointensity stack since 75 ka (NAPIS-75) and the duration of the Laschamp event[END_REF]. We attributed the most recent and accurate coupled K/Ar, 40Ar/39Ar and 238U/230Th dating of this excursion at 40,700 ± 950 y b2k [START_REF] Singer | 40Ar/39Ar, K-Ar and 230Th-238U dating of the Laschamp excursion: a radio isotopic tie point for ice core and climate chronologies[END_REF] [START_REF] Aharon | Meltwater flooding events in the Gulf of Mexico revisited: Implications for rapid climate changes during the last deglaciation[END_REF].

Results: clay mineralogy and sedimentology

The clay mineral fraction of the detrital sediments deposited in the Orca Basin during the MIS3 is mainly composed of illite (~57%), while smectite (~18%), chlorite (~13%) and kaolinite (~11%) contents are less important (Fig. 3). This average clay mineralogical composition is in agreement with previous studies, which demonstrated that glacial GOM sediments are enriched in illite and chlorite, compared with interglacial ones which are mainly composed of smectite (50-86% of the clay association) during the Holocene and the last deglaciation [START_REF] Montero-Serrano | Changes in precipitation regimes over North America during the Holocene as recorded by mineralogy and geochemistry of Gulf of Mexico sediments[END_REF][START_REF] Sionneau | Provenance of freshwater pulses in the Gulf of Mexico during the last deglaciation[END_REF].

The clay mineral record in core MD02-2552 can be divided into four different time intervals (Fig. 3). Periods between 26.9 and 31.4 ka and between 37.3 and 42.6 ka are characterized by high illite (I) and chlorite (C) contents (I + C~75%; Table 2). Smectite (S) and kaolinite (K) are more abundant during the two other periods (31.4-37.3 ka and 42.6-45.3 ka). As a result, major and abrupt changes (at 31.4, 37.3 and 42.6 ka) of the C/K and S/(I + C) ratios highlight the transitions between these different intervals (Fig. 4).

Variations of the illite and chlorite contents seem correlated throughout the entire record. As this observation could result from the calculation method (a semi-quantitative approach using percentages), we calculated the correlation coefficient between illite and chlorite using their rough diffraction intensities (counts/second). The high correlation coefficient (R 2 = 0.74; number of samples = 206) suggests that illite and chlorite are indeed linked to each other. This result points out a common origin for both minerals. In that frame, the northeastern province of the Mississippi River watershed and the Great Lakes area (I + C = 77%; Table 1) appear to be the best candidate as a source of these two clay minerals since the southwestern province, an alternative source for illite, is poor in chlorite (I + C = 39%; Table 1). The changes in the clay mineral record are also related to the magnetic susceptibility values, which display similar variations than the C/K ratio over the studied interval (Fig. 4b).

Higher magnetic susceptibility is associated with illite and chlorite-rich intervals while very low values of magnetic susceptibility correspond to increased smectite and kaolinite contents (Fig. 3). This result suggests a common provenance for illite, chlorite and magnetic minerals, likely from the northeastern province [START_REF] Kujau | Mississippi River discharge over the last w560,000 years e indications from X-ray fluorescence core-scanning[END_REF].

The smectite typically derives from the northwestern Mississippi River watershed area, whereas kaolinite may originate from both the southwestern province and/or from the kaolinite-rich southeastern province. As demonstrated by [START_REF] Sionneau | Clay mineral distributions in and around the Mississippi River watershed and Northern Gulf of Mexico: sources and transport patterns[END_REF], the clay mineral distribution in the northern GOM is mainly influenced by relative fluvial contribution (Mississippi River is the dominant source of terrigenous sediments whereas all other rivers inputs have more local influences) and by oceanic surface circulation (especially the Loop Current which is the dominant hydrologic feature of the GOM). Considering the sediment dispersal pattern in the GOM, kaolinite-rich suspended sediments from rivers of the southeastern United States are mostly transported southward over the Florida shelf and do not influence sedimentation on the Louisiana continental slope [START_REF] Balsam | Sea-floor sediment distribution in the Gulf of Mexico[END_REF][START_REF] Sionneau | Clay mineral distributions in and around the Mississippi River watershed and Northern Gulf of Mexico: sources and transport patterns[END_REF]. This observation suggests that kaolinite recovered in the Orca Basin mainly derives from the southwestern province. Moreover, the kaolinite record shows a strong positive correlation with the a* parameter of reflectance e reflecting the reddish color of the sediment e and with the first derivative at 570 nm (not shown) reflecting the hematite content [START_REF] Balsam | Sea-floor sediment distribution in the Gulf of Mexico[END_REF]. Kaolinite likely is derived from the red soils cropping out in the southwestern province of the Mississippi River watershed [START_REF] Sionneau | Clay mineral distributions in and around the Mississippi River watershed and Northern Gulf of Mexico: sources and transport patterns[END_REF]. Finally, kaolinite and smectite-rich intervals (31.4e37.3 ka and 42.6e45.3 ka) occurred during phase of low precipitation over Florida as suggested by pollen evidence [START_REF] Grimm | Evidence for warm wet Heinrich events in Florida[END_REF]. This observation does not support an enhanced detrital supplies from the southeastern province at that time.

To summarize, as smectite (S) mainly comes from the northwestern Mississippi River watershed, illite and chlorite (I + C) from the northeastern Mississippi River watershed and the Great Lakes area and kaolinite (K) from the southwestern mineralogical province, clay mineral ratio S/(I + C) and C/K may therefore document the main origin of the detrital supplies. The S/(I + C) ratio indicates some variability within the smectite and kaolinite-rich intervals, which mainly results from varying smectite content as the C/K ratio remains rather low and constant over these intervals (Fig. 4).

The more recent glacial illite and chlorite-rich interval (29.6 -31.4 ka) is episodically interrupted by short-term smectite-rich episodes with smectite content up to 68% of the clay mineral fraction between 28.4 and 28.7 ka, at 29.1 ka and between 29.8 and 30.5 ka (Fig. 3).

We interpreted these intervals as representing major detrital and freshwater discharges from the southwestern margin of the LIS similar to meltwater events observed during the last deglaciation [START_REF] Montero-Serrano | Sedimentary evidence of deglacial megafloods in northern Gulf of Mexico (Pigmy Basin)[END_REF][START_REF] Sionneau | Provenance of freshwater pulses in the Gulf of Mexico during the last deglaciation[END_REF]. The three short smectiterich events (28.4-28.7 ka, 29.1 ka and 29.8-30.5 ka; Fig. 3) appear to correlate with negative excursions of the δ 18 O SW-GOM record documented in core MD02-2551 [START_REF] Hill | Laurentide Ice Sheet meltwater and abrupt climate change during the last glaciation[END_REF].

The comparison between mean grain-size of detrital sediments deposited in the Orca Basin during the MIS3 and the clay mineralogical contents indicates a slightly finer mean grain-size (≤8 µm) during the illite and chlorite-rich intervals whereas mean grain size is coarser (~9.5 µm) during smectite and kaolinite-rich intervals. Moreover, grain-size trends are similar to insoluble residue abundance documented in core MD02-2551 (not shown), which was interpreted as representing increased influx from the Mississippi River [START_REF] Hill | Abrupt Climate Change during the Last Glacial Period: a Gulf of Mexico Perspective (Theses and dissertations[END_REF]. Our results suggest that mean grain-size is slightly coarser as terrigenous flux increased. Grainsize is partly related to the hydrodynamical regime of the Mississippi River. Increased grainsize may thus indicate the erosion of the Mississippi River fluvial deposits caused by highenergy episodes that promoted the remobilization of coarser particles. The lack of clear correlation between the interval of enhanced Mississippi River influx observed between 31.4 and 37.3 ka and meltwater pulses recorded by [START_REF] Hill | Laurentide Ice Sheet meltwater and abrupt climate change during the last glaciation[END_REF] suggests that the coarsening of grain size may be related to erosional processes caused by increased Overall mineralogical and sedimentological data indicate major and rapid modifications of the terrigenous supply within MIS3 (Table 2): detrital sedimentation results from a mixing between the illite and chlorite-rich northeastern province and Great Lakes area and the smectite-rich northwestern province between 26.9 and 31.4 ka and between 37.3 and 42.6 ka whereas the main contributors appear to be the illite and kaolinite-rich southwestern and smectite-rich northwestern provinces between 31.4 and 37.3 ka and between 42.6 and 45.3 ka (Fig. 5). Although the supplies from the northwestern and northeastern provinces may be linked to variable glacial activity along the southern margin of the LIS (i.e. phases of retreat/growth, proglacial lakes, activity of glacial lobes; [START_REF] Sionneau | Clay mineral distributions in and around the Mississippi River watershed and Northern Gulf of Mexico: sources and transport patterns[END_REF][START_REF] Sionneau | Provenance of freshwater pulses in the Gulf of Mexico during the last deglaciation[END_REF][START_REF] Montero-Serrano | Changes in precipitation regimes over North America during the Holocene as recorded by mineralogy and geochemistry of Gulf of Mexico sediments[END_REF] the supply of kaolinite from the southwestern province may only be explained by enhanced precipitation over this area. Such changes imply strong modifications of environmental conditions over the North American continent during MIS3.

Discussion: glacial activity of the LIS and moisture transfers from the GOM during MIS3

The clay and sedimentological records from the Orca Basin were compared with previously published paleo-environmental records including the Mississippi River discharge intensity [START_REF] Hill | Abrupt Climate Change during the Last Glacial Period: a Gulf of Mexico Perspective (Theses and dissertations[END_REF] and lower Mississippi terrace levels [START_REF] Rittenour | Development of an OSL chronology for Late Pleistocene channel belts in the lower Mississippi valley, USA[END_REF], loess and paleosoil deposition [START_REF] Forman | Chronological evidence for multiples periods of loess deposition during the Late Pleistocene in the Missouri and Mississippi River Valley, United States: implication for the activity of the Laurentide Ice Sheet[END_REF][START_REF] Johnson | Stratigraphy and environmental reconstruction at the middle Wisconsinan Gilman Canyon formation type locality, Buzzard's Roost, southwestern Nebraska[END_REF][START_REF] Wang | A Mid-Late Quaternary loess-paleosol record in Simmons Farm in southern Illinois, USA[END_REF][START_REF] Pierce | A loess-paleosol record of climate and glacial history over the past two glacial interglacial cycles (150 ka), southern Jackson Hole, Wyoming[END_REF], lacustrine records [START_REF] Jacobs | Lacustrine evidence for moisture changes in the Nebraska Sand Hills during Marine Isotope Stage 3[END_REF][START_REF] Wood | Lacustrine sediments in Porter Cave, Central Indiana, USA and possible relation to Laurentide ice sheet marginal positions in the middle and late Wisconsinan[END_REF], braided vs. meandering river systems in the Atlantic coastal plains [START_REF] Leigh | Late Pleistocene braided rivers of the Atlantic Coastal Plain, USA[END_REF], pollen association and vegetation [START_REF] Fredlund | Late Quaternary pollen record from Cheyenne Bottoms, Kansas[END_REF][START_REF] Baker | Mid-Wisconsinan environments on the eastern Great Plains[END_REF][START_REF] Pierce | A loess-paleosol record of climate and glacial history over the past two glacial interglacial cycles (150 ka), southern Jackson Hole, Wyoming[END_REF] and summer precipitation over Florida [START_REF] Grimm | Evidence for warm wet Heinrich events in Florida[END_REF][START_REF] Donders | Impact of the Atlantic Warm Pool on precipitation and temperature in Florida during North Atlantic cold spells[END_REF]. When we compare data from different cores recovered in the Gulf of Mexico and various continental archives, however, it is important to keep in mind that all records have independent age models which all contain uncertainties. The continental records have been dated using radiocarbon ages, optically stimulated luminescence (OSL) or thermoluminescence (TL) techniques leading to rather different age uncertainties. OSL dating is generally more accurate for recent studies due to technological development, but the overall uncertainty is _5%. The range of age estimate for TL dating, including the error, is larger than for radiocarbon dating. Nevertheless, thanks to the use of mixed dating techniques, the comparison between continental and marine records including the TL and OSL age uncertainties is still meaningful (Fig. S-1) although the phasing between records may be somehow imprecise. Additional information on the chronological frame of these records (dates and error) is given in Fig. S-1. The comparison of these records allows the identification of the distribution of the main wet/arid areas over the Mississippi River watershed as well as the identification of the LIS areas displaying glacial activity during MIS3.

Our results were also compared with the oxygen isotopic composition of northern GOM surface waters [START_REF] Hill | Laurentide Ice Sheet meltwater and abrupt climate change during the last glaciation[END_REF][START_REF] Flower | Laurentide Ice Sheet Meltwater and the Atlantic Meridional Overturning Circulation during the Last Glacial Cycle: a View from the Gulf of Mexico[END_REF] and the mean summer insolation at 30° and 45°N (Fig. 4) in order to propose moisture transfer patterns and glacial activity of the LIS that may be consistent with both continental and marine evidences (Fig. 6). The resulting hypotheses on precipitation, moisture transfer and wind distributions during MIS3 were compared with global climate simulations for the MIS3 [START_REF] Van Meerbeeck | How did Marine Isotope Stage 3 and Last Glacial Maximum climates differ? e perspectives from equilibrium simulations[END_REF]) and with regional climate simulations for summer during the LGM [START_REF] Bromwich | LGM summer climate on the southwestern margin of the Laurentide Ice Sheet: wet or dry?[END_REF] in order to test their consistency. (29.6e31.4 ka and 37.3e42.6 ka) The sedimentary record from the GOM indicates that the detrital fraction mainly derives from the northeastern province encompassing the Great Lakes area during these two time intervals. The various environmental records provide heterogeneous evidence of wet or dry conditions over North America, reflecting regional or global climate. The deposition of the loess in Illinois (Roxana silt formation) and in Iowa (Pisgah formation), linked to arid climatic conditions and to the exposure of glacially-derived sediments [START_REF] Forman | Chronological evidence for multiples periods of loess deposition during the Late Pleistocene in the Missouri and Mississippi River Valley, United States: implication for the activity of the Laurentide Ice Sheet[END_REF][START_REF] Wang | A Mid-Late Quaternary loess-paleosol record in Simmons Farm in southern Illinois, USA[END_REF], indicates that arid and glacial processes were dominant features throughout the whole MIS3 although records of glacial activity are very scarce on the southeastern margin of the LIS, likely obliterated by the LGM maximum glacial advance.

(I ? C)-rich intervals

On the other hand, there are several pieces of evidence (Fig. 6a) that precipitation may have been abundant on the northeastern and southeastern provinces over these illite and chlorite-rich periods, including: (1) the development of braiding on the Atlantic Coastal margin [START_REF] Leigh | Late Pleistocene braided rivers of the Atlantic Coastal Plain, USA[END_REF]; (2) the elevation of the downstream southern lower Mississippi River Valley terraces [START_REF] Rittenour | Development of an OSL chronology for Late Pleistocene channel belts in the lower Mississippi valley, USA[END_REF] reflecting flooding episodes; and (3) the development of wet conditions in Florida [START_REF] Grimm | Evidence for warm wet Heinrich events in Florida[END_REF][START_REF] Donders | Impact of the Atlantic Warm Pool on precipitation and temperature in Florida during North Atlantic cold spells[END_REF]. Wetter conditions over the southeastern province do not induce an increased supply of kaolinite-rich sediments toward the Orca Basin since detrital supplies from this province are distributed southward on the Florida shelf as a result of the main sediment dispersal patterns forced by oceanic circulation [START_REF] Balsam | Sea-floor sediment distribution in the Gulf of Mexico[END_REF][START_REF] Sionneau | Clay mineral distributions in and around the Mississippi River watershed and Northern Gulf of Mexico: sources and transport patterns[END_REF]). Similar regional differences in precipitation during MIS3 were also evident in a recent review of vegetation records [START_REF] Jiménez-Moreno | Millennial-scale variability during the last glacial in vegetation records from North America[END_REF].

As indicated by the short smectite-rich intervals in the mineralogical record, the most recent illite and chlorite-rich interval (29.6-31.4 ka) is marked by two meltwater episodes originating from the northwestern province, suggesting glacial advance of the Des Moines and James glacial lobes in the late MIS3-early MIS2 (Fig. 6b), similar with events punctuating the last deglaciation [START_REF] Montero-Serrano | Sedimentary evidence of deglacial megafloods in northern Gulf of Mexico (Pigmy Basin)[END_REF][START_REF] Sionneau | Provenance of freshwater pulses in the Gulf of Mexico during the last deglaciation[END_REF].

In summary, the illite and chlorite-rich periods correspond to an enhanced glacial activity of the southeastern LIS margin with short-term episodic contributions from the southwestern margin in the most recent part of the record, which is consistent with the reconstructed LIS margin for MIS3 [START_REF] Dyke | The Laurentide and Innuitian ice sheets during the Last Glacial Maximum[END_REF][START_REF] Van Meerbeeck | How did Marine Isotope Stage 3 and Last Glacial Maximum climates differ? e perspectives from equilibrium simulations[END_REF].

During these periods, precipitation occurred mainly along the eastern part of the North American continent, while the southwestern and northwestern provinces experienced dry conditions, pointing out that the general moisture pattern was somehow similar with present-day winter situations. Such a configuration suggests that the Polar Jet Stream was blocked below 40_N on its western side while located above 40_N on eastern side, displaying a dominant meridional component, preventing moisture inflow from the GOM toward the western Mississippi River watershed while promoting precipitation on the Atlantic margin (Fig. 6a andb). Meanwhile the Bermuda High was likely not in its westward position, in order to promote the convergence of air masses and the associated precipitation belt both in Florida and along the Atlantic coast. (31.4e37.3 and 42.6e45.3 ka) These two periods are marked by an increased detrital supply originating from the western provinces both north and south, suggesting a westward position of moisture inflow from the GOM and a southwestern position of the associated precipitation belt (Figs. 3,4,6c and 6d). Pollen and vegetation records from Kansas and Nebraska support the development of wet conditions over the western provinces [START_REF] Fredlund | Late Quaternary pollen record from Cheyenne Bottoms, Kansas[END_REF][START_REF] Johnson | Stratigraphy and environmental reconstruction at the middle Wisconsinan Gilman Canyon formation type locality, Buzzard's Roost, southwestern Nebraska[END_REF][START_REF] Baker | Mid-Wisconsinan environments on the eastern Great Plains[END_REF]. Meanwhile, the Roxana loess deposition demonstrates the persistence of cold and arid conditions in Illinois [START_REF] Forman | Chronological evidence for multiples periods of loess deposition during the Late Pleistocene in the Missouri and Mississippi River Valley, United States: implication for the activity of the Laurentide Ice Sheet[END_REF] suggesting that the Jet Stream was likely located below 45°N, somewhere in between the north and the southwestern provinces, with a dominant zonal component (Fig. 6c). The shift from meandered to braided river system after 30 ka suggests reduced precipitations over the Atlantic Coastal margin [START_REF] Leigh | Late Pleistocene braided rivers of the Atlantic Coastal Plain, USA[END_REF] at least during the last kaolinite and smectite-rich period (31.4-37.3 ka). This theory is supported by the development of glacial activity on the northeastern province [START_REF] Wood | Lacustrine sediments in Porter Cave, Central Indiana, USA and possible relation to Laurentide ice sheet marginal positions in the middle and late Wisconsinan[END_REF] and by the drier climatic conditions over Florida [START_REF] Grimm | Evidence for warm wet Heinrich events in Florida[END_REF][START_REF] Donders | Impact of the Atlantic Warm Pool on precipitation and temperature in Florida during North Atlantic cold spells[END_REF]. The occurrence of dry climatic conditions along the Atlantic margin points out a westward migration of the Bermuda High, favoring the displacement of the main moisture flux toward the central interior (Fig. 6c).

(K ? S)-rich intervals

The recurrent occurrence of smectite during this interval -which does not match the main meltwater events as recorded by the δ 18 OSW [START_REF] Hill | Laurentide Ice Sheet meltwater and abrupt climate change during the last glaciation[END_REF][START_REF] Flower | Laurentide Ice Sheet Meltwater and the Atlantic Meridional Overturning Circulation during the Last Glacial Cycle: a View from the Gulf of Mexico[END_REF] -suggests episodic intrusion of the southerly moisture flux and associated precipitation belt over the northwestern province (Fig. 6d). Recent climate model simulations suggest that humid and warm air masses, promoting enhanced precipitation over the northwestern province, originated from the GOM. Humidity generated over the Pacific Ocean was confined over the western coasts of the United States during the MIS3 [START_REF] Van Meerbeeck | How did Marine Isotope Stage 3 and Last Glacial Maximum climates differ? e perspectives from equilibrium simulations[END_REF]. The development of episodic wet periods interrupting generally arid conditions over the northwestern province is also consistent with episodic paleosoils development interbedded in the Roxana Silt Formation in the central lowland and Great Plains area [START_REF] Wang | A Mid-Late Quaternary loess-paleosol record in Simmons Farm in southern Illinois, USA[END_REF][START_REF] Pierce | A loess-paleosol record of climate and glacial history over the past two glacial interglacial cycles (150 ka), southern Jackson Hole, Wyoming[END_REF]. Moreover the specific mean grain-size (<10 µm) characterizing sediment deposited during this interval correspond to sortable silt sized particles and supports the hypothesis of the sediments being reworked from loess formations such as the Roxana silt during episodic precipitations.

In summary, these kaolinite and smectite-rich intervals reflect the westward migration of the southerly flow from the GOM, promoting the development of moist conditions over the southwestern province while the southeastern province experienced dry conditions. The sedimentological data indicate that the moisture flow may have episodically penetrated northward during summer promoting precipitation on the northwestern province. [START_REF] Knox | Sensitivity of modern and Holocene floods to climate change[END_REF] shown that Mississippi River paleoflood intensity, during the Holocene, increased significantly when humid and warm air masses from the GOM circulated toward the northern Mississippi River watershed. [START_REF] Bromwich | LGM summer climate on the southwestern margin of the Laurentide Ice Sheet: wet or dry?[END_REF] demonstrated with modeling studies that episodic summer precipitation occurred along the LIS margin during the last glaciation as the inflow of moisture from the GOM encountered the cold katabatic winds from the ice-sheet. This simulation also indicates that the distribution of precipitation was likely affected by minor changes in large-scale circulation, whose variability may explain the alternation of wet/ dry conditions over the northwestern province [START_REF] Bromwich | LGM summer climate on the southwestern margin of the Laurentide Ice Sheet: wet or dry?[END_REF].

MIS3 global climate simulation did not e so far e reconstruct episodic penetration of humid and warm air-masses from the GOM toward interior North America.

Nevertheless, considering that MIS3 climate conditions are somehow complex and hard to disentangle (oscillating from cold stadials to warm interstadials with contrasting extension of the LIS) we postulated that MIS3 climate conditions may be intermediate between the one simulated for the Holocene and LGM [START_REF] Van Meerbeeck | How did Marine Isotope Stage 3 and Last Glacial Maximum climates differ? e perspectives from equilibrium simulations[END_REF][START_REF] Brandefelt | A coupled climate model simulation of Marine Isotope Stage 3 stadial climate[END_REF]. Thus the simulated annual precipitation amount is substantially higher in MIS3 model than in LGM model with a significant increase over the Great Lakes area and eastern coasts of North America, while it was lower, however, over the US plains [START_REF] Van Meerbeeck | How did Marine Isotope Stage 3 and Last Glacial Maximum climates differ? e perspectives from equilibrium simulations[END_REF][START_REF] Brandefelt | A coupled climate model simulation of Marine Isotope Stage 3 stadial climate[END_REF]. As a whole, climate simulations of MIS3 evidencing enhanced precipitation over the eastern coasts of North America are partly in agreement with our data. Our records not only allow identification of general trends during MIS3 but also rather provide detailed and subtle variations of precipitation distribution that models simulation did not yet allow obtaining in routine.

In that frame, our mineralogical dataset from the Orca Basin is globally consistent with results of these climate simulations for the illite and chlorite-rich periods. But climate simulations did not -so far -successfully reproduce the observed enhanced detrital contribution from the northwestern during the smectite and kaolinite-rich intervals. In that sense, our data, which give information about the continental erosion driven by precipitation distribution and/or glacial processes over the North American continent during the MIS3, provide additional and precise constrains for further simulation of MIS3 climate.

Relation between meltwater events and insolation

The δ 18 OSW from the Orca Basin shows six major meltwater events between 28.5 and 30 ka, between 31.3 and 34 ka, around 35 ka, between 37.2 and 39.6 ka, between 42.8 and 44 ka and between 44.5 and 43.3 ka (Hill et al., 2006;[START_REF] Flower | Laurentide Ice Sheet Meltwater and the Atlantic Meridional Overturning Circulation during the Last Glacial Cycle: a View from the Gulf of Mexico[END_REF]. The main meltwater events recorded in the Gulf of Mexico are not associated with similar modifications of the terrigenous signal (Fig. 4). The sedimentological and mineralogical records of the meltwater discharges F1 and F6 are comparable to the signature of the main deglacial meltwater event (14.1-14.6 cal ka) characterizing the last deglaciation suggesting destabilization of glacial lobes along the southwestern margin of the LIS [START_REF] Montero-Serrano | Sedimentary evidence of deglacial megafloods in northern Gulf of Mexico (Pigmy Basin)[END_REF][START_REF] Sionneau | Provenance of freshwater pulses in the Gulf of Mexico during the last deglaciation[END_REF]. By contrast, the two main meltwater events F2 and F4 are not characterized by any change of the clay association. However, they are contemporaneous with two important phases of the lower Mississippi River terraces [START_REF] Rittenour | Development of an OSL chronology for Late Pleistocene channel belts in the lower Mississippi valley, USA[END_REF] suggesting enhanced detrital supply but constant provenance. The mismatch between the mineralogical record and the meltwater pulses as recorded by the δ 18 O measured on foraminifera is crucial since it indicates that some variations of the detrital provenance during MIS3 were not controlled by meltwater floods although it has been shown to be the case during last deglaciation [START_REF] Sionneau | Provenance of freshwater pulses in the Gulf of Mexico during the last deglaciation[END_REF]. In that frame, some of mineralogical variations observed in the Orca Basin rather record changes in precipitation patters over the North American continent.

In our study, the main meltwater pulses appear to precede the clay mineralogical transitions that characterize atmospheric reorganizations above the GOM and the North American continent. Meltwater floods F2 and F5 occurred just before eastward shifts of the main precipitation belt at 31.4 and 42.6 ka respectively, while the migration of the precipitation belt from the Atlantic Coastal margin to the western Mississippi River and Rio Grande River watersheds at 37.3 ka. This suggests that the meltwater discharges may be one part of the chain of events that triggered the atmospheric re-organization revealed by our sedimentological records. This relationship between the meltwater inputs and seasonality in the North Atlantic Ocean was investigated by [START_REF] Flower | Laurentide Ice Sheet Meltwater and the Atlantic Meridional Overturning Circulation during the Last Glacial Cycle: a View from the Gulf of Mexico[END_REF] which proposed the "meltwater capacitor" hypothesis made of four components:

(1) increase summer insolation, (2) ice-sheet meltwater inputs, which (3) inhibits winter deep convection in the northern North Atlantic and reduces Atlantic Meridional Overturning Circulation (AMOC), and (4) increased continentality -due to expanded winter sea ice -promoting hypercold winters.

The timing of the atmospheric circulation re-organization over North America as evidenced by our results suggests the influence of insolation variations. Indeed, surface conditions in the GOM have been shown to be mainly controlled by low-latitude summer insolation while being insensitive to winter conditions [START_REF] Ziegler | Persistent summer expansion of the Atlantic Warm Pool during glacial abrupt cold events[END_REF]. Climate simulations for MIS3 evidence that orbital insolation forcing leads to enhanced northern hemisphere seasonality, with warm summers resulting from increase summer insolation, whereas winter insolation did not change substantially [START_REF] Van Meerbeeck | How did Marine Isotope Stage 3 and Last Glacial Maximum climates differ? e perspectives from equilibrium simulations[END_REF][START_REF] Brandefelt | A coupled climate model simulation of Marine Isotope Stage 3 stadial climate[END_REF]. Enhanced seasonality was proposed to explain the simultaneous occurrence of dry conditions at Lake Petén Itza in Central America [START_REF] Hodell | An 85-ka record of climate change in lowland Central America[END_REF], a southward position of the ITCZ, warm and moist conditions in Florida [START_REF] Grimm | Evidence for warm wet Heinrich events in Florida[END_REF] during the coldest periods of the MIS3, while the North Atlantic Ocean was experiencing cold sea-surface conditions and reduced AMOC.

Although the variations of summer insolation during MIS3 appear too slow compared with the occurrence of melting events, they are consistent with the timing of the main modifications of atmospheric configurations: the westward migration of the precipitation belt occurred when the insolation change rates at 45_ and 30_N were at a maximum and when the difference in interhemispheric insolation was at its minimum (37.3 ka), whereas the shift back to its eastern position coincides with lower rates of summer insolation change (31.4 and 42.6 ka), when the differences between northern and southern insolation were at a maximum (Fig. 4). [START_REF] Nürnberg | Interacting Loop Current variability and Mississippi River discharge over the past 400 kyrs[END_REF] pointed out a strengthened, northward flowing Loop Current in line with the northward position of the Inter-tropical Convergence Zone when insolation became more important in the northern hemisphere than in the southern hemisphere (i.e. after 37.3 ka), allowing northeastern Gulf of Mexico surface hydrographic conditions to approach those of the Caribbean. The increase of GOM sea surface temperatures would enhance evaporation in the northern GOM, which would promote the intensification of the humidity transfers toward the North American continent, the strengthening precipitations over the northwestern province and the supply of smectite rich detrital sediments transported by the Mississippi River.

Concluding remarks

The GOM clay mineral and sedimentological signals from Orca Basin core MD02-2552 allow determination of the geographical sectors of the LIS contributing to the major meltwater events as recorded in the δ 18 OSW during MIS3. The southeastern margin is active throughout MIS3, while the southwestern margin contributed to the short-term massive discharge around 29 ka (based on δ 18 OSW records) similar to the major meltwater events that punctuated the last deglaciation. Major changes of the clay mineral association e at 31.4, 37.3 and 42.6 ka e reflect modifications of the respective western and northeastern province contributions, which cannot be attributed to glacial activity but rather result from changing precipitation distribution.

Combining sedimentological records from the GOM with previously published climate-related archives from the North American continent lead us to propose two main schematic patterns of moisture inflow and precipitation distribution that prevailed during MIS3. A dominant meridional component of the Polar Jet Stream associated with an eastward position of the Bermuda High provided precipitation along the Atlantic Coastal margin while a zonal Jet Stream and a westward Bermuda High promoted rainfall over the western Mississippi River drainage basin provinces. This last pattern is characterized by episodic northward penetration of the moisture flow, shown by the alternation of wet/dry sequences in the northwestern province, which may be due to minor changes in large-scale circulation as suggested by regional climate simulations.

The main atmospheric re-organizations, occurring after the largest and longest meltwater events, are consistent with insolation variations, being synchronous with extreme summer insolation differences between the north and south hemispheres.

Meltwater discharge, which may have modified the LIS configuration and the GOM hydrological properties and ultimately affected the large-scale circulation, likely played a role in triggering atmospheric reorganization by crossing a threshold, although the insolation variation rate appears to be the main driver of the system. [START_REF] Hill | Laurentide Ice Sheet meltwater and abrupt climate change during the last glaciation[END_REF] used in this study [circles represent MD02-2551 dates, gray star and hexagons indicate the stratigraphic position of 14C dates converted in calendar years [START_REF] Fairbanks | Radiocarbon calibration curve spanning 0 to 50,000 years BP based on paired 230TH/234U/238U and 14C dates on pristine corals[END_REF] and the gray rectangle indicates the stratigraphic position of the Laschamp geomagnetic event from core MD02-2552]. [START_REF] Hill | Laurentide Ice Sheet meltwater and abrupt climate change during the last glaciation[END_REF][START_REF] Flower | Laurentide Ice Sheet Meltwater and the Atlantic Meridional Overturning Circulation during the Last Glacial Cycle: a View from the Gulf of Mexico[END_REF]. Limits between (I + C)-rich and (S + K)-rich intervals [START_REF] Sionneau | Clay mineral distributions in and around the Mississippi River watershed and Northern Gulf of Mexico: sources and transport patterns[END_REF]. [START_REF] Sionneau | Clay mineral distributions in and around the Mississippi River watershed and Northern Gulf of Mexico: sources and transport patterns[END_REF] as well as the estimated extent of the LIS between 32 and 35.5 ka BP [START_REF] Dyke | The Laurentide and Innuitian ice sheets during the Last Glacial Maximum[END_REF][START_REF] Van Meerbeeck | How did Marine Isotope Stage 3 and Last Glacial Maximum climates differ? e perspectives from equilibrium simulations[END_REF]. The moisture export from the Atlantic Warm Pool and the GOM is indicated by black arrows; the estimated position of the Polar Jet Stream by dotted blue arrows (adapted from [START_REF] Kutzbach | Simulation of the climate of 18,000 yr BP: results for the North American/North Atlantic/European sector and comparison with the geologic records[END_REF][START_REF] Van Meerbeeck | How did Marine Isotope Stage 3 and Last Glacial Maximum climates differ? e perspectives from equilibrium simulations[END_REF]. H: Bermuda High, LW: Lake Wisconsin glacial lobe; EL: Erie Lobe, JL: James lobe; DML: Des Moines lobe. Numbered circles refer to study sites used in the discussion (1: [START_REF] Pierce | A loess-paleosol record of climate and glacial history over the past two glacial interglacial cycles (150 ka), southern Jackson Hole, Wyoming[END_REF]2: Jacobs et al., 2007;3: Forman et al., 1992;4: Johnson et al., 2007;5: Baker et al., 2009;6:Wood et al., 2010;7: Fredlund, 1995;8: Forman et al., 1992;9:Wang et al., 2009;10: Rittenour et al., 2005;11: Rittenour et al., 2005;12: Leigh et al., 2004;and 13: Grimm et al., 2006;[START_REF] Donders | Impact of the Atlantic Warm Pool on precipitation and temperature in Florida during North Atlantic cold spells[END_REF]. White circle: no data; blue circle: humid conditions; red circle: arid conditions; green circle: presence of glacial activity.

Figure captions

Table 1 Composition of the four main clay-mineral provinces of North America, the upper and the lower Mississippi River watersheds (for more details see [START_REF] Sionneau | Clay mineral distributions in and around the Mississippi River watershed and Northern Gulf of Mexico: sources and transport patterns[END_REF]. S: smectite, I: illite, K: kaolinite, C: chlorite.

Table 2 Average composition of the four time intervals observed on the clay mineralogical record (S: smectite, I: illite, K: kaolinite, C: chlorite).

Fig. 1 .

 1 Fig. 1. Location of (a) the main mineralogical province in and around the Mississippi River watershed and limit of the Laurentide Ice Sheet (LIS) during MIS3 (Dyke et al., 2002); (b) the Orca Basin on the Louisiana continental slope; (c) the two cores reported in this study.

Fig. 2 .

 2 Fig. 2. Correlation between cores MD02-2551 (Hill et al., 2006) and MD02-2552 (Orca Basin) using magnetic susceptibility, table of radiocarbon ages from core MD02-2552 and extrapolated age model. (a e bottom) Magnetic susceptibility record from core MD02-2551; (b e left) magnetic susceptibility record from core MD02-2552 (gray rectangle indicates

Fig. 3 .

 3 Fig. 3. Clay mineral and sedimentological records from the Orca Basin during MIS3 (26e46 ka). a: illite %; b: chlorite %; c: magnetic susceptibility; d: smectite %; e: accumulation rate (cm/ka); f: kaolinite % (red curve) and a* reflectance parameter (orange curve); g: mean grain-size (mm) from core MD02-2552. Limits between (I + C)rich and (S + K)-rich intervals are indicated by vertical black lines. S: smectite, I: illite, K: kaolinite; C: chlorite. Arrows indicate the main continental provenance of the detrital sediments (NE: Great Lakes area and northeastern part of the Mississippi River watershed; NW: Missouri River watershed; SW: southwestern Mississippi River watershed).

Fig. 4 .

 4 Fig. 4. Comparison between clay mineral record from core MD02-2552 and other paleoclimatic records of the Last Glacial period (26-46 ka BP). a: summer insolation at 30°N and 30°S; b: chlorite to kaolinite ratio (blue) and magnetic susceptibility (purple); c: ratio between smectite and (illite + chlorite); d: kaolinite % (red) and a* reflectance parameter (orange); e: δ 18 OSW record (MD02-2551) F1 to F6 1/4 meltwater floods (Hill

  are indicated by vertical black lines. Arrows indicate the main continental provenance of the detrital sediments (NE: Great Lakes area and northeastern part of the Mississippi River watershed; NW: Missouri River watershed; SW: southwestern Mississippi River watershed).

Fig. 5 .

 5 Fig. 5. Distribution of the samples from the (I ? C)-rich (with diamonds), (K ? S)-rich (gray stars) intervals and short smectite-rich episodes (black circles) in a ternary diagram. The main North American mineralogical provinces data are reported in this diagram[START_REF] Sionneau | Clay mineral distributions in and around the Mississippi River watershed and Northern Gulf of Mexico: sources and transport patterns[END_REF].

Fig. 6 .

 6 Fig. 6. Reconstruction of atmospheric circulation pattern over North America. a: (I + C)rich intervals; b: smectite-rich events occurring during (I + C)-rich intervals; c: (K + S)rich intervals; d: specific smectite supply during (K + S)-rich intervals. The main mineralogical provinces of North America are indicated[START_REF] Sionneau | Clay mineral distributions in and around the Mississippi River watershed and Northern Gulf of Mexico: sources and transport patterns[END_REF] as well as

Acknowledgments

This work is dedicated to the memory of our friend and colleague Ben Flower who passed away too early. We thank the IMAGES (International Marine Past Global Change Study) program and the IPEV (Institut Polaire Français, Paul-Emile Victor) for a memorable cruise in the Gulf of Mexico on the R/V Marion Dufresne in 2002. TS is very grateful to A. Hood for English improvements. This study was financially supported by the UMR Geosystemes of the University of Lille 1 (France). The authors thank the editor Henning A. Bauch and the two anonymous reviewers for their helpful and constructive comments which greatly improved this manuscript.


Yannis Merlet

Simon Rouchier

Arnaud Jay

Nicolas Cellier

Monika Woloszyn

Integration of phasing on multi-objective optimization of building stock energy retrofit

Keywords: Multi-objective optimization, building stocks, retrofit, phasing, planning

This article presents the integration of phasing (ie. temporal distribution of retrofit actions over time) into multi-objective optimization of retrofit. The aim of this method is to get closer to real world practice in the construction sites. The case study is carried out on a small building stock with the NSGA-II genetic algorithm. The search space of the optimization are vertical and horizontal walls and windows of each building; objective functions are heating demand, price of the proposed retrofit and an overheating indicator based on adaptive comfort. Overheating and heating demand are evaluated using EnergyPlus simulations.

Phasing is implemented directly into the optimization formalisation with a separated chromosome describing temporality. As a result, different retrofit strategies were obtained by integrating phasing than with a standard optimisation with no temporal planning of operations.The main difference lies into the which building is selected to be retrofitted first, and in the improved performance of each retrofit material proposed : it led to an increase of performance of 10% in the overheating while thermal performance decreased for 2% in the retrofit strategies possible in reality when including the phasing. These results highlight the importance of formulating the optimization problem as close as possible to the real world constraints in construction in order to have accurate retrofit strategies. 1

Highlights

Optimal retrofit plans for building stocks are generated using genetic algorithm The phasing of retrofit actions is integrated in the optimisation search space Results show that proposed optimal strategies are different when phasing is integrated

Introduction

According to the International Energy Agency [START_REF]Statistics -World -Total Primary Energy Supply (TPES) by source (chart)[END_REF], buildings are responsible for 30% of the worldwide primary energy use. The energy efficiency of buildings is a key to meet the ambitious target of 1.5°C of climate change.

The Intergovernmental Panel on Climate Change suggests a decrease of building energy demand of 8 to 14% by 2030 [START_REF] Babiker | Chapter 4 -Strengthening and Implementing the Global Response[END_REF] in order to meet with proposed scenarios.

In addition, the building stock is renewed in France at a 1% yearly rate [START_REF]Programme Rage, Analyse détaillée du parc résidentiel existant[END_REF] and existing buildings are often considered architectural heritage [START_REF] Kohler | The building stock as a research object[END_REF]: the highest potential for energy savings therefore lies in retrofitting the existing building stock. Generally, property managers base their retrofitting decisions on expert knowledge, then attempt to balance and optimize these decisions with constraints such as the global cost, including public financial assistance, energy efficiency, or comfort of the tenants. Although the solutions proposed by experts are generally suitable, they are not necessarily the most efficient.

A step further could be to automatize the balancing of the constraints with simple methods like weighted sum or weighted product. The proposed solution would then be part of the optimal solutions, but would be unique [START_REF] Gossard | Multi-objective optimization of a building envelope for thermal performance using genetic algorithms and artificial neural network[END_REF]. This limits the power of the decision maker: such methods could thus suffer of a low acceptability because of the lack of control on the process [START_REF] Mela | Comparative study of multiple criteria decision making methods for building design[END_REF]. The weighted sum method suffers from another drawback, which is the difficulty to rank objectives among themselves. This difficulty has also been showed in different approaches at building stock level using multi-criteria decision aid methods like REDIS [START_REF] Gade | REDIS: A value-based decision support tool for renovation of building portfolios[END_REF]. Consequently, multi-objective optimization (MOO) is a promising approach to efficiently propose a set of optimal solutions so the experts may focus on selecting one solution among several optimal candidates. Among MOO methods, genetic algorithms has been extensively used to optimize building retrofit, as stated in the review of Costa-Carrapiço [START_REF] Costa-Carrapiço | A systematic review of genetic algorithm-based multi-objective optimisation for building retrofitting strategies towards energy efficiency[END_REF].

Multi-objective optimization has also been used to set up energy policies at larger scales. Tools have been developed to allow the evaluation of energy efficiency measures at city scale such as Stockholm [START_REF] Pasichnyi | Data-driven strategic planning of building energy retrofitting: The case of Stockholm[END_REF]: buildings are first broken down into clusters and three energy conservation measures are evaluated regarding CO 2 emission, heat demand and economic criteria. A similar approach has been carried out at the region level in Italy [START_REF] Guariso | Multi-objective planning of building stock renovation[END_REF] and assesses energy efficiency measures based on a cost-benefit approach on environmental and economic criteria. Such methods help decision makers generate efficient energy policies but do not enable planning if and when the measures will be implemented.

In order to be useful to decision makers, MOO should be as close as possible to the real-life construction management workflow. A key point of any building stock management is the phasing plan of the construction work. The phasing of a construction work is how each action is broken down and arranged on a timeline with respect to construction constraints, site requirements, or time constraints. This timeline can last from less than a month on simple construction sites to a few years when dealing with a whole neighbourhood or a building stock managed by the same owner.

Phasing has been extensively studied in civil engineering at the construction site level [START_REF] Zhou | A review of methods and algorithms for optimizing construction scheduling[END_REF] in order to optimize the scheduling of the construction. The prioritization of retrofit between multiple buildings has been studied by [START_REF] Grant | A prioritization scheme for seismic intervention in school buildings in Italy[END_REF] with the seismic risk as an objective function. This objective function is calculated with subjective weights given to each variable of the problem (economy, safety, regulations) in order to come up with a mono-objective optimization problem. This is an efficient method if the decision maker is able to affect a weight to each objective, but it can only be applied if all objectives may be ranked. Another way to deal with the phasing plan of construction is the use of a risk-based approach to carry out decisions about the retrofit. Taillandier [START_REF] Taillandier | Elaboration of a long-term maintenance plan for building stock based on arbitration using a risk approach[END_REF] qualitatively evaluates whether an action should be undertaken or not and aims to rank actions. However, each action must be proposed by an expert: the method loses efficiency as the size of the building stock increases. Moreover, the choice of action is subjective as the expert is influenced by his experience. Finally, Rivallain [START_REF] Rivallain | Étude de l'aide à la décision par optimisation multicritère des programmes de réhabilitation énergétique séquentielle des bâtiments existants[END_REF] proposed a method to sequence each retrofit action for optimization. This method was applied to two small fictional buildings and was limited to one retrofit action per year.

The purpose of this paper is to propose a formulation of temporal arrangement of retrofit strategies in the multi-objective optimization of a building stock, and then observe whether including this temporal dimension has any impact on the strategies proposed by optimization. This approach aims to get closer to the real world practice and to enable the planning of efficient retrofit projects for building stocks thanks to multi-objective optimization. In our terminology, the term of "stock" refers to a set of buildings managed by a unique property owner, with shared portfolio for refurbishment funds (e.g. social housing). The paper first describes the general framework for the optimization, then details the specifics of the implementation of temporal phasing in the optimization. Finally, outputs of the optimization are compared in order to put forward the effect of the integration of temporal distribution of construction on optimal retrofit strategies.

Optimization methodology

In order to allow optimizing different and often contradictory objectives, we use multi-objective optimization.

The formulation of the problem plays a significant role in the success of the process and in the interpretability of the results. Thus the problem should be carefully formulated with regards to which parameters to optimize, the decision space including the possible values of parameters, and the objective functions of the model.

Figure 1: General optimization workflow

Figure 1 illustrates the global optimization process: in our case the aim is to generate optimal retrofit strategies for a building stock, which will form a set of candidates for decision (Pareto front). The global optimization process can be broken down into 3 main parts: the optimization algorithm which should consistently find optimal solutions; the decision space which is an input of the optimization algorithm; the objective functions in which the building stock performance are evaluated.

The objective function receives an individual to evaluate, which details the retrofit strategies components. This is part of the optimization algorithm which is chosen in section 2.3.

Each of these components is detailed hereafter.

Objective functions

Building managers are optimizing retrofit plans on various objectives covering energy, environment, comfort of the tenants, costs... As a starting point, we choose to optimize retrofit strategies based on 3 objective functions selected in different fields based on the importance of the criteria for building managers in social housing. Thus the following objective functions are selected:

Heating demand : weighted average of the heating needs in kWh/m 2 of all of the buildings for all of the years of the retrofit plan Overheating : sum of the °C.hours above the 90% operative temperature comfort zone [START_REF] Ashrae | ANSI/ASHRAE 55-2004: Thermal Environmental Conditions for Human Occupancy[END_REF] over all years of the retrofit plan Cost : sum of the costs (in ¿) of all retrofit actions (global construction budget) Concerning the overheating objective, it should be noted that in France, air conditioning is generally not provided in residential buildings. Summer comfort is an increasing concern as heatwaves occurrences become more frequent.

The definition of the time span is important, as it may impact the choice of retrofit actions. Here the time span of 20 years has been chosen, matching the average lifetime of retrofit actions. Indeed, datasheets for insulation materials show a lifetime of 15-25 years when properly implemented. Windows' lifetime lies between 20 and 25 years according to manufacturers.

Decision space

The decision space is composed of the possibles values for all parameters to be varied through the optimization process. In our case, the decision space was designed using the expert knowledge of engineering offices that completed multiple energy retrofits as project manager and as on-site management.

Each of the retrofitting actions is broken down into elementary tasks that deal with one component of one building (e.g. Change insulation: 12cm of rockwool on ceiling of building 1 ).

An example of decision space is available in the section 3.

Optimization algorithm

The characteristics of our problem guide the choice of the optimization algorithm:

The decision space is discrete. For instance, insulation materials are available in a limited number of thicknesses, and thus of R-values.

It is preferable to keep multiple separate objectives, rather than a single weighted sum of indicators for the decision makers to be able to apply preferences later on.

Thus, genetic programming is a suitable approach to deal with this problem. As shown by Evins [START_REF] Evins | A review of computational optimisation methods applied to sustainable building design[END_REF], other optimization methods do not meet our needs on either of the two points listed above while limiting the number of evaluations needed. Within genetic programming, the NSGA2 ( [START_REF] Valkanas | Skyline ranking ?? la IR[END_REF]) algorithm has been widely used and its robustness has been validated by multiple studies in building physics [START_REF] Evins | A review of computational optimisation methods applied to sustainable building design[END_REF][START_REF] Machairas | Algorithms for optimization of building design: A review[END_REF]. Finally, it is applicable to large decision spaces, such as large combinatorial problems that can occur when dealing with building stocks. Genetic algorithms mimic evolution by reproducing a population of individuals, and adapting them to their environment. In the end of the evolutionary process, only optimal individuals to their environment remain : they were optimized according their objective of survival in this environment. An individual features its chromosome, which is a representation of the set of parameters, and its fitness, which is the performance of the individual on each objective function. In each chromosome, one gene represents one parameter of the model to optimize. In order to explore the decision space of possible values for the parameters, chromosomes may vary through mutation or crossover.

We chose to use an efficient implementation of NSGA2 available in the DEAP Python library [START_REF] Fortin | DEAP : Evolutionary Algorithms Made Easy[END_REF]. This implementation stands out with its improvement of the calculation of the crowding distance, as detailed in Fortin and Parizeau [START_REF] Fortin | Revisiting the NSGA-II crowding-distance computation[END_REF].

Integration of temporality in optimization

The main goal of our work is to integrate temporality in the multi-objective optimization algorithm with different levels of complexity while being able to compare the outputs of the optimization. We chose to implement 2 types of temporality in the optimization: sequencing and phasing. They will be compared with a base scenario, excluding temporality issues. In the base scenario, all operations are carried at the beginning of the first year. This is the reference scenario, which will be used to compare the outcome of the other scenario. No constraints were imposed on the budget either on base or sequenced optimization.

Implementations of sequencing

Sequencing is the first step in adding temporality in the retrofitting actions. In this approach, presented in Figure 2, one retrofit action is carried out every year on one building (e.g On year 2, insulation is replaced with 10cm of rockwool on Ceiling of building 2 ).

The implementation of sequencing into the optimization algorithm is proposed by adding an extra chromosome that describes the temporality of actions. Consequently, each individual has now two chromosomes, as shown in Figure 3.

As previously stated, only one retrofit action is carried out at each stage (here, each stage equals one year). Consequently, in the case of sequencing, the chromosome that describes the temporality, visible on Figure 3, cannot include duplicate values, which means that specific mutation and crossover operators should be used. [START_REF] Cicirello | Modeling GA Performance for Control Parameter Optimization 2 Largest Common Subgraph Genetic[END_REF] proposed a crossover operator that respects the discrepancy and does not slow down nor reduces diversity [START_REF] Rainville | Evolutionary Optimization of Low-Discrepancy Sequences[END_REF].

Implementation of phasing

Phasing is meant here as a generalisation of sequencing. The main difference is that multiple retrofit actions may be carried out the same year. Here, the available yearly budget sets the limit to the yearly number of possible retrofit actions. Technically, it has been done by adding a phasing chromosome to the sequencing chromosome, as shown in Figure 4. is affected to a phase with respect to their order and the available budget by phase.

Retrofit actions exceeding the budget are not applied on the building stock, and not evaluated. If an individual has a lot of non-applied actions due to budget limits, the convergence speed of the optimization may be affected. The investigated building stock is composed of 3 apartment blocks, chosen as representative of the whole

Summary of the optimization scenarios

EnergyPlus modeling and settings

The choice of EnergyPlus algorithm and parameters reflects the needs of the optimization and the need to describe accurately the buildings: having comparable values for the overheating and heating needs criteria.

Consequently the shadowing calculation is kept to the minimum, and no reflections for the radiation were computed. Moreover, convection algorithm were kept to simple indoor and outdoor heat transfer coefficients.

According to the EnergyPlus documentation, these settings have a low impact (less than 1.5% difference) on all output criteria. Used timestep is 30min.

Schedules

Occupation and heating schedules are selected to allow a practical comparison between retrofit strategies.

Standard schedules from the French Thermal Regulation are selected ( [START_REF] Cstb | Arrêté du 30 avril 2013 portant approbation de la méthode de calcul Th-BCE 2012 prévue aux articles 4, 5 et 6 de l'arrêté du 26 octobre 2010 relatif aux caractéristiques thermiques et aux exigences de performance énergétique des bâtiments nouveaux et des[END_REF]). An example is shown by Tab.

2. Old apartment blocks like those buildings are often naturally ventilated, and although the absence of mechanical ventilation is easy to model, past studies showed that in this case the occupant behavior had a great impact on the ventilation rate ( [START_REF] Andersen | Window opening behaviour modelled from measurements in Danish dwellings[END_REF][START_REF] Haldi | Interactions with window openings by office occupants[END_REF]). Indeed, natural ventilation through the window openings has a major influence on the overheating indicator calculated at each evaluation of the model. The model for windows opening proposed by [START_REF] Haldi | Interactions with window openings by office occupants[END_REF] accounts for indoor and outdoor temperatures, but adds a large computational cost to each evaluation. We have therefore chosen a simple assumption. As all buildings are located in a quiet area, the model includes the following natural ventilation rule: If T indoor > 26°C and

T indoor > T outdoor then tenants are opening windows in order to facilitate natural ventilation.

Air tightness has been modeled with a constant air flow equal to 0.7 vol/h. This is an observed measurement in old collective housing buildings [START_REF] Litvak | Airtightness of French dwellings Results from field measurement studies[END_REF].

Zoning

Zoning of the building is kept to the minimum of zones in order to speed up calculation while having an acceptable accuracy on simulation results. On such simple building shapes, it has been shown that a limited amount of zones is enough to have accurate results for the heating demand [START_REF] Heidarinejad | Demonstration of reduced-order urban scale building energy models[END_REF]. Consequently we chose to split each building in 7 zones:

2 zones for the ground floor: one south, one north 2 zones for the top floor: one south, one north 2 zones for other floors: one north, one south 1 zone for not heated spaces such has stairs and circulations.

An illustration of this zoning is given Figure 6 3.

Weather

The weather file selected in a typical reference year (TRY) of Trappes (France). This TRY files has been generated with Meteonorm software with data from the GEBA (Global Energy Balance Archive), from the World Meteorological Organization (WMO/OMM) Climato-logical Normals 1961-1990. It is the weather file used as reference is the French Thermal Regulation [START_REF] Cstb | Arrêté du 30 avril 2013 portant approbation de la méthode de calcul Th-BCE 2012 prévue aux articles 4, 5 et 6 de l'arrêté du 26 octobre 2010 relatif aux caractéristiques thermiques et aux exigences de performance énergétique des bâtiments nouveaux et des[END_REF]. The weather data are used for all of the 20 years of evaluation.

Response of the model

First, annual heating needs and the overheating criteria were computed. They are shown in Table 3. Buildings are in accordance with their energy label provided by the property manager(cf. Table 1). Building 2 overheats slightly less than the two other buildings. This is due to the difference of building shape: since Building 2 is a high-rise building, it has a lower surface south oriented and a lower roof surface, thus less surface directly exposed to high solar radiations.

Then, in order to verify the usability of the model, we plotted the following data over a typical winter and a typical summer week:

Air temperature of a south oriented zone Air temperature of a north oriented zone

Outdoor air temperature

Direct horizontal solar radiation

As shown in Figure 7a, the south zone reaches more than 35°C. This is due to the fact that during the day, the occupants are scheduled to be out of their apartment, therefore they can not open the window to ventilate. Moreover, the building has no insulation and a fair amount of windows without solar shadings (27%) which ensures a quick rise of temperature on days with high solar radiation. It can be noted that as soon as occupants come back home, the temperature drops dramatically because of the windows' opening, modelled as stated in section 3.2.1.

In winter (Figure 7b), the model reaches the setpoint temperature flawlessly as the heater is modelled as an ideal heating system. It is striking to realize that the building has low inertia therefore drops quickly to the low temperature setpoints each day. It can also be noted that the building is sensitive to solar gain even in winter, thanks to its large windows area.

The same analysis can be made with the other buildings which share the same typology as this one.

Parameters of the model to optimize

The present case study focuses on the retrofit of the building envelope. For each of the three buildings, we optimized vertical walls, ceilings and floors as well as windows. Each of these variables to optimize is a parameter of the model. There are three buildings with 4 parameters to optimize on each one, hence 12 parameters which are listed as parts of the chromosome Type of operation in Figure 3.

Decision space

The decision space is the set of possible parameter values of the model to be optimized. The parameters can be broken down into two types:

Window properties: genes 4, 8, 12 of the pictured chromosome as shown in Figure 3.

Wall properties (vertical walls, floors and ceilings): all other genes.

For the windows parameters, the decision space is defined by the possible U-values, solar factor and visible transmittance that may be applied to all windows of a building.Possible values, taken from a manufacturer catalogue, are: For walls, the decision space covers different insulation materials. Each material may replace the current insulation of the wall, which is external on all of the three buildings. Possible materials are: Each of these materials has its own thermal properties and its price is computed according to expert knowledge provided by engineering companies. The price can be split in two parts: the cost of the material itself, that depends on the thickness and the type of the material, and the price of the construction that depends only on the material.

Hyperparameters of the algorithm

The NSGA2 algorithm has 3 main hyperparameters to be set: the number of individuals, number of generations and crossover probability. [START_REF] Wright | The robustness of genetic algorithms in solving unconstrained building optimization problems[END_REF] and [START_REF] Evins | A review of computational optimisation methods applied to sustainable building design[END_REF] state that convergence was reached in genetic algorithm optimization on 12 parameters with 30 individuals and 10 generations with a crossover probability in the range [0.8;1]. After checking the convergence and the repeatability of the optimisation for multiple hyperparameters, the following parameters are chosen: The validity of these parameters is checked after the optimization through hypervolume monitoring and qualitative evaluation of convergence. problem. Indeed, in Figure 8, the best performances seem to be achieved by the base optimization, then the phasing optimization and finally the sequenced optimization. This is due to the fact that in the base scenario, all of the retrofit actions are done at the very beginning, from the first year. In the sequenced optimization, the retrofit actions are spread over 12 years and in the phasing optimization over 4 years. As the evaluation has been carried out on 20 years, this implies that the amount of years where the building has a poor performance is the longest for the sequenced optimization, which explains its lower performance compared to the two other scenarios.

Additional discussions will be proposed in section 4.2.2.

Global behavior of the optimization and convergence

First of all, convergence of the optimization has to be checked, and the hypervolume and its evolution is a meaningful criteria to do so [START_REF] Zitzler | Performance Assessment of Multiobjective Optimizers: An Analysis and Review[END_REF]. Figure 10 shows the evolution of the hypervolumes along generations for base, sequenced and phased optimization. Hypervolume progression shows a convergence of phased and sequenced optimisation towards the Pareto front that is obtained with based optimisation. However, the gap of hypervolume values at generation 83 for phased optimization could question the convergence of the optimization, but small variability of hypervolumes between the 3 fronts at generation 100 increase the confidence in the convergence of this optimization. The gap at generation 83 is due to the progression of the Pareto front on the overheating objective for solutions that cost between 1100 and 1250¿/m 2 , the evolution on other criterias is not significant.

Interpretation of the results

The content of the retrofit strategies shows an overall difference between strategies from the base optimization and phased strategies. The main differences lie in the retrofit of the windows and in the thickness of the proposed insulation.

First of all observations, the higher the cost of the retrofit strategies, the more windows are treated: cheapest strategies do not retrofit any windows, strategies a bit more costly retrofit windows on one building, etc... This can be shown on Tables 7 and8. Theses tables split the Pareto front in 8 clusters depending on how which building gets its windows retrofitted. In the first three columns of this table is detailed whether the windows get retrofitted for every building: if the building's windows are treated, the value in this column is "1". In the following columns, the mean values and the standard deviation for each objective function are 7 and8 to describe the retrofit of windows, which is detailed in the previous paragraph.

We can see a difference between in which building is treated when not all buildings are retrofitted. In the phased optimization, windows from Building 3 are treated first, then Building 1. In base optimization, windows from Building 1 are retrofitted first, then windows from Building 3. For bot of the optimization, windows from Building 2 are retrofitted in last.

On Figures 11 and12, few differences are visible about the distribution of the solutions. However, in the phased optimisation, the transition between the solutions that are retrofitting the windows of Building 3 and the solutions retrofitting the windows of Building 1 and Building 3 is more clear and occurs at a lower cost than in the base optimization. This is confirmed by the datas from Tables 7 and8. As the only differences between both of the optimizations are the integration of the temporality and the integration of a maximal cost of retrofit, and the fact that the concerned solutions are costing 600 to 700¿/m 2 , this observation can be accounted on the integration of temporality. For both optimizations, it is sensible to retrofit windows Building 1 and Building 3 first as their window-331 to-wall ratio is higher than Building 2 (0,27 for Building 1 and 0,23 for Building 3, only 0,16 for Building We noticed that insulation proposed on phased optimization tend to be thicker than proposed insulation on base optimization. This is due to the fact that retrofit actions are limited by the budget in the case of phased optimization, thus the algorithm proposes solutions where less walls are retrofitted, but with a higher insulation.

For both of the optimization, we can notice that optimal retrofit solutions tend to insulate the largest parts of the buildings more. For example, optimal strategies for the high-rise building features a good insulation (R > 3 K/W) on vertical walls whereas the thermal resistance of ceilings and floors can be as low as R = 1, 7 K/W in some optimal strategies. Similarly, optimal strategies for Building 1 tend prioritize the insulation of roofs and ceilings over walls. This is due to the fact that this building is low-rise and features a greater amount of windows on vertical walls (27% of vertical surface).

Finally, we can conclude that the content of the optimal retrofit strategies does change with the integration of temporality. The same conclusion can be drawn for sequenced and phased optimization, and that increase the confidence we have in the result of the optimizations even with the convergence difference shown in section 4.2. Moreover, the fact that the differences between optimal strategies proposed for base and phased optimization can be explained is increasing our confidence into the results.

Benefits and limitations

In the literature, sequenced optimization of energy retrofit started to be taken into account [START_REF] Rivallain | Étude de l'aide à la décision par optimisation multicritère des programmes de réhabilitation énergétique séquentielle des bâtiments existants[END_REF] but was limited to one retrofit action per year. The real world practice in construction is to break down a major retrofit operation in small phases containing multiple retrofit actions per year: the method aims to replicate this practice.

The proposed method enables the elaboration of optimized retrofit strategies for a small building stock and includes a temporal dimension in each strategy, in order to describe how the retrofit action should be planned. Results show a small improvement between the performance of the proposed strategies when compared to an optimization without phasing. The main result is that proposed strategies differ when the optimization is carried out with phasing.

The major implication of this finding is that optimal strategies depend on how the problem is formulated compared to the reality of retrofit actions: the closer the optimization process to the constraints of the property manager, the more relevant the results will be .

Limitations of the work relates to two main areas. First of all, the cost criteria could be improved by accounting inflation, or by optimizing the life-cycle cost of the building, as proposed by Milic et al. [START_REF] Milić | Evaluation of energy renovation strategies for 12 historic building types using LCC optimization[END_REF]. This would bring a new economy metric to the decision maker, although the construction cost would remain a strong constraint for the realization of the retrofit work.

Secondly, the optimization algorithm, NSGA-II, is suitable for our problem with 12 parameters and 3 objective functions [START_REF] Tuhus-Dubrow | Genetic-algorithm based approach to optimize building envelope design for residential buildings[END_REF][START_REF] Hamdy | A performance comparison of multi-objective optimization algorithms for solving nearly-zero-energy-building design problems[END_REF]. Some limitations have however been found on the quality of the Pareto front generated which can be improved by NSGA-III [START_REF] Ciro | A NSGA-II and NSGA-III comparison for solving an open shop scheduling problem with resource constraints[END_REF], especially on constrained optimization.

Conclusion

A method is proposed for the elaboration of optimal retrofit strategies of building stocks, including the planning of retrofit actions over time. We applied this method on a small building stock of three buildings as a test case.

The major finding is that integrating the temporal aspect of operations into the optimization leads to different optimal strategies. The major difference between phased and non-phased strategies is illustrated with the order of windows retrofit along the buildings of the stock. This difference is illustrated on Figure 9, as we can see that objective function values are improved on the cost but can not be as good on the heating needs and overheating objective, as explained in Section 4.1. This highlights the importance of formulating the optimization problem as close as possible to the constraints of decision makers, in order to generate realistic and useful optimal strategies.

Once the method proposed in this paper is applied, resulting strategies can then be limited to a few strategies through multicriteria decision aid with the decision maker, in order to account for non-measurable objectives such as politics, feeling of the tenants... This guarantees that the decision maker is part of the process while ensuring that the final decision is optimal.

Considering the importance of the formulation of the problem on the relevance of optimal strategies, further studies can be carried out to evaluate the sensitivity of the problem to different parameters such as climate change or occupant behavior. The variability of the weather can also be investigated as more frequent heatwaves may influence the overheating objective. Lastly, an additional objective function can be optimized as well, such as an environmental objective (CO 2 emitted by the building along its life cycle and environmental cost of the retrofit).

Figure 2 :

 2 Figure 2: Workflow for base and sequenced optimization

Figure 3 :

 3 Figure 3: Chromosomes setup for the optimization

Figure 4 :

 4 Figure 4: Creation of phasing chromosome

Figure 5 :

 5 Figure 5: Summary of optimization scenarios

  stockProposed optimization scenarios are applied here on a social housing stock located close to Paris, France.

Figure 6 :

 6 Figure 6: Building 1 with its zoning: each color represent a thermal zone. Grey is for unheated spaces such as stairs an circulation

0 2 AFigure 7

 27 Figure 7: Building 1 15

Figure 9 :

 9 Figure 9: Comparison of optimal retrofit strategies

Figure 10 :

 10 Figure 10: Hypervolume of Pareto front along generations

Figures 11 and 12

 12 Figures 11 and 12 are using the same coding of Tables7 and 8to describe the retrofit of windows, which

Figure 11 :

 11 Figure 11: Individual from Pareto front function of retrofitted windows: base optimization

Table 1 :

 1 Initial characteristics of the buildings.Buildings were modeled in EnergyPlus using Design Builder for the geometry. Their characteristics are listed in Tab. 1. They are initially poorly or not insulated, and have never been renovated before.Building models are detailed in the following section.

		Building 1	Building 2	Building 3
	Total floor area	3020 m 2	850 m 2	6667 m 2
	Shape	Low-rise	High-rise	Low-rise
	Energy label	D (151-230kWh/m 2 /year) E (231-330kWh/m 2 /year)	D
	Number of floors	5	9	5
	Year of construction	<1979	<1979	<1979
	Window to wall ratio	27%	24%	14%
	R-Value walls (m 2 .K/W)	1.25	1.25	3.1
	U window (W/m 2 .K)	2.4	2.4	2.6

Table 2 :

 2 Temperature heating setpoint from[START_REF] Cstb | Arrêté du 30 avril 2013 portant approbation de la méthode de calcul Th-BCE 2012 prévue aux articles 4, 5 et 6 de l'arrêté du 26 octobre 2010 relatif aux caractéristiques thermiques et aux exigences de performance énergétique des bâtiments nouveaux et des[END_REF]

		Mon-Fri (except Wed)	Wednesday Weekend
	00:00-09:00	19°C	19°C	19°C
	09:00-14:00	16°C	16°C	19°C
	14:00-18:00	16°C	19°C	19°C
	18:00-00:00	19°C	19°C	19°C

Table 3 :

 3 Simulated characteristics of the buildings before retrofit

		Building 1	Building 2	Building 3
	Heating needs 146 kWh/m 2 228 kWh/m 2 191 kWh/m 2
	Overheating	297 °C.h/m

2

180 °C.h/m 2 306 °C.h/m 2

Table 4 :

 4 Description of the decision space for windows

	U w values (W/m 2 .K)	0.8	1	1.2	1.4	2.0
	Solar factor	0.76 0.73 0.67 0.64 0.61
	Visible Transmittance 0.81 0.83 0.86 0.88 0.9

Table 5 :

 5 Description of the decision space for walls

	Materials	Thicknesses (cm)
	Glasswool (λ = 0.04 W/m 2 .K)	2, 4, 6, 8, 10, 12, 14, 16, 18, 20
	Rockwool (λ = 0.042 W/m 2 .K)	2, 4, 6, 8, 10, 12, 14, 16, 18, 20
	Polystyrene (λ = 0.032 W/m 2 .K) 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
	Polyurethane (λ = 0.03 W/m 2 .K) 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

Table 6 :

 6 Hyperparameters of NSGA2 for our case study

	Number of individuals	96
	Number of generations 100
	Crossover probability	0.8
	Mutation probability	0.2

Table 7 :

 7 Mean and standard deviation of solutions function of retrofitted windows: base optimization

		Windows		Heating needs (kWh/m2.yr) Overheating (°C.h/m2.yr)	Cost ¿/m2.yr
	Building Building Building		Standard		Standard		Standard
	1	2	3	Mean	Deviation	Mean	Deviation	Mean Deviation
	0	0	0	108.6	1.9	603	45	219	69
	0	0	1	102.7	1.6	650	70	600
	0	1	0	N/A	N/A	N/A	N/A	N/A	N/A
	0	1	1	101	0.1	743	66	1206
	1	0	0	109	1.3	537	19	361	57
	1	0	1	102	1.7	711	192	882
	1	1	0	111	1.8	495	2.7	828	94
	1	1	1	102	1.9	748	196	1400
				N/A: no retrofit strategies for this case
				1: windows retrofitted on this building
				0: windows not retrofitted on this building

Table 8 :

 8 Mean and standard deviation of solutions function of retrofitted windows: phased optimizationWith the same data-exploration methods, we focused the analysis on insulation thickness. Even if thermal conductivities of insulations are different, it is a fair approximation of the global behavior of the optimization.

		Windows		Heating needs	Overheating		Cost
	Building Building Building		Standard	Standard		Standard
	1	2	3	Moyenne Deviation Mean Deviation Mean Deviation
	0	0	0	115	3.4	656	85	249	71
	0	0	1	109	1.9	663	86	531	119
	0	1	0	N/A	N/A	N/A	N/A	N/A	N/A
	0	1	1	106	0.2	794	56	1257	124
	1	0	0	116	1.2	547	12	365	24
	1	0	1	107	1.8	778	170	774	164
	1	1	0	119	2.6	514	4.2	886	79
	1	1	1	107	1.8	775	149	1315	194
			N/A: no retrofit strategies for this case
			1: windows retrofitted on this building
			0: windows not retrofitted on this building

Acknowledgments

The authors would like to acknowledge French National Research Agency (ANR) for its funding within ANR-15-CE22-0011 Reha-Parcs project.

First of all, the global behavior of the optimization will be verified. Then we will compare the optimal strategies given by the optimization with base, sequencing or phasing.

Pareto front at the end of the optimization : overview

On Figure 8, the Pareto fronts of the optimal retrofit strategies are compared. The first one concerns the base optimization, which includes no temporality effect. The second one is the sequenced optimization, where one retrofit task is proposed per year. The third one is the phased optimization which enables multiple tasks to be carried on the same year. In each subplot of Figure 8, we can see individuals that are "dominated" if we take only two objectives into account. It can be noticed on Figure 9: as the individuals perform less on the cost and heating needs objective, they perform better on the overheating objective. This behavior is expected in a multi-objective optimization and enables the verification of the implementation of the algorithm for our problem.

The three Pareto fronts are different and this difference can be explained by the formulation of the

Utility of the integration of phasing

Originally, the motivation for the integration of phasing is to get closer to real world practice. The integration of phasing was done in the optimization and gave sensible results, in accordance with the base optimization and with real world figures. The question is now whether the integration of phasing proposes different solutions than the base optimization. In order to compare strategies proposed in the base and phased optimization, we plotted the performance of the building on its final state, i.e. on the last year of the 20 years period considered for the evaluation of the performance. This plot is available on Figure 13. First of all, Figure 13 show that final states of phased optimal strategies have not the same performance than optimal strategies generated in base optimization. Indeed, retrofit strategies on Pareto front for phased optimization have in average a better performance on overheating objective and have in average a worse performance on the cost and heating needs. Moreover, as stated in Section 4.2.1, strategies differ between base and phased optimization mainly concerning the choice of windows to be retrofitted. This implies that the implementation of phasing in the optimization results in different optimal strategies than those proposed by the base version of the optimization.